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| Invited talks | ||
|---|---|---|
| Sergey Bezrukov | Bethseda, MD | Membrane Channels: Solutions of Diffusion Problems for Single-Molecular Studies |
| Werner Ebeling | Berlin | New developments in the theory of active Brownian motion |
| Adam Gadomski | Bydgoszcz | Kinetics of growth process controlled by
convective fluctuations as
seen by mesoscopic non-equilibrium thermodynamics Abstract: A kinetic model, suitable for growing phenomena of soft-matter type (biopolymers; colloids and surfactants), where the process is controlled by a fluctuating local convective velocity field of the arriving particles, is considered. In contrast to a master-equation approach, inferred as a special case from some application of the mass-conservation law [1], in the present work the consideration is made in terms of mesoscopic nonequilibrium thermodynamics (MNET) [2]. A curvature-dependent thermodynamic potential (an energetic barrier of the process) is derived, and the diffusion function, in a form factorising to a time- as well potential- (or, internal state variable) dependent sub-quantities, is gained. No violation of the detailed balance is assured [2]. Some 'practical cases', concerned with algebraic time-correlations of the above mentioned fluctuating velocity field [1], have been analysed, mostly toward the application of MNET to protein (lysozyme) crystal growth, see [3] and refs. therein. [1] J. Luczka et al. Phys. Rev. E 63, 051401 (2002). [2] D. Reguera, J.M. Rubi, J. Chem. Phys. 115, 7100 (2001); I. Santamaria-Holek, Ph.D. Thesis, University of Barcelona, 2003. [3] A. Gadomski, J. Siodmiak, Cryst. Res. Technol. 37, 281 (2002); P.G. Vekilov, J.I.D. Alexander, Chem Rev. 100, 2061 (2000). |
| Piotr Garbaczewski | Zielona Góra | Dynamics of uncertainty Abstract: Shannon entropy of a given probability distribution is a natural measure of uncertainty, and thus (un) predictability, in procedures of data acquisition for various model systems. A particular attention is paid to the so-called information entropy of a continuous probability distribution and the relationship with its coarse grained version. Classical dynamical, stochastical and quantum systems (in their pure states) in general give rise to time dependent probability densities and information entropies. We addres an issue of suitable balance equations, with emphasis on the information entropy production. In particular, we design a thermodynamical formalism for Markovian diffusion processes. We proceed in the same vein to extract a physical meaning of the information and/or uncertainty dynamics associated with the Schroedinger picture evolution of quantum wave packets. |
| Zbigniew J. Grzywna | Gliwice | On the Smoluchowski Equations Addressed to Polymers Abstract: Two distinguish classes of equations known, as „Smoluchowski equations” will be analysed. First, known as high viscosity limit of Kramers equation describes the process of diffusion with drift and reads: 
(1)where f(•) stands for time, position or probability density dependent drift coefficient. The second, known as „Smoluchowski Coagulation Equation” has a form  (2)where Ki,j is the rate constant of aggregation (coagulation kernel), and describes the second order irreversible aggregation process  (i, j=1, 2, ...) (3)with P, as a unit aggregate. References: 1. Zbigniew J. Grzywna, Jacek K. Stolarczyk, Polimery, 46(5), 351-358, (2001). 2. Zbigniew J.Grzywna, Jacek K. Stolarczyk, International Journal of Modern Physics C, 13(9), 1301 – 1312 (2002). 3. Jacek K. Stolarczyk, Zbigniew J. Grzywna, Krzysztof K.Koziol, Polymer 45, 1525-1532 (2004). 4. Zbigniew J. Grzywna, Anna Michalec, Acta Physica Polonica B, 35(4),1463-1470 (2004). 5. Galina, H., Lechowicz, J.B., Adv. Polym. Sci., 137, 135-172 (1998). 6. H. Risken, The Fokker-Planck Equation, Springer-Verlag Berlin and Heidelberg,1996. 7. M.Doi, S.F.Edwards, Dynamics of polymer solutions, Oxford University Press, 1986. |
| Peter Hänggi | Augsburg | Nonmarkovian Stochastic Resonance |
| Janusz Hołyst | Warszawa | Mean field theory for evolving networks Abstract: Applications of the mean-field approach for scale-free networks are presented. Average path lengths, clustering coefficients, supremacy distributions and spin ordering in such networks are analysed. Analytic results have been compared to extensive numerical simulations finding a very good agreement. |
| Robert Hołyst | Warszawa | Separation process in binary polymer/liquid
crystal mixtures Abstract: The study of growth of polymer domains in liquid crystalline matrices by the static light scattering has been hampered by the multiple scattering of light. Using a well controlled sequence of temperature jumps and quenches we have eliminated this effect. The growth of polymer domains in the smectic and isotropic matrices is governed by diffusion. In the nematic phase it is strongly influenced by the elastic forces. These forces are due to the deformations in the director (orientational field) in the nematic phase. In all cases the scaling law for the scattering intensity is obeyed except at small wave-vectors. We have found out that the latter indicates that during the separation process the bi-continuous network breaks down continuously into separated domains. |
| Jan Iwaniszewski | Toruń | Charge transport through coupled quantum dots
in the presence of dynamical disorder Abstract: Charge transport throught small tunneling structures is of great interest due to the possibility of investigation of single electron effects, as well as due to many prospect applications. Defects with some internal degrees of freedom which are contained in the bulk material, may dynamically modify the structures and their parameters. We consider a simple two-state model of such defect in the problem of charge transport through a system of two coupled quantum dots attached to electron leads. Interaction with the defect causes stochastic variation of system parameters what is mimicked by a dichotomic noise. We discuss the influence of this noise on charge transport through the dots, in particular we describe the phenomena of resonant suppresion and increase of the current for specific values of the correlation time of the noise. |
| Czesław Jędrzejek | Poznań | Models versus reality for selected networking areas Abstract: Internet is an extremely complex system. It involves: constrainsts of IP technology, that was not meant to be real time and is basically best-effort, economy (pricing, many players in a decentralised system, stiff price for meaningful changes), legal and political issues, behavioural issues (human interaction, malicious acts), and deployment issues. All these factors change very quickly, and meaningful measurements of global significance are difficult to be obtained. In such environement, models of small things, preferred by research community, in general, are not sufficient. In addition, some fundamental flows in a research practice contribute to little impact. False perception in late-1990s of underprovisioned backbones with respect to the existing and potential traffic was a significant cause of the Internet bubble. Crucial for Internet functioning are: ability of delivering new services and voice over Internet, and security. Despite 10 years of research and development, technologies perceived to be crucial to achieve this goal: Quality of Service (QoS) and Public Key Infrastructure (PKI), both failed to be widely deployed. In this work relations of assumptions of these technologies to real life issues are analysed. Detailed results for transport latencies are presented using QoS schemes for a software router. Some conclusions on ways of improvement of research versus deployment positioning are given. |
| Joseph Klafter | Tel Aviv | Single Molecule Dynamics |
| Adam Kleczkowski | Cambridge | Parameter estimation and prediction for
the course of a single epidemic Abstract: Predictions in epidemiology are mainly made on the basis of a mean behaviour of an ensemble of replicates. However, in practical applications we are often interested in predicting a course of a disease in a single particular population. Close inspection of many examples of replicate disease progress curves shows that once a trajectory is chosen, the variability is low. In contrast, the between-replicate variability is often very high, resulting in a high degree of unpredictability based on the average behaviour. A prediction of a future course of an epidemic can be based on partial observations of this population and on complete past observations of similar populations. A hierarchical Bayesian approach is a natural choice for a replicate-based prediction method, enabling us to combine partial information about a particular realisation with a behaviour of other realisations. Our paper explores this idea for a set of contrasting population dynamics in which a fungal pathogen, Rhizoctonia solani spreads among plant hosts. We show that even a very limited set of data can be used to narrow down predictions for a development of a single epidemic, even if the variability between individual epidemics is very large. This has profound implications for data collection and analysis as well as for a design of control strategies. We also discuss the relevance of our results in a broader ecological context, particularly for describing invasion and persistence of species. |
| Michał Kurzyński | Poznań | Statistical physics of biological molecular
machines Abstract: Each biological molecular machine can be considered an effective chemo-chemical enzymatic machine occurring in multitude conformational substates. In particular, this statement holds true for the actomyosin motors that drive the animal muscles. A technique is presented with the help of which the machine's flux-force dependences can be expressed in terms of the mean first-passage times in a random movement between some distinguished conformational substates of the enzymatic protein. Relative role of the power stroke and the Brownian ratchet mechanisms in the actomyosin motor action is discussed and a possibility of multiple stepping per one ATP molecule hydrolysed is indicated. |
| M. Howard Lee | Athens, GA | Love in van der Waals equation Abstract: The equation of state bearing the name van der Waals is known to almost everyone in physics. It was proposed in 1873, before the old quantum theory and long before modern statistical mechanics. Yet it has remained a useful and popular model to this date, more than a hundred years later. The main appeal perhaps is its simplicity in describing the gas liquid transition that is not surpassed by the modern theories. Can one say anything new about this model now? Probably not likely except perhaps, put it figuratively, love--almost like a love triangle--contained in a cubic equation that characterizes this model. The solutions are among the loveliest in the literature of cubic equations. |
| Jerzy Łuczka | Katowice | Phase transition in a system of coupled
mesoscopic rings Abstract: I study a generation of non-zero magnetic flux out of unbiased thermal current fluctuations in a collection of identical mesoscopic rings which are coupled via mutual inductances. The influence of thermal Nyquist fluctuations are described in terms of a set of Langevin equations or a corresponding Fokker-Planck equation, respectively. In the limit of infinitely many constituents, the steady-state of the system is determined by a nonlinear, mean field-like Fokker-Planck equation. The system exhibits in this thermodynamic limit a second-order phase transition: the average flux through each cylinder changes continuously from zero to non-zero value and the phase diagram depicts a critical line. |
| Władysław A. Majewski | Gdańsk | Quantization, dynamical maps, entanglement
and all that Abstract: We outline the scheme for quantization of dynamical maps and describe the quantization of correlations as well. Great emphasis will be put on the structure of positive maps and on characterization of states. A relation between these two areas will be discussed. |
| Danuta Makowiec | Gdańsk | New challenges in cellular automata due to
net topology Abstract: Cellular automata are dynamical systems consisting of many interacting automatons which are located at nodes of some regular lattice. Recent discoveries in the real networks properties (e.g. small-world property, power-low distribution of the network node degree) push the interest into the research on how the manipulation in the underlying lattice influence the cellular automata characteristics. The totalistic transition rule is perfectly suited for starting such investigations. We consider features of the global state with respect to the initial state in the cellular automata of the ferromagnetic type on the the square lattice rewired either stochastically or intentionally. The preference means the more linked node is the higher probability to get attract other links is put. Then we study the phenomena known as bootstrap percolation in the cellular automata located on a square lattice where the extra edges are introduces either stochastically or intentionally. We hope that our results could serve an entrance point to remodeling biologically motivated systems such as the network of Hodgkin-Huxley neurons with firing patterns property or the synchronize action of the so-called sine - node : the network of heart cell that build the first natural peacemaker. |
| Fabio Marchesoni | Camerino | Asymmetric Confinement in a Noisy Bistable Device Abstract: A Brownian particle hopping in a symmetric double-well potential can be statistically confined into a single well by the simultaneous action of (a) two periodic input signals, one tilting the minima, the other one modulating the barrier height; (b) an additive and a purely multiplicative random signal, generated by a unique source and thus preserving a certain degree of statistical correlation. In view of technological implementation, such a basic mechanism for asymmetric confinement can be conveniently maximized by tuning the input signal parameters (correlation time, phase/time lag, amplitudes), thus revealing a resonant localization mechanism of wide applicability. |
| Jarosław Piasecki | Warszawa | The Bose gas beyond mean field Abstract: The gas of bosons at thermal equilibrium with purely repulsive pair interaction can be given a polymer representation yielding a classicallike formula for the grand-canonical partition function. A self-consistent relation between the density and the chemical potential can be then derived by the Mayer graph technique. For a low density gas, the Kac scaling of the pair potential permits to determine analytically the dominant corrections to the pressure and to the one-particle density matrix beyond mean field. Open questions concerning the existence and the location of the Bose-Einstein condensation remain a fascinating field of research. |
| Jose Miguel Rubi Capaceti | Barcelona | Nonequilibrium equalities for small systems Abstract: We present a class of nonequilibrium equalities for processes in which work is given to the system whereas it exanges heat and mass with its environment. The framework proposed to that end, based upon the formulation of a mesoscopic thermodynamics, can also be used to analyze the case when the transition of the state of the system takes place when the bath is in a stationary state. In the case of a nucleation process, the corresponding equality reduces to the nucleation theorem. |
| Francesc Sagues | Barcelona | Deterministic vs. stochastic control of 3D
excitation waves Abstract: Autowaves constitute one of the most rewarding examples of self-organizing phenomena in extended active systems. In particular 3D geometries allow the development of complex structures known as "scroll waves". Under particular conditions, scroll waves may undergo intrinsic instabilities leading to highly irregular scenarios of wave propagation. We will concentrate on one such instability mechanisms, which is genuine of weakly excitable media. After describing it, we will discuss two possible mechanisms to tame the wave turbulence episodes it leads to. One is based on a deterministic, time periodic and homogeneous forcing, whereas the second one consists in prescribing a spatiotemporally distributed random modulation of the system's excitability. Implications in relation to some scenarios of cardiac fibrillation will be briefly sketched. |
| Lutz Schimansky-Geier | Berlin | Stochastic Excitable Systems Abstract: Excitability is a wide spread phenomenon in physics and life sciences. Usually this behaviour is modeled by deterministic or stochastic Markovian evolution laws which require at minimum the introduction of two dynamical variables (the activator and the inhibitor) or the consideration of a single variable system with a complicated reset condition. An alternative as often used in neuroscciences is the consideration of a discrete variable with a few states whose evolution is governed by Non Markovian laws defined, for example, by non-exponential waiting time densities in certain states. We show exemplarily how a stochastic FitzHugh-Nagumo dynamics can be mapped on a three state circular Non Markovian model. Two different situations - resonant and non resonant spiking - are considered. For non resonant systems we also apply periodic signals and study stochastic resonance. |
| Zuzanna Siwy | Gainesville, FL | The role of surface charge in transport properties of nanotubes |
| Igor M. Sokolov | Berlin | Epidemics in Heterogeneous Populations: Networks
and Percolation Abstract: Spatial models for spread of an epidemic may be mapped onto bond percolation, immunization of some subjects corresponds to a site percolation problem. The properties of epidemic spreading are thus strongly dependent on the disorder in the strength of contacts between individuals and on the distribution of the number of contacts. In some networks the percolation threshold is zero if the fluctuations in the number of contacts diverge. We consider several models of such networks and discuss the influence of correlations in strength and number of contacts on the percolation properties of such networks and thus on epidemic spreading. |
| Peter Talkner | Augsburg | Rate description of Fokker-Planck processes
with time-dependent parameters Abstract: The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time-dependent parameters such as periodic external forces or slowly fluctuating barriers heights. A criterion is provided under which condition a kinetic description with time-dependent frozen rates applies and non-adiabatic corrections to the frozen rates are given. The presented theory opens the possibility to recover the long-time dynamics of the original continuous process by means of an appropriate random decoration of the discrete states. |
| Tian Yow Tsong | Taipei | Biocatalytic wheel as a Brownian motor,
and its core engine Abstract: I will examine a classical biocatalyst, enzyme, and redress it to form a transducer of the free energy, electric, acoustic, or other types of energy. This modification is necessary to explain many recent experiments in which enzymes are shown to perform, as well, the pump, motor, and locomotion functions resembling that of their macroscopic counterparts. A biocatalyst is a mere rate enhancer but an energy transducer must also be able to extract, store or rectify energy, or perform all these functions in one catalytic turnover. The catalytic wheel will perform all these complex tasks. A Conformational Coupling Model for ion or molecular pumping, and a Barrier Surfing Model for track-guided locomotion or particle transport are examples. The catalytic wheel we have constructed is shown to be a Brownian Motor, and the core engine powering the wheel may be applicable to other bio-molecular devices, and to certain dynamic systems, as well. TY Tsong, CH Chang. Physica A 321:124-138 (2003) Yu A Makhnovskii et al. Phys Rev E 69, 021102 (2004) VM Rozenbaum et al. J Phys Chem In press (2004) TY Tsong, CH Chang. Assoc Asia Pacific Phys Soc Bull 13-2:12-18 http://www.aapps.org/archive/bulletin/vol13/13_2/13_2_p12p18abs.html |
| Karina Weron | Wrocław | Scaling properties of the diffusion process
underlying the Havrilak-Negami model Abstract: We present a generalization of the exponential Debye relaxation based on the continuous-time random walk (CTRW) framework. We show how to modify the random-walk scenario underlying the classical response in order to derive the empirical Havriliak-Negami function, commonly used to fit the experimental relaxation data. The turnover from the exponential Debye to the power-law Havriliak-Negami relaxation response is associated with a new type of a coupled memory CTRW driving a fractional dynamics. |
| Renat M. Yulmetyev | Kazan | Memory effects in Lennard-Jones
liquids Abstract: We report the results of calculation of diffusion coefficients for Lennard-Jones liquids, based on the idea of time-scale invariance of relaxation processes in liquids. The obtained results were compared with the molecular dynamics data for the Lennard-Jones system and a good agreement of our theory with these data over a wide range of densities and temperatures was obtained. By calculations of the non-Markovity parameter we have numerically estimated statistical memory effects of diffusion in detail. |
| Kacper Zalewski | Kraków | Quantum statistics and multiple particle
production Abstract: In high energy scattering processes large sets of identical particles are produced. Effects of the symmetry with respect to permutations are clearly seen in the data. They have been used to extract information about the regions where the hadron production occurs. |
| Jan J. Żebrowski | Warszawa | Observations and modeling of intermittency
and homoclinic orbits Abstract: We are investigating nonlinear instabilities in human heart rate variability. We focus on phenomena with characteristic, easily recognizable features which are well known in physics. We are able to show three groups of evidence. The first is an ever expanding roster of such cases of heart rate variability pathology which exhibit type I intermittency. This phenomenon, known very well from textbooks on chaos theory, occurs in those dynamical systems which have come close to a saddle-node bifurcation. Thus, identification of the type of intermittency may have an important bearing on the modeling of heart rate variability. We show that the differences in the properties of the intermittency found in human heart rate variability may be explained by simple models with dichotomous parameter change and dichotomous noise. We also discuss other types of intermittency that occur in human heart rate variability. The second group of evidence of instabilities are observations of homoclinic orbits and the gluing bifurcation in measured heart rate variability. Finally, we show how using a pair of coupled modified van der Pol Duffing oscillators - we are able to model the behavior of the sino-atrial node and of the atrio-ventricular node (elements of the conduction system of the heart) in such a way as to obtain homoclinic orbits comparable with those measured during the sino-atrial block in a human. |
| Wojciech H. Żurek | Los Alamos | Environment - Assisted Invariance, Ignorance,
and Information in Quantum Physics Abstract: I shall discuss environment - assisted invariance (symmetry exhibited by correlated quantum states) and describe how it can be used to understand the nature of ignorance, and, hence, the origin of probabilities in quantum physics. |
| Lectures | ||
|---|---|---|
| Antoni C. Mitu¶ | Wrocław | Temporal and spatial local-structure - based scales in 2D LJ liquid
Abstract: We discuss the concepts of well-defined spatial and temporal scales related to local solid-like structure in 2D Lennard-Jones liquid. Preliminary results indicate an existence of power-law distributions of sizes of clusters of solid-like atoms and their fractal spatial distribution. Temporal development of those clusters displays a scale approximately two orders of magnitude larger than a typical oscillation time. Those results are discussed in the light of recent studies of short-time thermodynamics in classical liquids. |
| Ryszard Zygadło | Kraków | Two Markovian models leading to the Pascalian
(1D ultrarelativistic) stationary distribution Abstract: The target Pascalian stationary probability density of the linear kinetics is found to be that one which is required for the weights distribution of the driving white shot noise. The quasilinear equation of the corresponding Brownian motion model is analuzed by the use of the probability theory result concerning the first crossing the line by the trajectory of the Wiener process. It is shown that the different sctochastic dynamics can converge to the same equilibrium distribution. |
| Posters | ||
|---|---|---|
| Note: If you are not an invited speaker, you
may also present your contribution during the Symposium, but be prepared to present a
poster unless you have been specifically informed by the organizers that you can
give an oral presentation. Posters accepted by the Organizing Committee may be displayed throughout the Symposium. There will be a pre-poster session, where each poster can be briefly presented by one of the authors. The pre-poster session will run on a "3 by 3" basis: Each contributor to the pre-poster session will have an opportunity to talk for up to 3 (three) minutes and present up to 3 (three) transparencies. No discussion is supposed to take place during the pre-poster session. |
||
| Volodymyr Babin, Robert Hołyst | Warszawa | Evaporation of sub-micrometer
droplets Abstract: Evaporation of a sub-micrometer liquid droplet is studied numerically within the diffuse-interface hydrodynamic model supplemented by the van der Waals equation of state. The system consisting of a droplet and saturated vapor is put in a container with the temperature on the container?s walls kept fixed. Two cases are considered: (i) the temperature is increased only on the walls, and (ii) the temperature is increased in the whole system uniformly. |
| Przemysław Borys, Zbigniew J. Grzywna | Gliwice | A source of diffusion in deterministic
chaotic maps Abstract: In this paper we discuss the transition in chaotic maps, from exponential growth of the variance of particle positions, governed by the Lyapunov exponent to a diffusive growth of various type. Consequences of this transition and ways of generating subdiffusive and superdiffusive behaviors are also discussed. |
| J. Bryła, Teodor Buchner | Warszawa | Analysis of phase space structure of
a 1-D discrete system using global and local symbolic dynamics. Abstract: Symbolic dynamics, in which the system trajectory is represented as a string of symbols, appears as a convenient method for the analysis of properties of chaotic attractors. In this presentation, we show that - using a non-canonical coding scheme based on a moving partition point - we are able to access such properties of the phase space of a dynamical system as the localization of unstable periodic orbits and of their stable invariant manifolds. Applying different coding schemes enables us to obtain different information about the phase space structure. The choice of the coding scheme gives different context to standard tools of symbolic dynamics so may be regarded as a separate method itself. We present results for the 1-D case taking the logistic map as a numerical example. The extension to higher dimension is also discussed. Also the theoretical background of the methods used is given. |
| Marcin Chrenowski | Kraków | Hysteresis in chemical systems Abstract: Hysteresis is a phenomenon which occurs in many physical and chemical systems. It is also present in sociology, economics and many other areas. Recently much attention has been paid to the investigation of 'generic' models of hysteretic phenomena and much progress has been achieved in the mathematical theory of hysteresis. However, most of work on hysteresis in chemical systems is still concentrated on the phenomenological description of the phenomenon, without taking into account recent progress in the mathematical theory. The poster shows possible applications of the Preisach model of hysteresis to the description of adsorption-desorption process in porous media. A simple three-box model for simulation of the process is also proposed. |
| Michał Cie¶la, Lech Longa, Hans-Reiner Trebin | Kraków, Stuttgart | Corrletions in the isotropic phase of chiral liquid crystals. |
| Andrzej Cukrowski, Anna Kolbus | Warszawa | On validity of linear phenomenological nonequilibrium
thermodynamics equations in chemical kinetics Abstract: The chemical equilibrium state is treated as a fundamental "reference frame" in description of chemical reaction. A new definition of chemical potential is introduced in which this equilibrium state is shown to be more important than the typical standard state. In a definition of reactive absolute activities for components in chemical reaction such a chemical potential is used. The chemical reaction rate is shown to be proportional to a thermodynamic force defined as the difference of reactive absolute activities of reactants and products. This new force is shown to be equivalent to the force following from elementary chemical kinetics and is compared with the reduced affinity X as well as with the force of Ross and Mazur X_RM = 1 - exp(-X). The new force coincides with X and X_RM near to the chemical equilibrium state. A range of the molar fraction of product in which a difference between the new force and X is relatively small is much larger than it would be for the forces X_RM and X. It means that for some chemical reactions the formalism of linear nonequilibrium thermodynamics can be used in a wider range than usually expected. Particular analysis is presented for the reaction A + B <--> C + D. |
| Olgierd Cybulski, Volodymyr Babin, Robert Hołyst | Warszawa | Fleming-Viot Processes Abstract: The spontaneous division of space in Fleming-Viot processes is studied in terms of the nonextensive thermodynamics. We analyze a system of N different types of Brownian particles confined in a box. Particles of different types annihilate each other when they come into close contact. This loss of particles is compensated by the duplication of randomly choosen particles of the same type as being annihilated. Thus the total number of particles of each type is kept constant. In the stationary state the system is divided into N separate subregions each occupied by particles of different type. Inside each subregion the particle density distribution minimizes the Renyi entropy production. We show that also sum of these entropy productions in the stationary state is minimized, i.e. the resulting boundaries between different types adopt a configuration which minimizes the total entropy production. Irrespective of the initial conditions the evolution of system leads to decreasing of the total entropy production monotonically in time. However, the stationary state is not always unique - the entropy production may have several local minima for different configurations. We study the coexistence of such metastable states as the function of shape of the box. |
| Sergey Denysov | Dresden | Hamiltonian Ratchets |
| Gabriela Dudek, Przemysław Borys, Zbigniew J. Grzywna | Gliwice | On the way of coding of self similar
aggregates Abstract: In this paper we present the method of the image compression and decompression which base on a piksel array. We also investigate the influence of the noise ratio and quant accuracy on the quality of the images after compression and the compression efficiency. We analyse the microscope images of precious stones, such as: diamond, pearl, emerald, ruby etc; the rock images which come from Mars and the images of herbs, such as plantago lanceolata, plantago major, glechoma hederacea, Mentha xpiperata etc. In the compression scheme, we have also established a probability based method for finding the main building domains of the object. |
| Bartłomiej Dybiec, Ewa Gudowska-Nowak | Kraków | Activation process driven by strongly non-Gaussian noises Abstract: The constructive role of non-Gaussian random fluctuations is studied in the context of the passage over the dichotomously switching potential barrier. Our attention focuses on the interplay of the effects of independent sources of fluctuations: an additive stable noise representing non-equilibrium external random force acting on the system and a fluctuating barrier. In particular, the influence of the structure of stable noises on the mean escape time and on the phenomenon of resonant activation (RA) is investigated. By use of the numerical Monte Carlo method it is documented that the suitable choice of the barrier switching rate and random external fields may produce resonant phenomenon leading to the enhancement of the kinetics and the shortest, most efficient reaction time. |
| Aneta Goska | Warszawa | Chaotic synchronization in coupled oscillators on scale-free networks |
| Paweł F. Góra | Kraków | Population explosion suppressed by noise:
Stationary distributions and how to simulate them Abstract: We show that two dynamical systems exhibiting very different deterministic behaviors have very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically simulating these systems. In particular, we show that there exists a noise level that is optimal in the sense that the interval during which discrete-time versions of the systems remain physical is maximized. Analytical results are illustrated by numerical examples. |
| Andrzej Grabowski | Warszawa | The SIS model of epidemic spreading in a
hierarchical social network Abstract: The phenomenon of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The SIS model with temporal immunity to a disease and a time of incubation, is used. In our model spatial localization of the individuals, effectiveness of different interpersonal interactions, belonging to different social groups and mobility of a contemporary community are taken into account. The structure of interpersonal connections is based on a scale-free network. Typical relations characterizing spreading process like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. Our results are compared with solutions of the Master equation for the spreading process and good agreement of the character of this process is found. |
| Els Heinsalu | Tartu | Pecularities of Brownian motion in tilted
double-periodic potentials Abstract: We study the transport of overdamped Brownian particles in tilted piecewise linear potentials with two barriers per period. In general the transport of particles in doubly periodic potentials has character similar to that in simple potentials, exhibiting at the same time in certain parameter regions qualitatively different features. As the most unexpected result it is found that diffusion coefficient can have two maxima. We show also that in the wide range of tilting force the transport can be realized through two different Poissonian processes, having at a certain tilt an enhancement of the coherence. |
| Krzysztof Iskra, M. Siliszczyk, Michael V. Alania | Siedlce, Tbilisi | Energy spectrum of galactic cosmic
rays long period variations in the turbulent
interplanetary magnetic field Abstract: Based on the modeling and experimental study it is shown that temporal changes of the power rigidity spectrum exponent of galactic cosmic ray intensity long-period variations completely is determined by the dependence of the diffusion coefficient on the structure of the turbulence of the interplanetary magnetic field for minima and maxima epochs of solar activity. Namely, energy range part of the interplanetary magnetic field turbulence for the scope of 2x10-7 - 4x10-6 Hz frequencies is responsible for the formation of the rigidity spectrum of galactic cosmic ray variations registered by neutron monitors. |
| Jan Iwaniszewski, Aleksander Wozinski | Toruń | Ratchets with dichotomic fluctuations - an
analytical approach Abstract: We present an analytical approach to a stochastic ratchet problem. It basis on the partial noise-averaging method which has been proposed recently for the resonant activation problem (JI, PRE 68, 027105 (2003)). We consider fluctuating force and fluctuating potential types of ratchets with fluctuations caused by a dichotomic noise. The obtained approximate formula for stochastic current applies for any value of the noise correlation time $\tau$, and tends to exact results as $\tau\rightarrow 0$ and $\tau\rightarrow\infty$. We compare our results with the exact (for the piecewise linear potential) and numerical results. |
| Paweł Jakubczyk | Warszawa | The influence of droplet size on line
tension Abstract: Within the effective interfacial Hamiltonian approach we evaluate the excess line free energy associated with cylinder-shaped droplets sessile on a stripe-like chemical inhomogeneity of a planar substrate. In the case of short-range intermolecular forces the droplet morphology and the corresponding expression for the line tension - which includes the inhomogeneity finite width effects - are derived and discussed as functions of temperature and increasing width. The width-dependent contributions to the line tension change their structure at the stripe wetting temperature T_W1: for T |
| Wojciech Józefowicz, Lech Longa | Kraków | Monte Carlo Simulation of chiral Gay-Berne system. |
| Agnieszka Jurlewicz, Bożena Szabat | Wrocław | Temperature Dependent Cluster Model of the Cole-Davidson
Relaxation Response Abstract: Some new theoretical results regarding the glass transition for both ''strong'' and ''fragile'' glassy systems are presented. We propose a way to pass from the Debye to the Cole-Davidson response based on the probabilistic cluster model of the relaxation phenomenon. We show that random characteristics of the relaxation contributions of the individual clusters to both responses can be substituted by deterministic quantities describing the average relaxation rate ${\cal B}(T)$ and the average cluster size ${\cal N}(T)$. We discuss the explicit forms of ${\cal B}(T)$ and ${\cal N}(T)$ as the functions of temperature $T$ that result from the behaviour of the loss peak frequency $\omega_{p}(T)$ for the relaxing system. |
| Adam Kleczkowski, Bartłomiej Dybiec, Christopher Gilligan | Cambridge, Kraków | Controlling disease spread on networks with incomplete knowledge Abstract: Models for control of highly infectious diseases on local, small-world and scale-free networks are considered, with only partial information accessible about the status of individuals and their connections. We consider a case when individuals can be infectious before producing symptoms and thus before detection. |
| Nickolay Korabel | Dresden | Fractal anomalous diffusion in intermittent dynamical systems Abstract: Fractal anomalous diffusion in intermittent dynamical systems presentation_abstract = Generalised diffusion coefficient (GDC) is investigated for a class of nonlinear deterministic maps generating sub-diffusion. We show that GDC has a non-monotonic, irregular dependence on a control parameters of the map on all scales. We give qualitative explanation of the observed phenomenon. Continuous time random walk (CTRW) theory is sutably modefied to capture the coarse behaviour of GDC. The probability density function (PDF) for such processes has complex structure while on a coarse scale is governed by a time fractional diffusion equation. We find a good quantitative agreement between analytical coarse grained PDF with numerically obtained value of the GDC and experimental PDF. The phase transition from normal to anomalous diffusion is shown to be accompanied with the suppression of the generalized diffusion coefficient. |
| Tadeusz Kosztołowicz | Kielce | From the solutions of diffusion equation to the solutions of subdiffusive
one Abstract: Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation with fractional time derivative. The Green's functions satisfy the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentartion profiles in a multi-part system where different kinds of transport occurs in each part of it. As an example, we find the solution of subdiffusive equation for the system composed of two parts with normal diffusion and subdiffusion. |
| Małgorzata Kotulska, Stanisława Koronkiewicz, Sławomir Kalinowski | Wrocław, Olsztyn | Sensitivity of $1/f^\alpha$ noise
from electro-nanopores in BLM to chemical environment Abstract: Random fluctuations of nanopores produce two types of response, noise with Lorentzian spectrum $S(f)\sim f^{-2}$ and flicker noise (FN) with spectral density $S(f)=A\gamma_O^2/f^\alpha$, $A=S(1 Hz)/\gamma_O^2$, where $\alpha\not=2$, $A$ is the Hooge parameter and $\gamma_O$ is the open state conductance. The first characteristics can be modeled by a dichotomous Markov process in the pore. FN is more difficult to explain in terms of a simple Markovian model, without assuming the power-law distribution of the relaxation times in the two-state Markov process. It is studied if the stochastic process of the pore fluctuations, expressed by Hooge parameter A and the FN exponent $\alpha$, may provide information about the chemical environment of the pore. The discrete two-state Markov model has been tested on the nanopores generated in BLM by electrical current. The study showed that FN may result from fluctuations with continuous distribution of the conductivity states, which contradicts the two-state Markov models. Sensitivity of the characteristics to ionic strength of the electrolyte confirmed results from other nanopores, displaying correlations between various parameters. Cholesterol in BLM showed minor influence on the stochastic characteristics of the pore. |
| Małgorzata Krawczyk | Kraków | Gel electrophoresis of DNA - new measurements
and the particle model Abstract: Recent data are reported on the velocity v and the diffusion coefficient D of long, linear molecules of DNA in an electrophoretic experiment. The results are compared with those of computer simulations within the particle model of Barkema and Newman. Experimental facts, i.e. an increase of v and D with the field intensity - are reproduced in the calculations. The range of field is identified where the geometration effect appears. |
| Andrzej Krawiecki | Warszawa | Dynamic phase transition in the Ising model
on a scale-free network |
| Lech Longa, Piotr Grzybowski, Silvano Romano, E. Virga | Kraków, Padova | Minimal Coupling Model of Biaxial Nematic Phase |
| Marek Litniewski | Warszawa | On the applicability of the Smoluchowski approach to diffusion controlled rections the molecular dynamics simultions and theory. |
| Marcin Magdziarz, Aleksander Weron | Wrocław | Ornstein-Uhlenbeck processes with Levy noise via fractional calculus Abstract: We consider three types of fractional differential equations with Levy Noise. Obtained solutions have Long Range Dependence (LRD) property and heavy tails. As a special case we study fractional Langevin equations and properties of their solutions. It leads to a correction of a recent paper "Generalized Ornstein-Uhlenbeck processes and associated self-similar processes", J.Phys.A:Math.Gen.36(2003),3961 by S.C.Lim and S.V.Muniady. We have employed the approximation of the generalized Mittag-Leffler function. As a byproduct we obtain a new type Vasicek model of term structure in finance. |
| Anna Michalec, Zbigniew J. Grzywna | Gliwice | On the possible stochastic processes behind the Generalized Smoluchowski Equation Abstract: The Generalized Class of Uni-dimensional Smoluchowski Equations $$W_t = -cf(\cdot)W_x + D(\cdot)W_{xx}$$ where $(\cdot)$ stans for time position or probability density dependence, and their respective Langevin equations, is considered. Possible generalizations of Orstein-Uhlenbeck process and its nature is analysed based on comparison between Langevin solution and velocity fields obtained elsewhere [1]. [1] Zbigniew J. Grzywna, Anna Michalec, Acta Physica Polonica B35, 1463 (2004). |
| Renata Modzelewska, A. Gil, Krzysztof Iskra, Michael V. Alania | Siedlce, Tbilisi | On anisotropy of galactic cosmic rays
in the regular and stochastic interplanetary magnetic field Abstract: 27-day variations of galactic cosmic rays (GCR) intensity and anisotropy have been studied for different the qA>0 and the qA<0 solar magnetic cycles. It is shown that for the minima epochs of the qA>0 cycles the amplitudes of the 27-day variations of intensity and anisotropy of GCR are significantly greater than that for the qA<0 solar magnetic cycle. Results of the solutions of the Parker's transport equation and obtained from the experimental data are in a good agreement in the energy range of GCR registered by neutron monitors (1-35 GeV) on the Earth surface. An interpretation based on the modern theory of GCR propagation has been suggested. |
| Rafael Morgado Silva, Lech Longa | Brasilia, Kraków | Synchronization on non-linear systems with memory |
| Mariusz Niemiec, Wiesław Olchawa, Jerzy Łuczka | Opole, Katowice | Growth process controlled by convective velocity field - fluctuations in time and in space |
| Anna Ochab-Marcinek | Kraków | Pattern Formation in A Stochastic Model of Population Growth |
| Marco Patriarca, E. Szelestey, Els Heinsalu | Helsinki, Tartu | Langevin description of dislocation dynamics Abstract: The Langevin description of dislocation dynamics is used to describe a dislocation moving in the periodic Peierls potential due to the lattice structure and under the action of an external applied stress. The system is studied numerically in various parameter ranges. Differences and analogies with the problem of a Brownian particle in a tilted periodic potential are discussed. |
| Paweł Pa¶ciak, Krzysztof Kułakowski, Ewa Gudowska-Nowak | Kraków | Diffusion coefficient in an electrophoretic ratchet Abstract: For molecules moving in an asymmetrical but periodic potential under the action of fluctuations, a net drift can be observed even if the applied force is zero. Here we use the cellular-automaton-particle model to simulate the gel electrophoresis of DNA under the action of zero-integrated electric field. The applied field is piecewise-constant with a zero time-average. Mean electrophoretic velocity of DNA chains varies as a function of pulse duration and exhibits a characteristic maximum. The same approach is used to investigate the diffusion coefficient and its dependence on field frequency. Our studies demonstrate a simple ratchet-type mechanism which can be used in electrophoretic separation processes. |
| Otto Reifert, Antoni C. Mitu¶ | Wolfsburg, Wrocław | Law of corresponding states and boundary of
locally ordered condensed matter in 2D Lennard-Jones system Abstract: We analyze the boundary (in temperature - density and pressure - temperature variables) of an existence of locally solid-like ordered clusters in 2D Lennard-Jones liquid. The border line p(T) forms a natural continuation of liquid-gas coexistence line beyond the critical point. The closely related concept of a law of corresponding states for the concentration of local solid-like atoms is discussed. |
| Piotr Romiszowski, Andrzej Sikorski | Warszawa | Computer Simulations of Adsorbed Polymer Chains Abstract: We studied the properties of simple models of linear and star-branched polymer chains adsorbed on a flat surface. The polymer model chains were constructed of identical united atoms (homopolymers) and were restricted to a simple cubic lattice. Three different macromolecular architectures of the chain: linear, star-branched with 3 branches of equal length and cyclic (ring) polymers were studied. We employed the excluded volume as the only intrachain potential introduced into the model. The model chains were adsorbed on an impenetrable surface with the lateral motions possible. In the Monte Carlo simulation algorithm the conformation of a polymer chain was randomly changed using a set of micromodifications. We carried out series of simulations for chains of different lengths in a wide temperature range. It was shown that a transition from a three-dimensional chain (weak adsorption) to an almost two-dimensional case (strong adsorption) was observed. The structure and the dynamics of the model chains were determined. Results show that the ring polymers are more adsorbed than the linear and star-branched chains of the same length at the same temperature. |
| Krzysztof Sadlej | Warszawa | Microstructure of a dilute sedimenting suspension |
| Andrzej Sikorski, Piotr Romiszowski | Warszawa | Simple model of a polypeptide chain translocation through
a pore Abstract: In this work we studied a simple model of a polypeptide chain escaping from a confinement. Each amino acid residue of the model chain was represented by an united atom located at the of alpha carbon position. The model chain was restricted to a flexible [310] lattice. The binary potential introduced into the model consisted of the long-range contact interaction between a pair of amino acid residues and the excluded volume. The formation of the secondary structures (a-helices) was enhanced by the introduction of a local helical potential. The chains were built of hydrophilic (P) and hydrophobic (H) residues and the polypeptides consisted of heptets -HHPPHPP-. In the Monte Carlo simulations we used a Metropolis-like sampling algorithm. The main object of the simulation was the process of translocation of the chain through a hole (a pore) in an impenetrable surface. The influence of the chain length, the size of the hole and the strength of the helical potential on the translocation process were investigated. It was found that the translocation time of the chain depends mainly on the size of the coiled chain and scales roughly quadratic with its length. |
| Mariusz Sozański | Warszawa | Statistical and dynamical measures of simple
irreversible processes Abstract: A simple model of an irreversible process is introduced in the form of an iterated map. The model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a computer random number generator) or a deterministic process (e.g. the tent map). We compare the time series obtained from the above implementations of the model using statistical methods (such as DFA). The conclusion is that using statistical methods the two versions of the model are indistinguishable. The advantage of this observation is that we may calculate the Lyapunov exponent for the model. As a result we obtain an equation relating the DFA exponents (a statistical measure) with the Lyapunov exponent for such models. On the other hand, typical statistical properties can also be calculated, as - for example - the diffusion coefficient (using the Green-Kubo method for one-dimensional maps) for a particle, the movement of which is defined by the above model. |
| Mariusz Sozański, Jan J. Żebrowski | Warszawa | On the application of DFA to the analysis of
unimodal maps Abstract: Chaotic time series obtained from simple dynamical systems (the tent map and the logistic map) are analyzed by means of Detrended Fluctuation Analysis (DFA) a widely used method for quantifying long-range correlations in time series obtained from complex systems. The first conclusion is that time series obtained from stochastic (noise-driven) and deterministic systems may be indistinguishable using the DFA method. We introduce the adaptive DFA exponent and show that it is related to the structure of the periodic orbit. We discuss the meaning of persistence and antipersistence in the context of deterministic series. For chaotic time series, we find that only a large level of additive noise can alter the short-range DFA exponent. Finally, a relation between the DFA exponents and the control parameter of the map is studied. We show that DFA is sensitive to different kinds of nonlinear transitions (such as crisis). |
| Jacek Szkutnik | Kraków | Stick-slip to steady slip transition in the Rice-Ruina
model Abstract: We analyze the Rice-Ruina state and rate dependent friction model. The system consists of a mass body driven by a spring with constant velocity on a dry, rough surface. Two regimes of motion are observed: stick-slip and steady sliding. The stability of the steady sliding depends on the model parameters. Numerical and analytical results show a transition between two regimes. Hopf-like oscillations are not observed: the system passes directly from uniform to stick slip motion. The calculations are performed also for two driven masses. Then, the transition has the same character and it appears at the same point. |
| Marcin Tabaka, Jose Maria Sancho, Francesc Sagues | Kraków, Barcelona | Coherence Resonance in a Spatially Extended System Abstract: There are many examples demonstrating that noise can lead to ordered behavior in nonlinear systems. The representative examples of these phenomena are stochastic resonance, the effects of noise-induced order and coherence resonance. We study numerically an excitable two-dimensional system described by the FitzHugh-Nagumo model under external noisy driving. The presence of noise activated waves in the system. The coherence resonance has been also observed; we obtained it for the spatially extended system, while most of previous research on that phenomenon concerned homogeneous or point systems. |
| Anna Wawrzyńczak, Michael V. Alania | Siedlce, Tbilisi | Short period fluctuations of galactic
cosmic rays intensity during the forbush effect Abstract: Fluctuations of galactic cosmic rays (GCR) intensity during the sporadic and recurrent changes caused by shock waves and magnetic clouds in the interplanetary space based on the neutron monitor's 1-5 minutes data have been studied. These various types of decreases of GCR, called Forbush effects, are results of the existence of the shock waves and magnetic clouds in interplanetary space created after the solar flares very often accompanied by solar coronal mass ejecta (CME). In connection with these the stochastic changes of the interplanetary magnetic field (IMF) strength in the large range of the frequencies, (10-7 - 10-5 ) Hz. based on in situ measurements in the interplanetary space have been investigated as well. It is shown that for many Forbush effects of GCR intensity the distributions of the reliable signals corresponding to various range of the frequencies observed by neutron monitors are different for the beginning, decreasing and recovery periods indicating about the structural changes of the IMF; a significant changes in the IMF's structure has been revealed mostly for the By and Bz components of the IMF. |
| Marek Wolf | Wrocław | Random Walk on prime numbers Abstract: The one-dimensional random walk (RW), where steps up and down are performed according to the occurence of special primes, is defined. Some quantities characterizing RW are investigated. The mean fluctuation function $F(l)$ displays perfect power law dependence $F(l)\sim l^{1/2}$ indicating that the defined RW is not correlated. The number of returns of this special RW to the origin is investigated. It turns out, that this {\it single}, very special, realization of RW is typical one in the sense, that the usual characteristics used to measure RW, take the values close to the ones averaged over {\it all} random walks. This fact suggests that random numbers of good quality could be obtained by means of RW on prime numbers. The fractal structure on the subset of primes is also found. |
| Ryszard Zygadło | Kraków | Martingale integrals over Poissonian processes
and the Ito-type equations with white shot noise Abstract: The construction of the Ito-type stochastic integrals and differential equations for compound Poisson processes is provided. The general martingale and nonanticipating properties of the ordinary (Gaussian) Ito theory are conserved. These properties appear particularly important if the stochastic description has to be proposed according to the games theory or the linear relaxation (or the exponential growth) requirements. In contrast to the ordinary Ito theory the (uncorrelated) parametric fluctuation of a definite sign can be still modelled by asymmetric white shot noises, so the general scope of applications is not restricted by the positivity requirements. The possible use of the developed formalism in econophysics is addressed. |
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