相关论文: Autonomous multispecies reaction-diffusion systems…
Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
A method for classifying $n$-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional two-species reaction-diffusion model with nearest neighbor interactions admitting uniform product…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
The most general single species autonomous reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced. The stationary solutions of such models, as well as their dynamics, are discussed. To study dynamics of…
We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…
The evolution of the two-point functions of autonomous one-dimensional single-species reaction-diffusion systems with nearest-neighbor interaction and translationally-invariant initial conditions is investigated. It is shown that the…
We construct explicit examples of one-dimensional driven diffusive systems for two and three species of interacting particles, defined by asymmetric dynamical rules which do not obey detailed balance, but whose nonequilibrium…
The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective…
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
In an effort to effectively model observed patterns in the spatial configuration of individuals of multiple species in nature, we introduce the saturated pairwise interaction Gibbs point process. Its main strength lies in its ability to…
We study one dimensional stochastic particle systems with exclusion interaction that each site can be occupied by at most one particle, and homogeneous jumping rates. Alimohammadi and Ahmadi previously classified 28 Yang-Baxter integrable…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…
A one-dimensional (1D) $q$-state Potts model with $N$ sites, $m$-site interaction $K$ in a field $H$ is studied for arbitrary values of $m$. Exact results for the partition function and the two-point correlation function are obtained at…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…