论文标题
随机重置下的恒定内核聚集
Aggregation with constant kernel under stochastic resetting
论文作者
论文摘要
用恒定核的二进制聚集模型进行随机重置：任何大小的聚集体在独立随机时期爆炸成单体。这些重置时间是泊松分布的，该过程的速率称为重置率。主方程在任何大小的聚集体浓度的生成函数中产生一个Bernoulli-Type方程，可以准确求解。这种重置处方会导致骨料密度的非平衡稳态，这是骨料大小的函数，由重置速率的函数重新缩放。如果将重置速率设置为汇总尺寸（减一个），则给定尺寸的聚集体的稳态密度将最大化。
The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the process is called the resetting rate. The master equation yields a Bernoulli-type equation in the generating function of the concentration of aggregates of any size, which can be solved exactly. This resetting prescription leads to a non-equilibrium steady state for the densities of aggregates, which is a function of the size of the aggregate, rescaled by a function of the resetting rate. The steady-state density of aggregates of a given size is maximised if the resetting rate is set to the quotient of the aggregation rate by the size of the aggregate (minus one).
