论文标题
由源驱动的简化凝血碎裂系统中自发振荡的起源
Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source
论文作者
论文摘要
我们考虑一个粒子聚合簇的系统，并经过质量依赖性率的凝结和碎裂过程。每个单体粒子都可以用较大的簇聚集，每个簇可以碎片成与聚集速率成正比的单个单体。簇密度的动力学由一组Smoluchowski方程组件，我们考虑以恒定速率增加单体源。可以简化整个动力学，以求解独特的非线性微分方程，该方程在特定的参数范围内显示自振荡，并且对于系统中的许多不同群集而言，它足够大。这种集体现象是由于存在波动的阻尼系数引起的，并且与在更一般的物理系统（例如van der pol振荡器）中观察到的liénard自我振荡机制密切相关。
We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentation processes with mass dependent rates. Each monomer particle can aggregate with larger clusters, and each cluster can fragment into individual monomers with a rate directly proportional to the aggregation rate. The dynamics of the cluster densities is governed by a set of Smoluchowski equations, and we consider the addition of a source of monomers at constant rate. The whole dynamics can be reduced to solving a unique non-linear differential equation which displays self-oscillations in a specific range of parameters, and for a number of distinct clusters in the system large enough. This collective phenomenon is due to the presence of a fluctuating damping coefficient and is closely related to the Liénard self-oscillation mechanism observed in a more general class of physical systems such as the van der Pol oscillator.
