Applications of 𝑝-adic numbers: from physics to geology

In this short review we present the basic applications of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -adic numbers: from physics, string theory and quantum mechanics, to geology, transport in porous disordered media. Opposite to applications to physics (they were started long ago and this is the well established field of research), applications to geology are recent and we discuss motivations and one concrete mathematical model in more detail. Porous disordered media is a complex geological structure which plays an important role, e.g., in geological studies of oil resources. Such a media has a tree-like structure and it can be modeled with the aid of fractal geometry. <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -adic fields can be used as mathematical models of special fractal structures and hence they can be applied to model transport in disordered porous media.

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