Dynamics importance sampling for the activation problem in nonequilibrium continuous systems and maps

A numerical approach based on dynamic importance sampling (DIMS) is introduced to investigate the activation problem in two-dimensional nonequilibrium systems. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. A shift in the position of the escape path compared to a heteroclinic trajectory calculated in the limit of zero noise intensity is directly observed. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities.

[1]  J. P. Woerdman,et al.  Correlated fluctuations in the polarization modes of a vertical-cavity semiconductor laser , 1999 .

[2]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[4]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[5]  D. Ludwig.  Persistence of Dynamical Systems under Random Perturbations , 1975 .

[6]  C. Dellago,et al.  Transition path sampling and the calculation of rate constants , 1998 .

[7]  M. V. Day,et al.  Recent progress on the small parameter exit problem , 1987 .

[8]  J. P. Woerdman,et al.  PHYSICAL INSIGHT INTO THE POLARIZATION DYNAMICS OF SEMICONDUCTOR VERTICAL-CAVITY LASERS , 1998 .

[9]  Willemsen Mb,et al.  Anatomy of a polarization switch of a vertical-cavity semiconductor laser , 2000 .

[10]  V. I. Mel'Nikov,et al.  The Kramers problem : fifty years of development , 1991 .

[11]  Thomas B. Woolf,et al.  Path corrected functionals of stochastic trajectories: towards relative free energy and reaction coordinate calculations , 1998 .

[12]  F. Jülicher,et al.  Modeling molecular motors , 1997 .

[13]  Vadim N. Smelyanskiy,et al.  Observable and hidden singular features of large fluctuations in nonequilibrium systems , 1994 .

[14]  J. P. Woerdman,et al.  Polarization fluctuations in vertical-cavity semiconductor lasers , 1998 .

[15]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[16]  Dykman,et al.  Large fluctuations and fluctuational transitions in systems driven by colored Gaussian noise: A high-frequency noise. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[17]  D. G. Luchinsky,et al.  Irreversibility of classical fluctuations studied in analogue electrical circuits , 1997, Nature.

[18]  Riccardo Mannella,et al.  Stochastic resonance in perspective , 1995 .

[19]  Robert S. Maier,et al.  A scaling theory of bifurcations in the symmetric weak-noise escape problem , 1996 .

[20]  Graham,et al.  Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems. , 1985, Physical review. A, General physics.

[21]  M. Magnasco,et al.  Forced thermal ratchets. , 1993, Physical review letters.

[22]  Riccardo Mannella,et al.  Integration Of Stochastic Differential Equations On A Computer , 2002 .

[23]  J. P. Woerdman,et al.  POLARIZATION FLUCTUATIONS DEMONSTRATE NONLINEAR ANISOTROPY OF A VERTICAL-CAVITY SEMICONDUCTOR LASER , 1998 .

[24]  A Bandrivskyy,et al.  Fast monte carlo simulations and singularities in the probability distributions of nonequilibrium systems. , 2003, Physical review letters.

[25]  Vadim N. Smelyanskiy,et al.  Topological features of large fluctuations to the interior of a limit cycle , 1997 .

[26]  Vadim N. Smelyanskiy,et al.  Resonant directed diffusion in nonadiabatically driven systems , 1998 .

[27]  D M Zuckerman,et al.  Efficient dynamic importance sampling of rare events in one dimension. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Robert Graham,et al.  Existence of a potential for dissipative dynamical systems , 1984 .

[29]  How an anomalous cusp bifurcates in a weak-noise system , 2000, Physical review letters.

[30]  Woerdman,et al.  Anatomy of a polarization switch of a vertical-cavity semiconductor laser , 2000, Physical review letters.

[31]  Maier,et al.  Effect of focusing and caustics on exit phenomena in systems lacking detailed balance. , 1993, Physical review letters.

[32]  S. Beri,et al.  Noise-induced shift of singularities in the pattern of optimal paths , 2003 .

[33]  Surmounting oscillating barriers: path-integral approach for weak noise , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  V. N. Chizhevsky,et al.  Optimal timing for targeting periodic orbits in a loss-driven CO2 laser☆ , 1997 .

[35]  R. Eisenberg,et al.  Diffusion as a chemical reaction: Stochastic trajectories between fixed concentrations , 1995 .

[36]  Stein,et al.  Optimal paths and the prehistory problem for large fluctuations in noise-driven systems. , 1992, Physical review letters.

[37]  H. Jauslin,et al.  Nondifferentiable potentials for nonequilibrium steady states , 1987 .

[38]  Riccardo Mannella,et al.  Observation of saddle-point avoidance in noise-induced escape. , 1999 .

[39]  Peter Grassberger,et al.  Noise-induced escape from attractors , 1989 .

[40]  R. Graham.  Macroscopic potentials, bifurcations and noise in dissipative systems , 1987 .