Frequencies and resonances around L4L_4 in the elliptic restricted three-body problem

The stability of the Lagrangian point $L_4$ is investigated in the elliptic restricted three-body problem by using Floquet's theory. Stable and unstable domains are determined in the parameter plane of the mass parameter and the eccentricity by computing the characteristic exponents. Frequencies of motion around $L_4$ have been determined both in the stable and unstable domains and fitting functions for the frequencies are derived depending on the mass parameter and the eccentricity. Resonances between the frequencies are studied in the whole parameter plane. It is shown that the 1:1 resonances are not restricted only to single curves but extend to the whole unstable domain. In the unstable domains longer escape times of the test particle from the neighbourhood of $L_4$ are related to certain resonances, but changing the parameters the same resonances may lead to faster escape

QCD corrections to e+ e- --> 4 jets

We report on the next-to-leading order QCD calculation for e+ e- --> 4 jets. We explain some modern techniques which have been used to calculate the one-loop amplitudes efficiently. We further report on the general purpose numerical program ``Mercutio'', which can be used to calculate any infrared safe four-jet quantity in electron-positron annihilation at next-to-leading order.Comment: 4 pages, talk given at the UK Phenomenology Workshop on Collider Physics, Durham, 19-24 September 199

Deformation mechanics of deep surface flaw cracks

A combined analytical and experimental program was conducted to determine the deformation characteristics of deep surface cracks in Mode I loading. An approximate plane finite element analysis was performed to make a parameter study on the influence of crack depth, crack geometry, and stress level on plastic zones, crack opening displacement, and back surface dimpling in Fe-3Si steel and 2219-T87 aluminum. Surface replication and profiling techniques were used to examine back surface dimple configurations in 2219-T87 aluminum. Interferometry and holography were used to evaluate the potential of various optical techniques to detect small surface dimples on large surface areas

Semiclassical model for calculating fully differential ionization cross sections of the H2_2 molecule

Fully differential cross sections are calculated for the ionization of H$_2$ by fast charged projectiles using a semiclassical model developed previously for the ionization of atoms. The method is tested in case of 4 keV electron and 6 MeV proton projectiles. The obtained results show good agreement with the available experimental data. Interference effects due to the two-center character of the target are also observed and analyzed.Comment: 11 pages, 4 figure

Group-theoretic models of the inversion process in bacterial genomes

The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog

Nonlinear screening and stopping power in two-dimensional electron gases

We have used density functional theory to study the nonlinear screening properties of a two-dimensional (2D) electron gas. In particular, we consider the screening of an external static point charge of magnitude Z as a function of the distance of the charge from the plane of the gas. The self-consistent screening potentials are then used to determine the 2D stopping power in the low velocity limit based on the momentum transfer cross-section. Calculations as a function of Z establish the limits of validity of linear and quadratic response theory calculations, and show that nonlinear screening theory already provides significant corrections in the case of protons. In contrast to the 3D situation, we find that the nonlinearly screened potential supports a bound state even in the high density limit. This behaviour is elucidated with the derivation of a high density screening theorem which proves that the screening charge can be calculated perturbatively in the high density limit for arbitrary dimensions. However, the theorem has particularly interesting implications in 2D where, contrary to expectations, we find that perturbation theory remains valid even when the perturbing potential supports bound states.Comment: 23 pages, 15 figures in RevTeX