Graduate Student Seminar

Speaker: Dr. Hans Werner Van Wyk  

Title:  Anomalous Diffusion: Applications, Models, Numerical Approximation

Abstract:  For many diffusion processes encountered in nature, Fick's classic constitutive law for diffusive fluxes is not valid. The heat equation can often still be used to describe these 'anomalous' diffusions, as long as the standard Laplace operator is replaced with its more mysterious counterpart, the fractional Laplacian. This non-local integro-differential operator has been applied in fields ranging from quantum mechanics to animal foraging and mathematical finance. While a standard definition for the fractional Laplacian exists on unbounded domains, various modeling approaches give rise to different (but related) generalizations on bounded domains. We discuss two particular such models, their uses, and their numerical approximation.