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TMF, 2017, Volume 190, Number 1, Pages 179–190 (Mi tmf9142)  

This article is cited in 4 scientific papers (total in 4 papers)

Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions

K. Oleschkoa, A. Yu. Khrennikovb

a Centro de Geociencias, Universidad Nacional Autónoma de México (UNAM), Campus UNAM Juriquilla, Querétaro, México
b International Center for Mathematical Modelling in Physics and Cognitive Sciences, Mathematical Institute, Linnaeus University, Växjö, Sweden

Abstract: In a very general setting, we discuss possibilities of applying $p$-adics to geophysics using a $p$-adic diffusion representation of the master equations for the dynamics of a fluid in capillaries in porous media and formulate several mathematical problems motivated by such applications. We stress that $p$-adic wavelets are a powerful tool for obtaining analytic solutions of diffusion equations. Because $p$-adic diffusion is a special case of fractional diffusion, which is closely related to the fractal structure of the configuration space, $p$-adic geophysics can be regarded as a new approach to fractal modeling of geophysical processes.

Keywords: master equation, geophysics, water-in-oil and oil-in-water emulsions, $p$-adic number, $p$-adic diffusion, quasilinear $p$-adic diffusion

Funding Agency Grant Number
CONACYT - Consejo Nacional de Ciencia y Tecnología 312-2015
168638
This paper was financially supported by the project SENER-CONACYT-Hidrocarburos, Yacimiento Petrolero como un Reactor Fractal, N 168638 and the Consejo Nacional de Ciencia y Tecnología (CONACYT), Mexico, under grant 312-2015, Fronteras de la Ciencia.


DOI: https://doi.org/10.4213/tmf9142

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English version:
Theoretical and Mathematical Physics, 2017, 190:1, 154–163

Bibliographic databases:

Received: 03.01.2016

Citation: K. Oleschko, A. Yu. Khrennikov, “Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions”, TMF, 190:1 (2017), 179–190; Theoret. and Math. Phys., 190:1 (2017), 154–163

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Oleschko K. Khrennikov A., “Transport Through a Network of Capillaries From Ultrametric Diffusion Equation With Quadratic Nonlinearity”, Russ. J. Math. Phys., 24:4 (2017), 505–516  crossref  mathscinet  zmath  isi  scopus
    2. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    3. Lozada Aguilar M.A., Khrennikov A., Oleschko K., de Jesus Correa M., “Quantum Bayesian Perspective For Intelligence Reservoir Characterization, Monitoring and Management”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 375:2106 (2017), 20160398  crossref  mathscinet  isi  scopus
    4. V A. Antoniouk, K. Oleschko, A. N. Kochubei, A. Yu. Khrennikov, “A stochastic $p$-adic model of the capillary flow in porous random medium”, Physica A, 505 (2018), 763–777  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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