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The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…

Analysis of PDEs · Mathematics 2017-02-13 Klemens Fellner , Bao Quoc Tang

We show that solutions of the chemical reaction-diffusion system associated to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which…

Numerical Analysis · Mathematics 2017-04-05 Fatma Mohamed , Casian Pantea , Adrian Tudorascu

We study diffusion of particles on the surface of a sphere toward a partially reactive circular target with partly reversible binding kinetics. We solve the coupled diffusion-reaction equations and obtain the exact expressions for the…

Statistical Mechanics · Physics 2019-11-05 Denis S. Grebenkov

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations…

Statistical Mechanics · Physics 2017-07-04 Jordan M. Horowitz

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…

Analysis of PDEs · Mathematics 2018-05-09 Klemens Fellner , Bao Q. Tang

Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…

Dynamical Systems · Mathematics 2025-02-18 Carlos Barajas , Jean-Jacques Slotine , Domitilla Del Vecchio

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modelling. The formulae for the first collision time and the mean reaction time are derived for the case…

Numerical Analysis · Mathematics 2016-03-17 F Li , M Chen , R Erban , Y Cao

Smoluchowski-type models for diffusion-influenced reactions (A+B -> C) can be formulated within two frameworks: the probabilistic-based approach for a pair A, B of reacting particles and the concentration-based approach for systems in…

Chemical Physics · Physics 2019-01-16 Mauricio J. del Razo , Hong Qian , Frank Noé

A general and local reactive boundary condition (RBC) for studying first-order equilibrium reactions using the lattice Boltzmann method (LBM) is presented. Its main characteristics are accurate reproduction of wall diffusion, invariance to…

Computational Physics · Physics 2023-06-21 Julius Weinmiller , Martin P. Lautenschlaeger , Benjamin Kellers , Timo Danner , Arnulf Latz

A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz…

Numerical Analysis · Mathematics 2024-05-07 Wei Qu , Yuan-Yuan Huang , Sean Hon , Siu-Long Lei

Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…

Pattern Formation and Solitons · Physics 2014-07-17 Anton S. Zadorin , Yannick Rondelez , Jean-Christophe Galas , André Estevez-Torres

The stochastic description of chemical reaction networks with the kinetic chemical master equation (CME) is important for studying biological cells, but it suffers from the curse of dimensionality: The amount of data to be stored grows…

Numerical Analysis · Mathematics 2024-08-02 Lukas Einkemmer , Julian Mangott , Martina Prugger

The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in…

Quantitative Methods · Quantitative Biology 2013-04-22 Mark B. Flegg , S. Jonathan Chapman , Likun Zheng , Radek Erban

We use a generic framework, namely the gradient discretisation method (GDM), to propose a unified numerical analysis for general time-dependent convection-diffusion-reaction models. We establish novel results for convergence rates of…

Numerical Analysis · Mathematics 2025-07-03 Hasan Alzubaidi , Yahya Alnashri

In this paper, based on the previous work [B. Shi, Z. Guo, Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E 79 (2009) 016701], we develop a general multiple-relaxation-time (MRT) lattice Boltzmann model for…

Computational Physics · Physics 2016-04-01 Zhenhua Chai , Baochang Shi , Zhaoli Guo

Learning models with categorical variables requires optimizing expectations over discrete distributions, a setting in which stochastic gradient-based optimization is challenging due to the non-differentiability of categorical sampling. A…

Machine Learning · Computer Science 2026-02-10 Samson Gourevitch , Alain Durmus , Eric Moulines , Jimmy Olsson , Yazid Janati

Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction…

Systems and Control · Computer Science 2012-12-21 Marko Seslija , Arjan van der Schaft , Jacquelien M. A. Scherpen

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…

Statistical Mechanics · Physics 2009-11-11 Elisheva Cohen , David A. Kessler , Herbert Levine

The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…

Other Condensed Matter · Physics 2007-05-23 Serge Shpyrko , Vladimir M. Sysoev

A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--$\newrho$ model for irreversible…

Biological Physics · Physics 2010-05-12 J. Lipkova , K. C. Zygalakis , S. J. Chapman , R. Erban