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An efficient approach to obtaining the exit location distribution and the mean first passage time based on the GCM method

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  • Wang, Jianlong
  • Leng, Xiaolei
  • Liu, Xianbin

Abstract

In this paper, according to the probability evolution analysis, we developed a new procedure based on the Generalized Cell Mapping method to get the exit location distribution and the mean first passage time of the weak noise excited system. With the Generalized Cell Mapping method, the original stochastic process is converted into a Markov chain. Moreover, the eigenvalue problem of the elliptic differential operator for the escape problem is simplified into an eigenvalue problem of the probability transition matrix. Thus, the exit location distribution and the mean first passage time of the system can be easily derived by solving the transition matrix’s eigenvalues and eigenvectors. By applying to the Maier–Stein system, Kramers problem, and the Vibro-impact system, shows the Generalized Cell Mapping method could save us a lot of time and provide us much better results compared with the directed Monte Carlo simulation.

Suggested Citation

  • Wang, Jianlong & Leng, Xiaolei & Liu, Xianbin, 2021. "An efficient approach to obtaining the exit location distribution and the mean first passage time based on the GCM method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    • Handle: RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001096
    DOI: 10.1016/j.physa.2021.125837
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    References listed on IDEAS

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    1. Byrne, D.J. & Coffey, W.T. & Kalmykov, Yu.P. & Titov, S.V., 2019. "On a simple derivation of the very low damping escape rate for classical spins by modifying the method of Kramers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    2. Coffey, W.T. & Crothers, D.S.F. & Titov, S.V., 2001. "Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 330-350.
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    Cited by:

    1. Yang, Yun & Ma, Changxi & Ling, Gang, 2022. "Pre-location for temporary distribution station of urban emergency materials considering priority under COVID-19: A case study of Wuhan City, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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