Quantum-mechanical analogies for classical post-collision interaction effects in (e, 2e) collisions

A method is proposed for approximately computing the post collisional interaction of the two escaping electrons in otherwise standard first order ionisation calculations. At intermediate energies and in asymmetric kinematics the effects are found to be very small. The interactions of these electrons with the residual ion are considered through the use of distorted waves. For the slow one the latter are used in the calculations but for the fast one their effect is investigated using Fourier transforms. These interactions play a significant role.     

The stress intensity factors for two collinear edge cracks in a rotating disc

Summary The problem of determining the stress intensity factors and the crack formation energy of two edge cracks of unequal length on the same diameter of a finite rotating elastic disc is reduced to the solution of two coupled singular integral equations. Numerical results are given.

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Zusammenfassung Das Problem der Bestimmung der Spannungsintensitätsfaktoren und der Rissbildungsenergie van zwei Kantenrissen ungleicher Länge auf denselben Durchmesser in einer endlichen rotierenden elastischen Scheibe wird auf die Lösung von zwei zusammengeschriebenen singulären Integralgleichnungen reduziert. Es werden numerische Resultate gegeben.

     

Angular distributions in the double ionization of noble gases by electron impact

Electron-impact double ionization of noble gases is investigated theoretically for the case of high incident energies (5 keV). An ab initio calculation is made including partial correlation in the initial state as well as in the final state. The results of the calculations are compared with those of other theories and with the first available (e, 3e) experimental data on krypton 4p ⁶.     

Thermal properties of potassium dichromate

Thermosonimetry, DTA, high temperature XRD and hot stage microscopy have been used to study the thermal behaviour of K₂Cr₂O₇. A rapid triclinic to monoclinic phase transformation occurs at 543 K slowly reversible at 508 K. Severe crystallite fracturing is associated with the reverse transition and manifests anomalous X-ray intensities which have been previously interpreted as metastable phase formation. On reheating, the transformation occurs at 528 K. Possible interpretations of the temperature hystereses are given.

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Zusammenfassung Thermosonimetrie, DTA, Hochtemperatur-XRD und Mikroskopie in heißem Zustand wurden zur Untersuchung des thermischen Verhaltens von K₂Cr₂O₇ eingesetzt. Eine schnelle Phasenänderung von der triklinen zur monoklinen Form findet bei 543 K statt, welche bei 508 K langsam reversibel ist. Der schwere Kristallbruch ist mit dem umgekehrten Übergang verbunden und weist anomale Röntgenstrahlen-Intensitäten auf, welche früher als Bildung einer metastabilen Phase gedeutet wurden. Bei wiederholtem Aufheizen geht die Änderung bei 528 K vor sich. Mögliche Deutungen der Temperaturhysterese werden gegeben.

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Résumé On a étudié le comportement thermique de K₂Cr₂O₇ par thermosonimétrie, ATD, diffraction des rayons X à haute température et microscopie avec platina chauffante. Une transformation rapide de la phase triclinique à la phase monoclinique a lieu à 543 K et est lentement réversible à 508 K. Un fractionnement important des cristallites est associé à la transition inverse et se manifeste par des intensités anormales des raies de diffraction X, ce qui a été préalablement interprété comme la formation d'une phase métastable. Lors d'un nouvel échauffement, la transformation a lieu à 528 K. Diverses interprétations possibles de l'hystérèse de température sont proposées.

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₂₂₇ - , , - . 543 - , 508 . - , . 528 . .

     

The stress intensity factor of a Griffith crack which is opened by a thin symmetric wedge

In this paper, the author makes use of a recent development in the theory of triple integral equations to derive formulae for the stress intensity factor and crack shape of a Griffith crack which is opened by a thin symmetric wedge. The use of these formulae is then illustrated by a consideration of two particular cases.

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Zusammenfassung In dieser Arbeit benützt der Autor eine neuere Entwicklung in der Theorie dreifacher Integralgleichungen, um Formeln für den Spannungsintensitätsfaktor und die Form eines Griffithschen Risses abzuleiten, welcher durch einen dünnen symmetrischen Keil geöffnet wird. Der Gebrauch dieser Formeln wird dann durch Betrachtung zweier Sonderfälle erläutert.

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This paper was written while the author was on leave of absence from The University of Glassgow, Scoland. It was prepared as a part of the work of the Applied Mathematics Research Group at North Carolina State University through the Grant AF-AFOSR-69-1779 and is under the joint sponsorship of AFOSR, ARO and ONR through the Joint Services Advisory Group.     

Kohlen

Ohne Zusammenfassung     

Antiplane shear of a strip containing a staggered array of rigid line inclusions

Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an Isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically, we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces, see Figure 1. It should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite two-dimensional material containing a staggered array of rigid inclusions (see [1] for a review of antiplane problems in the literature). The problem is reduced in standard fashion [2–6] to a mixed boundary value problem in a rectangular domain, whose closed form solution given in terms of integrals of Weierstrassian Elliptic functions, is obtained via triple sine series techniques. The effective shear modulus of the reinforced strip can now be calculated and compared with the shear modulus of a strip without inclusions. Also obtained are the stress singularity factors at the end tips of the inclusions. Numerical results are presented for several different reinforcement geometries.