Solid-state study of hydrazonium tartrate and deuterated hydrazonium tartrate enantiomers

A study of the crystallographic, optical, and thermochemical properties of hydrazonium tartrate and deuterated hydrazonium tartrate enantiomers is described. Crystals of the enantiomers are orthorhombic with a tetramolecular cell. The space group is P2₁2₁2₁ with the lattice parameters a₀ = 7.640 ± 0.002 Å, b₀ = 13.441 ± 0.003 Å, and c₀ = 7.029 ± 0.002 Å. No change in lattice parameters is observed on deuteration. Optical second harmonic powder analysis shows the crystals to be phase matchable at 1.06 μm with d^2ω = 11 d^2ωα-SiO₂. The optical nonlinearity being unaffected by deuterium substitution is attributed to the nonlinear electronic polarizability of the hydrogen bonds. Crystals are transparent from 239 nm to 1.61 μm. Deuteration shifts the long wavelength cutoff to 2.07 μm, without affecting the band edge.     

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Error estimates for the three-field formulation with bubble stabilization

In this paper we prove convergence and error estimates for the so-called 3-field formulation using piecewise linear finite elements stabilized with boundary bubbles. Optimal error bounds are proved in and in the broken norm for the internal variable , and in suitable weighted norms for the other variables and .     

Low-Energy Universality in Three-Body Models

 We study the low-energy universality observed in three-body models through a scale-independent approach. From the already estimated infinite number of three-body excited energy states, which happen in the limit when the energy of the subsystem goes to zero, we are able to identify the lower energies of the helium trimers as possible examples of Thomas-Efimov states. By considering this example, we illustrate the usefulness of a scaling function, which we have defined. The approach is applied to bosonic systems of three identical particles, and also to the case where two kinds of particles are present. Received June 30, 1999; revised July 27, 1999; accepted for publication August 29, 1999