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2. Nanoionics from a quantum mechanics point of view: Mathematical modeling and numerical simulation.
- Author
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Sepúlveda, Paulina, Muga, Ignacio, Sainz, Norberto, Rojas, René G., and Ossandón, Sebastián
- Subjects
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QUANTUM mechanics , *ELECTROMAGNETIC fields , *ELECTROMAGNETIC induction , *ELECTROMAGNETIC coupling , *MATHEMATICAL models , *TRP channels - Abstract
Solid nano-structures exhibiting fast ion transport (cations moving in anionic crystal structures) are becoming increasingly relevant in industrial applications. However, it is challenging to model their mechanics due to the presence of electromagnetic couplings. In this paper, a mathematical, physical, and computational framework is introduced, for a cation particle moving through an anion sub-lattice structure in the presence of two electromagnetic fields: an external electromagnetic field; and a self-induced electromagnetic field coming from back-reaction phenomena caused by the relative movement of cations with respect to the mentioned structure. Our approach seeks to incorporate magnetic effects, such as magnetic induction and spin of cations, which are not incorporated in other models, mainly due to the intrinsic difficulty of 3D effects. We propose a quantum mechanical formalism based on a Schrödinger-type equation, where a wave function models the behavior of a cation in presence of an external electromagnetic potential, coupled with transient and self-induced electromagnetic effects. To solve the model, a space–time coupled numerical scheme is presented, which allows the possibility of time-evolving electromagnetic effects. The technique uses finite-elements in space and time-marching schemes in time. While a time-explicit marching scheme is used to update the magnetic and electric-potential fields, a time-implicit marching scheme is used to solve the coupled Schrödinger equation. This strategy allows us to update the electromagnetic contributions and wave functions at each time-step. Numerical examples in one and two spatial dimensions (and evolving in time) have been implemented for some meaningful models obtained from nanoionics literature. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Investigation of Source Rock Heating and Structural Changes in the Electromagnetic Fields Using Experimental and Mathematical Modeling.
- Author
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Kovaleva, Liana, Zinnatullin, Rasul, Musin, Airat, Kireev, Victor, Karamov, Tagir, and Spasennykh, Mikhail
- Subjects
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ELECTROMAGNETIC fields , *HEAT of formation , *COMPUTATIONAL electromagnetics , *MATHEMATICAL models , *MICROWAVE heating - Abstract
The paper presents the results of an experimental study of heating and the structural resultant changes of source rocks under the influence of the electromagnetic field in the microwave and radio-frequency ranges. The samples from the Bazhenov Formation (West Siberia, Russia) and the Domanic Formation (Ural, Russia) have been tested. It is shown that samples from these formations demonstrate very different heating rates at the same electromagnetic field parameters and the their heating rate depends on the type of the electromagnetic field (radio-frequency or microwave) applied. The temperature of the Bazhenov Formation samples reaches 300 °C within one hundred seconds of the microwave treatment but it slowly rises to 200 °C after twelve minutes of the radio-frequency influence. The samples of the carbonate Domanic Formation heat up more slowly in the microwave field (within two hundred seconds) and to lower temperatures in the radio-frequency (150 °C) than the Bazhenov Formation samples. The study of the structure of the samples before and after experiments on the electromagnetic treatment shows fracture formation during the heating process. Numerical simulations of heating dynamics of source rock samples have been based on a simple mathematical model of the electromagnetic influence and main features of heating for different types of source rock have been revealed. The opportunities for application of electromagnetic heating for oil source rock recovery are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
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