相关论文: Fractal Diffusion in Smooth Dynamical Systems with…

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…

In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…

Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions.…

We show that the intermittent and self-similar fluctuations displayed by a slow crack during the propagation in a heterogeneous medium can be quantitatively described by an extension of a classical statistical model for fracture. The model…

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…

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…

We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…

We study dynamical properties of strongly coupled chiral matter by using holographic method. We demonstrate, at both linear and nonlinear levels, that perturbations on thermodynamically unstable backgrounds within the spinodal region of…

Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…

The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complicated scenario of multiple…

We introduce a novel approach linking fractal geometry to partially hyperbolic dynamics, revealing several new phenomena related to regularity jumps and rigidity. One key result demonstrates a sharp phase transition for partially hyperbolic…

We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…

Accretion occurs across a large range of scales and physical regimes. Despite this diversity in the physics, the observed properties show remarkably similarity. The theory of propagating fluctuations, in which broad-band variability within…

We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…

This paper deals with the theoretical and numerical analysis of dynamic fracture of dissimilar chain consisting of masses lined by springs. Such a structure exhibits quite different dynamic properties in comparison with a symmetrical…

We study X-ray diffraction in smectic liquid crystal multilayers. Such systems are fabricated as freely suspended films and have a unique layered structure. As such, they can be described as organic Bragg mirrors with sub-nanometer…

If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…