Solution of Some Structural Analysis Problems by Orthogonal Collocation

Abstract

Application of the method of orthogonal collocation to boundary value problems in structural and applied mechanics is investigated. Typical boundary value problems, such as the torsion of rectangular bars and the bending of plates, are employed as illustrative examples. Simplicity in application and good accuracy of orthogonal collocation are demonstrated by the solution of such complex problems as the large deflection analysis of rectangular isotropic, orthotropic, and sandwich plates. Results are compared wherever possible with existing solutions based on much more laborious and lengthy methods of computation. Excellent agreements are obtained.     

A simple leading particle explanation for linear momentum transfer systematics

A simple formula based on leading particle models of nucleon-nucleon collisions is used to evaluate the average momentum transfer in central heavy ion collisions at energies from 20 to 150 MeV/u. This formula, which reproduces a number of the features of the observed systematics, offers a straightforward explanation for the approximate universality of fractional linear momentum transfer as a function of velocity, the dependence of fractional momentum transfer on target mass and the greater fractional momentum transfer of the proton as compared to heavy ion projectiles.     

Model for the evolution of hot and compressed spherical nuclei

A hydrodynamical approach and the Thomas Fermi approximation have been used to study the evolution of hot and compressed nuclei. Spherical symmetry was assumed in the calculation. The dynamical equations have been transformed into “Schrödinger like” equations (using the Madelung transformation) and were solved numerically. Dissipation was simulated in the same way as in the Navier-Stokes equation by introducing shear and bulk viscosities. Global as well as local thermal equilibrium have been studied. The model has been applied to small amplitude oscillations (the breathing mode) and to the stability of hot and compressed nuclei. It was found that compression is more efficient to break nuclei than thermal excitation. The relaxation time for global equilibrium was estimated to be of the order of 10^?22 s. It was found that the results obtained in the case of global and local thermal equilibrium are very similar.     

Anomalous magnetic moment of theW-bosons and non-standardZ 0 W + W − coupling in polarizede − e + collisions

We study quantitatively the reactions \(e^ + e^ - \to W^ + e\bar \nu _e \) ,e _R ^? e ⁺ and the rare decay \(Z^0 \to W^ \pm l^ \mp \mathop {\nu _e }\limits^{( - )} \) forl=e, μ and τ, as a test for anomalous γW ⁺ W ^? andZ ⁰ W ⁺ W ^? structure. If κ denotes the anomalous magnetic moment of theW-boson and ω its anomalous coupling to theZ ⁰, values of |ω|>2.5 and |κ|>1.5 can be ruled out at LEP and SLC rather easily. This will put constraints on composite model building.     

Inclusive fragment production in84Kr +197Au atE/A=35 MeV

Inclusive cross sections of intermediate mass fragments from the reaction⁸⁴Kr+¹⁹⁷Au atE/A=35 MeV were measured over the range 8°≦Θ _lab≦70° with a low detection threshold. A moving-source parameterization was used to fit the double-differential cross sections. The integrated cross section for fragment production exceeds the total reaction cross section thus indicating a large probability for multi-fragment processes. The deduced large temperature parameters can be explained by assuming emission from a rotating source. From the comparison to reactions with¹²C and⁴⁰Ar projectiles at E/A=30 MeV a systematics of inclusive fragment production as a function of the projectile mass is obtained.     

Positron-Lithium Atom and Electron-Lithium Atom Scattering Systems at Intermediate and High Energies

The coupled-channel optical method is used to study positron scattering by atomic lithium at energies ranging from the ionization threshold to 60eV, The present method simultaneously treats the target channels and the positronium （Ps） channels in the coupled-channel method together with the continuum effects via an ab-initio optical potential. Ionization, elastic and inelastic cross sections in target channels, and the total cross section are also reported and compared with other theoretical and experimental data. A comparative study with the corresponding electron-lithium data is also reported.