Publications

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Consider a standard SIAM journal article containing theoretical results. Each theorem has a proof that typically builds on previous developments. Since every theorem stems from a firm foundation, the research community can trust a result without further evidence. One could thus argue that a theorem does not require a proof because surely an author would not publish it if no proof existed to back it up. Furthermore, respectable reviewers and editors expect proofs without exception, and papers containing proof-less theorems will likely go unpublished.

Scientific data collections grow ever larger, both in terms of the size of individual data items and of the number and complexity of items. To use and manage them, it is important to directly address issues of robust and actionable provenance. We identify three key drivers as our focus: managing the size and complexity of metadata, lack of a priori information to match usage intents between publishers and consumers of data, and support for campaigns over collections of data driven by multi-disciplinary, collaborating teams. We introduce the Hoarde abstraction as an attempt to formalize a way of looking at collections of data to make them more tractable for later use. Hoarde leverages middleware and systems infrastructures for scientific and technical data management. Through the lens of a select group of challenging data usage scenarios, we discuss some of the aspects of implementation, usage, and forward portability of this new view on data management.

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In an ongoing project at Sandia National Laboratories, we are attempting to develop a novel style of superconducting digital processing, based on a new model of reversible computation called Asynchronous Ballistic Reversible Computing (ABRC). We envision an approach in which polarized flux-ons scatter elastically from near-lossless functional components, reversibly updating the local digital state of the circuit, while dissipating only a small fraction of the input fluxon energy. This approach to superconducting digital computation is sufficiently unconventional that an appropriate methodology for hand-design of such circuits is not immediately obvious. To gain insight into the design principles that are applicable in this new domain, we are creating a software tool to automatically enumerate possible topologies of reactive, undamped Josephson junction circuits, and sweep the parameter space of each circuit searching for designs exhibiting desired dynamical behaviors. But first, we identified by hand a circuit implementing the simplest possible nontrivial ABRC functional behavior with bits encoded as conserved polarized fluxons, namely, a one-bit reversible memory cell with one bidirectional I/O port. We expect the tool to be useful for designing more complex circuits.

Meshfree discretization of surface partial differential equations is appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analysis from the GMLS literature applies to their scheme. With this interpretation, their approach may then be unified with recent work developing compatible meshfree discretizations for the div-grad problem in R^d. Informally, this is analogous to an extension of collocated finite differences to staggered finite difference methods, but in the manifold setting and with unstructured nodal data. In this way, we obtain a compatible meshfree discretization of elliptic problems on manifolds which is naturally stable for problems with material interfaces, without the need to introduce numerical dissipation or local enrichment near the interface. As a result, we provide convergence studies illustrating the high-order convergence and stability of the approach for manufactured solutions and for an adaptation of the classical five-strip benchmark to a cylindrical manifold.

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