New quasi-exactly solvable Hamiltonians in two dimensions

Quasi-exactly solvable Schrödinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a finite-dimensional Lie algebra of first order differential operators—the hidden symmetry algebra. In this paper we develop some general techniques for constructing quasi-exactly solvable operators. Our methods are applied to provide a wide variety of new explicit two-dimensional examples (on both flat and curved spaces) of quasi-exactly solvable Hamiltonians, corresponding to both semisimple and more general classes of Lie algebras.Supported in Part by DGICYT Grant PS 89-0011.Supported in Part by an NSERC Grant.Supported in Part by NSF Grant DMS 92-04192.     

A Model for Continuous Production Control with Warning Signals to Fault Occurrences

The advance of computer, automation and control technology has led to the adoption of continuous control and monitoring of production processes in high technology industries. By monitoring the state of the production process continuously, occurrence of any faults in the production process can be identified with zero or negligible detection delay. As a result, the costs of defective products, loss in yield and restoration are minimized. On the other hand, the sensitivity of the continuous monitoring system could result in very frequent repair and maintenance of the process, causing frequent disruptions of production. This paper addresses the question of the determination of the optimal level at which warning signals should be given of fault occurrences in a production system that is continuously monitored. A model is developed from which the expected total costs per time unit can be derived. A numerical example illustrates the determination of the optimal warning level under this framework.     

A Non-Parametric Approach to Model Evaluation

All existing tests and criteria for model evaluation are based on the sum of squared residuals. These measures do not evaluate the performance of a model in predicting turning points in the variable of interest. Here, three tests are proposed to evaluate models on the basis of their ability to predict turning points and to give an unbiased prediction of the relative order of magnitude of changes. Five models are evaluated using the proposed tests. Results indicate that the tests expose facets of models that R² and sum of squared residuals are unable to highlight. Hence, the tests are suggested to complement existing model evaluation techniques.     

Stereospecific synthesis of a new class of aminocyclitol with the conduramine D-2 configuration

A new aminocyclitol derived from bicyclo[4.2.0^1,6]octane was synthesized starting from cyclooctatetraene. Photooxygenation of trans-7,8-diacetoxy-bicyclo[4.2.0]octa-2,4-diene afforded a bicyclic endoperoxide. Reduction of the endoperoxide with thiourea followed by a palladium-catalyzed ionization/cyclization reaction gave an oxazolidinone derivative. Oxidation of the double bond in the oxazolidinone with KMnO₄ followed by acetylation gave the oxazolidinone-tetraacetate whose exact configuration was determined by X-ray diffraction analysis. Hydrolysis of the oxazolidinone ring and removal of the acetate groups furnished the desired aminocyclitol.     

Importance of explicit vectorization for CPU and GPU software performance

Much of the current focus in high-performance computing is on multi-threading, multi-computing, and graphics processing unit (GPU) computing. However, vectorization and non-parallel optimization techniques, which can often be employed additionally, are less frequently discussed. In this paper, we present an analysis of several optimizations done on both central processing unit (CPU) and GPU implementations of a particular computationally intensive Metropolis Monte Carlo algorithm. Explicit vectorization on the CPU and the equivalent, explicit memory coalescing, on the GPU are found to be critical to achieving good performance of this algorithm in both environments. The fully-optimized CPU version achieves a 9× to 12× speedup over the original CPU version, in addition to speedup from multi-threading. This is 2× faster than the fully-optimized GPU version, indicating the importance of optimizing CPU implementations.     

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou’s result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator. Research supported in part by the Deutsche Forschungsgemeinschaft. Research supported by NSERC grant # RGPIN 105490-2004. Research supported in part by the Humboldt Foundation and the National Science Foundation, Grant No. DMS-0603754. Research supported in part by the NSF, Grant No. 33-585-7510-2-30.     

An experimental study of a radial wall jet formed by the normal impingement of a round synthetic jet

The flow field of a radial wall jet created by the impingement of a round synthetic jet normal to a flat surface was characterized using hot-wire anemometry. In the synthetic wall jets the width of the outer layer was observed to increase linearly with the radial distance along the wall, while the local maximum velocity varied inversely. The synthetic wall jet exhibits self-similar behavior as distinguished by the collapse of the mean and rms velocity profiles when normalized by the outer layer scaling variables. Increasing the actuator driving amplitude at a fixed frequency (i) increased the growth rate of the outer layer, and (ii) decreased the decay rate of the local velocity maximum. The flow field of the synthetic wall jet was dominated by vortical structures associated with the actuator driving frequency, and harmonics connected with the interaction of the produced vortex structures. For the actuator conditions investigated, neither the classical laminar nor fully turbulent analytical solutions for continuous wall jets were amenable to modeling the synthetic wall jet profile due to the transitional and unsteady nature of the synthetic wall jet.