28th Marian Smoluchowski Symposium on Statistical Physics ...28th Marian Smoluchowski Symposium on Statistical Physics KRAKÓW, POLAND, SEPTEMBER 14–17, 2015 Monday, September 14

28th Marian Smoluchowski Symposium onStatistical Physics

KRAKÓW, POLAND, SEPTEMBER 14–17, 2015

organized by:

Jagiellonian University

Marian Smoluchowski Mark Kac ComplexInstitute of Physics System Research Center

Symposium Organizing Committee: M. Smoluchowski Institute of Physics, Jagiellonian University, St. Łojasiewicza 11, 30–348 Kraków, Polande–mail [email protected] WWW http://www.smoluchowski.if.uj.edu.pl/

28th Marian Smoluchowski Symposium on Statistical PhysicsKRAKÓW, POLAND, SEPTEMBER 14–17, 2015

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International Scientific Committee: Local Organizing Committee:Paweł F. Góra (Kraków, Poland) Michał CieslaLech Longa (Kraków, Poland) Bartłomiej DybiecRalf Metzler (Potsdam, Germany) Ewa Gudowska-NowakM. Howard Lee (Athens GA, USA) Paweł F. GóraMiguel J. Rubi (Barcelona, Spain) Lech LongaIgor M. Sokolov (Berlin, Germany) Katarzyna OlesLutz Schimansky-Geier (Berlin, Germany) Grzegorz Pajak

Łukasz KusmierzBartosz Lisowski

Maciej MajkaMichał Swiatek

Wojciech Tomczyk

Conference Chairs:Ewa Gudowska-Nowak

Bartłomiej Dybiec

Conference Secretary:Ewa Witkowska

Symposium Organizing Committee: M. Smoluchowski Institute of Physics, Jagiellonian University, St. Łojasiewicza 11, 30–348 Kraków, Polande–mail [email protected] WWW http://www.smoluchowski.if.uj.edu.pl/


Monday, September 14Collegium Novum, Gołebia 24

Chairperson: Andrzej Fulinski900 - 910 Ewa Gudowska-Nowak Opening address

Bartłomiej Dybiec910 - 940 Gleb Oshanin Active microrheology in dense crowded sys-

tems (p. 5)940 - 1010 Zbigniew J. Grzywna On nonuniqueness of the description of diffu-

sion with adsorption (p. 6)1010 - 1040 M. Howard Lee Why must ergodic trajectories start almost

everywhere, but not everywhere, from ergo-dic surfaces? (p. 6)

1040 - 1100 Aleksander Weron ARFIMA modeling for single particle trackingdata (p. 18)

1100 - 1120 Alexander Blumen Dynamics in complex systems: geometric andtopological aspects (p. 18)

1120 - 1200 Coffee break

Chairperson: Gleb Oshanin1200 - 1230 Igor M. Sokolov Nanophase separation in a slit pore: From

picture to numbers and back (p. 7)1230 - 1300 Adam Gadomski Formation of transient pores in

(bio)membranes and other soft-mattersystems, an important task addressed by(nano)thermodynamics (p. 8)

1300 - 1330 Tadeusz Kosztołowicz Random walk model of subdiffusion in amembrane system (p. 19)

1330 - 1500 Lunch

Chairperson: Zbigniew J. Grzywna1500 - 1530 Dick Bedeaux Small and large system thermodynamics

(p. 9)1530 - 1600 Signe Kjelstrup Transport of heat and mass in the presence

of a chemical reaction (p. 10)1600 - 1630 J. Miguel Rubi Heat engine driven by photon tunneling in

many-body systems (p. 10)1630 - 1700 Robert Alicki Solar cell as a heat engine. Where is the pi-

ston? (p. 11)


Chairperson: J. Miguel Rubi1730 - 1800 Bogdan Nowakowski Reaction-diffusion model for embryo morpho-

genesis (p. 11)1800 - 1820 Annie Lemarchand Evaluation of reaction fluxes in stationary and

oscillating far-from-equilibrium biological sys-tems (p. 19)

Evening Get-together

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Tuesday, September 15Collegium Novum, Gołebia 24

Chairperson: Signe Kjelstrup900 - 930 Ralf Metzler Dynamics in structured and crowded environ-

ments (p. 7)930 - 1000 Jin Wang Landscape and flux of classical and quantum

non-equilibrium systems (p. 12)1000 - 1030 Horacio Wio KPZ dynamics: Novel aspects from a variatio-

nal perspective (p. 13)1030 - 1050 John Lapeyre Weak ergodicity breaking and Brownian mo-

tion (p. 19)1050 - 1110 Katarzyna Górska Photoluminescence decay, stretched expo-

nentials and Lévy stable distributions (p. 20)1110 - 1130 Roberto Deza Stochastic dissipative solitons (p. 20)


1200 - 1305 Lutz Schimansky-Geier Active Brownian particles: From individual tocollective behaviour (p. 13)

1305 - 1500 Lunch

Chairperson: Ralf Metzler1500 - 1530 Katja Lindenberg Arrays of stochastic oscillators: Nonlocal co-

upling, clustering, and wave formation (p. 13)1530 - 1550 Andrzej Krawiecki Synchronization of chaotic oscillators on hy-

pergraphs (p. 20)1550 - 1610 Franco Ferrari Energy minimization and Monte Carlo simula-

tions of polymer knots (p. 21)1610 - 1630 Maciej Majka Non-Gaussian polymers described by alpha-

stable chain statistics: Model, effective inte-ractions in binary mixtures, and application toon-surface separation (p. 21)


Chairperson: Igor M. Sokolov1700 - 1730 Tomasz Srokowski Stochastic dynamics for systems with Lévy fli-

ghts and nonhomogeneously distributed traps(p. 14)

1730 - 1800 Karol A. Penson Fractional operators, Lévy-stable distributionsand Bessel-type polynomials (p. 14)

1800 - 1820 Piotr Weber Gaussian diffusion with drift interrupted byLévy walk (p. 21)

1820 - 1840 Łukasz Kusmierz Lévy flights with stochastic resetting (p. 22)

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Wednesday, September 16Collegium Novum, Gołebia 24

Chairperson: Andrzej Krawiecki900 - 930 Krzysztof Kułakowski Heider balance, asymmetric ties, and gender

segregation (p. 15)930 - 1000 Paolo Grigolini Unification of behavioral sciences: Chal-

lenging non-equilibrium statistical physics(p. 15)

1000 - 1030 Dante Chialvo Brain dynamics: What is critical about it?(p. 16)

1030 - 1050 Jeremi Ochab How we move is universal: Scaling in humanmotor activity (p. 22)

1050 - 1110 Janusz A. Hołyst Diffusion on hierarchical systems of weakly-coupled networks (p. 23)


1200 - 1305 Peter Hänggi Anomalous heat diffusion (p. 16)

1305 - 1500 Lunch

Chairperson: Dante Chialvo1500 - 1530 Jacek Miekisz Spatial aspects and time delays in gene regu-

lation (p. 17)1530 - 1600 Anna Ochab-Marcinek Modeling stochastic gene expression: A few

solutions by geometric construction (p. 17)


Chairperson: Janusz A. Hołyst1630 - 1700 Jerzy Łuczka Efficiency of the asymmetric SQUID driven by

periodic current (p. 5)1700 - 1720 Łukasz Machura Current-flux characteristics in mesoscopic

nonsuperconducting rings (p. 24)1720 - 1740 Jakub Spiechowicz Diffusion anomalies in AC driven Brownian

ratchets (p. 23)

2000 Banquet

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Thursday, September 17Department of Physics, Astronomy and Applied Computer Sciences, Łojasiewicza 11

Chairperson: Paweł F. Góra900 - 1100 Pre-poster session

1100 - 1130 Coffee break1130 - 1330 Poster session1330 - 1500 Lunch and closing address

City Center (Monday – Wednesday)

lectures Collegium Novum Gołebia 24lunches & get together U Pecherza (Collegium Maius) Jagiellonska 15banquet Wentzl Rynek Główny 19bus departure point Parking Karmelicka 26

Dept. of Physics, Astronomy and Appl. Comp. Sci., Łojasiewicza 11 (Thursday)

poster session Department of Physics Łojasiewicza 11tram stops trams no: 18, 52 “Norymberska”, “Ruczaj”

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Invited Talks

Gleb Oshanin, Theoretical Condensed Matter, University Pierre & Marie Curie, Paris, FranceActive microrheology in dense crowded systemsAbstract: In this talk I will survey our recent analytical and numerical results obtained for a mini-mal model, which mimics standard experimental settings of active microrheology and consists ofa tracer particle subject to a constant external force in a crowded medium composed of identicalhard-core particles performing unbiased random walks constrained by a mutual exclusion. I willshow that the tracer particle motion is essentially dependent on the geometry of the system: Incase of single files, in which the initial order of particles is preserved at all times since the partic-les can not bypass each other, all cumulants of the tracer particle displacement show the samesublinear dependence on time. In quasi-one-dimensional systems, such as, e.g., two-dimensionalstripes or three-dimensional elongated capillaries, the tracer particle velocity ultimately attains aconstant value, but the variance of the tracer particle displacement exhibits a surprising super-diffusive growth at intermediate times, which then crosses over to a giant diffusion at later times.We proceed to show that in the latter case dynamics of the tracer particle is subordinated to somehidden fractional Brownian motion process. In two-dimensional systems and in slit pores, the va-riance shows a weakly super-diffusive growth which crosses over to ordinary diffusion. We alsoanalyse the dependence of the terminal velocity on the magnitude of the force, and show that insome cases it may be a non-monotonic function of the latter exhibiting the so-called negative dif-ferential mobility. A set of other questions, such as, e.g., convergence of the distribution functionto a Gaussian, emerging interactions between biased particles when several such particles arepresent, and tracer diffusion on crowded comb-like structures will also be discussed.

Jerzy Łuczka, Institute of Physics, University of Silesia, Katowice, Poland and Silesian Center forEducation and Interdisciplinary Research, University of Silesia, Chorzów, PolandEfficiency of the asymmetric SQUID driven by periodic currentAbstract: A SQUID - A Superconducting Quantum Interference Device - is one of the most impor-tant instruments found in the majority of research laboratories worldwide. It has been successfullyused not only for magnetometry but also for testing the fundamentals of quantum mechanics aswell as for investigating the chaotic complexity in classical physics. Yet, a number of open pro-blems of this setup still remain to be resolved. A prominent example may be the efficiency of theSQUID as a thermodynamical machine converting the input energy into its other forms. In con-trast to a Carnot-type engine operating between two heat reservoirs of different temperatures,the SQUID is coupled to only one bath of fixed constant temperature.

An asymmetric SQUID is studied. It is constructed as a loop with three Josephson junctions:two of them are placed in one arm whereas the third is located in the other arm. Additionally,the SQUID is threaded by an external magnetic flux and driven by a time periodic current. Thisdevice operates as a ratchet far from equilibrium and rectifies the thermal fluctuations into thedirected motion. In the 6-dimensional space of the system parameters, we have revealed theset in which the efficiency is globally maximal. We detect an intriguing feature of the thermalnoise enhanced efficiency and show how the efficiency of the device can be tuned by tailoringthe external magnetic field. The approach can also be applied to evaluate the efficiency of othersystems frequently encountered in condensed matter as well as biological physics.

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Invited Talks(continued)

Zbigniew J. Grzywna, Przemysław Borys, Department of Physical Chemistry and Technology ofPolymers, Silesian University of Technology, GliwiceOn nonuniqueness of the description of diffusion with adsorptionAbstract: To analyze any problem in physics we need a formulation, in most of the cases, in aform of differential equation. Having done it we usually ask the following three questions:

(1) Existence (of at least one solution)(2) Uniqueness (i.e. either one or zero solutions)(3) Stability (often called continuous dependence of solution upon the data)

and the other three when we do care of applications

(1) Construction (of the “physical” solution)(2) Regularity (i.e. how “substitable” is the found solution)(3) Approximation (when exact construction is not possible).

Having in mind the above we’ll address our efforts to the process of diffusion with partially immo-bilized adsorption. Two approaches will be used:

(1) nonlinear PDE of second order

∂c

∂t=

∂

∂x

[D0f(c)

∂c

∂x

],

where limc→0 f(c) = 1.(2) subdiffusion equation of the form:

∂c

∂t= Dα

∂1−α

∂t1−α∂2c

∂x2.

We will try to show how much the first is nonlinear i.e. shows the nonlinear properties (localexistence, bifurcation, blow-up, etc), and how much “physical” is the second one.

M. Howard Lee, University of Georgia, Athens, GA, USAWhy must ergodic trajectories start almost everywhere, but not everywhere, from ergodicsurfaces?Abstract: The classical theory of the ergodic hypothesis asserts that to be ergodic, trajectoriesmay not start everywhere from ergodic surfaces. By comparing the ergometric theory of theergodic hypothesis due to the speaker, this remarkable condition is studied by aid of the analyticaltheory of chaos in one dimension.

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Igor M. Sokolov, Institute of Physics, Humboldt University Berlin, Berlin, GermanyNanophase separation in a slit pore: From picture to numbers and backAbstract: We consider an interesting effect of nanoscale separation of alcohol and water in a slitpore between a mica crystal and a graphene sheet, as observed in scanning force microscopy[1,2]. The case is interesting as showing quite a complex interplay between the experiment usingmodern imaging techniques, and the theory. The first questions to be answered are: what is seen,what relevant information is contained in the image, and how this information can be extracted.None of these questions can be answered without having a solid theoretical description of thesituation. We discuss how and to what extent the effective interaction potentials between themolecules can be obtained from the image, and how they can be used in order to predict otherimportant properties of the system, those that cannot be immediately obtained from the expe-riment [3]. Our discussion touches several basic issues of foundations of statistical mechanics,theory of statistical inference, and of inverse problems.

[1] N. Severin, I.M. Sokolov, and J.P. Rabe, Langmuir, 30, 3455-3459 (2014)[2] N. Severin, J. Gienger, V. Scenev, P. Lange, I.M. Sokolov, and J.P. Rabe, Nano Lett. 15, 1171-1176 (1915)[3] J. Gienger, N. Severin, J.P.Rabe and I.M. Sokolov, arXiv:1505.03011

Ralf Metzler, University of Potsdam, Potsdam, Germany and Tampere University of Technology,Tampere, FinlandDynamics in structured and crowded environmentsAbstract: Crowding is an integral part of the cytoplasmic fluid of living biological cells. It severelyaffects molecular reactions as well as passive diffusion of tracer particles. I will address theimpact of crowding in model systems on the looping dynamics of individual polymeric chains [1]and discuss the self diffusion of more complex crowder particles [2]. Moreover I will show thehighly correlated motion of large tracer particles in flexible gel like structures [3].

The last part of the talk will briefly address active, superdiffusive motion in crowded biologicalcells including the motion of molecular motors [4] and cellular flows [5].

[1] J. Shin, A. G. Cherstvy, and R. Metzler, Soft Matter 11, 472 (2015).[2] J. Shin, A. G. Cherstvy, and R. Metzler, E-print arXiv:1507.01176.[3] A. Godec, M. Bauer, and R. Metzler, New J Phys 16, 092002 (2014).[4] I. Goychuk, V. O. Kharchenko, and R. Metzler, Phys Chem Chem Phys 16, 16524 (2014).[5] J. F. Reverey, J.-H. Jeon, H. Bao, M. Leippe, R. Metzler, and C. Selhuber-Unkel, Sci Rep 5, 11690 (2015).

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Adam Gadomski, Dept. of Physics, Institute of Mathematics & Physics, University of Science andTechnology (UTP), Bydgoszcz, PolandFormation of transient pores in (bio)membranes and other soft-matter systems, an impor-tant task addressed by (nano)thermodynamicsAbstract: A viscoelastic, membrane-type system, is naturally designed to form transient pores(or, channels) on-purpose in order to accommodate various surface/line tension changing condi-tion, occurring for example in extracellular environmental conditions [1].

Multilamellar or unilamellar vesicles and/or virial capsids of quasi-spherical shapes would beexamples of such systems, also mimicking either typical or specific (pathological) conditions inwhich such systems have to cope with [2,3].

The transient pores emerging in them are a type of remedium to survive in harsh conditionsor to follow an adaptation to them. The free energy of the system, undergoing typically its decre-ase in the course of the process, is tightly related with dynamics of pores’ openings and closures,accompanied by their subsequent changes in the system’s entropy production [4], also acceptinga restricted equilibrium condition or a certain drive out of it [3].

In this paper, the pore closing, descending, dynamics under specific, merely polyelectrolyteinfluencing circumstances, will be of interest, being well describable in terms of flux-force, andOnsager reciprocal relations concerning scheme [4], invoking fairly a mesoscopic nonequilibriumthermodynamics’ framework, cf. [5], and refs. therein.

The overall pore closing effect in viral capsids will be loosely attributed to auxetic mechanicalcharacteristics, with negative Poisson ratio [3,5]. Some other related, facilitated-lubrication naturalsystem [6], will be invoked for comparative reasons.

Acknowledgement: Cooperation with Piotr Bełdowski (UTP, PL) and Ivan Santamaria-Holek (UNAM, CampusJuriquilla, MX) is acknowledged, and a support by UTP BS 39/2014 is mentioned.

[1] W. Colomb, S.K. Sarkar, Phys. Life Rev. 13, 107 (2015).[2] E. Karatekin et al., Biophys. J. 84, 1734 (2003); R. Ryham et al., Biophys. J. 101, 2929 (2011).[3] P. van der Schoot, R. Bruinsma, PRE 71, 061928 (2005).[4] R. Martinez-Balbuena et al., Eur. Biophys. J. (2015); http://link.springer.com/article/10.1007%2Fs00249-015-

1051-8.[5] A. Gadomski, J. Siódmiak, Phys. Statu Solidi B 242, 538 (2005).[6] A. Gadomski et al., Math. Biosci. 244, 188 (2013).

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Sondre Schnell1, Dick Bedeaux2, Signe Kjelstrup21Dep. of Chem. and Biomolecular Eng., Univ. of California, Berkeley, CA, USA2Dep. of Chem., Norwegian Univ. of Science and Technology, Trondheim, NorwaySmall and large system thermodynamicsAbstract: Schnell et al. [1-3] recently developed the Small System Method to calculate ther-modynamic properties of large systems from the properties of small systems. This speeds upa precise calculation of most thermodynamic properties. The scaling laws for the small systemwere derived from Hill’s method [4].

We show how the method can be used to compute thermodynamic data for the macroscopiclimit from knowledge of fluctuations in the small system. The rapid and precise method offersan alternative to more difficult computations of thermodynamic factors from Kirkwood-Buff in-tegrals. When multiplied with computed Maxwell-Stefan coefficients, the thermodynamic factorgives Fick’s diffusion coefficient, which can be compared with experiments. Excellent agreementwas found between computed predictions and experiments for several binary systems, Liu et al.[5-7].

The success of the procedure has several interesting implications. In the first place, theprocedure helps to define smallness, and precise thermodynamic relations on the nano-meterscale. In the second place, it helps define when local equilibrium, or validity of thermodynamicrelations, can be expected. Given certain conditions, Hill’s method provides the same systematicbasis for large and small systems.

Exact expressions for finite-volume Kirkwood-Buff (KB) integrals were derived for hyperspheres in one, two, and three dimensions by Krüger et al. [8]. From this, accurate values of KB in-tegrals were obtained for infinite systems using molecular dynamics simulations. It is shown thatthey converge much better than the traditional expressions. Using the Kirkwood-Buff integrals,one can calculate the thermodynamic factors and next the activity coefficient of components inmixtures.

[1] SK Schnell, TJH Vlugt, J-M Simon, D Bedeaux, S Kjelstrup; Chemical Physics Letters 504 (2011) 199–201.[2] SK Schnell, X Liu, J-M Simon, A Bardow, D Bedeaux, TJH Vlugt and S Kjelstrup, J. Phys. Chem. B, 115

(2011) 10911.[3] SK Schnell, TJH Vlugt, J-M Simon, D Bedeaux and S Kjelstrup, Molecular Physics 110 (2012) 1069.[4] TL Hill, Thermodynamics of Small Systems. Parts I and II, Dover, New York, 1994[5] X Liu, SK Schnell, J-M Simon, D Bedeaux, S Kjelstrup, A Bardow and TJH Vlugt, J. Phys. Chem. B, 115

(2011) 12921–12929.[6] X Liu, A Martín-Calvo, E McGarrity, SK Schnell, S Calero, J-M Simon, D Bedeaux, S Kjelstrup, A Bardow and

TJH Vlugt, Ind. Eng. Chem. Res. 51 (2012) 10247.[7] X Liu, SK Schnell, J-M Simon, P Krüger, D Bedeaux, S Kjelstrup, A Bardow, TJH Vlugt, Int. J. Thermophys.

34 (2013) 1169-1196.[8] P Kruger, SK Schnell, D Bedeaux, S Kjelstrup, TJH Vlugt and J-M Simon, J. Phys. Chem. Letters 4 (2013)

235-238.

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Ragnhild Skorpa1, Signe Kjelstrup1, Thijs J.H. Vlugt2, Dick Bedeaux11Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway2Process and Energy Laboratory, Delft University of Technology, Delft, The NetherlandsTransport of heat and mass in the presence of a chemical reactionAbstract: In their famous textbook from 1960, Bird, Stewart and Lightfoot [1] state that “TheDufour energy flux q* is quite complex of nature and usually of minor importance”. Contributionsfrom Dufour effects in the equations of transport have therefore mostly been neglected [2,3], inparticular when the chemical reaction has been assumed at equilibrium. We have studied anexample of diffusive energy transport in a chemically reacting mixture, and have shown that thepresence of the reaction modifies the thermal conductivity of the system in a significant manner[2,3]. The aim of the work [4] is to add to the description of heat and mass transfer in a chemicallyreacting system (dissociation of hydrogen) away from chemical equilibrium. As example we takethe hydrogen dissociation reaction. The reaction is modelled in a classical way by moleculardynamics simulations. Thermodynamic properties are calculated using the small system method[4,5] and transport data are obtained from non-equilibrium molecular dynamics simulations [6].The Dufour effect is substantial, and the thermal conductivity and diffusion coefficient change inthe presence of this reaction. The analytical solution to the coupled transport phenomena [6] isfound using classical non-equilibrium thermodynamics.

[1] R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport phenomena, 2nd ed. Wiley, New York (2006).[2] J. N. Butler and R. S. Brokaw, J. Chem. Phys., 26:1636 (1957).[3] R. Taylor and R. Krishna, Multicomponent Mass Transfer, Wiley, New York (1993).[4] R. Skorpa, J-M. Simon, D. Bedeaux and S. Kjelstrup, Phys. Chem. Chem. Phys. 16 (2013) 1227[5] S. K. Schnell, R. Skorpa, D. Bedeaux, S. Kjelstrup, T. J.H. Vlugt, J-M. Simon, J. Chem. Phys. 141 (2014)

144501[6] R. Skorpa, T. J. H. Vlugt, D. Bedeaux and S. Kjelstrup, J. Phys. Chem. C (2015) DOI:

10.1021/acs.jpcc.5b02562

I. Latella, A. Pérez-Madrid, J. Miguel Rubi, S.-A. Biehs, P. Ben-Abdallah,Department of Fundamental Physics, University of Barcelona, Barcelona, SpainHeat engine driven by photon tunneling in many-body systemsAbstract: Near-field heat engines are devices that convert the evanescent thermal field suppor-ted by a primary source into usable mechanical energy. By analyzing the thermodynamic per-formance of three-body near-field heat engines, we demonstrate that the power they supply canbe substantially larger than that of two-body systems, showing their strong potential for energyharvesting. Theoretical limits for energy and entropy fluxes in three-body systems are discus-sed and compared with their corresponding two-body counterparts. Such considerations confirmthat the thermodynamic availability in energy-conversion processes driven by three-body photontunneling can exceed the thermodynamic availability in two-body systems.

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Robert Alicki, Institute of Theoretical Physics and Astrophysics, University of Gdansk, Gdansk,PolandSolar cell as a heat engine. Where is the piston?Abstract: Solar cells are engines converting energy supplied by a photon flux into work. Allknown types of macroscopic engines and turbines are also self-oscillating systems which yielda periodic motion at the expense of a usually non-periodic source of energy. The very definitionof work in the formalism of quantum open systems suggests the hypothesis that the oscillating“piston” is a necessary ingredient of the work extraction process. This aspect of solar cell ope-ration is absent in the existing descriptions and the main goal of this talk is to argue that plasmaoscillations provide the physical implementation of a piston. The obtained formulas explain in asimple way the meaning of “light temperature”, the Carnot bound, and the linear relation betweenthe open circuit voltage and the device temperature.

B. Nowakowski1,3, A. Lemarchand2, P. Dziekan1, L. Signon2, J.S. Hansen41Polish Academy of Sciences, Institute of Physical Chemistry, Warsaw, Poland2Université Pierre et Marie Curie, CNRS, Laboratoire de Physique Théorique de la Matière Con-densée, Paris, France3Warsaw University of Life Sciences, Physics Laboratory, Warsaw, Poland4The Department of Science, Systems and Models, Roskilde University, Roskilde, DenmarkReaction-diffusion model for embryo morphogenesisAbstract: We propose a reaction-diffusion model intended to mimic axial segmentation duringsomitogenesis. The system is based on elementary processes of chemical species, unlike ma-thematical modeling of morphogenesis. A periodic structure, corresponding to axial segmentationobserved in experiments of embryonic development, is formed due to Turing mechanism. As themodel is constructed on microscopic processes, besides the deterministic description we are ableto study as well the genuine stochastic and molecular dynamics of the system. The comparisonof deterministic and stochastic approaches [1] indicates that fluctuations accelerate the formationof the periodic pattern and increase its stability. The perturbations of developmental process in-troduced by local source or sink of morphogen are examined [2]. The simulations of dynamics atthe molecular level by means of DSMC [3] and MD [4] methods prove that the Turing structurescan develop in nanoscale domains.

[1] A. Lemarchand and B. Nowakowski, EPL 94 (2011) 48004.[2] P. Dziekan, L. Signon, B. Nowakowski, and A. Lemarchand, Journal of Chemical Physics 139 (2013) 114107.[3] P. Dziekan, A. Lemarchand, and B. Nowakowski, Journal of Chemical Physics 137 (2012) 074107.[4] P. Dziekan, J.S. Hansen, B. Nowakowski, Journal of Chemical Physics 141 (2014) 124106.

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Jin Wang, Department of Chemistry, Stony Brook, NY, USALandscape and flux of classical and quantum non-equilibrium systemsAbstract: We decompose the driving force for open systems into two components: the underlyingprobability landscape and the curl probability flux. We show both play the key roles in dynamicsand thermodynamics. We illustrate this through an example of cell cycle. A Mexican hat shapedlandscape emerges. While the landscape attracts the system down to the oscillation ring valley,we found that the progression of a cell cycle is determined by two driving forces: curl flux foracceleration and potential barriers for deceleration along the cycle path. This provides a physicaland global quantification of cell cycle and further predicts the key genes and regulations for thecell cycle from the global topography of the landscape and curl flux.

We also established a theoretical framework in terms of the curl flux, population land-scape, and coherence for non-equilibrium quantum systems at steady state, through exploringthe energy and charge transport in molecular processes. The curl quantum flux plays the keyrole in determining transport properties and the system reaches equilibrium when flux vanishes.The novel curl quantum flux reflects the degree of non-equilibriumness and the time-irreversibility.We found an analytical expression for the quantum flux and its relationship to the environmen-tal pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and thequantum tunneling. Furthermore, we investigated another quantum signature, the coherence,quantitatively measured by the non-zero off diagonal element of the density matrix. Populationsof states give the probabilities of individual states and therefore quantify the population land-scape. Both curl flux and coherence depend on steady state population landscape. Besides theenvironment-assistance which can give dramatic enhancement of coherence and quantum fluxwith high voltage at a fixed tunneling strength, the quantum flux is promoted by the coherence inthe regime of small tunneling while reduced by the coherence in the regime of large tunneling,due to the non-monotonic relationship between the coherence and tunneling. This is in contrastto the previously found linear relationship. For the systems coupled to bosonic (photonic andphononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (elec-tronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltagedue to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studiedthe non-equilibrium thermodynamics and established the analytical connections of curl quantumflux to the transport quantities such as energy (charge) transfer efficiency, chemical reaction effi-ciency, energy dissipation, heat and electric currents observed in the experiments. We observeda perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference).Our theoretical predicted behavior of the electric current with respect to the voltage is in goodagreements with the recent experiments on electron transfer in single molecules.

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Horacio S. Wio, University of Cantabria-CSIC, Santander, SpainKPZ dynamics: Novel aspects from a variational perspectiveAbstract: A variational approach has been recently introduced allowing to define a non-equilibrium thermodynamic-like potential (NEP) for the paradigmatic KPZ equation as well asfor other related kinetic equations. For the KPZ case, the knowledge of such a potential togetherwith its numerical evaluation (in 1, 2 and 3 dimensions) allowed us to obtain information aboutthe system’s time dynamical behavior. Such an analysis opens new perspectives over possiblerelations between the NEP asymptotic behavior and critical exponents. In addition, the KPZ no-nequilibrium potential admits a functional Taylor expansion that results to be naturally truncatedat third order, giving rise to a related nonlinear stochastic partial differential equation offeringsome insight on the origin of a diffusive instability as well as on the asymptotic time behavior. Thevariational scheme is also exploited to inquire on the dynamical behavior of the KPZ equationthrough a path-integral approach. All these aspects offers novel points of view, shedding light onparticular aspects of KPZ dynamics.

Lutz Schimansky-Geier, Department of Physics, Humboldt-University Berlin, Berlin, GermanyActive Brownian particles: From individual to collective behaviourAbstract: Single self-propelled particles as well as ensembles of self-propelled particles areexamples of non-equilibrium states in the interdisciplinary research at the borderline betweenphysics and biology. Interesting examples and measurements of self-moving objects come frombiology, these are bacteria, eukaryots, amoeba, insects, fishes and animals. But also in physicsself-moving objects are known, which are active colloids and moving spots in reaction-diffusionsystems.

I will review models of self-propelled particles from a viewpoint of statistical physics. Specialattention is payed to the influence of noise on the dynamics of single particles and on the exhi-bition of spatial structures in groups of interacting moving particles. In detail, the determinationof velocity distribution function, the calculation of diffusion coefficients and correlation functions,properties of swarms, the connection between the micro-dynamics of particles and the macro-dynamics of ensembles of particles, the response to external forces and many different examplesare considered.

Katja Lindenberg, D. Escaff and I. Pinto, Department of Chemistry and Biochemistry, Universityof California San Diego, La Jolla, USAArrays of stochastic oscillators: Nonlocal coupling, clustering, and wave formationAbstract: We consider an array of units each of which can be in one of three states. Unidirectio-nal transitions between these states are governed by Markovian rate processes. The interactionsbetween units occur through a dependence of the transition rates of a unit on the states of theunits with which it interacts. This coupling is nonlocal, that is, it is neither an all-to-all interac-tion (referred as global coupling), nor is it a nearest neighbor interaction (referred to as localcoupling).The coupling is chosen so as to disfavor the crowding of interacting units in the samestate. As a result, there is no global synchronization. Instead, the resultant spatiotemporal confi-guration is one of clusters that move at a constant speed and that can be interpreted as travelingwaves. We develop a mean field theory to describe the cluster formation and analyze this modelanalytically. The predictions of the model are compared favorably with the results obtained bydirect numerical simulations.

[1] D. Escaff, Italo’Ivo Lima Dias Pinto, and K. Lindenberg, Phys. Rev. E 90 , 052111 (2014)

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Tomasz Srokowski, Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, PolandStochastic dynamics for systems with Lévy flights and nonhomogeneously distributedtrapsAbstract: The stochastic transport in a medium containing traps can be described using a sub-ordination technique. If the traps are nonhomogeneously distributed, that method is modified byintroducing a position-dependent intensity of a random time distribution. The problem resolvesitself to a Langevin equation with a multiplicative noise which defines a process subsequentlysubordinated to the random time. In the absence of an external potential, the system reveals abehaviour typical for an anomalous transport: the nonlinear growth of the variance for the Gaus-sian stochastic stimulation. On the other hand, for the general stable Levy statistics the randomforce requires a modification to get a finite variance and this aim can be accomplished by intro-ducing an additional multiplicative noise at the boundary. The density distribution asymptotics iseither a stretched Gaussian or a power-law. The density distribution converges to a stationarystate when a potential is introduced and the relaxation pattern depends both on the potential andon the medium nonhomogeneity. For the harmonic oscillator the Cole-Cole form of the relaxationis always observed but the effective relaxation time substantially differs for different values of thenonhomogeneity parameter. In the case of a nonlinear oscillator, in turn, the relaxation pattern isexponential at large time. The medium nonhomogeneity can make the variance finite for the Levyflights even if the potential is relatively weak.

K. A. Penson, Sorbonne Universités, Univ. Paris VI, LPTMC, Paris , FranceFractional operators, Lévy-stable distributions and Bessel-type polynomialsAbstract: We demonstrate that the theory of classical Bessel polynomials and of their relevantgeneralizations can be naturally framed within the formalism of certain fractional differential ope-rators. These variants of Bessel polynomials can be conceived as the Stieltjes moments of pro-perly regularized one-sided Lévy-stable distributions. We present the complete theory of thesepolynomials including their explicit forms, Rodrigues-type formulas and their links with the combi-natorics via generalized Stirling numbers. Applications of this method to the relativistic Schrödin-ger (Salpeter) and relativistic heat equations are considered.*) work done in collaboration with K. Gorska (Cracow, Poland) and G. Dattoli (ENEA, Italy)

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M. J. Krawczyk, M. del Castillo-Mussot, E. Hernandez-Ramirez, G. G.Naumis, Krzysztof Kułakowski, AGH University of Science and Technology, Faculty of Physicsand Applied Computer Science, Kraków, PolandHeider balance, asymmetric ties, and gender segregationAbstract: To remove a cognitive dissonance in interpersonal relations, people tend to divide ouracquaintances into friendly and hostile parts, both groups internally friendly and mutually hostile.This process is modeled as an evolution towards the Heider balance. A set of differential equ-ations have been proposed and validated (Kulakowski et al, IJMPC 16 (2005) 707) to model theHeider dynamics of this social and psychological process. Here we generalize the model by in-cluding the initial asymmetry of the interpersonal relations and the direct reciprocity effect whichremoves this asymmetry. Our model is applied to the data on enmity and friendship in 37 schoolclasses and 4 groups of teachers in Mexico. For each class, a stable balanced partition is obta-ined into two groups. The gender structure of the groups reveals stronger gender segregation inyounger classes, i.e. of age below 12 years, a fact consistent with other general empirical results.

Paolo Grigolini, Center of Nonlinear Science of the University of North Texas, Denton, TX, USAUnification of behavioral sciences: Challenging non-equilibrium statistical physicsAbstract: One of the fundamental assumptions of statistical physics is the hypothesis that theaverages over infinitely many copies of the same system coincide with the time averages over thetime evolution of a single system, ergodicity condition. The tracking of single molecules diffusingin biological cells shows that this assumption is violated. On the other hand, the study of systemswith a finite number of interacting units reveals that at criticality a non-ordinary statistical condi-tion, with scale-free time fluctuations, called temporal complexity, emerges. Temporal complexityis the signature of occurrence of non-Poisson renewal events and is the generator of the sameergodicity breaking as that observed in molecular diffusion in biologic cells.

The breakdown of the equivalence between ensemble and time averages requires the revi-sion of the traditional theories of response of systems of interest to external stimuli. This revisionmust be compatible with the important fact that the perturbed system is not at equilibrium, andgenerates a new linear response theory. This new linear response theory shows that temporalcomplexity generating systems are not sensitive to the influence of systems with a fixed timescale, this being a new phenomenon termed complexity management.

Upon increase of the perturbation intensity, the complexity management phenomenon turnsinto the complexity matching phenomenon: The exchange of information between two networksof interacting units becomes maximally efficient when both systems are at criticality.

On the basis of these theoretical results we propose a unification project, moving from bio-logy to anthropology, to sociology and to economics, resting on the crucial role of criticality. Ac-cording to this project the ergodicity breaking revealed by the tracking of single molecules shouldbe due to the cooperation-induced criticality of the biological cell.

We establish a connection with the subject of evolutionary game theory, and with the chal-lenging issue of altruism emergence. We find that the majority of the attempts currently madeare affected by the local nature of the play. We discuss the possible benefits of bypassing localitylimits through criticality-induced long-range correlation. We argue that complexity managementand complexity matching, and especially the non-ergodic form of them, may become the essentialtheoretical ingredient to help the progress of evolutionary game theory.

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Dante Chialvo, Consejo Nacional de Investigaciones Cientificas y Tecnologicas (CONICET), Bu-enos Aires, ArgentinaBrain dynamics: What is critical about it?Abstract: Highly correlated brain dynamics produces synchronized states with no behavioralvalue, while weakly correlated dynamics prevent information flow. In between these states, theunique dynamical features of the critical state endow the brain with properties which are funda-mental for adaptive behavior. We discuss the idea put forward two decades ago by Per Bak thatthe working brain stays at an intermediate (critical) regime characterized by power-law correla-tions. This proposal is now supported by a wide body of empirical evidence at different scalesdemonstrating that the spatiotemporal brain dynamics exhibit key signatures of critical dynamics,previously recognized in other complex systems. The rationale behind this program will be di-scussed with an account of the most recent results.

Peter Hänggi, Department of Physics, University of Augsburg, Augsburg, GermanyAnomalous heat diffusionAbstract: Abstract: The field of Statistical Physics provides many different tools, which are basedeither on microscopic approaches or on a more phenomenological level to describe the spread ofheat in classical and quantum regimes in realistic and more idealized model systems of arbitrarydimensions. Typical such powerful tools are first principles Linear Response Theory for trans-port coefficients, yielding the celebrated Green-Kubo formulas, the stochastic theory of RandomWalks, or mesoscopic approaches such as the more practical treatments in terms of kinetic trans-port equations.

In low dimensional systems the transport of heat in form of diffusive spread or heat fluxbetween reservoirs of differing ambient temperatures typically may exhibit anomalous featuressuch as the violation of the Fourier Law with length-dependent heat conductivities or the diffusivespread of heat that occurs faster than normal [1, 2].

In this talk we discuss recent results how the dynamics of energy spread occurring in one-dimensional nonlinear lattices relates to anomalous diffusion behavior and heat conductivities.Moreover we explain how the carriers of heat, typically referred to as phonons, may be givenmeaning in a regime with nonlinear interaction forces beyond the ballistic behavior originatingfrom solely harmonic (linear) interaction forces. The underlying physical mechanism of scatteringthen renders corresponding mean free paths of such effective phonons finite [3].

* This talk is based on a multinational collaboration involving members from the University ofAugsburg, MPI-PKS Dresden, National University of Singapore, Tongji University and the FudanUniversity in Shanghai. Some pertinent own references are given below.

[1] A.V. Zarbudaev, S. Denisov and P. Hänggi, Perturbation spreading in many-particle systems: A random walkapproach, Phys. Rev. Lett. 106: 180061(2011); ibid, Phys. Rev. Lett. 109, 069903 (2012).

[2] S. Liu, P. Hänggi, N. Li, J. Ren, and B. Li, Anomalous heat diffusion, Phys. Rev. Lett. 112: 040601 (2014)[3] S. Liu, J. Liu, P. Hänggi, C. Wu, and B. Li, Triggering waves in Nonlinear Lattices: Quest for anaharmonic

phonons and corresponding mean free paths, Phys. Rev. B 90, 174304 (2014).

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Jacek Miekisz, Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Infor-matics and Mechanics, University of Warsaw, Warsaw, PolandSpatial aspects and time delays in gene regulationAbstract: Classical models of gene expression and regulation do not take into account transportof mRNA and protein molecules within cells. Moreover, they treat biochemical processes as in-stantaneous. We present two approaches to deal with time delays which arise in such situations.The process of transcription takes a certain amount of time. We introduce a fixed time delay inMaster equation for a self-repressing gene. We solve equations for expected value and varianceof the number of protein molecules in the stationary state in the mean-field approximation. Wealso construct and analyze a spatial Markov chain with random walks of biomolecules.

Anna Ochab-Marcinek, Institute of Physical Chemistry of the Polish Academy of Sciences, War-saw, PolandModeling stochastic gene expression: A few solutions by geometric constructionAbstract: Living cells are systems of a very small volume. The abundance of particular typesof proteins can be as low as hundreds, tens, or even single molecules. At such low concentra-tions of reactants, biochemical reactions undergo strong fluctuations. In addition, proteins areproduced in random bursts and cell division results in uneven distribution of inherited moleculesin the daughter cells, which is another source of noise. Traditionally, gene expression has beenmodeled using Master equations. However, this method is difficult and provides solutions to onlya few simplest models. The analysis of the solutions is additionally complicated by the fact thatthe resulting probability distributions are discrete.

For this reason, we use an alternative approach in which the number of particles is assumedto be still large enough that it can be modeled by a continuous variable. We also assume thatgene-transcription factor binding reactions can be accurately described by Hill kinetics. In sucha case, it turns out that we gain the ability of a simple description of the properties of proteindistributions: For a class of models we can obtain solutions by geometric construction, whichallows us to find the number of minima and maxima of the distributions. In some cases, thisapproach can be interpreted in terms of a nonlinear noise filter which transforms the transcriptionfactor distribution into a different distribution of proteins produced by the downstream gene. In thistalk, I will show several solutions obtained with the proposed method, for self-regulated genes andcascades.

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Talks

Aleksander Weron, Wroclaw University of Technology, Wrocław, PolandARFIMA modeling for single particle tracking dataAbstract: Accurately characterizing the anomalous diffusion of a tracer particle has become acentral issue in biophysics. We present an autoregressive fractionally integrated moving average(ARFIMA) process as an appropriate model for fractional anomalous diffusion data with measu-rament errors.

[1] K. Burnecki, E. Kepten, Eldad Yu. Garini, G. Sikora, Grzegorz and A. Weron, Sci. Rep. 5,11306 (2015).

Alexander Blumen and Oliver Mülken, Theoretical Polymer Physics, University of Freiburg, Fre-iburg, GermanyDynamics in complex systems: Geometric and topological aspectsAbstract: Dynamical processes in complex systems are of much interest and recently some wereshown to be determined by quantum aspects. Given that the classical description of dynamicalprocesses often follows a master-equation-type formalism, it is interesting to determine in how farsuch quantum aspects can be taken into account along lines akin to the classical ones. Focusingon time-evolution operators in statistical and in quantum mechanics, it turns out that there existclose parallels between continuous time random walks (CTRW) and continuous time quantumwalks (CTQW) [1,2,3,4].

Now, both the CTQW and the CTRW problems are linear, and many results obtained insolving CTRW (such as eigenvalues and eigenfunctions) can be readily reutilized for CTQW.However, the physically relevant properties of the two models differ vastly: In the absence oftraps CTQW are time-inversion symmetric and no energy equipartition takes place at long times.Also, the quantum system keeps memory of the initial conditions, a fact exemplified by the oc-currence of quasi- revivals [2,4]. This presentation will recall this and additional features, such asthe topology dependence of the CTQW, ranging from very efficient transport on regular latticesto localization and trapping effects in disordered systems [3]. Also the CTQW results will be com-pared to the corresponding CTRW results on topologically equivalent networks. In this way thesimilarities and differences between purely classical and purely quantum mechanical processescan be explored systematically [5-7].

Here a fundamental quantity of interest is the efficiency of the transport. As will be shown,the efficiency is reflected in the exact and in the average return probabilities, as well as in themean survival probabilities when absorbing traps are present. The problem is, of course, relatedto the question of localization [8]. Especially when studying transport over fractal networks (Sier-pinski gaskets, Sierpinski carpets and dual structures), changes in the localization behaviour areobserved. Similar situations occur when the transport takes place over randomly distributed sites;this makes it possible to readily compare the quantum results to classical percolation theory. Itturns out that for two-dimensional finite lattices also the overall form influences the transport [9].

[1] I.M. Sokolov, J. Klafter, A. Blumen, Phys. Today 55, (11) 48 (2002)[2] O. Mülken, A. Blumen, Phys. Rev. E 71, 036128 (2005)[3] O. Mülken, A. Blumen, Phys. Rev. E 73, 066117 (2006)[4] O. Mülken, A. Blumen, Physics Reports 502, 37 (2011)[5] E. Agliari, A. Blumen, O. Mülken, J. Phys. A 41, 445301 (2008)[6] E. Agliari, A. Blumen, O. Mülken, Phys. Rev. A 82, 012305 (2010)[7] E. Agliari, A. Blumen, O. Mülken, Intern. J. Bifurc. Chaos 20, 271 (2010)[8] D. Zoltán, A. Anishchenko, T. Kiss, A. Blumen, O. Mülken, Phys. Rev. E 90, 032113 (2014)[9] A. Anishchenko, A. Blumen, O. Mülken, Phys. Rev. E 88, 062126 (2013)

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Tadeusz Kosztołowicz, Institute of Physics, Jan Kochanowski University, Kielce, PolandRandom walk model of subdiffusion in a membrane systemAbstract: Using two random walk models in a system with a thin membrane we find the Green’sfunctions describing various kinds of diffusion in this system. The models differ in the assump-tions concerning how the particle is stopped or reflected by the membrane when the particle’sattempts to pass through it fail. To find the Green’s function we use a particle’s random walkmodels in a system in which the time and spatial variable are discrete; after this, we pass fromdiscrete to continuous variables. As examples we present the Green’s functions for a membranesystem in which subdiffusion or slow subdiffusion occurs and we briefly discuss the properties ofthe functions. The Green’s functions provide a new boundary condition at the membrane. Thisboundary condition shows that the additional ‘memory effect’, represented by the fractional de-rivative, is created by the membrane. This effect is also created by the membrane for a normaldiffusion case.

[1] T. Kosztołowicz, arXiv cond. mat. 1505.05199 (2015) (submitted).[2] T. Kosztołowicz, Phys. Rev. E 91, 022102 (2015).

Annie Lemarchand, Sorbonne Universités, UPMC Univ. Paris 06, Laboratoire de Physique Théo-rique de la Matière Condensée, Paris Cedex, France and CNRS, UMR 7600 LPTMC, Paris,FranceEvaluation of reaction fluxes in stationary and oscillating far-from-equilibrium biologicalsystemsAbstract: The complex spatio-temporal structures that appear in chemical and biological sys-tems require far-from-equilibrium conditions which may lead to the circulation of reaction fluxes. Iinvestigate how time asymmetry of cross-correlation functions of concentration fluctuations maybe exploited to determine reaction fluxes at the cellular level, using tagged species and fluore-scence correlation spectroscopy (FCS). Considering the master equation as a reference, I willshow that, far from a bifurcation, the Langevin approach provides a reliable tool to compute ana-lytical expressions for time correlation functions. Biochemical mechanisms associated with bista-bility and oscillations issued from a Hopf bifurcation or a saddle-node infinite period bifurcationare considered. The blind use of the simple relation obtained when assuming a linear determi-nistic dynamics is proved to often lead to a poor estimation of the value of the reaction flux andeven of its sign.

[1] C. Bianca and A. Lemarchand, Physica A, doi:10.1016/j.physa.2015.06.012, in press

John Lapeyre, Spanish National Research Council (IDAEA-CSIC), and ICFO - The Institute ofPhotonic Sciences Mediterranean Technology Park, Barcelona, SpainWeak ergodicity breaking and Brownian motionAbstract: I will discuss anomalous diffusion arising from Brownian motion on heterogeneousmedia. A well-known example is the random walk on a critical percolation process. I will presentrecent work on a different source of disorder that produces an anomaly that is associated withweak ergodicity breaking. I will place the models in the context of recent work on the continuous-time random walk and trapping models.

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Katarzyna Górska, Department of Theoretical Astrophysics, H. Niewodniczanski Institute of Nuc-lear Physics, Polish Academy of Sciences, Kraków, PolandPhotoluminescence decay, stretched exponentials and Lévy stable distributionsAbstract: Recent experiments have shown that photoluminescence decay of silicon nanocrystalscan be described by the stretched exponential function. I will show that the associated decay pro-bability rate is the one-sided Levy stable distribution. Moreover, I will show that the dynamicsleading to photoluminescence decay is an anomalous diffusion type and it can be modeled interms of fractional Fokker-Planck equation.

Roberto Deza, IFIMAR (Mar del Plata Institute for Physical Research), CONICET (National Co-uncil for Scientific and Technical Research) and UNMdP (National University of Mar del Plata),Mar del Plata (Bs. As.), ArgentinaStochastic dissipative solitonsAbstract: By effect of aggregating currents, some systems display an effective diffusion coeffi-cient that becomes negative in a range of the order parameter, giving rise to bistability amonghomogeneous states (HS). By applying a proper multiplicative noise, localized (pinning) statesare shown to become stable at the expense of one of the HS. They are however not static, buttheir location fluctuates with a variance that increases with the noise intensity. The numericalresults are supported by an analytical estimate in the spirit of the so-called “solvability condition”.

Andrzej Krawiecki, Faculty of Physics, Warsaw University of Technology, Warsaw, PolandSynchronization of chaotic oscillators on hypergraphsAbstract: The problem of synchronization of identical chaotic oscillators on hypergraphs is stu-died theoretically and via numerical simulations. Hypergraphs are generalized graphs, in whichgroups of more than two nodes are connected by hyperedges. In the systems under study cha-otic oscillators are placed in the nodes and the hyperedges correspond to nonlinear “many-body”interactions among groups of connected oscillators. It is shown that for p-hypergraphs, in whicheach hyperedge connects exactly p nodes, and assuming certain symmetry properties of the in-teractions corresponding to the hyperedges, the problem of the stability of the synchronized statecan be reduced to that for a system of oscillators on a (possibly weighted) graph obtained byassuming all-to-all coupling among the nodes connected by each hyperedge. The latter problemcan be further analyzed using the standard Master Stability Function approach. As an exam-ple, systems of the Lorentz, Chen and Lü oscillators on complex scale-free p-hypergraphs areconsidered, where it is shown that the stable synchronized state can coexist with the fixed pointattractors corresponding to the oscillation death. In a general case of hypergraphs with differenthyperedges connecting possibly different numbers of nodes and corresponding to different formsof nonlinear interactions among the oscillators the problem of the stability of the synchronizedstate can be reduced to that for a system of oscillators on a multiplex network. In this case ad-ditional assumptions concerning the topology of the hypergraph or the form of the interactionsamong oscillators are necessary in order to use the Master Stability Function approach.

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Talks(continued)

Franco Ferrari, Institute of Physics, University of Szczecin, Szczecin, PolandEnergy minimization and Monte Carlo simulations of polymer knotsAbstract: Polymer rings, also called catenanes in the chemical literature, constitute a frequentlyoccurring motif in nature and in artificial soft matter materials. Very often in DNA and sometimes inproteins, these rings form very complicated knots. Knots are also relevant in polymer materials,for instance by increasing their breakability or altering their elastic behavior. The study of themechanical and thermal properties of polymer knots poses several challenges and is a highlyinterdisciplinary problem. To obtain a satisfactory statistics, several hundreds of billions of knotconformations must be sampled during a Monte Carlo simulation. This requires the developmentof fast algorithms that are able to take into account the topological properties of the knot. On theother side, the energy landscape of a polymer knot is very complex. Sophisticated algorithmsof energy minimization are necessary in order to explore this landscape. In this talk the resultsof a recent study of the statistical mechanics of very long polymer knots will be presented. Inthe investigation, the Wang-Landau multicanonical Monte Carlo algorithm has been used. Thepolymers are mainly, but not only, defined on a lattice. Some of the problems arising in MonteCarlo numerical simulations and in exploring the energy landscape of very long polymer knots willbe discussed together with their solution. The results obtained in understanding the mechanicaland thermal properties of these interesting physical systems will be shown.

Maciej Majka, M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandNon-Gaussian polymers described by alpha-stable chain statistics: Model, effective inte-ractions in binary mixtures, and application to on-surface separationAbstract: While the Gaussian chain model is a classical description of a polymeric chain, certainconditions, such as non-Gaussian distribution of persistence lengths, adsorption to the surfaceor the presence of the power-law spatial correlations in the thermal noise can result in the heavy-tailed statistics describing the chain. In order to reproduce this non-typical behavior, the alphastable chain model is introduced. In its framework it is possible to calculate the entire hierarchyof analytical results describing the chain. This includes the distribution of nodes around the masscenter of the chain, the coarse-grained chain-chain interaction, effective interactions in the pre-sence of smaller chains and the stability conditions for binary mixtures. This last result providesa natural generalization of the spinodal decomposition condition for the Gaussian particles. Thiscondition is further applied to compare the ‘on-surface’ and ‘in the bulk’ phase separation of thebinary mixture. Finally, four different scenarios of simultaneous mixing and demixing in the two-and three-dimensional systems are predicted depending on system parameters.

Piotr Weber, Piotr Pepłowski, Department of Informatics, Faculty of Physics, Astronomy and In-formatics, Nicolaus Copernicus University, Torun, PolandGaussian diffusion with drift interrupted by Lévy walkAbstract: We present a stochastic process that links two competing processes in one model- Gaussian diffusion with drift and one sided Lévy walks - leading to anomalous diffusion. Weobtain macroscopic density in Laplace and Fourier space for this model and derive fractionaldifferential equation for probability density function for a model in long time and spatial limits.Numerical and analytical solutions for certain values of parameters are presented.

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Łukasz Kusmierz, M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Polandand Institute of Automatics, AGH University of Science and Technology, Kraków, PolandLévy flights with stochastic resettingAbstract: I will describe two extensions of a recently proposed model of diffusion with stochasticresetting [1]. In both models Lévy α-stable jumps are included and both serve as a randomsearch strategy. The first model[2] takes place in a discrete time and a mean first passage timeis considered, whereas in the second model[3] time is continuous and a meean first arrival timeis of interest. Parameters optimizing the search strategy in function of a distance to the targethave been calculated. As it turns out, in the first model there appear a sharp transition betweendifferent strategies.*) work done in collaboration with G. Schehr, S. Majumdar (Univ. Paris-Sud, CNRS, LPTMS,UMR 8626, Orsay, France), S. Sabhapandit (Raman Research Institute, Bangalore, India), andE. Gudowska-Nowak (M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Po-land).

[1] Evans, M. R., and Majumdar S. N.; Phys. Rev. Lett. 106(16) (2011), 160601.[2] Kusmierz, L., Majumdar, S. N., Sabhapandit, S., and Schehr, G.; Phys. Rev. Lett. 113(22) (2014), 220602 .[3] Kusmierz L., Gudowska-Nowak E.; arXiv:1508.03184

Jeremi Ochab, M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandHow we move is universal: Scaling in human motor activityAbstract: Human motor activity displays complex temporal patterns – on the one hand constra-ined by the circadian rythm and the usual wake-sleep cycle, on the other resulting from a myriadof minute individual movements – whose fluctuations appear over a wide range of temporal sca-les, from days to seconds. Are activity fluctuations across temporal scales intrinsically different,or is there a universal description encompassing them? Is this description universal across indi-viduals?

In this talk, we analyse spontaneous motor activity of healthy individuals recorded with awristwatch accelerometers in two different conditions: during a week of regular sleep and a weekof chronic partial sleep deprivation.

The temporal activity pattern clearly shows non-Gaussian long-range fluctuations. Behavio-ural symptoms of lack of sleep can be evaluated by analysing statistics of duration times of activeand resting states, and alteration of behavioural organization can be assessed by comparingexponents of the detected power-law distributions of rest periods. Moreover, we study the scalingof average fluctuations across temporal scales and determine a universal law in motor activityfluctuations. Results are highly reminiscent of the universality described for the average shape ofavalanches in systems exhibiting cracking noise.

Beyond its theoretical relevance, the present results may allow to develop objective markersof healthy/pathological human motor activity. In this instance, the separation of power-law expo-nents for rested and sleep deprived subjects might constitute a measure of the severity of sleepdeprivation and the effects of sleep disorders.

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Grzegorz Siudem1 and Janusz A. Hołyst1,2,31Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University ofTechnology, Warsaw, Poland2Netherlands Institute for Advanced Study in the Humanities and Social Sciences, Wassenaar,The Netherlands3ITMO University, Saint Petersburg, RussiaDiffusion on hierarchical systems of weakly-coupled networksAbstract: We present a new framework to analyse diffusion dynamics within weakly-couplednetworks (interconnected networks) by means of separation of time scales. Using an adiabaticapproximation we reduced system dynamics to a Markov chain with aggregated variables andderived a transport equation that is analogous to Fick’s First Law and includes a driving force.The entropy production is the sum of microscopic entropy transport, which results from particlemigration between networks of different topologies and a macroscopic entropy production of theMarkov chain. Equilibrium particles distributions between different sub-networks depend only oninternal sub-network parameters. Our framework, confirmed by numerical simulations, is alsouseful for considering diffusion in nested systems corresponding to hierarchical networks withseveral different time scales thus it can serve to uncover hidden hierarchy levels from observa-tions of diffusion processes.

Jakub Spiechowicz, Institute of Physics, University of Silesia, Katowice, PolandDiffusion anomalies in ac driven Brownian ratchetsAbstract: We study diffusion in ratchet systems [1]. As a particular experimental realization weconsider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux.We analyze mean-square displacement of the Josephson phase and find that within selected pa-rameter regimes it evolves in three distinct stages: initially as superdiffusion, next as subdiffusionand finally as normal diffusion in the asymptotic long-time limit. We show how crossover timesthat separates these stages can be controlled by temperature and an external magnetic flux. Thefirst two stages can last many orders longer than characteristic time scales of the system thus be-ing comfortably detectable experimentally. The origin of abnormal behavior is noticeable relatedto the ratchet form of the potential revealing an entirely new mechanism of emergence of ano-malous diffusion. Moreover, a normal diffusion coefficient exhibits non-monotonic dependenceon temperature leading to an intriguing phenomenon of thermal noise suppressed diffusion. Theproposed setup for experimental verification of our findings provides a new and promising testingground for investigating anomalies in diffusion phenomena.

[1] J. Spiechowicz and J. Łuczka, Diffusion anomalies in ac-driven Brownian ratchets, Phys. Rev. E 91, 062104(2015)

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Łukasz Machura, Institute of Physics, University of Silesia, Katowice, PolandCurrent-flux characteristics in mesoscopic nonsuperconducting ringsAbstract: The world of mesoscopic objects is one of the most intriguing domains of science, ho-wever, in many respects it still remains terra incognita. The mesoscopic world is characterized bythe small length scales and low temperatures. At sub-Kelvin temperatures, the length scales areof the order of micrometers. A prominent example of such a mesoscopic system is a normal non-superconducting metal ring threaded by a magnetic flux. Such a ring can support a ’persistentcurrent’ and occurs when electrons maintain their phase coherence around the ring. It is purelya quantum mechanical phenomenon and, in fact, a manifestation of the famous Aharonov–Bohmeffect. Persistent currents were predicted by Hund in 1938 [1] and until the early 1990s theirdetection has been considered an experimental challenge.

Quite a recent, successful experiment on 33 rings, performed by Bluhm et al [2] showedfor the first time an agreement with theory and provided the impetus for this study. The ringsinvestigated were very small, each only between one and two microns in diameter and 140 na-nometres thick, and made of the high-purity gold. Each one was scanned individually, unlike pastexperiments. In total they were scanned approximately 10 million times.

We study the current vs the external constant magnetic flux characteristics of the systemdriven by both the classical and the quantum thermal fluctuations. The problem is formulatedin the framework of a Langevin equation. Two scenarios are considered: one in which thermalfluctuations of the dissipative part of the current are modelled by classical Johnson-Nyquist noiseand one in which quantum character of thermal fluctuations is taken into account in terms of aquantum Smoluchowski equation. In addition we extend the analysis of the electrical currents forthe rings with the quantum dot following the model proposed by Moskalets [3] for a mesoscopicring containing a potential barrier with a resonant level..

The impact of the amplitude and phase of the transmission coefficient of the electron througha quantum dot on current characteristics is analyzed. In tailored parameter regimes, both sce-narios can exhibit the transition from para– to diamagnetic response of the ring current versusexternal magnetic flux [4]. This might qualitatively reproduce the experimental results of Bluhm atal [1].

[1] F. Hund, Ann. Phys. 32 (1938) 102; F. Hund, Ann. Phys. 5 (1996) 1.[2] H. Bluhm, N.C. Koshnick, J.A. Bert, M.E. Huber, K.A. Moler, Phys. Rev. Lett. 102 (2009) 136802.[3] M.V. Moskalets, Europhys. Lett. 39 (1997) 425.[4] L. Machura, Sz. Rogozinski, J. Łuczka, J. Phys. Condens. Matter 22 (2010) 422201; Sz. Rogozinski, L.

Machura, J. Łuczka, Eur. Phys. J. Spec. Top. 187 (2010) 5; L. Machura and J. Luczka Phys. Lett. A 379(2015) 1654.

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Posters

1P. Bełdowski1, 2, L.Schimansky-Geier2, A. Gadomski11Department of Physics, Institute of Mathematics and Physics, University of Science and Tech-nology, Bydgoszcz, Poland2Institut für Physik, Humboldt–Universität zu Berlin, Berlin, GermanyMolecular-level viscoelasticity, and its basic fingerprintAbstract: This work presents a molecular dynamics studies on the role of micelles in the lubrica-tion process, taking place in the synovial joints. The MARTINI [1] coarse-grained (CG) force fieldhas been used to mimic lipid-water interactions. The DPC and DPPC lipids are aggregated informs of spherical micelles and bilayers, respectively. Interactions of micelle with bilayer/micellein presence of polarizable water are checked during (in)elastic collisions of micelles when theyare pushed toward each other. Shape changes and rotation of micelles, as well as water dipolesorientation around micelles, are measured by the molecular dynamics package LAMMPS [2]. Weattempt to address these results toward understanding a mechanism of facilitated lubrication innatural joints [3].

Acknowledgement: This work is supported by UTP BS 39/2014.

[1] S. J. Marrink et al., J. Phys. Chem. B, 2007, 111, 7812-7824.[2] http://lammps.sandia.gov/[3] A. Gadomski et al., Tribology Lett., 2008, 30, 83-90; Z. Pawlak, A. Oloyede, Biosystems, 2008, 94, 193-201.

2Monika Krasowska1, Michał Ciesla2, Anna Strzelewicz1, Aleksandra Rybak1, Gabriela Dudek11Department of Physical Chemistry and Technology of Polymers, Silesian University of Techno-logy, Gliwice, Poland,2M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandLévy flight applied to structure analysis of mixed matrix membranesAbstract: Mixed matrix membranes for gas separation, i.e. materials comprising polymer withdispersed inorganic fillers, are investigated. The examined membranes are composed of ethyl-cellulose and magnetic powder. Transport properties of membranes may depend on many pa-rameters such as polymeric matrix used, type of powder, its amount, granulation and molecularclusters (if any). The structure of pattern formed by the magnetic powder used in membranematrix is studied. Random walk on a membrane structure is considered. The description of thesystem is based on the phenomenological and molecular approaches. Lévy flights are a parti-cular class of generalized random walk in which the step lengths during the walk are describedby a ‘heavy-tailed’ probability distribution. Within membranes structure, a tracer molecule is al-lowed to perform a Cauchy random walk with uncorrelated steps. Our analysis shows that thepresence of magnetic particles in membrane matrix significantly influences the motion, which inan obstacle-free space would be a superdiffusive type.

[1] M. Krasowska, A. Rybak, G. Dudek, A. Strzelewicz, K. Pawelek, Z.J. Grzywna, Structure morphology pro-blems in the air separation by magnetic membranes, Journal of Membrane Science, 415-6 2012 864-870

[2] A. Strzelewicz M. Krasowska, G. Dudek, A. Rybak, R. Turczyn, M. Ciesla, Anomalous diffusion on fractalstructure of magnetic membranes, Acta Physica Polonica B, 44 (2013) 955-965

[3] M. Ciesla, B. Dybiec, I. M. Sokolov, E. Gudowska-Nowak, Taming Lévy flights in confined crowded geometries,Journal of Chemical Phycics, 142 (2015) 16904

[4] R. Metzler, J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach, Phy-sics Reports 339 (2000) 1-77

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3Aleksandra Rybak1, Monika Krasowska1, Gabriela Dudek1, Anna Strzelewicz1, Michał Ciesla21Department of Physical Chemistry and Technology of Polymers, Silesian University of Techno-logy, Gliwice, Poland,2M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandPoly(2,6-dimethyl-1,4-phenylene oxide) membranes with different granulation of magneticpowder - structure and transport propertiesAbstract: The research focuses on the analysis of structure and transport properties of membra-nes based on poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) matrix and magnetic powder. Theinvestigated membranes are inhomogeneous, i.e. there are some molecular clusters of differentsize which definitely can influence the membrane properties. Transport properties of membranesdepend on many parameters such as: type of powder, its amount and granulation. The structureof pattern formed by magnetic particles and their aggregates in membrane matrix is studied. Thedescription of the system is based on the phenomenological and molecular (random walk on afractal lattice) approaches. The fractal dimension of random walk dw, and the fractal dimension ofmembrane structure df are evaluated. The influence of granulation of dispersed magnetic powderon the gas transport properties through the membranes is determined.

[1] S. Havlin, D. Ben-Avraham, Diffusion in disordered media, Advances in Physics, 36, 695-798, (1987)[2] R. Metzler, W.G. Glockle, T.F.Nonnenmacher, Fractional model equation for anomalous diffusion, Physica A,

211 (1994) 13-24[3] J. Klafter, I.M. Sokolov, First Steps in Random Walks, Oxford University Press (2011)[4] A. Rybak, M. Krasowska, A. Strzelewicz, Z.J. Grzywna,” Smoluchowski type” equations for modelling of air

separation by membranes with various structure. Acta Physica Polonica B 40 (2009) 1001-1008[5] M. Krasowska, A. Rybak, G. Dudek, A. Strzelewicz, K. Pawelek, Z.J. Grzywna, Structure morphology pro-

blems in the air separation by magnetic membranes, Journal of Membrane Science 2012[6] A. Strzelewicz M. Krasowska, G. Dudek, A. Rybak, R. Turczyn, M. Ciesla, Anomalous diffusion on fractal

structure of magnetic membranes, Acta Physica Polonica B, 44 (2013) 955-965

4Paweł Karbowniczek1, Michał Ciesla21Institute of Physics, Cracow University of Technology, Kraków, Poland,2M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandRandom sequential adsorption of bent-core particlesAbstract: Bent-core particles are of great interest due to their applications in the liquid crystalindustry. We study the random sequential adsorption of such particles on a two-dimensionalsurface. In our research, we consider both oriented and unoriented particles. We investigatethe influence of the type of the arm edges, the apex angle and the thickness on the adsorptionproperties. Packing is analyzed by means of the jamming limit coverage. Structure properties areillustrated by a radial distribution function and order parameters.

Acknowledgments: This work was supported by Grant No. DEC-2013/11/B/ST3/04247 of the National ScienceCentre in Poland.

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5Rogelma Ferreira, Centro de Ciências Exatas e Tecnológicas, Universidade Federal do Recôn-cavo da Bahia, Bahia, BrazilAnomalous law of coolingAbstract: We analyze the temperature relaxation phenomena of systems in contact with a ther-mal reservoir that undergoes a non-Markovian diffusion process. From a generalized Langevinequation, we show that the temperature is governed by a law of cooling of the Newton’s lawtype in which the relaxation time depends on the velocity autocorrelation and is then characteri-zed by the memory function. The analysis of the temperature decay reveals the existence of ananomalous cooling in which the temperature may oscillate. Despite this anomalous behavior, weshow that the variation of entropy remains always positive in accordance with the second law ofthermodynamics.

6Piotr J. Górski1, Agnieszka Czaplicka2, Janusz A. Hołyst1,31 Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University ofTechnology, Warsaw, Poland2 Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca,Spain3 ITMO University, Saint Petersburg, RussiaCoevolution of hierarchical adaptive random boolean networksAbstract: Random Boolean networks (RBNs) are one of the simplified models used to studyand compare certain properties of complex systems, driven by information processing. RBNs aregeneric and that is why they have been applied in many different fields including gene regulatorynetworks (GRNs). Here we propose a hierarchical adaptive random Boolean Network (HARBN)as a system consisting of distinct adaptive RBNs (ARBNs) - subnetworks - connected by a set ofpermanent interlinks.

We investigate mean node information, mean edge information as well as mean node de-gree. Information measures and internal subnetworks topology of HARBN coevolve and reachsteady- states that are specific for a given network structure. The main natural feature of ARBNs,i.e. their adaptability, is preserved in HARBNs and they evolve towards critical configurationswhich is documented by power law distributions of network attractor lengths. The mean length ofsuch attractors possesses a minimum for a certain specific value of quotient between the densityof interlinks and the density of all links in networks. A similar minimum exists for the mean steady-state connectivity. On the other hand the mean information processed by a single node or a singlelink increases with the number of interlinks added to the system.

In the proposed model it is very interesting that adding just a few interlinks to separatedsubnetworks changes the values of all observables and the effect is especially striking for meanattractor lengths. The modular network displays extremal values of its observables when sub-networks are connected with a density a few times lower than a mean density of all links. Wesuggest that the introduced HARBNs can be a step forward towards modeling of GRNs where amodular structure is present.

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7Tomasz Gradowski and Andrzej Krawiecki, Faculty of Physics, Warsaw University of Technology,Warsaw, PolandPhase synchronization in regular hypergraphsAbstract: The subject of our study is phase synchronization of limit-cycle oscillators placed innodes of regular hypergraphs. Hypergraphs [1] are generalized graphs, where edges connectingpairs of vertices are replaced with hyperedges connecting groups of vertices. n-uniform hyper-graphs, i.e., with constant number of nodes in each hyperedge equal n, constructed on regularstructures such as square, triangular or hexagonal 2D and 3D lattices are under consideration.Hypergraphs of this type are obtained by connecting n neighboring vertices with overlappinghyperedges (so-called plaquette models). By introducing nonlinear diffusive coupling betweennodes in each hyperedge, multiparticle interactions, which cannot be separated into pair interac-tions, are studied.

State of the oscillator placed in vertex vi is described by the phase θi, which evolves accor-ding to the generalized Kuramoto model [2]:

θi = ωi + λ∑e:vi∈esin

∑θj∈e

θj − |e|θi

where ωi is a natural frequency taken from a normal distribution, λ is a coupling parameter, edenotes a hyperedge, |e| is a number of vertices attached to a hyperedge e, the former sum isover a set of hyperedges attached to the node i and the latter sum is over all nodes attached toeach above-mentioned hyperedge.

For large enough values of λ, depending on initial conditions, the system exhibits phasesynchronization, when all the phases form one tight cluster. Also, depending on the size of hype-redges, various multi-cluster synchronization scenarios are possible (cluster synchronization).

[1] G. Ghoshal et al., Phys. Rev. E 79, 066118 (2009)[2] S.H. Strogatz, Physica D 143, 1 (2000)

8Viktor Holubec, Charles University in Prague, Faculty of Mathematics and Physics, Departmentof Macromolecular Physics, Praha, Czech RepublicEfficiency at and near maximum power of low-dissipation heat enginesAbstract: A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in termsof efficiency and the ratio of power to its maximum value can be optimized independently of mostdetails of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated ontwo specific trade-off measures. The first one is designed for finding optimal efficiency for a givenoutput power and clearly reveals diseconomy of engines working at maximum power.

Within the second example we derive universal lower and upper bounds on the efficiencyat maximum trade-off given by the product of power and efficiency. The results are illustrated ona model of a diffusion-based heat engine. Such engines operate in the low-dissipation regimegiven that the used driving minimizes the work dissipated during the isothermal branches. Thepeculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.

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9Łukasz Kusmierz and Ewa Gudowska-Nowak, M. Smoluchowski Institute of Physics, JagiellonianUniversity, Kraków, PolandOptimal first arrival times in Lévy random walk with resettingAbstract: We consider diffusive motion of a particle performing a random walk with Lévy distri-buted jump lengths and subject to resetting mechanism bringing the walker to an initial positionat uniformly distributed times. In the limit of infinite number of steps and for long times, the pro-cess converges to a super-diffusive motion with resetting. We derive formula for a mean firstarrival time (MFAT) to a predefined target position reached by a meandering particle and analyzeefficiency of the proposed searching strategy by investigating criteria for an optimal (a shortestpossible) MFAT.

10Katarzyna D. Lewandowska1 and Tadeusz Kosztołowicz21Department of Radiological Informatics and Statistics, Medical University of Gdansk, Gdansk,Poland2Institute of Physics, Jan Kochanowski University, Kielce, PolandModelling of subdiffusion–reaction processesAbstract: We consider subdiffusion–reaction processes with reactions of a type A −→ B andA+B −→ B. In the second process we assume that particles A are mobile whereas B — staticand that particles B are distributed homogeneously. In both processes a rule that reactions canonly occur between particles which continue to exist is taken into account. Although in both pro-cesses a probability of the vanishing of particle A due to a reaction is independent of both timeand space variables we show that subdiffusion–reaction equations describing these processesas well as their Green’s functions are qualitatively different. The reason for this difference is asfollows. In the case of the latter reaction, particles A and B have to meet with some probabilitybefore the reaction occurs in contradiction with the case of the former reaction. We base the me-thod considered in this paper on a random walk model in a system with both discrete time andspace variables. Then, the system with discrete variables is transformed into a system with bothcontinuous time and space variables. As an example we use these models to find the Green’sfunctions for a subdiffusive–reaction system which is bounded by a partially absorbing wall. Thisexample shows how the model can be used to analyze the subdiffusion–reaction process in asystem with partially absorbing or reflecting thin membranes. Employing a simple phenomenolo-gical model, we also derive equations related to the reaction parameters used in the consideredmodels.

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11Bartosz Lisowski, M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Polandand Unit of Pharmacoepidemiology and Pharmacoeconomics, Faculty of Pharmacy, JagiellonianUniversity Medical College, Kraków, Poland“Cargo-mooring” as an operating principle for molecular motorsAbstract: Navigating through an ever–changing and unsteady environment, and utilizing che-mical energy, molecular motors transport the cell’s crucial components, such as organelles andvesicles filled with neurotransmitter. They generate force and pull cargo, as they literally walkalong the polymeric tracks, e.g. microtubules.

What we suggest in this paper is that the motor protein is not really pulling its load. The loadis subject to diffusion and the motor may be doing little else than rectifying the fluctuations, i.e.ratcheting the load’s diffusion. Below we present a detailed model to show how such ratchetingcan quantitatively account for observed data.

The consequence of such a mechanism is the dependence of the transport’s speed and effi-cacy not only on the motor, but also on the cargo (especially its size) and on the environment (i.e.its viscosity and structure). Current experimental works rarely provide this type of information forin vivo studies. We suggest that even small differences between assays can impact the outcome.Our results agree with those obtained in wet laboratories and provide novel insight in a molecularmotor’s functioning.

12Marcin Minkowski, Magdalena Załuska-KoturInstitute of Physics, Polish Academy of Sciences, Warsaw, PolandMonte Carlo simulations of self-organising nanostructures in PbTe/CdTe multilayer sys-temAbstract: Immiscibility in many-component systems leads to self-organisation of the matter onthe microscopic level. One of the most common systems used for quantum dots formation isPbTe/CdTe heterostructure. It has been shown that a single thin PbTe layer stacked between tworelatively thick CdTe layers undergoes upon annealing a topological transition from 2D layer to1D percolation network, which later disintegrates into 1D islands and finally into 0D quantum dots[1]. The whole process occurs while the system is in the solid state phase.

More recently emergence of various nanostructures during multilayer PbTe/CdTe growth hasbeen observed [2]. The character of those structures depends on the growth temperature. Only atlow temperatures expected perpendicular 2D layers have been observed. At higher temperaturesPbTe formed column-like objects of various shapes and dimensions embedded in CdTe. At evenhigher temperatures complete separation of both phases has been observed with CdTe depositedon the top of PbTe.

We assume that diffusion is a key factor that leads to formation of all those nanostructures.We reproduce the experimental results of [2] by means of Monte Carlo simulations based ona simple lattice gas model. We simulate growth of a multilayer system with diffusive processesoccuring within the bulk and on the surface. Immiscibility of the system is realised by strongattractive interactions between particles of the same type. We find that depending on the growthtemperature different structures are observed, similarly to the experiment.

[1] H. Groiss, I. Daruka, K. Koike, M. Yano, G. Hesser, G. Springholz, N. Zakharov, P. Werner, F. Schaffler, APLMater. 2 012105 (2014)

[2] 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)

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13Maciej J. Mrowinski1, Robert A. Kosinski1,21Faculty of Physics, Warsaw University of Technology, Warszawa, Poland2Central Institute of Labor Protection - National Research Institute, Warszawa, PolandCycle entropy of cellular automataAbstract: Cellular automata, popularised by Stephen Wolfram, are dynamical systems of discretecells whose states evolve in time [2]. In the simplest, one-dimensional case, cells that comprisea cellular automaton are arranged on a linear lattice (one-dimensional array). The set of all po-ssible cell states is also discrete and finite. The state of each cell changes according to a localtransition rule that determines the next state as a function of the current state and the state ofcell’s neighbourhood. Neighbourhood is usually symmetric and consists of r cells to the left of agiven cell, the cell itself, and r cells to the right. One of the most important problems in the theoryof cellular automata is their classification, that is the assignment of automata to some complexityclasses. Many classification schemes have been proposed and each uses different dynamicalproperties of cellular automata to distinguish between classes.

There are many parameters that can be used to predict the dynamics of cellular automataor partition rule spaces [1]. Entropy of cellular automata, treated as a parameter that can be usedto measure complexity, may be defined in many different ways. Shannon entropy calculated bycounting the occur- rences of blocks in global configurations of cellular automata is computatio-nally inexpensive and allows, to some extent, for separation of complexity classes. In our work,we study a variant of entropy whose definition was inspired by Boltzmann’s entropy. It is a sim-ple parameter that consolidates information about lengths of limit cycles and number of states inbasins of attraction [3] into a single value:

h(L) =∑i

Ti +Ni

kLlnTi

where k is the number of states, Ti is the length of i-th cycle, Ni is the number of states thatlead to the i-th cycle (its basin of attraction) and L is the length of global configuration. In theory,entropy defined this way should be high for chaotic automata (long cycles) and low for periodicautomata (short cycles).

In order to determine how h(L) behaves when computed for automata that belong to variouscom- plexity classes, we used a large sample of one-dimensional cellular automata rules fromthe (k = 2, r = 4) space with symmetrical neighbourhood. The sample consisted of 64000 rulesthat were manually clas- sified according to a detailed classification scheme. Our results suggestthat entropy h(L) can serve a similar purpose as input entropy. However, unlike input entropy,h(L) contains information about the entire configuration space and is independent of the choiceof initial conditions. Unfortunately, this comes at a price - input entropy is far simpler to computeand h(L) can only be exactly computed for short cellular automata.

[1] Gina M. B. Oliveira, Pedro P. B. de Oliveira, Nizam Omar. Definition and application of a five-parametercharacterization of one-dimensional cellular automata rule space. Artificial Life, 7(3):277–301, 2001.

[2] Stephen Wolfram. A New Kind of Science. Wolfram Media, 2002.[3] A. Wuensche, M. Lesser. The Global Dynamics of Cellular Automata: An Atlas of Basin of Attraction Fields

of One-Dimensional Cellular Automata. Santa Fe Institute studies in the sciences of complexity. Addison-Wesley, 1992.

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14Lech Longa and Grzegorz Pajak, Marian Smoluchowski Institute of Physics, Department of Sta-tistical Physics, Jagiellonian University, Kraków, PolandThe role of chirality and flexopolarization on the stability of one–dimensional modulatednematic–like phasesAbstract: Recently discovered modulated nematic–like structures have become a major field ofactivity in the liquid crystal research across the world [1–5]. The observations for dimers, trimersand bent–core systems indicate that there are at least two types of one–dimensional modulatednematic–like phases. One of them is the twist–bend nematic phase (NTB), where the directorrotates on the cone like in the smectic C* but without long–range translational order of molecules.The second phase is the splay–bend nematic (NSB), where the main director performs in–plane,chirality–free modulation. These phases were theoretically predicted in [6–8] and observed insimulations [9, 10]. Theoretical description of these structures is also found in [11–16].

In this work we would like to propose in depth exploration of Landau–deGennes theory(LdeG) of chiral nematics, supplemented by flexopolarization terms [11, 16]. With the helicitymode expansion for the alignment tensor and the polarization fields, we use a systematic analysisof such a LdeG theory to identify all one–dimensional modulated structures and the associatedphase transitions.

Interestingly, besides nematic and cholesteric phases, we find four different periodic structu-res, of which one has not been reported so far. These new structures are longitudinal (Nlp) andtransverse (Ntp) periodic waves where polarization vector changes periodically in one dimensionbeing parallel and perpendicular, respectively, to the wave vector. The other two phases have allcharacteristic features ofNTB andNSB although their fine structure differs from that taken into ac-count in previously considered models. More specifically, the NTB phase appears at least weaklybiaxial with the angle between the main director and the wave vector, θ, varying with with tem-perature of the system. In the very weekly biaxial NSB phase all helicity modes are present andthe structure is non-chiral for non-chiral materials and chiral otherwise. Here we present someexemplary variations of the biaxiality measure and the angle along the direction of modulation,and phase diagrams showing competition among these various nematic-like structures.

Acknowledgments: This work is supported by the Grant No. DEC-2013/11/B/ST3/04247 of the NationalScience Centre in Poland and partly supported by Cracovian Consortium ”Materia-Energia-Przyszłosc” im. MarianaSmoluchowskiego within the KNOW grant.

[1] V. Görtz, C. Southern, N. W. Roberts, H. F. Gleeson and J. W. Goodby, Soft Matter 5, 463 (2009)[2] V. Borshch, Y-K Kim, J. Xiang, M. Gao, A. Jákli, V. P. Panov, J. K. Vij, C. T. Imrie, M-G. Tamba, G. H. Mehl and

O. D. Lavrentovich, Nat. Commun. 4, 2635 (2013)[3] A. Zep, S. Aya, K. Aihara, K. Ema, D. Pociecha. K. Madrak, P. Berantowicz, H. Takezoe and E. Górecka, J.

Mater. Chem. C 1, 46 (2013)[4] D. Chen, M. Nakata, R. Shao, M. R. Tuchband, M. Shuai, U. Baumeister, W. Weissflog, D. M. Walba, M. A.

Glaser, J. E. Maclennan and N. A. Clark, Phys. Rev. E 89, 022506 (2014)[5] Y. Wang, G. Singh, D. M. Agra-Kooijman, M. Gao, H. K. Bisoyi, C. Xue, M. R. Fisch, S. Kumar and Q. Li,

CrystEngComm 17, 2778 (2015)[6] R. B. Meyer, Phys. Rev. Lett. 22, 918 (1969)[7] V. L. Lorman and B. Mettout, Phys. Rev. Lett. 82, 940 (1999)[8] I. Dozov, Europhys. Lett. 56, 247 (2001)[9] R. Memmer, Liq. Cryst. 29, 483 (2002)

[10] S. M. Shamid, S. Dhakal and J. V. Selinger, Phys. Rev. E 87, 052503 (2013)[11] L. Longa and H.-R. Trebin, Phys. Rev. A 42, 3453 (1990)[12] G. P. Alexander and J. M. Yeomans Phys. Rev. Lett. 99, 067801 (2007)

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[13] N. Vaupotic, M. Cepic, M. A. Osipov and E. Górecka, Phys. Rev. E 89, 030501 (2014)[14] E. I. Kats and V. V. Lebedev, JETP Letters 100, 110 (2014)[15] C. Greco, G. R. Luckhurst and A. Ferrarini, Soft Matter 10, 9318 (2014)[16] S. M. Shamid, D. W. Allender and J. V. Selinger Phys. Rev. Lett. 113, 237801 (2014)

15Grzegorz Pajak1 and Mikhail A. Osipov21M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland2Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, UKMolecular description of smectic phases: Tilting rod–like molecules versus non–tiltingbent–core systemsAbstract: Description of transitions into the Smectic C (SmC) phase for rod–like molecules islimited to the approximate scenarios [see, for instance, 1–3], which does not allow to captureall properties of this transition. Here we present the systematic expansion of the mean–fieldpotential for the uniaxial rod–like particle [4], where we include all orientational and translationsorder parameters. Numerical results are presented in a number of different phase diagrams usingthe coordinates suggested by McMillan: temperature versus coupling constant responsible forsmectic interaction strength [5]. This model covers all possible phase transitions among phasesallowed by symmetry reduction including: (i) Iostropic (Iso) → Nematic (N) → Smectic A (SmA)→ SmC, (ii) I→ N→ SmC, (iii) I→ SmC, and (iv) I→ SmA→ SmC. Temperature variations ofrelevant order parameters in all phases is discussed for various phase sequences and topologiesof the phase diagrams.

Few years ago it was reported that in the bent–core materials ferroelectric order has beenobserved in the form of orthogonal smectic A (SmAF) phase with nonzero polarization vector[6–8], which is the only proper ferroelectric liquid in nature confirmed experimentally so far. Ear-lier the improper ferroelectricity in chiral tilted smectics was investigated for years, where nonzeropolarization is induced by a tilt primary order parameter [9, 10]. Here we derive model interactionpotentials for polar bent–core molecules in the form of three polarizability centers and the trans-verse electric dipole located along its C2 symmetry axis [11]. Temperature variation of the orderparameters for various phase sequences were obtained within mean–field approximation, and allthe results are combined in the phase diagrams. In this model the transition from nonpolar SmABto polar SmAF is either of the first or of the second order depending on the strength of dipolarinteractions. In the end we are going to discuss differences and similarities between behaviors ofsystem described by these models.

[1] A. Poniewierski and T. J. Sluckin, Mol. Phys. 73, 199 (1991)[2] A. S. Govind and N. V. Madhusudana, Eur. Phys. Lett. 55, 505 (2001)[3] M. V. Gorkunov, M. A. Osipov, J. P. F. Lagerwall and F. Giesselmann, Phys. Rev. E 76, 051706 (2007)[4] G. Pajak and M. A. Osipov, Phys. Rev. E 88, 012507 (2013)[5] W. L. McMillan, Phys. Rev. A 4, 1238 (1971)[6] R. A. Reddy, Ch. Zhu, R. Shao, E. Korblova, T. Gong, Yo. Shen, E. Garcia, M. A. Glaser, J. E. Maclennan, D.

M. Walba and N. A. Clark, Science 332, 72 (2011)[7] L. Guo, E. Górecka, D. Pociecha, N. Vaupotic, M. Cepic, R. A. Reddy, K. Gornik, F. Araoka, N. A. Clark, D. M.

Walba, K. Ishikawa and H. Takezoe, Phys. Rev. E 84, 031706 (2011)[8] Y. P. Panarin, M. Nagaraj, S. Sreenilayam, J. K. Vij, A. Lehmann and C. Tschierske, Phys. Rev. Lett. 107,

247801 (2011)[9] M. A. Osipov and M. V. Gorkunov, Phys. Rev. E 77, 031701 (2008)

[10] M. Osipov and G. Pajak, Phys. Rev. E 85, 021701 (2012)[11] M. A. Osipov and G. Pajak, Eur. Phys. J. E 37, 79 (2014)

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16Michał Ciesla1, Robert M. Ziff2 and Grzegorz Pajak11Marian Smoluchowski Institute of Physics, Department of Statistical Physics, Jagiellonian Uni-versity, Kraków, Poland2Center for the Study of Complex Systems and Department of Chemical Engineering, Universityof Michigan, Ann Arbor, MI, USAIn search of optimal particle geometries giving maximal coverage for two–dimensionalrandom sequential adsorptionAbstract: The random sequential adsorption of various particle shapes is studied in order todetermine the influence of particle anisotropy, α, on the saturated random packing θmax. For alltested particles there is an optimal level of anisotropy (α = 1 + x for dimers; here x is the halfdistance between the closest sphere centres) which maximizes the saturated packing fraction.

It is found that a concave shape, with additional blocking area, derived from a dimer of disksgives a packing fraction of 0.5833 [1], which is comparable to the maximum packing fraction ofellipsoids and spherocylinders [2, 3] and higher than other studied geometries [4]. Discussionwhy this shape is beneficial for random sequential adsorption is given.

Acknowledgments: This work is supported by Cracovian Consortium ‚„Materia-Energia-Przyszłosc“ im. Ma-riana Smoluchowskiego’ within the KNOW (Krajowy Naukowy Osrodek Wiodacy) grant and partly supported by theGrant No. DEC-2013/11/B/ST3/04247 of the National Science Centre in Poland.

[1] M. Ciesla, G. Pajak and R. M. Ziff, accepted for publication in Phys. Chem. Chem. Phys., DOI:10.1039/c5cp03873a (2015)

[2] J. D. Sherwood, J. Phys. A 23, 2827 (1990)[3] P. Viot, G. Tarjus, S. Ricci and J. Talbot, J. Chem. Phys. 97, 5212 (1992)[4] M. Ciesla, Phys. Rev. E 89, 042404 (2014)

17Mateusz Piwnik1, Tomasz Klinkosz2, Katarzyna D. Lewandowska2, Tadeusz Kosztołowicz11Institute of Physics, Jak Kochanowski University, Kielce, Poland2Department of Radiological Informatics and Statistics, Medical University of Gdansk, Gdansk,PolandSubdiffusion – reaction processes in the system with partially absorbing wallAbstract: We consider the subdiffusive system with a partially absorbing wall in which a mobileparticle A can react with a static particle B. Reactions of a type A+B→ B can only occur betweenparticles which continue to exist at time of a reaction. We determine the Green’s function bymeans of the generating function method. An accumulation of the mobile substance near themembrane can be observed. We discuss the influence of the membrane permeability on thesubdiffusion – reaction process.

34


Posters(continued)

18Artem Ryabov1, Viktor Holubec1, Dominik Lips2, Petr Chvosta1, Philipp Maass21Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromole-cular Physics, Praha, Czech Republic2Universitat Osnabrueck, Fachbereich Physik, Osnabrueck, GermanyOn asymptotic behavior of work distributions for driven Brownian motionAbstract: We propose a simple conjecture for the functional form of the asymptotic behavior ofwork distributions for driven overdamped Brownian motion of a particle in confining potentials.This conjecture is motivated by the fact that these functional forms are independent of the velo-city of the driving for all potentials and protocols, where explicit analytical solutions for the workdistributions have been derived in the literature. To test the conjecture, we use Brownian dyna-mics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which isbased on the contraction principle of large deviation theory. Our tests suggest that the conjectureis valid for potentials with a confinement equal to or weaker than the parabolic one, both for equ-ilibrium and for nonequilibrium distributions of the initial particle position. In addition we obtain anew analytical solution for the asymptotic behavior of the work distribution for the V-potential byapplication of the EN theory, and we extend this theory to nonequilibrated initial particle positions.

19Andrzej Sikorski, Department of Chemistry, University of Warsaw, Warsaw, PolandDiffusion in a crowded environment: Simulations within the frame of the Dynamic LatticeLiquid (DLL)Abstract: A simple model of lateral motion in a membrane is presented. We perform extensiveand systematic simulation studies of two-dimensional fluid motion in a complex crowded envi-ronment. In contrast to other works we focused on cooperative phenomena that occurred wherethe motion of particles takes place in a dense system. Our main goal was to answer the follo-wing question: how do fluid molecules move in an environment that has a complex structure andassuming that motion of fluid molecules is highly correlated. The Dynamic Lattice Liquid (DLL)model, which can work with the highest fluid density, was employed]. It became the basis fora parallel algorithm, which took into account coincidences of attempts of elementary molecularmotion resulting in local cooperative structural transformations. Within the frame of the DLL mo-del we considered cooperative motions of fluid particles in an environment that contained staticobstacles. We studied the dynamic properties of the system like the mean square displacement,the relaxation time of position as a function of the concentration of obstacles. The changes of hy-drodynamic interactions were also investigated by studies of the distribution of cooperative looplength. The subdiffusive motion of the liquid in the matrix of immobilized obstacles was found.It was shown that the percolation threshold calculated from the dynamic behavior of the liquidmolecules is considerably higher than that determined from the cluster analysis.

35


Posters(continued)

20Jacek Siódmiak, Department of Physics, Institute of Mathematics and Physics, University ofScience and Technology in Bydgoszcz, Bydgoszcz, PolandBiomolecular crystallization as a source of the color noise and nanometric thermal gra-dientsAbstract: Crystallization of the biomolecules is a very complex process. In the initial phase thespontaneous aggregations occurs which results in the formation of the disordered nucleus. Sub-sequently, self-organization of the nucleus is followed by the appropriate crystal growth. Whenthe size of a crystal reaches a few micrometers and the crystal surfaces are formed, terracesmay be formed due to surface defects. Macromolecules which migrated from the solution ontothe crystal surface have to diffuse to the positions localized at the foot of the terraces which arethe most favorable thermodynamically. Biomolecular crystals are of the non-Kossel type (complexstructure with several molecules per unit cell in non-equivalent positions) therefore their surfaceis 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 withprobability proportional to the Boltzman factor. Therefore, in contrast to the classical random walk,each step is performed at different rate. In consequence the crystal growth rate is also disturbed.In contrast to the classical random walk that generates white noise, this type of diffusion can be asource of the color noise. The power spectrum depends on the distribution of the macromolecu-les that form the terrace. Another factor affecting the characteristics of the power spectrum is thepresence of nano-scale temperature gradients appearing in places of uncompensated stresses,e.g.: on the edges of the terraces as well the edges of surface defects.

Here we present the results of the coarse grained Metropolis Monte Carlo simulation ofthe surface diffusion performed by the growth unit. The simulations are carried out on a three-dimensional cubic lattice. Power spectra that are obtained for different mappings of terraces indi-cate that the biomolecular crystallization can be characterized by the color noise. The presenceof the color noise can impede the interpretation of the results obtained e.g. by the dynamic scat-tering methods.

36


Posters(continued)

21Grzegorz Siudem1,2, Grzegorz Swiatek2,1Faculty of Physics, Warsaw University of Technology, Warsaw, Poland2Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw,PolandDiagonal stationary points of Bethe free energyAbstract: Belief Propagation Algorithm, proposed by Judea Pearl, is a useful tool in the problemof inference in different mathematical structures (e.g. random Markov fields, Bayesian networks).BP Algorithm defines dynamics of so-called “beliefs”, which, in fact, are numbers connected withevery node of considered structure. If BP algorithm reaches its fixed point it allow one to calculatethe marginal probabilities for the considered structure. Wide range of important problems in sta-tistical physics, computer science and engineering are equivalent to calculation of the marginalprobabilities of the relevant structure. Thus, BP algorithm provides a useful (and fast!) tool forsolving such problems.

We investigate stationary points of the Bethe Free Energy for the Ising model on a 2-dimensional lattice. Such stationary points are also fixed points of BP algorithms. In the absenceof an external field, by symmetry reasons one expects the fixed points to have constant meansat all sites. This is shown not to be the case. There is a critical value of the coupling parameterwhich is equal to the phase transition parameter on the computation tree, above which fixed po-ints appear with means that are variable though constant on diagonals of the lattice and hencethe term “diagonal stationary points”. We will present a rigorous analytic proof of their existenceand computer-obtained examples of diagonal stationary points which are local maxima of theBethe functional and hence stable equilibria for message passing.

22Joanna Toruniewska1, Krzysztof Suchecki1, Janusz A. Hołyst1,21 Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University ofTechnology, Warsaw, Poland2 ITMO University, Saint Petersburg, RussiaCo-evolution of the Potts model and topology of interactionsAbstract: The Potts model with network dynamics, described by the canonical ensemble hasbeen considered. Three states have been found in the system. Fragmented network (orderedclusters state) is one of them and it has been found unstable - after a sufficiently long time thesystem arrives at a stable globally ordered state. It has been found that the system orders throughthe near-linear growth of the largest clusters. Based on the observation of the results it has beenfound that growth of the largest cluster is caused by state dynamics. The analytical prediction ofgrowth of that cluster has been proposed. The prediction is based on transfer of surface nodesfrom smaller to larger clusters. Only surface nodes (nodes with only one connection in theircluster) participate in this process. The surface size is not predicted analytically, but is a requiredinput from numerical simulation to correctly reproduce observed behavior. Analytical descriptioncorrectly describes the transition from the local to the global ordered state.

37


Posters(continued)

23Paulina Trybek, Institute of Physics, University of Silesia, Katowice, PolandApplication of multifractal detrended fluctuation analysis in biomedical signalsAbstract: The method proposed is based on study scaling properties of the fluctuations in thetime series. MDFA has become a popular method with a wide range of applications in the study ofnonlinear phenomena including aspects of biomedical signal analysis. We consider the surfaceelectromyographic (sEMG) signals, obtained from a group of people suffering from dysfunction ofthe sphincter ani externus muscle, including rectal cancer. The analyzed signals were recordedat the different levels of treatment process - before surgery and successively with 1, 6, 12 -months after. Based on the parameters describing multifractal spectra like the Hurst exponent orspectrum half –width, the states before and after treatment are compared.

24Ryszard Wojnar, IPPT PAN Institute of Fundamental Technological Research, Warsaw, PolandBogoliubov’s chains for one-component two-dimensional crystalsAbstract: The evolution of an N -particle system on a two-dimensional surface is given by Lio-uville’s equation for the probability density function fN(q1, q2, . . . , qN , p1, p2, . . . , pN , t) in 4N di-mensional phase space (2 space and 2 momentum coordinates per particle). Theory of one-component two-dimensional crystal is a special case of statistical theory of many particle sys-tems. Bogoliubov’s hierarchy (sometimes called the BBGKY hierarchy) is a set of equationsdescribing the dynamics of system of a large number of interacting particles. The equation foran s-particle distribution function (probability density function) fs(q1, q2, . . . , qs, p1, p2, . . . , ps, t)in the BBGKY hierarchy includes the (s + 1)-particle distribution function thus forming a co-upled chain of equations. Unlike the fluids, the crystals with their lattice can be completely de-scribed by the first equation of the Bogoliubov’s chain, in the basic assumption of multiplicityf2(q1, q2, p1, p2, t) = f1(q1, p1, t)f1(q1, p1, t). This is known as the self-consistent approach. In thisapproach the kinetic equation is derived, which describes the crystal as a system of the mutuallyrelated particles, and allows for systems with two-particle potentials to determine Born’s spectrumof the crystal lattice.

[1] N.N. Bogoliubov, Problems of a Dynamical Theory in Statistical Physics, Gostekhisdat, Moskva 1946 (inRussian). English translation in: J. de Boer, G.E. Uhlenbeck (Eds.), in: Studies in Statistical Mechanics, vol.1, North-Holland, Amsterdam1962.

[2] I. P. Bazarov, Statistical Theory of the Crystalline State [in Russian], Moscow State Univ., Moskva 1972.[3] I.P. Bazarov and P.N. Nikolaev, Method of statistical operators in the theory of crystals, Teoret. Mat. Fiz. 41

(3) 424–430 (1979).[4] I. P. Bazarov and E. V. Gevorkyan, Statistical Theory of Solid and Liquid Crystals [in Russian], Moscow State

Univ., Moskva 1983.[5] A. Yu. Zakharov and I. K. Loktionov, Classical statistics of one-componrnt systems with model potentials,

Theoretical and Mathematical Physics 119 (1) 534 - 539 (1999).[6] A. I. Karasevskii and V. V. Lubashenko, Binary distribution functions of atoms of simple crystals, Phys. Rev. B

66, 054302 (2002)

38


Posters(continued)

25Wojciech Tomczyk, Lech Longa, Grzegorz PajakM. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandBent-core molecules with biaxial arms forming nematic twist-bend phase: a generalisedMaier-Saupe theoryAbstract: A newly observed - heliconical (twist-bend) nematic phase (Ntb) of nanoscale pitch [1]has recently caught much of attention. Initially, the theoretical concept of this phase has beenpresented by R. B. Meyer [2] in 1973, where he assumed that the director of the moleculesprecesses on a cone forming an oblique helicoidal structure. Subsequently in 2001 Dozov [3], in2002 Memmer [4] and in 2004 Lorman et al. [5], suggested that the formation of the Ntb can befacilitated by the shape of bent-core molecules.

Here we present theoretical investigations on relation between biaxiality and stability of ne-matic twist-bend phase. We generalize a Maier-Saupe type of model for Ntb presented by Grecoet al. [6], where we introduce molecular biaxiality on both of the arms of the molecule, quantifiedby a 3x3, second-rank traceless symmetric tensor Q. The detailed results show the influence ofthe molecular biaxiality parameter [7] on the relative stability of the isotropic phase, nematic, Ntband the related phase transitions.

Acknowledgments: This work was supported by Grant No. DEC-2013/11/B/ST3/04247 of the National ScienceCentre in Poland.

[1] V. Borshch, Y-K Kim, J. Xiang, M. Gao, A. Jákli, V. P. Panov, J. K. Vij, C. T. Imrie, M-G. Tamba, G. H. Mehl andO. D. Lavrentovich, Nature Communications 4, 2635 (2013).

[2] R. B. Meyer, “Structural Problems in Liquid Crystal Physics”, pp. 273-373 in Les Houches Summer Schoolin Theoretical Physics, 1973. Molecular Fluids, R. Balian and G. Weil (eds.) (Gordon and Breach, New York,1976).

[3] I. Dozov, Europhys. Lett. 56, 247 (2001).[4] R. Memmer, Liq. Cryst. 29, 483 (2002).[5] V. L. Lorman and B. Mettout, Phys. Rev. E 69, 061710 (2004).[6] C. Greco, G. R. Luckhurst and A. Ferrarini, Soft Matter 10, 9318 (2014).[7] R. Berardi, L. Muccioli, S. Orlandi, M. Ricci and C. Zannoni, J. Phys.: Condens. Matter 20, 463101.1 (2008).

26Michał Ciesla and Aleksandra NowakM. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, PolandRevealing kinetics information from saturated random packingsAbstract: Imagine a surface on which we place randomly a lot of identical disks in a followingfashion: disks are placed one after the other, but newly placed particles cannot intersect with anyother disks placed previously. Additionally, once placed on the plane, a particle cannot change itsposition or disappear. The adding process ends when there is no place for placing another diskon a surface. Such a set of disks is called a saturated random packing. The question is: can wesay something about the order of particles placement by analysing the saturated random packingonly?

39


List of participants

Alicki Robert Gdansk, Poland [email protected] Dick Trondheim, Norway [email protected]łdowski Piotr Bydgoszcz, Poland [email protected] Alexander Freiburg, Germany [email protected] Chialvo Buenos Aires, Argentina [email protected] Michał Kraków, Poland [email protected] Roberto Mar del Plata, Argentina [email protected] Bartłomiej Kraków, Poland [email protected] Franco Szczecin Poland [email protected] Rogelma Bahia, Brazil [email protected] Andrzej Kraków, Poland [email protected] Adam Bydgoszcz, Poland [email protected]óra Paweł F. Kraków, Poland [email protected]órska Katarzyna Kraków, Poland [email protected]órski Piotr Warszawa, Poland [email protected] Tomasz Warszawa, Poland [email protected] Paolo Denton, Texas, USA [email protected] Zbigniew J. Gliwice, Poland [email protected] Ewa Kraków, Poland [email protected]änggi Peter Augsburg, Germany [email protected] Viktor Prague, Czech Republic [email protected]łyst Janusz A. Warszawa, Poland [email protected] Signe Trondheim, Norway [email protected]łowicz Tadeusz Kielce, Poland [email protected] Andrzej Warszawa, Poland [email protected]łakowski Krzysztof Kraków, Poland [email protected] Łukasz Kraków, Poland [email protected] John Barcelona, Spain [email protected] M. Howard Athens GA, USA [email protected] Annie Paris, France [email protected] Katarzyna Gdansk, Poland [email protected] Katja La Jolla, CA, USA [email protected] Adam Poznan, Poland [email protected] Bartosz Kraków, Poland [email protected] Lech Kraków, Poland [email protected]Łuczka Jerzy Katowice, Poland [email protected]

40


List of participants (continued)

Machura Łukasz Katowice, Poland [email protected] Maciej Kraków, Poland [email protected] Ralf Potsdam, Germany [email protected] Jacek Warszawa, Poland [email protected] Marcin Warszawa, Poland [email protected] Maciej Warszawa, Poland [email protected] Maciej Kraków, Poland [email protected] Bogdan Warszawa, Poland [email protected]’Callaghan Eimear Bristol, UK Eimear.O’[email protected] Jeremi Kraków, Poland [email protected] Anna Warszawa, Poland [email protected] Katarzyna Kraków, Poland [email protected] Fernando Brasília, Brazil [email protected] Gleb Paris, France [email protected] Grzegorz Kraków, Poland [email protected] Karol A. Paris, France [email protected] Ryszard Opole, Poland [email protected] Mateusz Kielce, Poland [email protected] J. Miguel Barcelona, Spain [email protected] Artem Prague, Czech Republic [email protected] Lutz Berlin, Germany [email protected] Andrzej Warszawa, Poland [email protected]ódmiak Jacek Bydgoszcz, Poland [email protected] Grzegorz Warszawa, Poland [email protected] Igor M. Berlin, Germany [email protected] Jakub Katowice, Poland [email protected] Natanael Kraków, Poland [email protected] Tomasz Kraków, Poland [email protected] Jerzy Kraków, Poland [email protected] Michał Kraków, Poland [email protected] Wojciech Kraków, Poland [email protected] Joanna Warszawa, Poland [email protected] Paulina Katowice, Poland [email protected] Jin Stony Brook, NY, USA [email protected] Piotr Torun, Poland [email protected] Aleksander Wrocław, Poland [email protected] Karina Wrocław, Poland [email protected] Horacio Santander, Spain [email protected] Ryszard Warszawa, Poland [email protected]

41


Index of active participants

Alicki, Robert, 1, 11

Bedeaux, Dick, 1, 9Bełdowski, Piotr, 25Blumen, Alexander, 1, 18

Chialvo, Dante, 3, 16Ciesla, Michał, 25, 26, 39

Deza, Roberto, 2, 20

Ferrari, Franco, 2, 21Ferreira, Rogelma, 27

Gadomski, Adam, 1, 8Grigolini, Paolo, 3, 15Grzywna, Zbigniew J., 1, 6Górska, Katarzyna, 2, 20Górski, Piotr, 27, 28

Holubec, Viktor, 28Hołyst, Janusz A., 3, 23Hänggi, Peter, 3, 16

Kjelstrup, Signe, 1, 10Kosztołowicz, Tadeusz, 1, 19, 29Krawiecki, Andrzej, 2, 20Kułakowski, Krzysztof, 3, 15Kusmierz, Łukasz, 22, 29

Lapeyre, John, 2, 19Lee, Howard, 1, 6Lemarchand, Annie, 1, 19Lewandowska, Katarzyna D., 29Lindenberg, Katja, 2, 13Lisowski, Bartosz, 30Łuczka, Jerzy, 3, 5

Machura, Łukasz, 3, 24Majka, Maciej, 2, 21Metzler, Ralf, 2, 7Miekisz, Jacek, 3, 17Minkowski, Marcin, 30Mrowinski, Maciej, 31

Nowakowski, Bogdan, 1, 11

Ochab, Jeremi, 3, 22Ochab-Marcinek, Anna, 3, 17Oshanin, Gleb, 1, 5

Pajak, Grzegorz, 32–34Penson, Karol A., 2, 14Piwnik, Mateusz, 34

Rubi, Miguel, 1, 10Ryabov, Artem, 35

Schimansky-Geier, Lutz, 2, 13Sikorski, Andrzej, 35Siudem, Grzegorz, 37Siódmiak, Jacek, 36Sokolov, Igor M., 1, 7Spiechowicz, Jakub, 3, 23Srokowski, Tomasz, 2, 14

Tomczyk, Wojciech, 39Toruniewska, Joanna, 37Trybek, Paulina, 38

Wang, Jin, 2, 12Weber, Piotr, 2, 21Weron, Aleksander, 1, 18Wio, Horacio, 2, 13Wojnar, Ryszard, 38

42

28th Marian Smoluchowski Symposium on Statistical PhysicsA

Monday14/09

Tuesday15/09

Wednesday16/09

Thursday17/09

900 - 1120A

G. OshaninZ. GrzywnaM. H. LeeA. WeronA. Blumen

900 - 1130

R. MetzlerJ. WangH. WioJ. LapeyreK. GórskaR. Deza

900 - 1110

K. KułakowskiP. GrigoliniD. ChialvoJ. OchabJ. A. Hołyst

900 - 1100

Pre-poster session

1120 - 1200A

Coffee break1130 - 1200



Coffee break1200 - 1330A

I. M. SokolovA. GadomskiT. Kosztołowicz

1200 - 1305

L. Schimansky-Geier1200 - 1305

P. Hänggi1130 - 1330

Poster session

1330 - 1500A

Lunch1305 - 1500

Lunch1305 - 1500

Lunch1330 - 1500

Lunch andclosing address

1500 - 1700A

D. BedeauxS. KjelstrupJ. M. RubiR. Alicki

1500 - 1630A

K. LindenbergA. KrawieckiF. FerrariM. Majka

1500 - 1600

J. MiekiszA. Ochab-Marcinek

1700 - 1730A



Coffee break1730 - 1820A

B. NowakowskiA. Lemarchand

1700 - 1840

T. SrokowskiK. A. PensonP. WeberŁ. Kusmierz

1630 - 1740

J. ŁuczkaŁ. MachuraJ. Spiechowicz

EveningGet-together

2000 -Banquet

Detailed program pages 1 – 4.Abstracts: invited talks 5 – 17, talks 18 – 24, posters 25 – 39.List of participants 40 – 41. Index 42.Maps 4.

Documents

28th Marian Smoluchowski Symposium on Statistical Physics ...28th Marian Smoluchowski Symposium on Statistical Physics KRAKÓW, POLAND, SEPTEMBER 14–17, 2015 Monday, September 14