| Invited lectures | ||
| Marcel Ausloos | Liege | Foreign currency exchange rates and stock market
indices: a short introduction to Patterns, Trends, Predictions,
Scaling Laws, Models, Strategies... Abstarct: Two topics pertaining to financial data analysis are discussed from a numerical and physical point of view. The analysis requests to find out whether coherent or/and random sequences exist in financial fluctuations. The scaling regime(s) is(are) found when possible. First, the extended detrended fluctuation analysis method allows an analysis of foreign exchange currency rates. The distribution of fluctuations of the exchange rates for EUR with respect to various currencies is shown to be Gaussian only for the central part of the distribution, and have fat tails for the large size fluctuations. For the period between Jan. 1995 and Jan. 1999, the time-dependent exponent of these exchange rate fluctuations for EUR and that of the 11 currencies which form the EUR can be studied. Next, daily data of the DJIA and the S&P500 are used in a search of predictors for crash days. The mean index "divergence" and the index oscillation "convergence" are calculated. The case of rallies, the fluctuations before and after crashes and rallies are discussed in the framework of the sand pile avalanches model. Considerations on avoiding stock market crashes are given as conclusions. |
| Sergey Bezrukov | Bethseda, MD | Ion channels, negative resistance, and sensory
signals Abstract: |
| Yves Elskens | Marseille | Transport in wave-particle hamiltonian systems Abstract: The analytical calculation of transport for a chaotic motion is a longstanding issue. As yet it has been limited to special symplectic maps [1], and to the chaotic motion of a particle in a set of longitudinal waves with random phases, having all the same wave-number and large amplitude [2-4]. The universality of the latter model will be shown for a quite general set of longitudinal waves with random phases. The main property of chaos to matter is the non-confinement of a chaotic orbit in velocity. The particle experiences first a non-chaotic quasilinear diffusion, then a chaotic one. If the wave amplitudes are large enough, the chaotic regime merges with the initial quasilinear regime. The technique applied here in the case of prescribed waves may be applied to other chaotic transport encountered in various fields of physics. Bibliography:
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| Z. Farkas, I. Derenyi, T. Fulop, and T. Vicsek | Budapest | Dynamics of biopolymers: Application to DNA
translocation throug a pore Abstract: The dynamics of polymer translocation through a pore has been the subject of interesting recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations in 3D to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double spiral (pulling this bead with the help of an optical tweezer). We focused on several questions: i) What are the actual forces (of dynamic and entropic origin) acting between the parts of the pore-wall-bead complex, ii) what are the pulling mechanisms iii) and how the dynamics of the uptake is modified by the bead attached to the end of the DNA. Our theoretical estimates and computer simulations suggest a new interpretation of the experimental observations. In addition, Our approach allows testing various existing hypotheses on the dynamics of translocation of DNA through a hole as well as on the forces arising when biopolymers are pulled. |
| Henrik Flyvbjerg | Copenhagen | Calibrating an Optical Trap Abstract: We want to study the diffusion, if that is what it is, of an ion channel in E.coli by monitoring the movement of a small bead attached to the channel and held in an optical trap. What we see is the bead. What we measure is the bead's motion while part of the larger system. What we want is information about the ion channels motion. To deduce that, we need precision measurements, i.e., a good calibration of the bead-in-trap system. That is just an overdamped harmonic oscillator at finite temperature, right? Well, it is a little more complicated. |
| Tomasz Kapitaniak | Łódź | Route to hyperchaos Abstract: Chaotic attractor becomes hyperchaotic when the second Lyapunov exponent becomes positive. Hyperchaotic attractors are common in higher-dimensional dynamical systems (at least two-dimensional map or four-dimensional flow). Chaos-hyperchaos transition is mediated by the changes in the stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor. Bifurcations of unstable periodic orbits occur in the neighborhood of the chaos-hyperchaos transition point where we observe unstable variable dimensionality i.e., the second transient Lyapunov exponent oscillates around zero. We give evidence that the chaos-hyperchaos transition is initiated by (i) the saddle-repeller bifurcation of a particular unstable periodic orbit usually of low period, (ii) appearance of repelling node in the saddle-node bifurcation after which the chaotic attractor becomes riddled, (iii) absorption of the repeller (unstable node or focus) originally located out of the attractor by the growing attractor. |
| Joseph Klafter | Tel Aviv | Anomaly and Strong Anomaly in Diffusion Processes Abstract: Several aspects of anomalous diffusion and their relationship to Levy flights and walks will be reviewd. The basic ideas of Levy walks will be summarized within the continuous time random walk (CTRW) approach. Emphasis will be put on the ballistic-localized motion dichotomy and on Sinai-type diffusion using iterated maps as examples. |
| Stefan Linz, Martin Raible, Peter Hanggi | Augsburg | Stochastic field equations for amorphous film growth |
| Thomas Lux | Kiel | The Multi-Fractal Model of Asset Returns: f(alpha) and GMM Estimation Abstract: |
| Ralf Metzler | Cambridge, MA | Anomalous transport and fractional dynamics Abstract: We introduce a generalised Fokker-Planck framework for systems that are governed by a scale-free power-law memory. From the continuous time Chapman-Kolmogorov equation, we derive the generalisation of the phase space Klein-Kramers equation that exhibits a fractional time derivative. From this, fractional analogues of the Rayleigh and Smoluchowski equation are obtained. The main characteristic is the occurrence of Mittag-Leffler relaxation that replaces the traditional exponential relaxation of modes and that interpolates between an initial stretched exponential law and a final power-law decay. We visualize the changes that arise due to the presence of the memory for the fractional Ornstein Uhlenbeck process. It is shown that fractional dynamics is a natural generalisation of the classical equations that arise in the Brownian case. |
| Pal Ormos | Szeged | Conformational motions and proton pumping in bacteriorhodopsin Abstract: |
| Juan M. R. Parrondo | Madrid | Paradoxical gambling games based on Brownian
ratchets Abstract: Two loosing gambling games can yield, when played alternately, a steady increase of capital. These games have been inspired by the functioning of flashing ratchets. They point out that result of the alternation of stochastic dynamics can be unexpected. In the seminar, I will present and discuss the original paradox and some of its variants, and how are the games related with Brownian motors. |
| Kazimierz Sobczyk | Warszawa | Stochastic dynamical systems and maximum information entropy method Abstract: In the lecture the most essential features and recent problems of stochastic nonlinear dynamics will be presented with emphasis on methods and results obtained very recently. Starting from the historical origins of stochastic dynamics (the Langevin equation for a Brownian praticle), the general stochastic governing equations for a wide class of physical systems are presented and interpreted (e.g. regular stochastic systems, Ito/Stratonovich equations, stochastic equations in Hilbert space). The most notable qualitative and quantitative methods for stochastic nonlinear systems are expounded and illustrated; for example, the existence and uniqueness theorem and its restrictions, explosions of solutions, Khasminski limit theorem (stochastic averaging method), stationary solutions, noise-induced phase transitions, and stochastic bifurcations. In the second part of the lecture the extension of the method of maximum entropy (introduced first in statistical physics for simple situations - Jaynes (1957)) to general stochastic systems is presented and illustrated numerically. Bibliography:
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| Sorin Solomon | Jerusalem | Why was the Pareto Individual Wealth Distribution
constant for the the last 100 troubled years? Abstract: Using the Generalised Lotka Volterra (GLV) model adapted to deal with multi agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a "fair" market, the wealth distribution among individual investors fulfills a power law. We then argue that "fair play" for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent $\alpha \sim 3/2$. In particular we relate it to the average number of individuals L depending on the average wealth: $\alpha \sim L/(L-1)$. Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent $\beta \sim \alpha \sim 3/2$. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order $\gamma \sim 2 \alpha \sim 3$. These results are consistent with recent experimental measurements of these power law exponents ([Maslov and Mills 2001] for $\beta$ and [Gopikrishnan et al. 1999] for $\gamma$). |
| Walter Strunz | Essen | Stochastic Schroedinger equation for quantum
Brownian motion Abstract: Quantum Brownian motion is most often described in terms of the evolution of the reduced density operator. Here we present an alternative approach leading to a stochastic equation for a state vector of the Brownian particle. The reduced density operator is recovered as the ensemble mean over these pure states. Remarkably, in the classical limit, the solutions of the stochastic Schroedinger equation are well localized wave packets whose centroids follow the corresponding classical Langevin equation. |
| Peter Talkner | Villingen | Power spectrum, detrended fluctuations analysis and Hurst analysis:
Application to daily meteorological parameters of last century Abstract: |
| Tamas Vicsek | Budapest | "Statistical physics" of social
groups Abstract: The interpretation of collective human behavior represents a great challenge for social sciences. Here we discuss an emerging approach to this problem based on the exact methods of statistical physics. We demonstrate that in cases when the interactions between the members of a group are relatively well defined (e.g, pedestrian traffic, network formation, synchronization, panic, etc) the corresponding many particle models reproduce relevant aspects of the observed phenomena. Simulating models in a computer has the following advantages: i) by changing the parameters different situations can easily be created ii) the results of an intervention can be prognosed and iii) more efficient design of the conditions for the optimal outcome can be assisted. In addition to possible applications, our approach is useful in providing a deeper insight into the details of the mechanisms determining collective phenomena occurring in social groups. |
| Eli Zlotkin | Jerusalem | Neurotoxic polypeptides as a model pesticide Abstract: AaIT is an insect selective neurotoxic polypeptide derived from scorpion venom. The fast excitatory paralysis induced by AaIT is a result of a presynaptic effect, due to an exclusive and specific perturbation of sodium conductance as a consequence of toxin binding to external loops of the insect voltage gated sodium channel [VGSC] and modification of its gating mechanism. A recent genetic-molecular approach using a mammal-insect chimeric gene construct of the sodium channel enabled the localization of AaIT's target site on the insect VGSC. With the above pharmacological background our presentation will be focused on certain practical agrotechnical aspects: Firstly, the toxin serves as a factor for the genetic engineering of insect infective baculoviruses, resulting in potent and selective bioinsecticides. The efficacy of the AaIT-expressing recombinant baculovirus is attributed mainly to its ability to continuously provide and translocate the gene of the expressed toxin to the insect central nervous system. Secondly, the toxin may serve as a device for insecticide resistance management based on the pharmacological flexibility of the insect VGSC as revealed by the occurrence of an allosteric antagonism (or negative cross resistance) between the AaIT and certain sodium channel insecticides (pyrethroides). Channel mutations conferring resistance to pyrethroids (KDR-phenomenon) may greatly increase susceptibility to the AaIT-expressing bioinsecticides. Thus it is offered to employ either a simultaneous or an alternate application of allosterically coupled pairs of antagonistic (or negatively cross resisting) toxicants instead of constantly developing new classes of insecticides. |
| Lectures and oral presentations | ||
| Adam Gadomski | Bydgoszcz | Macromolecular crustalization in electrolyte:
How to try to deal with? Abstract: An experimentally-supported scenario on how macromolecules may crystallize in an elecrolyte has been drawn. It is assumed that the crystallization proceeds in a mass-convection regime, i.e. being driven by a constant electrostatic force up to the double-layer possibly of Stern type surrounding the growing crystal. All the subtleties of the scenario proposed are assigned to the electrostatic double-layer surrounding the crystal under growth which stands for the so-called active zone of the growing object, being for simplicity assumed to be (quasi)spherical. In the offerd modelling there is at least a place of performing stability analysis for the growing process as well as including a noise as reasonable perturbation of the otherwise deterministic growing conditions. There is perhaps a place of applying time-temperature equivalence principle characteristic of (bio)polymeric systems of partial (dis)order. |
| Piotr Garbaczewski | Zielona Góra | Signatures of randomness in quantum chaos Abstract: We give a detailed discussion of universal probability laws and associated with them parametric stochastic processes that appear to underlie so-called generic level-spacing probability distributions (appropriate for GOE, GUE and GSE universality classes in quantum chaos). We demonstrate that a well defined family of radial Ornstein-Uhlenbeck processes displays an ergodic behaviour deriving from the existence of asymptotic invariant probability densities. All known universality classes are covered by this argument. Novel universality classes are predicted on that basis as well. A common feature of those parametric processes is an asymptotic balance between the radial (Bessel-type) repulsion and the harmonic attraction as manifested in the general form of forward drifts $b(x) = {{N-1}\over {2x}} - x$, ($N =2,3,5$ correspond respectively to the GOE, GUE and GSE cases). |
| J. A. Hołyst, W. Just, E. Reibold, H. Benner, K. Kacperski, P. Fronczak | Warszawa | Limits of chaos control Abstract: Chaos control by time - delayed feedback method is analysed in details. It is shown analytically that a single delay term can stabilised only such unstable periodic orbits that fulfil the relation (( < 2 where ( is the largest Lapunov exponent while ( is the period of the stabilised orbit. To overcome this limit and control longer or more unstable orbits one needs to use several or even an infinite number of control delays terms. Another limitation of control possibilities are stable branches of Lapunov exponents that can become unstable as the control force is applied. Numerical simulations and experimental data with diode resonator confirm results of our analytic investigations. Bibliography:
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| Annie Lemarchand, Bogdan Nowakowski | Paris, Warszawa | Stochastic effects in a thermochemical system with Newtonian cooling Abstract: In order to improve the mesoscopic description of thermochemical systems, we build a new master equation including the stochastic modeling of energy transfer. We give the explicit expression of the master equation in the case of Semenov model for explosive reaction and Newtonian heat exchange with the walls of the reactor. It has a complicated integro-differential form taking into account the continuous spectrum of possible temperature transitions due to Newtonian cooling. Contrary to the previous derivations of master equations for exothermal reactions [G. Nicolis and M. Malek Mansour, Phys. Rev. A 29, 2845 (1984)], our approach does not require any matching to the deterministic description in the macroscopic limit. The main hypothesis on which our mesoscopic approach relies is the assumed Maxwellian form of the particle velocity distribution. The good agreement between the results deduced from Monte Carlo simulations of the master equation and from simulations (DSMC) of the microscopic particle dynamics allows us to validate the mesoscopic description we propose for conditions preserving the Maxwellian character of velocity distribution. In the parameter domain where Semenov model admits a single stationary state and in the vicinity of the bifurcation associated with the emergence of bistability, the master equation allows us to quantify the dispersion of induction times as a function of system size. Marked stochastic effects are observed in connection with the existence of transient bimodality [G. Nicolis and F. Baras, J. Stat. Phys. 48, 1071 (1987)] for the probability distribution of temperature. |
| Jerzy Łuczka | Katowice | Interacting Brownian motors driven by dichotomic fluctuations |
| Jarosław Piasecki | Warszawa | Drift velocity induced by collisions Abstract: We consider the motion of a hard point separating two semi-infinite subvolumes of a hard point gas. The partitionning tagged particel is mechanically identical to the particles of the surrounding gas. At the initial moment it is at rest having to the right and to the left of it gases in thermodynamic equilibrium. Its furthetr stochastic motion, entirely induced by collisions, can be detrmined rigorously. It turns out that in the case of equal initial pressures the tagged particle acquires asymptotically a drift velocit oriented towards the higher temperature region. There is no drift if the temperatures and densities combine to produce on both sides equal particle fluxes. Although the qualitative agreement with Boltzmann's theory is found, the Boltzmann equation does not predict correctly the thermodynamic conditions under which the drift vanishes. |
| Bogdan Stec | Houston, TX | Protein function and glassy state of matter |
| J. Stolarczyk, and Z. J. Grzywna | Gliwice | On the application of PIFS-SF to dendrites analysis. |
| Posters | ||
| M. V. Alania | Siedlce | Investigation of stochastic variation of galactic
cosmic ray intensity based on the experimental data and theoretical
modeling Abstract: Data of interplanetary magnetic field, solar wind velocity and intensity of galactic cosmic rays obtained by satellites and ground neutron monitors have been used to study short and long period fluctuations of all above mentioned parameters and theirs interrelationships. Stochastic nature of the structure of the interplanetary magnetic field and solar wind velocity is well pronounced (almost directly without any time delay) in the changes of the intensity of galactic cosmic rays for relatively high frequencies of turbulence ( 10-2-10-4) Hz), while in the region of the lower frequencies (10-5-10-7) Hz there is observed some retarding caused by the propagation of solar wind with the velocity much less than the diffusive velocity of galactic cosmic ray particles. To describe the regime of the interplanetary magnetic field fluctuations and its role in the galactic cosmic rays intensity fluctuations the Fokker-Planck equation and the Parker's transport equation with drift and adiabatic cooling of cosmic particles have been used for different epochs of solar activity. Besides of the analytical solutions which are possible for the much simplified cases the numerical solutions of Parker's full transport equation with diffusion, convection, drift and adiabatic cooling of galactic cosmic ray particles are considered. |
| K. Bochenek | Kraków | Electronic properties of random polymers: Why are the melanines black? |
| H. Busch | Darmstadt | The effect of colored noise on networks of nonlinear oscillators Abstract: We discuss noise-induced pattern formation in different two-dimensional networks of nonlinear oscillators, namely a sequence of biochemical reactions and the Lorenz system. The main focus of the work is on the dependence of these patterns on the correlation time (i.e. the color) of exponentially correlated Gaussian noise. It is seen that in the non-chaotic case the homogeneity (or average cluster size) goes through a minimum with higher correlation time, while in its chaotic regime the Lorenz system shows a higher degree of synchronization, when the correlation time of the noise is increased. In order to elucidate the origin of this phenomenon, the effect of colored noise on the individual oscillator is investigated. It is shown that the specific dependence of the network's homogeneity on the noise correlation time arises from an interplay of the collective behavior and the properties of the single oscillators. |
| D. di Caprio, J. Stafiej, and J. P. Badiali | Paris and Warszawa | Electric variable fluctuations in interfacial Coulombic systems |
| B. Cichocki, P. Szymczak | Warszawa | Dynamic scattering functions for interacting Brownian
particles Abstract: Dynamic scattering functions for hard sphere suspension are analyzed. Dynamics of the system is assumed to be governed by generalized Smoluchowski equation. To calculate the scattering functions we take a combination of the Enskog-type term and the mode-mode coupling one as a model of irreducible memory kernel. The relaxation time spectrum method is used to perform the calculations. |
| A. S. Cukrowski, J. Fort, S. Fritzsche | Kielce, Girona, Leipzig | Simple models for nonequilibrium effects in bimolecular
chemical reaction in a dilute gas Abstract: Two models for reactive cross sections are introduced to analyze noneqilibrium effects connected with proceeding of the bimolecular chemical reaction A + A <--> B + B in a dilute gas: 1. the line-of-centers model, 2. the reverse model leading to negative values of the Arrhenius activation energy. The perturbation method of solution of the Boltzmann solution is used to obtain analytical expressions for the rate constant of chemical reaction and for the nonequilibrium Shizgal-Karplus temperatures. It is shown that if the molar fraction of product is large enough the relative change of the rate of chemical reaction is constant, i.e. does not depend on the molar fraction. Replacing the equilibrium temperature by the nonequilibrium one (depending on the molar fractions) in the equilibrium equations for forward and reverse rate constants confirms these results. |
| B. Dybiec | Kraków | Shape of the potential barrier and resonant activation |
| Z. J. Grzywna, M. Krasowska, J. Stolarczyk | Gliwice | Generalized Fractal Analysis of Neurons in Goldfish Retina |
| B. Jagoda, P. Bialic, Ł. Ćwiklik | Kraków | Stochastic simulations of TPD spectra |
| M. Kotulska, S. Koronkiewicz, and S. Kalinowski | Wrocław | On non-stationary nature of chronopotentiometric time series from electroporated BLM |
| T. Kosztołowicz | Kielce | Anomalous diffusion in a membrane system |
| Z. Koza | Wrocław | The Maximal Force Exerted by a Molecular Motor |
| S. Kozieł, W. A. Majewski | Gdańsk | Evolution of entanglement for jump type quantum dynamics |
| A. Krawiecki | Warszawa | System size effects in stochastic resonance with spatiotemporal periodic signal |
| L. Machura, M. Kostur, J. Łuczka | Katowice | Inertial effects in thermal ratchets driven by dichotomic fluctuations |
| D. Makowiec, P. Gnaciński | Gdańsk | Analysis of financial time series |
| S. Matyjaskiewicz, A. Krawiecki | Warszawa | Information measure applied to stochastic multiresonance |
| M. Niemiec, A. Gadomski, and J. Łuczka | Opole, Bydgosz, Katowice | Evolution of a grain system: Influence of the surface tension |
| J. Stafiej, and J. P. Badiali | Paris and Warszawa | The role o the diffusion on the morphology of a passive layer. A 2D simulation study. |
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