Mathematical modelling of proton migration in Earth mantle
| Autor: | Vadim Bobrovskiy, Juan Galvis, Alexey Kaplin, Alexander Sinitsyn, Marco Tognoli, Paolo Trucco |
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| Rok vydání: | 2022 |
| Předmět: |
Vlasov-Maxwell equations
non-linear hyperbolic sh-Gordon equation Applied Mathematics Mathematical model Vlasov-Maxwell equations harmonic oscillator time and 3D-space discretization finite element space earthquake non-linear hyperbolic sh-Gordon equation transport equation boundary-value problem upper-lower solution FOS: Physical sciences finite element space Geophysics (physics.geo-ph) boundary-value problem Physics - Geophysics Mathematical model harmonic oscillator earthquake transport equation Modeling and Simulation upper-lower solution time and 3D-space discretization |
| Zdroj: | Mathematical Modelling of Natural Phenomena. 17:14 |
| ISSN: | 1760-6101 0973-5348 |
| DOI: | 10.1051/mmnp/2022018 |
| Popis: | In the study, we address the mathematical problem of proton migration in the Earth’s mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x, t) and then reconstructing the distribution function f(x,v,t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric. |
| Databáze: | OpenAIRE |
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