相关论文: General Reaction-Diffusion Processes With Separabl…
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 class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
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…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…
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…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method,…
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…
We consider general models of coupled reaction-diffusion systems for interacting variants of the same species. When the total population becomes large with intensive competition, we prove that the frequencies (i.e. proportions) of the…
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.…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes,…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…