Related papers: Deterministic Diffusion
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
The questions of justification of the Gibbs canonical distribution for systems with elastic impacts are discussed. A special attention is paid to the description of probability measures with densities depending on the system energy.
We describe the influence of hard wall confinement and lateral dimension on the low temperature transport properties of long diffusive channels and ballistic crosses fabricated in an InSb/InxAl1-xSb heterostructure. Partially diffuse…
A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
We show, both heuristically and numerically, that three-dimensional periodic Lorentz gases -- clouds of particles scattering off crystalline arrays of hard spheres -- often exhibit normal diffusion, even when there are gaps through which…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct…
The first part of the paper is an introduction to the theory of probabilistic concurrent systems under a partial order semantics. Key definitions and results are given and illustrated on examples. The second part includes contributions. We…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…