Nontrivial Exponent for Simple Diffusion

Details Nontrivial Exponent for Simple Diffusion Nontrivial Exponent for Simple Diffusion

1996-05-14

arxiv.org/abs/cond-mat/9605084v2

Phys. Rev. Lett. 77 (1996) 2867

Physics

Condensed Matter

Minor typos corrected, affecting table of exponents. 4 pages, REVTEX, 1 eps figure. Uses epsf.sty and multicol.sty

Scientific paper

10.1103/PhysRevLett.77.2867

The diffusion equation \partial_t\phi = \nabla^2\phi is considered, with initial condition \phi( _x_ ,0) a gaussian random variable with zero mean. Using a simple approximate theory we show that the probability p_n(t_1,t_2) that \phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim [\ln(t_2/t_1)]^n(t_1/t_2)^{-\theta}. The exponent \theta has predicted values 0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with simulation results.

Affiliated with

Also associated with

No associations

Rating

Nontrivial Exponent for Simple Diffusion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nontrivial Exponent for Simple Diffusion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nontrivial Exponent for Simple Diffusion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-313906