Knudsen Layer for Gas Mixtures

The Knudsen layer in rarefied gas dynamics is essentially described by a half-space boundary-value problem of the linearized Boltzmann equation, in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity (Milne problem). This problem is considered for a binary mixture of hard-sphere gases, and the existence and uniqueness of the solution, as well as some asymptotic properties, are proved. The proof is an extension of that of the corresponding theorem for a single-component gas given by Bardos, Caflisch, and Nicolaenko [Comm. Pure Appl. Math. 39:323 (1986)]. Some estimates on the convergence of the solution in a finite slab to the solution of the Milne problem are also obtained.     

On the Far Infra Red Excitation of LO Vibrations in Thick Single Crystals

New experiments show that the solution of the complicated problem of Far Infrared (FIR) absorption by crystals of very low symmetry, illuminated at quasi-normal incidence, might have a simple solution, which has been suggested now that a number of spectroscopic studies on monoclinic Triglycine Sulphate (TGS) are available: i) in a first classical approximation where only the strongest bands are considered, the absorption spectrum depends only on the direction of the electric field E of the IR radiation, and Transverse Optic (TO) vibrations are directly excited with electric dipole variations dp parallel to E. ii) in a second approximation looking only at the weakest absorption bands, it depends only on the direction of the wave vector k and Longitudinal Optic (LO) vibrations are excited with dp parallel to k and extinction coefficients 3 orders of magnitude smaller.     

Global Well-Posedness for the KP-I Equation on the Background of a Non-Localized Solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).     

Self-consistent problem of the excitation of beams of magnetostatic waves

An analytical solution is obtained for the self-consistent problem of the excitation of beams of magnetostatic waves by a converter of arbitrary type. Radiation patterns are calculated numerically for stripline converters at the frequencies where magnetostatic surface waves exist. Zh. Tekh. Fiz. 68, 95–101 (August 1998)     

Modeling of certain nonuniform processes in semiconductor technology

In this paper two problems are formulated and solved: the problem of diffusion in a two-phase system with a moving boundary, and the problem of taking into account the finite reaction rate for formation of the new phase. A numerical solution is found by a variational method, which has a number of practical advantages. Zh. Tekh. Fiz. 68, 75–82 (April 1998)     

Two-dimensional scattering of electromagnetic waves from a permeable inclusion in an anisotropic medium

Integrodifferential equations for the cross section of the scatterer and a collocation method are used to obtain a numerical solution of the problem of scattering of an H-polarized wave by an anisotropic layer of a three-layer dielectric structure. Zh. Tekh. Fiz. 68, 84–88 (January 1998)     

Generalized Jordan-Wigner transformations and the Ising-Onsager problem

Another possible method for obtaining Onsager’s solution for the 2D Ising model is presented. In contrast to previous methods, the method proposed here makes it possible to study the problem in a weak external magnetic field. Generalized Jordan-Wigner transformations in the form introduced by Kochmański [J. Tech. Phys. 36, 485 (1995)] are employed. Zh. éksp. Teor. Fiz. 111, 1717–1731 (May 1997)     

Pomraning–Eddington approximation for radiative transfer in a homogeneous solid cylinder

Abstract

The radiative transfer in a solid cylinder containing a homogeneous turbid medium with anisotropic scattering is considered. The medium has a diffuse and specular reflecting boundary illuminated by an external incidence and contains an internal energy source. This general problem can be solved in terms of the solution of the corresponding source-free problem with a specular reflecting boundary and isotropic external incidence. The Pomraning–Eddington approximation is used to solve the source-free problem. Three different weight functions are used to verify the boundary condition to find the constants of the solution. The partial flux, the irradiance and the net flux at the boundary for the general problem are calculated.     

Soliton-magnon scattering in a two-dimensional isotropic magnetic material

We use the generalized σ-model to analytically study the solution of the problem of magnon scattering in two-dimensional isotropic ferromagnets and antiferromagnets in the presence of a Belavin-Polyakov soliton. We obtain the exact analytical solution to this problem for the partial mode with the azimuthal quantum number m=1. The scattering amplitude for other values of m (i.e., values not equal to unity) are studied analytically in the long-and short-wavelength approximations and also numerically for an arbitrary value of the wave number. We establish the general laws governing the soliton-magnon interaction. For a magnetic material of finite dimensions we calculate the frequencies of the magnon modes. We also use the data on local modes to derive the equations of motion of the soliton. Finally, we calculate the low-temperature (long-wavelength) asymptotic behavior of the magnon density of states due to the soliton-magnon interaction. Zh. éksp. Teor. Fiz. 116, 1091–1114 (September 1999)     

Surface flow of liquid in an electric field

An analytic solution is proposed for a model problem which demonstrates the occurrence of a surface flow of weakly conducting liquid in an electric field which was previously observed experimentally by the author. Zh. Tekh. Fiz. 69, 127–128 (June 1999)     

On an integral equation arising in the transport of radiation through a slab involving internal reflection

In an earlier contribution to this journal [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)], we derived an integral equation for the transmission of radiation through a slab of finite thickness which incorporated internal reflection at the surfaces. Here we generalise the problem to the case when there is a source on each face and the reflection coefficients are different at each face. We also discuss numerical and analytic solutions of the equation discussed in [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)] when the reflection is governed by the Fresnel conditions. We obtain numerical and graphical results for the reflection and transmission coefficients, the scalar intensity and current and the emergent angular distributions at each face. The incident source is either a mono-directional beam or a smoothly varying distribution which goes from isotropic to a normal beam. Of particular interest is the philosophy of the numerical solution and whether a direct numerical approach is more effective than one involving a more elegant analytical solution using replication and the Hilbert problem. We also develop the solution of this problem using diffusion theory and compare the results with the exact transport solution. An erratum to this article is available at .     

Calculating shock-wave processes in bubbly liquids

A complete solution is given to the problem of the decay of an arbitrary discontinuity in a onevelocity model for a bubbly liquid and is used to analyze the propagation and interaction of shock waves in liquids with gas bubbles. Zh. Tekh. Fiz. 68, 12–19 (November 1998)     

A Two-Phase Free Boundary Problem for the Nonlinear Heat Equation

Abstract

A two-phase free boundary problem associated with nonlinear heat conduction is considered. The problem is mapped into two one-phase moving boundary problems for the linear heat equation, connected through a constraint on the relative motion of their moving boundaries. Existence and uniqueness of the solution is proved for small times and a particular exact solution is discussed.     

Solution of dispersion relations for planar waveguides in the case of complex roots

A method for calculating the complex roots of a nonlinear equation is described whereby the solution of the problem is reduced to quadratures. Applications of the method to the investigation of dispersion relations for various open waveguide structures with a complex dielectric permittivity are discussed. The possibilities of the prismatic excitation of modes corresponding to the roots of the dispersion relations on different Riemann sheets are analyzed. Solutions are obtained for the inverse problems of reconstructing complex mode propagation constants and determining the parameters of films that guide waveguide and leaky modes. The solution is based on processing of the angular dependence of the reflection coefficient in a prismatic excitation scheme. Zh. Tekh. Fiz. 68, 88–95 (April 1998)     

An adaptive multilevel local defect correction technique with application to combustion

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory usage. The above properties are illustrated by successfully applying the new algorithm to a simple heat transfer problem with an analytical solution, and by subsequently solving the more complex problem of an axisymmetric laminar Bunsen flame with one-step chemistry. The simulation data show excellent agreement with results previously published in the literature.     

Conformational Analysis of Baclofen Analogues by 1H and 13C NMR: Phaclofen,Saclofen, and Hydroxy-Saclofen. Influence of the Anionic Moiety

The conformations of three analogues of baclofen 1: phaclofen, saclofen, and hydroxy-saclofen 2–4, potent GABA_B antagonists, in solution (D₂O) are estimated from high-resolution (300 MHz) H NMR coupling data. Conformations and populations of conformers are calculated by means of a modified Karplus-like relationship for the vicinal coupling constants. H NMR spectral analysis evidences how 1–3 keep in solution the preferred a conformation around C3-C4 bond. A partial rotation is set up around C2–C3 bond (the conformations about C2–C3 are all highly populated in solution) particularly for 2 and 3 while 1 shows a relative preferred a conformation. This evidences the influence of the anionic moiety.     

Motion of a particle in a static magnetic field and the field of a monochromatic electromagnetic plane wave

A solution of the equation of motion of a charged particle in an external electromagnetic field comprising a superposition of a uniform static magnetic field and the field of a monochromatic, elliptically polarized electromagnetic plane wave is obtained as the solution of a Cauchy problem. The resonance case is investigated. An analysis of the resulting solution is given. Zh. Tekh. Fiz. 69, 106–110 (May 1999)     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

Abstract

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

Entangled Quantum States

Entangled quantum states are an important component of quantum computingtechniques such as quantum error correction, dense coding, and quantumteleportation. We determine the requirements for a state in the Hilbert space C ⁹to be entangled and a solution to the corresponding factorization problem if thisis not the case.     

Influence of the evaporation coefficient on the strong condensation of a monatomic gas

The influence of the evaporation coefficient on the supersonic condensation of a monatomic gas on a flat surface is studied on the basis of the kinetic theory. The formulation of the problem allows for the possible existence of a shock-wave type solution near the surface. The regions of admissible values of the parameters characterizing the state of the gas beyond the Knudsen layer are determined for different values of the evaporation coefficient. Zh. Tekh. Fiz. 67, 21–25 (October 1997)