Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7375008 | Physica A: Statistical Mechanics and its Applications | 2018 | 19 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alexandra V. Antoniouk, Klaudia Oleschko, Anatoly N. Kochubei, Andrei Yu. Khrennikov,