Continuous Time Random Walks in finite domains and general boundary conditions: some formal considerations
- Asociacion EURATOM-CIEMAT
- CIEMAT, Madrid
- ORNL
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behavior of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 931157
- Journal Information:
- Journal of Physics A-Mathematical and Theoretical, Vol. 41, Issue 5
- Country of Publication:
- United States
- Language:
- English
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