Exit-time of mean-field particles system

Mean field limit for interacting particles

Mean-field theory for pedestrian outflow through an exit.

The average pedestrian flow through an exit is one of the most important indices in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model using cellular automata, is extended by taking into account realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a th...

Maximal Mean Exit Time Related To The p-Laplace Operator∗

In this paper we introduce a boundary value problem involving powers of the p-Laplace operator. We will then prove a variant of Talenti inequality which shows that the Schwarz symmetrization of the solution of the boundary value problem is majorized by the solution of the appropriately symmetrized version of the problem. The case of equality is also investigated. Finally, as an application, we ...

Mean Exit Time and Escape Probability for a Tumor Growth System under Non-Gaussian noise

Effects of non-Gaussian α−stable Lévy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit time and escape probability problems are formulated in a differential-integral equation with a fractional Laplacian operator. Numerical simulations are conducted to eva...

Mean-field theory of random close packings of axisymmetric particles.

Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis, in particular, for shapes like dimers, spherocylinders and ellipsoids of revolution. Here we present a mean-field formalism to estimate the packing density ...