Stochastic, Physical, and Numerical Experiments in Anomalous Diffusion
Vaughan R. Voller
Civil, Environmental and Geo- Engineering, University of Minnesota
Since the time of Fick (mid 1850's), it has been known that the length scale associated with a normal diffusion transport process increases with the square root of time. However, clear evidence shows that diffusion in some systems ( for example, break through of contaminants or foraging patterns of grazers) is anomalous. That is, in anomolous systems the associated length scale changes with a time exponent that is less than (sub-diffusion) or greater than (super-diffusion) the expected value of the square root exponent of n=1/2. Voller presents some simple stochastic, physical and numerical experiments that demonstrate how anomalous diffusion behaviors can be induced. In particular, he considers engineering systems related to infiltration of moisture into porous heterogeneous soils and solidification phase change of metal matrix composites.
