Oscillations in Aggregation-Shattering Processes

S. A. Matveev, P. L. Krapivsky, A. P. Smirnov, E. E. Tyrtyshnikov, N. V. Brilliantov

    Research output: Contribution to journalArticlepeer-review

    28 Citations (Scopus)


    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.

    Original languageEnglish
    Article number260601
    JournalPhysical Review Letters
    Issue number26
    Publication statusPublished - 28 Dec 2017


    Dive into the research topics of 'Oscillations in Aggregation-Shattering Processes'. Together they form a unique fingerprint.

    Cite this