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Title: Oscillations in Aggregation-Shattering Processes
Authors: Matveev, S. A.
Krapivsky, P. L.
Smirnov, A. P.
Tyrtyshnikov, E. E.
Brilliantov, Nikolai V.
First Published: 28-Dec-2017
Publisher: American Physical Society
Citation: Physical Review Letters, 2017, 119 (26), 260601
Abstract: We observe never-ending oscillations in systems undergoing collision-controlled aggregation and shattering. Specifically, we investigate aggregation-shattering processes with aggregation kernels Ki,j=(i/j)a+(j/i)a and shattering kernels Fi,j=λKi,j, where i and j are cluster sizes, and parameter λ quantifies the strength of shattering. When 0≤a<1/2, there are no oscillations, and the system monotonically approaches a steady state for all values of λ; in this region, we obtain an analytical solution for the stationary cluster size distribution. Numerical solutions of the rate equations show that oscillations emerge in the 1/2<a≤1 range. When λ is sufficiently large, oscillations decay and eventually disappear, while for λ<λc(a), oscillations apparently persist forever. Thus, never-ending oscillations can arise in closed aggregation-shattering processes without sinks and sources of particles.
DOI Link: 10.1103/PhysRevLett.119.260601
ISSN: 0031-9007
eISSN: 1079-7114
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, American Physical Society. Deposited with reference to the publisher’s open access archiving policy. (
Appears in Collections:Published Articles, Dept. of Mathematics

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