Mean action time for diffusive processes

For a number of diffusive processes involving heat and masstransfer, a convenient and easy way to solve for penetration time ordepth is to consider an averaged quantity called mean action time.This approach was originally developed by Alex McNabb, incollaboration with other researchers. It is possible to solve formean action time without actually solving the full diffusionproblem, which may be nonlinear, and may have internal movingboundaries. Mean action time satisfies a linear Poisson equation,and only works for finite problems. We review some nice propertiesof mean action time, and discuss some recent novel applications