Anomalous diffusion

Anomalous diffusion is a term used to describe a diffusion process with a non-linear relationship to time, in contrast to a typical diffusion process, in which the mean squared displacement (MSD), σ_r², of a particle is a linear function of time. Physically, the MSD can be considered the amount of space the particle has "explored" in the system.

Diffusion is often described by a power law^[1][2], σ_r² ~ Dt^α, where D is the diffusion coefficient and t is the elapsed time. In a typical diffusion process, α = 1. If α > 1, the phenomenon is called super-diffusion. Super-diffusion can be the result of active cellular transport processes. If α < 1, the particle undergoes sub-diffusion. Recently, the role of Anomalous diffusion has received attention within the literature to describe many physical scenarios, most prominently within crowded systems, for example protein diffusion within cells, or diffusion through porous media.

Sub-diffusion has been proposed as a measure of macromolecular crowding in the cytoplasm.

Types of Anomalous diffusion

Of interest within the scientific community, when one an anomalous-type diffusion process, is to then understand the underlying mechanism which has caused it. There are a number of frameworks which give rise to anomalous diffusion that are currently in vogue within the statistical physics community. These are continuous-time random walks (CTRW) and fractional Brownian motion (fBm), and diffusion on fractal topology.

Related Topics

• Levy flights
• Random walks
• Percolation
• Long term correlations
• long range dependencies
• Hurst exponent
• Detrended fluctuatoin analysis [DFA]

References

• Avi Caspi, Rony Granek, and Michael Elbaum. "Diffusion and directed motion in cellular transport." Physical Review E 66, 011916 (2002).
• Matthias Weiss, Markus Elsner, Fredrik Kartberg, and Tommy Nilsson. "Anomalous Subdiffusion Is a Measure for Cytoplasmic Crowding in Living Cells." Biophysical Journal 87 : 3518-3524 (2004)
• Jean-Philippe Bouchaud. "Anomalous diffusion in disordered media." Physics Reports 195 (4-5) : 127-293 (1990).
• A. von Kameke et al., "Propagation of a chemical wave front in a quasi-two-dimensional superdiffusive flow", Phys. Rev. E 81 6 (2010).

External links

• Boltzmann's transformation, Parabolic law (animation)
• Anomalous interface shift kinetics (Computer simulations and Experiments)

This chemistry-related article is a stub. You can help Wikipedia by expanding it. v d e

This physics-related article is a stub. You can help Wikipedia by expanding it. v d e