  We develop simple diffusion-advection models to estimate the average time it
takes fish to reach one of the boundaries of an enclosure and the population
distribution over time moving in the enclosure (such as a lake or slough). We
start with a combination of random walks and directed movement and then, from
these, proceeding to the associated Partial Differential Equations and their
solution. We also find the evolution of the population distribution and
communities composition over time moving in the enclosure. Although this model
was developed with fish movements in mind it has wide-ranging applicability
scaling from the molecular to human and action from inert to deliberate.

Analysis of PDEs;Quantitative Methods