相关论文: Fokker-Planck equation on metric graphs

The present work analyzes stationary distributions of active Brownian particles in a harmonic trap. Generally, obtaining stationary distributions for this system is non-trivial, and up to date no exact expressions are available. In this…

We study a particular generalisation of the classical Kramers model describing Brownian particles in the external potential. The generalised model includes the stochastic force which is modelled as an additive random noise that depends upon…

Starting from the hyperbolic Brownian motion as a time-changed Brownian motion, we explore a set of probabilistic models--related to the SABR model in mathematical finance--which can be obtained by geometry-preserving transformations, and…

We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time…

In this brief note, we report a formal mathematical observation: we are about to breach a major century-old barrier in the analysis of interacting particle systems. More precisely, it is well-known that in…

Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…

The Integrate-and-Fire model is a Fokker-Planck equation arising in neuroscience. It describes the evolution of the probability density of the neuronal membrane potential and fitting has shown that the inclusion of a em superlinear drift…

We describe a new approach for modeling the transport of high energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically…

We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular…

In the paper we give a lower bound for the number of vertices of a given graph using its chromatic number. We find the graphs for which this bound is exact. The results are applied in the theory of Foklman numbers.

We show that there is a PDE formulation in terms of Fokker-Planck equations for weak optimal transport problems. The main novelty is that we introduce a minimization problem involving Fokker-Planck equations in the extended sense of…

First we show that physics-informed neural networks are not suitable for a large class of parabolic partial differential equations including the Fokker-Planck equation. Then we devise an algorithm to compute solutions of the Fokker-Planck…

This study investigates the asymptotic dynamics of solutions to the Fokker-Planck-Kolmogorov (FPK) equation, with a specific focus on ship roll stability in dynamic sea conditions. Utilizing a fourth-order filter, we conduct a thorough…

Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or by a Fermi pencil-beam equation. We present a rigorous approximation analysis of these three models…

Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…

Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and…

The paper is a continuation of the study started in \cite{Yorzh1}. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of $\delta$ type. Either an…

We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within mean-field interaction. Relying on a slow-fast viewpoint and on the theory of approximately invariant manifolds we…

In this paper, we have considered flat Friedmann-Lema\^{i}tre-Robertson-Walker metric in the framework of perfect fluid models and modified $f(G)$ gravity (where $G$ is the Gauss Bonnet invariant). Particularly, we have considered…