Publications

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Solid-state {sup 1}H magic angle spinning (MAS) NMR was used to investigate sulfonated Diels-Alder poly(phenlylene) polymer membranes. Under high spinning speed {sup 1}H MAS conditions, the proton environments of the sulfonic acid and phenylene polymer backbone are resolved. A double-quantum (DQ) filter using the rotor-synchronized back-to-back (BABA) NMR multiple-pulse sequence allowed the selective suppression of the sulfonic proton environment in the {sup 1}H MAS NMR spectra. This DQ filter in conjunction with a spin diffusion NMR experiment was then used to measure the domain size of the sulfonic acid component within the membrane. In addition, the temperature dependence of the sulfonic acid spin-spin relaxation time (T{sub 2}) was determined, providing an estimate of the activation energy for the proton dynamics of the dehydrated membrane.

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The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

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A novel solution method has been developed to solve the linear Boltzmann equation on an unstructured triangular mesh. Instead of tackling the first-order form of the equation, this approach is based on the even/odd-parity form in conjunction with the conventional mdtigroup discrete-ordinates approximation. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, and the method is well suited for massively parallel computers.

A novel solution method has been developed to solve the coupled electron-photon transport problem on an unstructured triangular mesh. Instead of tackling the first-order form of the linear Boltzmann equation, this approach is based on the second-order form in conjunction with the conventional multi-group discrete-ordinates approximation. The highly forward-peaked electron scattering is modeled with a multigroup Legendre expansion derived from the Goudsmit-Saunderson theory. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, a method that is well suited for massively parallel computers.

A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages to using an established discrete ordinates solver, e.g., immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and synthetic radiation environments. The cross sections have been successfully used in the DORT, TWODANT, and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down and elastic-scattering portions of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion.

Satellite electronics may be subjected to a large fluence of protons from the Van Allen belt and from solar flares. To determine if unhardened electronics will survive a radiation environment, the total ionizing dose and displacement damage to the electronics must be determined. Several computer codes are available for modeling proton transport, ranging in complexity for a very-efficient straight-line approximation to general-geometry time-dependent Monte Carlo transport, with corresponding increase in computer run time. For most satellite applications, neutrons can be neglected in the analysis. However, neutrons may be important for modeling heavily shielded compartments for personnel and electronics.