Related papers: Analysis of patterns formed by two-component diffu…
We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting…
Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also…
Fickian yet non-Gaussian diffusion is observed in several biological and soft matter systems, yet the underlying mechanisms behind the emergence of non-Gaussianity while retaining a linear mean square displacement remain speculative. Here,…
Intracellular processes often rely on the timely encounter of mobile reaction partners, including intermittently motor-driven organelles. The underlying cytoskeletal network presents a complex landscape that both directs particle movement…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
Laplace's first law of errors, which states that the frequency of an error can be represented as an exponential function of the error magnitude, was overlooked for many decades but was recently shown to describe the statistical behavior of…
This study focused on the expansion in polydisperse granular materials owing to mechanical annealing, which involved compression and decompression. Following minor annealing, the polydisperse systems exhibited compaction as well as the…
We report computer simulation studies of the kinetics of ordering of a two dimensional system of particles on a template with a one dimensional periodic pattern. In equilibrium one obtains a re-entrant liquid-solid-liquid phase transition…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation and experiment. The mixture exhibits a partial clustering in…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…
Collective diffusion coefficient in a one dimensional lattice gas adsorbate is calculated using variational approach. Particles interact via either a long-range, or a long range electron-gas-mediated (for a metallic substrate), or a…
Powdered materials of sizes ranging from nanometers to microns are widely used in materials science and are carefully selected to enhance the performance of a matrix. Fillers have been used in order to improve, among the others, mechanical,…
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…