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1/f fluctuations in diffusion processes of effective space dimension less than one

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1 Author(s)
Agu, Masahiro ; Department of Electronics, Faculty of Engineering, Ibaraki University, Hitachi, Ibaraki, 360, Japan

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It is shown that the stationary fluctuations described by the diffusion equation of an effective space dimension less than one have a 1/f spectrum. A physical diffusion model equivalent to such a low dimensional diffusion process is proposed. Here, a singular disturbance of temperature fluctuation is assumed to diffuse with the space‐dependent diffusion coefficient D(r)=D0(1+κr-m)θ. Here, D0 is the constant part of the diffusion coefficient and κr-m represents the effect of local temperature enhancement of the background medium caused by the singular disturbance itself, where r is the distance from the singular disturbance at r=0, and m and θ positive constants.

Published in:

Journal of Applied Physics  (Volume:54 ,  Issue: 3 )