相关论文: Large-Scale Simulations of Diffusion-Limited n-Spe…

The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be…

This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in…

We study the critical behavior of the pair annihilation model (PAM) with diffusion in one, two and three dimensions, using the pair approximation (PA) and Monte Carlo simulation. Of principal interest is the dependence of the critical…

We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…

The contact process with diffusion (PCPD) defined by the binary reactions 2 B -> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed.…

We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process, a vital stage in bioseparation. We prove stability and error estimates for both constant and affine…

An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…

We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle…

Image tokenization plays a central role in modern generative modeling by mapping visual inputs into compact representations that serve as an intermediate signal between pixels and generative models. Diffusion-based decoders have recently…

We treat the accurate simulation of the calcination reaction in particles, where the particles are large and, thus, the inner-particle processes must be resolved. Because these processes need to be described with coupled partial…

The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 69 036112 (2004)) are explored in two dimensions. This model exhibits site occupation restriction and explicit diffusion of isolated…

The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…

We use cosmological simulations to explore the large-scale effects of reionization. Since reionization is a process that involves a large dynamic range - from galaxies to rare bright quasars - we need to be able to cover a significant…

In the paper, we consider the large time behavior of solutions to the convection-diffusion equation u_t - Delta u + nabla cdot f(u) = 0 in R^n times [0,infinity), where f(u) ~ u^q as u --> 0. Under the assumption that q >= 1+1/(n+beta) and…

In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…

We propose a simple model of columnar growth through {\it diffusion limited aggregation} (DLA). Consider a graph $G_N\times\N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if…

The $\alpha$-decay chains of $^{288-287}115$ are studied along with the possible cluster decay modes by using the preformed cluster model (PCM). The calculated $\alpha$-decay half-lives are compared with experimental data and other model…

Low-dose CT (LDCT) protocols reduce radiation exposure but increase image noise, compromising diagnostic confidence. Diffusion-based generative models have shown promise for LDCT denoising by learning image priors and performing iterative…

We propose a simple model for reaction-diffusion systems with orientational constraints on the reactivity of particles, and map it onto a field theory with upper critical dimension d_c=2. To two-loop level the long-time particle density…

We find a continuum of extinction rates for solutions $u(y,\tau)\ge 0$ of the fast diffusion equation $u_\tau=\Delta u^m$ in a subrange of exponents $m\in (0,1)$. The equation is posed in $\ren$ for times up to the extinction time $T>0$.…