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Relevance of sampling schemes in light of Ruelle's linear response theory

Lucarini, V., Kuna, T., Wouters, J. and Faranda, D. (2012) Relevance of sampling schemes in light of Ruelle's linear response theory. Nonlinearity, 25 (5). p. 1311. ISSN 1361-6544

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To link to this article DOI: 10.1088/0951-7715/25/5/1311

Abstract/Summary

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Item Type:Article
Refereed:Yes
Divisions:Interdisciplinary centres and themes > Walker Institute for Climate System Research
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
ID Code:27146
Uncontrolled Keywords:05.45.Pq Numerical simulations of chaotic systems 02.30.Rz Integral equations 02.60.Lj Ordinary and partial differential equations; boundary value problems 02.60.Nm Integral and integrodifferential equations 02.30.Hq Ordinary differential equations 02.60.Cb Numerical simulation; solution of equations 03B47 34C28 Complex behavior, chaotic systems (See mainly 37Dxx) 34D10 Perturbations 62D05 Sampling theory, sample surveys 65P20 Numerical chaos
Publisher:IOP Publishing

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