Related papers: Taking the reaction-diffusion master equation to t…
We study the effect of confinement on diffusion limited bimolecular reactions within a lattice model where a small number of reactants diffuse amongst a much larger number of inert particles. When the number of inert particles is held…
The reconnection rate is obtained for the simplest case of 2D symmetric reconnection in an incompressible plasma. In the short note (Erkaev et al., Phys. Rev. Lett.,84, 1455 (2000)), the reconnection rate is found by matching the outer…
We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…
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 consider the reaction zone that grows between separated regions of diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the framework of the mean-fieldlike reaction-diffusion equations. For distances from the centre…
In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete…
We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero.…
A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space,…
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
The Drift-Diffusion Model (DDM) is widely used in neuropsychological studies to understand the decision process by incorporating both reaction times and subjects' responses. Various models have been developed to estimate DDM parameters,…