相关论文: Microscopic Derivation of Causal Diffusion Equatio…
We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators…
We study consequences of gauge invariance and charge conservation of an electron gas in a strong random potential perturbed by a weak electromagnetic field. We use quantum equations of motion and Ward identities for one- and two-particle…
We investigate spin transport in the anisotropic Heisenberg chain in the limit of high temperatures ({\beta} \to 0). We particularly focus on diffusion and the quantitative evaluation of diffusion constants from current autocorrelations as…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in…
Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace…
Standard diffusion models are flexible estimators of complex distributions, but they do not encode causal structures and therefore do not by themselves support causal analysis. We propose a causality-encoded diffusion framework that…
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $\beta \in (0,1)$. The fundamental solution for the Cauchy problem is…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
This article starts over the backwards diffusion problem by replacing the \emph{noncausal} diffusion equation, the direct problem, by the \emph{causal} diffusion model developed in \cite{Kow11} for the case of constant diffusion speed. For…
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…
The fractional diffusion equation is derived from the master equation of continuous-time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion…
In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…
In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the…