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A stochastic p-adic model of the capillary flow in porous random medium

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  • Antoniouk, Alexandra V.
  • Oleschko, Klaudia
  • Kochubei, Anatoly N.
  • Khrennikov, Andrei Yu.

Abstract

We develop the p-adic model of propagation of fluids (e.g., oil or water) in capillary networks in a porous random medium. The hierarchic structure of a system of capillaries is mathematically modeled by endowing trees of capillaries with the structure of an ultrametric space. Considerations are restricted to the case of idealized networks represented by homogeneous p-trees with p branches leaving each vertex, where p >1 is a prime number. Such trees are realized as the fields of p-adic numbers. We introduce and study an inhomogeneous Markov process describing the penetration of fluid into a porous random medium.

Suggested Citation

  • Antoniouk, Alexandra V. & Oleschko, Klaudia & Kochubei, Anatoly N. & Khrennikov, Andrei Yu., 2018. "A stochastic p-adic model of the capillary flow in porous random medium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 763-777.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:763-777
    DOI: 10.1016/j.physa.2018.03.049
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Dragovich, Branko & Khrennikov, Andrei Yu. & Mišić, Nataša Ž., 2017. "Ultrametrics in the genetic code and the genome," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 350-358.
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    1. Bikulov, A.Kh. & Zubarev, A.P., 2021. "Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

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