当前位置: X-MOL 学术Phys. Rev. E › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Competition in a system of Brownian particles: Encouraging achievers
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-15 , DOI: 10.1103/physreve.106.034125
P L Krapivsky 1, 2 , Ohad Vilk 3, 4, 5 , Baruch Meerson 3
Affiliation  

We introduce and analytically and numerically study a simple model of interagent competition, where underachievement is strongly discouraged. We consider N1 particles performing independent Brownian motions on the line. Two particles are selected at random and at random times, and the particle closest to the origin is reset to it. We show that, in the limit of N, the dynamics of the coarse-grained particle density field can be described by a nonlocal hydrodynamic theory which was encountered in a study of the spatial extent of epidemics in a critical regime. The hydrodynamic theory predicts relaxation of the system toward a stationary density profile of the “swarm” of particles, which exhibits a power-law decay at large distances. An interesting feature of this relaxation is a nonstationary “halo” around the stationary solution, which continues to expand in a self-similar manner. The expansion is ultimately arrested by finite-N effects at a distance of order N from the origin, which gives an estimate of the average radius of the swarm. The hydrodynamic theory does not capture the behavior of the particle farthest from the origin—the current leader. We suggest a simple scenario for typical fluctuations of the leader's distance from the origin and show that the mean distance continues to grow indefinitely as t. Finally, we extend the inter-agent competition from n=2 to an arbitrary number n of competing Brownian particles (nN). Our analytical predictions are supported by Monte Carlo simulations.

中文翻译:

布朗粒子系统中的竞争:鼓励成就者

我们引入并分析和数值研究了一个简单的代理间竞争模型,强烈不鼓励成绩不佳。我们认为ñ1粒子在线上进行独立的布朗运动。随机和随机时间选择两个粒子,最接近原点的粒子被重置为它。我们证明,在极限ñ,粗粒度粒子密度场的动力学可以通过非局部流体动力学理论来描述,该理论在临界状态下流行病的空间范围研究中遇到。流体动力学理论预测系统将向粒子“群”的固定密度分布弛豫,该分布在远距离处表现出幂律衰减。这种松弛的一个有趣特征是围绕固定解的非固定“光环”,它继续以自相似的方式扩展。膨胀最终被有限-ñ距离有序的效果ñ从原点,它给出了群体平均半径的估计。流体动力学理论没有捕捉到离原点最远的粒子——当前的领导者——的行为。我们为领导者与原点的距离的典型波动提出了一个简单的场景,并表明平均距离继续无限增长. 最后,我们将代理间竞争从n=2到任意数n竞争布朗粒子(nñ)。我们的分析预测得到了蒙特卡洛模拟的支持。
更新日期:2022-09-16
down
wechat
bug