Brownian motion of fractal particles: Levy flights from white noise

Details Brownian motion of fractal particles: Levy flights from white noise Brownian motion of fractal particles: Levy flights from white noise

2005-11-14

arxiv.org/abs/cond-mat/0511307v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, two columns

Scientific paper

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 Levy 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 Levy 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.

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