A new concept in friction testing

Methods of measuring friction are reviewed and their shortcomings discussed. The advantages of using the wide range of test speeds, environmental conditions and recording facilities available on a tensile test machine are indicated and a new apparatus designed to fit a tensile tester is described. The design concepts are outlined in some detail and the factors limiting stick-slip motion are indicated. The apparatus can be used either for studies of materials or as an aid to product selection. Test results on a polyurethane rubber, covering a range of velocities and temperatures, illustrate the former, and tests on windscreen wiper blades under both wet and dry conditions illustrate the latter. Although primarily designed for testing the friction of polymers the apparatus is of universal application and can be used for measuring, against a chosen substrate, the coefficients of friction of metals, fabrics, paper, glass, leather, or any other material capable of being mounted in a vertical plane. It is not suitable for particulate matter such as sand, but could be used, for example, for studying the effect of floor finishes on a range of flooring materials.     

Nondestructive spatial heterodyne imaging of cold atoms

We demonstrate a new method for nondestructive imaging of laser-cooled atoms. This spatial heterodyne technique forms a phase image by interfering a strong reference laser beam with a weak probe beam that passes through the cold atom cloud. The figure of merit equals or exceeds that of phase-contrast imaging, and the technique can be used over a wider range of spatial scales. We show images of a dark-spot magneto-optic trap taken with imaging fluences as low as 61 pJ/cm(2) at a detuning of 11? , resulting in 0.0004 photons scattered per atom.     

Groups with Polycyclic Non-Normal Subgroups

The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16     

Temperature effects on the emission properties of Yb-doped optical fibers

Ytterbium-doped fiber lasers are making impressive leaps in power production. Yet in spite of fiber’s large surface area to volume ratio which is beneficial for cooling, such power inevitably leads to high core temperatures that in turn affect the laser performance. In this paper, the temperature effects on the emission and fluorescence lifetime of ytterbium-doped optical fibers are investigated. From these the temperature dependent emission and absorption cross-sections are calculated.     

Plants and Fibonacci

The universality of many features of plant patterns and phyllotaxis has mystified and intrigued natural scientists for at least four hundred years. It is remarkable that, to date, there is no widely accepted theory to explain the observations. We hope that the ideas explained below lead towards increased understanding     

Theory of oscillation type viscometers IV: A thick disk

The viscous drag exerted by a fluid on an oscillating disk is determined by methods similar to those used in Part III. The present paper differs from Part III in that the boundary layer thickness is assumed here to be small compared with both the thickness and the radius of the disk. An extrapolation of the formulae derived here agree sufficiently well, however, with those derived for the thin disk (boundary layer thickness large compared with the thickness but small compared with the radius) that it is possible to make an interpolation between the present formulae and those of Part III that will permit the evaluation of the drag for arbitrary shape disks provided the boundary layer thickness is small compared with the radius.

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Zusammenfassung Der Einfluss der Zähigkeitskräfte auf eine in einer Flüssigkeit schwingende Scheibe wird nach den gleichen Methoden wie in Tiel III behandelt. Jedoch wird im Unterschied dazu vorausgesetzt, dass die Grenzschichtdicke klein ist im Verhältnis zur Dicke und zum Radius der Scheibe. Die abgeleiteten Formeln lassen sich mit gutem Ergebnis für die dünne Scheibe extrapolieren (hier ist die Grenzschichtdicke jedoch gross, verglichen mit der Scheibendicke, aber klein gegenüber dem Radius), so dass es möglich ist, zwischen diesen Formeln und denen des Teils III zu interpolieren. Damit wird die Berechnung des Reibungsmomentes für Scheiben unterschiedlichster Form ermöglicht, vorausgesetzt, dass die Grenzschichtdicke klein ist gegenüber dem Radius der Scheibe.

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This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under contract No. AF 18 (600) 1548. Reproduction in whole or in part is permitted for any purpose of the United States Government. Part of the work was done while one of the authors (G. F. N.) was being supported by a grant from the Alfred P. Sloan Foundation.     

The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems

A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering. The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator. A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed. The relationship of the scattering theory and Backlund transformations is brought out. In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems.