Compact waves in microscopic nonlinear diffusion

作者：Hurtado P I^*; Krapivsky P L

来源：Physical Review E, 2012, 85(6): 060103.

DOI：10.1103/PhysRevE.85.060103

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 similar to t(mu)eta, where mu %26lt; 1/2+da is an 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 behaviors and robust features. We also examine the discharge of a nonlinear rarefaction wave into vacuum. Our results suggest the existence of universal scaling behaviors at the fluctuating level in nonlinear diffusion.

• 出版日期2012-6-21