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Oscillations in Aggregation-Shattering Processes
S A Matveev1,2,3, P L Krapivsky4, A P Smirnov2,3
1Skolkovo Institute of Science and Technology, 143026 Moscow, Russia.
Abstract:
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
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