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Advection and dispersion in time and space |
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| Authors: | B Baeumer DA Benson MM Meerschaert |
| Institution: | aDepartment of Mathematics and Statistics, University of Otago, Dunedin, New Zealand bDesert Research Institute, 2215 Raggio Parkway, Reno NV 89512, USA cDepartment of Physics, University of Nevada, Reno NV 89557, USA |
| Abstract: | Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly. |
| Keywords: | Anomalous diffusion Continuous time random walks First passage time Fractional calculus Subdiffusion Power laws |
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