相关论文: Large-Scale Simulations of Diffusion-Limited n-Spe…
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…
Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the…
Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy…
We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…
We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…
Many systems that can be described in terms of diffusion-limited `chemical' reactions display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. Their…
Numerical simulations and cluster mean-field approximations with coherent anomaly extrapolation show that the critical line of the 1d annihilation fission process is separated into two regions. In both the small and high diffusion cases the…
Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\in \mathbb Z^+$…
Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a…
The single-species annihilation reaction A+A->0 is studied in the presence of random advecting field. In order to determine possible infrared behavior of the system all stable fixed points are presented to two-loop approximation in double…
The exact solution for a system with two-particle annihilation and decoagulation has been studied. The spectrum of the Hamiltonian of the system is found. It is shown that the steady state is two-fold degenerate. The average number density…
We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical…
Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the…
We consider the Fast Diffusion Equation $u_t=\Delta u^m$ posed in a bounded smooth domain $\Omega\subset \RR^d$ with homogeneous Dirichlet conditions; the exponent range is $m_s=(d-2)_+/(d+2)<m<1$. It is known that bounded positive…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
Let $u$ be the solution of $u_t=\Delta\log u$ in $\R^N\times (0,T)$, N=3 or $N\ge 5$, with initial value $u_0$ satisfying $B_{k_1}(x,0)\le u_0\le B_{k_2}(x,0)$ for some constants $k_1>k_2>0$ where $B_k(x,t)…
A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate…
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by…
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…
We derive the multi-fractal scaling of probability distributions of multi-particle configurations for the binary reaction-diffusion system $A+A \to \emptyset$ in $d \leq 2$ and for the ternary system $3A \to \emptyset$ in $d=1$. For the…