Memory of fracture in information geometry

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2024-10-10 DOI:10.1016/j.chaos.2024.115608

{"title":"Memory of fracture in information geometry","authors":"","doi":"10.1016/j.chaos.2024.115608","DOIUrl":null,"url":null,"abstract":"<div><div>In this study, the memory effect of the fracture phenomenon in information geometry is discussed. The input–output relation in a complex system as an application of fractional calculus generates the power law for the time and response time distribution, which determines the memory effect. The exponent of the response time distribution is related to the one of the various power laws for fracture phenomena, including earthquakes. The one of them is the shape parameter of the Weibull distribution, which indicates uniformity in the material. The exponent of the response time distribution is also linked to the magnitude of the change rate in the information density and the non-extensivity of the information in the statistical manifold for the response time distribution. From the discussion of the properties of their exponents, the memory effect of a fracture depends on the response time distribution with the uniformity of the material and reflects the information density for parameters related to the fracture and the non-extensivity of the information in the statistical manifold for the response time distribution. Moreover, we propose a method to understand fracture phenomena using information geometry for the response time distribution.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077924011603","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

In this study, the memory effect of the fracture phenomenon in information geometry is discussed. The input–output relation in a complex system as an application of fractional calculus generates the power law for the time and response time distribution, which determines the memory effect. The exponent of the response time distribution is related to the one of the various power laws for fracture phenomena, including earthquakes. The one of them is the shape parameter of the Weibull distribution, which indicates uniformity in the material. The exponent of the response time distribution is also linked to the magnitude of the change rate in the information density and the non-extensivity of the information in the statistical manifold for the response time distribution. From the discussion of the properties of their exponents, the memory effect of a fracture depends on the response time distribution with the uniformity of the material and reflects the information density for parameters related to the fracture and the non-extensivity of the information in the statistical manifold for the response time distribution. Moreover, we propose a method to understand fracture phenomena using information geometry for the response time distribution.

查看原文本刊更多论文

信息几何中的断裂记忆

本研究讨论了信息几何中断裂现象的记忆效应。作为分数微积分的应用，复杂系统中的输入输出关系产生了时间和响应时间分布的幂律，从而决定了记忆效应。响应时间分布的指数与断裂现象（包括地震）的各种幂律之一相关。其中一个是表示材料均匀性的威布尔分布的形状参数。响应时间分布的指数也与响应时间分布统计流形中信息密度变化率的大小和信息的非扩展性有关。通过对其指数性质的讨论，断裂的记忆效应取决于材料均匀性的响应时间分布，并反映了与断裂相关参数的信息密度和响应时间分布统计流形中信息的非扩展性。此外，我们还提出了一种利用响应时间分布的信息几何学来理解断裂现象的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.