The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measured values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. This type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.
Classical density functional theory (DFT) is used to calculate the structure of the electrical double layer and the differential capacitance of model molten salts. The DFT is shown to give good qualitative agreement with Monte Carlo simulations in the molten salt regime. The DFT is then applied to three common molten salts, KCl, LiCl, and LiKCl, modeled as charged hard spheres near a planar charged surface. The DFT predicts strong layering of the ions near the surface, with the oscillatory density profiles extending to larger distances for larger electrostatic interactions resulting from either lower temperature or lower dielectric constant. In conclusion, overall the differential capacitance is found to be bell-shaped, in agreement with recent theories and simulations for ionic liquids and molten salts, but contrary to the results of the classical Gouy-Chapman theory.
The Computer Science Research Institute (CSRI) brings university faculty and students to Sandia National Laboratories for focused collaborative research on computer science, computational science, and mathematics problems that are critical to the mission of the laboratories, the Department of Energy, and the United States. The CSRI provides a mechanism by which university researchers learn about and impact national— and global—scale problems while simultaneously bringing new ideas from the academic research community to bear on these important problems. A key component of CSRI programs over the last decade has been an active and productive summer program where students from around the country conduct internships at CSRI. Each student is paired with a Sandia staff member who serves as technical advisor and mentor. The goals of the summer program are to expose the students to research in mathematical and computer sciences at Sandia and to conduct a meaningful and impactful summer research project with their Sandia mentor. Every effort is made to align summer projects with the student's research objectives and all work is coordinated with the ongoing research activities of the Sandia mentor in alignment with Sandia technical thrusts. For the 2013 CSRI Proceedings, research articles have been organized into the following broad technical focus areas — Computational Mathematics and Algorithms, Combinatorial Algorithms and Visualization, Advanced Architectures and Systems Software, Computational Applications — which are well aligned with Sandia's strategic thrusts in computer and information sciences.