Generalization of a nonstandard approach in dynamic diffraction theory to the case of deformed crystal

A nonstandard X-ray diffraction theory for crystals taking lattice deformation into account is generalized in this paper. The vector of atomic-plane displacement is introduced in a model of crystal polarizability in analogy with the Takagi generalized dynamic theory. The solution of the wave equation is sought using the technique of expanding the field amplitude and vector operators in terms of the Fourier polarizability component χ _H in accordance with the multiscale method. It is shown that, in the general case, taking lattice distortions into account requires consideration of various characteristic spatial regions for the diffraction equation. This corresponds wholly to the basic idea of the multiscale method. The particular case of the displacement field depending on a single scale is considered. If a relative change in deformation occurs at a length on the order of the extinction length in this case, then equations generalizing the Takagi equations to the case of arbitrary diffraction geometry are obtained as a result.     

Generalization of the rainbow Airy theory to nonuniform spheres

Rainbow techniques permit measurement of refractive indices, and hence the temperatures of liquid droplets through determination of the absolute angular position of a rainbow interference image in space. The Airy theory, which is commonly used to explain the rainbow effect, permits the determination of a unique refractive-index value, even in the presence of nonuniformities in the droplet. An extension of this theory to spheres that exhibit internal refractive-index gradients is proposed. The case of burning droplets is considered as an example of such spheres, and the results obtained are successfully compared with those presented in the literature.     

Generalization and applications of the Sasakawa theory

The Sasakawa theory of scattering is phrased in the form of a Fredhohn reduction technique for integral equations possessing a fixed-point singularity in their kernels. This permits the generalization of this theory to a large variety of scattering integral equations. Some specific applications include the two-particle off-shell and multichannel scattering problems. In the first instance a rank-three approximation to the fully off-shell transition matrix is derived which is exact on and half-off shell, satisfies off-shell unitarity, and which possesses no unphysical singularities. In the second problem it is shown how the method leads to the generation of a unitary approximation to the multichannel amplitudes.     

Generalization of the Toda chain system to the elliptic curve case

We propose a system of two equations which, when some of its parameters vanish, separates into two equations describing independent one-dimensional Toda chains. The system has its foundation in the discrete transformations of the Landau-Lifshitz equation which is closely connected with elliptic curves. Nontrivial solutions of the system are found in an explicit form.     

A formal theory of the conductivity and application to the giant magnetoresistance

The transport in a system with inhomogeneous elastic scattering is described in terms of a probabilityconserved Boltzmann equation. We demonstrate that the spatially varied current density depends only on the voltage drop between the ends of the sample. This fact enables us to develop a formal and general theory for the conductivity without determining the actual electric field inside the sample. The theory is first applied to multilayer systems and shown to recover the previous theory. By including the spin-dependent interface scattering and bulk scattering, we employ our theory to account for the giant magnetoresistance (MR) in magnetic granular systems with both spherical and cylindrical granules. The results obtained reproduce the experimental dependence of the MR on annealing temperature.     

Ion transport in porous electrodes with mixed conductivity

A method for studying dc ion transport in porous mixed-conductivity electrodes in the course of the electrochemical reaction taking place in them has been suggested. The dependences of the proton conductivity of porous electrodes used in direct electrochemical energy converters (electrolyzers, fuel cells) on their composition and structure have been presented. These data are of practical importance and can be used to analyze ohmic losses in the electrodes and membrane electrode assembly and also to devise novel electrode materials.     

Contribution to the theory of mixed ising spin systems

An effective-field theory of mixed spin—1/2 and spin-1 Ising system with random bond and crystal-field interactions is developed. The general expressions for evaluating the thermodynamic quantities are obtained. In the last section, transition temperature and tricritical behavior are examined for the mixed ferromagnetic spin system withz=3, wherez is the coordination number. The obtained results are reasonable in comparison with exact and approximate ones. Owing to the simplicity, the present method can be applied to a wide class of the random systems.     

Generalization of Sturm-Liouville theory to a system of ordinary differential equations with Dirac type spectrum

The Sturm-Liouville theory is generalized to Dirac-equation-like systems of ordinary differential equations. It is shown how the comparison theorem and conversion to integral equations can be generalized.Dedicated to Walter Thirring on his 60^th birthday     

Signal propagation in the general theory of relativity with viscosity and thermal conductivity: Linear theory

The Eckart-Landau-Lifshitz classical relativistic models of a viscous, heat-conducting fluid are known to lead to an infinite signal propagation velocity. This infinite value contradicts the postulate of a limiting signal velocity, equal to the velocity of light in vacuum. It is suggested that this paradox might be resolved by incorporating internal relaxation processes in the particles of the medium. It has been shown previously that in the special theory of relativity the velocity of a signal in a viscous, heat-conducting fluid with inheritance turns out to be finite. That assertion is proved in the present paper within the framework of the general theory of relativity in the approximation of a weak gravitational field.Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–18, May, 1993.     

On the theory of nonlinear thermal conductivity

A nonlinear differential equation of thermal conductivity is derived phenomenologically from the general principles of construction of functional Q invariant to the inversion operation I(r →–r), and the temperature evolution dynamics is analyzed in the nonstationary case. The proposed method makes it possible to reveal some general regularities in the physical behavior of such systems for describing irreversible phenomena in self-organization processes. It is noted that an analogous situation may take place, for example, in strongly inhomogeneous structures with stochastic internal heat fluxes.     

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations.Resulting nonlinear ordinary differential equations are solved numerically employing the Runge-Kutta shooting method.In order to check the accuracy of the method,these equations are also solved using bvp4c built-in routine in Matlab.Both solutions are in excellent agreement.The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs.The novelty of this analysis is the self-similar solution of the threedimensional boundary layer flow in the presence of mixed convection,viscous dissipation and variable thermal conductivity.     

Generalization of the momentum-space subtraction procedure for renormalized perturbation theory

The momentum-space subtraction procedure for defining renormalized Feynman integrals is modified to allow for subtraction operators more general than the usual Taylor operators. The added generality permits one to assign subtraction degree less than four to some terms of the unperturbed Lagrangian.     

Ionic conductivity of mixed silver halide crystals

To evaluate the effects of mixed halides on the lattice defect parameters of the silver halides, we have measured the ionic conductivity both of the entire range of mixed AgBr-AgCl single crystals, aftd also of several iodide-doped crystals. For the AgBr-AgCl system, the intrinsic conductivity at a given temperature decreases monotonically from pure AgBr to pure AgCl. The deduced Frenkel defect formation energy varies only a little from 0 to 50 mole % AgCl, and then increases rapidly with further increase in AgCl content, closely paralleling the ratio of bulk modulus to dielectric constant. The defect formation energy in these crystals hence reflects the average macroscopic properties of the solid solution. For the iodide-doped crystals, however, the results are quite different. Small amounts-of iodide cause large increases in the conductivity of AgBr andiAgCl, especially in the latter. These results suggest that the elastic strain introduced by the oversized iodide ion exerts an appreciable local effect on the Frenkel defect formation, in contrast to the crystal-averaged response found for the AgBr-AgCl solid solutions. Furthermore, the Arrhenius plots for the conductivitiei of the AgBr: I specimens show curvature which suggests a temperature-dependent pairing of the solute.