ИСТИНА

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} = λK_{i,j} with 0 < λ << 1. For a > 0.5 and λ < λ_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.