33rd M. Smoluchowski Symposium on Statistical Physics

3-4 December 2020
Europe/Warsaw timezone

Steady oscillations in kinetic model of aggregation process with collisional fragmentation

3 Dec 2020, 18:19
1m
poster

Speaker

Dr. Sergey Matveev (Skolkovo Institute of Science and Technology)

Description

In this work, we study a kinetic model of aggregation process with collisional fragmentation with use of two efficient implementations of numerical methods: direct simulation Monte Carlo and finite-difference scheme exploiting the low-rank matrix representations of the utilized kinetic coefficients. We concentrate our efforts on the analysis of the solutions for a particular class of non-local aggregation kernels
$$K_{i,j} = i^a j^{-a} + i^{-a} j^{a},$$ with multiplicative expression for the fragmentation rates $F_{i,j} = \lambda K_{i,j}$ with $0 < \lambda \ll 1$. For $a > 0.5$ and $\lambda < \lambda_{c}$ never-ending collective oscillations of the aggregates' concentrations take place[1].

The main contribution of this work is cross-validation of our previous observations with the utilization of the well-known stochastic acceptance-rejection method [2] and its modification to an accounting of the fragmentation events.

[1] Brilliantov N. V., Otieno W., Matveev S. A., Smirnov A. P., Tyrtyshnikov E. E., Krapivsky P. L. (2018) // Steady oscillations in aggregation-fragmentation processes. Physical Review E, 98(1), 012109.
[2] Garcia A. L., Van Den Broeck C., Aertsens M., Serneels R. (1987) // A Monte Carlo simulation of coagulation. Physica A: Statistical Mechanics and its Applications, 143(3), 535-546.

Primary authors

Dr. Sergey Matveev (Skolkovo Institute of Science and Technology) Mr. Aleksei Kalinov (Skolkovo Institute of Science and Technology) Prof. Pavel Krapivsky (Boston University) Prof. Nikolai Brilliantov (Skolkovo Institute of Science and Technology)

Presentation Materials

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