Focusing of an electromagnetic plane wave into a uniaxial crystal by a Wood lens

High frequency fields, refracted by a geometry containing a Wood lens placed at a certain distance from a planar uniaxial interface, are derived by using Maslov’s method. The geometrical optics approximation generally valid for high frequency fields fails in the vicinity of a caustic. Maslov’s method is a systematic procedure for predicting the field in the caustic region, combining the simplicity of the ray and the generality of the transform method. Numerical computations are made for the field pattern around the caustic by using Maslov’s method. The results are found to be in good agreement with those obtained using Kirchhoff’s approximation.      

Equivalent network parameters of millimeter wave E-plane septum discontinuities with finite conductivity

The equivalent T—network parameters of millimeter wave E—plane discontinuities of bilateral metal septa with finite conductivity are calculated by the method of lines. An efficient approach is presented to extend this numerical method to EM boundary value problems with imperfectly conducting metal boundaries parallel to the discretization lines. Numerical results of both equivalent reactances and resistances in the T—network are obtained. The insertion losses of a Ka—band filter are calculated based on the lossy equivalent circuit. Numerical results are in agreement with the published experimental results.     

Perturbative evaluation of universal constants for a quartic map

We discuss a perturbative scheme for the determination of the bifurcation rate δ for a specific map, by extending Virendra Singh’s method of evaluating the scaling factor α. The method is applied to a quartic map and the values obtained, α = 1.690781026 and δ = 7.23682924 are in good agreement with the numerically computed values reported in the literature. The perturbative approach is found to be more efficient than other existing methods.     

Hamilton—Jacobi quantization of constrained systems

The path integral quantization of contrained systems is analysed using Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac’s method. Presented at the 10th Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June, 2001.     

Electron impact excitation of hydrogen and helium in Coulomb-projected Born methods

Coulomb-projected Born methods for the theoretical study of electron impact excitation of hydrogen and helium are reviewed. The results obtained by using different forms of Coulomb-projected Born methods are compared with other theoretical and experimental results and analyzed. The inadequacy of the variable charge Coulomb-projected Born approximation (VCCPB)—the most recent form of the Coulomb-projected Born methods—in giving good results in processes where exchange is dominant is discussed in detail. The ‘modified’ VCCPB approximation obtained by modifying the VCCPB method to remove its shortcomings is also discussed and its application to electron impact excitation of 2³ s state of helium is studied.     

Comparative analysis of approximate and exact models in inflationary cosmology

A method of constructing and analyzing exact solutions for inflationary cosmology models with a self-action scalar by introducing an effective self-action potential is suggested. On the basis of exact solutions for complete and “shortened” equations obtained in the “slow-descent” approximation, their comparative analysis is made. It is shown that the results obtained for approximate models that are conventionally used for comparison with experimental data may differ greatly from those for exact models because of the structural instability of models with inflation. Ul'anovsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 14–20, January, 2000.     

Asymptotic behavior of ω in general quintom model

For the quintom models with arbitrary potential , the asymptotic value of equation of state parameter ω is obtained by a new method. In this method, ω of stable attractors are calculated by using the ratio d ln V/d ln a in asymptotic region. All the known results, have been obtained by other methods, are reproduced by this method as specific examples.     

Effect of preparation on Hg−Ba−Ca−Cu−O superconductors

Some main features of the non-linear synthesis process are described by theoretical considerations. Results of typical preparation methods are compared to each other and to those obtained by the experiments designed specially for the study of the effect of synthesis on the superconducting properties of Hg−Ba−Ca−Cu−O compounds. As is shown, the controlled Hg-vapour pressure method, the sealed tube with phase formation procedure, the high-pressure synthesis and the freeze-drying method seem to be unambiguously reliable to provide high-quality samples. Significant deviations from these fundamental synthesis routes can lead to significant deviations of superconducting parameters.     

Multiple (<Emphasis Type="Italic">G</Emphasis>′/<Emphasis Type="Italic">G</Emphasis>)-expansion method and its applications to nonlinear evolution equations in mathematical physics

In this paper, an extended multiple (G′/G)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this method can also be used to deal with some high-dimensional and variable coefficients’ nonlinear evolution equations.     

Calculation of hyperfine splitting in mesons using configuration interaction approach

The spin–spin mass splitting of light, heavy and mixed mesons are described within a good accuracy in the potential model with screened potential. We conclude that the long-range part of the potential cannot be pure scalar and that a vector–scalar mixture is favored. Excellent spin–spin splittings of heavy quarkonia are obtained with the same parameters as the ones which give the correct average mass spectrum. The results are obtained by going beyond the usually used perturbation method, namely using a configuration interaction approach. Received: 19 September 2000 / Revised version: 19 April 2001 / Published online: 3 August 2001     

Investigation of the Effect of the Plasma Thin-Film Coating System Si − O − C − N on the Surface Hardening of High-Speed Steel

The results of studying changes in the strength properties of the surface of a tool product from high-speed steel (HSS) of the W6Mo5Cr4V2 type after its hardening by the application of the Si−O−C−N micron plasma coating system are presented. The study is conducted by comparing the properties of the surface, evaluated by the same methods before and after coating. In this case, the sample goes through a complete cycle of mechanical and heat treatment designed for the product before coating. The results of evaluation of the adhesive strength of the coating using the proposed method of recalculation are given, and the correspondence between the index of destruction of the coating of the VDI 3198: 1992-08 technique and the delamination coefficient is obtained. The study itself is carried out by indenting and scratching the surface with HV, HRC and HRB-type indenters in the load variation range of 0.1–200 N, which makes it possible to simulate different levels of contact pressure in the surface layer of the substrate and at the base–coating interface. It is shown that the application of a thin-film coating of the Si−O−C−N system by the plasma method makes it possible, in addition to standard heat treatment of HSS steel, to increase the surface resistance to penetration and scratching with harder bodies. The causes of the obtained positive effect are analyzed and the limits of the expediency of applying plasma hardening depending on the contact task are described. These results make it possible to consider the method of the additional plasma hardening of HSS steel as promising for implementation.     

GaAsSb/GaAs quantum well growth by MOCVD hydride epitaxy with laser sputtering of antimony

A new method of obtaining quantum-size GaAs_1−x Sb_x (x⩽0.45) layers is proposed. The method consists in laser vaporization of solid metallic antimony near the substrate directly in the reactor. The antimony concentration is set by the antimony sputtering time with the arsine flux shut off. The polarization of the photoluminescence of the obtained layers indicates the formation of quantum wires. The heterostructures obtained are used to fabricate laser diodes. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 84–88 (10 July 1998)     

Deconvolution of complex echo signals by the maximum entropy method in ultrasonic nondestructive inspection

The problem of inversion of convolution with the echo signal point source function is considered with the use of the regularization and maximum entropy method and further reconstruction of two-dimensional images by the method of projection in the spectral domain. The inverse convolution problem is solved for the complex-valued signal that is obtained from the real valued signal through the Hilbert transform. Numerical and experimental simulation is performed. A possibility of enhancing the echo signal along the ray’s resolution and of lowering the spectrum’s noise level with the use of complex signals (pseudo-random sequences) is demonstrated. The results are compared with those obtained using the autoregression method and the reference hologram method.     

Coupled Rearrangement Channel Calculation of the Hyperfine Structure of the dtμ Molecule

Hyperfine structure splittings are calculated for the J = v = 1 state of the dtμ molecule. The splittings are determined by the accurate three-body wave function obtained by coupled rearrangement channel method using the updated physical constants. The result obtained is in good agreement with the previous calculation within ∼0.07 meV. The discrepancy is due to the accuracy of the three-body wave function. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nonequilibrium phase transition in v-group semimetals,induced by ultrashort laser pulses

Coherent, totally symmetric large-amplitude phonons in bismuth and antimony were investigated by the pump—probe method using femtosecond laser pulses. The obtained results are compared to time-resolved Raman data. It is shown that intense photoexcitation by laser pulses with a duration shorter than the lifetime and reverse phonon frequency in Bi and Sb can lead to a nonequilibrium semimetal—metal phase transition, most likely caused by the instability of the crystal’s electron subsystem.     

Electrical resistivity of liquid binary and ternary alloys

New method of calculation of the electrical resistivity of liquid and amorphous alloys is presented. The method is based on the Morgan–Howson–S̆aub (MHS̆) model but the pseudopotentials are replaced by the scattering matrix operators. The Fermi energy is properly determined by the accurate values of the phase shifts. The model depends on a very small number of universal parameters and gives stable results. The calculated values of the resistivity agree well with available experimental data for a substantial number of binary alloys. Moreover, the results for some ternary alloys were also obtained.     

Measurement of K X-ray intensity ratios in Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn employing carbon and nitrogen projectiles – VTT method

A method is suggested to effect the self absorption correction in a different way to estimate the K X-ray intensity ratios particularly when heavy ions are used as projectiles. Employing this method, the K_β/K_α intensity ratios are measured in some 3d shell elements by using Carbon and Nitrogen ions as exciting agents. The K_β/K_α intensity ratios thus obtained in the present work are compared with the intensity ratios due to some previous authors and also with Scofield theoretical values. Received 14 August 2000 and Received in final form 3 January 2001     

Calculation of energy characteristics for Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>–Si structures with single quantum wells

Energy characteristics of Si_1–x Ge _x –Si quantum-size structures with single quantum wells were calculated numerically based on a four-band k·p method. Analytical expressions for the Luttinger parameters are obtained as functions of the component composition of Si_1–x Ge _x compounds. Analytical expressions for the energy ħω of optical band-to-band transitions are obtained in an effective mass approximation and agree well with numerical calculations by the k·p method. This allows one to determine accurately a range of changes while varying the component compositions and thickness of the active and barrier layers.     

PPP Hamiltonian for polar polycyclic aromatic hydrocarbons

Total energies of charged states and configurations of different spin multiplicity of two polar non-alternant polycyclic aromatic hdrocarbons (PAH), namely, pentaheptafulvalene and azulene, calculated by means of a Multi-Configurational (MCSCF) method which includes correlation only amongst π orbitals, have been fitted by exact solutions of the Pariser-Parr-Pople (PPP) and the Hubbard Hamiltonians for π electrons. As both molecules are planar, such an approach is in principle feasible. As found in our previous analysis of PAH, PPP fittings are significantly better than those attained with the Hubbard Hamiltonian. In addition, parameters for the Hubbard Hamiltonian are around twice those derived for the PPP model, indicating that parameters are not model independent. Fitted PPP parameters are close to those derived from a similar study of the PAH 2, 5, 8-trihydrogenated phenalene and those originally proposed by Pariser et al. providing further support to a wide applicability of the fitted parameters. Fittings obtained for a MCSCF method that MM298001also includes σσ and σπ correlations (MCSCF/MP2) are slightly less accurate giving an on-site repulsion 10–15% smaller. The accuracy of the fittings further diminishes when parameters are derived from energies obtained by means of a DFT method (B3LYP) with an additional decrease in U of 5–25%. In the latter two cases, parameters have to be considered as effective, accounting for effects of σ orbitals not explicitly included in the model Hamiltonians. Electron affinities, ionization energies and dipole moments, calculated by means of the model Hamiltonians, are compared to those derived from DFT and ab initio methods and, whenever available, to experimental data.     

Application of tomography method in millimeter wavelengths band II. Experimental

Tomographycal methods of image reconstruction of two-dimensional objects, surfaces or subsurface regions in millimeter wavelengths band are suggested and considered. Experimental images obtained using antennas and waveguiding lines of different types and radiation frequencyf≈33÷35GHz are represented. Volumetric dielectric objects and plane-parallel ferrite (or dielectric) plates distributed in free space or in homogeneous dielectric medium have been taken as objects under investigation. It is shown that in the frequency band under consideration, the images of investigated objects with characteristic dimensionA≈2λ÷7λ may be obtained by first-order diffraction tomography method (Born, Rytov or high frequency approximation of the first-order for electromagnetic field).