相关论文: On the Hughes Model and Numerical Aspects

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…

We consider a stochastic, continuous state and time opinion model where each agent's opinion locally interacts with other agents' opinions in the system, and there is also exogenous randomness. The interaction tends to create clusters of…

This work studies a robot-assisted crowd evacuation problem where we control a small group of robots to guide a large human crowd to safe locations. The challenge lies in how to model human-robot interactions and design robot controls to…

Present data, both from direct Higgs search and from analysis of electroweak data, are starting to become rather restrictive on the possible values for the mass of the standard model Higgs. We discuss a new physics scenario based on a model…

We investigate a convective Brinkman--Forchheimer problem coupled with a heat equation. The investigated model considers thermal diffusion and viscosity depending on the temperature. We prove the existence of a solution without restriction…

We present the newly developed stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Mathematically Parker transport equation (PTE) describing non-stationary transport of charged particles in the…

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often…

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…

We develop a numerical method for solving a free boundary problem which describes shape relaxation, by surface tension, of a long and thin bubble of an inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. The method of…

We present a method how to estimate from experimental data of a turbulent velocity field the drift and the diffusion coefficient of a Fokker-Planck equation. It is shown that solutions of this Fokker-Planck equation reproduce with high…

In this paper, we study a generalized Camassa-Holm (gCH) model with both dissipation and dispersion, which has (N + 1)-order nonlinearities and includes the following three integrable equations: the Camassa-Holm, the Degasperis-Procesi, and…

We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for…

In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…

A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…

The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For…

We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…

The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…

Inspired by the paper Greenhalgh et al. [5] we investigate a class of two dimensional stochastic differential equations related to susceptible-infected-susceptible epidemic models with demographic stochasticity. While preserving the key…

As an example for complex systems with extreme events we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows grasping extreme…