标题： 具有对随机输入的阶梯式响应的跑动-翻转运动 显示英文标题

标题： Run-and-tumble motion with step-like responses to a stochastic input

摘要： 我们研究一种简单的跑停随机游走，其从跑模式切换到停模式以及反向的切换频率取决于一个随机信号。 我们考虑一种特别尖锐、阶梯状的依赖关系，其中当信号从下方穿过某个特定值（例如 y_1 ）时，跑至停的切换概率从零跳变为一。 同样，当信号从上方穿过另一个值（y_2 < y_1 ）时，停至跑的切换概率也出现类似的跳跃。 我们感兴趣的是表征信号噪声对随机行走者长期行为的影响。 我们考虑随机信号的两种不同的时间演化方式。 在一种情况下，信号动力学是一个独立的随机过程，不依赖于跑停运动。 在这种情况下，我们可以解析地计算跑持续时间和停持续时间的均值和完整分布函数。 在第二种情况下，我们假设信号动力学受到随机行走者空间位置的影响。 对于这个系统，我们数值测量了随机行走者的稳态位置分布。 我们讨论了我们的系统与大肠杆菌趋化性之间的一些相似之处和差异，大肠杆菌趋化性是自然界中另一种广为人知的跑停运动。 显示英文摘要

摘要： We study a simple run-and-tumble random walk whose switching frequency from run mode to tumble mode and the reverse depend on a stochastic signal. We consider a particularly sharp, step-like dependence, where the run to tumble switching probability jumps from zero to one as the signal crosses a particular value (say y_1 ) from below. Similarly, tumble to run switching probability also shows a jump like this as the signal crosses another value (y_2 < y_1 ) from above. We are interested in characterizing the effect of signaling noise on the long time behavior of the random walker. We consider two different time-evolutions of the stochastic signal. In one case, the signal dynamics is an independent stochastic process and does not depend on the run-and-tumble motion. In this case we can analytically calculate the mean value and the complete distribution function of the run duration and tumble duration. In the second case, we assume that the signal dynamics is influenced by the spatial location of the random walker. For this system, we numerically measure the steady state position distribution of the random walker. We discuss some similarities and differences between our system and E.coli chemotaxis, which is another well-known run-and-tumble motion encountered in nature.