Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term

Details Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term

2003-10-03

arxiv.org/abs/cond-mat/0310063v2

Physical Review E Vol. 69, 061114 (2004).

Physics

Condensed Matter

Statistical Mechanics

This article is an expanded version of a talk given at IHP workshop "Dynamics, Growth and Singularities of Continuous Media",

Scientific paper

10.1103/PhysRevE.69.061114

In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov type in the sense that they carry a constant flux of mass from small masses to large. We derive a ``locality criterion'', expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissiblesolution. Whether a given kernel leads to a gelation transition or not can be determined by computing the mass capacity of the Kolmogorov spectrum. As an example, we compute the exact stationary state for the family of kernels,$K_\zeta(m_1,m_2)=(m_1m_2)^{\zeta/2}$ which includes both gelling and non-gelling cases, reproducing the known solution in the case $\zeta=0$. Surprisingly, the Kolmogorov constant is the same for all kernels in this family.

Affiliated with

Also associated with

No associations

Rating

Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term 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 Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stationary Kolmogorov Solutions of the Smoluchowski Aggregation Equation with a Source Term will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-570974