We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the oscillations with respect to fluctuations and noise.

翻译：我们重新审视了两种基本直接模拟蒙特卡洛方法,以模拟集成动能学,并将其推广到碰撞碎裂(散乱)的集成过程;我们测试了扩展方法的性能和准确性,并以适用于同一模型的高效确定性有限差异方法比较其性能;我们验证了测试问题的随机方法,并运用这些方法来核实最近在确定性模拟中检测到的集成-碎裂动能学中是否存在振动系统;我们确认,这些系统中的密度出现了稳定的振动,并证明振动在波动和噪音方面的稳定性。