Penta­chloro‐1,3,6‐tris­(diethyl­phenyl­phosphino)­dirhenium(II,III)

The title complex [systematic name: penta­chloro‐1κ³Cl,2κ²Cl‐tris(diethylphenylphosphino)‐1κP,2κ²P‐dirhenium(II,III)(Re—Re)], 1,3,6‐Re₂Cl₅(PEt₂Ph)₃ or [Re₂Cl₅(C₁₀H₁₅P)₃], consists of dirhenium mol­ecules with eclipsed structures similar to those of previously characterized 1,3,6‐Re₂Cl₅(PR₃)₃ compounds. The Re—Re bond distance is 2.2262 (3) Å and the metal–metal bond order is 3.5.     

Flux growth and structure of two compounds with the EuIn2P2 structure type,AIn2P2 (A = Ca and Sr), and a new structure type,BaIn2P2

Single crystals of the new Zintl phases AIn₂P₂ [A = Ca (calcium indium phosphide), Sr (strontium indium phosphide) and Ba (barium indium phosphide)] have been synthesized from a reactive indium flux. CaIn₂P₂ and SrIn₂P₂ are isostructural with EuIn₂P₂ and crystallize in the space group P6₃/mmc. The alkaline earth cations A are located at a site with m symmetry; In and P are located at sites with 3m symmetry. The structure type consists of layers of A²⁺ cations separated by [In₂P₂]²⁻ anions that contain [In₂P₆] eclipsed ethane‐like units that are further connected by shared P atoms. This yields a double layer of six‐membered rings in which the In—In bonds are parallel to the c axis and to one another. BaIn₂P₂ crystallizes in a new structure type in the space group P2₁/m with Z = 4, with all atoms residing on sites of mirror symmetry. The structure contains layers of Ba²⁺ cations separated by [In₂P₂]²⁻ layers of staggered [In₂P₆] units that form a mixture of four‐, five‐ and six‐membered rings. As a consequence of this more complicated layered structure, both the steric and electronic requirements of the large Ba²⁺ cation are met.     

The role of resonant interactions in the dynamic stability of elastic systems

A resonance phenomenon which can occur in elastic systems supporting wave motion is discussed. An analytical and numerical study of the dynamic stability of a cylindrical shell under axial compression illustrates the potential importance of this resonance phenomenon for imperfection-sensitive structures.     

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.