ABSTRACT
Over the few last decades, there has been a growing interest in non-Fickian or anomalous transport processes. Both through experiments and theory it has been known for about half a century that dispersivities or dispersion coecients grow with time or scale of observation (e.g., Figure 5.1 in Gelhar [1993]). e standard description of an anomalous dispersive process is one where the mean square displacement (MSD) goes asymptotically as time to some power, b other than 1. If 0 < β < 1, then the process is called subdispersive, and if b > 1, then it is superdispersive. Lévy processes (Samorodnitsky and Taqqu, 1994; Sato, 1999), which do not have a nite second moment, fall into the superdispersive category. e case where b = 1 corresponds to a classical Fickian motion (though there are innitely many processes with b = 1 that are not Fickian [Kong and Cohen, 1989; Cushman and O’Malley, 2012a]).
