Method for solving heat-conduction boundary-value problems in a region with a boundary in uniform motion

A modification of the Lyubov method is used to solve boundary-value problems of the head-conduction (or diffusion) equation near a boundary in uniform motion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 62–71, January, 1971.     

Electromagnetic-Wave Propagation in a Half-Space with a Curvilinear Impedance Boundary

We study propagation of electromagnetic waves in a vacuum half-space with a one-dimensional distortion of the impedance boundary whose profile is smooth on the wavelength scale. We suggest a method allowing one to obtain the solution of this problem on the basis of a more simple boundary-value problem with the same geometry of the boundary, but with a zero Dirichlet boundary condition.     

A diffusion-based approximate model for radiation heat transfer in a solar thermochemical reactor

An approximate numerical method for fast calculations of the radiation heat transfer in a solar thermochemical reactor cavity is formulated based on the separate treatment of the solar and thermal radiative exchange by the diffusion approach. The usual P₁ approximation is generalized by applying an equivalent radiation diffusion coefficient for the optically thin central part of the cavity. The resulting boundary-value problems are solved using the finite element algorithm. The accuracy of the model is assessed by comparing the results to those obtained by a pathlength-based Monte Carlo simulation. The applicability of the proposed model is demonstrated by performing calculations for an example problem, which incorporates a range of parameters typical for a solar chemical reactor and the spectral radiative properties of polydisperse zinc oxide particles.     

Computation of demagnetizing fields and particle distribution in magnetic fluid with inhomogeneous density

A new algorithm for calculating magnetic fields in a concentrated magnetic fluid with inhomogeneous density is proposed. Inhomogeneity of the fluid is caused by magnetophoresis. In this case, the diffusion and magnetostatic parts of the problem are tightly linked together and are solved jointly. The dynamic diffusion equation is solved by the finite volume method and, to calculate the magnetic field inside the fluid, an iterative process is performed in parallel. The solution to the problem is sought in Cartesian coordinates, and the computational domain is decomposed into rectangular elements. This technique eliminates the need to solve the related boundary-value problem for magnetic fields, accelerates computations and eliminates the error caused by the finite sizes of the outer region. Formulas describing the contribution of the rectangular element to the field intensity in the case of a plane problem are given. Magnetic and concentration fields inside the magnetic fluid filling a rectangular cavity generated under the action of the uniform external filed are calculated.     

On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering

The authors developed a numerical method of the boundary-value problem solution in the vectorial radiative transfer theory applicable to the turbid media with an arbitrary three-dimensional geometry. The method is based on the solution representation as the sum of an anisotropic part that contains all the singularities of the exact solution and a smooth regular part. The regular part of the solution could be found numerically by the finite element method that enables to extend the approach to the arbitrary medium geometry. The anisotropic part of the solution is determined analytically by the special form of the small-angle approximation. The method development is performed by the examples of the boundary-value problems for the plane unidirectional and point isotropic sources in a turbid medium slab.     

Finite-element methods for junction problems for coaxial and radial waveguides

We apply the method of mixed finite elements to the junction problem for coaxial and radial waveguides. The problem is reduced to an internal boundary-value problem with nonlocal boundary-value conditions. In the low-frequency range, we compare the results of the finite-element method with the Otto relationship.     

The Theory of Block Structures in Problems on the Strength of Galleries and Constructions with Multiple Connections

Doklady Physics - It is shown that the boundary-value problem for a layered medium with parallel multiple cavities is reduced to the Riemann vector problem. To solve it, a factorization method is...     

Interaction of an atom with a laser field of intraatomic strength

The specific features of the nonlinear optical response of an atom at a laser pulse field of intraatomic strength have been investigated. An effective mathematical method, based on the expansion of the wave function in the basis of eigenfunctions of an axially symmetric boundary-value problem, is proposed to calculate the atomic response.     

Nonsymmetric electromagnetic oscillations in a sphere with circular hole

The initial boundary-value problem is reduced to an infinite system of linear algebraic equations of the second kind with compact operator. The system can be solved by the truncation method with any predetermined accuracy. A few first eigenfrequencies of a sphere with circular hole are calculated. They correspond to oscillations with azimuthal index equal to one. The influence of resonant regimes (in particular, the mode coupling effect) of the considered structure on its scattering properties is studied. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 4, pp. 336–347, April 2006.     

A new method for solving the problem of diffraction by a compact obstacle in a layered medium

We propose a new method for solving the two-dimensional problem of diffraction by a cylindrical body in a layered medium. Unlike the traditional methods, the boundary-value problem is reduced to solving the integral equation for the scattering pattern of the body. As an illustration of this method, we consider the problem of scattering by a round cylinder located in a dielectric layer between two homogeneous half-spaces. Technical University of Communication and Information Science, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 874–888, July, 1998.     

Investigation of velocity field of gas flow moving behind a piston in rectangular branch pipe

The two-dimensional boundary-value problem of the unsteady flow of an incompressible viscous gas moving behind the piston in a “long” rectangular branch pipe is solved. An analytic solution is constructed for two velocity components with a refining polynomial, which reduces to a system of nonlinear algebraic equations after the substitution into the governing system of equations. By virtue of the solution uniqueness of the boundary-value problem under study, the only solution is found from obtained values of the refining polynomial constants for each point of the branch pipe internal space for the velocity components in analytic form.     

Temperature measurement of a surface exposed to a low-temperature plasma flux

A method of measuring the surface temperature in the region exposed to a low-temperature plasma flux is suggested. The boundary-value problem of heat conduction for the unsteady case is analytically solved by means of the Laplace transformation. Analysis of the analytical relationships shows that this method measures temperature with a high accuracy in real time. Its application in formation of micro-and nanostructures in a low-temperature plasma is considered.     

A diffusion problem in a region with a moving boundary

We consider the first linear diffusion problem in a semiinfinite region with a boundary moving in accordance with a quadratic law. For the case of uniformly decelerating motion of the boundary, the solution of the problem is obtained by the Green's function, method under the most general boundary conditions; the solution of the problem for the case of uniformly accelerated motion of the boundary is obtained by an operator method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 102–110, December, 1970.     

Order parameter oscillations in a bounded solid solution and their bifurcations upon cooling

A nonlinear boundary-value problem for the Landau-Khalatnikov equation, which models the time evolution of the order parameter in a binary solution, is considered. A parameter characterizing the closeness of the alloy temperature to the critical temperature is introduced. This parameter depends on the dimensionless diffusivity. A change in this parameter results in successive bifurcations of solutions; so the order parameter corresponds to an oscillating steady-state structure to which almost all nonsteady-state solutions of the boundary-value problem are drawn after a long period of time.     

Obtaining of preset electrostatic fields in a quasi-electrode system

A method for obtaining electrostatic fields of a preset form in a quasi-electrode cylindrical system is considered. “Distributed” electrodes (filamentary conductors) make it possible to solve the inverse boundary-value problem, viz., to preset an azimuthal electric potential distribution over the cylinder surface for obtaining the required field in the cylinder, thus ensuring a larger working region as compared to an obviously electrode system.     

Simulation of deformation and fracture of coated material with account for propagation of a Lüders-Chernov band in the steel substrate

The paper studies deformation and fracture of boride-coated steel. The dynamic boundary-value problem is solved in the plane strain statement by the finite difference method. The geometry of the coating-substrate interface corresponds to those experimentally observed and is explicitly specified in the calculations. The mechanical response of the steel substrate is described by an elastoplastic model of isotropically hardening material with relations for slow flows. The peculiarities of plastic strain localization and fracture during the propagation of a Lüders-Chernov band in the steel substrate are investigated under tension.     

A diffusion problem in a two-medium system

A solution is obtained to the boundary-value diffusion-equation problem in a system of two anisotropic semiinfinite media, separated by a movable boundary region. The solution is obtained for arbitrary initial values and concentration on the boundary region. Thus, this class of boundary-value problems is completely solved in the given range.     

Field of an Electric Dipole Surrounded by a Small Plasma Spheroid with a Cavity

We obtain and analyze a solution of the boundary-value problem for the field of an electric dipole centered in a vacuum cavity inside a small plasma spheroid. The influence of the cavity size on the field enhancement in an outer vacuum region is analyzed as a function of the curvature of the plasma-spheroid surface. The results are compared with the case of a sphere with similar cavity.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 2, pp. 142–151, February 2005     

Solution of the Dirichlet problem for the Laplace equation for a multiply connected region with point symmetry

A method is proposed which uses an expansion of the potential in irreducible representations of the symmetry group of the field-defining elements of a system. A boundary-value problem is solved for multipole systems with planar plate electrodes for the C _nv symmetry group. A quadrature expression is obtained for the field potential of these systems. Constraints imposed on the electrode potentials, under which such a solution is possible, are determined. Results of calculations of the potential distribution are presented for various specific systems. Zh. Tekh. Fiz. 69, 1–9 (March 1999)     

On the sharp front-type solution of the Nagumo equation with nonlinear diffusion and convection

This paper is concerned with the Nagumo equation with nonlinear degenerate diffusion and convection which arises in several problems of population dynamics, chemical reactions and others. A sharp front-type solution with a minimum speed to this model equation is analysed using different methods. One of the methods is to solve the travelling wave equations and compute an exact solution which describes the sharp travelling wavefront. The second method is to solve numerically an initial-moving boundary-value problem for the partial differential equation and obtain an approximation for this sharp front-type solution.