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The components of the physical forces between noble gas atoms, alkali ions, and halogen ions are analyzed and a data base developed from analysis of the two-body potential data, the alkali–halide molecular data, and the noble gas crystal and salt crystal data. A satisfactory global fit to this molecular and crystal data is then reproduced by the model to within several percent. Surface potentials are evaluated for noble gas atoms on noble gas surfaces and salt crystal surfaces with surface tension neglected. Within this context, the noble gas surface potentials on noble gas and salt crystals are considered to be accurate to within several percent.

The resonance phenomena and energy transfer associated with a set of coupled nonlinear differential equations are analyzed using asymptotic methods. The equations describe the motion of a beam-pendulum system which exhibits autoparametric excitation. Precise conditions under which resonant or nonresonant oscillations arise, are obtained. These conditions not only depend upon the physical parameters of the system but also upon the energy of the oscillations (i.e., initial conditions). In general, the envelopes of the resonant oscillations are periodic of long period and there is intermittent energy transfer between the pendulum and beam modes.

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Early space radiation shield code development relied on Monte Carlo methods and made important contributions to the space program. Monte Carlo methods have resorted to restricted one-dimensional problems leading to imperfect representation of appropriate boundary conditions. Even so, intensive computational requirements resulted and shield evaluation was made near the end of the design process. Resolving shielding issues usually had a negative impact on the design. Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary concept to the final design. For the last few decades, we have pursued deterministic solutions of the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard Finite Element Method (FEM) geometry common to engineering design methods. A single ray trace in such geometry requires 14 milliseconds and limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given.

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