Time scale separation in superstatistical complex systems

超统计复杂系统中的时间尺度分离

• 批准号: EP/E049257/1
• 负责人: Christian Beck
• 金额: $ 37.33万
• 依托单位: Queen Mary University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE049257%2F1
• 关键词: Time; scale; separation; superstatistical; complex

Complex system often exhibit a dynamics that can be regarded as superpositionof several dynamics on different time scales.A simple example is a Brownian partice that moves in an inhomogeneousenvironment which exhibits temperature fluctuations in space and time on a relatively large scale. There is a superposition of two relevant stochastic processes,a fast one given by the velocity of the particle and a much slower onedescribing changes in the environment. It has become common to call thesetypes of systems 'superstatistical' since they consist of a superposition of twostatistics, a fast one as described by ordinary statistical mechanicsand a much slower one describing changes of the environment. The superstatistics is very general and has been recently applied to a variety of complex systems, including hydrodynamicturbulence, pattern forming nonequilibrium systems, solar flares, cosmic rays,wind velocity fluctuations, hydro-climatic fluctuations, share price evolution,random networks and random matrix theory.The aim of the research proposal is twofold.On the theoretical side, the aim is to develop a generalisedstatistical mechanics formalism that describes a large variety of complexsystems of the above type in an effective way. Rather thantaking into account every detail of the complex system, one seeksfor an effective description with few relevant variables. For thisthe methods of thermodynamics are generalised:One starts with more general entropy functionsthat take into account changes of the environment(or, in general, large-scale fluctuations of a relevant system parameter) as well. An extended theory also takes into account how fast the local system relaxes to equilibrium,thus describing finite time scale separation effects.On the applied side, the aim is to apply the above theory to a large variety of time series generated by different complexsystems (pattern forming granular gases, brain activityduring epileptic seizures, earthquake activity in Japan and California, evolutionof share price indices, velocity differences in turbulent flows).It will be investigated which superstatistical phenomena are universal(i.e. independent of details of the complex system studied) and whichare specific to a particular system. Possible universality classeswill be extracted directly from the data. Application-specific modelswill be developed to explain the observed probability distributionsof the slowly varying system parameters.

复杂系统的动力学往往可以看作是不同时间尺度上的几个动力学的叠加，一个简单的例子是布朗粒子在一个不稳定的环境中运动，它在空间和时间上表现出相对较大的温度波动。有两个相关的随机过程的叠加，一个是由粒子的速度给出的快速过程，另一个是描述环境变化的慢得多的过程。这类系统通常被称为“超统计”，因为它们由两种统计数据的叠加组成，一种是普通统计力学描述的快速统计数据，另一种是描述环境变化的慢得多的统计数据。超统计量是非常普遍的，最近已被应用于各种复杂系统，包括流体动力学湍流，模式形成非平衡系统，太阳耀斑，宇宙射线，风速波动，水文气候波动，股价演变，随机网络和随机矩阵理论。研究建议的目的是双重的。在理论方面，其目的是发展一种广义统计力学形式，以有效的方式描述上述类型的各种复杂系统。而不是考虑到复杂系统的每一个细节，人们寻求一个有效的描述与少数相关变量。为此，热力学的方法被普遍化了：一个是从更一般的熵函数开始，它也考虑了环境的变化（或者，一般来说，相关系统参数的大尺度波动）。一个扩展的理论也考虑了局部系统松弛到平衡的速度，从而描述了有限时间尺度的分离效应。在应用方面，目的是将上述理论应用于由不同复杂系统产生的大量时间序列（颗粒状气体的形成模式，癫痫发作时的大脑活动，日本和加州的地震活动，股价指数的演变，将研究哪些超统计现象是普遍的（即与所研究的复杂系统的细节无关），哪些是特定系统所特有的。可能的普适性类将直接从数据中提取。将开发特定于应用的模型来解释观测到的缓慢变化的系统参数的概率分布。

项目成果

Superstatistical analysis of sea-level fluctuations

海平面波动的超统计分析

• DOI: 10.1016/j.physa.2014.08.068
• 发表时间: 2015
• 期刊: Statistical Mechanics and its Applications
• 作者: Rabassa P

Transitions between superstatistical regimes: Validity, breakdown and applications

• DOI: 10.1016/j.physa.2017.09.109
• 发表时间: 2018-03-01
• 期刊: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
• 影响因子: 3.3
• 作者: Jizba, Petr;Korbel, Jan;Beck, Christian
• 通讯作者: Beck, Christian

Superstatistics of Blaschke products

Blaschke 产品的超级统计

• DOI: 10.1080/14689367.2015.1062978
• 发表时间: 2015
• 期刊: Dynamical Systems
• 作者: Penrose C

Recent developments in superstatistics

• DOI: 10.1590/s0103-97332009000400003
• 发表时间: 2009-08-01
• 期刊: BRAZILIAN JOURNAL OF PHYSICS
• 影响因子: 1.6
• 作者: Beck, Christian

Extreme Value Laws for Superstatistics

• DOI: 10.3390/e16105523
• 发表时间: 2014-10-01
• 期刊: ENTROPY
• 影响因子: 2.7
• 作者: Rabassa, Pau;Beck, Christian
• 通讯作者: Beck, Christian