台球系统的逃逸和缩放特性研究。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0222215
Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech, Edson Denis Leonel
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引用次数: 0

摘要

我们研究了一个台球系统中逃逸粒子的一些统计特性,该系统的边界由两个控制参数描述,边界上有一个洞。首先,我们分析了不同孔洞位置和大小下的存活概率。我们注意到,当洞部分或全部位于相空间中的大型稳定岛上时,存活概率呈指数衰减,并带有特征性的幂律尾部。我们发现,存活概率与孔的大小呈比例不变性。与此相反,置于主要混沌区域的洞的存活概率偏离了指数衰减。我们同时引入了两个洞,并通过盆地熵和盆地边界熵研究了不同洞大小和控制参数下逃逸盆地的复杂性。我们发现了这些熵与系统参数之间的非微妙关系,并证明在特定的控制参数区间内,盆地熵表现出缩放不变性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An investigation of escape and scaling properties of a billiard system.

We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice that the survival probability follows an exponential decay with a characteristic power-law tail when the hole is positioned partially or entirely over large stability islands in phase space. We find that the survival probability exhibits scaling invariance with respect to the hole size. In contrast, the survival probability for holes placed in predominantly chaotic regions deviates from the exponential decay. We introduce two holes simultaneously and investigate the complexity of the escape basins for different hole sizes and control parameters by means of the basin entropy and the basin boundary entropy. We find a non-trivial relation between these entropies and the system's parameters and show that the basin entropy exhibits scaling invariance for a specific control parameter interval.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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