论文标题
在有肥沃部位的线上运行式颗粒
Run-and-tumble particles on a line with a fertile site
论文作者
论文摘要
我们提出了一个在原始位置肥沃部位的线上的跑步颗粒(RTP)模型。经过肥沃的部位后,奔跑的颗粒会产生新的颗粒,直到它翻转方向。创建新颗粒的过程是由生育功能(距离肥沃部位的距离)建模的,乘以生育率。如果初始条件对应于具有均匀概率密度的单个RTP,则系统是偶然不变的。运动方程可以通过原点的右迁移密度在拉普拉斯域中求解。在很大程度上,该密度仅以仅取决于生育功能和生育率的速率呈指数增长。此外,RTPS的总密度(除以原始右手的密度)达到了不取决于初始条件的固定状态,并在肥沃的部位呈现局部最小值。
We propose a model of run-and-tumble particles (RTPs) on a line with a fertile site at the origin. After going through the fertile site, a run-and-tumble particle gives rise to new particles until it flips direction. The process of creation of new particles is modelled by a fertility function (of the distance to the fertile site), multiplied by a fertility rate. If the initial conditions correspond to a single RTP with even probability density, the system is parity-invariant. The equations of motion can be solved in the Laplace domain, in terms of the density of right-movers at the origin. At large time, this density is shown to grow exponentially, at a rate that depends only on the fertility function and fertility rate. Moreover, the total density of RTPs (divided by the density of right-movers at the origin), reaches a stationary state that does not depend on the initial conditions, and presents a local minimum at the fertile site.