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• W4385444710 abstract "Four-dimensional mathematical models of structurally related (conjugated, entangled, and dual) phenomena of dissipation and cumulation of electrical energy (an external source in continuous media) are discussed, accompanied by the formation of cumulative-dissipative structures (CDSs) and their ordering into a regular system—a dynamic dissipative “crystal” with long-range dynamic order. The excitation of new degrees of freedom in such systems provides attractiveness or geometric self-focusing of energy-mass-momentum flows (EMMF) for the entire regular system. As a result of cumulation, EMMF structures acquire hyper-properties. Thus, when lightning is formed as a CDS, the local air conductivity increases by 1015 times. The cumulation of EMMF in rendered structures is a common property of media activated to form 4-D structures. The basis of such a dissipative structure is an attractor, the end result of which is a cumulative jet from an attractor with hyper-properties. Therefore, these structures are cumulative-dissipative. We discuss a method for describing these structures and prove that cumulative processes in plasmoids exist and can be described theoretically, although not with the help of full-fledged mathematical 4-D models. It has been theoretically and experimentally proven that the cumulation of the electric field due to the ambipolar drift of the plasma is an inherent property of the current-carrying gas-discharge plasma. The results obtained by modeling shock waves of the electric field ( <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$E/N)$ </tex-math></inline-formula> can be useful to explain the cumulative formation in the heliosphere, atmosphere, and ionosphere of the Earth since the Earth has a negative charge of about 500 000 C, and the Sun positively charged at the level of 1400 C. Based on the mathematical approach, classification of shock waves and types of cumulation in 4-D space-time will be carried out." @default.
• W4385444710 created "2023-08-02" @default.
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• W4385444710 date "2023-08-01" @default.
• W4385444710 modified "2023-09-27" @default.
• W4385444710 title "Model of Ambipolar Processes in Cumulative-Dissipative Self-Focusing Structures in Plasma—Part 1: Perturbation Theory for Vysikaylo’s Structures in Plasma With Current" @default.
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• W4385444710 doi "https://doi.org/10.1109/tps.2023.3296771" @default.
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