Compact Waves in Microscopic Nonlinear Diffusion

Details Compact Waves in Microscopic Nonlinear Diffusion Compact Waves in Microscopic Nonlinear Diffusion

2011-12-27

arxiv.org/abs/1112.5988v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from vacuum. In $d$ spatial dimensions, the front advances as $t^{1/(2+da)}$ according to hydrodynamics, with $a$ the nonlinearity exponent. We show that fluctuations in the front position grow as $\sim t^{\mu} \eta$, where $\mu<1/(2+da)$ is a new exponent that we measure and $\eta$ is a random variable whose distribution we characterize. Fluctuating corrections to hydrodynamic profiles give rise to an excess penetration into vacuum, revealing scaling and universal behavior. We also examine the discharge of a nonlinear rarefaction wave into vacuum. Our results suggest the existence of universal scaling behavior at the fluctuating level in nonlinear diffusion.

Affiliated with

Also associated with

No associations

Rating

Compact Waves in Microscopic Nonlinear 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 Compact Waves in Microscopic Nonlinear Diffusion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compact Waves in Microscopic Nonlinear Diffusion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-37462