Related papers: Oil and water: a two-type internal aggregation mod…
Consider the system of particles on ${\Bbb Z}^d$ where particles are of two types, $A$ and $B$, and execute simple random walks in continuous time. Particles do not interact with their own type, but when a type $A$ particle meets a type $B$…
We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added…
The main focus of marine oil spill modelling is often on where the oil will end up, i.e., on the horizontal transport. However, due to current shear, wind drag, and the different physical, chemical and biological processes that affect oil…
The problem of leak detection in a pipeline with nonlinear friction is considered. A distributed observer-based method is proposed which applies a linearised, distributed adaptive observer design to the nonlinear model. The methodology is…
We consider a cluster growth model on Z^d, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It…
In the open circular billiard particles are placed initially with a uniform distribution in their positions inside a planar circular vesicle. They all have velocities of the same magnitude, whose initial directions are also uniformly…
We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-\alpha}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse…
Drops of water at room temperature were released in hot oil, which had a temperature higher than that of the boiling point of water. Initially, the drop temperature increases slowly mainly due to heat transfer diffusion; convective heat…
In this article we study a non-local diffusion problem that involves three different fractional Laplacian operators acting on two domains. Each domain has an associated operator that governs the diffusion on it, and the third operator…
The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor…
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…
Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill…
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…
Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the timescale of observation and so is often described as anomalous. In order to help better understand this phenomenon,…
Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce…
Recent measurements of nitrogen and alpha elements in over 20 damped Ly-alpha systems (DLA) are compared with similar measurements for numerous emission line objects and stars. It is found that the DLA distribution in the N/alpha-alpha/H…
We study the scaling limits of three different aggregation models on the integer lattice Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform…
Based on Brownian Dynamics computer simulations in two dimensions we investigate aggregation scenarios of colloidal particles with directional interactions induced by multiple external fields. To this end we propose a model which allows…
Motivated by multiphase flow in reservoirs, we propose and study a two-species sandpile model in two dimensions. A pile of particles becomes unstable and topples if, at least one of the following two conditions is fulfilled: 1) the number…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…