Brownian motion of fractal particles: Lévy flights from white noise

Kiran M. Kolwankar
(Please use for correspondence this email).

Submission date: 14. Nov. 2005
Pages: 7
paper submitted to: Physical review : E
PACS-Numbers: 05.40.-a, 05.10.Gg, 05.45.Df, 87.10.+e
Keywords and phrases: brownian motion, fractal, fractional calculus, levy process
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Abstract:
We generalise the Langevin equation with Gaussian white noise by replacing the velocity term by a local fractional derivative. The solution of this equation is a Lévy process. We further consider the Brownian motion of a fractal particle, for example, a colloidal aggregate or a biological molecule and argue that it leads to a Lévy flight. This effect can also be described using the local fractional Langevin equation. The implications of this development to other complex data series are discussed.