posted on 2018-04-30, 08:58authored byS. A. Matveev, P. L. Krapivsky, A. P. Smirnov, E. E. Tyrtyshnikov, Nikolai V. Brilliantov
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
History
Citation
Physical Review Letters, 2017, 119 (26), 260601
Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics