相关论文: On the Hughes Model and Numerical Aspects

To well understand crowd behavior, microscopic models have been developed in recent decades, in which an individual's behavioral/psychological status can be modeled and simulated. A well-known model is the social-force model innovated by…

We present a numerical method for the solution of Newton's problem of least resistance in the class of convex functions using a convex hull approach. We observe that the numerically computed solutions possess some symmetry. Further, their…

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…

We formulate a data-driven method for constructing finite volume discretizations of a dynamical system's underlying Continuity / Fokker-Planck equation. A method is employed that allows for flexibility in partitioning state space,…

We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…

In a crowd model based on leader-follower interactions, where positions of the leaders are viewed as the control input, up-to-date solutions rely on knowledge of the agents' coordinates. In practice, it is more realistic to exploit…

A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…

In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model couples the incompressible Navier--Stokes equations with an…

In the framework of the stochastic theory for hierarchical clustering, we investigate the time-dependent solutions of the Fokker-Planck equation describing the statistics of dark matter halos, and discuss the typical timescales needed for…

This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the…

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…

Aggregate load modeling is of fundamental importance for systematic analysis and design of various demand response strategies. Instead of keeping track of the trajectories of individual loads, the aggregate modeling problem focuses on…

The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…

Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated…

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…

This work addresses the development of the Riemann-Hilbert problem (RHP) formalism (the Fokas method) for the Camassa-Holm equation under periodic boundary conditions. Particularly, we present a representation of the solution to this…

We analyse a generalised Fokker-Planck equation by making essential use of its linearisability through a Cole-Hopf transformation. We determine solutions of travelling wave and multi-kink type by resorting to a geometric construction in the…

In light of no discovered new physics at the LHC, ideas which tackle the Hierarchy Problem without novelties around the TeV scale must be taken seriously. Such is a cosmological relaxation model of the Higgs mass, proposed in the pre-LHC…

Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…

We study a Fokker-Planck equation modelling the firing rates of two interacting populations of neurons. This model arises in computational neuroscience when considering, for example, bistable visual perception problems and is based on a…