Related papers: Analysis of patterns formed by two-component diffu…
We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and…
The diffusion and coalescence of individual atoms on a nanostructured surface are treated in a purely statistical way. From this, analytical formulas are derived which, from a known initial state, give the final cluster size distribution on…
We consider advection of small inertial particles by a random fluid flow with a strong steady shear component. It is known that inertial particles suspended in a random flow can exhibit clusterization even if the flow is incompressible. We…
One way of getting a better view of data is using frequent patterns. In this paper frequent patterns are subsets that occur a minimal number of times in a stream of itemsets. However, the discovery of frequent patterns in streams has always…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Superficial (two dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in…
Brownian particles interacting via repulsive soft-core potentials can spontaneously aggregate, despite repelling each other, and form periodic crystals of particle clusters. We study this phenomenon in low-dimensional situations (one and…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds shows that molecular clouds exhibit a preferred length scale for collapse that depends on the mass-to-flux ratio and neutral-ion collision time…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
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…
A topic of intense current investigation pursues the question how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random…
The dynamics and spontaneous organization of coupled particles is a classic problem in modeling and applied mathematics. Here we examine the behavior of particles coupled by the Ricker potential, exhibiting finite local repulsion…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…
We present some results of Monte Carlo simulations for the deposition of particles of different sizes on a two-dimensional substrate. The particles are linear, height one, and can be deposited randomly only in the two, $x$ and $y$…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…