Qian H, Raymond G M, Bassingthwaighte J B
Department of Applied Mathematics, University of Washington, Seattle 98195, USA.
Biophys Chem. 1999 Jul 19;80(1):1-5. doi: 10.1016/s0301-4622(99)00031-9.
Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in two dimensions, but non-singular in three dimensions. This discovery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discussed.
一维和二维中布朗粒子浓度的波动，或者浓度的任何合理测量，比如荧光相关光谱法中的测量，被证明是具有长尾的随机分形。波动的功率谱(S(\omega))在(\omega = 0)处奇异，对于一维扩散，(S(\omega))近似为(\omega^{-1/2})；对于二维扩散，(S(\omega))近似为(\log\omega)；而在三维中是非奇异的。这一发现为可能的长记忆分形行为提供了一种简单的物理机制，并讨论了其对各种生物过程的影响。
