Sparse Automatic Differentiation for Large-Scale Computations Using Abstract Elementary Algebra

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, built-in elementary algebra typically has limited functionality and often restricts flexibility of mathematical models and analysis types that can be applied to those models. To overcome this limitation, a number of domain-specific languages with more feature-rich built-in data types have been proposed. In this paper, we argue that if numerical libraries and solvers are designed to use abstract elementary algebra rather than language-specific built-in algebra, modern mainstream languages can be as effective as any domain-specific language. We illustrate our ideas using the example of sparse Jacobian matrix computation. We implement an automatic differentiation method that takes advantage of sparse system structures and is straightforward to parallelize in MPI setting. Furthermore, we show that the computational cost scales linearly with the size of the system.Comment: Submitted to ACM Transactions on Mathematical Softwar

Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization

Recent experiments have demonstrated synchronization of fiber laser arrays at low and moderate pump levels. It has been suggested that a key dynamical process leading to synchronized behavior is the differential phase shift induced by the gain media. We explore theoretically the role of this effect in generating inphase dynamics. We find that its presence can substantially enhance the degree of inphase stability to an extent that could be practically important. At the same time, our analysis shows that a gain-dependent phase shift is not a necessary ingredient in the dynamical selection of the inphase state, thus, leading us to reconsider the essential mechanism behind inphase selection in fiber laser arrays

Book Review: The Archaeology of Antislavery Resistance, by Terrance M. Weik

Review of The Archaeology of Antislavery Resistance, by Terrance M. Weik, 2012, University Press of Florida, Gainesville, 204 pp., 16 black and white figures, 3 maps, references, index, $69.95 (cloth),$19.95 (paper)

Fluidic packaging of microengine and microrocket devices for high pressure and high temperature operation

The fluidic packaging of Power MEMS devices such as the MIT microengine and microrocket requires the fabrication of hermetic seals capable of withstanding temperature in the range 20-600/spl deg/C and pressures in the range 100-300 atm. We describe an approach to such packaging by attaching Kovar metal tubes to a silicon device using glass seal technology. Failure due to fracture of the seals is a significant reliability concern in the baseline process: microscopy revealed a large number of voids in the glass, pre-cracks in the glass and silicon, and poor wetting of the glass to silicon. The effects of various processing and materials parameters on these phenomena were examined. A robust procedure, based on the use of metal-coated silicon substrates, was developed to ensure good wetting. The bending strength of single-tube specimens was determined at several temperatures. The dominant failure mode changed from fracture at room temperature to yielding of the glass and Kovar at 600/spl deg/C. The strength in tension at room temperature was analyzed using Weibull statistics; these results indicate a probability of survival of 0.99 at an operational pressure of 125 atm at room temperature for single tubes and a corresponding probability of 0.9 for a packaged device with 11 joints. The residual stresses were analyzed using the method of finite elements and recommendations for the improvement of packaging reliability are suggested

Interaction between Aniline Derivatives and Single-Walled Carbon Nanotubes Investigated by Fluorescence and Quantum-Chemical Methods

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Critical properties of a continuous family of XY noncollinear magnets

Monte Carlo methods are used to study a family of three dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets.Comment: 5 pages, 3 figures, minor changes, published versio