A general theoretical framework for introducing many-body or lattice effects into gas/solid scattering is presented. The theory is presently restricted to classical scattering off harmonic lattices but is otherwise completely general. It is nonperturbative and valid for arbitrary lattice temperature. The theory is based on a formulation of lattice dynamics suggested by and related to the Kubo–Mori theory of generalized Brownian motion. This formulation leads to a generalized Langevin equation (GLE) in which only the coordinates of the gas atom and the n∼1–6 surface atoms directly struck by the gas atom appear explicitly. The remainder of the lattice, which functions as a harmonic heat bath, affects the collision through a friction kernel and a Gaussian random force appearing in the GLE. The GLE can be solved in terms of a tractable number of (n+1) -particle gas–surface trajectories using approximate stochastic techniques. Stochastic solution yields thermally averaged temporal gas particle probability distribution functions (pdf). From the long time limit of these pdf’s all temperature dependent gas–surface cross sections can be found. In the limit of zero friction, the theory gives a convenient method for calculating atom–oscillator thermally averaged cross sections which circumvents laborious Monte Carlo classical trajectory sampling and which can be generalized to treat other gas phase collision problems.

Exact generalized Fokker–Planck equations are derived from the linear Mori–Kubo generalized Langevin equation for the case of Gaussian but non-Markovian noise. Fokker–Planck equations which generate the momentum and phase space probability distribution functions (pdf’s) for free Brownian particles and the phase space pdf for Brownian oscillators are presented. Also given is the generalized diffusion equation for the free Brownian particle pdf in the zero inertia limit. The generalized Fokker–Planck equations are similar in structure to the corresponding phenomenological equations. They, however, involve time-dependent friction and frequency functions rather than phenomenological constants. Explicit results for the frequency and friction functions are given for the Debye solid model. These functions enter as simple multiplicative factors rather than as retarded kernels. Further the phase space Fokker–Planck equations contain an extra diffusive term, a mixed phase space second partial derivative, not occurring in the phenomenological equations. For short times the generalized Fokker–Planck equations reduce to the appropriate Liouville equations. For systems with long time tail decay, e.g., the hydrodynamical Brownian particle and an oscillator in a harmonic lattice, the generalized equations do not asymptotically reduce to the phenomenological equations since these latter predict exponential decay. Moreover the exact generalized equations are not equivalent to the familiar approximate generalized Fokker–Planck equations with retarded kernels except when both types of equations reduce to the phenomenological form. The value of the approximate equations with retarded kernels as an improvement upon the phenomenological equations is thus subject to question.

Zwanzig's approach to inelastic atom/harmonic chain scattering is recast in a form which suggests generalization to atomic collisions with real solid surfaces. We reduce the infinite set of equations of motion for the impinging atom and harmonic chain to a pair of equations of motion. These equations describe the collision of the incident particle with a generalized Langevin oscillator. The first and second fluctuation-dissipation theorems for the Langevin oscillator are verified and their implications for the scattering process are discussed.

A comprehensive theoretical framework for classical trajectory simulations of many-body chemical processes is presented. This framework generalizes previous theoretical methods designed to treat the many-body problems arising in gas molecule collisions off perfect harmonic solids [S. A. Adelman and J. D. Doll, J. Chem. Phys. 64, 2374 (1976); S. A. Adelman and B. J. Garrison, J. Chem. Phys. 65, 3571 (1976)]. The present version of the theory is not restricted to the harmonic systems and thus provides a formal framework for treating liquid state as well as solid state chemical phenomena. Basic to the theory is the molecular time scale generalized Langevin equation (MTGLE), a formally exact representation of the dynamics of a chemical system coupled to an arbitrary heat bath in an arbitrary manner. The MTGLE is equivalent to but distinct from the conventional [Mori–Kubo] generalized Langevin representation. It, however, is more natural for chemical dynamics simulation work because in the MTGLE the apparent vibrational frequencies of the chemical system are those which govern the molecular time scale response of the system. In the conventional Langevin representation, the apparent vibrational frequencies are those which govern the static reponse of the chemical system. The MTGLE is next rigorously transformed into an effective equation of motion for a fictitious nearest neighbor collinear harmonic chain. The parameters characterizing the chain are calculable from the velocity autocorrelation function of the chemical system. The rigorous chain representation of many-body dynamics: (i) provides a simple quasiphysical picture of energy transfer between the heat bath and chemical system during a chemical process; (ii) provides an equivalent Hamiltonian for the chemical system; (iii) permits one to construct a sequence of heat bath models whose response converges to that of the true heat bath in a rapid and systematic manner. The heat bath models are sets of collinear nearest neighbor harmonic chains composed of N=1,2,3,... fictitious atoms. Atom N in the chain is subject to time-local functional damping and is driven by a white noise stochastic force. The remaining atoms 1,2,...N-1 are undamped. The heat bath models (i) produce effective equations of motion for the chemical process which do not involve time nonlocal kernels and which may, hence, be readily solved by standard classical trajectory methods; (ii) allow one to rigorously generalize the Fokker–Planck theory of stochastic dynamics to non-Markovian systems. Finally, the treatment of selected chemical processes via the theory is briefly outlined.

Research into etiology of marital aggression has focused primarily on psychosocial, political, and cultural factors, to the exclusion of physiological influences. Fifty-three partner abusive men, 45 maritally satisfied, and 32 maritally discordant, nonviolent men were evaluated for past history of head injury, by a physician who was not informed of group membership and aggression history. Logistic regressions confirmed that head injury was a significant predictor of being a battered. The implications of these findings for both marital aggression and post-head injury rehabilitation are discussed.