Mean exit time for diffusion on irregular domains

Space–time fractional diffusion on bounded domains

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 transit time and mean residence time for linear diffusion–convection–reaction transport system

Characteristic times for transport processes in biological systems may be evaluated as mean transit times (MTTs) (for transit states) or mean residence times (MRT) (for steady states). It is shown in a general framework of a (linear) reaction–diffusion–convection equation that these two times are related. Analytical formulas are also derived to calculate moments of exit time distribution using ...

High-Order Embedded Finite Difference Schemes for Initial Boundary Value Problems on Time Dependent Irregular Domains

This paper considers a family of spatially discrete approximations, including boundary treatment, to initial boundary value problems in evolving bounded domains. The presented method is based on the Cartesian grid embedded Finite-Difference method, which was initially introduced by Abarbanel and Ditkowski (ICASE Report No. 96-8, 1996; and J. Comput. Phys. 133(2), 1997) and Ditkowski (Ph.D. thes...

A simple finite difference method for time-dependent, variable coefficient Stokes flow on irregular domains

We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on staggered Cartesian grids, avoiding the need for expensive remeshing operations, and can be applied to flows in both two and three dimensions. It uses fully implic...