Oscillations in Aggregation-Shattering Processes

• Published in: Physical review letters Vol. 119; no. 26; p. 260601
• Main Authors: Matveev, S A, Krapivsky, P L, Smirnov, A P, Tyrtyshnikov, E E, Brilliantov, N V
• Format: Journal Article
• Language: English
• Published: United States 29-12-2017
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.119.260601

We observe never-ending oscillations in systems undergoing collision-controlled aggregation and shattering. Specifically, we investigate aggregation-shattering processes with aggregation kernels K_{i,j}=(i/j)^{a}+(j/i)^{a} and shattering kernels F_{i,j}=λK_{i,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<λ_{c}(a), oscillations apparently persist forever. Thus, never-ending oscillations can arise in closed aggregation-shattering processes without sinks and sources of particles.