Open Access
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 14
Number of page(s) 24
Published online 09 June 2022
  1. R. Adams and J. Fournier, Sobolev Spaces, Academic Press, New York (2003). [Google Scholar]
  2. M.S. Alnœs, J. Blechta et al., The FEniCS Project Version 1.5. Arch. Numer. Softw. 3 (2015) 100. [Google Scholar]
  3. W. Bangerth, R. Hartmann and G. Kanschat, Deal. II—a general-purpose object-oriented finite element library. ACM Trans. Math. Softw. 33 (2007) 24–es. [CrossRef] [Google Scholar]
  4. V. Bobrovskiy, Software and hardware of international spatially distributed monitoring network for investigation local and global effects prior to the strong earthquakes. Ph.D. thesis. Geophysics. (in Russian), Russian State University for Geological Prospecting, Moscow (2016). [Google Scholar]
  5. V. Bobrovskiy and D. Kuznetsov, Seismic global conception on the example of strongest earthquakes with M8+ occurred in 2001-2015 (in Russian). Scientific World, Moscow (2016). [Google Scholar]
  6. V. Bobrovskiy, F. Stoppa, L. Nicoli and Y. Losyeva, Nonstationary electrical activity in the tectonosphere-atmosphere interface retrieving by multielectrode sensors: case study of three major earthquakes in Central Italy with M 6. Earth Sci. Inf. 10 (2017) 269–285. [CrossRef] [Google Scholar]
  7. P. Braasch, Semilineare elliptische Differentialgleichungen und das Vlasov-Maxwell-System. Utz, Verlag Wiss. (1997). [Google Scholar]
  8. J.W. Cooley and J.W. Tukey, An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19 (1965) 297–301. [Google Scholar]
  9. L. Fortuin, The wave equation in a medium with a time-dependent boundary. J. Acoust. Soc. Am. 53 (1973) 1683–1685. [CrossRef] [Google Scholar]
  10. H. Gao, C. Liu, J. Shi, S. Pan, T. Huang, X. Lu, H.-T. Wang, D. Xing and J. Sun, Superionic silica-water and silica-hydrogen compounds in the deep interiors of Uranus and Neptune. Phys. Rev. Lett. 128 (2022) 035702. [CrossRef] [PubMed] [Google Scholar]
  11. D. Gayer, C. O’Sullivan et al., FreeCAD visualization of realistic 3D physical optics beams within a CAD system-model, in vol. 9914 of Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VIII. International Society for Optics and Photonics (2016) 99142Y. [Google Scholar]
  12. C. Geuzaine and J.-F. Remacle, Gmsh: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int. J. Numer. Methods Eng. 79 (2009) 1309–1331. [CrossRef] [Google Scholar]
  13. M. Hanfland, R.J. Hemley and H.-k. Mao, Novel infrared vibron absorption in solid hydrogen at megabar pressures. Phys. Rev. Lett. 70 (1993) 3760–3763. [CrossRef] [PubMed] [Google Scholar]
  14. Y. He et al., Superionic iron alloys and their seismic velocities in Earth’s inner core. Nature 602 (2022) 258–262. [CrossRef] [PubMed] [Google Scholar]
  15. R.J. Hemley, Z.G. Soos, M. Hanfland and H.-k. Mao, Charge-transfer states in dense hydrogen. Nature 369 (1994) 384–387. [CrossRef] [Google Scholar]
  16. M. Hou, Y. He, B. Jang, S. Sun, Y. Zhuang, L. Deng, R. Tang, J. Chen, F. Ke, Y. Meng, V. Prakapenka, B. Chen, J. Shim, J. Liu, D. Kim, Q. Hu, C. Pickard, R.J. Needs and H-K. Mao, Superionic iron oxide—hydroxide in Earth’s deep mantle. Nat. Geosci. 14 (2021) 174–178. [CrossRef] [Google Scholar]
  17. W. Kauzmann, Quantum Chemistry. Academic, New York (1957). [Google Scholar]
  18. D. Kuznetsov, Practice of short-term prediction of earthquakes: astro-, cosmo-geophysical impulses of Vernadsky-Vlasov-Vorob jev-Prigozhin on the vertical sequence of underground electrodes at PedInstitute fault at the magnetic meridian of Petropavlovsk-Kamchatsky. All-Union Institute for science and technical information (VINITI), Moscow (1991) 1–9. [Google Scholar]
  19. V. Larin, Hypothesis of a primordially hydride earth. Moscow, Izdatel’stvo Nedra (1980). [Google Scholar]
  20. K. Lee, A mixed problem for hyperbolic equations with time-dependent domain. J. Math. Anal. Appl. 16 (1966) 471–495. [Google Scholar]
  21. A. Logg, K.-A. Mardal, G.N. Wells et al., Automated Solution of Differential Equations by the Finite Element Method. Springer (2012). [Google Scholar]
  22. M. Millot, S. Hamel, J. Rygg, P.M. Celliers, G.W. Collins, F. Coppari, D.E. Fratanduono, R. Jeanloz, D.C. Swift and J.H. Eggert, Experimental evidence for superionic water ice using shock compression. Nat. Phys. 14 (2018) 297–302. [CrossRef] [Google Scholar]
  23. M.N. Nabighian, Electromagnetic methods in applied geophysics. Soc. of Exploration Geophysicists, Tulsa, Okla (1993). [Google Scholar]
  24. M. Nishi, T. Irifune, J. Tsuchiya, Y. Tange, Y. Nishihara, K. Fujino and Y. Higo, Stability of hydrous silicate at high pressures and water transport to the deep lower mantle. Nat. Geosci. 7 (2014) 224–227. [CrossRef] [Google Scholar]
  25. C. Pao, Nonlinear Parabolic and Elliptic Equations. Springer (1992). [Google Scholar]
  26. G.A. Rudykh, N.A. Sidorov and A.V. Sinitsyn, Nonstationary solutions of the two-particle Vlasov—Maxwell system. Dokl. Math. 34 (1989) 700–701. [Google Scholar]
  27. A. Sinitsyn, V. Vedenyapin and E. Dulov, Kinetic Boltzmann, Vlasov and related equations. Elsevier (2011). [Google Scholar]
  28. A.H. Squillacote, J. Ahrens, C. Law, B. Geveci, K. Moreland and B. King, Vol. 366 of The paraview guide. Kitware Clifton Park, NY (2007). [Google Scholar]
  29. E. Sugimura, T. Komabayashi, K. Ohta, K. Hirose, Y. Ohishi and L. Dubrovinsky, Experimental evidence of superionic conduction in H2O ice. J. Chew,. Phys. 137 (2012) 194505. [CrossRef] [PubMed] [Google Scholar]
  30. V. Surkov and M. Hayakawa, Ultra and Extremely Low Frequency Electromagnetic Fields. Springer, Tokyo, Japan (2014). [Google Scholar]
  31. S. Uyeda, T. Nagao, Y. Orihara, T. Yamaguchi and I. Takahashi, Geoelectric potential changes: possible precursors to earthquakes in Japan. Proc Natl Acad Sci USA 97 (2000) 4561–4566. [CrossRef] [PubMed] [Google Scholar]
  32. P.P. Varostos and K. Alexopoulos, Physical properties of the variation of the electric fields of the Earth preceding earthquakes. Tectonophysics 110 (1984) 73–98. [CrossRef] [Google Scholar]
  33. V. Vernadsky, Gas exchange in earth’s crust. Proc. St. Petersburg Royal Acad. Sci. 6 (1912) 141–162. [Google Scholar]
  34. A.A. Vlasov, Many-particle theory and its application to plasma. Gordon and Breach (1961). [Google Scholar]

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