Related papers: Langevin equations for reaction-diffusion processe…
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation, instead it is based upon a dynamical…
A procedure is introduced for deriving a coarse-grained dissipative particle dynamics from molecular dynamics. The rules of the dissipative particle dynamics are derived from the underlying molecular interactions, and a Langevin equation is…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…
We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time…
The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of {\it…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
For the first time, the energy diffusion approximation is confronted at the percent level with the exact numerical modeling of thermal decay of a metastable state. The latter is performed using the quasistationary decay rates resulting from…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions can be written as a euclideen Schr\"odinger equation in which the wave function is the probability distribution and the Hamiltonian is…
The Langevin theory of the polarization of a dilute collection of dipoles by an external field is often included in introductory solid state physics and physical chemistry curricula. The average polarization is calculated assuming the…
Diffusion studies of adsorbates moving on a surface are often analyzed using 2D Langevin simulations. These simulations are computationally cheap and offer valuable insight into the dynamics, however, they simplify the complex interactions…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the…
We analyze bimolecular reactions that proceed by a long-ranged reactive interaction, using a field theoretic approach that takes into account fluctuations. We consider both the one-species, $A+A \to \emptyset$ reaction and the two-species,…
Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
In this paper, we extend some of the multilevel convergence results obtained by Xu and Zhu in [Xu and Zhu, M3AS 2008], to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners…