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Kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts
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Watkins, N. W., Credgington, D., Sanchez, R., Rosenberg, S. J. and Chapman, S. C.. (2009) Kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.79 (No.4 Part 1). article no. 041124 . ISSN 1539-3755
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Official URL: http://dx.doi.org/10.1103/PhysRevE.79.041124
Abstract
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Divisions: | Faculty of Science > Physics |
| Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) |
| Publisher: | American Physical Society |
| ISSN: | 1539-3755 |
| Date: | April 2009 |
| Volume: | Vol.79 |
| Number: | No.4 Part 1 |
| Number of Pages: | 9 |
| Page Range: | article no. 041124 |
| Identification Number: | 10.1103/PhysRevE.79.041124 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Science and Technology Facilities Council (Great Britain) (STFC), National Science Foundation (U.S.) (NSF) |
| Grant number: | NSF PHY05-51164 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/27961 |
Data sourced from Thomson Reuters' Web of Knowledge
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