Brownian sampling in an unbounded space.
As a particle undergoes translational Brownian motion in an unbounded space, the particle samples the space. Traditionally the sampling in N dimensions is quantified in terms of average squared distance traversed (<x . x>). However, another quantitative measure of the sampled space is the total number (n) of equispaced regions (of size LN) sampled after a particle moves with a diffusion coefficient (D) for a time (t). Calculations show that the average <n>=a(Dt/L2)b. Results are given for a and b for 1, 2, 3, and 4 dimensions.
Velegol
Darrell
D
Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802, USA. velegol@psu.edu