The relationship between physical observables and the potential energy surface in the He-HF system

This paper examines the effect of infinitesimal functional variations in a rigid rotor He-HF potential surface on several different types of observables: inelastic cross sections, rate constants, and rotational energy level populations. The dynamics and kinetic observables studied were found to be sensitive to a large number of Legendre components of the potential with the region of highest sensitivity dependent upon the energy or temperature as well as the states related by the individual observable. Sensitivity to the entire surface tends to show a large degree of structure due to competition among sensitivities to the individual potential components. Significant information loss has been observed in the transition from microscopic to macroscopic observables.     

Kinetic model for hydrocarbon-assisted particulate boron combustion

A kinetic model is presented to describe the high temperature (1800 K < T < 3000 K) surface oxidation of particulate boron in a hydrocarbon combustion environment. The model includes a homogeneous gas-phase B/O/H/C oxidation mechanism consisting of 19 chemical species and 58 forward and reverse elementary reactions, multi-component gas-phase diffusion, and a heterogeneous surface oxidation mechanism consisting of ‘elementary’ adsorption and desorption reaction steps. Thermochemical and kinetic parameters for the surface reactions are estimated from available experimental data and/or elementary transition state arguments. The kinetic processes are treated using a generalized kinetics code, with embedded sensitivity analysis, for the combustion of a one-dimensional (particle radius), spherical particle. Model results are presented for the oxidation of a 200 μm boron particle in a JP-4/air mixture at ambient temperatures of 1400 K and 2000 K. These results include temperature and gas-phase species profiles as a function of radial distance and particle burning rates. © 1994 John Wiley & Sons, Inc.     

Optimal control of classical molecular dynamics: A perturbation formulation and the existence of multiple solutions

This paper considers the prospect for there being multiple solutions to the control of classically modelled molecular dynamical systems. The research presented here follows up on a parallel study based on quantum mechanics. For polyatomic molecules it is generally expected that a classical mechanical model will be adequate and necessary as a means for designing optical fields for molecular control. The prospect for multiple control field solutions existing in this domain is important to establish in terms of ultimate laboratory realization of molecular control. A general formulation of the multiplicity problem is considered and the existence of a denumerably infinite number of solutions for the control field amplitude is shown to be the case under certain mild limitations on the physical variables.     

A scaling theoretical analysis of vibrational relaxation experiments: rotational effects and long-range collisions

Expressions for the quantum number scaling of vibration—translation (VT) and vibration—vibration (VV) rates are derived. The derivation uses the recently developed scaling theory of non-reactive processes and invokes the assumption of rotational equilibrium. However, the VV and VT scaling relationships include rotational effects through the rotational energy gaps and the rotational distributions. The variables in this theory are a fundamental set of rates and the average collision range, l_c, for the particular inelastic process. The physically transparent meaning of these variables, combined with the a priori nature of the scaling coefficients, allows one to investigate actual dynamical effects and not just merely fit data. A detailed analysis of VV energy transfer in the COCO system is presented. Three conclusions are drawn: (1) rotational effects are crucially important in the scaling of the rates; (2) the process is predominantly long-range with l_c = 5.5 ± 0.5 au; and, (3) the available experimental data is consistent with single quanta vibrational changes in the VV rates.     

Mechanism analysis of controlled quantum dynamics in the coordinate representation

There are increasing numbers of successful numerical simulations as well as laboratory tests of controlled quantum phenomena. However, little is understood about the control mechanisms, especially in strongly driven systems. In this paper, mechanism is defined in terms of the significant quantum pathways induced by the control field, connecting the initial state to the final target state. The present work focuses on understanding mechanism in the coordinate representation, which is natural for many dynamical systems. The quantum amplitudes defining the mechanistic pathways are determined by a special procedure called coding Hamiltonians to access mechanistic pathways (CHAMP). Numerical procedures are presented for performing CHAMP calculations in a stable fashion. Mechanism determination is illustrated for excitation of a model linear triatomic molecule. Mechanisms are revealed for optimal control fields as well as for suboptimally driven systems including snapshots in time of the evolving mechanism and the effect of field noise on the mechanism. The high order multiphoton processes involved in the example produce many interfering pathways to create the final state, yet the dynamics and the mechanism are robust to reasonable levels of noise.     

Analytical HDMR formulas for functions expressed as quadratic polynomials with a multivariate normal distribution

High Dimensional Model Representation (HDMR) is a general set of quantitative model assessment and analysis tools for systems with many variables. A general formulation for the HDMR component functions with independent and correlated variables was obtained previously. Since the HDMR component functions generally are coupled to one another and involve multi-dimensional integrals, explicit formulas for the component functions are not available for an arbitrary function with an arbitrary probability distribution amongst their variables. This paper presents analytical formulas for the HDMR component functions and the corresponding sensitivity indexes for the common case of a function expressed as a quadratic polynomial with a multivariate normal distribution over its variables. This advance is important for practical applications of HDMR with correlated variables.     

Hyperfine structure and nuclear moments of99Ru and101Ru

The atomic-beam magnetic-resonance method in combination with the triple resonance technique has been used to determine the nuclear magnetic dipole moments of⁹⁹Ru and¹⁰¹Ru. The moments are deduced fromrf transition measurements in the⁵F₅ and⁵F₄ states at magnetic fields between 770 and 2400 Oe. In order to reduce the part of the uncertainty of the moments which arises from the uncertainty of the hyperfine structure constants more precise values of the constants than those available up to now were determined from low field measurements. After making corrections for hyperfine and Zeeman interactions with neighbouring atomic states we obtain the following values for the magnetic dipole moments:μ ₉₉=?0.6381 (51)μ _N andμ ₁₀₁=?0.7152 (60)μ _N (uncorrected for diamagnetic shielding). The results of the present work combined with the results of an earlier hyperfine structure investigation in the⁵F multiplet are analysed with respect to the effective-operator formalism. From this analysis we obtain the following values for the electric quadrupole moments:Q ₉₉=0.076 (7) b andQ ₁₀₁=0.44 (4) b (uncorrected for Sternheimer shielding or antishielding).     

Absorption intensities for the 4-0 through 7-0 overtone bands of HCl

We have measured the absorption intesities for a number of rotation-vibration lines in the 4-0 through 7-0 overtone bands of HCl utilizing a Fourier transform spectrometer and a 409.6 m path length White cell. Individual line strengths, band strengths, dipole matrix elements, and Herman-Wallis factors are presented.