Henry, B. I. and Langlands, Trevor 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.
|Item Type:||Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)|
|Additional Information:||Chapter 2. Electronic copy held USQ Library For more information contact Dr Trevor Langlands Trevor.Langlands@usq.edu.au|
|Uncontrolled Keywords:||fractional calculus; anomalous subdiffusion; random walks; superdiffusion|
|Subjects:||230000 Mathematical Sciences > 230200 Statistics > 230202 Stochastic Analysis and Modelling
230000 Mathematical Sciences > 230100 Mathematics > 230107 Differential, Difference and Integral Equations
230000 Mathematical Sciences > 230100 Mathematics > 230113 Dynamical Systems
|Depositing User:||Dr Trevor Langlands|
|Date Deposited:||19 Sep 2010 02:21|
|Last Modified:||02 Jul 2013 23:53|
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