The Interaction of Shocks with Dispersive Waves II. Incompressible-Integrable Limit

This is the second in a two-part series of articles in which we analyze a system similar in structure to the well-known Zakharov equations from weak plasma turbulence theory, but with a nonlinear conservation equation allowing finite time shock formation. In this article we analyze the incompressible limit in which the shock speed is large compared to the underlying group velocity of the dispersive wave (a situation typically encountered in applications). After presenting some exact solutions of the full system, a multiscale perturbation method is used to resolve several basic wave interactions. The analysis breaks down into two categories: the nonlinear limit and the linear limit, corresponding to the form of the equations when the group velocity to shock speed ratio, denoted by ε, is zero. The former case is an integrable limit in which the model reduces to the cubic nonlinear Schrödinger equation governing the dispersive wave envelope. We focus on the interaction of a “fast” shock wave and a single hump soliton. In the latter case, the ε=0 problem reduces to the linear Schrödinger equation, and the focus is on a fast shock interacting with a dispersive wave whose amplitude is cusped and exponentially decaying. To motivate the time scales and structure of the shock-dispersive wave interactions at lowest orders, we first analyze a simpler system of ordinary differential equations structurally similar to the original system. Then we return to the fully coupled partial differential equations and develop a multiscale asymptotic method to derive the effective leading-order shock equations and the leading-order modulation equations governing the phase and amplitude of the dispersive wave envelope. The leading-order interaction equations admit a fairly complete analysis based on characteristic methods. Conditions are derived in which: (a) the shock passes through the soliton, (b) the shock is completely blocked by the soliton, or (c) the shock reverses direction. In the linear limit, a phenomenon is described in which the dispersive wave induces the formation of a second, transient shock front in the rapidly moving hyperbolic wave. In all cases, we can characterize the long-time dynamics of the shock. The influence of the shock on the dispersive wave is manifested, to leading order, in the generalized frequency of the dispersive wave: the fast-time part of the frequency is the shock wave itself. Hence, the frequency undergoes a sudden jump across the shock layer.In the last section, a sequence of numerical experiments depicting some of the interesting interactions predicted by the analysis is performed on the leading-order shock equations.     

Sputtering yield of chromium by argon and xenon ions with energies from 50 to 500 eV

A radioactive tracer technique is described for the quantitative measurement of the sputtering yield of a target material electroplated on a copper substrate. Sputtering yields of chromium by argon and xenon ions with energies from 50 to 500 eV are reported. The ion beams, having a current density ranging from 0.01 to 0.1 mA/cm² at an operating pressure of 2×10^–5 Torr, were produced by a low-energy ion gun. The sputtered atoms were collected on an aluminum foil surrounding the target. ⁵¹Cr was used as the tracer isotope. The results indicate that the radioactive tracer technique is sensitive enough in measuring the extremely small amount of sputtered material at low ion currents and low ion energies.     

Properties of neodymium-doped aluminophosphate laser glasses

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 90–95, January, 1992.     

Developing a risk-assesment methodology in the U.K.defence industry

As a leading defence equipment company, the Dynamics Divisionof British Aerospace Defence Company (BAeDef(DD)) has experiencedthe worst effects of post-Coldwar defence cuts, a global recession,and a determination by the U.K. Government to achieve greatervalue for money in defence procurement. The major tenet of thisnew approach to defence prwurement was 'eyes on, hands off',promoting a shift of the management of project risks from theMinistry of Defence (MOD) to industry. Initial industry reactionwas sceptical but bxame increasingly compliant as tenderingrequirements included visibility of contractors' risk assessment.This paper describes the risk-assessment methodology createdby BAeDef(DD) to meet these changed conditions. The human and organizational aspects of these developments onrisk have helped create a pro-active risk-management cultureat BAeDef(DD). Continuous assessment of project risks providesthe impetus for wider thinking beyond risk-taking or risk-aversionpreferences, leading to greater realism in planning. Decisionsto implement risk resolution measures require competence incost-benefit analysis. The conditions to foster this new behaviourare better-informed senior management, with the rejection ofbad news eliminated at all levels, and the laying of a pathto becoming a learning company.     

A refined stress-strain analysis in the load transfer zone of flat specimens of high-strength unidirectional composites in uniaxial tension 1. Theoretical analysis

With the use of an analytical approach developed, the influence of distribution of a tangential load on the stress concentration in uniaxially tensioned flat specimens of high-strength unidirectional composites near the grips of a testing machine is evaluated. In view of singularity of the analytical solution derived at the points of discontinuity of boundary conditions, for estimating the stress concentration, it is suggested to employ the averaged value of longitudinal stresses, which is calculated by means of an improper integral across the thickness of a near-surface layer. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 787–796, November–December, 2006.     

Propagation of a focused light beam in a circuital system of tunnel-coupled waveguides

The propagation of a pencil beam in a circuital system of tunnel-coupled waveguides is considered. It is shown that the beam periodically focuses into a point when moving along the trajectory. A maximal number of waveguides supporting the propagation of the beam can be estimated in simple terms. The cross-sectional area of the waveguides can be subdivided into three zone with the beam pulsing only in the central one.     

Structure of (Ba0.7Sr0.3)TiO3 films prepared by chemical solution deposition during crystallization on a sublayer

Barium strontium titanate (BST) films on Si-SiO₂-Ti-Pt substrates are prepared by chemical solution deposition upon crystallization on a sublayer. The structure of the BST films is investigated using transmission electron microscopy, high-resolution electron microscopy, and x-ray diffraction analysis.     

Nonlinear-optical and micro-Raman diagnostics of thin films and nanostructures of ABO3 ferroelectrics

Ferroelectric composite two-dimensional ferroelectric/aluminum oxide nanostructures were studied. A porous aluminum oxide matrix was used as a template into which a ferroelectric precursor was introduced, followed by annealing. The prepared nanostructures were studied using optical second harmonic generation and micro-Raman scattering.