Related papers: Theory for Diffusion-Limited Oscillating Chemical …
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
We use a boolean cellular automaton model to describe the diffusion limited dynamics of the irreversible reaction A+A->A+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which…
Reactive lattice gas automata provide a microscopic approachto the dynamics of spatially-distributed reacting systems. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the…
We study the effect of confinement on diffusion limited bimolecular reactions within a lattice model where a small number of reactants diffuse amongst a much larger number of inert particles. When the number of inert particles is held…
We present an analysis of diffusion in terms of the spontaneous density fluctuations in a non-thermal two-species fluid modeled by a lattice gas automaton. The power spectrum of the density correlation function is computed with statistical…
We study a kinetically constrained lattice glass model in which continuous local densities are randomly redistributed on neighbouring sites with a kinetic constraint that inhibits the process at high densities, and a random bias accounting…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
We present an extension of a simple automaton model to incorporate non-local interactions extending over a spatial range in lattice gases. {}From the viewpoint of Statistical Mechanics, the lattice gas with interaction range may serve as a…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect…
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…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
The family of autonomous reaction-diffusion models on a one-dimensional lattice with boundaries is studied. By autonomous, it is meant that the evolution equation for n-point functions contain only n- or less- point functions. It is shown…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in…
A periodic Kolmogorov type flow is implemented in a lattice gas automaton. For given aspect ratios of the automaton universe and within a range of Reynolds number values, the averaged flow evolves towards a stationary two-dimensional $ABC$…