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We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…

Chemical Physics · Physics 2023-10-03 Denis S. Grebenkov

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…

Molecular Networks · Quantitative Biology 2019-03-04 David J. Warne , Ruth E. Baker , Matthew J. Simpson

Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…

Analysis of PDEs · Mathematics 2026-02-23 Marzia Bisi , Davide Cusseddu , Ana Jacinta Soares , Romina Travaglini

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Analysis of PDEs · Mathematics 2024-10-31 Rômulo Damasclin Chaves dos Santos , Jorge Henrique de Oliveira Sales

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…

Machine Learning · Computer Science 2025-12-18 Hanqing Jin , Renyuan Xu , Yanzhao Yang

Stochastic boundary conditions for interactions with a particle reservoir are discussed in many-particle systems. We introduce the boundary conditions with the injection rate and the momentum distribution of particles coming from a particle…

Statistical Mechanics · Physics 2017-04-26 Tooru Taniguchi , Shin-ichi Sawada

The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to…

Quantitative Methods · Quantitative Biology 2020-10-02 Christian A. Yates , Adam George , Armand Jordana , Cameron A. Smith , Andrew B. Duncan , Konstantinos C. Zygalakis

Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…

Numerical Analysis · Mathematics 2024-09-16 Eddel Elí Ojeda Avilés , Jae-Hun Jung , Daniel Olmos Liceaga

The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a…

Statistical Mechanics · Physics 2009-10-31 M. J. E. Richardson , Y. Kafri

We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…

Statistical Mechanics · Physics 2007-05-23 S. Bouzat , H. S. Wio

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…

Probability · Mathematics 2018-01-15 Pavel Mozgunov , Marco Beccuti , Andras Horvath , Thomas Jaki , Roberta Sirovich , Enrico Bibbona

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…

Analysis of PDEs · Mathematics 2015-11-20 Vandana Sharma , Jeff Morgan

Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…

Dynamical Systems · Mathematics 2022-08-12 Shuang Liu , Li-Tien Cheng , Bo Li

Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…

Numerical Analysis · Mathematics 2025-08-11 Akash Sharma

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…

Statistical Mechanics · Physics 2015-06-16 Malbor Asllani , Tommaso Biancalani , Duccio Fanelli , Alan J. McKane

Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…

Computational Physics · Physics 2018-05-09 Jason A. Wagoner , Vijay S. Pande

Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…

Statistical Mechanics · Physics 2026-02-09 Mauricio J. del Razo , Tommaso Lamma , Wout Merbis

Traditional stochastic modeling of reactive systems limits the domain of applicability of the associated path thermodynamics to systems involving a single elementary reaction at the origin of each observed change in composition. An…

Statistical Mechanics · Physics 2023-01-18 F. Baras , A. L. Garcia , M. Malek Mansour

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…

Analysis of PDEs · Mathematics 2018-02-19 Emilie Blanc , Stefan Engblom , Andreas Hellander , Per Lötstedt

In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption at a reactive surface, which takes into account stochastic switching of a diffusing particle's conformational state. For simplicity,…

Statistical Mechanics · Physics 2022-09-21 Paul C. Bressloff