We present a novel form of collective oscillatory behavior in the kinetics of irreversible coagulation with a constant input of monomers and removal of large clusters. For a broad class of collision rates, this system reaches a non-equilibrium stationary state at large times and the cluster size distribution tends to a universal form characterised by a constant flux of mass through the space of cluster sizes. Universality, in this context, means that the stationary state becomes independent of the cut-off as the cut-off grows. This universality is lost, however, if the aggregation rate between large and small clusters increases sufficiently steeply as a function of cluster sizes. We identify a transition to a regime in which the stationary state vanishes as the cut-off grows. This non-universal stationary state becomes unstable, however, as the cut-off is increased and undergoes a Hopf bifurcation. After this bifurcation, the stationary kinetics are replaced by persistent and periodic collective oscillations. These oscillations carry pulses of mass through the space of cluster sizes. As a result, the average mass flux remains constant. Furthermore, universality is partially restored in the sense that the scaling of the period and amplitude of oscillation is inherited from the dynamical scaling exponents of the universal regime. The implications of this new type of long-time asymptotic behaviour for other driven non-equilibrium systems are discussed.
Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source
我们考虑一个系统的聚集团的颗粒，受到凝聚和破碎过程的质量依赖率。每个单体颗粒可以聚集成更大的簇，并且每个簇可以以与聚集速率成正比的速率碎裂成单个单体。的集群密度的动力学是由一组Smoluchowski方程，我们认为，除了在恒定速率的单体源。整个动力学可以归结为求解一个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，并且对于系统中足够大的一些不同的簇。这种集体现象是由于存在波动的阻尼系数，并且与在更一般的物理系统中观察到的Liénard自振荡机制密切相关，例如van der Pol振荡器。
