Eikonal Approximation to 5D Wave Equations and the 4D Space-Time Metric

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold.     

Photo-orientation at liquid crystal—polymer interfaces

It is suggested that liquid crystal—polymer interfaces are coupled systems, in which the components mutually influence the orientational state of each other. The photo-orientation process at liquid crystal-polymer interfaces provides a striking example of such a coupling. Experiments show that the anisotropic structure generated by polarised light at a polymer surface is strongly affected by the phase of the liquid crystal covering the polymer. Photo-orientation is significantly more efficient when the liquid crystal is in the isotropic phase than when it exhibits orientational order. The observations are interpreted by assuming that in the smectic and nematic phases the liquid crystal stabilises to a large extent polymer chain-segments aligned parallel to the director, while it blocks the photo-induced formation of chain-segments in the perpendicular direction. Other situations, in which the coupling between the liquid crystal and the polymer can be important, are also discussed briefly.     

Phonon scattering from the boundaries of small crystals embedded in a dielectric porous-glass matrix

The thermal conductivity of porous glass with randomly distributed connecting pores ～70 Å in size (glass porosity ～25%), as well as of a porous glass + NaCl composite, was measured in the temperature range 5–300 K. NaCl filled one fourth of the pores in the composite. The experimental results on the composite thermal conductivity can be accounted for only by assuming that phonons scatter from the boundaries of NaCl nanocrystals embedded in channels of the porous glass.     

Composition of the Cobalt Sulfide Coating after Its Electrochemical Reduction

X-ray photoelectrom spectroscopy was used to study the composition of the initial and electrochemically reduced cobalt coating formed by the adsorption procedure involving treatment of a carbon glass electrode in a solution of Co(II) ammine complexes, hydrolytic washing in water, and conversion to sulfide in Na₂S solution.     

Coulomb drag of conduction electrons in spatially separated two-dimensional layers: An effective-parameter approximation

The Coulomb drag of electrons in spatially separated two-dimensional layers is considered under conditions of electron heating when the nonequilibrium distribution of electrons in the first layer can be described by macroparameters, such as the effective temperature. The nonequilibrium response is calculated using a projection operator that is an obvious generalization of the Mori operator to the case of nonequilibrium systems.     

Back Reaction in Static Einstein Spaces—Change of Entropy

Using the thermodynamical approach and the method of York, the back-reaction of anti-de Sitter Schwarzschild black hole in thermal equilibrium with conformal spin-2 field is studied. It is found that both approaches give identical results.     

Dynamics of energy release in a low-voltage pulsed arc in air

The influence of the discharge conditions on the dynamics of energy release is considered for pulsed arcs in air at initial pressures from 10⁵ to 8×10⁵ Pa and a low-voltage capacitor voltage of up to 400 V. A novel method for determining the resistance of the discharge channel in the final stage of a spark discharge is proposed. The method is applied to estimating the discharge channel parameters.     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

Magnetic field penetration into half-space for type-II superconductors of the second kind

Equations that simulate the magnetic induction and current density distributions in half-space in view of the power I-V characteristic are derived. The magnetization front velocity is determined for a given mean rate of external magnetic field variation at the boundary of the sample. An integral condition for the electrical resistance (nonlinearly depending on the magnetic field) under which the magnetic flux penetrates into the sample with a finite rate is found. An analytical solution that simulates the power variation of the magnetic field at the boundary is given. The Bean generalized model describing the current density distribution near the critical current is considered. It is shown that solutions like shock waves may arise beyond the applicability domain of the Bean model.