- Book学术

发布求助

文献互助智能选刊最新文献

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2024-09-17 DOI:10.1016/j.chaos.2024.115522

{"title":"Influence of an environment changing in time on crucial events: From geophysics to biology","authors":"","doi":"10.1016/j.chaos.2024.115522","DOIUrl":null,"url":null,"abstract":"<div>This paper is devoted to the study of the interaction between two distinct forms of non-stationary processes, which we will refer to as non-stationarity of the first and second kind. The non-stationarity of the first kind is caused by criticality-generated events that we call crucial events. Crucial events signal ergodicity breaking emerging from the interaction between the units of the complex system under study, indicating that the non stationarity of first kind has an internal origin. The non-stationarity of second kind is due to the influence on the system of interest of an environment changing in time, thereby implying an external origin. In this paper we show that the non-stationarity of first kind, measured by an inverse power law index <math><mi>μ</mi></math> is characterized by singularities at <math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn></mrow></math> and <math><mrow><mi>μ</mi><mo>=</mo><mn>3</mn></mrow></math>. We realize the interaction between the non-stationarity of first kind and the non-stationarity of second kind with a model frequently adopted to study earthquakes, namely, a system of main-shocks assumed to be crucial events, generating a cascade of after-shocks simulating the changing in time environment. We prove that the after-shocks significantly affect the detection of anomalous scaling, but in the case <math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></math>, which is sufficiently far from <math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn></mrow></math> and <math><mrow><mi>μ</mi><mo>=</mo><mn>3</mn></mrow></math>, both sources of singularities being strongly affected by the non-stationarity of second kind. To explain why it is possible to detect for earthquakes the value <math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>06</mn></mrow></math>, proposed in earlier work and very close to the singularity <math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn></mrow></math>, we advocate a new theoretical perspective, involving a deviation from the traditional concept of criticality in physics and borrowing suggestions from biology. This new approach is based on the truncation of inverse power laws that has the effect of shifting the intermediate asymptotics to short-time region, without weakening their role for information transmission. This leads us to the conclusion that the whole planet is a living system.</div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3000,"publicationDate":"2024-09-17","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/S0960077924010749","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

摘要

本文致力于研究两种不同形式的非稳态过程之间的相互作用，我们将其分别称为第一种和第二种非稳态过程。第一种非稳态是由临界产生的事件引起的，我们称之为关键事件。临界事件标志着所研究的复杂系统各单元之间的相互作用产生了遍历性破坏，表明第一种非静止性有其内在原因。第二种非静止性是由于随时间变化的环境对所研究系统的影响，从而意味着非静止性是由外部因素引起的。在本文中，我们证明了以反幂律指数 μ 衡量的第一类非静止性在 μ=2 和 μ=3 时具有奇异性。我们用研究地震时经常采用的一种模型来实现第一类非稳态和第二类非稳态之间的相互作用，即假定一个主震系统是关键事件，产生一连串模拟时间环境变化的余震。我们证明，余震会显著影响异常缩放的检测，但在μ=2.5的情况下，与μ=2和μ=3相差甚远，这两种奇异性来源都受到第二类非稳态的强烈影响。为了解释为什么在地震中可以检测到早先工作中提出的、非常接近奇点 μ=2 的值μ=2.06，我们提出了一个新的理论视角，它偏离了物理学中传统的临界概念，并借鉴了生物学中的建议。这种新方法基于对反幂律的截断，其效果是将中间渐近线转移到短时区域，而不会削弱它们在信息传输中的作用。这使我们得出结论：整个地球就是一个生命系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Influence of an environment changing in time on crucial events: From geophysics to biology

This paper is devoted to the study of the interaction between two distinct forms of non-stationary processes, which we will refer to as non-stationarity of the first and second kind. The non-stationarity of the first kind is caused by criticality-generated events that we call crucial events. Crucial events signal ergodicity breaking emerging from the interaction between the units of the complex system under study, indicating that the non stationarity of first kind has an internal origin. The non-stationarity of second kind is due to the influence on the system of interest of an environment changing in time, thereby implying an external origin. In this paper we show that the non-stationarity of first kind, measured by an inverse power law index $μ$ is characterized by singularities at $μ = 2$ and $μ = 3$ . We realize the interaction between the non-stationarity of first kind and the non-stationarity of second kind with a model frequently adopted to study earthquakes, namely, a system of main-shocks assumed to be crucial events, generating a cascade of after-shocks simulating the changing in time environment. We prove that the after-shocks significantly affect the detection of anomalous scaling, but in the case $μ = 2.5$ , which is sufficiently far from $μ = 2$ and $μ = 3$ , both sources of singularities being strongly affected by the non-stationarity of second kind. To explain why it is possible to detect for earthquakes the value $μ = 2.06$ , proposed in earlier work and very close to the singularity $μ = 2$ , we advocate a new theoretical perspective, involving a deviation from the traditional concept of criticality in physics and borrowing suggestions from biology. This new approach is based on the truncation of inverse power laws that has the effect of shifting the intermediate asymptotics to short-time region, without weakening their role for information transmission. This leads us to the conclusion that the whole planet is a living system.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.