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

Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471, Kuna, T., Wouters, J. ORCID: https://orcid.org/0000-0001-5418-7657 and Faranda, D. (2012) Relevance of sampling schemes in light of Ruelle's linear response theory. Nonlinearity, 25 (5). p. 1311. ISSN 1361-6544 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/27146
Item Type	Article
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE) Interdisciplinary Research Centres (IDRCs) > Walker Institute Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
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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