spin orbital coupling is influenced by conditions 1 and 3, with respect to both the internal and external heavy atom effects.8 Since few data existed to verify con-dition9 2, we undertook the investigation of the monobromonaphthonorbornenes. Quite surprisingly, we did not find a direct relation between the distance of the heavy atom from the chromophoric naphthalene and the degree of singlet-triplet state mixing. As mentioned above, we considered this as good evidence for other mechanisms73-13 in addition to spin orbital coupling, such as spin vibronic coupling and photochemistry.The results also made it necessary to invoke a special role to the back lobe of the carbon-bromine bond in electronic state mixing. The data on the dibromonaphthonorbornenes reported in this paper further serve to emphasize the complex mechanisms involved in the heavy atom effect, especially those governing radiationless deactivation of the triplet state. (8) See ref 6, Chapters 7 and 8. (9) (a) K.

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While a wealth of experience in the development of uncertainty quantification methods and software tools exists at present, a cohesive software package utilizing massively parallel computing resources does not. The thrust of the work to be discussed herein is the development of such a toolkit, which has leveraged existing software frameworks (e.g., DAKOTA (Design Analysis Kit for OpTimizAtion)) where possible, and has undertaken additional development efforts when necessary. The contributions of this paper are two-fold. One, the design and structure of the toolkit from a software perspective will be discussed, detailing some of its distinguishing features. Second, the toolkit's capabilities will be demonstrated by applying a subset of its available uncertainty quantification techniques to an example problem involving multiple engineering disciplines, nonlinear solid mechanics and soil mechanics. This example problem will demonstrate the toolkit's suitability in quantifying uncertainty in engineering applications of interest modeled using very large computational system models.

A fundamental challenge for the quantification of uncertainty in solid mechanics is understanding how microscale material variability is manifested at the macroscale. In an era of petascale computing and future exascale computing, it is now possible to perform direct numerical simulations (DNS) in solid mechanics where the microstructure is modeled directly in a macroscale structure. Using this DNS capability, we investigate the macroscale response of polycrystalline microstructures and the accuracy of homogenization theory for upscaling the microscale response. Using a massively parallel finite-element code, we perform an ensemble of direct numerical simulations in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model approximately 420 thousand grains within an I-beam. The inherently random DNS results are compared with corresponding simulations based on the deterministic governing equations and material properties obtained from homogenization theory. Evidence is sought for both surface effects and other higher-order effects as predicted by homogenization theory for macroscale structures containing finite microstructures.