Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 2, Pages 125-141

Mean action time for diffusive processes

Kerry Landman1 and Mark Mcguinness2

1Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia
2School of Mathematical and Computing Sciences, Victoria University of Wellington, Wellington, New Zealand

Copyright © 2000 Kerry Landman and Mark Mcguinness. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a number of diffusive processes involving heat and mass transfer, a convenient and easy way to solve for penetration time or depth is to consider an averaged quantity called mean action time. This approach was originally developed by Alex McNabb, in collaboration with other researchers. It is possible to solve for mean action time without actually solving the full diffusion problem, which may be nonlinear, and may have internal moving boundaries. Mean action time satisfies a linear Poisson equation, and only works for finite problems. We review some nice properties of mean action time, and discuss some recent novel applications.