Related papers: Reaction Diffusion Models in One Dimension with Di…
We present results from computer simulations for diffusion-limited $n$-species annihilation, $A_i+A_j\to0$ $(i,j=1,2,...,n;i\neq j)$, on the line, for lattices of up to $2^{28}$ sites, and where the process proceeds to completion (no…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
We construct series expansions for the scaling variables (which transform multiplicatively under a renormalization group (RG) transformation) in examples where the RG flows, going from an unstable (Wilson's) fixed point to a stable…
Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…
In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works. In the first part…
We present a method for computing resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address the problem, we shift the computational…
Healthy and sick individuals (A and B particles) diffuse independently with diffusion constants D_A and D_B. Sick individuals upon encounter infect healthy ones (at rate k), but may also spontaneously recover (at rate 1/\tau). The…
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…
As a mathematical theory for the stochasstic, nonlinear dynamics of individuals within a population, Delbr\"{u}ck-Gillespie process (DGP) $n(t)\in\mathbb{Z}^N$, is a birth-death system with state-dependent rates which contain the system…
We consider diffusion-limited reactions A_i + A_j -> 0 (1 <= i < j <= q) in d space dimensions. For q > 2 and d >= 2 we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is…
The one-dimensional (1D) $t-J$ model is investigated using the density matrix renormalization group (DMRG) method. We report for the first time a generalization of the DMRG method to the case of arbitrary band filling and prove a theorem…
We study one dimensional models of diatomic molecules where both the electrons and nuclei are treated as quantum particles, going beyond the usual Born-Oppenheimer approximation. The continuous system is approximated by a grid which…
Simulating more than seconds of microstructure evolution in systems involving almost athermally or very fast diffusing species such as self-interstitial atom (SIA) clusters currently relies on mean-field or coarse-graining techniques.…
We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the…
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…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with…