Estimates for low-frequency elastic scattering by a rigid body

When a plane elastic wave is scattered by a rigid body the surface integral of the traction, projected along the direction of polarization of the incident wave, provides the leading low-frequency approximation for the scattering amplitudes. Two kinds of lower and upper bounds for the surface traction integral are given. One is based on the geometrical characteristics of the scatterer and is expressed in terms of corresponding values of the best fitting interior and exterior confocal triaxial ellipsoids. The case of best fitting interior and exterior spheres is examined as a special case. These bounds are sharp in the sense that they both become equalities when the scatterer degenerates to an ellipsoid. The other kind of lower and upper bounds involve the capacity of the scatterer. All estimates were obtained by using the generalized Dirichlet and Thomson Principles of Potential Theory in Elastostatics. Furthermore, all constants appearing in the bounds are given in terms of the ratio of the phase velocities for the transverse and the longitudinal wave. An upper bound for scattering by a cube at normal incidence is also included.This work was done while both authors were visiting the Department of Mathematics of The University of Tennessee at Knoxville. The second author wishes to acknowledge partial support from The University of Tennessee Science Alliance.     

Configuration space Faddeev calculations

Three nucleon ground state wave functions are displayed graphically in configuration space. Both the Schrödinger functions and the Faddeev amplitudes from which they are constructed are plotted. It is demonstrated that for the case where the two-nucleon interaction contains strong repulsion at short distances, the Faddeev amplitude bears no resemblance to the Schrödinger function, and is not even positive definite. Furthermore, the Faddeev amplitude is a much smoother function of the three independent coordinate variables, and is therefore much easier to calculate. Certain intuitive features of the Schrödinger wave function are seen to be present.     

Flashlamp-pumped laser performance of LiCaAIF6:Cr3+

The results of flashlamp pumping of the LiCaAIF₆:Cr³⁺ (Cr:LiCAF) laser crystal are reported. We have so far obtained slope efficiencies as high as 1.55% in a close-coupled, diffusely reflecting cavity. Based on the measured insertion loss of the presently available material, we predict that an efficiency of about 4% will be obtained when low-loss material becomes available. This extrapolated efficiency is comparable with the performance of a high-quality alexandrite laser rod in the same apparatus.     

Effect of temperature on rectified diffusion during ultrasound-induced heating

Experimental observations of delayed-onset cavitation during ultrasound insonation have been suggested as being caused by a change in the size distribution of the bubble population due to rectified diffusion. To investigate this hypothesis, a single bubble model is used here to explore the effect of heating and the subsequent elevated temperatures on the rectified diffusion process. Numerical solution of the model, which includes the temperature dependences of seven relevant physical parameters, allows quantification of the change in the pressure threshold for rectified diffusion, as well as the importance of the bulk liquid saturation concentration in determining bubble evolution. Although elevated temperatures and liquid supersaturation reduce the rectified diffusion threshold, it remains coincident with the inertial cavitation thresholds at submicron bubble sizes at all temperatures. This observation suggests that changes in the nucleation environment, rather than bubble growth due to rectified diffusion, is a more likely cause of delayed-onset cavitation events.     

"Learn on the fly": a hybrid classical and quantum-mechanical molecular dynamics simulation

We describe and test a novel molecular dynamics method which combines quantum-mechanical embedding and classical force model optimization into a unified scheme free of the boundary region, and the transferability problems which these techniques, taken separately, involve. The scheme is based on the idea of augmenting a unique, simple parametrized force model by incorporating in it, at run time, the quantum-mechanical information necessary to ensure accurate trajectories. The scheme is tested on a number of silicon systems composed of up to approximately 200 000 atoms.     

Single-mode plane-polarized ytterbium-doped large-core fiber laser with 633-W continuous-wave output power

We demonstrate a cladding-pumped single-mode plane-polarized ytterbium-doped fiber laser generating 633 W of continuous-wave output power at 1.1 microm with 67% slope efficiency and a polarization extinction ratio better than 16 dB. The laser is end pumped through both fiber ends and shows no evidence of roll-over, even at the highest output power, which is limited only by the available pump power.