Related papers: Diffusion over a saddle with a Langevin equation
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
The purpose of this paper is to provide a formula for the effective diffusion operator obtained by projecting the 3-dimensional diffusion equation onto a 2-dimensional plane, assuming reflective boundary conditions at two surfaces in…
The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…
We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…
In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as…
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…
The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass…
Kramer's approach to the rate of the thermally activated escape from a metastable state is extended to field theory. Diffusion rate in the 1+1-dimensional Sine-Gordon model as a function of temperature and friction coefficient is evaluated…
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The non-linear Langevin equation for the motion of the piston is derived from first principles for the case when the…
We consider a situation commonly encountered in microfluidics: two streams of miscible liquids are brought at a junction to flow side by side within a microchannel, allowing solutes to diffuse from one stream to the other and possibly…
In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law…
Heavy vehicles (HVs) pose a significant challenge to maintaining a smooth traffic flow on the freeway because they are slower moving and create large blind spots. It is therefore desirable for the followers of HVs to perform lane changes…
In this work I show how a diffusion-advection equation in three space-dimensions may have its advection term weakly limited to a velocity field localized to a moving curve. This is rigorously accomplished through the technique of…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…