Stochastic fractal behavior in concentration fluctuation and fluorescence correlation spectroscopy

Fluctuations in the concentration of Brownian particles in one and two dime nsions, or any reasonable measurement of the concentration such as in fluor escence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spect:rum of the fluctu ation S(omega) similar to omega(-1/2) for diffusion in one dimension, - log omega in two dimensions, but non-singular in three dimensions. This discov ery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discuss ed. (C) 1999 Elsevier Science B.V. All rights reserved.