A kinetic equation for linear stable fractional motion with applications to space plasma physics
- British Antarctic Survey, Cambridge, UK
- ORNL
- University of Warwick, UK
Levy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining {alpha}-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst 'sizes' and 'durations' in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.
- 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:
- 951287
- Journal Information:
- Physical Review E, Vol. 79, Issue 4; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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