A coordinated physicomathematical model for the propagation of a soliton-like electromagnetic pulse in a heterogeneous medium is developed in the presence of strong discontinuities in the electromagnetic field. The mo...A coordinated physicomathematical model for the propagation of a soliton-like electromagnetic pulse in a heterogeneous medium is developed in the presence of strong discontinuities in the electromagnetic field. The model is based on the reduction of Maxwell’s equations to the well-studied wave equation. When the electromagnetic pulse was specified, its amplitude modulation was taken into account, as was the nonstationary broadening of the spectral line. Conditions for matching the momentum for the first initial boundary-value problem are obtained. The time dispersion of the electrical induction is taken into account in terms of the function of signal conditioning which takes account of the broadening of its spectral line and integration over the continuous spectrum. With this approach, it is not necessary to neglect spatial derivatives, and also to use spatial nonlocal relations to take account of the effect of surface charge, surface current, and spatial dispersion of electrical induction at the interfaces of adjacent media.展开更多
A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a ro...A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a rough surface, was developed. Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality. For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current. This approach lets one avoid the necessity to set surface impedances depending on the structure of the field being determined and on the material properties.展开更多
文摘A coordinated physicomathematical model for the propagation of a soliton-like electromagnetic pulse in a heterogeneous medium is developed in the presence of strong discontinuities in the electromagnetic field. The model is based on the reduction of Maxwell’s equations to the well-studied wave equation. When the electromagnetic pulse was specified, its amplitude modulation was taken into account, as was the nonstationary broadening of the spectral line. Conditions for matching the momentum for the first initial boundary-value problem are obtained. The time dispersion of the electrical induction is taken into account in terms of the function of signal conditioning which takes account of the broadening of its spectral line and integration over the continuous spectrum. With this approach, it is not necessary to neglect spatial derivatives, and also to use spatial nonlocal relations to take account of the effect of surface charge, surface current, and spatial dispersion of electrical induction at the interfaces of adjacent media.
文摘A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a rough surface, was developed. Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality. For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current. This approach lets one avoid the necessity to set surface impedances depending on the structure of the field being determined and on the material properties.
