Magnetic forming studies

Investigation of the tensile strength dependability on the characteristic time over which a pressure pulse is applied to a metal workpiece shows that the mechanical properties of these materials are functions of the rate at which the material is undergoing strain. These results and techniques are used in magnetomotive metal forming

Inversion of Gamow's Formula and Inverse Scattering

We present a pedagogical description of the inversion of Gamow's tunnelling formula and we compare it with the corresponding classical problem. We also discuss the issue of uniqueness in the solution and the result is compared with that obtained by the method of Gel'fand and Levitan. We hope that the article will be a valuable source to students who have studied classical mechanics and have some familiarity with quantum mechanics.Comment: LaTeX, 6 figurs in eps format. New abstract; notation in last equation has been correcte

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Curvature fluctuations and Lyapunov exponent at Melting

We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solid. For clusters, the Lyapunov exponent generally varies linearly with the total energy, but the slope changes sharply at the melting transition. In the bulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity in the variance of the curvature of the potential energy surface. In these systems there are two mechanisms of chaos -- local instability and parametric instability. We calculate the contribution of the parametric instability towards the chaoticity of these systems using a recently proposed formalism. The contribution of parametric instability is a continuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies that the melting in small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev

Characteristic distributions of finite-time Lyapunov exponents

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has a characteristic shape. For intermittent dynamics, and at crises, dynamical correlations lead to distributions with stretched exponential tails, while for fully-developed chaos the probability density has a cusp. Exact results are presented for the logistic map, $x \to 4x(1-x)$. At intermittency the density is markedly asymmetric, while for `typical' chaos, it is known that the central limit theorem obtains and a Gaussian density results. Local analysis provides information on the variation of predictability on dynamical attractors. These densities, which are used to characterize the {\sl nonuniform} spatial organization on chaotic attractors are robust to noise and can therefore be measured from experimental data.Comment: To be appear in Phys. Rev

The Tolman VII solution, trapped null orbits and w - modes

The Tolman VII solution is an exact static spherically symmetric perfect fluid solution of Einstein's equations that exhibits a surprisingly good approximation to a neutron star. We show that this solution exhibits trapped null orbits in a causal region even for a tenuity (total radius to mass ratio) $> 3$. In this region the dynamical part of the potential for axial w - modes dominates over the centrifugal part.Comment: 5 pages revtex. 10 figures png. Further information at http://grtensor.phy.queensu.ca/tolmanvii