An introduction to fractional diffusion

Henry, B. I. and Langlands, Trevor ORCID: and Straka, P. (2010) An introduction to fractional diffusion. In: Proceedings of the 22nd Canberra International Physics Summer School, 8-19 Dec 2008, Canberra, Australia.

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The mathematical description of diffusion has a long history with many different formulations including phenomenological models based on conservation of mass and constitutive laws; probabilistic models based on random walks and central limit theorems; microscopic stochastic models based on Brownian motion and Langevin equations; and mesoscopic stochastic models based on master equations and Fokker-Planck equations. A fundamental result common to the different approaches is that the mean square displacement of a diffusing particle scales linearly with time. However there have been numerous experimental measurements in which the mean square displacement of diffusing particles scales as a fractional order power law in time. In recent years a great deal of progress has been made in extending the different models for diffusion to incorporate this fractional diffusion. The tools of fractional calculus have proven very useful in these developments, linking together fractional constitutive laws, continuous time random walks, fractional Langevin equations and fractional Brownian motions. These notes provide a tutorial style overview of standard and fractional diffusion processes.

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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Chapter 2. Electronic copy held USQ Library For more information contact Dr Trevor Langlands
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited: 19 Sep 2010 02:21
Last Modified: 02 Jul 2013 23:53
Uncontrolled Keywords: fractional calculus; anomalous subdiffusion; random walks; superdiffusion
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
02 Physical Sciences > 0299 Other Physical Sciences > 029902 Complex Physical Systems
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling
51 PHYSICAL SCIENCES > 5199 Other physical sciences > 519901 Complex physical systems
49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490410 Partial differential equations
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
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