Advective–diffusive mass transfer in binary regular structures in the steady-state regime

Having analyzed the stationary processes of admixture transfer in two-phase regular structures with taking into account periodical character of advective phenomena, we propose a method of constructing exact analytic solutions for such class of boundary value problems. This technique is based on the application of integral transformations individually for each contacting domain. The relation between these corresponding integral transformations is obtained from the nonideal boundary conditions. We have obtained the analytic solution of a diffusion problem for a two-phase layer of a regular structure with advective mass transfer mechanism in one of its phases. The expressions describing admixture flow through a certain body surface are derived, mass flows through the interface is investigated. Having analyzed the concentration of migrating particles in the structural elements of the body and the admixture flow through the given body surface, we present results graphically. The conditions of the existence of a limit passage from the contact boundary value problem of advective diffusion in regular structures to the continual model of advective two-way heterodiffusion are determined. A natural dimensionless form is introduced.     

Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body

We study the problem on the diffraction of electromagnetic waves on a solid body in free space. To analyze the integro-differential equations describing this phenomenon, we use the theory of pseudodifferential operators. We evaluate the asymptotic expansion of the symbol and prove the ellipticity and Fredholmness with index zero of the problem operator.     

Thermostressed State of a Hollow Glass Cylinder under the Action of Electromagnetic Radiation

We present a method for solving the problem of finding the thermostressed state of a hollow glass cylinder subjected to the action of electromagnetic radiation of the infrared frequency range. In the approximation of a nonradiating body, we derive a system of equations for determining the spectral densities of the energy fluxes of the effective radiation from the surfaces and the corresponding relations for heat generation. We present the results of numerical simulations.     

The first initial–boundary-value problem for a nonlinear model of the electrodynamics of vibrating elastic media

The first initial–boundary-value problem for nonlinear differential equations describing the interactions of a vibrating electroconductive body and the electromagnetic field is studied. We assume that the motion of the body occurs at velocities that are much smaller than the velocity of propagation of the electromagnetic waves through the elastic medium. The model under study consists of two coupled differential equations; one of them is the hyperbolic equation (an analogue of the Lamé system) and the other is the parabolic equation (an analogue of the diffusion Maxwell system). We prove an existence and uniqueness result. The proof is based on the classical Faedo–Galerkin method.     

Langevin equation of a fluid particle in wall-induced turbulence

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-induced turbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer). The analysis is based on the asymptotic behavior at a large Reynolds number. We use the Lagrangian Kolmogorov theory, recently derived asymptotic expressions for the spatial distribution of turbulent energy dissipation, and also newly derived reciprocity relations analogous to the Onsager relations supplemented with recent measurement results. The long-time limit of the derived Langevin equation yields the diffusion equation for admixture dispersion in wall-induced turbulence.     

Nonlinear electrodynamic lensing of electromagnetic waves in a magnetic dipole field

We consider propagation of electromagnetic waves in magnetic dipole and gravitational fields proceeding in accordance with the nonlinear vacuum electrodynamics laws. We derive formulas describing the effect of nonlinear electrodynamic lensing of electromagnetic waves in the magnetic dipole field. We show that rotation of the magnetic dipole moment about an axis noncoincident with this moment leads to a nonlinear electrodynamic modulation of the electromagnetic radiation intensity by frequencies that are multiples of the dipole rotation frequency. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 85–94, January, 2007.     

A Carleman estimate for the linear magnetoelastic waves system and an inverse source problem in a bounded conductive medium

ABSTRACT

In this paper, we consider an inverse problem for the simultaneous diffusion process of elastic and electromagnetic waves in an isotropic heterogeneous elastic body which is identified with an open bounded domain. From the mathematical point of view, the system under consideration can be viewed as the coupling between the hyperbolic system of elastic waves and a parabolic system for the magnetic field. We study an inverse problem of determining the external source terms by observations data in a neighborhood of the boundary and we prove the Hölder stability. For the proof, we show a Carleman estimate for the displacement and the magnetic field of the magnetoelastic system.     

On the far field patterns for electromagnetic scattering by a chiral obstacle in a chiral environment

A time-harmonic plane electromagnetic wave is scattered by a chiral body in a chiral environment. The body is either a perfect conductor, or a dielectric, or a scatterer with an impedance surface. Using the Huygens's principle, we construct in closed forms both the left-circularly polarized and right-circularly polarized electric far field patterns for such chiral media. We prove reciprocity relations and general scattering theorems for chiral materials which are a generalization of those obtained by Twersky for achiral electromagnetic scattering. In the special case when the directions of incidence and observation are the same we prove the associated forward scattering theorems.     

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.     

Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux

The propagation of shock waves in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux, which has a variable azimuthally fluid velocity together with a variable axial fluid velocity, is investigated. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The fluid velocities in the ambient medium are assume to be vary and obey power laws. The density of the ambient medium is assumed to be constant, the heat conduction is express in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α_R are assumed to vary with temperature and density. In order to obtain the similarity solutions the angular velocity of the ambient medium is assume to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameter and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.     

The electromagnetic field of a dipole radiation source in a slowly moving conducting medium

We solve the problem of determining the electromagnetic field created by a dipole radiation source in a conducting, homogeneous, isotropic, slowly moving medium. The investigations are carried out depending on the orientation of the dipole source and the velocity vector of the medium.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 28, 1988, pp. 31–35.     

Plasmon resonance and heat generation in nanostructures

In this paper, the photothermal effects of plasmon resonance are investigated. Metal nanoparticles efficiently generate heat in the presence of electromagnetic radiation. The process is strongly enhanced when a fixed frequency of the incident wave illuminates on nanoparticles such that plasmon resonance happens. We introduce the electromagnetic radiation model and show exactly how and when the plasmon resonance happens. We then construct the heat generation and transfer theory and derive the heat effect induced by plasmon resonance. Finally, the heat generation under plasmon resonance in a concentric nanoshell structure is considered specially, and excited result is obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

Temperature fields and stresses in a system of plane-parallel layers under heating by electromagnetic radiation

We determine and study the temperature fields and stresses arising in heating of a system of two plane-parallel layers of different transparency by electromagnetic radiation. We discuss the possibility of using the results obtained to develop rational programs for thermal processing of electrovacuum devices with a glass shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 28, 1988, pp. 21–26.     

Nonlinear Electromagnetic Delay of Electromagnetic Signals Propagating in the Magnetic Meridian Plane of Pulsars and Magnetars

We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.     

Modeling analysis of the electromagnetic braking action on rotating solid cylinders

The electromagnetic diffusion and the electromechanical phenomena arising in a solid cylinder rotating inside a magnetic field are here analyzed. The study is developed through a time stepping Finite Element voltage-driven formulation, employing the sliding mesh technique for handling the cylinder motion. The influence on the dynamic behavior and energy dissipation of the material electric and magnetic properties, the geometrical parameters and the supply conditions is investigated considering a model problem.     

Self-action of a point charge in classical electrodynamics

A direct calculation demonstrates that the causal Green function for classical equations of an electromagnetic field contains an additional singular term cancelling the divergence in the self-action of a point charge. Thus, the problem of mass renormalization is avoided. An exact relativistic expression for the self-action force is presented as a sum of two terms. The first one gives the radiation damping and the second one describes the electromagnetic component of the particle momentum depending on its velocity and acceleration. Accordingly, the work of the force also consists of two terms: the radiation energy and the electromagnetic component of the particle energy. To perform the calculations, we have to extend the radial spherical coordinate in the -function argument to negative values.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 2, pp. 256–269, November, 1995.     

Quantum statistical theory of radiation friction of a relativistic electron

We comprehensively investigate the effect of quantum space-time nonlocality that accounts for retardation of the electron interaction with both the electron’s own radiation field and the fluctuation field of the electromagnetic vacuum. We rigorously show that the quantum nonlocality effect eliminates the self-acceleration and the causality violation paradoxes that are inherent in the classical theory of radiation friction. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 478–496, March, 2009.     

Modeling the reactive processes within a catalytic porous medium

A one-dimensional modelling approach to the reactive processes within a heated homogeneously premixed fuel–air mixture in its passage through a non-adiabatic catalytically reactive porous medium is described. The main focus of this contribution was comparison of the results obtained while using different modeling approaches that include mass diffusion to solid pores versus neglecting it; single step reaction versus detailed kinetic simulation; adiabatic versus non-adiabatic reactor operation; two different approaches accounting for radiation heat transfer. This model was tailored to our experimental results so as to obtain original kinetic data for corresponding global reactions for different types of catalysts and validate at the same time the predictive approaches.     

基于几何光学法和惠更斯原理的微波暗室性能分析

微波暗室在导弹导引仿真中已广泛使用,针对导弹导引仿真试验中用到的微波暗室的静区性能评估问题,分别建立了基于几何光学法和惠更斯原理的评价分析模型.此模型考虑了暗室空间内各个壁面电磁辐射的相互影响,将壁面看作次级余弦辐射体,建立了描述壁面任一点垂直辐射强度的积分微分方程.通过离散方法将问题转化为求解线性方程组的数值问题.计算得到暗室壁面辐射强度分布以及性能指标γ.结果表明,垂直反射率为0.5时不满足要求,而0.05时满足要求.最后考察了模型的收敛性,随着离散度的增高,计算结果趋于稳定.