Mechanical properties of epoxy resins and glass/epoxy composites at cryogenic temperatures

The mechanical properties of four modified-epoxy resin systems were investigated. Tensile properties (including strength, modulus, and elongation), notch toughness, impact strength, the coefficient of linear thermal contraction, and thermal-shock resistance were determined for cast-resin specimens at 75, ?320, and ?423°F. Inter-laminar shear strengths (Naval Ordnance Laboratory horizontal shear and short-span shear) were obtained for glass-filament-wound-composite specimens at the three temperatures.

The two systems with the best cryogenic properties were a hybridepoxy/polyurethane (resin 4A) and a highly modified bisphenol-A epoxy (resin 2). In choosing the optimum system, the same tests (except for notch toughness, impact strength, and short-span shear) were performed on filament-wound-composite specimens at the three temperatures. In these tests the performance of resin 4A was better than, or at least comparable to, that of resin 2.     

Multi-Center Vector Field Methods for Wave Equations

We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is the repulsiveness or nontrapping conditions on the flow corresponding to the wave equation. Thus this method is limited to potential perturbations which are repulsive, that is the radial derivative pointing away from the origin. In this work, we generalize this method to include potentials which are repulsive relative to a line in space (in three or higher dimensions), among other cases. This method is based on constructing multi-centered vector fields as multipliers, cancellation lemmas and energy localization.     

Ionic dissociation of aqueous hydrobromic acid. V. Estimate from refractive index and density measurements

The refractive index of aqueous hydrobromic acid was measured up to 19.6m at 0.25 and 60°C. The density of dilute solutions, 0.0676 to 2.76m, was measured at 25°C to high accuracy. These and supplementary data from the literature yielded apparent molar volumes and refractivities. The latter showed the shallow maximum at low concentrations (less than 1.5m) and the gentle linear decline with increasing concentrations, characteristic of strong electrolytes up to about 8 m. The abrupt decline of the apparent molar refractivity with increasing concentrations is interpreted in terms of the association of hydrobromic acid. The apparent molar volumes can also be interpreted, though only quantitatively, in these terms. The results are related to the previously obtained proton nmr data, concerning the extent of association.     

A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta

Price's Law states that linear perturbations of a Schwarzschild black hole fall off as t−2?−3 for t→∞ provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their time derivative is zero), then the decay is predicted to be t−2?−4. We give a proof of t−2?−2 decay for general data in the form of weighted L¹ to L^∞ bounds for solutions of the Regge–Wheeler equation. For initially static perturbations we obtain t−2?−3. The proof is based on an integral representation of the solution which follows from self-adjoint spectral theory. We apply two different perturbative arguments in order to construct the corresponding spectral measure and the decay bounds are obtained by appropriate oscillatory integral estimates.     

Nonautonomous Hamiltonians

We present a theory of resonances for a class of nonautonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of instability is radiative decay, due to resonant coupling of the discrete modes to the continuum modes by the time-dependent perturbation. This results in a slow transfer of energy from the discrete modes to the continuum. The rate of decay of solutions is slow and hence the decaying bound states can be viewed as metastable. The ideas are closely related to the authors' work on (i) a time-dependent approach to the instability of eigenvalues embedded in the continuous spectra, and (ii) resonances, radiation damping, and instability in Hamiltonian nonlinear wave equations. The theory is applied to a general class of Schrödinger equations. The phenomenon of ionization may be viewed as a resonance problem of the type we consider and we apply our theory to find the rate of ionization, spectral line shift, and local decay estimates for such Hamiltonians.     

Spin effects in hadron scattering at very high energies

In this paper a spin-dependent diffractive model is studied for πN and NN elastic scattering. We find non-trivial results for spin correlation parameters which persist at high energies and have very distinct features in the dip region. It is stressed that these parameters provide good tests of pomeron factorization.