Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

Stress concentration in a three-layer plate with two cylindrical cavities

The stressed state of a thick three-layer plate with two circular holes is studied. Resolving functions are expressed in terms of Kolosov-Muskhelishvili integral potentials and modified Bessel functions. The problem is reduced to solving an infinite set of linear algebraic equations.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 25–28, 1987.     

The Barnett approximation in the theory of hydrodynamic fluctuations

The Langevin dynamics and fluctuational-dissipative relationships for the hydrodynamic fluctuations for systems which are described in the third Barnett order with respect to the gradients of the hydrodynamic variables are generalized on the basis of a kinetic approach.     

Acoustic field in a closed layered shell with resonant systems

The acoustic field inside a shell excited by a spatially inhomogeneous harmonic pressure field is studied. The shell is assumed to have a finite length, a set of orthogonal stiffening ribs, two ends bounding the acoustic volume, and a sound-insulating structure, which includes layers of sound-insulating material, resonant elements, and an interior panel. The shell is considered to be orthotropic with boundary conditions corresponding to a free support. For the acoustic field in the closed volume, analytical expressions are derived with allowance for the elastoacoustic interaction of the shell with the sound-insulating layers and with the medium both inside the shell (with arbitrary impedance values at the ends) and outside it. These expressions are used to investigate the effect of different types of resonant systems on the sound field inside the shell.     

Metastable States in Antiprotonic Helium Atoms: An Island of Stability in a Sea of Continuum

 In this contribution we consider a phenomenon of metastable states in antiprotonic helium atoms, precise spectroscopy of these states and a present-day study of the electromagnetic properties of antiprotons. Received October 16, 2001; accepted for publication November 13, 2001     

Effect of hydrogen on the photoelectronic properties of GaAs/InGaAs quantum-well heterostructures with an island palladium layer on the surface

The effect of hydrogen on the photoluminescence and planar conductivity of GaAs/InGaAs quantum-well heterostructures with an island Pd layer at the anodically oxidized surface was studied. Unlike continuous deposited Pd layers, island layers do not cause the formation of defects in the GaAs surface region and yet the Pd layer maintains high catalytic activity with respect to hydrogen. It is found that the thermal treatment of such a structure in a hydrogen atmosphere causes atomic-hydrogen passivation of the defects in quantum wells. Studies of the characteristics of planar photoresistors with an island Pd layer acting as hydrogen sensors show that their hydrogen detectivity is approximately two orders of magnitude higher than that of diode structures with continuous Pd layers.     

Why and how to avoid standard kinetic equations I. Principles and band conduction problem

A review of ideas leading to full rejection of any finite or partially-infinite order kinetic equation linearized in external field is given on grounds of the time-convolution Generalized Master Equations (GME). By two examples (two-level and band conduction problem), it is shown how standard kinetic equations result from GME in the lowest order approximations which obscure, however, a direct correspondence with the Kubo linear response theory. Without approximations, on the other hand, the rigorous approach is shown to be fully equivalent with the Kubo results. It is argued and illustrated that usual technical simplicity and seeming physical lucidity of standard theories (connected with the presence of field-independent transfer or scattering rates in the fielddependent linearized theory) are just owing to structural features which are solely due to the lowest order approximations involved. These features (i.e. also the possibility of standard physical interpretation of kinetic phenomena) are proved to disappear completely as far as the theory goes properly to higher orders.