任意尺寸滚动颗粒的通用性质,Physical Review E

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任意尺寸滚动颗粒的通用性质
Physical Review E ( IF 2.2 ) Pub Date : 2020-10-27 , DOI: 10.1103/physreve.102.042133
Francesco Mori , Pierre Le Doussal , Satya N. Majumdar , Grégory Schehr

我们考虑一个活跃的滚滚粒子（RTP）

d

尺寸，从原点开始并随时间间隔发展

[0 ， Ť]

。我们检查了RTP动力学的三种不同模型：具有瞬时滚动的标准RTP模型，具有瞬时运行的变体以及其中滚动和运行均非瞬时的通用模型。对于这些模型中的每一个，我们将Sparre Andersen定理用于离散时间随机游动，以准确计算出

X

组件不会更改注册时间

Ť

，表明它不依赖于

d

。作为此结果的结果，我们精确计算了其他

X

-组件属性，即最大时间的分布和记录统计信息，表明它们是通用的，即它们不依赖于

d

。而且，我们证明，如果速度

v

从一般概率分布中得出，每次翻滚后粒子的“随机数”都是随机的。我们的发现被数值模拟所证实。其中一些结果已在最近的一封信中宣布。牧师 124，090603（2020）]。

"点击查看英文标题和摘要"

Universal properties of a run-and-tumble particle in arbitrary dimension

We consider an active run-and-tumble particle (RTP) in

d

dimensions, starting from the origin and evolving over a time interval

[0, t]

. We examine three different models for the dynamics of the RTP: the standard RTP model with instantaneous tumblings, a variant with instantaneous runs and a general model in which both the tumblings and the runs are noninstantaneous. For each of these models, we use the Sparre Andersen theorem for discrete-time random walks to compute exactly the probability that the

x

component does not change sign up to time

t

, showing that it does not depend on

d

. As a consequence of this result, we compute exactly other

x

-component properties, namely, the distribution of the time of the maximum and the record statistics, showing that they are universal, i.e., they do not depend on

d

. Moreover, we show that these universal results hold also if the speed

v

of the particle after each tumbling is random, drawn from a generic probability distribution. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 124, 090603 (2020)].

更新日期：2020-10-30

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