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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…

Soft Condensed Matter · Physics 2013-05-29 Jeremy D. Schmit , Ercan Kamber , Jané Kondev

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…

Plasma Physics · Physics 2009-11-07 Nikolai V. Erkaev , Vladimir S. Semenov , Ilya V. Alexeev , Helfried K. Biernat

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…

Probability · Mathematics 2021-08-10 Conrado da Costa , Bernardo Freitas Paulo da Costa , Daniel Valesin

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…

Analysis of PDEs · Mathematics 2021-08-24 Jichen Yang , Jens D. M. Rademacher

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…

Condensed Matter · Physics 2009-10-22 Stephen Cornell , Zbigniew Koza , Michel Droz

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…

Numerical Analysis · Mathematics 2023-08-11 Ying Chen , Zhenhua Chai , Baochang Shi

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.…

Probability · Mathematics 2017-06-21 Freddy Hernández , Milton Jara , Fábio J. Valentim

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…

Statistical Mechanics · Physics 2024-04-23 Chuandong Lin , Kai H. Luo , Huilin Lai

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…

Statistical Mechanics · Physics 2015-05-14 Sven Dorosz , Michel Pleimling

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…

Numerical Analysis · Mathematics 2023-12-18 Jan Eliáš , Hao Yin , Gianluca Cusatis

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…

Numerical Analysis · Mathematics 2025-04-07 Taylor Kearney , Ricardo Ruiz-Baier , Mark B. Flegg

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.…

Numerical Analysis · Mathematics 2010-04-06 M. Paramasivam , S. Valarmathi , J. J. H. Miller

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…

Machine Learning · Statistics 2026-02-24 Saptarshi Roy , Alessandro Rinaldo , Purnamrita Sarkar

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,…

Systems and Control · Computer Science 2016-04-05 Saber Jafarizadeh

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,…

Quantitative Methods · Quantitative Biology 2017-07-27 Youfang Cao , Anna Terebus , Jie Liang

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…

Subcellular Processes · Quantitative Biology 2019-04-24 Wei-Xiang Chew , Kazunari Kaizu , Masaki Watabe , Sithi V. Muniandy , Koichi Takahashi , Satya N. V. Arjunan

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…

Quantitative Methods · Quantitative Biology 2016-02-17 Atiyo Ghosh , Tatiana T. Marquez-Lago

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…

Numerical Analysis · Mathematics 2014-12-19 Simon Cotter , Radek Erban

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…

Disordered Systems and Neural Networks · Physics 2010-11-10 A. Wolff , I. Lohmar , J. Krug , Y. Frank , O. Biham

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,…

Applications · Statistics 2025-07-03 Zekai Jin , Yaakov Stern , Seonjoo Lee