Magnetic linear birefringence in paramagnetic rare-earth garnets YbAG,YbGG, and GdGG in high magnetic fields and at low temperatures

A theoretical and experimental study of the magnetic linear birefringence (MLB) in paramagnetic rare-earth garnets YbAG, YbGG, and GdGG is presented. Starting from the microscopic theory of the polarizability tensor it is shown that the MLB in systems of ions with ground state represented by well isolated Kramers doublet (Yb-garnets) can be described by time-even invariants of new type, arising from the mixing of excited states into the ground doublet. Particularly, the MLB is found to be a linear function of the magnetic field in the region of magnetic saturation. On the other hand, the MLB in systems of S-state ions (GdGG) can be described by the classical Akulov-Callen-Callen theory which yields the quadratic dependence on the magnetic moment. The predicted type of the magnetic field and temperature dependence in the garnets studied is well reproduced by the measurements in applied fields up to 5 T and temperature range 4·2–50 K.Dedicated to Dr. Svatopluk Krupika on the occasion of his 65th birthday.     

Nonlinear mathematical model for intensive steel quenching and its analytical solution in closed form

In the present paper the nonlinear mathematical model for intensive steel quenching processes is considered. This model involves the hyperbolic heat conduction equation, the initial conditions and the Newton type nonlinear boundary conditions characterizing the boiling process on quenchant surface. The reduction of the original problem to the Volterra type nonlinear integral equation is the essence of offered approach. Besides, in the present work some analytical procedure for solving of obtained nonlinear equation is proposed. It is proved that this analytical procedure permits finding the unique solution of the original nonlinear model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical propagator method solutions for the linear parabolic initial boundary-value problems

On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial-boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial-boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi-implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are formulated for the case of constant coefficients of parabolic equation by using Green function approach. Solubility of the linear initial-boundary value problem with Newton boundary conditions containing lower order derivatives is discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modification of the dielectric properties of copper-doped CdIn2S4 single crystal

The study of the dielectric properties of a CdIn₂S₄〈3 mol % Cu〉 single crystal in alternating-current (ac) electric fields with frequencies f = 5 × 10⁴?3.5 × 10⁷ Hz has revealed the origin of dielectric loss (relaxation loss that is changed by the through current loss at high frequencies). It has been found that CdIn₂S₄〈Cu〉 has permittivity increment Δ?′ = 123, relaxation frequency f _r = 2.3 × 10⁴ Hz, and relaxation time τ = 43 μs. The doping of CdIn₂S₄ single crystal with copper (3 mol %) is established to substantially increase the permittivity (?′), dielectric loss tangent (tanδ), and ac conductivity (σ_ac). In this case, the frequency dispersion of ?′ and tanδ increases and that of σ_ac decreases.     

Basicity of a System of Exponents with a Piecewise Linear Phase in Variable Spaces

A system of exponents with a piecewise linear phase is considered in the paper. The criteria of basicity, completeness and minimality of this system in Lebesgue space of functions with variable summability exponent are established.