The calculation of resonance separatrices for the near-integrable case of the standard mapping

The standard mapping arises in many physical applications, including the analysis of nonlinear resonant acoustic oscillations in a closed tube. A perturbation expansion, in powers of the amplitude parameter, is given for the calculation of the fixed points of various orders and the associated separatrices. It is shown how exact homoclinic orbits can be calculated numerically. Explicit analytic expressions are given for the separatrices associated with the first four resonances when the perturbation parameter is small.     

Dynamics of Si-H vibrations in an amorphous environment

We present results of the first vibrational photon-echo, transient-grating, and temperature dependent transient-bleaching experiments on a-Si:H. Using these techniques, and the infrared light of a free electron laser, the vibrational population decay and phase relaxation of the Si-H stretching mode were investigated. Careful analysis of the data indicates that the vibrational energy relaxes directly into Si-H bending modes and Si phonons, with a distribution of rates determined by the amorphous host. Conversely, the pure dephasing appears to be single exponential, and can be modeled by dephasing via two-phonon interactions.     

Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

Computational and dynamic NMR investigation of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane

The structure and rotational barrier for the mesityl-silicon bond of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane have been investigated by ¹H- and ¹³C-variable temperature nuclear magnetic resonance (NMR) as well as by density functional theory structural calculations. The calculations show that the lowest energy structure has C₂ symmetry with nonequivalent ortho methyl groups, consistent with the crystal structure and solution NMR. The nonequivalent ortho methyl groups exchange through a C_s transition state with a calculated relative free energy of 11.0 kcal mol⁻¹. The barrier for this rotation found by dynamic NMR is 13.4 ± 0.2 kcal mol⁻¹ at 298 K.     

Facile Hydrolysis and Alcoholysis of Palladium Acetate

Palladium(II) acetate is readily converted into [Pd₃(μ²‐OH)(OAc)₅] ( 1 ) in the presence of water in a range of organic solvents and is also slowly converted in the solid state. Complex 1 can also be formed in nominally anhydrous solvents. Similarly, the analogous alkoxide complexes [Pd₃(μ²‐OR)(OAc)₅] ( 3 ) are easily formed in solutions of palladium(II) acetate containing a range of alcohols. An examination of a representative Wacker‐type oxidation shows that the Pd‐OH complex 1 and a related Pd‐oxo complex 4 can be excluded as potential catalytic intermediates in the absence of exogenous water.     

Cationated cyclopropanes as reaction intermediates in mass spectra: an earlier incarnation of ion-neutral complexes

The appearance a decade ago of the concept of ion-neutral complexes as intermediates in unimolecular decompositions constituted a major advance in mechanistic interpretation of mass spectra. The concept, however, was not new; it goes back to the introduction of the cationated cyclopropane in the mid-1950s. Its development did not occur via a smooth progression; rather, its history bridges a sharp discontinuity. The early workers, in a curious historical quirk, failed to generalize on the idea beyond complexes in which the neutral component is cyclopropane or a closely related species. Hence it took an independent rediscovery of the concept to usher in the rapid growth and wide application that characterize its present stage of development.