Related papers: On relation between generalized diffusion equation…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
Dissipaton theory had been proposed as an exact and nonperturbative approach to deal with open quantum system dynamics, where the influence of Gaussian environment is characterized by statistical quasi-particles named as dissipatons. In…
We discuss fluctuation-dissipation relations valid under general conditions even out of equilibrium. The response function is expressed in terms of unperperturbed correlation functions, where contributions peculiar to non-equilibrium can…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
The present paper is aimed at studying the microscopic origin of the jump diffusion. Starting from the $N$-body Liouville equation and making only the assumption that molecular reorientation is overdamped, we derive and solve the new…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the…