Ramakrishna, S. Anantha ; Kumar, N. (1999) Diffusion of particles moving with constant speed Physical Review E, 60 (2). pp. 13811389. ISSN 1063651X

PDF
 Publisher Version
773kB 
Official URL: http://pre.aps.org/abstract/PRE/v60/i2/p1381_1
Related URL: http://dx.doi.org/10.1103/PhysRevE.60.1381
Abstract
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A FokkerPlanck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement <x^{n}> along with an approximate expression for the marginal probability distribution function P(x,t) are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time (8t) only after which the diffusion approximation becomes valid. This factor of 8 is a wellknown experimental fact. A persistence exponent of 0.435±0.005 is calculated for this process in two dimensions by studying the survival probability of the particle in a semiinfinite medium. The case of a stochastic amplifying medium is also discussed.
Item Type:  Article 

Source:  Copyright of this article belongs to American Physical Society. 
ID Code:  18352 
Deposited On:  17 Nov 2010 09:27 
Last Modified:  17 May 2016 03:04 
Repository Staff Only: item control page