Robert Lipton

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New variational principles are introduced, describing the eective conductivity tensor for anisotropic two-phase heat conducting composites with interfacial surface resistance between phases. These principles reduce to those of Hashin and Shtrikman in the limit of vanishing surface resistance. The new principles allow for an unconstrained class of trial(More)
Acknowledgments I would like to express my sincere gratitude to my research advisor Professor Blaise Bourdin for the suggestion of the topic. This dissertation would have not been possible without his continuous support, help, guidance, and endless patience. It is a pleasure to give thanks to all my professors at Louisiana State University, and especially(More)
Although epidemiology is necessarily involved with elucidating causal processes, we argue that there is little practical need, having described an epidemiological result, to then explicitly label it as causal (or not). Doing so is a convention which obscures the valuable core work of epidemiology as an important constituent of public health practice. We(More)
We introduce asymptotic expansions for recovering the local field behavior inside multiscale composite architectures in the presence of residual stress. The theory applies to zones containing abrupt changes in the composite microgeometry. This includes the interfaces between plies inside fiber reinforced laminates. The asymptotic expansions are used to(More)
We p rovide a reciprocal relation linking the eective conductivity of a composite with highly conducting phase interfaces to that of a composite with the same phase geometry but with an electrical contact resistance at phase interfaces. A eld relationship linking the electric eld inside a composite with highly conducting phase interfaces to the current in a(More)