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Stochastic modeling of movement for Helium particles in a graphite channel

Author

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  • Zhang, Jingqi
  • Fouladirad, Mitra
  • Limnios, Nikolaos
  • Magnico, Pierre

Abstract

In this article, we present a stochastic model for the movement of Helium particles within a graphite channel, focusing on Knudsen diffusion. We develop a semi-Markov model to describe the movement of the particle, derive the stationary distribution of its mean position, and analyze the model’s asymptotic properties. To validate the model, we compare its theoretical outcomes with Monte Carlo simulations. As temperature significantly influences on the movement of particles, two situations are studied for high and low temperature. In both cases, theoretical and simulation results by Monte Carlo coincide. Furthermore, we propose estimation methods for the local parameters of the model and demonstrate its application using data from Molecular Dynamics simulations.

Suggested Citation

  • Zhang, Jingqi & Fouladirad, Mitra & Limnios, Nikolaos & Magnico, Pierre, 2025. "Stochastic modeling of movement for Helium particles in a graphite channel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 675(C).
    • Handle: RePEc:eee:phsmap:v:675:y:2025:i:c:s0378437125004704
    DOI: 10.1016/j.physa.2025.130818
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    References listed on IDEAS

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    1. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    2. Wang, Hui & Chen, Li & Qu, Zhiguo & Yin, Ying & Kang, Qinjun & Yu, Bo & Tao, Wen-Quan, 2020. "Modeling of multi-scale transport phenomena in shale gas production — A critical review," Applied Energy, Elsevier, vol. 262(C).
    3. Irene Votsi & Nikolaos Limnios & George Tsaklidis & Eleftheria Papadimitriou, 2012. "Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 685-703, September.
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