PMID: 15244637Jul 13, 2004Paper

Simple jumping process with memory: transport equation and diffusion

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A Kamińska, T Srokowski

Abstract

We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.

References

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May 9, 1994·Physical Review Letters·C R DoeringJ Riordan
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Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E Ben-Naim, P L Krapivsky
Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Srokowski
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Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Kamińska, T Srokowski

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Citations

Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Srokowski, A Kamińska
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tomasz Srokowski
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Srokowski
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tomasz Srokowski
Jun 13, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tomasz Srokowski
Oct 21, 2017·Physical Review Letters·Karel ProesmansChristian Van den Broeck
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Srokowski, A Kamińska
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tomasz Srokowski
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C Van den Broeck, R Toral

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