Related papers: Comment on "Scaling behavior of classical wave tra…
A quantitative relationship between the diffusion coefficient $D$ of a tagged particle in a liquid and the entropy $S$ of that liquid has long been sought, as it would allow entropy to be inferred directly from diffusion measurements and…
We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time-independent. We start with the stochastic equation of motion for a…
Under certain circumstances, the time behavior of a random walk is modulated by logarithmic periodic oscillations. The goal of this paper is to present a simple and pedagogical explanation of the origin of this modulation for diffusion on a…
A particle driven by deterministic chaos and moving in a spatially extended environment can exhibit normal diffusion, with its mean square displacement growing proportional to the time. Here we consider the dependence of the diffusion…
We present extensive molecular dynamics simulations of the motion of a single linear rigid molecule in a two-dimensional random array of fixed obstacles. The diffusion constant for the center of mass translation, $D_{\rm CM}$, and for…
It is shown that the distribution functions of the diffusion coefficient are very similar in the standard model of quantum diffusion in a disordered metal and in a model of classical diffusion in a disordered medium: in both cases the…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
In this study, we experimentally investigated the time dependence of the statistical properties of two-dimensional drying crack patterns to determine the functional form of fragment size distribution. Experiments using a thin layer of a…
The shear-transformation-zone (STZ) theory has been remarkably successful in accounting for broadly peaked, frequency-dependent, viscoelastic responses of amorphous systems near their glass temperatures $T_g$. This success is based on the…
We present results on a meso-scale model for amorphous matter in athermal, quasi-static (a-AQS), steady state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size, $L$, of: i) statistics of…
The ability to separate and analyze chemical species with high resolution, sensitivity, and throughput is central to the development of microfluidics systems. Deterministic lateral displacement (DLD) is a continuous separation method based…
We investigate the localization of electrons hopping on quasi-1D strips in the presence of random magnetic field. In the weak-disorder region, by perturbative analytical techniques, we derive scaling laws for the localization length,…
We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the…
Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the relations of finite-size scaling for different parameters characterizing the level statistics. The obtained results are compared with the…
A key interest in geomorphology is to predict how the shear stress $\tau$ exerted by a turbulent flow of air or liquid onto an erodible sediment bed affects the transport load $M\tilde g$ (i.e., the submerged weight of transported…
In a recent paper the mean square displacement (MSD), <R^2(T)>, of a particle carried by a turbulent liquid over time T has been shown to be proportional to T^6/5, meaning that the motion of the particle is slightly super-diffusive. In some…
We propose explicit forms for the steady state distributions governing fully developed turbulence in two and three spatial dimensions. We base our proposals on the crucial importance of the area and volume preserving diffeomorphisms in the…
Wavefunction collapse models modify Schrodinger's equation so that it describes the rapid evolution of a superposition of macroscopically distinguishable states to one of them. This provides a phenomenological basis for a physical…