Related papers: Quantum graphs with mixed dynamics: the transport/…
This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
We describe operators driving the time evolution of singular diffusion on finite graphs whose vertices are allowed to carry masses. The operators are defined by the method of quadratic forms on suitable Hilbert spaces. The model also covers…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
We propose a model to implement and simulate different traffic-flow conditions in terms of quantum graphs hosting an ($N$+1)-level dot at each site, which allows us to keep track of the type and of the destination of each vehicle. By…
Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term.…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has…
The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…