Session 1

#1 Percolation properties of hydrogen bond network in ionic liquids -non-polar substances solutions

Atamas, Nataliia (National Taras Shevchenko University of KYiv)

Ionic liquids (IL) are a new class of materials that are used in various sectors of the chemical industry and in the future may become an alternative to the replacement of volatile organic solvents in hazardous chemical plants. Using experimental research methods possible to determine the existence of hydrogen bonds between the cations and anions in the ionic liquid, which form a continuous network of hydrogen bonds between them, hardly sensitive to the addition of polar or non-polar substances. Experimentally shows the correlation of abnormal behavior solubility of non-polar substances in IL with molecular size of the soluble substance. It is also established that the addition of non-polar substances in IL leads to an anomalous temperature dependence of the solubility of non-polar substances in various concentrations. With increasing temperature, a decrease in the solubility of non-polar substances in ionic liquids. Determine the cause, the phenomena described above, through the analysis of the structural and dynamic properties of ionic liquid systems - non-polar material allows numerical simulation. It gives an opportunity to assess the impact of non-polar substances on the formation of the local structure and dynamic properties of an ionic liquid, which was done in the present study for systems dimetilimidazolium chloride (dmim+/Cl-)-non-polar substance (argon, methane, benzene). The method of molecular dynamics (MD) in research was carried out using a modified software package DL_POLY_4.05 with a time step of 2fs, and periodic boundary conditions. Atoms cations dmim+ and anions Cl- is a solid, charged model systems with fixed geometry. To describe the interactions at short distances between the components of the ionic liquid was used potential of Buckingham. The unit cell volume posted the experimental values ??of the density of the ionic liquid at T = 400K. The stabilization system in the NVT ensemble was conducted by a thermostat Behrenzen. The electrostatic interaction at short distances achieved using point charges on each atom system. The long-range electrostatic interactions between particles allows for the use of Ewald summation . Calculations were carried out as follows: the stabilization of the system under study was achieved for 8*105 steps, followed by 8*105 steps of calculations. All radial distribution function (RDF) were prepared in increments of about 200fs. All calculations were performed for a system consisting of chlorine ions 192, 192 dmim+ and one molecule of solute at a temperature T = 400 K, at which the system is in the liquid state. Using the MD allowed to analyze the impact of the size of the non-polar solute molecules (argon, methane and benzene) on the hydrogen bonds nets of the IL. From calculation it found that the energy properties of the studied systems are determined only by the properties of non-polar solute molecules. Network of hydrogen bonds between the components of the IL keeps its percolation properties in the event of dissolution of relatively small molecules (argon), molecular size does not exceed the maximum possible length of the hydrogen bond. When dissolved molecular diameter comparable with the length of the hydrogen bond or slightly above (methane), movement of the solute molecule may occur due to a change of the hydrogen bonds between the components of the IL and by its adjustment. Dissolution of molecules whose size is much higher than the maximum length of a hydrogen bond leads to a radical restructuring of the network of hydrogen bonds in the system until it loses the percolation properties. Thus, we have shown that the larger molecules of dissolved substances in IL, the stronger its impact on the restructuring of the ionic liquid, which affects the solubility of non-polar substances and IL.

#2 Program libraries PRAND and RNGAVXLIB for random number generation: employing parallelism of modern GPUs and CPUs

Barash, Lev (Landau Institute for Theoretical Physics)

Guskova, Maria; Shchur, Lev (Science Center in Chernogolovka, Chernogolovka, Russian Fed. / Rus Föd.)

We present the program library PRAND for parallel pseudorandom number generation. It contains realizations for the generators, which are based on the parallel evolution of toral automorphisms (GM19, GM31, GM61, GM29.1, GM55.4, GQ58.1, GQ58.3, GQ58.4), also the generators MRG32K3A, LFSR113 and MT19937, i.e. modern and reliable modern PRNG algorithms.Using massive parallelism of modern GPUs and SIMD parallelism of modern CPUs substantially improves performance of the generators. For each of the generators the library includes: the ability to jump ahead inside RNG sequence and the ability to initialize up to 10^{19}independent streams with the block splitting method; single-threaded realizations for GPU, which can be used in Monte Carlo calculations, where the computational threads and nodes can be used in any way chosen by an application; multi-threaded realizations for GPU - employing many GPU threads in order to substantially speed up the calculations. Fortran compatibility has been tested and examples of using the PRAND library from Fortran are included. We present the random number generator (RNG) library RNGAVXLIB, which contains fast AVX realizations of a number of modern random number generators, and also the abilities to jump ahead inside a RNG sequence and to initialize up to 10^{19} independent random number streams with block splitting method. Fast AVX implementations produce exactly the same output sequence as the original algorithms. Usage of AVX vectorization allows to substantially improve performance of the generators. The new realizations are up to 2 times faster than the SSE realizations implemented in the previous version of the library, and up to 40 times faster compared to the original algorithms written in ANSI C.
[1] L.Yu. Barash, L.N. Shchur, PRAND: GPU accelerated parallel random number generation library: Using most reliable algorithms and applying parallelism of modern GPUs and CPUs, Computer Physics Communications, 185(4), 1343-1353 (2014). [2] M.S. Guskova, L.Yu. Barash. L.N. Shchur, RNGAVXLIB: Program library for random number generation, AVX realization, Computer Physics Communications, in press (2016), http://dx.doi.org/10.1016/j.cpc.2015.11.001

#3 Improving and testing the population annealing algorithm

Barash, Lev (Landau Institute for Theoretical Physics)

Borovsky, Michal (University of Pavol Jozef Safarik in Kosice, Kosice, Slovakia / Slowakei); Weigel, Martin (Applied Mathematics Research Center, Coventry, Un. Kingdom / Ver Königr.); Shchur, Lev (Landau Institute for Theoretical Physics, Chernogolovka, Russian Fed. / Rus Föd.)

We analyze the recently proposed algorithm for computational statistical physics. The realization of the algorithm for GPU is developed. We study influence of parameters of the algorithm on the accuracy of calculations of the 2D Ising model and on the speed of CPU and GPU programs. We improve the algorithm using a number of techniques such as adaptive temperature step and WHAM and analyze the results.

#4 Transporting hydrogen ions through structurally anisotropic, effectively one dimensional amphiphilic passages, as applied in terms of fractional dynamics

Beldowski, Piotr (University of Science and Technology)

Weber, Piotr (Collegium Medicum, Nicolaus Copernicus University, Bydgoszcz, Poland / Polen); Peplowski, Piotr (Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Torun, Poland / Polen); Kruszewska, Natalia; Gadomski, Adam (University of Science and Technology, Bydgoszcz, Poland / Polen)

Hydration repulsion is a complex electrostatic phenomenon that contributes greatly to the hydration lubrication in natural articulating systems, of ultra-low friction coefficient’s values [1]. The electrostatics itself cannot explain up to sufficient detail the overall facilitated (physiologic) lubrication effect on the proper articulation of the friction biosystem. What is inevitably desirable is an involvement of local dynamics in such biosystems [2]. In what follows, we would like to present a fractional-dynamics and flickering electric-field extension [3] of a previously published work [3] on nanoscale lubrication as realized in terms of some drifted Smoluchowski-type dynamics, leading to a very crude view of transporting hydrogen ions through a linear entropic channel, with a cut-off effect at the channel’s end. The proposed extension is based on a fractional equation, in which the drift term (responsible for proton velocity) is modeled by a fractional derivative of Riesz type [5]; the coefficient preceding the fractional operator is however independent of a state variable. In contrast, the velocity drift term derived in [4] is state variable dependent, whereas the drift operator is of standard (non-fractional) form. In both cases, we can perform simulations of probability densities governed by them. The upshot is that, we can compare these two description of evolution. Our analytical argumentation is to be validated by a molecular dynamics simulation based on λ-dynamics calculus as described in [6]. In addition, assumed that the channel has been thermally activated [7], we can support the overall picture by a type of (kinetic) dedicated Monte Carlo experiment. We address this study to rationalize the effect of facilitated (physiologic) lubrication as seen from nanoscale point of view [8]. References 1 J. Klein, Friction 1, 1-23, (2013). 2 A. Gadomski, Biosystems 94 ,215-217 (2008). 3 C. Doering, B. Ermentrou,t G. Oster, Biophysical Journal 69, 2256-2267 (1995). 4 A. Gadomski et. al, Acta Physica Pol. B 44, 1801-1820 (2013). 5 P. Weber, P. Pepłowski, Acta Physica Pol. B 45, 2067-2077 (2014). 6 M. G. Wolf, G. Groenhof, J. Computational Chemistry 35, 657-671 (2014). 7 J.M. Rubí, D. Reguera, Chemical Physics 375, 518-522 (2010). 8 A. Gadomski, Z. Pawlak, A. Oloyede, Tribology Lett. 30, 83-90 (2008).

#5 Heterogeneously Charged Colloids under confinement and in the bulk

Bianchi, Emanuela (Technical University of Vienna)

The effective interactions between heterogeneously charged particles, also referred to as inverse patchy colloids (IPCs), are characterized by a non-trivial interplay between attractive and repulsive directional interactions [1]. Within this class of systems, we consider IPCs with two charged polar regions and one oppositely charged equatorial belt. In the first part of the talk, we investigate the assembly of these colloids under planar confinement under thermodynamic conditions that favor the formation of extended aggregates [2,3]: (i) a general tendency to form quasi two-dimensional aggregates is observed irrespective of the extent of the confinement, (ii) a clear distinction can be made between the formation of ordered and disordered aggregates based on the specific features of the inter-particle interactions, and (iii) a simple way to tune via experimentally accessible parameters the ordering of IPCs in the vicinity of a possibly charged substrate is presented. In the second part of the talk, we consider IPC systems in the bulk and we investigate the formation of ordered equilibrium structures [4,5]. In particular, we select IPC systems that exhibit a bulk phase diagram characterized by a broad region where a structure composed of parallel monolayers is stable and we report about the effect of the parameters of the particle-particle interaction potential on the whole phase diagram.
[1] E. Bianchi, G. Kahl, and C. N. Likos Soft Matter 7, 8313 (2011)
[2] E. Bianchi, C. N. Likos, and G. Kahl ACS Nano 7, 4657 (2013)
[3] E. Bianchi, C. N. Likos, and G. Kahl, NANO letters 14, 3412 (2014) [4] E. Noya, G. Doppelbauer, I. Kolovos, G. Kahl, and E. Bianchi, Soft Matter 10, 8464 (2014)
[5] E. Noya, and E. Bianchi, J. Phys.: Condens. Matter, 27, 234103 (2015)

#6 MuCa vs WL: A comparison

Bittner, Elmar (ITP, Universität Heidelberg)

Janke, Wolfhard (ITP, Universität Leipzig, Leipzig, Germany / Deutschland)

We perform a competitive analysis to study the relative performance of the two best-known generalized-ensemble algorithms: the multicanonical Monte Carlo and the Wang-Landau method. To keep things as simple and clear as possible, we take the exactly solvable two-dimensional Ising model as test case and we show also some results for the three-dimensional Ising model.

#7 Interplay between geometrical constrains and alphabet size in the design of patchy polymers

Cardelli, Chiara (Universität Wien)

Bianco, Valentino; Coluzza, Ivan (Computational Physics Group, University of Vienna, Vienna, Austria / Österreich)

Patchy polymers can be designed to self-assemble into specific structures. The aim of polymer design is to find a sequence of particles along the chain that will fold into a target structure, according to a given ”alphabet” of interacting particles [1-2]. The alphabet size and the geometrical constraints introduced by the patches affects the designability of the polymer. Here we study, via Monte Carlo simulation, how the alphabet size and the number of patches determine the phase space of the sequences and make the polymer designable. [1] Coluzza, Ivan, and Christoph Dellago. ”The configurational space of colloidal patchy polymers with heterogeneous sequences.” Journal of Physics: Condensed Matter 24.28 (2012): 284111. [2] Coluzza, Ivan, et al. ”Sequence controlled self-knotting colloidal patchy polymers.” Physical review letters 110.7 (2013): 075501.

#8 Dynamics of Ordering in Ising Ferromagnets: Dependence upon initial correlation

Chakraborty, Saikat (Jawaharlal Nehru Centre for Advanced Scientific Research)

Das, Subir K. (Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India / Indien)

Dynamics of domain coarsening in ferromagnetic Ising model, following quench to zero tem- perature, is studied via Glauber spin-flip Monte Carlo simulations in space dimensions d = 2 and 3. Primary objective has been to quantify the decay exponent, θ, of the persistence proba- bility P(t), fractal dimensionality, df, of the persistent spins, corresponding dynamical exponent, z, and domain growth exponent, α, for varying correlation in the initial configurations, prepared at or above the critical temperature. Through appropriate scaling analyses, we estimate the values of the above mentioned quantities of interest for quenches from infinite and critical temperatures, and establish the validity of a scaling relation involving these [1]. It is observed [2, 3] that θ and df strongly depend upon the initial equilibrium correlation length, though the dependence is less prominent in higher dimensions. Further, this work [3] resolves a controversy related to the value of α in d = 3. References [1] G. Manoj and P. Ray, J. Phys. A: Math and General 33, L109 (2000). [2] S. Chakraborty and S. K. Das, European Phys. J. B 88, 160 (2015). [3] S. Chakraborty and S. K. Das, arXiv:1509.07590 (2015).

#9 Structural properties of a fluid of deformable spherical colloids

Chalupa, Patrick (TU Wien)

Kahl, Gerhard (TU Wien, Vienna, Austria / Österreich)

Colloidal particles with complex internal architecture (such as dendrimers) have been viewed over many years as spherical, effective particles, inscribed into a sphere with a radius of roughly the radius of gyration. However, in reality in an ensemble of concentrated macromolecules, these particles constantly change their shape, influenced by other particles in the close vicinity. These deviations from the spherical shape become apparent if one considers such an ensemble at the monomeric level in computer simulations: each macromolecule is assembled by simple, interconnected beads, which interact among each other via suitable potentials. Considering an ensemble of such molecules (typically a few hundred) allows a detailed analysis of the overall shape of these colloids [2, 3, 4]. We have performed Monte Carlo simulations of an ensemble of spherical (effective) colloids which are allowed - in addition to the conventional spatial moves - to continuously deform into prolate or oblate ellipsoids of revolution, guided by an energetic penalty; this deformation is considered as an additional ``Monte Carlo move''. Following the idea put forward by Batista and Miller [4], we consider simple hard spheres: the deformation keeps the volume fixed and maintains the hard-body character of the interaction. While in the original contribution [4], the crystallization was studied in detail, we have focused in our investigations on the disordered, fluid phase. To be more specific we have analysed the spatial and the orientational structure of an ensemble of particles in terms of pair distribution functions and suitably defined order parameters, that characterize the interplay between spatial and orientational order. [1] P.M. Maiti, T. Cagin, G. Wang, and W.A. Goddad III, Macromolecules 37, 6236 (2004) [2] A.M. Naylor, W.A. Goddard III, G.: Kiefer, and D.A. Tomalia, JACS 111, 2339 (1989) [3] I.A. Georgiou, P. Ziherl, and G. Kahl, EPL 106, 44004 (2014) [4] V.M.O. Batista and M. Miller, Phys. Rev. Lett. 105, 088305 (2010)

#10 Critical behaviour of some classical lattice spin models involving singular interactions

Chamati, Hassan (Institute of Solid State Physics, Bulgarian Academy of Sciences)

Romano, Silvano (Physics department, University of Pavia, Pavia, Italy / Italien)

We address the critical behavior of a few classical lattice--spin $O(n)$ models, associated with one- and two-dimensional lattices, and interacting via a pair potential restricted to nearest neighbors and being isotropic in spin space. When the potential involves a continuous function of the scalar product, the Mermin--Wagner theorem and its generalizations exclude orientational order at all finite temperatures in the thermodynamic limit, and exclude phase transitions at finite temperatures for one-dimensional systems. We have considered here some comparatively simple functions of the scalar product which are bounded from below, diverge to $+\infty$ for certain mutual orientations, and are continuous almost everywhere with integrable singularities. Exact solutions are presented for the one-dimensional case, showing absence of phase transitions and absence of orientational order at all finite temperatures in the thermodynamic limit; for the two-dimesional case and in the absence of more stringent mathematical results, extensive simulations carried out on some of them point to the absence of orientational order at all finite temperatures, and suggest the existence of a Berezinski\v\i-Kosterlitz-Thouless transition. References: [1] H. Chamati and S. Romano, Phys. Rev. E 92 (2015) 012135.

#11 Sample Space Reducing processes and Targeted diffusion in complex networks: Universality in Scaling

Corominas-Murtra, Bernat (Section for the Science of Complex Systems of the MUW)

Hanel, Rudolf; Thurner, Stefan (Section for the Science of Complex Systems of the MUW, Wien, Austria / Österreich)

Traffic-related problems, modelling of animal migrations or microbial dynamics can be modelled as diffusion prob- lems. However, a crucial feature escapes from the classical diffusive approach, namely, the common existence of a target towards which diffusion processes tend to go. This crucial point has recently attracted the attention of re- searchers both at the theoretical level [1,2] and at the practical level, including studies over diffusion of information packets through the internet [3] or the urban mobility patterns [4]. We refer to the process of diffusion where there is a target or end point as targeted diffusion . In this talk we will show how the recently proposed framework of the Sample Space Reducing processes [1] can accommodate the processes of targeted diffusion in a natural way, providing a solid background for the understanding of the traffic problems in real systems as well as for the prediction of universal behaviours. In particular, a remarkable regularity emerges when considering targeted diffusion as a model for real systems: Whereas in the usual diffusion process over graphs the underlying graph topology determines the statistics of visits over nodes, in a targeted diffusion process, the underlying topology seems to be irrelevant to large extent, giving a probability of visiting a node p ( v i ) ∼ i − 1 (where i is the rank of the node in terms of number of visits after a large number of experiments), namely, Zipf’s law. This striking result, which has been predicted mathematically and tested numerically, has deep consequences in the comprehension of the organisation of information flows or traffic over complex networks. To end with, other consequences of the application of the framework of Sample Space Reducing processes and targeted diffusion –such as the role of noise– to the study of real flows in complex networks will be discussed. [1] Corominas-Murtra, B, Hanel, R, Thurner S (2014) Understanding scaling through history-dependent processes with collapsing sample space Proc Natl Acad Sci USA 112, 5348–5353.
[2] Perkins, T, Foxall, E, Glass, L, Edwards, R, (2014) A scaling law for random walks on networks. Nature Comms 5 :5121. [3] Sen, S, and Wang, J (2004) Analyzing peer-to-peer traffic across large networks IEEE/ACM Transactions on Networking 12(2) 219–232 [4] Louail, T, Lenormand, M, Picornell, M, Garc ́ıa Cantu ́, O, Herranz, R, Frias-Martinez, E, J. Ramasco, J, and Barth ́elemy, M (2015) Uncovering the spatial structure of mobility networks Nature Comms 6:6007

#12 Lattice Boltzmann simulation of morfogenesys in bioprinted tissue-constuctructs

Cristea, Artur (Romanian Academy - Timisoara Division)

Understanding the principles of morphogenesis is indispensable for developing efficient strategies to build living tissues in the laboratory. Our objective is to predict the time course of the fusion of multicellular systems. Computational methods, like Lattice Boltzmann, proved to be appropiate in pointing out dominant morphogenetic mechanisms. Tissue fusion is essential in tissue printing, an emergent technique based on computer-controlled deposition of multicellular building blocks along with supportive hydrogels. The Lattice Boltzmann (LB) method proves to be efficient for modeling mesoscopic fluid-like flows in biological tissue constructs. The LB model was used to simulate a process that is relevant for tissue printing: the sidewise fusion of contiguous cylinders made of cohesive cells in a hydrogel. This process is analytically tractable and may be used to find a biologically relevant range of model parameters and to establish the time scale of the simulations. Then, using these parameters, the model allows to simulate the evolution of more complex structures, which cannot be described analytically. Fusion eventually gave rise to a tubular construct, in qualitative agreement with 3D tissue printing experiments. Our computer simulation code is based on parallel computing, implemented using the CUDA libraries on nVidia K40 GPU blades. This work is part of the Romanian Academy project for 2016-2020 and was financially supported through the UEFISCDI project number PN-II-ID-PCE-2011-3-0516.

#13 Rational Design of Molecularly Imprinted Polymers

Dobnikar, Jure (Beijing University of Chemical Technology)

Curk, Tine; Frenkel, Daan (University of Cambridge, Cambridge, Un. Kingdom / Ver Königr.)

The term `Molecularly Imprinted Polymers' (MIPs) is used to denote polymer matrices thathave been "imprinted", i.e. cross-linked in the presence of a template molecule, therebyacquiring selective affinity towards its template. The cross-linking process endows the polymer matrix with a chemical `memory', such that the target molecules can subsequently be recognized by the matrix. MIPs have been used in applications such as solid-phase extraction, chiral separation, and catalysis. They can act as molecular sensors, and mimic antibodies or enzymes.They can selectively bind drugs, proteins, or even whole bacteria. The efficiency of the molecular recognition process depends on the initial ligand concentration, the template-ligand binding affinity, and the stifness of the polymer matrix. Here, we present a generic, coarse-grained statistical mechanics model that captures thekey features of molecular recognition. The model provides an integrated description of the MIP formation process and of the subsequent binding of analytes. For the simplest case of divalent particles (i.e. particles with 2 receptors), we derive analytical expressions for the binding free energy and, from that, the adsorption isotherm of analytes on a MIP. For the general case of multivalent particles, we use Monte Carlo simulations to obtain the adsorption isotherms. Two important measures of the quality of a MIP are: i) How much more efficientis binding of a given analyte to imprinted (MIP) than to a non-imprinted matrix (NIP), and ii) How well can we separate two analytes that are only slightly different (e.g., of the same size and with the same number - but different spatial pattern - of the receptors)? In order to address these questions, we evaluate standard measures of MIP specificity, such as the imprinting factor (IF) and the separation factor (SF), as a function of matrix and analyte properties and identify the optimal range of the control parameters such as templateand ligand concentrations and polymer matrix stiffness. Our work provides insight into thegeneric features of MIPs operation and leads to a set of simple design principles. T. Curk, J. Dobnikar, D. Frenkel, Soft Matter Advanced Article (2015); selected for cover image

#14 Nanoparticle Organization in Polymer Layers

Dobnikar, Jure (Beijing University of Chemical Technology)

Curk, Tine; Frenkel, Daan (University of Cambridge, Cambridge, Un. Kingdom / Ver Königr.)

The organization of nanoparticles within grafted polymer layers is governed by the interplay of polymer-induced entropic interactions and the action of externally applied fields. The competition between the tendency for macro-phase separation of colloids and polymers and the elastic-like penalty for deforming the grafted layer results in the micro-phase separation, i.e. finite colloidal clusters characterized by a well-defined length scale. Depending on the conditions, these clusters are isolated or laterally percolating. The morphology of the observed patterns can be controlled by the external fields, which opens up new routes for the design of thin structured films. Here we report Monte Carlo and molecular dynamics simulations that demonstrate that ordered structures can be achieved by compressing a “sandwich” of two grafted polymer layers, or by squeezing a coated nanotube, with nanoparticles in between. We show that the pattern formation can be efficiently controlled by the applied pressure, while the characteristic length-scale, that is, the typical width of the patterns, is sensitive to the length of the polymers. Based on the results of the simulations, we derive an approximate equation of state for nanosandwiches. T. Curk, F. J. Martinez-Veracoechea, D. Frenkel, J. Dobnikar, Nano Letters 4 2617 (2014) T. Curk, F. J. Martinez-Veracoechea, D. Frenkel, J. Dobnikar, Soft Matter 9 5565 (2013)

#15 Representation of the grand partition function of a cell model: state equation in the mean-field approximation

Dobush, Oksana (Institute for Condensed Matter Physics of NAS of Ukraine)

Kozlovskii, Mykhailo (Institute for Condensed Matter Physics of NAS of Ukraine, Lviv, Ukraine)

We propose the method of calculating the grand partition function of multiparticle system, in which constituents interact with each other via potential, that include repulsive and attractive components. The cell model, which was introduced to describe critical phenomena and phase transitions, is used to provide calculations. According to this model, total volume V of a system, is divided into Nv elementary cells of volume v = V/ Nv , each of which can host an arbitrary number of particles. Only a form of interaction potential as well as values of its parameters both with size of elementary cell are required to make computation within this method. Therefore the Morse potential is chosen as an interaction potential to provide estimations. We apply an exact procedure of integration over particles coordinates and summation over number of particles, that makes it possible to obtain an evident expression for the grand partition function of the fluid cell model in the form of multiple integral over collective variables. As it can be seen directly from the structure of the transition jacobian, the present multiparticle model appeared to be different from the Ising model, which is widely used to describe fluid systems. The state equation, which is valid for wide temperature ranges both above and below the critical one, is derived in mean-field approximation. The pressure calculated for the cell model at temperatures above the critical one is found to be continuously increasing function of temperature and density. Isotherms of pressure as a function of density have horizontal parts at temperatures below the critical one. This fact states about occurance of the first order phase transition in the present model.

#16 Contact Kinetics in Fractal Macromolecules

Dolgushev, Maxim (Physikalisches Institut, Universität Freiburg)

Guérin, Thomas (Université de Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, Talence, France / Frankreich); Blumen, Alexander (Physikalisches Institut, Universität Freiburg, Freiburg, Germany / Deutschland); Bénichou, Olivier; Voituriez, Raphaël (Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, Paris, France / Frankreich)

We investigate the effect of the complex connectivity of macromolecules on the contact kinetics by focusing on the case of fractal macromolecules [1]. In our theoretical description, the non-Markovian feature of monomer motion, arising from the interactions with the other monomers, is captured by accounting for the non-equilibrium conformations of the macromolecule at the very instant of first contact. This analysis reveals a scaling relation for the mean first contact time (MFCT) as a function of the equilibrium distance between the reactive monomers and of the spectral dimension of the macromolecule, which is independent on the microscopic details of the macromolecules. We show that the non-Markovian effects increase for the structures with higher degree of hyperbranching, for which the conformations at first contact are getting much more different from equilibrium looping conformations. Our theoretical predictions are in excellent agreement with numerical stochastic simulations. [1] M. Dolgushev, T. Guérin, A. Blumen, O. Bénichou, and R. Voituriez, Phys. Rev. Lett.

#17 Enhancement of the Kondo effect by the induced electron pairing

Domanski, Tadeusz (Institute of Physics, M. Curie Sklodowska University)

Superconductivity and magnetic order are usually thought to be conflicting (competing) phenomena. We show, however, that in quantum dots coupled between the conducting and superconducting reservoirs the spin screening can be substantially amplified by the electron pairing. Using the numerical renormalization group calculations and the selfconsistent perturbative methods we provide arguments for the Kondo resonance broadening due to the proximity induced electron pairing. This couterintuitive phenomenon should be feasible experimentally from the charge transport measurements.

#18 Equilibrium properties of catalytically-activated reactions on Bethe lattice

Dudka, Maxym (Institute for Condensed Matter Physics)

Bénichou, Olivier (Laboratoire de Physique Théorique de la Matière Condensée, Université Paris 6, Paris, France / Frankreich); Oshanin, Gleb (Laboratoire de Physique Théorique de la Matiére Condensée, Université Paris 6, Paris, France / Frankreich); Dietrich, Siegfried (Max Planck Institute for Intelligent Systems, Stuttgart, Germany / Deutschland)

Catalytically activated reactions involve particles that react only in the presence of another agent, a catalyst, and remain chemically inactive otherwise. Such processes are widespread in nature and also involved in a variety of technological and industrial applications [1]. To study equilibrium and out of equilibrium properties of such reactions various theoretical approaches were elaborated [2]. If one is only interested in the thermodynamic properties of the monolayers of adsorbed molecules, formed in the course of catalytically-activated reactions, one realises that they are very similar to the properties of the adsorbates modelled by athermal hard core lattice gases. T herefore we study the order-disorder transitions in a lattice-gas model of a catalytically-activated reaction on a regular lattice with adsorption sites and some catalytic elemets. We consider reactions A+A → ⊘ for the A hard-core particles, which are in thermal contact with their vapour phase (acting as a reservoir maintained at a constant chemical potential μ) so that may adsorb onto empty adsorption site and may desorb from the lattice. We consider two different models: first one with some fraction p of the bonds connecting neighbouring adsorption sites possesses special catalytic properties so that any two As appearing on the sites connected by such a catalytic bond instantaneously react and desorb, while in second one the p denotes fraction of the adsorption sites with catalytic properties causing neighbouring A particles to react and desorb if one of them occupies a catalytic site. We focus on the case of annealed disorder in the distribution of the catalytic bonds or sites, which corresponds to the situation when reaction may take place at any point on the lattice but happens a finite probability p. Extending classical analysis of Runnels [3] performed for the critical behavior of a gas of hard molecules on the Cayley tree with coordination number 3 to our models, we provide an exact solution for interior of an infinitely large Cayley tree, the so-called Bethe lattice. We show that models exhibit a rich critical behavior depending on values of p and μ undergoing transition to ordered state and reentrant order-disorder transition. For the model with catalytic bonds both transitions are continuous with a finite jump in compressibility. For model with catalytic sites the transition to an ordered state is always continuous, while the re-entrant transition into the disordered phase, depending on the value of p , may be either continuous or discontinuous with a finite jump of density. [1] G. C. Bond, Heterogeneous Catalysis: Principles and Applications (Clarendon, Oxford, 1987). [2] D-J. Liu and J. W. Evans, Prog. Surf. Sci. 88, 393 (2013). [3] L. K. Runnels, J. Math. Phys. 8, 2081 (1967).

#19 Entanglement negativity in free lattice models

Eisler, Viktor (Institute for Theoretical Physics, TU Graz)

Zimborás, Zoltán (Department of Computer Science, University College London, London, Austria / Österreich)

In pure states of many-body quantum systems, entanglement is routinely studied via the Renyi entropies, which give a complete characterization of the bipartite case. The situation becomes more complicated for mixed states, e.g. if the system is composed of more than two parts, and one is interested in the entanglement between two non-complementary pieces. In such a scenario the entanglement can be characterized by a suitable measure called logarithmic negativity which has been the focus of recent interest. Similarly to pure-state entanglement, most of our analytical understanding of negativity in many-body lattice systems originates from studying Gaussian states. In this talk I would like to give an overview about the available methods to extract information about the entanglement negativity in free lattice models. In particular, I will present some new results on tripartite entanglement in ground states of critical lattice models in one and two dimensions and, furthermore, even for systems driven far from equilibrium.

#20 The effect of anaesthetics on the properties of a lipid membrane in the biologically relevant phase: a computer simulation study

Fabian, Balazs (Institut UTINAM, Université de Franche-Comté)

Darvas, Maria (SISSA, Sector of Molecular and Statistical Biophysics, Trieste, Italy / Italien); Picaud, Sylvain (Institut UTINAM, Université de Franche-Comté, Besançon, France / Frankreich); Sega, Marcello (Institut für Computergestützte Biologische Chemie, University of Vienna, Vienna, Austria / Österreich); Jedlovszky, Pal (Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Budapest, Hungary / Ungarn)

Molecular dynamics simulations of the fully hydrated neat dipalmitoylphosphatidylcholine (DPPC) membrane as well as DPPC membranes containing four different general anaesthetic molecules, namely chloroform, halothane, diethyl ether and enflurane, have been simulated at two different pressures, i.e., at 1 bar and 1000 bar, at the temperature of 310 K. At this temperature the model used in this study is known to be in the biologically most relevant liquid crystalline (L α ) phase. To find out which properties of the membrane might possibly be related to the molecular mechanism of anaesthesia, we have been looking for properties that change in the same way in the presence of any general anaesthetic molecule, and change in the opposite way by the increase of pressure. This way, we have ruled out the density distribution of various groups along the membrane normal axis, orientation of the lipid heads and tails, self-association of the anaesthetics, as well as the local order of the lipid tails as possible molecular reasons of anaesthesia. On the other hand, we have found that the molecular surface area, and hence also the molecular volume of the membrane, is increased by the presence of any anaesthetic molecule, and decreased by the pressure, in accordance with the more than half a century old critical volume hypothesis. We have also found that anaesthetic molecules prefer two different positions along the membrane normal axis, namely the middle of the membrane and the outer edge of the hydrocarbon region, close to the polar headgroups. The increase of pressure is found to decrease the former, and increase the latter preference, and hence it might also be related to the pressure reversal of anaesthesia.

#21 Mesoscopic virial equation for nonequilibrium statistical mechanics

Falasco, Gianmaria (Institut für Theoretische Physik, Universität Leipzig)

Baldovin, Fulvio (Department of Physics and Astronomy, University of Padova, Padova, Italy / Italien); Kroy, Klaus (Institut für Theoretische Physik, Universität Leipzig, Leipzig, Germany / Deutschland); Baiesi, Marco (Department of Physics and Astronomy, University of Padova, Padova, Italy / Italien)

We derive a mesoscopic virial equation governing energy partition between conjugate position and momentum variables of individual degrees of freedom. It is shown to hold for a wide class of nonequilibrium steady states with stochastic (Langevin) and deterministic (Nose-Hoover) dynamics, and to extend to collective modes for models of heat-conducting lattices. Upon summation over all degrees of freedom, a generalized macroscopic virial theorem ensues which involves dissipative heat flows on the same footing with state variables. It allows for the derivation of nonequilibrium state equations, as exemplified for inertial Brownian motion with solid friction and active Brownian particles subject to inhomogeneous pressure.

#22 Temperature response in nonequilibrium stochastic systems

Falasco, Gianmaria (Universität Leipzig)

Baiesi, Marco (University of Padova, Padova, Italy / Italien)

In my contribution I will introduce a theory for the linear response to a change of the reservoirs’ temperature in out-of-equilibtium systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the result is an extension of Kubo’s formula which allows to compute nonequilibrium thermal susceptibilities from unperturbed correlation functions. These correlations contain a novel form of entropy flow due to temperature unbalances, next to the standard entropy flow of stochastic energetics and to complementary time-symmetric dynamical aspects. As an example, the theory is applied to numerical simulations of heat conducting lattices under large thermal gradients in order to calculate their non-equilibrium heat capacity and thermal expansion coefficient.
[1] G. Falasco and M. Baiesi, arXiv:1509.03139 (2015).

#23 Hybrid crystal-liquid phase in inverse patchy colloids

Ferrari, Silvano (Technische Universität Wien)

Bianchi, Emanuela; Kahl, Gerhard (Technische Universität Wien, Wien, Austria / Österreich)

Axially symmetric colloids with a spherical, negatively charged core and two positively charged patches located at their poles are termed in the literature [1] inverse patchy colloids (IPCs). Such particles are characterized by a complex interplay between the regions of like-unlike charge. Recent studies showed that IPCs can aggregate in a phase composed of parallel hexagonal planes [2], and studied the dependence of the phase from the model parameters (charge, patch amplitude, interaction range) [3]. In this contribution we present another phase, composed by parallel planes that are separated by interlayers of IPCs aligned orthogonally to the IPCs in the planes. Particles in the planes and particles in the interlayers have different melting points, so that at intermediate temperature the latter are in the fluid phase, and will diffuse between the planes; hence the name crystal-liquid structure for this hybrid phase. We also show that the stability of this phase depends in a highly sensitive manner on the patch amplitude: for deviations larger than 5% on the 45° optimal angular extension, the phase is no longer stable.
[1] E. Bianchi, G. Kahl, C.N. Likos, Soft Matter 7, 8313 (2011) [2] E. G. Noya, I. Kolovos, G. Doppelbauer, G. Kahl, E. Bianchi, Soft Matter 10, 8464 (2014) [3] E. G. Noya, E. Bianchi, J. Phys.: Condens. Matter 27 234103 (2015)

#24 Direct evidence for strong crossover of collective excitations and positive sound dispersion in the supercritical state of fluids

Fomin, Yuriy (Institute for High Pressure Physics Russian Academy of Science)

Ryzhov, Valentin; Tsiok, Elena; Brazhkin, Vadim (Institute for High Pressure Physics RAS, Troitsk, Moscow, Russian Fed. / Rus Föd.); Trachenko, Kostya (School of Physics and Astronomy Queen Mary, University of London, London, Un. Kingdom / Ver Königr.)

Supercritical state has been viewed as an intermediate state between gases and liquids with largely unknown physical properties. Here, we address the important ability of supercritical fluids to sustain collective excitations. We directly study propagating modes on the basis of correlation functions calculated from extensive molecular dynamics simulations, and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line introduced in our recent publications [1-6] but becomes devoid of transverse modes above the line where it supports longitudinal modes only. Important thermodynamic implications of this finding are discussed. We directly detect positive sound dispersion (PSD) below the Frenkel line where transverse modes are operative, quantitatively explain its magnitude on the basis of transverse and longitudinal velocities. PSD disappears above the Frenkel line which therefore demarcates the supercritical phase diagram into two areas where PSD does and does not operate. [1] V. V. Brazhkin, A. G. Lyapin, V. N. Ryzhov, K. Trachenko, Yu. D. Fomin, E. N. Tsiok, Where is the supercritical region on the phase diagram? Physics-Uspekhi 55(11), 1061 (2012) [2] V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov and Kostya Trachenko, Two liquid states of matter: A new dynamic line on a phase diagram, Physical Review E 85, 031203 (2012) [3] V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov and Kostya Trachenko, Universal crossover of liquid dynamics in supercritical region, JETP Letters 95, 179 (2012). 4] V. V. Brazhkin, Yu.D. Fomin, A.G. Lyapin, V. N. Ryzhov, E.N. Tsiok and K. Trachenko, "Liquid-gas" transition in the supercritical region: Fundamental changes in the particle dynamics, Physical Review Letters 111, 145901 (2013). [5] Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok and V. V. Brazhkin, Thermodynamic properties of supercritical carbon dioxide:Widom and Frenkel lines, Phys. Rev. E 91 , 022111 (2015). [6] Yu. D. Fomin, V. N. Ryzhov, E. N. Tsiok and V. V. Brazhkin, Dynamical crossover line in supercritical water, Scientific Reports 5, 14234 (2015).

#25 McMillan-Mayer Solution Theory in a Semigrand Isothermal-Isochoric Ensemble

Gómez-Estévez, Juan Luis (Universitat de Barcelona)

The McMillan Mayer (MM) theory of solutions was formulated originally in the context of the grand canonical ensemble (GCE) [1-3] . If we consider a solution formed only by a solute s and a solvent w, the "natural variables" are the chemical potentials of each component, the volume and the temperature. Because the GCE approach is not so much familiar as the canonical ensemble within the solution chemistry community [4] and for more practical reasons , in this work a new version of the MM theory which employs a semigrand isothermal-isochoric ensemble is presented. This approach allows a more complete analogy with the usual canonical ensemble view where the solvent does not appear in a explicit way (MM level). By using the maximun term method [3], a semigrand partition function is obtained from the grand canonical partition function of the original MM theory. The solute pair correlation function and the thermodynamic properties of the solution are obtained in a very general form.. Also, the possibility for obtaining the "excess" thermodynamics of the solution by means of a charging process is discussed. Finally ,as an easy example, the thermodynamic properties of an "ideal solution" are calculated and commented. References [1] W.G. McMillan, J.E.Mayer, J.Chem. Phys. 13, 276 (1945). [2] J. L. Gómez-Estévez, Pure Appl. Chem. 85 , 105 (2013). [3] T.L. Hill, Introduction to Statistical Thermodynamics , Addison Wesley, Reading, Ma(1960). [4] J. Goodisman, Statistical Thermodynamics for Chemists , John-Wiley and Sons, New York (1997).

#26 Non-linear relaxation in a spatially uniform plasma at the end of the relaxation processes

Gorev, Vyacheslav (Oles Honchar Dnipropetrovsk National University)

Sokolovsky, Alexander (Oles Honchar Dnipropetrovsk National University, Dnipropetrovsk, Ukraine)

The processes of temperature and velocity relaxation in a spatially homogenous two-component electron-ion plasma are investigated on the basis of the generalized [1] Chapman–Enskog method. The relaxation processes are investigated at their end. Terms quadratic in small deviations of the electron temperature and velocity from their equilibrium values are taken into account. The pioneering investigation of relaxation processes in a spatially homogenous plasma was made by Landau [2]. He derived his well-known kinetic equation, investigated the problem of temperature relaxation, and obtained the temperature relaxation rate in the leading order in the small square root of the electron-to-ion mass ratio, σ. Later Spitzer obtained [3] a correction to the Landau result for the temperature relaxation rate in higher orders in σ. The velocity relaxation rate is investigated in book [4]. All these results are obtained in the framework of the linear relaxation theory (linear in small deviations of the electron temperature and velocity from their equilibrium values). Besides, all these results are obtained on the basis of the local equilibrium assumption (LEA), which states that the component distribution functions (CDFs) are Maxwellian ones with time-dependent temperatures and velocities. But, as shown in [5], the LEA is not an exact solution of the Landau kinetic equation [2]. It is shown [5] that a small deviation τ of the electron temperature from its equilibrium value and a small deviation un of the electron velocity from its equilibrium value can be chosen as reduced description parameters (RDPs) of the system. In our work [6] we investigated the problem of the CDF derivation on the basis of the Landau kinetic equation in the framework of the linear relaxation theory. We showed that the LEA is the solution of the Landau kinetic equation in the leading order in σ and obtained corrections of higher orders in σ to the LEA results. But at some stage of the system evolution corrections which are linear in un, τ but of higher orders in σ can be comparable with corrections which are quadratic in un, τ but of the leading order in σ. So the problem of the quadratic relaxation theory is important. The CDFs and time equations for the RDPs are obtained [7] in the framework of the quadratic relaxation theory (QRT). It is shown that in the framework of the QRT the LEA does not give correct results for some parts of the CDFs even in the one-polynomial approximation and in the leading order in σ. It is also shown that the contributions of the QRT to the time equations for the reduced description parameters slow down the relaxation processes. [1] V.N. Gorev and A.I. Sokolovsky, Proceedings of Institute of mathematics of NAS of Ukraine, 2014, 11, No. 1, 67. [2] L.D. Landau, ZhETF, 1937, 7, 203 (in Russian). [3] Ishimaru S. Basic principles of plasma physics : a statistical approach, Oxford, Westview press, 1994. [4] A.A. Rukhadze, A.F. Alexandrov and L.S. Bogdankevich Principles of Plasma Electrodynamics, Moscow, URSS, 2013. [5] A.I. Sokolovsky, V.N. Gorev and Z.Yu. Chelbaevsky, Problems of Atomic Science and Technology, 2012, No 1, 230. [6] V.N. Gorev, A.I. Sokolovsky and Z.Yu. Chelbaevsky, Condensed Matter Physics, 2015, V. 18, No. 3, 33001. [7] V.N.Gorev and A.I.Sokolovsky, Vìsn. Dnìpropetr. unìv., Ser. Fìz. radioelectron, 2015, Vol. 23, No. 1, 13.

#27 Quantum relaxation of the transverse Ising model

Hafner, Jonas (Saarland University)

Rieger, Heiko (Saarland University, Saarbrücken, Germany / Deutschland)

We present three di erent approaches (approximations) to investigate the non-equilibrium quantum relaxation of the transverse Ising model af- ter a quantum quench. Furthermore, these methods allow us to describe the quantum dynamic of any many-body system. On the one hand we use a new kind of dynamical mean- eld theory by constructing a cou-pled system of di erential equations and interrupt them by a general mean- eld approximation in time (hierarchy of correlation functions or dynamical mean- eld theory of di erent orders). On the other hand we show two more straightforward methods. A series expansion of the time evolution operator gives not only exact results for the short-term pro le. Moreover, it is a possibility to investigate an in nite many-body sys- tem. The time-dependent perturbation theory o ers another possibility to study the short-term pro le. In our results we observe a light cone in two dimensions that is similar to the one dimensional case. Nevertheless, it shows a completely di erent behaviour. For example, the two dimen-sional model seems to thermalize in contrast to the one dimensional model.

#28 Phantom ideal ring polymer chains in a slit geometry

Halun, Joanna (Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology)

Usatenko, Zoryana (Institute of Physics, Cracow University of Technology, Cracow, Poland / Polen)

The investigation of dilute solution of phantom ideal (Gaussian ) ring polymer chains confined in a slit geometry of two repulsive walls, two inert walls and for the mixed case of one inert and one repulsive wall was performed. Taking into account the well known polymer – magnet analogy developed by de Gennes [1] the calculations of depletion interaction potentials, depletion forces and the forces which exert phantom ideal ring polymer chains on the surfaces were performed in the fixed space dimensions d=3. The obtained results indicate that confining of the phantom ideal ring polymer chains to a slit geometry results in the loss of configurational entropy and leads to arising of the repulsive forces which exert phantom ideal ring polymer chains on the surfaces. The obtained results are in qualitative agreement with previous results obtained by Monte Carlo simulations [2]. [1] P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979). [2] R.Matthews, A.A. Louis, J.M.Yeomans, Confinement of knotted polymers in a slit, Molecular Physics, V.109, 2011, P.1289-1295.

#29 Many-body critical Casimir interactions in colloidal suspensions

Hucht, Fred (Universität Duisburg-Essen)

We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the Z 2 symmetry of the system is broken by the particles. We present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions. Hendrik Hobrecht and Alfred Hucht, Phys. Rev. E 92, 042315 (2015), http://dx.doi.org/10.1103/PhysRevE.92.042315

#30 Corner contribution to cluster numbers in two and three dimensions

Igloi, Ferenc (Wigner Research Centre for Physics, Budapest)

Kovacs, Istvan (Wigner Research Centre for Physics, Budapest, Budapest, Hungary / Ungarn)

We study the number of clusters in 2d and 3d critical percolation, NG, which intersect a given subset of bonds, G. If G represents the interface between a subsystem and the environment, then NG is related to the entanglement entropy of the critical diluted quantum Ising model. Due to corners in G there are singular corrections to NG, which scale as bGln(LG), LG being the linear size of G and the prefactor, bG, is found to be universal. In 2d the prefactor bG is calculated exactly through conformal invariance making use of the Cardy-Peschel formula. The numerical results indicate that logarithmic finite-size corrections exist in the free-energy of three-dimensional critical systems. These investigations are extended to the Fortuin-Kasteleyn clusters in the critical Potts models, also with bond disorder. I. A. Kovacs, F. Igloi and J. Cardy, Phys. Rev. B 86, 214203 (2012). I. A. Kovacs and F. Igloi, Phys. Rev. B 89, 174202 (2014). I. A. Kovacs, J.-Ch. Angl es d’Auriac and F. Igloi, J. Stat. Mech. P09019, (2014).

#31 Revealing the signature of dipolar interactions in dynamic spectra of polydisperse magnetic nanoparticles

Ivanov, Alexey (Ural Federal University )

Zverev, Vladimir (Ural Federal University, Ekaterinburg, Russian Fed. / Rus Föd.); Kantorovich, Sofia (University of Vienna, Vienna, Austria / Österreich)

We investigate, via modified mean field approach, the dynamic magnetic response of a polydisperse dipolar suspension to a weak, linear polarised, AC field. We introduce an additional term into the Fokker-Planck equation, which takes into account dipole-dipole interaction in the form of the first order perturbation, and allows for particle polydispersity. The analytical expressions, obtained for the real and imaginary dynamic susceptibilities, predict three measurable effects: the increase of the real part low-frequency plateaux; the enhanced growth of the imaginary part in the low-frequency range; and the shift of the imaginary part maximum. Our theoretical predictions find an experimental confirmation and explain the changes in the spectrum. As we show in the present contribution, the analysis of the spectra based on the Debye ideal gas approximation can lead to highly pronounced inconsistency in the determination of characteristic relaxations. We are confident that the presented theoretical predictions will serve as a motivation for further and more detailed AC susceptometry experiments. The research is supported by Russian Science Foundation Grant No. 15-12-10003. S.S.K. is grateful to the FWF START-Projekt Y 627-N27 and EU-Project 642774 ETN-Colldense.

#32 Stable knot phases of semiflexible polymers

Janke, Wolfhard (Universität Leipzig)

Marenz, Martin (Universität Leipzig, Leipzig, Germany / Deutschland)

We investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase diagram for the complete range of semiflexible polymers, from flexible to stiff. By varying the internal bending stiffness, the model exhibits different pseudo phases like bent, hairpin or toroidal. In particular, we find thermodynamically stable knots and unusual transitions into these ``knotted'' phases with a clear phase coexistence, but almost no change in the mean total energy and hence no latent heat. It will be explained how we arrive at these intriguing results by computer simulations based on a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method and discussed how one can understand these effects by basic statistical physics properties. M. Marenz and W. Janke, arXiv:1506.07376 (cond-mat.soft).

#33 Simulation study of low-frequency normal modes of soft colloidal glasses

Jaramillo Cano, Diego Felipe (University of Vienna)

Camargo, Manuel (Centro de Investigaciones, Universidad Antonio Nariño, Campus Farallones, Cali, Colombia / Kolumbien)

A common feature for amorphous materials is the impossibility to describe their low-frequency normal modes as plane waves as is the case for crystalline solids. This fact has important consequences on the related density of states (DOS) and on the thermodynamical and mechanical properties of the system. On the other hand, colloidal suspensions have been used as model systems to study various phenomena that occur in condensed matter systems, such as atomic liquids, crystals, and glasses. Particularly, recent studies on suspensions of soft colloids (i.e. hydrogel particles) above the glass transition shown the presence of a boson peak, i.e. an excess of low-frequency modes in the DOS [PRL 108: 095501 (2012)]. The performed analysis was based on comparison with a "2D shadow system" having the same configuration and interactions as those of the soft colloids. Since this approach completely neglects the over-damped dynamics of colloidal systems, in this work we employ Brownian dynamics simulations to assess the effect due to the solvent presence on the low-frequency modes and the associated DOS of soft colloidal glasses. To model soft colloids we resort to a generic coarse-grained interaction, that has been successfully used to describe star polymers, hydrogel particles and micelles, and which strength can be modulated by several physico-chemical factors.

#34 Caveats of mean first-passage time methods applied to crystallization

Jungblut, Swetlana (Universität Wien)

On the example of the crystallization transition in an undercooled Lennard-Jones fluid, I will show that the mean first-passage based methods may underestimate the reaction rates. Then, I will provide a reason for the discrepancies in the values for the crystallization rates obtained with mean first-passage time and transition interface path sampling methods and emphasize the importance of a good definition of the reaction coordinate when applying mean first-passage time techniques.

#35 Universal shape properties of mesoscopic polymer chains and polymer stars

Kalyuzhnyi, Ostap (Institute for Condensed Matter Physics)

Ilnytskyi, Jaroslav (Institute for Condensed Matter Physics, Lviv, Ukraine); von Ferber, Cristian (Applied Mathematics Research Centre, Coventry, Un. Kingdom / Ver Königr.); Holovatch, Yurij (Institute for Condensed Matter Physics, Lviv, Ukraine)

We study shape characteristics, such as mean prolateness, asphericity and size ratio, of long flexible polymer chains and star-shape polymers in solvents of varying quality. These properties are universal and shared by polymers of different chemical content depending on the space dimension d only. So far, the shape characteristics have been analyzed using mainly the self avoiding walk representation of polymer chains on a lattice, whereas the off-lattice simulations are more scarce. In this study we employ the dissipative particle dynamics simulations in 3D . For the case of linear chains in a good solvent, we found the distributions for all shape characteristics to be rather broad [1], but their average values to agree well with the renormalization group results [2,3,4] and Monte Carlo simulations of lattice models [5,6]. The homo-star polymers are considered in a solvent of variable quality. The changes undergone by the shape characteristics with varying solvent quality are in a good agreement with available data of previous studies [7]. In addition, we discuss a broader range of such characteristics and comment on their maxima observed near the θ-point of a solvent [8]. The hetero-stars, characterised by variable solubility for individual arms, are also studied [8]. Various combinations of arms solubility are considered leading to specific conformations and affecting the shape characteristics of these molecules. We see such systems as the micellogenes with tunable aggregation abilities. [1]. O. Kalyuzhnyi, Ja. Ilnytskyi, Yu. Holovatch. J. Phys. Stud . 18 (2014) 4602. [2]. O. Jagodzinski, E. Eisenriegler, K. Kremer, J. Phys.I(France) 2 (1992) 2243. [3]. J.A. Aronovitz, D.R. Nelson, J. Physique 47 (1986) 1445. [4]. M. Behamou, G. Mahoux, J. Physique Lett . 46 (1985) L689. [5]. O. Jagodzinski, E. Eisenriegler, K. Kremer, J. Phys. I (France) 2 (1992) 2243. [6]. M. Bishop, C.J. Saltiel, J. Chem. Phys. 88 (1988) 6594. [7]. M. M. Nardai, G. Zifferer, J. Chem. Phys. 131 (2009) 124903. [8]. O. Kalyuzhnyi, Ja. Ilnytskyi, C. von Ferber, Yu. Holovatch, in preparation .

#36 Thermodynamic perturbation theory for inverse patchy colloids

Kalyuzhnyi, Yurij (Institute for Condensed Matter Physics)

Stepanenko, Oleksandr (Institute for Condensed Matter Physics, Lviv, Ukraine)

Recently a multi-density integral equation formalism for the novel class of the patchy colloidal particles, represented by the inverse patchy colloids [1] (IPC), have been proposed [2]. These colloids have been introduced for the purpose of the theoretical and computer simulation description of the colloidal particles with heterogeneously charged surface. In contrast to convential patchy colloids, which are characterized by strong attractive patch-patch interaction, interaction between the patches of the IPC are repulsive, i.e. attractive interaction is valid between the patches on one particle and part of the colloidal particle surface of the other particle, which is free of the patches. Due to strong orientationally dependent attractive interaction these colloidal systems exhibit new and very interesting physics, in particular they have rather unusual and rich phase behavior [3,4]. While integral equation approach developed earlier appeares to be very accurate in predicting the structure and thermodynamic properties of the IPC models, solution of the corresponding integral equation closure relations requir application of rather complicated numerical methods. In this contribution we propose alternative approach, which is based on the extension of the Wertheim's thermodynamic perturbation theory (TPT) for associating fluids. In contrast to the integral equation approach our version of the TPT is much simpler and almost completely analytical. The theory is developed for the general case of any number of patches. Predictions of the theory for thermodynamical properties of the one-patch version of the IPC model appeares to be in good quantitative agreement with corresponding computer simulation and integral equation predictions. References 1. E.Bianchi, G.Kahl, C.N.Likos, Soft Matter 7, 8313(2011). 2. Y.V.Kalyuzhnyi, E.Bianchi, S.Ferrari, G.Kahl, J.Chem.Phys. 142, 114108(2015) 3. E.Bianchi, C.L.Likos, G.Kahl, Nano Lett. 14,3412(2014). 4. E.G.Noya, I.Kolovos, G.Doppelbauer, G.Kahl, E.Bianchi, Soft Matter 10, 8464(2014).

#37 Dynamical network evolution and coarse-graining of evolved symmetric structures

Karalus, Steffen (Universität zu Köln)

Krug, Joachim (Universität zu Köln, Köln, Germany / Deutschland)

Evolutionary optimization can be applied to find network structures with a prescribed power-law scaling in the spectrum of the graph Laplacian. The graph Laplacian appears as time evolution operator in a broad class of dynamics on networks. In the context of diffusion processes the power-law scaling yields a non-trivial anomalous diffusion behavior characterized by the power-law exponent, the so-called spectral dimension of the network. The resulting evolved networks are found to exhibit heterogeneous structures consisting of densely connected cores on the one hand and sparse peripheries on the other hand [1]. Homogeneity in the evolved networks can be enforced by introducing degree-regularity as additional constraint. In this case, the evolving networks are kept k -regular and therefore locally homogeneous in the course of the evolution. The resulting networks are found to be homogeneous on large scales as well and highly symmetric on small scales. The symmetry can be exploited in a systematic coarse-graining separating the Laplacian spectra into contributions from the symmetric motifs and the underlying large-scale structures. These backbones are indeed particularly relevant for the spectral scaling in the evolved networks and provide an intuitive view of how the anomalous diffusion can be realized [2]. [1] S. Karalus and M. Porto, EPL 99, 38002 (2012). [2] S. Karalus and J. Krug, EPL 111, 38003 (2015).

#38 Analytical results for the distribution of shortest path lengths in random networks

Katzav, Eytan (Hebrew University)

The increasing interest in network research in recent years is motivated by the realization that a large variety of systems and processes which involve interacting objects can be described by network models. In these models, the objects are represented by nodes and the interactions are expressed by edges. The interactions between non-adjacent pairs of nodes are facilitated by paths going through intermediate nodes and edges. The shortest paths between such pairs are of particular importance because they provide the strongest interactions and fastest response. Therefore, the distribution of shortest path lengths is of great relevance to many dynamical processes taking place on networks such as communication, navigation and epidemic spreading. While the average of this distribution has been studied extensively, the analytical calculation of the entire distribution has remained an open problem. In this presentation a novel analytical approach for calculating the distribution of shortest path lengths in random networks will be discussed. This approach is based on recursion equations, and applies to a large family of network types, which includes Erdos-Renyi networks [1], regular graphs and more generally, configuration model networks [2]. The results are found to be in agreement with numerical simulations for a broad range of networks, sizes and connectivities. Being analytical this approach allows shedding light on various phenomena such as an interesting local-global relation between the degree of a specific node and the mean distance of paths originating from it. Another interesting observation is the fact that networks become spherical (namely, almost all nodes are equidistant from each other) in the dense limit. [1] E. Katzav, M. Nitzan, D. ben-Avraham, P. L. Krapivsky, R. Kuhn, N. Ross and O. Biham, Analytical results for the distribution of shortest path lengths in random networks, EPL 111, 26006 (2015). [2] M. Nitzan, E. Katzav, R. Kuhn and O. Biham, Distance distribution in configuration model networks, preprint.

#39 Aging in the (2+1)-Dimensional Kardar-Parisi-Zhang Model under Various Dimer Lattice-Gas Dynamics

Kelling, Jeffrey (Helmholtz-Zentrum Dresden-Rossendorf)

Odor, Geza (MTA-EK-MFA Institute of Technical Physics and Materials Science, Budapest, Hungary / Ungarn); Gemming, Sibylle (Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany / Deutschland)

Extensive dynamical simluations of a 2 dimensional driven dimer lattice gas are presented, which can be mapped to (2+1) dimensional surface growth in the Kardar-Parisi-Zhang (KPZ) or Edwards-Wilkinson unversality classes. From this autocorrelation and autoresponse functions have been determined for the KPZ universality class and the underlying lattice gas. Studying the effects of different dimer lattice gas dynamics revealed strong differences in the aging behavior of the stochastic cellular automaton (SCA) and the random sequential update models. We show numerical evidence for nontrivial corrections as well as different universal scaling behaviors.

#40 Scaling and Finite-Size Scaling above the Upper Critical Dimension

Kenna, Ralph (Applied Mathematics Research Centre and L^4 Collaboration)

Flores-Sola, Emilio (Applied Mathematics Research Centre and L^4 Collaboration, Coventry, Un. Kingdom / Ver Königr.); Berche, Bertrand (UniversitŽe de Lorraine, Nancy, France / Frankreich); Weigel, Martin (Applied Mathematics Research Centre and L^4 Collaboration, Coventry, Un. Kingdom / Ver Königr.)

It is well known that hyperscaling, in its standard form, fails above the upper critical dimension which itself is determined by the Ginzburg criterion. Critical phenomena there are governed by Gaussian fixed points in the renormalization group formalism and Landau mean-field theories deliver exact values of the critical exponents. However, finite-size theories have long been puzzling above upper-critical dimensionality. For example, one had to distinguish between short long-range and long long-range behaviour of the correlation function. Also, an extra length scale, dubbed the thermodynamic length, was introduced to control finite-size scaling, the universality of which has been debated. Here we show that this standard picture is flawed. We introduce a new pseudocritical exponent characterising the finite-size correlation length. This obviates the need for a thermodynamic length and the separation of short long-range and long long-range behaviour. The Ginzburg criterion is also modified. Two new scaling relations arise – one to extend hyperscaling to high dimensions and the other analogous to the one introduced by Fisher 50 years ago. Moreover, finite-size scaling is shown to be universal provided the correct scaling window is chosen. Finally, the role of Fourier modes is elucidated.

#41 Spontaneous pulsing states in an active particle system

Klein, Sarah (Universität des Saarlandes / Université Paris-Saclay)

In this work we present a two­lane ASEP­-like model. We study a system with a closed end on the right and an open end on the left with two different species. The species defines the stepping direction, either to the solely to the left or to the right. The particles can change between the two symmetric lanes and furthermore convert from one type to the other, meaning that they change their intrinsic direction with a given constant rate. This model which was inspired by [1] shows for some parameters a periodic behavior for the particles densities of both types. The system is rapidly filled up to a total density close to one and then starts to empty with a moving front from the closed end to the open end. Here we study a discrete space mean­-field approximation which also exhibits this pulsing behavior. We present numerical results from the particle model and compare them to the mean-field predictions, both analytical and numerical. From numerical integration of the mean-field equations we find oscillatory behavior which can be explained by a stability analysis. [1] C. Lin, et al., Journal of Statistical Mechanics: Theory and Experiment, 2011(09): P09027, 2011.

#42 Structure and dynamics of human disease networks

Klimek, Peter (MedUniWien)

The state of health of patients is typically not characterized by a single disease alone but by multiple (comorbid) medical conditions. These comorbidities may depend strongly on age and gender. We propose a specific phenomenological comorbidity network of human diseases that is based on medical claims data of the entire population of Austria. The network contains all statistically significant comorbidity relations that pose a substantial risk to male or female patients. We show that the network undergoes dramatic structural changes across the lifetime of patients. Disease networks for children consist of a single, strongly interconnected cluster. During adolescence and adulthood further disease clusters emerge that are related to specific classes of diseases, such as circulatory, mental, or genitourinary disorders. For people over 65 these clusters start to merge, and highly connected hubs dominate the network. We develop a diffusion model to show that patients predominantly develop diseases that are in close network proximity to disorders that they already suffer. The model explains more than 85% of the variance of all disease incidents in the population. We also show how this newly developed statistical network framework can be used to quantify age- and gender-dependent relative risks for each possible comorbidity of type 1 and 2 diabetes and test whether the association may be consequential or causal. This allows us, for example, to confirm the highly controversial relation of increased risk for Parkinson’s disease in diabetics, using a 10 times larger cohort than previous studies on this relation or to identify significant differences in the progression of sleep disorders and congestive heart failure in diabetic patients.

#43 Swelling of polyelectrolyte gels in salt solutions: analytical model vs. simulations

Kosovan, Peter (Department of Physical and Macromolecular Chemistry)

Richter, Tobias; Holm, Christian (University of Stuttgart, Stuttgart, Germany / Deutschland)

We use hybrid molecular dynamics / Monte Carlo simulations and coarse-grained polymer models to study the swelling of polyelectrolyte gels in salt solutions. Besides existing industrial applications, such gels have been recently proposed as a promising agent for water desalination. We employ the semi-grandcanonical ensemble to investigate partitioning of the salt between the bulk solution and the gel, the salt-induced de-swelling of the gels and their mechanical properties under free swelling equlibrium and under compression. We compare our findings to the analytical model of Katchalsky and Michaeli which explicitly accounts for electrostatic effects. The partitioning of small ions predicted by the model well captures the deviations from the simple Donnan approximation, observed in the simulation data. In contrast, the original model highly overestimates the gel swelling, predicting even chain stretching beyond contour length. With a modified, where we replace the Gaussian elasticity with the Langevin function for finite extensibility, we obtain nearly quantitative agreement between theory and simulations both for the swelling ratio and for the partitioning of salt, across the whole range of studied gel parameters and salt concentrations. The modified model thus provides a very good description of swelling of polyelectrolyte gels in salt solution, and can be used for computationally inexpensive theoretical predictions of water desalination using hydrogels.

#44 Computer simulations of polyelectrolytes

Uhlik, Filip (Charles University)

Polyelectrolytes are polymers with ionizable groups. Under suitable conditions, polyelectrolytes are soluble in aqueous media. This property makes them attractive to biological, medicinal and environment-friendly applications that require organization of matter at nanoscale and can range from drug carriers, water pollutants removal, sea water desalination, coatings, oil recovery to nafion membranes in fuel cells. In some of them, e.g. as thickening agents, super-absorbents in diapers or flocculants, they have already reached mass production. Many of natural macromolecules (e.g. nucleic acids, proteins, pectins, heparins) are polyelectrolytes too. Polyelectrolytes are conveniently divided into strong (also called quenched, e.g. polystyrene sulfonic acid) and weak (also called annealed, e.g. polyacrylic acid). While strong polyelectrolytes remain fully ionized, the degree of ionization of weak polyelectrolytes can be influenced by both pH and ionic strength and is coupled to polymer conformations. This responsiveness to external stimuli makes weak polyelectrolytes particularly attractive to applications. However, their behavior is quite complex especially if we consider different conditions given by Bjerrum and Debye lengths, solvent quality, polymer concentration, branching and topology. In this contribution we describe a general and efficient simulation technique based on hybrid Monte Carlo method in reaction ensemble suitable for studying polyelectrolytes under various conditions together with results for selected types of branching (e.g. polymer stars, combs and brushes), addition of salt with different valency, phenomena in polyelectrolyte gels and behavior of frustrated polyelectrolytes in poor solvents in order to illustrate both the capability of the method and the interesting phenomena in polyelectrolytes.

#45 Horizons and free path distributions in quasiperiodic Lorentz gases

Kraemer, Atahualpa (Friedrich-Alexander University Erlangen-Nürnberg)

Schmiedeberg, Micahel (Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany / Deutschland); Sanders, David P. (National Autonomous University of Mexico, Mexico City, Germany / Deutschland)

Embedding a quasiperiodic array of scatters into a higher-dimensional periodic hyperlattice, using the method described in [1], we study the structure of quasiperiodic Lorentz gases, i.e., particles bouncing elastically off fixed obstacles arranged in quasiperiodic lattices. We show that quasiperiodic Lorentz gases generically exhibit a regime with infinite horizon, that is, empty channels through which the particles move without colliding, when the obstacles are small enough. For the critical radius at which these channels disappear, however, a new regime namely "locally finite horizon" arises. <br /> We explore analytically and numerically what type of free flight length distribution exhibit these two regimens. We observe a power law distribution, with exponent -3 for the infinite horizon regime; as expected from periodic Sinai billiard [2], and with exponent -5 for the locally finite horizon; previously observed only in a Lorentz gas formed by superposing three incommensurable periodic lattices in the Boltzmann-Grad limit [3] where the radius of the obstacles tends to zero. <br /> [1] Kraemer, Atahualpa S., and David P. Sanders. "Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures." Phys. Rev. Lett. 111.12 (2013): 125501.<br /> [2] Bouchaud, Jean-Philippe, and Pierre Le Doussal. "Numerical study of ad-dimensional periodic Lorentz gas with universal properties." <i>J. of Stat. Phys.</i> 41.1-2 (1985): 225-248. <br /> [3] Marklof, Jens, and Andreas Strömbergsson. "Power-law distributions for the free path length in Lorentz gases." <i>J. of Stat. Phys.</i> 155.6 (2014): 1072-1086. [4] Kraemer, Atahualpa S., Michael Schmiedeberg, and David P. Sanders. " Horizons and free path distributions in quasiperiodic Lorentz gases" Phys. Rev. E 92(2015): 052131

#46 Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks

Krasnytska, Mariana (Institute for Condensed Matter Physics of the National Acad. Sci. of Ukraine )

The Ising model on annealed complex networks with degree distribution decaying algebraically as P(K)≈1/Kλ has a second-order phase transition at finite temperature if λ>3. In the absence of space dimensionality, λ controls the transition strength; mean-field theory applies for λ>5 but critical exponents are λ-dependent if λ<5. Here we show that, as for regular lattices, the celebrated Lee-Yang circle theorem is obeyed for the former case [1]. However, unlike on regular lattices where it is independent of dimensionality, the circle theorem fails on complex networks when λ< 5. We discuss the importance of this result for both theory and experiments on phase transitions and critical phenomena. We also investigate the finite-size scaling of Lee-Yang zeros in both regimes as well as the multiplicative logarithmic corrections which occur at λ=

#47 On the discontinuity of the specific heat of the Ising model on a scale-free network

Krasnytska, Mariana (Institute for Condensed Matter Physics of the National Acad. Sci. of Ukraine )

M. Krasnytska1,2,4, B. Berche2,4, Yu. Holovatch1,4, R. Kenna3,4 1Institute for Condensed Matter Physics, National Acad. Sci. of Ukraine, UA--79011 Lviv, Ukraine 2Institut Jean Lamour, CNRS/UMR 7198, Groupe de Physique Statistique, Universite de Lorraine, BP 70239, F-54506 Vandoeuvre -l‘es-Nancy Cedex, France 3Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom 4Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry L4 We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay P(K)≈ 1/Kλ. It is well established that the model is characterized by classical mean-field exponents for λ>5. In this report we show that the specific-heat discontinuity δch at the critical point remains λ-dependent even for λ>5: δch=3(λ-5)(λ-1)/[2(λ-3)2] and attains its mean-field value δch=3/2 only in the limit λ→∞ [1]. We compare this behaviour with recent measurements of the d dependency of δch made for the Ising model on lattices with d>4 [2]. [1] M. Krasnytska, B. Berche, Yu. Holovatch and R. Kenna, Condens. Matter Phys. 19 (2015), to appear; arXiv:1510.06216. [2] P. H. Lundow and K. Markstrom, Nucl. Phys. B 895 (2015) 305.

#48 Interplay of directed transport and diffusive motion inside cellular protrusions

Krämer, Isabella (Arnold Sommerfeld Center for Theoretical Physics, LMU München)

Frey, Erwin (Arnold Sommerfeld Center for Theoretical Physics, LMU München, München, Germany / Deutschland)

Linear cellular protrusions like filopodia, microvilli or stereocilia are characterized by their finger-like structure that is connected to the cell body at one end, the base, and extends into the surroundings at the other end, the tip. A membrane enclosing the protrusion separates the inside of the protrusion from the extracellular and prevents in- and outflux other than at the base. Inside the protrusion bundles of parallel actin- filaments are embedded into cytoplasm so that different types of motion interact with each other: directed transport of cargo towards the tip on the actin-filaments and diffusive motion inside the cytoplasm. Motivated by this biological process we study the steady-state behaviour of a totally asymmetric simple exclusion process (TASEP) that is weakly coupled to different diffusive environments and focus on systems that are closed at the tip of the TASEP. We derive an exact equation that relates the average total occupation on the TASEP to the average total occupation on the diffusive lattice coupled to it. This mass balance equation represents a global detailed balance for the exchange between the two lattices, where detailed balance does not hold locally for any pair of sites but for the two lattices in total. We show that the steady-state profile on the TASEP is given by a localized domain wall whose position can be determined using the mass balance equation. By further exploiting this global detailed balance equation we find an analytic expression for the nearest-neighbour correlations on the TASEP.

#49 Green Kubo theory of thermal conductivity enhancement of nanofluid

Kumar, Tankeshwar (Guru Jambheshwar University of Science & Technology)

Srivastava, Sunita (Panjab University, Chandigarh, India / Indien)

Methods of enhancing the thermal conductivity of heat transfer fluid has been of great interest to scientists and engineers. Colloidal dispersion of nanoparticles in the base fluids enhances the thermal conductivity of the fluid called nanofluid. Metals, nitrates, oxides and non-metals like carbon nanotube can be used as nanoparticles while liquids like ethylene glycol, mineral oils and water can be used as base fluids [1-4]. Depending on the size, shape and volume fraction, different nanoparticles on mixing enhances the thermal conductivity of the base fluid to different extent. With the aim of developing a microscopic theory which could successfully explain the enhancement of the thermal conductivity of nanofluid, in the present work, we begin with the Green- Kubo formula for the calculation of thermal conductivity of the base fluids. A theoretical method has been proposed to incorporate the effect of nanoparticles on the dynamics of base fluid [5]. Thermal conductivity of the base fluid enclosed between two nanoparticles has been found to enhance significantly for smaller distances. However, if the distance between two nanoparticles is larger than a certain value, the base fluid does not experience any enhancement in the thermal conductivity. Nanoparticles owing to their motion are expected to be at all possible locations and hence on averaging, the thermal conductivity of base fluids gets enhanced. Results have been obtained for different volume fractions of nanoparticles. It is found that our theory predicts results in agreement with simulation studies [6] and improves upon the prediction of Maxwell model [7]. Our theory has the flexibility to incorporate the effect of temperature and the size of nano particles for various nanofluids. References: [1] Hammand Younes, G. Christensen, D.Li, H.Hong and A.A. Ghaferi, Journal of Nanofluids, 4, 2015, 107-132[2] R. Srikan D. Rao, M. Subhrahmanyam and K. Vamsi, Proc. ImechE Part J:Engg Tribol, 223 203 (2009) [3]J.Buongiorno et al, J. Appl. Phys 106, 094312 (2009) [4] S. Iijima, Nature 354, 56 (1991) [5] K. Tankeshwar, K.N. Pathak and S. Ranganthan, J.Phys.: Condens. Matter, 1, 6181, (1989)., 1, 6193, (1989) [6] H. Kang, Y. Zhang and Mo Yang, Appl. Phys.A 103, 1001, (2011) [7] J.C. Maxwell, A treatise on Electricity and Magnetism, Oxford University Press, Cambridge, 435 2nd Ed. (190

#50 Protein molecular machines and Maxwell's demons

Kurzynski, Michal (Faculty of Physics, A. Mickiewicz University)

Formally, the protein molecular machines are enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. On the mesoscopic level, the dynamics of proteins is described by a network of transitions between conformational states composing what is presently called their native state ensemble. All chemical reactions proceed due to thermal fluctuations, thus the entropy production in the free energy-transduction processes is to be described by the (possibly generalized) fluctuation theorem. In such a context , the problem of Maxwell’s demon can be considered. The energy processing has to be distinguished from the organization processing. From the former point of view, Maxwell’s demon utilizes entropy reduction for the performance of work, whereas from the latter, for the creation of information. We shown that the generalized fluctuation theorem with entropy reduction is fulfilled only for the enzymatic molecular machines with the stochastic dynamics that offers a possibility of choice of the output reaction realization in variety of ways, what creates some information. The particular model of such a dynamics was investigated, described by the network displaying, like networks of the systems biology, a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. From a broader biological perspective, three suppositions could be of especial importance: (i) a possibility of the choice is characteristic for many intrinsically disordered proteins, (ii) the tight coupling between output and input fluxes results not from the lack of slippage, but from the compensation of the entropy production by the information creation, and (iii) this is the reason for most protein machines to operate as dimers or higher organized structures.

#51 Depletion interaction potential for ideal and real polymer chains with EVI in a solution of mesoscopic colloidal particles of big size

Kuterba, Piotr (Jagiellonian University)

Usatenko, Zoryana (Cracow University of Technology, Cracow, Poland / Polen)

Investigation of a dilute solution of ideal and real linear polymer chains with excluded volume interactions (EVI) in a good solvent immersed in a confined geometry of two colloidal particles of big size and between wall and colloidal particle for different boundary conditions (b.c.) such as: Dirichlet-Dirichlet, Neumann-Neumann and Dirichlet-Neumann which corresponds to the situation of two repulsive walls, two inert walls and for the mixed case of one repulsive and one inert wall were performed. Taking into account the well known correspondence between the field theoretical φ4 O(n)-vector model in the limit n-> 0 and the behavior of long-flexible polymer chains in a good solvent and Derjaguin approximation for the case of big colloidal particles the calculation of the correspondent depletion interaction potentials were calculated for all above mentioned cases. The obtained results indicate, that the depletion interaction potential for the case of two big colloidal particles with repulsive surfaces is smaller than for the case of big colloidal particle near the surface. In general case introducing the curvature for two surfaces leads to the reducing of the correspondent depletion interaction potentials. The obtained results are in good qualitative agreement with previous theoretical investigations.

#52 Mechanical durability of materials used in increased risk conditions

Slosorz, Zuzanna (CNBOP -PIB)

Rakowska, Joanna; Sleczkowski, Bartlomiej (CNBOP - PIB, Jozefow, Poland / Polen)

During fire fighting operations rescue services use personal protective equipment and firefighting equipment [1]. During rescue operations rescuers work in conditions of increased risk (high temperature, pressure changes, impact of hazardous substances). Ensuring the safety of the rescuers and victims is extremely important. And it can be carried out only under the conditions that the rescuers are properly protected using protective clothing and effective rescue equipment [2]. However, as every material, the used products have a limited range of use and expire date, and they are disposable. Often when the date expires or the product is to be used again, it does not meet the set requirements [3,4]. Preliminary tests to determine the ability of long-term application of materials used by the rescue services were planned. Based on research material degradation of clothing and the components of fire fighting equipment will be documented. The aim of the research is confirming the necessity to carry out endurance tests and the justification of issuing certificates for the equipment used during rescue operations. Endurance tests of materials and equipment used by rescuers will be carried out during research. Degree of tear and the endurance of materials (before and after aging and exposure to factors occurring during fire fighting operations) after the research will be specified.
Research carried out as part of status activities, research project 016/BC/CNBOP-PIB/MNiSW/2011-2016

#53 The use of surfactants as ingredients of degreasing agent for metal alloys

Radwan, Katarzyna (CNBOP-PIB)

Rakowska, Joanna; Porycka, Bozenna (CNBOP-PIB, Józefów, Poland / Polen)

Metalworking is used in many industries, and to make the use of metals possible, proper preparation of the surface is essential. One of the stages is a degreasing of metals, which aims to remove surface contaminants, such as oil impurities. In this process is used acidic degreasing or alkaline baths, using cleaning and degreasing properties of the surfactants. The mechanism of removing contaminants is based on lowering the surface tension of the washing solution and the formation of a film on the surface of impurities binding dirt with an aqueous solution. Efficient removal of oily substances is made possible by selecting the appropriate composition and concentration of the composition of surfactants. The study was aimed to determine the effectiveness of surfactants as potential components of the composition for cleaning metal. Degreasing effectiveness was determined by testing the wettability of the surface of metals, and the ability to emulsify oil contamination. The research was financially supported by MNiSW as project 016/BC/CNBOP-PIB/2011-2016

#54 Impact of fire-fighting foam-forming ingredients on corrosivity of fire extinguishing systems

Radwan, Katarzyna (CNBOP-PIB)

Rakowska, Joanna (CNBOP-PIB, Józefów, Poland / Polen); Brojanowska, Agnieszka (Faculty of Materials Science and Engineering, Warsaw University of Technology, Warszawa, Poland / Polen); Trzaskowski, Wincenty (CNBOP-PIB, Józefów, Poland / Polen)

Elements of fire extinguishing systems and fire fittings for feeding fire-fighting foams are usually made ​​of alloy steel, brass and aluminium. Fire-fighting equipment should be characterized by high efficiency and operational reliability. Due to the chemical composition, foam concentrates can affect the corrosiveness of metal components extinguishing systems [1, 2]. Raw material base of foam concentrates are surfactants. Some of them may also be corrosion inhibitors and protect the materials from corrosion. The study aimed to determine the impact of surfactants of different types, which are components of fire-fighting foam on extinguishing metal armatures. The study of the corrosive properties was performed by electroless method (stabilization of corrosion potential in an open system - OCP) and direct current (potentiodynamic study - PD). The research was financially supported by MNiSW as project 016/BC/CNBOP-PIB/2011-2016

Session 2

#1 Critical Casimir interactions between Janus particles

Labbé-Laurent, Marcel (Max-Planck-Institut für Intelligente Systeme)

Dietrich, Siegfried (Max-Planck-Institut für Intelligente Systeme, Stuttgart, Germany / Deutschland)

Recently there is strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and of Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a chemically structured substrate. A modification of the Derjaguin approximation turns out to be generally reliable. Based on this approach we have in addition derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.

#2 Monte Carlo Sampling in Chaotic Systems

Leitão, Jorge C. (Max Planck Institute for the Physics of Complex Systems)

Lopes, J. M. Viana Parente (Faculdade de Ciências da Universidade do Porto, Porto, Portugal); Altmann, Eduardo G. (Max Planck Institute for the Physics of Complex Systems, Dresden, Germany / Deutschland)

In this talk I show how rare trajectories of chaotic systems can be efficiently sampled using Importance Sampling Monte Carlo methods. I focus on two problems: long-living trajectories in chaotic scattering and trajectories with low chaoticity (small finite time Lyapunov exponents) in closed systems. The critical issue in both problems, which this talk answers, is how to taylor traditional Monte Carlo and Transition Path Sampling to overcome the extreme fractal landscapes found in phase-spaces of chaotic systems. References: [1] J. C. Leitão, J. Lopes, E. G. Altmann (2013). Monte Carlo Sampling in Fractal Landscapes. Physical Review Letters, 110(22), 220601 [2] J. C. Leitão, J. Lopes, E. G. Altmann (2014). Efficiency of Monte Carlo sampling in chaotic systems. Physical Review E, 90(5), 052916.

#3 Nucleation and growth of cluster crystals

Leitold, Christian (Universität Wien)

Dellago, Christoph (University of Vienna, Wien, Austria / Österreich)

We study the formation of cluster phases in the GEM-n system for n=4[1]. The interaction between two particles separated by a distance r is given by u(r) = ε exp(-r4/σ4), where ε and σ determine the energy and length scale, respectively. Due to the finite value of this pair potential for zero separation between two particles, the system can form a cluster crystal. In such a crystal, at high enough densities a number of particles can sit on top of each other at one single lattice site. In addition, hopping events can occur where a single particle jumps from its cluster to an adjacent one at another lattice site. The GEM-n potential can be seen as the effective interaction of certain amphiphilic dendrimers, which are also able to form cluster crystals[2]. In our work, we investigate which microscopic mechanisms lead to the formation of such a GEM-4 cluster crystal from a supercooled liquid in the low-temperature region of the phase diagram. To achieve this goal, we combine direct molecular dynamics simulations and umbrella sampling with replica exchange. With the latter method, we calculate the free energy as a function of the size of the largest crystalline nucleus in the system, both at constant volume and at constant pressure. We also calculate the particle mobility in the supercooled liquid as a function of temperature. As it turns out, for low temperatures the supercooled liquid shows glass-like behavior with very slow dynamics. Therefore, for the nucleation studies, the temperature needs to be carefully selected: It should be high enough to allow for reasonable nucleation timescales and low enough to fall within the region of the phase diagram with distinct cluster phases. In order to define crystalline particles, we use bond-order parameters based on a Voronoi construction to analyze the local neighborhood of particles[3]. Traditionally used methods based on a fixed cutoff radius often sensitively depend on the actual choice of the cutoff radius. Conversely, the Voronoi-based method is parameter free, continuous in the particle positions, and adapts well to varying local densities. [1] Kai Zhang, P. Charbonneau and B. M. Mladek, PRL 105, 245701 (2010) [2] D. A. Lenz, B. M. Mladek, C. N. Likos, G. Kahl, and R. Blaak, JPCB 115 (22), 7218 (2011) [3] W. Mickel, S. C. Kapfer, G. E. Schröder-Türk, and K. Mecke, JCP 138, 044501 (2013)

#4 Maxwell-Boltzmann statistics of N quantum-particles in equilibrium.

Lemmens, Lucien (Universiteit Antwerpen)

One of the questions often asked by researchers working in Nano-systems is the use of expressions from statistical quantum mechanics that assume the thermodynamic limit in their derivation. This limiting process simplifies the derivations and makes the formulation more compact. A similar question often occurs in ordinary statistics. The subject is then the number of samples needed to use the normal distribution. Probability theory, considered as a part of mathematics, gives via the central limit theorem a guide line wether it is allowed to use that approach or not. Although the word probability is frequently used, the mathematical discipline named probability theory is not. Indeed the probability space is not even mentioned and the probability assignment is also not discussed. What I tried to do is, using the Kolmogorov approach, go trough the mathematics and apply it to a set of N non-interacting particles all described by the same Hamiltonian. Furthermore I assumed that the eigenvalues and the Hilbert space are known. Given these constraints on the theoretical approach, the choice of the probability assignment remains: it should be noted that only the properties of the assignment are determined in probability theory. The expression is given by the discipline, in our case the quantum model. Taking the set of eigenvalues as outcomes, keeping it countable there are no measurability precautions and the maximum entropy approach can be used, assuming that the total energy and the number of particles, N, are the constraints in the probabilistic model. This approach allows some new investigations: the outcomes in probability form a set: this implies that order statistics has to be used to make statements about the lowest (highest) energy state or their range. In order to analyse the relation between the energy-spectrum and the number of particles, the variation of the energy range has been calculated in function of the number of particles for quantum harmonic oscillators. It is found that the variation, the expectation divided by the standard deviation, behaves as a power law N α for a sufficient number of oscillators. The probability space leading to the Maxwell-Boltzmann and the appropriate probability assignment is straight forward. For identical particles the development in both disciplines diverges in the sense that the same words are used for completely different properties: for example exchange is in probability theory a property of the probability density while in quantum statistics it indicates a property of the particles, the same situation happens for distribution: in probability theory it is a probability while the Fermi distribution is an expectation value.

#5 Critical Exponents Can Be Different on the Two Sides of a Transition: A Generic Mechanism

Léonard, Frédéric (Université Pierre et Marie Curie Paris VI - LPTMC)

We present models where γ + and γ - , the exponents of the susceptibility in the high- and low-temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The Z q -invariant models are the simplest examples for two-component order parameters (N=2) and the model with icosahedral symmetry for (N=3). We accurately compute γ + - γ - as well as the ratio ν/ν' of the exponents of the two correlation lengths present for T &lt; T c .

#6 Novel coarse-graining approach for Star polymer - linear Homopolymer mixtures

Locatelli, Emanuele (Universität Wien)

Likos, Christos (University of Vienna, Vienna, Austria / Österreich)

We present a novel coarse-graining approach, suitable for star polymer mixtures. The approach is based on the calculation of the effective interaction between a star polymer and a single monomer, which can be used to coarse-grain the interaction between a star and a complex object. The effective interaction has been calculated numerically for star polymers of different functionalities f and for different degrees of polymerization N. We find that these potentials can be scaled following the star polymer scaling laws. We test our approach, calculating the effective interaction between a star polymer and a linear homopolymer, comparing the results obtained from coarse graining and monomer resolved simulations. We employ this technique to study star - linear homopolymer mixtures, focusing on the limit of very long homopolymers.

#7 Air Traffic, Boarding of Passengers and Scaling Exponents

Mahnke, Reinhard (Rostock University)

Here we study an airplane boarding model, introduced earlier by Frette and Hemmer [1], with the aim to determine precisely the asymptotic power--law scaling behavior of the mean boarding time $\langle t_b \rangle$ and other related quantities for large number of passengers $N$. The power--law scaling $\langle t_b \rangle \propto N^{\alpha}$ has been earlier stated in [1], with the exponent $\alpha = 0.69 \pm 0.01$ being evaluated from the data within $2 \le N \le 16$. Our analysis is based on Monte Carlo simulation data for very large system sizes up to $N=2^{16}=65 536$. In analogy with critical phenomena, we have used appropriate scaling ansatz, which includes the leading term as some power of $N$, as well as power--law corrections to scaling. Our analysis clearly shows that the true (asymptotic) exponent $\alpha$ is $1/2$ ($\alpha = 0.5001 \pm 0.0001$). We have estimated also other exponents: $\nu = 1/2$ for the mean number of passengers taking seats simultaneously in one time step, $\beta=1$ for the second moment of $\langle t_b \rangle$ and $\gamma \approx 1/3$ for its variance. The difference between the asymptotic exponents and the effective exponents, extracted from relatively small system sizes, is explained by corrections to scaling, which are described by the correction--to--scaling exponent $\theta \approx 1/3$. In relation to critical phenomena, this model can serve as a toy example, clearly demonstrating the importance of corrections to scaling and the necessity to consider very large systems to obtain correct values of the exponents. [1] V. Frette, P. C. Hemmer: Time needed to board an airplane: A power law and the structure behind it, Phys. Rev. E \textbf{85}, 011130 (2012)

#8 Evidence of Aging and Dynamical Scaling During Collapse of a Polymer

Majumder, Suman (Institut für Theoretische Physik, Universität Leipzig)

Janke, Wolfhard (Institut für Theoretische Physik, Universität Leipzig, Leipzig, Germany / Deutschland)

We investigate a newly framed two-time property for the nonequilibrium evolution dynamics during the collapse of a homopolymer via Monte Carlo simulations of a model polymer. Our results show evidence of aging effects, as observed in the slow dynamics of structural and spin glasses, along with the presence of a dynamical power-law scaling of the autocorrelation functions with respect to the ratio of cluster sizes at two different times. We estimate the value of the exponent, governing the scaling unambiguously by applying a finite-size scaling analysis to the numerical data. The value thus obtained obeys a bound which we predict via general theoretical arguments. The results presented should be of general validity and may trigger direct experimental verification in single-polymer dynamics.

#9 Defect-mediated melting of two-dimensional colloidal quasicrystals

Martinsons, Miriam (Friedrich-Alexander Universität Erlangen-Nürnberg)

Schmiedeberg, Michael (Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany / Deutschland)

Quasicrystals are structures that possess long range order but no translational symmetry. They can have any rotational symmetry including those that are forbidden in periodic crystals. There are additional degrees freedom in quasicrystals and therefore additional hydrodynamic modes, which are termed phasons. Phasons affect the properties of defects in quasicrystals and as a consequence the process of defect-mediated melting. An extension of the so-called KTHNY theory [1,2] predicts that the melting of two-dimensional quasicrystals occurs in two steps when increasing the temperature. First, thermally excited dislocation pairs dissociate and as a consequence destroy the quasi-long ranged positional order but not the orientational order. The expected intermediate phase was termed the pentahedratic phase [2]. In the second step, the dislocations dissociate into disclinations that destroy the orientational order as well. We use Monte-Carlo and Brownian dynamics simulations to study the melting process of decagonal colloidal quasicrystals. By analyzing the positional and bond-orientational correlation functions during the melting process we indeed observe an intermediate state with quasi-long ranged orientational order but only short ranged positional order. Detailed analyses reveal network-like structures composed of defects spanning through defect-free areas. When further increasing the temperature we find a coexistence between the intermediate phase and the fluid before the melting process is completed. Note that a similar coexistence has been reported for periodic crystals [3].
[1] P. De, R. A. Pelcovits, J. Phys. A 22 , 1167 (1989). [2] P. De, R. A. Pelcovits, Phys. Rev. B 38 , 5042 (1988). [3] S. C. Kapfer, W. Krauth, Phys. Rev. Lett. 114 , 035702 (2015).

#10 Self-organising structures in immiscible crystals

Minkowski, Marcin (Instytut Fizyki Polskiej Akademii Nauk)

Zaluska-Kotur, Magdalena; Karczewski, Grzegorz (Instytut Fizyki Polskiej Akademii Nauk, Warszawa, Poland / Polen)

We study crystals of two components, which in the ground state are complety separated. This feature, called immiscibility, is employed in manufacturing of various nanostructures, such as nanodots or nanowires. An example of such an immiscible system are PbTe/CdTe heterostructures. It has been shown in the growth experiment [1] that multilayer PbTe/CdTe structure undergoes thermally induced morphological changes from the horizontal ordering to the vertical columns and finally to the complete separation of the phases with CdTe on the top of PbTe. In order to explain those phenomena we have proposed a simple lattice gas model [2]. The model takes into account the adsorption of PbTe and CdTe particles on the surface as well as the diffusive processes occuring both on the surface and in the bulk. Strong attractive forces between particles of the same type assure the immiscibility of the system. The results of the Monte Carlo simulations reproduce the experimental findings. We also analyse the obtained results quantitatively by means of correlation functions. [1] G. Karczewski, M. Szot, S. Kret, K. Kowalczyk, S. Chusnutdinow, T. Wojtowicz, S. Schreyeck, K. Brunner, C. Schumacher, L.W. Molenkamp, Nanotechnology 26 135601 (2015) [2] M. Mińkowski, M.A. Załuska-Kotur, G. Karczewski, in preparation

#11 Simulating Proton Transfer Reactions in Liquid Water by Artificial Neural Networks

Morawietz, Tobias (Universität Wien)

Singraber, Andreas (Computergestützte Physik, Wien, Austria / Österreich); Behler, Jörg (Lehrstuhl für Theoretische Chemie, Bochum, Germany / Deutschland); Dellago, Christoph (Computergestützte Physik, Wien, Austria / Österreich)

Ab initio molecular dynamics (AIMD) simulations [1] based on density-functional theory (DFT) allow for a predictive description of the properties of water and enable the investigation of chemical reactions in the condensed phase [2]. While valuable information can be obtained, the high computational cost of AIMD simulations restricts their applications to rather small systems and short simulation times. In recent years, a new class of reactive interatomic potentials based on artificial neural networks (NNs) has emerged, which overcomes the limitations of AIMD simulations [3,4]. NN potentials have a very flexible functional form and are trained to energies and forces from DFT calculations of cluster or condensed-phase configurations. Once trained, NN potentials can be evaluated several orders of magnitude faster than the underlying reference data, thus allowing to perform accurate simulations on extended length and time scales. Recently [5], we have developed a series of six NN potentials for water based on different DFT approximations with and without van der Waals (vdW) corrections. Excellent agreement with the reference method and experimental data for a wide range of properties of crystalline and liquid water was found and the importance of vdW interactions for the thermodynamic anomalies of water could be highlighted. Here, we demonstrate the capability of NN potentials to describe chemical reactions in the condensed phase. We present structural and dynamical properties of the solvated proton and hydroxide ion, and discuss the influence of system size and nuclear quantum effects on the obtained results. [1] R. Car and M. Parrinello, Phys. Rev. Lett. 55 , 2471 (1985). [2] P.L. Geissler, C. Dellago, D. Chandler, J. Hutter, and M. Parrinello, Science 291 , 2121 (2001). [3] J. Behler and M. Parrinello, Phys. Rev. Lett. 98 , 146401 (2007). [4] J. Behler, J. Phys.: Condens. Matter 26 , 183001 (2014) [5] T. Morawietz, A. Singraber, C. Dellago, and J. Behler, submitted .

#12 Pressure-Induced Bulk-Melting in Water Ice

Moritz, Clemens (Universität Wien)

Dellago, Christoph (Computergestützte Physik, Wien, Austria / Österreich)

Apart from its rich phase diagram of thermodynamically stable phases, water ice can also be found in glassy phases called amorphous ices. While classically produced by rapid cooling, such ices also form when ice Ih, cooled to 77 K, is subjected to pressures on the order of 1 GPa. This process is called pressure induced amorphization (PIA) [1]. The occurrence of this process at certain temperatures and pressures has been related to the extrapolated melting line of Ice Ih as well as to a mechanical collapse of the crystal structure [2,3]. We approach the subject of PIA by studying pressure-induced bulk-melting in water ice using computer simulations employing the TIP4P/Ice water model [4]. In particular we use path-based rare-event techniques such as transition interface sampling (TIS) [5] to sample dynamical trajectories of melting events at successively lower temperatures and increased pressures. These calculations allow us to investigate the transition mechanism by analysing the resulting trajectories giving insight into the influence the increased pressure and reduced temperature has on the formation of defects within the crystal structure.
[1] O. Mishima, L.D. Calvert, and E. Whalley, Nature 310, 393 (1984). [2] T. Strässle, S. Klotz, G. Hamel, M. Koza, and H. Schober, Phys. Rev. Lett. 99, 175501 (2007). [3] J.S. Tse and D.D. Klug, Phys. Chem. Chem. Phys. 14, 8255 (2012). [4] J.L.F. Abascal, E. Sanz, R. García Fernández, and C. Vega, J. Chem. Phys. 122, 234511 (2005). [5] T.S. van Erp, D. Moroni, and P.G. Bolhuis, J. Chem. Phys. 118, 7762 (2003).

#13 Winding angle distributions for two-dimensional collapsing polymers

Narros, Arturo (Queen Mary University of London)

Prellberg, Thomas (Queen Mary University of London, London, Un. Kingdom / Ver Königr.)

We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for N-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as C log(N), with C=2 in the swollen phase (previously verified),and C=24/7 at the θ-point. At low temperatures weaker evidence demonstrates compatibility with the same scaling and a value of C=4 in the collapsed phase, also as theoretically predicted[1]. We will also show winding angle distribution and variance simulation results for self-avoiding trails (ISAT) model in swollen and collapse phase, and at critical point. Such results in collapse phase are seen for the first time in such model, where there is not theoretical predictions. Simulations were performed with a modified version of flatPERM algorithm[2], allowing to obtain the microcanonical partition function as a function of chain size, energy and winding. The quality of the data shows the expected corrections due to finite size, never seen so clearly before in both models[3].
Bibliography [1] B. Duplantier and H. Saleur. Phys. Rev. Lett., 60:2343–2346, (1988). [2] T. Prellberg and J. Krawczyk. Phys. Rev. Lett., 92:120602, (2004). [3] A. Narros, A. L. Owczarek, T. Prellberg,

#14 Designing highly specific probes with tunable affinity

Nerattini, Francesca (Universität Wien)

Tubiana, Luca; Coluzza, Ivan (University of Vienna, Vienna, Austria / Österreich)

Finding ligands able to bind with high specificity and tunable affinity to a target protein is one of the major challenges in medical research [1]. To this aim we develop a computational protocol based on the coarse-grained protein model ”Caterpillar” [2] that has proven to be quantitative for design and folding simulations. We apply the model to design proteins that bind specifically to a simple pocket. The generated pocket specific sequences can be tuned with different biding free energies, computed using the Caterpillar and verified with all atom MD simulations. [1] Dubacheva, Galina V., et al. ”Designing multivalent probes for tunable superselective targeting.” Proceedings of the National Academy of Sciences, 112.18 (2015): 5579-5584. [2] Coluzza, Ivan. ”A coarse-grained approach to protein design: learning from design to understand folding.” PloS one, 6.7 (2011).

#15 pH-responsive behaviour of linear weak polyelectrolytes

Nova, Lucie (Charles University)

Uhlik, Filip; Kosovan, Peter (Charles University, Prague 2, Czech Rep./Tschech. Rep.)

We studied the pH-responsive behaviour of long linear weak polyelectrolytes by means of Hybrid Monte Carlo simulations in the reaction ensemble. The chains consist of 100 beads. Each bead is a single weak acid, which can dissociate with the probability according to given Ka. The solvent was modelled as dielectric continuum. Several solvents (permittivities) were applied. No salt was added. The concentration effects on the titration and pH were studied. The problems of local pH and finite size effect are discussed. The shape and size properties of the chain are described by the dependence of Radius of gyration on the degree of dissociation alpha and on pH.

#16 How one can design a supramolecular magnetoresponsive coating using magnetic filament brushes

Novak, Ekaterina (Ural Federal University)

Sánchez, Pedro A. (University of Vienna, Wien, Austria / Österreich); Pyanzina, Elena (Ural Federal University, Ekaterinburg, Russian Fed. / Rus Föd.); Cerdà Pino, Joan (Instituto de Física Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain / Spanien); Sintes, Tomas (Instituto de FisŽica Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain / Spanien); Kantorovich, Sofia (University of Vienna, Wien, Austria / Österreich)

We study systems of magnetic colloids crosslinked with polymers to form permanent, polymer-like chains, with the magnetic colloids playing the role of polymer monomers. The control of the properties of these systems, known as magnetic filaments, has experienced a significant progress in recent years thanks to the enhancement of polymer crosslinking techniques. In this study, we propose to create a magnetoresponsive polymer brush-like system by replacing with magnetic filaments the densely end-grafted polymer chains that form a conventional polymer brush. Polymer brushes are widely used for the creation of stimuli-responsive surfaces, but available polymer molecules are unable to provide significant responses to external magnetic fields at room temperatures. The use of magnetic filaments will allow to control accurately the thickness and the local density of the brush—the two most important structural features of a coating—by means of external magnetic fields. Here, we investigate the intrinsic mechanisms responsible for the overall equilibrium structural properties of a brush made out of magnetic filaments. We focus on the influence of temperature and external fields on the self-assembly of magnetic beads from different filaments. In order to investigate the properties of this system, we perform extensive computer simulations with a coarse-grained model that takes into account the coupling between the magnetic moments of the colloids and the chain crosslinkers. We show that the structural constrains led by the crosslinkers and the grafting surface have a significant impact on the self-assembly properties. Finally, we discuss the structural changes in the brush and confirm their dependence on the control parameters—the temperature and the intensity of an characterize external magnetic field.

#17 Griffiths phases and localization in hierarchical modular networks

Odor, Geza (Centre for Energy Research, Institute of Technical Physics and Materials Science)

We study variants of hierarchical modular network models suggested by Kaiser and Hilgetag [ Front. in Neuroinform.,4 (2010) 8] to model functional brain connectivity, using extensive simulations and quenched mean-field theory (QMF), focusing on structures with a connection probability that decays exponentially with the level index [4]. Such networks can be embedded in two-dimensional Euclidean space. We explore the dynamic behavior of the contact process (CP) and threshold models on networks of this kind, including hierarchical trees. While in the small-world networks originally proposed to model brain connectivity, the topological heterogeneities are not strong enough to induce deviations from mean-field behavior, we show that a Griffiths phase can emerge under reduced connection probabilities, approaching the percolation threshold [1]. In this case the topological dimension of the networks is finite, and extended regions of bursty [2], power-law dynamics are observed. Localization in the steady state is also shown via QMF [3]. We investigate the effects of link asymmetry and coupling disorder, and show that localization can occur even in small-world networks with high connectivity in case of link disorder.
[1] Miugel A. Munoz, Róbert Juhász, Claudio Castellano, Géza Ódor, Phys. Rev. Lett. 105 (2010) 128701 [2] Géza Ódor, Phys. Rev. E 89, 042102 (2014) [3] Géza Ódor, Phys. Rev. E 90, 032110 (2014) [4] Géza Ódor, Ronald Dickman, Gergely Ódor, Sci. Rep. 5, 14451; doi: 10.1038/srep14451 (2015)

#18 Configurational phase transitions driven by energy spectrum and helical propensity in ideal heteropolymer proteinogenic chains in vacuo

Olivares-Quiroz, Luis (Universidad Autonoma de la Ciudad de Mexico)

Hernandez-Herran, Damian (Universidad Autonoma de la Ciudad de Mexico, Mexico City, Mexico / Mexiko)

Proteins belong to a large class of biological macromolecules capable to undergo thermodynamic phase transitions from random to quasi-crystalline three dimensional ordered structures. For a large class of proteins, such configurational phase transitions can be directly associated with a passage from non-biologically active states to states with high biological activity. In this work we present an extensive treatment of an statistical-mechanics based coarse grained model to discuss quantitatively the passage from high-entropy to low-entropy conformations in proteins and peptides in terms of the set of helical propensities wj and the penalty energies Uj associated to each amino acid residue along the chain. We present an analytical solution for the equilibrium partition function Zhet in the canonical ensemble for an ideal heteropolymer chain X1-X2-...XN composed by N non-interacting residues Xj. Two different mechanisms for the onset of the ground low-entropy conformation with energy ε0 are discussed. We apply this formalism to two test systems, proteins HEW-Lisozyme (PDB: 1DPLX) and RNase-A (PDB: 4OOH). Our results shown that our model is capable to predict both the transition temperature Tc and the maximum value for the specific heat Cp at the transition in a very good agreement with experimental values obtained elsewhere. In addition our results strongly suggest that protein folding early stages, i.e, collapse from random coil to molten globule structures, have a large entropic contribution and requires a cooperative effect among residues.

#19 Six-vertex model with domain wall boundary conditions in the Bethe-Peierls approximation

Pelizzola, Alessandro (Politecnico di Torino)

Cugliandolo, Leticia (Université Pierre et Marie Curie, Paris, France / Frankreich); Gonnella, Giuseppe (Università di Bari, Bari, Italy / Italien)

We use the Bethe–Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice with partial domain-wall boundary conditions. We show that this rather simple approximation yields results that are remarkably close to the exact ones when these are known, and allows one to estimate the location of the phase boundaries with relative little effort in cases in which exact results are not available.

#20 Emergence of periodic behaviours from randomness

Pickton, John (University of Nottingham)

Emergent periodic effects can be observed in a large variety of complex systems consisting of discrete objects, be they fireflies signalling to attract mates, synapses firing in the brain, pace-maker cells in the heart or anti-bunching of photons emerging from a cavity. Identifying and understanding the origins of periodic behaviour is a fundamental step towards being able to describe and control its occurrence. We discuss how periodic behaviours can arise in discrete systems where the underlying dynamics are purely random and irreversible. We consider non-interacting particles moving randomly on a network of nodes forming a closed loop. The population dynamics describing the number of particles at a node is a stochastic birth-death process, augmented by particles migrating randomly to adjacent nodes. This can result in the emergence of periodic behaviours occurring because of the interaction between the dynamics of the particles and the spatial structure through which they move. The conditions for this are that there be a preferred direction to migration and that the birth-death rates relative to the rate of migrations fall within a specified range. Three distinct classes of long term behaviour for the system emerge that are dependent on the relative values of the migration and birth-death rates.

#21 An Anisotropic Effective Model for the Simulation of Semiflexible Ring Polymers

Poier, Peter (Universität Wien)

We present an effective model for the description of a system of semiflexible ring polymers. An isotropic model, in which the ring polymers are only represented by their centers of mass, has already been investigated in [1]. However, it was also shown that the monomer-resolved system shows anisotropic features that cannot be accounted for in the isotropic effective model. This motivates us to introduce an anisotropic effective model for the description of semiflexible ring polymers, where the effective particles are soft disc-like molecules which are described not only by their center of mass but also by the direction in which their faces are oriented[2]. We find good agreement between the correlation functions in simulations of the anisotropic model and the monomer resolved system, especially for short and stiff ring polymers where the isotropic model was only able to provide an adequate description at very low densities. In addition, the analysis of the interactions in the anisotropic effective potential allows us to get a better understanding for the interaction between the semiflexible ring polymers.
[1] Bernabei, M.; Bacova, P.; Moreno, A. J.; Narros, A.; Likos, C. N. Soft Matter 2013, 9, 1287-1300 [2] Poier, P., Moreno, A. J.; Likos, C. N; Blaak R., Macromolecules 2015, 48, 4983-4997

#22 The self-assembling anisotropic particles: phase transition

Pyanzina, Elena (Ural Federal University)

Kantorovich, Sofia (University of Vienna, Vienna, Austria / Österreich); De Michele, Cristiano (Sapienza Universita di Roma, Rome, Italy / Italien)

The spontaneous thermodynamically equilibrium formation of reversible aggregates from basic building blocks is often referred to as self-assembly. Since scattering experiments easily provide the information on system structure in the form of structure factors, it is necessary to develop a formalism to theoretical calculations of density-density correlations based on the results of the predicted self-assembly and phase behaviour. We investigate the isotropic and nematic phases formed by sphere-cylinders that self-assemble in linear chain structures. First, we are trying to answer the question: How are the spatial correlations in the system influenced by the nematic order parameter? To do so, we distinguish between the spatial correlations in the plane perpendicular to the crystalline axis, and in the direction parallel to the latter. Following this separation, we put forward a theoretical approach to calculate structure factors (SFs) separately. We test our theoretical methods against the results of canonical NVT Monte Carlo simulations of hard cylinders with attractive sites on their bases and perform detailed analysis. Second, we investigate and compare average characteristics of the linear chain structures in the both phases. Finally, we investigate influence of particles shape, stacking energy and concentration on the isotropic-nematic transition to find out the critical parameters. E.S.P. was supported by the Grant of the President of the Russian Federation No MK-7131.2015.2. S.S.K. was partially supported by mol-a-ved 15-32-20549. C.D.M. acknowledges support from MIUR-PRIN. The research has been partially supported by Austrian Science Fund (FWF): START-Projekt Y 627-N27.

#23 The route to magnetic order in the spin-1/2 kagome Heisenberg antiferromagnet: The role of interlayer coupling

Richter, Johannes (University Magdeburg, Institute for Theoretical Physics)

While the existence of a gapped topological Z2 spin liquid on the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is now well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we provide a detailed analysis of this problem by using the coupled-cluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC J_perp, where we study ferro- as well as antiferromagnetic J_perp. We find that the spin-liquid ground state (GS) persists until relatively large strengths of the ILC. Only at |J^c_perp| ~ 0.15 the spin-liquid phase gives way for q=0 magnetic long-range order, where the transition between both phases is continuous and the critical strength of the ILC, |J^c_perp|, is almost independent of the sign of J_perp. Thus, by contrast to the quantum GS selection of the strictly two-dimensional KHAF at large spin $s$, the ILC leads first to a selection of the q=0 GS. Only at larger |J_perp| the ILC drives a first-order transition For more details, see O. Goetze and J. Richter, arXiv:1510.48898.

#24 Self-assembly in Dipolar Fluids

Ronti, Michela (University of Vienna)

Kantorovich, Sofia (University of Vienna, Vienna, Austria / Österreich)

We are studying low temperature structural transitions in dipolar hard spheres (DHS) combining grand-canonical Monte Carlo simulations and direct analytical theoretical calculations. DHS is characterized by long-range anisotropic interactions: it consists of a point dipole at the center of a hard sphere. We are interested in low temperature and low density phase behaviour of DHS systems. The debate on the existence of a critical point in DHS is still open. From a theoretical point of view the process of self-assembly is not responsible for a phase transition; this belief was completely reverted by theoretical studies showing that the process of self-assembly is alone capable to induce phase transition(1). On the other hand in the last years it was proved that no sign of critical behaviour is observed, implementing efficient and tailored Monte Carlo algorithms(2). Moreover a theoretical approach based on Density Functional Theory was developed: a series of structural transitions were discovered providing evidence of a hierarchy in the structures on cooling (chains, rings, branched structures)(3). We are performing free-energy calculations in order to draw the phase diagram of DHS model. Knowing the individual cluster partition functions allows us to calculate the free energy for any system density where the clusters can be considered as non-interacting. The relations between the partition functions can be obtained directly from grand-canonical Monte Carlo simulations (GCMC), with the constraint that all particles should form a single cluster. Comparing the numerical results with the theoretical ones shed light on the scenario of temperature induced structural transitions in magnetic nano colloids.

(1) T. Tlusty and S.A. Safran, Science 290, 1328 (2000) (2) L. Rovigatti, J. Russo and F. Sciortino, Soft Matter 8, 6310-6319 (2012) (3) S.S. Kantorovich, A.O. Ivanov, L. Rovigatti, J.M. Tavares and F. Sciortino, Phys. Chem. Chem. Phys. 17, 16601 (2015)

#25 The Price of Anarchy on Congestible Networks

Rose, Alex (University of Nottingham)

The efficiency of systems in which uncoordinated or “selfish” users compete for a resource whose value diminishes with shared usage can be quantified by the price of anarchy (POA). This measures the degradation of the performance of uncoordinated users as a group, relative to the social optimum achieved by coordination. One challenge is to discover properties that heighten the POA in such a system. As a simple theoretical paradigm, we consider routing traffic through a planar lattice network comprising congestible and non-congestible edges. We analyse the dependence of the POA on both the proportion of con- gestible edges in the network and the aspect ratio of the lattice. For lattices with aspect ratio 1:1, it is known that the POA monotonically increases with the proportion of congestible edges before abruptly falling back to unity at the directed percolation threshold of the lattice (B. Skinner, The price of anarchy is maximised at the percolation threshold. Phys. Rev. E 91 052126, 2015). We discover that the behaviour of the POA is very different for lattices greater in height than in width, in that its value increases through a series of ripples before falling to unity. We thereby construct an alternative explanation for the behaviour of the POA than that given by Skinner. We show that local maxima occur when the number of paths with the (joint) most variable edges out of all the paths of the network, is equal to the number of variable edges of each of these paths. The emergence of the structure in the POA that we reveal, occurs therefore at a particular confluence of the microscopic structure of the paths and the macroscopic struc- ture of the network.

#26 Soft self-assembled nanoparticles with temperature-dependent properties

Rovigatti, Lorenzo (Faculty of Physics, University of Vienna)

Capone, Barbara; Likos, Christos N. (Faculty of Physics, University of Vienna, Vienna, Austria / Österreich)

The fabrication of versatile building blocks that reliably self-assemble into different ordered phases is amongst the hottest topics in modern material science. Star polymers made of di-block copolymers grafted on a central anchoring point have shown to spontaneously self-assemble into soft patchy particles. Here we demonstrate that this system can be finely tuned by the physical/chemical parameters of the solution, allowing us to finely control the number and size of the attractive patches, as well as the shape of the particle, by means of changes in temperature and/or solvent quality[1]. As a result, the macroscopic behaviour can be changed without modifying the microscopic constituents. [1] L. Rovigatti, B. Capone and C. N. Likos, Nanoscale (2015)

#27 Universality of Static and Dynamic Response near the Demixing Transition of Binary Fluids

Roy, Sutapa (Max-Planck Institute for Intelligent Systems)

Dietrich, Siegfried (Max-Planck-Institute for Intelligent Systems, Stuttgart, Germany and Institute for Theoretical Physics IV, University of Stuttgart, Germany) ; Hoefling, Felix ( Max-Planck-Institute for Intelligent Systems, Stuttgart, Germany, Institute for Theoretical Physics IV, University of Stuttgart, Germany, and Department of Mathematics and Computer Science, Freie University at Berlin, Arnimallee 6, 14195 Berlin, Germany

The critical behavior of five symmetric binary Lennard-Jones mixtures, close to their demixing points, is studied computationally 1 via semi-grand canonical Monte Carlo and massively parallel molecular dynamics (MD) simulations. The binary fluids are chosen to cover a wide range of compressibilities, they differ in their number densities and in the interactions between unlike particles. The static quantities investigated include the phase diagram (both the binodals and the λ-line), the correlation length, and the concentration susceptibility as well as the compressibility and the pressure at the demixing point. Among the collective transport properties, the focus is on the interdiffusivity and the shear viscosity. Exploiting the computing resources of high-end GPUs 2 gives access to large-scale MD simulations of up to 87, 500 particles over 4 non-trivial orders of magnitude in time. The critical exponents of the singularities observed in the static quantities are in good agreement with what one expects from the three-dimensional Ising universality class 3 . For the dynamic quantitites, the critical singularities are much harder to access. The results are compatible with predictions from mode-coupling and dynamic renormalization group theories 4 and agree with previous computer simulations 5 . Further, the density dependence of the non-universal critical amplitudes is investigated, which is of interest for future simulation studies. In particular, two universal critical amplitude ratios are tested.

#28 1D Potts model with invisible states

Sarkanych, Petro (Institute for Condensed Matter Physics of NAS of Ukraine)

Holovatch, Yurij (Institute for Condensed Matter Physics of NAS of Ukraine, Lviv, Ukraine); Kenna, Ralph (Coventry University, Coventry, Un. Kingdom / Ver Königr.)

We present the exact solution of the 1D Potts model with invisible states. The model was introduced a few years ago [1] to explain some atypical phase transitions with spontaneous symmetry breaking. In addition to q ordinary Potts states this model possesses r states which do not interact, and thus contribute to the entropy, but not to the internal energy. The number of invisible states plays a role of a parameter, which changes the order of a phase transition. In the presence of two ordering fields, h1 and h2 the generalised Hamiltonian of the model reads: H=-Σi δ(si,si+1)Σα=1qδ(si,α)-h1Σi δ(si,1)-h2Σiδ(si,q+1), where the Potts spins are si=1, ... ,q,q+1, ... ,q+r, where q and r are the numbers of visible and invisible states respectively and where the sums span N sites of 1D lattice. Using the transfer matrix method we obtain the partition function of the model and further analyse partition function zeros in the complex T and h planes (Fisher and Lee-Yang zeros). We analyse the Yang-Lee edge and generalize the duality transformation which maps Lee-Yang zeros to Fisher zeros [2] for r>0. At h1=0 and Imh2=0 Fisher zeros accumulate along the line that intersects the real T-axis at T=0. This corresponds to the usual phase transition in a 1D system. However, for r+eh2<0 the line of zeros intersects the positive part of the real T-axis, which means an existence of a phase transition at non-zero temperature. This surprising result can be achieved if Imh2=iπ/2. As it has been shown recently, a complex magnetic field maps to the quantum coherence time [3]. Therefore, our approach manifests a connection between criticality in quantum and classical models.
[1] R. Tamura, S. Tanaka, and N. Kawashima, Prog. Theor. Phys. 124 (2010) 381. [2] Z. Glumac and K. Uzelac J. Phys. A 27 (1994) 7709. [3] B.-B Wei and R.-B. Liu, Phys. Rev. Lett. 114 (2015) 010601.

#29 How cross-links of different coordinations influence the mechanical properties of polymer networks

Shabbir, Huzaifa (Universität Wien)

Hartmann, Markus A (Computational Physic, Vienna, Austria / Österreich)

(Reversible) cross-linking is a common method to specifically tailor the mechanical properties of natural as well as synthetic polymeric systems. In biological materials, cross-links are often weaker than the covalent bonds holding the structure together. Thus, upon loading these bonds rupture take place before the covalent backbone fails, providing an efficient energy dissipation mechanism. Furthermore, the reversibility of the cross-links provides the material with a self healing mechanism because broken cross-links may reform after release of the load. In the context of biological materials such cross-links are often called “sacrificial bonds” and they can be found in a large variety of structures like bone, wood, silk and the mussel byssus [1]. While the coordination of cross-links (i.e. the number of monomers participating in one cross-link) often varies in real systems (e.g. depending on pH the Fe-DOPA complex in the mussel byssus is known to exist in the mono-, bis- and tris-state), theoretical and simulation work dealing with the effect of cross-links on the mechanics of polymeric networks mostly investigate the effect of two fold coordinated cross-links only. In the current study we aim at closing this gap, by explicitly investigating the mechanical response of a polymeric system as a function of the coordination of reversible cross-links.
Monte Carlo method is used to study the mechanical properties of cross-linked polymeric systems. The coordination of cross-links is controlled by using the framework given by potential of the REBO (Reactive Empirical Bond Order) type. This potential was initially developed for describing non-closed packed covalently bonded systems such as carbon and silicon. The main feature of the REBO potential is that the strength of an individual bond depends on the coordination of the involved atoms. The current study investigates the effect of different coordination (two- and three-fold) on the mechanical properties of polymeric systems including random fiber networks and aligned fiber bundles. For different cross-link densities, the computational load-displacement curves are obtained and some of the most important mechanical properties like the stiffness, strength and toughness are assessed. As previous work on two-fold coordinated cross-links was showing a strong dependence of the mechanical performance on the topology of formed cross-links [2-4], in the present investigation special emphasis is put on the interplay of topology and mechanics.
[1] Fantner et al., Biophysical Journal 90, 1411 (2006). [2] Nabavi et al., New Journal of Physics 16, 013003 (2014). [3] Nabavi et al., Bioinspired, Biomimetic and Nanobiomaterials 3, 139 (2014). [4] Nabavi et al., Physical Review E 91, 032603 (2015).

#30 On the simulation of Potts model using population annealing algorithm

Shchur, Lev (Landau Institute for Theoretical Physics, Science Center in Chernogolovka)

Barash, Lev (Landau Institute for Theoretical Physics, Science Center in Chernogolovka, Chernogolovka, Russian Fed. / Rus Föd.)

Population-annealing algorithm has been designed for the annealing of the system from the infinite temperature into the ground state [1-3]. We develop modification of the algorithm, which allows us drive population of system from low to higher temperatures. We apply modified algorithm to the investigation of first order transition in two-dimensional Potts model. We present preliminary results demonstrating hysteresis of observables with the temperature under the cooling and heating. We investigate how the width of hysteresis loop does depend on the speed of cooling/heating and on the other parameters of algorithm as temperature step, number of Monte Carlo sweeps between population reweighting’s, etc. We discuss efficiency of the method in comparison with other techniques used for the estimation of critical temperature of the first order phase transition and of the value of latency heat. 1. K. Hukushima, Y. Iba, AIP Conf. Proc. 690, 200 (2003) 2. J. Machta, Phys. Rev. E 82, 026704 (2010) 3. J. Machta, E.S. Ellis, J. Stat. Phys. 144, 541 (2011)

#31 Attainability of Carnot Efficiency with Autonomous Engines

Shiraishi, Naoto (The University of Tokyo)

It is well known that the maximum efficiency of the heat engine is given by the Carnot efficiency. The maximum efficiency is attained when the external operation on the engine is quasistatic. In addition, it has been established that the maximum efficiency of externally-operated small fluctuating systems is also given by the Carnot efficiency [1]. Although the Carnot cycle is externally operated, most engines from electric power plants to molecular motors are autonomous. Therefore, the maximum efficiency of autonomous engines is an important open problem. Here, we use the word autonomous to refer to systems in stationary states without any time-dependent external operation. Prominent models of autonomous engines are Feynman’s ratchet and the Buttiker-Landauer system, which cannot attain the Carnot efficiency even in the quasistatic limit due to the inevitable fluctuation of the engines [2,3]. As opposed to this, some elaborated models attain the Carnot efficiency [4-7]. Most of these previous studies have been devoted to specific models, and the comprehensive understanding of autonomous engines has been elusive. In this presentation, we clarify the general condition necessary for autonomous engines to attain the Carnot efficiency [8]. We first introduce a schematic model, an autonomous Carnot engine driven by a chemical potential difference. This engine clearly shows typical characteristics of autonomous heat engines: While in usual setups the maximum efficiency is less than the Carnot efficiency even with quasistatic limit, they can attain the Carnot efficiency in the presence of a special type of singularity. We then demonstrate that the general necessary condition for autonomous heat engines to attain the Carnot efficiency is the presence of a special type of singularity, which can reproduce the results on existing models of autonomous heat engines. [1] K. Sekimoto, Stochastic Energetics, Springer (2010). [2] J. M. R. Parrondo and P. Espanol, Am. J. Phys. 64, 1125 (1996). [3] T. Hondou and K. Sekimoto, Phys. Rev. E 62, 6021 (2000). [4] G. D. Mahan and J. O. Sofo, Proc. Nat. Acad. Sci. 93, 7436 (1996). [5] M. Horvat, T. Prosen, and G. Casati, Phys. Rev. E 80, 010102 (2009). [6] U. Seifert, Phys. Rev. Lett. 106, 020601 (2011). [7] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. Lett. 110, 040601 (2013). [8] N. Shiraishi, arXiv:1507.01396 (to appear in Phys. Rev. E).

#32 Studying the effect of dispersion corrections in ab initio water using neural network potentials

Singraber, Andreas (Universität Wien)

Morawietz, Tobias (Computergestützte Physik, Wien, Austria / Österreich); Behler, Jörg (Lehrstuhl für Theoretische Chemie, Bochum, Germany / Deutschland); Dellago, Christoph (Computergestützte Physik, Wien, Austria / Österreich)

In computational materials science the choice of an appropriate potential energy model is crucial to accurately predict the properties of materials. While sophisticated ab initio methods can be used to calculate energies and forces with high accuracy, their considerable computational cost limits their application to relatively small systems and makes large-scale molecular dynamics (MD) simulations impossible in most cases. Empirical potentials, on the other hand, are computationally far less demanding but also lack in accuracy, particularly if covalent bonds are broken or formed. An alternative approach put forward recently consists in training artificial neural networks (NN) to predict the energies and forces [1]. This new method provides the accuracy of first-principles calculations at a fraction of their computational cost. Here, we present neural network potentials for bulk water and ice based on RPBE and BLYP ab initio reference data and study the effect of dispersion corrections (D3) as proposed by Grimme et al [2]. From interface pinning simulations [3] of large systems we show that van der Waals corrections are essential to reproduce reasonable melting temperatures as well as water and ice densities. In addition we present our efforts to compute the temperature of maximum density (TMD) line for the RPBE-D3 and BLYP-D3 model at high negative pressures. [1] Behler, J., and Parrinello M., Phys. Rev. Lett. 98, 146401 (2007). [2] Grimme, S. et al., J. Chem. Phys. 132, 154104 (2010). [3] Pedersen, U. R., J. Chem. Phys. 139, 104102 (2013).

#33 Crystal morphology controlled surface diffusion of the biomolecules as a source of the color noise viewed in terms of crystal vs. solution point of view.

Siódmiak, Jacek (University of Science and Technology in Bydgoszcz)

Crystallization of biomolecules is a very complex process that takes place under specific conditions [1]. There are experimental methods which allow to monitor and control crystal growth process. Some methods, e.g. dynamic light scattering, single molecule tracking, and other dynamic methods are very sensitive to the temporal fluctuations of position, size, conformation, potential energy, etc. of single molecules and/or clusters. Such fluctuations in some cases can be treated as a noise disturbing appropriate signal [2]. In the model presented here macromolecules which migrate from the solution onto the crystal surface diffuse to the positions localized at the foot of the terraces formed on the crystal surface (Burton-Cabrera-Frank model of crystal growth) that are the most favorable thermodynamically [3]. Biomolecular crystals, in general, are of the non-Kossel type (complex structure with several molecules per unit cell in non-equivalent positions) [4] therefore their surface is not uniform and the surface diffusion performed by biomolecules is not a simple random walk. Each step involves breaking of bonds and the creation of entirely new ones and is executed with probability proportional to the Boltzman factor. Therefore, in contrast to the classical random walk, each step is performed at different rate [3]. The energy difference between two neighboring sites at the surface can be positive as well as negative. If it is positive, the energy necessary to perform the step is imbibed from the solution. If the energy change is negative, energy excess is exuded to the solution. Crystal-to-solution energy exchange can be a source of the noise localized in the nearest surroundings of the crystal surface, covering so-called double layer [5]. Such a noise can influence the behavior of not aggregated as wells as already aggregated biomolecules. In consequence, in contrast to the classical random walk that generates white noise, this type of diffusion can be a source of the color noise [6]. The power spectrum and exchange energy distribution of the noise depends on the distribution of the macromolecules which form the terrace. Power spectra obtained for different morphologies of terraces confirm that the biomolecular crystallization can be characterized by the color noise. The presence of the color noise can impede the interpretation of the results obtained e.g. by the dynamic scattering methods. References: [1] A. McPherson; Methods 34 (2004), 254–265. [2] P. Carlini, A. R. Bizzarri, S. Cannistraro; Physica D 16 (2002), 242-250. [3] J. Siódmiak, A. Gadomski; Int. J. Modern Phys. C 17 (2006), 1037-1054. [4] A. A. Chernov; J. Mat. Sci.: Materials in Electronics 12 (2001), 437–449. [5] A. Gadomski, J. Siódmiak, I. Santamaría-Holek; Physica A 392 (2013) 3155–3167. [6] J. Siódmiak, I. Santamaría-Holek, A. Gadomski; J. Chem. Phys. 132 (2010) 195103.

#34 From polymers to proteins: effect of side chains and cylindrical symmetry in the formation of secondary structures within Wang-Landau approach

Skrbic, Tatjana (University of Venice)

Badasyan, Artem (University of Nova Gorica, Materials Research Laboratory, Ajdovscina, Slovenia / Slowenien); Hoang, Trinh Xuan (Institute of Physics, Center for Computational Physics, Hanoi, Vietnam); Podgornik, Rudolf (University of Ljubljana, Ljubljana, Slovenia / Slowenien); Giacometti, Achille (University of Venice, Venice, Italy / Italien)

We study the equilibrium properties of a flexible homopolymer whose consecutive monomers are represented by impenetrable hard spherical beads, tangent to each other and non-consecutive monomers that interact via a square-well potential. To this aim, we use both replica exchange canonical simulations and micro-canonical Wang-Landau techniques and performing a close comparative analysis of the corresponding results, finding perfect agreement with each other and results previously reported in literature. The model is then refined in two different directions. By allowing partial overlapping between consecutive beads, we break the spherical symmetry, thus providing a sever constraint on the possible chian conformations. This leads to a ground state that is either helical, planar or globular, depending on the range of the interactions. Alternatively, we introduce additional spherical beads at specific positions to represent the steric hindrance of the side chains in real proteins. While for short chains, the ground state is found to be a globule, the helical ground state emerges for longer chains (few tens of beads). The combination of the two above effects is found to increase the stability of the secondary structures, in agreement with past results. The fundamental role played by the range of the square-well attraction is enlighted and it is shown to play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.

#35 Stabilizing the liquid-liquid transition in water-like liquids

Smallenburg, Frank (Heinrich-Heine-Universität Düsseldorf )

Filion, Laura (Utrecht University, Utrecht, Netherlands / Niederlande); Sciortino, Francesco (Universita di Roma La Sapienza, Rome, Italy / Italien)

One of the most controversial hypotheses for explaining the origin of the thermodynamic anomalies characterizing liquid water postulates the presence of a metastable liquid-liquid critical point [1]. According to this hypothesis, below the liquid-liquid critical temperature water can phase separate into two distinct liquid phases with different densities. Unfortunately, this critical temperature is expected to be deep inside the supercooled region for liquid water, where rapid crystallization prevents direct experimental observation of this phenomenon. In computer simulations crystallization is easier to control, and numerical evidence has been presented for the existence of this critical point in the well-known ST2 model [2]. However, this evidence has been questioned due to the possibility of an intervening crystal phase [3]. Here, we use a simple model for networked water-like liquids to explore the interplay between crystallization and liquid-liquid phase transitions, and show that a key role is played by the flexibility of the interparticle bonds. We show that this flexibility can be tuned to fully stabilize the liquid-liquid transition, such that it can be observed without risk of crystallization [4]. Finally, we apply the same concept to the ST2 model, and introduce a small amount of tunable flexibility in the model. This model can transform continuously from a flexible model, where the liquid-liquid critical point can be confirmed free of any crystallization, to the original ST2 model, where the critical point is metastable [5]. [1] P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Nature 360, 324 (1992). [2] Y. Liu, A. Z. Panagiotopoulos, and P. G. Debenedetti. J. Chem. Phys. 131, 104508 (2009). [3] D. T. Limmer and David Chandler. J. Chem. Phys. 135, 134503 (2011). [4] F. Smallenburg, L. Filion, F. Sciortino, Nat. Phys. 10, 653 (2014). [5] F. Smallenburg and F. Sciortino, Phys. Rev. Lett. 115, 015701 (2015).

#36 Generalized Langevin Equation for tracer particles in a nonequilibrium environment

Steffenoni, Stefano (Max Planck for Mathematics in the Science)

Falasco, Gianmaria (Istitute for Theoretical Physics, leipzig, Germany / Deutschland); Kroy, Klaus (Institute for Theoretical Physics, Leipzig, Germany / Deutschland)

Langevin equations describe the statistical fluctuations of mesoscopic systems driven by the dynamics of some fast degrees of freedom represented as noise. To achieve consistency with equilibrium statistical mechanics, it is sufficient that the noise correlations satisfy the fluctuation-dissipation theorem; an explicit coarse-graining of the underlying microscopic description is not required. Out of equilibrium, no such general leapfrog principle exists, and mesoscopic Langevin equations must be derived by explicitly integrating out the dynamics of the fast environmental degrees of freedom. We derive a generalized Langevin(1) equation for tracer particles weakly interacting with an environment that is driven out of equilibrium, applying non-equilibrium linear response theory. Integrating out the fast degrees of freedom we obtain an expression for the noise and the friction perceived by the tracers. Excess dynamical activity and probability currents can be used to quantify the breaking of the fluctuation-dissipation theorem and Onsager's reciprocal relations. As a consequence, t he action-reaction principle is found to be violated f or the environment-mediated interactions . (1) C. Maes, S. Steffenoni. Friction and noise for a probe in a nonequilibrium fluid. Phys Rev E 91, 022128 (2015)

#37 Non-Newtonian Hydrodynamics in Generalized Multiparticle Collision Dynamics

Toneian, David (TU Wien, Institute for Theoretical Physics)

Kahl, Gerhard (TU Wien, Institute for Theoretical Physics, Vienna, Austria / Österreich); Gompper, Gerhard; Winkler, Roland G. (Forschungszentrum Jülich, ICS-2 and IAS-2, Jülich, Germany / Deutschland)

Fluids play a key role as a solvent in soft matter systems, even if they are not the primary target of investigation. Take, for example, biological cells propelling themselves by beating with flagella, i.e., slender appendages attached to the cell body. To move efficiently, it is often favorable to have nearby cells beat synchronously, which is achieved via hydrodynamic interactions: The beat of one cell's flagellum induces a flow field in the surrounding medium, which propagates and influences neighboring flagella [1, 2]. To study emergent phenomena like these via computer simulations, one can neither simply neglect the solvent (one would remove the interactions mediated by the fluid, and thus the phenomenon of interest), nor simulate every single molecule of the solvent and the solute: since the characteristic time- and length-scales of the macroscopic solutes are orders of magnitude larger than those of the microscopic solvent particles, both the number of simulated particles and the simulation time would need to become prohibitively large. So-called mesoscopic simulation techniques, such as Multiparticle Collision Dynamics (abbreviated MPC), aim to achieve a compromise by reducing the number of degrees of freedom while capturing the relevant physical properties. In MPC's original formulation [3, 4], the solvent is modeled by point particles, each representing a volume of the fluid that is large compared to the extent of a single fluid molecule, but small compared to the mesoscopic objects (solutes) in the system. The latter are modeled similarly, except that multiple MPC particles can be linked by arbitrary interaction potentials to form, e.g., the surface membrane of a biological cell. The two alternating simulation steps of MPC ("streaming" and "collision") are designed to yield hydrodynamic behavior by conserving mass and momentum, while retaining a high degree of computational parallelism, so that large systems can be simulated efficiently, especially on graphics processing units (GPUs). While this approach has been successfully employed in a variety of problems in fluid dynamics, one shortcoming of MPC, as introduced initially, is its inability to simulate non-Newtonian (viscoelastic) solvents, which occur frequently in both industrial and biological applications. To overcome this limitation, we consider a generalization of MPC by coupling N+1 MPC solvent particles via N harmonic springs to form a linear polymer [5-7]. We show that this simulated fluid exhibits non-Newtonian behavior; in particular, we study the autocorrelation of the Fourier-transformed fluid velocity field, which is found to decay exponentially, but with superimposed oscillations. We also derive a corresponding theoretical expression, and demonstrate excellent agreement on both qualitative and quantitative levels. Furthermore, we investigate the fluid behavior in the long-time limit, and find that it asymptotically tends to that of a purely viscous fluid [7]. [1] Lauga, E., Powers, T. R., Rep. Prog. Phys. 72, 096601 (2009) [2] Elgeti, J., Winkler, R. G., Gompper, G., Rep. Prog. Phys. 78, 056601 (2015) [3] Malevanets, A., Kapral, R., J. Chem. Phys. 110, 8605 (1999) [4] Gompper, G., Ihle, T. Kroll, D. M., Winkler, R. G., Adv. Polym. Sci. 221, 1 (2009) [5] Tao, Y.-G., Götze, I. O., Gompper, G., J. Chem. Phys 128, 144902 (2008) [6] Kowalik, B., Winkler, R. G., J. Chem. Phys. 138, 104903 (2013) [7] Toneian, D., Diploma Thesis, TU Wien (2015)

#38 Local spin transformation in quantum and mesoscopic systems

Trimper, Steffen (Martin-Luther-University)

Motivated by the recent development in more refined magnetic orders and the coupling between electric and magnetic properties a new representation of spin variables is proposed in which the quantization axis is not fixed but it is locally changing. Due to the local transformation the system has lost spin rotation invariance and inversion symmetry and the related transformed models give rise to complicated spin orders. The related excitations become massive and the transverse fluctuations are not anymore diverging in d=2.In detail we discuss the quantum models as the Heisenberg model and the Dzyaloshinskii-Moriya (DZM) interaction, and moreover the isotropic non-linear sigma model with additional DZM in a mesoscopic realization. The resulting helical structures are analyzed both in equilibrium and dynamically based on the Landau-Lifshitz-Gilbert equation.The consequences for more complicated spin structures as skyrmions and the appearance of the magnetoelectric coupling are discussed.

#39 High Precision MC/RG Study of Elastic Fluctuations in Solid Membranes

Tröster, Andreas (Institut für Materialchemie TU Wien)

The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We provide additional insight into this problem [1] that results from combining Wilson’s momentum shell renormalization-group method with the power of modern computer simulations based on a recent optimization [2] of our Fourier Monte Carlo algorithm [3, 4]. We discuss the ideas and difficulties underlying this combined scheme and present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain for the the first time a numerical estimate for the value of the Wegner exponent ω that determines the leading correction to scaling. This in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data [2], and also sheds some light on the possible reasons for the dispersion of previously published numerical estimates for η. In particular, for the solid case, our numerical estimate for η is markedly smaller than that derived from other recent simulations [5], and we find clear evidence against “intrinsic ripples”, whose existence has recently been claimed in the graphene-related literature [6]. [1] A. Tröster, Phys. Rev. E 91 , 022132 (2015). [2] A. Tröster, Phys. Rev. B 87 , 104112 (2013). [3] A. Tröster, Phys. Rev. B 76 , 012402 (2007). [4] A. Tröster, Phys. Rev. Lett. 100 , 140602 (2008). [5] J. H. Los, M. I. Katsnelson, O. V. Yazyev, K. V. Zakharchenko, and A. Fasolino, Phys. Rev. B 80 , 121405 (2009). [6] A. Fasolino, J. Los, and M. I. Katsnelson, Nature Materials 6 , 858 (2007).

#40 Controlling the motion of knots on tensioned polymers and fibers

Tubiana, Luca (Universität Wien)

Topological entanglement is an ubiquitous feature of many biological as well as artificial polymers and fibers. While the equilibrium properties of entangled chains have been the subject of several studies, the characterization of knot dynamics remains relatively unexplored. In this talk, we report computational results on two different meanings of affecting the motion of a knot on two different systems. Specifically, we first show that external DC and AC electric fields acting longitudinally on a knotted dsDNA polymer can drive the knot along the chain. The driven knot dynamics appears to be characterized by topology-dependent length and timescales, suggesting that salient aspects of the intrinsic dynamics of knots in DNA chains could be probed experimentally by means of external, time-dependent electric fields. Secondly, we show that, on a tensioned microscopic flexible fiber, the onset of transverse waves caused by the mechanical driving of one end of the chain kinetically traps the knot in spatially localized states where the amplitude of the oscillations is maximal, while the knot normal diffusive dynamics is replaced by a discrete jump dynamics.

#41 Nonlinear electro-osmosis of dilute polymer solutions with low salinity

Uematsu, Yuki (Kyoto University)

Nonlinear behavior of electro-osmosis in dilute non-adsorbing polymer solutions with low salinity is investigated with Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the polymers and a no-slip wall is considered with Rotne-Prager approximation of Blake tensor. In a plug flow under a sufficiently strong applied electric field, the polymer migrates toward the bulk, forming a depletion layer thicker than the equilibrium one. Consequently, the electro-osmotic mobility increases nonlinearly with the electric field and gets saturated. This nonlinear mobility qualitatively does not depend on the details of rheological properties of the polymer solution. Analytical calculation of the kinetic theory for the same system reproduces quantitatively well the results of the Brownian dynamics simulation.

#42 Ring polymer chains with EVI in a slit of two repulsive walls: Massive field theory approach

Usatenko, Zoryana (Institute of Physics, Cracow University of Technology)

The massive field theory approach in a fixed space dimensions d<4 is applied for investigation of ring polymer chains in a good solvent with excluded volume interactions (EVI) confined to a slit of two parallel repulsive walls. The well known correspondence between the field theoretical φ 4 O(n)-vector model in the limit n-> 0 and the behavior of long-flexible polymer chains in a good solvent is used for calculation up to one-loop order the partition function of ring polymer chain with EVI, the depletion interaction potential, the depletion force and the force which exerts real ring polymer chain with EVI on the surfaces. The calculation of the correspondent partition function of ring polymer chain with EVI was performed via summation over all possible knot structures. It was found that the confining of a ring polymer chain with EVI to a slit geometry of two repulsive walls leads to the loss of configurational entropy and to arising of the repulsive force which exerts ring polymer chain on the surfaces. The analysis of the obtained results indicates that the value of the repulsive force which exerts ring polymer chain with EVI on the surfaces is bigger than the force exerted by phantom ideal ring polymer chain. Increasing of the slit size leads to decreasing of the value of the exerted force on the surfaces at the same value of the end-to-end distance. The obtained analytical results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations [1]. [1] R. Matthews, A.A. Louis, J.M. Yeomans, Confinement of knotted polymers in a slit, Molecular Physics, V.109, 2011, p.1289-1295.

#43 Permutation entropy as measure of complexity of cardiac rhythms

Wejer, Dorota (University of Gdansk)

Makowiec, Danuta (University of Gdansk, Gdansk, Poland / Polen)

Introduction: The autonomic nervous system is assumed to drive the cardiovascular system: the rhythm of heart contractions and the tension of vessels, in a way which ensures appropriate blood supply in different organs of a human body. Therefore, syncope which occurs after a change of the body position can be considered as a result of improper management of blood distribution. The head-up tilt (HUT) test is simple tool for provoking rapid changes in the dynamics of cardiovascular system in controlled conditions. Time intervals between subsequent heart contractions (RR-intervals) and systolic blood pressure (SBP) obtained during the HUT test are simple noninvasive measurements accessible from the test. Permutation entropy (PE) is a complexity measure which allows for examining dynamical features of a signal. It relies on occurrences of so-called ordinal patterns of fixed length. Considering extra patterns arising from different symbolization of signal values, we get a quantitative insight into the underlying dynamics. Aims: The main point of our research is finding differences in the complexity of cardiac rhythms caused by changing the position of body. We are also interested in describing the distinctions of signals complexity in healthy people and patients suffering from syncope. Methods: Changes to the standard algorithm were introduced to consider extra patterns corresponding to repeated values. The variety of signal symbolizations were applied to include new patterns into analysis. The time series were obtained by the head-up tilt test performed on healthy volunteers under the controlled breathing (13 males, 14 females; age: 20-39 yr, median age: 23 yr) and patients suffering from vasovagal faints (17 males, 37 females; age: 18-44 yr, median age: 23 yr). Results: We obtained that PE (RR) and PE(SBP) grow monotonically to the maximum archived at 8ms for RR-intervals and 1mmHg for SBP-levels, when the resolution of time series symbolization decreases. In the supine position, there were no differences in values of PE(RR) and PE(SBP) between healthy people and vasovagal patients. In case of the upright position, there were statistically significant differences for PE(RR) in series with resolution greater than 8ms in case of RR-intervals, and similarly for PE(SBP), when resolution was greater than 1mmHg. It resulted from the lack of large changes in the values of the RR and SBP in patients suffering from vasovagal faints in contrast to the healthy. Conclusions: Proposed by us approach to the permutation entropy allowed to detect the statistically significant difference in cardiovascular dynamics of healthy people and patients with vasovagal syncope. Acknowledgments: The authors thank to Szymon Budrejko and Beata Graff for providing data, Zbigniew R. Struzik for inspiring discussions. This work was supported by the National Science Centre, Poland, UMO: 2012/06/M/ST2/00480.

#44 Shifts of causality in cardiovascular system by transfer entropy method

Wejer, Dorota (University of Gdansk)

Makowiec, Danuta (University of Gdansk, Gdansk, Poland / Polen)

Introduction: The coupling between cardiac and vascular systems is realized by the mechanical interactions and the set of complex neural reflexes which are responsible for maintaining proper neutrinos distribution in the body. The baroreflex is a key mechanism in the set of neural reflexes because it provides a relatively fast negative feedback: decreasing the heart rate when the blood pressure is increased, and vice versa. The head-up tilt test is a method to provoke changes in the human cardiovascular system caused by a rapid change in the body position. We believe that heart periods and systolic blood pressure recorded during the head-up tilt test provide a noninvasive way to get insights into couplings between cardiac and vascular systems. Transfer entropy provides a model-free frame for studying causal interactions between coupled systems. Especially, it allows to measure changes in the information transfer between blood pressure and heart rate, so to test the model of baroreflex feedback loop, and to evaluate the activity of the baroreflex. Aims: T he estimation of information exchange between cardiac and vascular systems in response to the change of body position is our main purpose. We also hope to identify differences between healthy people and patients suffering from vasovagal faints. Methods: Transfer entropy with non-uniform embedding is used in estimations of the coupling between cardiac and vascular systems. The method is applied to signals of two types: heart periods, systolic blood pressure, increments of heart periods and changes in systolic blood pressure. The time series were obtained by the head-up tilt test performed on healthy volunteers under the controlled breathing (13 males, 14 females; age: 20-39 yr, median age: 23 yr) and patients suffering from vasovagal faints (17 males, 37 females; age: 18-44 yr, median age: 23 yr). Results: Transfer entropy estimates confirmed our believes about functioning of the baroreflex loop. Especially, in the first part of tilting, the expected high baroreflex activity and predominance influences of vascular system on cardiac system was found. Moreover, we observed the high value of transfer entropy from blood pressure changes to the heart periods increments in case of healthy people, but in case of vasovagal patients, the less value of transfer entropy was obtained. Also, we observed the oscillations in this transfer entropy in healthy people only. Conclusions: It has occurred that transfer entropy reveals the switch in the mechanisms driving the cardiovascular homeostasis evoked by the head-up tilt test in a way which very accurately restores the model of the baroreflex loop. Furthermore, differences in couplings between cardiac and vascular systems between healthy people and patients with vasovagal syncope have indicated at the reasons of syncope. The sympathetic activation, which was revealed by transfer entropy, occurred in different levels: high in healthy people and low in vasovagal patients. Acknowledgments: The authors thank to Szymon Budrejko and Beata Graff for providing data, Zbigniew R. Struzik and Luca Faes for inspiring discussions. Special thanks to Luca Faes for sharing codes. This work was supported by the National Science Centre, Poland, UMO: 2012/06/M/ST2/00480.

#45 Gauge invariant Hamiltonian for a system of two-level emitters interacting with electromagnetic field

Yarlik, Volodymyr (Dnipropetrovsk National University)

Lyagushyn, Sergij; Sokolovsky, Alexander (Dnipropetrovsk National University, Dnipropetrovsk, Ukraine)

In a number of papers [1] the Hamiltonian of quantum emitter systems interacting with electromagnetic field construction is based on using the generalized momentum operator for an electron of the working transition in an emitter atom. After neglecting the terms proportional to A2 this gives so called p-A-Hamiltonian, but the problem of such operation inaccuracy seems to be open. The Hamiltonian can be transformed to the gauge invariant form with field strength E in the dipole approximation. In literature closely connected with experiments [2] such form is regarded as an obvious analog of the classical Hamiltonian. But the rigorous analysis [3] shows that the right form of the Hamilton operator can be obtained from the gauge invariance requirements with a proper unitary gauge transformation. Thus, for obtaining physically valid results this transformation of the system statistical operator and operators of considered observables should be performed in every case. We put in life the programme of constructing the Hamilton function for one-electron atom system on the basis of the fundamental Lagrangian formulation of dynamics for a system of charges and electromagnetic field with taking into account the smallness of electron mass in comparison with that of core [4]. It is taken into account additionally that electrons on the whole move in the small vicinity of a core. Such atom consideration reduced to the two-body problem. The Hamiltonian form for atom system interacting with electromagnetic field is made more accurate with considering the contribution of vector potential derivatives with respect to coordinates. It is ascertained that in the framework of the mentioned approximations applying the dipole approximation is fully equivalent to the solution of the problem in the Coulomb gauge. It is done by dint of a unitary transformation that is actually a gauge one. Using the dipole approximation proves to be simpler because solving the problems in the Coulomb gauge requires an additional transformation of physical value operators. So we eliminate the necessity of using the approximation where the vector potential square is neglected. The results are concretized for two-level atoms. The right operator structure for the interaction Hamiltonian requires using matrix elements of the dipole moment operator under the obvious supposition about the real-valued interaction constants [5, 6]. We show that standard Hamiltonian of the system [3,5] are obtained after a canonical transformation of creation and annihilation photon operators. The consideration is performed in the framework of the many-body theory on the basis of the quantum Liouville equation for the statistical operator of the system.
References 1. N.N. Bogolyubov (Jr.), A.S. Shumovsky. Superradiance. - Dubna: JINR, 1987. - 88 p. (in Russian). 2. A.V. Andreyev, V.I. Yemelyanov, Yu.A. Ilyinskiy. Cooperative Phenomena in Optics. - Moscow: Nauka, 1988. - 288 p. (in Russian). 3. M.O. Scully, M.S. Zubairy. Quantum Optics. - Cambridge University Press, 1997. - 510 p. 4. S.F. Lyagushyn, A.I. Sokolovsky. To the problem of the Hamiltonian form for a system of two-level atoms interacting with electromagnetic field // Visnyk Dnipropetrovs'koho Universytetu. Seriya: Fizyka, Radioelektronika, Issue 22. - 2015, Vol. 23, No. 1.- P. 44-49. 5. L. Allen, J.H. Eberly. Optical Resonance and Two-Level Atoms. - John Wiley & Sons, 1975. - 224 p. 6. S.F. Lyagushyn, A.I. Sokolovsky. Kinetics of system of emitters and nonequilibrium electromagnetic field // Physics of Particles and Nuclei. - 2010. - Vol. 41, No. 7. - P. 1035 - 1038.

#46 Non-Equilibrium Statistical Mechanics of Magnetic Fluids

Zubarev, Andrey (Ural Federal University)

Magnetic Fiquids (MF) are stable suspensions of ferromagnetic single-domain nanoparticles in a non magnetic carrier liquid. They attract considerable interest of investigators and engineers due to rich set of their unique physical properties, which find active applications in many modern industrial and medical technologies. One of the attracting features of ferrofluids is their ability to vary, in the region about two orders of magnitudes, their dynamic properties under the action of applied magnetic field. It allows us to control dynamic behavior of MFs by using the moderate and even weak magnetic field, which can be easily created in laboratory or industrial conditions. The physical cause of thsee phenomena in MFs is in appearance, under the field action, of various heterogeneous structures, consisting of the magnetic particles. There are known linear chains, bulk drop-like aggregates, branched and some other structures. Non equilibrium behavior and phenomena in MFs present significant interest both from general scientific and practical points of view. From the theoretical viewpoint the main problem here is in the long-range and non-central character of magnetic and hydrodynamic interaction between the particles. Moreover, the hydrodynamic interaction is non-concervative and non-potential. We suggest a microscopical statistical model of evolution of the internal heterogeneous chains as well as effect of these chains on dynamic magnetic susceptibility and non-linear viscoelastic effects in the systems under study. In the framework of this model the chains are considered as specific heterogeneous fluctuations of the MF density. By using the statistical and thermodynamical approach we found stationary distribution gn of the chains over number n of particles in them in the equilibrium state. Then we have considered evolution of the chains ensemble after change of the applied magnetic field or/and the fluid shear rate. The analysis is based on the specially formulated chain of the Smoluchowski kinetic equations Solution of this system allows us to determine the time dependent distribution function gn(t) . Next, we have considered the MF as a suspension of the non spherical chain-like aggregates and applied results of statistical mechanics of suspensions of non spherical particles. It allowed us first, to derive macroscopical magnetodynamic and rheological equations of the systems and, second, to estimate their non-equilibrium characteristics (dynamic magnetic susceptibility, viscoelastic modulus, etc). For the first time this model allowed to get results which are in agreement with the known experiments and computer simulations. Analysis shows that the chains provoke very slow magnetic and rheological dynamics of the system and induce large, up to 1-2 orders of magnitudes, increase of viscosity of the system.

#47 The thermodynamic properties of n-pentane in the critical region

Abbaci, Azzedine (Univrsité badji Mokhtar)

RIZI, Aicha; Ladjama, Sabrina (Univrsité badji Mokhtar, Annaba, Algeria / Algerien)

An equation of state that predicts the thermodynamic behavior of normal pentane is presented. This equation takes into account the crossover from singular thermodynamic behavior asymptotically close to the critical point to regular thermodynamic behavior far away from the critical point, is formulated. The formulated equation based on the crossover transformation to a truncated classical Landau expansion. The equation is capable of representing the thermodynamic properties of n-pentane wide range of temperatures densities around the critical point. Comparisons of the P- r -T data, and theisochoric specific heat data measured by different authors are presented are presented.

#48 Design and Folding of proteins in explicit water

Bianco, Valentino (University of Vienna)

Coluzza, Ivan (University of Vienna, Vienna, Austria / Österreich); Franzese, Giancarlo (University of Barcelona, Barcelona, Spain / Spanien)

Protein/bio-polymer design concerns the “optimization” of a sequence of residues, given an alphabet of monomers, that folds in a target structure. We present a new approach, based on a combination of water-protein coarse-grain model able, for a wide range of temperatures and pressures, to deeply explore the configurational space of a water-protein solutions. Our model, accounting for the influence of protein interfaces on the thermodynamic properties of the hydration shell, is able to rationalize the stability of a protein against heating, cooling, and pressurization. We show how the design of specific target structures is affected by the solvent properties. In turn, we show how the folding properties for different sequences, designed at different thermodynamic conditions, change.

#49 Magnetically functionalized polymers

Blaak, Ronald (Universität Wien)

Likos, Christos N. (Computergestützte Physik, Wien, Austria / Österreich)

We explore the structural properties of magnetically functionalized star-polymers by means of computer simulations. The functional units are formed by superparamagnetic nanoparticles and are located only at the end of polymeric arms that are joined at the central core of the star-polymer. The natural steric interactions between the polymeric chains, which under good solvent conditions and low star density result in the characteristic star-shaped conformation, have to compete with the magnetic interactions stemming from the functionalized end-groups. The strength of this directionally dependent interaction is controlled by means of an external magnetic field, that for the case of superparamagnetic nanoparticles leads to parallel oriented magnetic dipoles. On augmenting the strength of the external field, their interaction result in the formation of one or more dipolar chains and a corresponding change in overall conformation of the macromolecules that mimics a soft patchy-like particle.

#50 Transferable Coarse-grained potential model for quantitative protein folding and design

Coluzza, Ivan (Universität Wien)

Protein folding and design are major biophysical problems [1-2], the solution of which would lead to important applications especially in medicine. Here we provide evidence of how a novel parametrization of the Caterpillar [3-6] model may be used for both quantitative protein design and folding. With computer simulations it is shown that, for a large set of real protein structures, the model produces designed sequences with similar physical properties to the corresponding natural occurring sequences. The designed sequences require further experimental testing. For an independent set of proteins, previously used as benchmark, the correct folded structure of both the designed and the natural sequences is also demonstrated. The equilibrium folding properties are characterized by free energy calculations. The resulting free energy pro- files not only are consistent among natural and designed proteins, but also show a remarkable precision when the folded structures are compared to the experimentally determined ones. Ultimately, the updated Caterpillar model is unique in the combination of its fundamental three features: its simplicity, its ability to produce natural foldable designed sequences, and its structure prediction precision. It is also remarkable that low frustration sequences can be obtained with such a simple and universal design procedure, and that the folding of natural proteins shows funnelled free energy landscapes without the need of any potentials based on the native structure. References [1] C. Clementi, Curr. Opin. Struct. Biol. 18, 10–5 (2008). [2] V. Tozzini, Curr. Opin. Struct. Biol. 15, 144–50 (2005). [3] I. Coluzza, Mol. Phys. 1–8 (2015). [4] I. Coluzza, PLoS One 9, e112852 (2014). [5] I. Coluzza, PLoS One 6, e20853 (2011). [6] I. Coluzza, P. van Oostrum, B. Capone, E. Reimhult, and C. Dellago, Phys. Rev. Lett. 110, 075501 (2013).

#51 Cavitation in water under tension: a molecular perspective

Menzl, Georg (University of Vienna)

Geiger, Philipp; Dellago, Christoph (University of Vienna, Austria/Österreich)

Water can be prepared in a metastable state under tension due to the free energetic cost of forming the vapor-liquid interface associated with bubble nucleation. Remarkably, strongly negative pressures in excess of -120 MPa can be reached experimentally before the liquid breaks under tension and cavitation occurs [1]. Recent interest in the topic is magnified by the discrepancy between estimates for the cavitation pressure obtained via different experimental methods [2], but due to the rapid nature of cavitation and the small size of the critical bubble at experimentally feasible conditions, the microscopic mechanism behind cavitation in water remains unclear.

#52 Quantifying the effect of particle curvature on the microstructure of cube-like magnetic colloids.

Donaldson, Joe (Universität Wien)

Kantorovich, Sofia (Computational Physics, Vienna, Austria / Österreich)

Materials with magnetic properties that can be governed using control parameters such as temperature, and/or external magnetic fields, are highly desirable functional systems. Colloidal suspensions of magnetic nanoparticles exhibit this behaviour in a highly responsive manner. Cube-like magnetic particles are one such example that is growing in popularity in the experimental community, making them of significant interest to study from a numerical and analytical point of view. We present here a combination of theoretical calculations and molecular dynamics simulations studying the behaviour of permanently magnetised dipolar cubes. The phenomena observed are a direct result of the fundamental relationship between the anisotropy of the magnetic interaction and the particles’ anisometric geometry.

#53 Glassy dynamics in plastic colloidal systems

Karner, Carina (University of Vienna)

Dellago, Christoph (University of Vienna, Vienna, Austria / Österreich)

Aspheric molecular or colloidal systems, with only a slight degree of anisotropy, often assemble into plastic crystals [1]. While plastic crystals exhibit the full positional order of a crystal, they can freely rotate around their center of mass, rendering them orientationally disordered. It is exactly this high orientational diffusivity which grants those materials high placticity, making them good candidates for solid state electrolytes in fuel cells, batteries and solar cells [2]. In the colloidal realm, plastic crystals are often realized by micron sized PMMA or polystyrene particles of polyhedral shape, such as truncated octahedrons, hexbipyramids or Buckminster fullerene shapes. In this work, we present computational evidence for glassy orientational dynamics in rotator phases of hard truncated octahedrons and hexbipyramids. Many hard colloidal plastic crystals transition into fully orientationally and translationally ordered crystals at higher packing fractions. At pressures where the rotator phase is metastable with respect to the fully ordered crystal, we find that the particles stop to rotate freely. Although the directors of neighbouring particles tend to align, the system does not develop parallel long range order. Instead, the particles assume one of a finite number of global orientations. Reorientations remain possible, but occur in big jumps, leading into one of the global orientations. We argue that this behavour is comparable to freezing in the six color Potts model where, after a very long time, the system becomes parallely ordered. Glassy orientational dynamics upon freezing may not be unique to truncated hexbipyramids and octahedrons, but might be a general feature of polyhedral rotator crystals. Hence, we hope that this work will inspire more research on general features of rotator-crystal transitions. [1] P. Damasceno, M. Engel, S. Glotzer, Science 2012 vol: 337 (6093) pp: 453-457 [2] L. Jin et al., Journal of the American Chemical Society 2012 vol: 134 (23) pp: 9688-97

#54 Electro-osmotic flow in bicomponent fluid

Bazarenko, Andrei (Universität Wien)

Sega, Marcello (Computergestützte Physik, Vienna, Austria / Österreich)

The electro-osmotic flow (EOF) is a widely used technique that uses the action of external electric fields on solvated ions to move fluids around in microfluidics devices. For homogeneous fluids, the characteristics of the flow can be well approximated by simple analytical models, but in multicomponent systems such as oil-in-water droplets one has to rely to numerical simulations. The purpose of this study is to investigate physical properties of the EOF in a bicomponent fluid by solving the coupled equations of motions of explicit ions in interaction with a continuous model of the flow. To do so we couple the hydrodynamics equations as solved by a Shan-Chen Lattice-Boltzmann method[1] to the molecular dynamics of the ions[2]. The presence of explicit ions allows us to go beyond the simple Poisson-Boltzmann approximations, and investigate a variety of EOF regimes.
[1]X. Shan, and H. Chen, Phys. Rev. E, 47, 1815-1819 (1993) [2]M. Sega, M. Sbragaglia, S. S. Kantorovich and A. Ivanov, Soft Matter, 9, 10092-10107 (2013)