Related papers: Langevin equations for reaction-diffusion processe…
We consider a reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$, and the…
Bubble nucleation has been studied on lattices using phenomenological Langevin equations. Recently there have been theoretical motivations for using these equations. These studies also conclude that the simple Langevin description requires…
We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
The response of an isolated granular fluid to small perturbations of the hydrodynamic fields is considered. The corresponding linear response functions are identified in terms of a formal solution to the Liouville equation including the…
We use the stochastic quantization method to obtain the free scalar propagator of a finite temperature field theory formulated in Minkowski spacetime. First we use the Markovian stochastic quantization approach to present the two-point…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the…
We introduce a new class of Fokker-Planck equations associated with an effective generalized thermodynamical framework. These equations describe a gas of Langevin particles in interaction. The free energy can take various forms which can…
Two different versions of relativistic Langevin equation in curved spacetime background are constructed, both are manifestly general covariant. It is argued that, from the observer's point of view, the version which takes the proper time of…
In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential.…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik \textit{et al}, J. Chem. Phys. {\bf 119}, 680 (2003); Banerjee \textit{et al}, Phys. Rev. E {\bf 65}, 021109 (2002)]…
We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…
Nuclear reactions govern major aspects of the chemical evolution of galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction…
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…
Colloidal particles that experience perfectly elastic collisions can be modelled using Langevin processes with specular reflection conditions. The article presents a discretisation scheme and offers a conjecture for the rate of convergence…
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…