## Efficient Monte Carlo Methods in Chaotic Systems

By: Jorge Leitão

From: Max Planck Institute for the Physics of Complex Systems

At: Instituto de Investigação Interdisciplinar, Anfiteatro

[2014-10-02]

Numerical simulations ofÃ‚Â (thermodynamical)Ã‚Â large systems have been one of the main fields of Statistical Physics in the last decades. Another field inÃ‚Â which numerical simulations are increasingly important is nonlinear dynamics. The problem in this case is to efficiently sample rare trajectories. Complicated structures in the phase-space,Ã‚Â such as fractals, make it difficult to find and sample such trajectories.In this talk we will show how Importance Sampling Monte Carlo methods developed in Statistical Physics can be adapted to problems in dynamical systems. We find that general properties of the system, such as the Lyapunov exponent, are crucial ingredients for the method. We also discuss how the complexity of the phase space affects the efficiency of the simulation and leads to a sub-optimal scaling with system size, a phenomenon known as critical slowing down in statistical physics.

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[1] J. C. LeitÃƒÂ£o, J. M. V. P. Lopes, and E. G. Altmann, Phys. Rev. Lett.Ã‚Â **110**, 220601 (2013).

[2] J. C. LeitÃƒÂ£o, E. G. Altmann, and J. M. V. P. Lopes,Ã‚Â arXiv:1407.5343Ã‚Â (2014).

**Project**UIDB/00618/2020