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Simulating Rare Events in Dynamical Processes

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Abstract

Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that are responsible for intermittency in a turbulent liquid, the active regions that allow a supercooled liquid to flow…. Simulating them in an efficient, accelerated way, is in fact quite simple.

In this paper we review a computational technique to study such rare events in both stochastic and Hamiltonian systems. The method is based on the evolution of a family of copies of the system which are replicated or killed in such a way as to favor the realization of the atypical trajectories. We illustrate this with various examples.

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Authors and Affiliations

  1. Università di Modena e Reggio Emilia, viale A. Allegri, 9, 42121, Reggio Emilia, Italy

    Cristian Giardina

  2. CNRS UMR 7636 PMMH, ESPCI, 10 rue Vauquelin, 75005, Paris, France

    Jorge Kurchan

  3. Sorbonne Paris Cite, LPMA, UMR 7599 CNRS, Univ. Paris Diderot, 75205, Paris, France

    Vivien Lecomte

  4. Sorbonne Paris Cite, MSC, UMR 7057 CNRS, Univ. Paris Diderot, 75205, Paris, France

    Julien Tailleur

Authors
  1. Cristian Giardina
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  2. Jorge Kurchan
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  3. Vivien Lecomte
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  4. Julien Tailleur
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Corresponding author

Correspondence to Cristian Giardina.

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Giardina, C., Kurchan, J., Lecomte, V. et al. Simulating Rare Events in Dynamical Processes. J Stat Phys 145, 787–811 (2011). https://doi.org/10.1007/s10955-011-0350-4

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  • DOI: https://doi.org/10.1007/s10955-011-0350-4

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