Light with a twist in its tail

Polarized light is a phenomenon familiar to anyone with a pair of polaroid sunglasses. Optical components that change the nature of the polarization from linear to circular are common in any undergraduate laboratory. Probably only physicists know that circularly polarized light carries with it an angular momentum that results from the spin of individual photons. Few physicists realize, however, that a light beam can also carry orbital angular momentum associated not with photon spin but with helical wavefronts. Beams of this type have been studied only over the last decade. In many instances orbital angular momentum behaves in a similar way to spin. But this is not always so: orbital angular momentum has its own distinctive properties and its own distinctive optical components. This article outlines the general behaviour of such beams; how they can be used to rotate microscopic particles; how they interact with nonlinear materials; the role they play in atom-light interactions and how the rotation of such beams results in a measurable frequency shift.     

Scheduling Production in a Heavily Constrained Plant – Anode Manufacture in an Aluminium Smelter

In this paper a mathematical model of an anode manufacturing plant is developed with the objective of assisting in the planning and scheduling of production for up to a month ahead. A model of the overall smelter already exists and is based on a monthly time frame. The anode plant is a part of this model but is a very heavily constrained area and it is necessary to have a daily planning model that will help to achieve the optimal level of operations as dictated by the overall model of the smelter. The anode area is responsible for the production of carbon blocks (called anodes) which are an integral part of the aluminium smelting process. The plant is also responsible for the delivery of all raw materials within the smelter. The model developed is a daily one replicated for up to a month ahead, interconnected by opening and closing stocks.     

Triplets and Hexagons

Two combinatorial methods for constructing a family of symmetric trivalent graphs are presented in this paper. Each family of graphs contains a member for every odd prime numberp. It is proved that in one of the families the girth is unbounded as a function ofp; the other family contains the smallest known trivalent graphs of girth 18 and 19.     

Modelling of recording system performance and its relationship to recording media properties

A recording system has been modelled which employs a peak detection scheme consisting of differentiator and cossover detector. The recording behaviours of head and tape combinations are included as variables and the effect of these on overall system error rates have been computed.     

Image enhancement and stress separation of thermoelastically measured data under random loading

Traditional thermoelastic stress analysis (TSA) presupposes that the structure being analyzed is cyclically loaded at a constant amplitude and frequency. This approach typically has been used to satisfy the adiabatic reversible assumptions. The authors employ an alternative signal analysis technique that enables one to evaluate the magnitude of the individual components of stress in a component subjected to a loading that is random in both frequency and magnitude. However, the nature of the measured information does not change; i.e., data are inherently noisy, and edge information is unreliable. The latter two aspects have caused many thermoelastic stress analyses to be more qualitative than quantitative. The present paper emphasizes developing the TSA technique into a practical, noncontacting quantitative method for stress analyzing actual engineering structures that are randomly loaded. In particular, ability to determine the individual stresses thermoelastically under random loading is demonstrated.     

Electron-beam-induced fracture of polymers

When a notched polymeric material is stressed, the notch opens into a wide crack tip, exposing a region of high stress concentration. The consequences of electron bombardment of the tip of such a stressed material under vacuum are explored here for the first time. Evidence is presented for electron-induced crack growth at stress far below that needed for crack growth due to stress alone. The electron current densities used in these experiments are sufficiently small that thermal heating of the zone near the crack tip is minimal. To provide information on the phenomena involved, we present simultaneous measurements of electron current, gas pressure, and sample load in response to periodic bombardment of the sample. Experiments involving the bombardment of un-notched polymers under stress are also described. Fractography of the unique structures obtained by fracture due to the combination of electron bombardment and stress are presented and interpreted in terms of a crosslinking mechanism.     

On the eigenvalue problem for fluid sloshing in a half-space

Summary The boundary-value problem for free oscillations of a liquid in a half-space, which is bounded above by a rigid plane that contains a circular aperture, is transformed to a homogeneous, Fredholm integral equation for the velocity distribution in the aperture. Rayleigh-Ritz approximations to the eigenvalues are obtained by expanding the velocity distribution in appropriately weighted Jacobi polynomials. Numerical results demonstrate that the convergence of the approximations is much stronger than that of the approximations developed by Henrici, Troesch and Wuytack; for example, retaining twelve terms in the Rayleigh-Ritz expansion yields the dominant eigenvalue within one part in 10^–8. A corresponding development is given for the two-dimensional problem, in which the aperture is an infinite strip.

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Résumé Le problème aux conditions limites pour les oscillations libres d'un liquide dans l'espace semi-infini sous un plan rigide contenant une ouverture circulaire est transformé en une équation intégrale homogène de Fredholm pour la distribution de vitesse dans l'ouverture. On obtient des approximations de Rayleigh-Ritz pour les valeurs propres en développant le champ de vitesse en série pondérée de polynômes de Jacobi. Les résultats numériques démontrent que la convergence des approximations est bien plus rapide que celle des approximations développées par Henrici, Troesch and Wuytack; par exemple, en retenant douze termes dans le développement de Rayleigh-Ritz on obtient la valeur propre dominante avec une erreur relative moindre que 10^–8. Un développement correspondant est donné pour le problème bidimensionnel, pour lequel l'ouverture est une bande infinie.

     

Small-scale integration of fused tapers

The Small-Scale Integration (SSI) of fused couplers is proposed. The idea is to make several couplers on a single continuous piece of fiber rather than making discrete couplers and then splicing them together. Rudimentary tooling was set up to fabricate the couplers. Nine devices were successfully integrated onto a single fiber. In addition, a theory of fused tapers was developed. The fabrication parameters are analytically related to fiber geometry, which in turn, is related to the optical performance of the device.