Time scale separation in superstatistical complex systems

Lead Research Organisation: Queen Mary, University of London
Department Name: Sch of Mathematical Sciences

Abstract

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.

Publications

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Beck C (2013) Statistics of Lagrangian quantum turbulence in Physical Review E

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Beck C (2011) Generalized statistical mechanics for superstatistical systems. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

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Beck C (2009) Recent developments in superstatistics in Brazilian Journal of Physics

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Jizba P (2018) Transitions between superstatistical regimes: Validity, breakdown and applications in Physica A: Statistical Mechanics and its Applications

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Penrose C (2015) Superstatistics of Blaschke products in Dynamical Systems

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Rabassa P (2015) Superstatistical analysis of sea-level fluctuations in Physica A: Statistical Mechanics and its Applications

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Rabassa P (2014) Extreme Value Laws for Superstatistics in Entropy

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Touchette H (2010) Brownian motion with dry friction: Fokker-Planck approach in Journal of Physics A: Mathematical and Theoretical

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Van Der Straeten E (2011) Dynamical modelling of superstatistical complex systems in Physica A: Statistical Mechanics and its Applications

 
Description This project was very successful in further developing the superstatistics concept,
a useful statistical methods for complex systems with time scale separation.
Tests were developed to check whether a given experimentally measured time
series is superstatistical or not. Important papers were published, for example on
developing a dynamical approach to superstatistical systems, based on
Fokker-Planck and Langevin equations. This allows for the construction of an
optimum superstatistical model.
Exploitation Route The superstatistics concept is very general and can be applied in
different areas. Most recently (2013/14) we also applied it to environmental time series, relevant for interdisciplinary aspects
in the Flood MEMORY project (EP/K013513/1)
Sectors Communities and Social Services/Policy,Environment,Healthcare,Transport

 
Description The research, originally treated in a theoretical way, turned out to have many practical applications. Recently we applied it to get a better understanding of the clustered statistics of storms, rainfall statistics, and flooding events, leading to new collaborative and interdisciplinary interaction within the Flood MEMORY project, where we could successfully apply the superstatistics concept. This may generate impact in the future, for better flood risk management and the well-being of society.
First Year Of Impact 2013
Sector Environment,Healthcare,Transport
Impact Types Societal

 
Description Chair of Statistical and Nonlinear Physics Division of European Physical Society (EPS)
Geographic Reach Europe 
Policy Influence Type Participation in a advisory committee
Impact enabling cooporation and career progress for physicists
URL http://www.eps.org/snpd
 
Description EPSRC panel meeting
Geographic Reach National 
Policy Influence Type Participation in a advisory committee
 
Description Isaac Newton Institute for Mathematical Sciences (Cambridge): Long term invited participant 'Mathematics of Fluid Earth'
Amount £1,600 (GBP)
Organisation University of Cambridge 
Department Isaac Newton Trust
Sector Academic/University
Country United Kingdom
Start 10/2013 
End 12/2013
 
Description Kavli Institute Theoretical Physics Santa Barbara (long-term visitor)
Amount $2,200 (USD)
Organisation Kavli Institute For Theoretical Physics 
Sector Academic/University
Country United States
Start 05/2013 
End 05/2013
 
Description Santa Fe Institute (invited speaker at workshop)
Amount $1,300 (USD)
Organisation Santa Fe Institute 
Sector Charity/Non Profit
Country United States
Start 05/2013 
End 05/2013
 
Title Superstatistical techniques 
Description A novel technique to analyse time series with varying parameters on different time scales 
Type Of Material Data analysis technique 
Year Produced 2008 
Provided To Others? Yes  
Impact Many people use the word 'superstatistics' in their own publications. 
 
Description Collaboration with Forschungszentrum Juelich 
Organisation Julich Research Centre
Country Germany 
Sector Public 
PI Contribution Joint paper in Nature Energy, with Dirk Witthaut
Collaborator Contribution Data analysis
Impact Joint publication: Nature Energy 3, 119-126 (2018)
Start Year 2017
 
Description Collaboration with MPI Goettingen 
Organisation Max Planck Society
Department Max Planck Institute for Dynamics and Self-Organization
Country Germany 
Sector Public 
PI Contribution Joint paper in Nature Energy with Benjamin Schaefer and Marc Timme
Collaborator Contribution Data analysis
Impact Nature Energy 3, 119-126 (2018)
Start Year 2017
 
Description Rockefeller University New York 
Organisation Rockefeller University
Country United States 
Sector Academic/University 
PI Contribution Joint papers with Prof E.G.D. Cohen
Collaborator Contribution Scientific inspiration
Impact Various publications
 
Description University of Texas at Austin 
Organisation University of Texas
Country United States 
Sector Academic/University 
PI Contribution various joint publications
Collaborator Contribution Scientific collaboration with Prof.Harry Swinney
Impact various joint publications
 
Description Conference Organisation of 1st EPS Statistical and Nonlinear Physics Conference Krakow 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact 120 scientists discussed stochastic modelling methods and statistical physics approaches
Year(s) Of Engagement Activity 2017
 
Description Conference on Dynamics of Complex Systems 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact The meeting further developed applications of complex systems research and sparked scientific discussions and interactions.
Year(s) Of Engagement Activity 2016
URL https://www2.warwick.ac.uk/fac/sci/maths/research/events/2015-16/nonsymposium/dcs/