The theoretical bases of mathematical modeling of nonisothermal adsorbtion and desorbtion in nanoporous catalytic zeolite media for the Langmuir’s nonlinear isotherm are given. They most fully determine the mechanism of adsorption equilibrium for nanoporous systems of ZSM-5 zeolite. The effective scheme of linearization of a nonlinear model is implemented. High-speed analytical solutions of the system of linearized boundary problems of adsorption and desorption in nanoporous media are justified and obtained using the Hevisides operational method.
Using the effective mass model for an electron within the layers of a nanosystem and rectangular potential wells and barriers for the effective potential of a GaN/AlN resonant tunneling structure, analytical solutions of the Schrödinger equation are obtained. The theory of a stationary electronic spectrum and wave functions of an electron is developed. Using the elastic continuum model, exact solutions of the equations describing the elastic displacement of the semiconductor medium of the studied nanostructure are obtained. Using these solutions, the theory of acoustic modes of the nanosystem has been developed. Using the Hamiltonian of acoustic phonons and electrons in the representation of secondary quantization, the quantummechanical theory of electron scattering on acoustic phonons is developed. Using the parameters of the nanosystem under study, based on the analysis of the poles of the Green's function, the displacements of the electronic spectrum associated with acoustic phonons at T = 0 К are obtained.
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