A simple classical prediction of quantal resonances in collinear reactive scattering

Quantal collinear reactive scattering computations have shown that in the vicinity of thresholds of reactant or product vibrational states, one finds resonances in the state to state reaction probability. We find that these resonances can be explained classically in terms of energy transfer between adiabatic reactant and product channels. This transfer is attributable to resonant periodic orbits, resonating between reactants and products. The classical condition for a quantal resonance is that the action of the orbit over one period be an integer (in units of h) and that the energy at which this occurs be lower than the adiabatic barrier heights of the resonating states. These conditions suffice for a prediction of the location of the quantal resonance within a 1% accuracy!     

Anti-plane shear fields with discontinuous deformation gradients near the tip of a crack in finite elastostatics

Summary This paper reconsiders the problem of determining the elastostatic field near the tip of a crack in an all-round infinite body deformed by a Mode III loading at infinity to a state of anti-plane shear. The problem is treated for a class of incompressible, homogeneous, isotropic elastic materials whose constitutive laws permit a loss of ellipticity in the governing displacement equation of equilibrium at sufficiently severe shearing strains. The analysis represents a generalization of that reported in an earlier study and, as before, is carried out for the small-scale nonlinear crack problem, in which a crack of finite length is replaced by a semi-infinite one, and the nonlinear field far from the crack-tip is matched to the near field predicted by the linearized theory. The methods employed in the present paper are necessarily largely qualitative, since they apply to all materials in the class considered. The principal feature of the resulting elastic field is the presence of two symmetrically located curves issuing from the crack-tip and bearing discontinuities in displacement gradient and stress.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.     

Generalized synthesis and physical properties of dialkoxy disulfides

A substrate study was undertaken in order to probe the scope of S(2)Cl(2) coupling of alcohols to form dialkoxy disulfides. Compounds 1b and 1f are new; along with 1a, 1c, 1h, and 1j, all of the title compounds are fully characterized, and the yields of 1a and 1c have been optimized from previously reported syntheses. The effect of the R-substituent about the OSSO moiety has been carefully probed as yields vary. A substrate and a solvent study of the coalescence behavior of this class was carried out. The origin of the inherently large barrier to rotation and the resultant thermal decomposition pathway is discussed. Both phenomena are shown to be solvent independent; hindered rotation is substrate independent. The decomposition of 1a is ca. 7 kcal/mol higher than the barrier to rotation about the S-S bond. The combined evidence suggests acyclic unsymmetric homolytic cleavage of the dialkoxy disulfide.     

Density functional theory calculations for endohedral complexes of non-pi C60H60 cage with small guest molecules

Hybrid density-functional theory (B3LYP) calculations were carried out to determine the structures and energies of endohedral complexes of non-pi C(60)H(60) with H(2), CO, and LiH. It was demonstrated that the endohedral complexes of C(60)H(60) with the above three guest molecules are more stable than the corresponding complexes with C(60). Furthermore, the interaction between C(60)H(60) and the inside H(2) or CO is negligible, but the formation of the LiH-C(60)H(60) complex is exothermic with a stabilization energy of -6.0 kcal/mol. While the bond lengths of H(2) and CO changed a little when placed inside the cages, that of the LiH molecule increased and decreased inside C(60)H(60) and C(60), respectively.     

Strong imploding shock,the representative curve

The representative curve of the ideal gas behind the front of a spherically, or cylindrically, symmetric strong imploding shock is shown to pass through the point where the reduced pressure is maximum, P(ζ_m) = P_max.     

On Time Discretizations for Spectral Methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.