Application of the Galerkin and Ritz methods to nonconservative problems of elastic stability

Zusammenfassung In dieser Arbeit werden nichtkonservative Probleme der elastischen Stabilität mittels des Galerkin- und des Ritz-Verfahrens behandelt.Zuerst wird bewiesen, dass die Resultate vonLeipholz bezüglich der Konvergenz des Galerkinschen Verfahrens für solche Probleme auf eine grössere Klasse zulässiger Versuchsfunktionen erweitert werden können. Danach wird das Hamiltonsche Prinzip für nichtkonservative mechanische Systeme so formuliert, dass die Ritzsche Methode auf nichtkonservative Probleme der elastischen Stabilität angewendet werden kann, im Gegensatz zur Ansicht, dass eine solche Anwendung nicht möglich ist. Zum Schluss werden einige angenäherte Lösungen des Beckschen Problems angeführt und verglichen, um die Begriffe zu erklären, die am Anfang dieser Arbeit dargestellt wurden.     

Relativistic photon mediated shocks

A system of equations governing the structure of a steady, relativistic radiation-dominated shock is derived, starting from the general form of the transfer equation obeyed by the photon distribution function. Closure is obtained by truncating the system of moment equations at some order. The anisotropy of the photon distribution function inside the shock is shown to increase with increasing shock velocity, approaching nearly perfect beaming at upstream Lorentz factors Gamma(-) >1. Solutions of the shock equations are presented for some range of upstream conditions. These solutions are shown to converge as the truncation order is increased.     

Hydrodynamic collimation of gamma-ray-burst fireballs

Analytic solutions are presented for the hydrodynamic collimation of a relativistic fireball by a surrounding baryonic wind emanating from a torus. The opening angle is shown to be the ratio of the power output of the inner fireball to that of the exterior baryonic wind. The gamma ray burst 990123 might thus be interpreted as a baryon-poor jet (BPJ) with an energy output of order 10(50) erg or less, collimated by a baryonic wind from a torus with an energy output of order 10(52.5) erg, roughly the geometric mean of the BPJ and its isotropic equivalent.     

Free vibrations of a simply supported,rectangular plate: An exact elasticity solution

An exact, three-dimensional solution for the free vibrations of simply supported, rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper. The solution, obtained in a semi-inverse fashion as was the solution of the elastostatic problem for such plates, satisfies all of the boundary conditions of the problem in a pointwise manner. It is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi-inverse solution. Other modes of oscillation may exist in the three-dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes. The two types of modes found are analogous to the flexural modes of classical plate theory and the thickness-twist modes, here called breathing modes, of Mindlin plate theory. Some numerical results are given which indicate that the predictions of Mindlin plates are uncannily good approximations to the flexural frequencies given by the present, three-dimensional analysis even for very thick plates. However, the predictions of Mindlin plate theory for the thickness-twist, or breathing, frequencies are not nearly so good. These discrepancies are discussed briefly in an appendix.     

Natural radiative lifetimes and hyperfine structure of the 4s26p2P32,12 levels of gallium

Natural radiative lifetimes and the signs of previously determined hyperfine coupling constants were determined for the $\text{4s}{}^2\text{6p}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>,</mtext><mtext>1</mtext><mtext>2</mtext>}}$ levels of gallium. The lifetimes were found to be 167(4) and 172(9) ns, respectively. In addition, the quadrupole moments of ⁶⁹Ga [0.17(3) b] and ⁷¹Ga [0.10(2) b] were deduced, and the isotope shifts in the 639.7 and 641.3 nm Ga lines were determined.