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Although the interaction of electromagnetic waves with dispersed systems has been studied for many decades, a number of important problems still remain unresolved. This primarily applies to systems with nonlinear properties composed of smaller particles, such as nano- and meso-particles. Also, since the interaction of electromagnetic waves with dispersed media leads to various induced effects, modeling the disperse media properties requires the problems of the interaction of the electromagnetic wave with disperse particles have to be solved simultaneously with the coupled heat and mass transfer problem with accounting for heating, evaporation and other effects, which that appear, for example, during interaction of the electromagnetic field with liquid crystal particles. The interaction of electromagnetic waves with nano- and meso-particles is particularly important when modeling and designing numerous technologies of nanomaterial manufacturing. In this work, the interaction of electromagnetic waves with a two-layer spherical nanostructure was investigated. The propagation of longitudinal electromagnetic waves, the influence of which can be very important in the case of meso- and nano-sized particles, and the influence of electromagnetic radiation on thermophysical processes were studied simultaneously. A new algorithm for modeling the interaction of longitudinal electromagnetic waves with the systems being studied here was developed using the solution of the Maxwell-Schrödinger equations. Several relevant examples of the interaction of electromagnetic waves with nonlinear media were investigated and the possibility of the Aharonov-Bohm effect for longitudinal waves, associated with the influence of the quantum nature of nanoparticles, was pointed out. The possibility of a noticeable contribution of longitudinal waves as components of the electromagnetic field in the case of meso- and nanosystems was pointed out. The densities of the heat sources caused by transverse and longitudinal waves were derived, heat exchange with these heat sources was studied, and the possibilities of phase transitions such as melting and evaporation caused by the heat sources were also explored. Here we also show that near the critical point, the relationship for the heat capacity in the form of a power function of the ratio of the difference between the critical temperature and the media temperature to the critical temperature can be expressed in terms of the densities of the heat sources caused by the transverse and longitudinal waves.
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