On the dual nature of partial theta functions and Appell-Lerch sums

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell--Lerch sums. In this sense, Appell--Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers-Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral $q$-series with mixed mock modular behaviour.Comment: To be published in Advances in Mathematic

A research program to reduce interior noise in general aviation airplanes

The relevance of KU-FRL test results in predicting (theoretically or semi-empirically) interior noise levels in general aviation aircraft was studied. As a result of this study, it was decided to make a few additions to the program. These additions are: (1) to use three (instead of two) noise sources in the plane wave tube to evaluate the influence of excitation spectrum on panel response, (2) to use theoretical and experimental data obtained in the course of the project to develop more efficient noise reduction materials (or procedures to apply these), or to develop guidelines for the design of such materials for procedures, and (3) to use nonstructural materials in the collection of specimens to be tested in the KU-FRL plane wave tube

Can grain growth explain transition disks?

Aims: Grain growth has been suggested as one possible explanation for the diminished dust optical depths in the inner regions of protoplanetary "transition" disks. In this work, we directly test this hypothesis in the context of current models of grain growth and transport. Methods: A set of dust evolution models with different disk shapes, masses, turbulence parameters, and drift efficiencies is combined with radiative transfer calculations in order to derive theoretical spectral energy distributions (SEDs) and images. Results: We find that grain growth and transport effects can indeed produce dips in the infrared SED, as typically found in observations of transition disks. Our models achieve the necessary reduction of mass in small dust by producing larger grains, yet not large enough to be fragmenting efficiently. However, this population of large grains is still detectable at millimeter wavelengths. Even if perfect sticking is assumed and radial drift is neglected, a large population of dust grains is left behind because the time scales on which they are swept up by the larger grains are too long. This mechanism thus fails to reproduce the large emission cavities observed in recent millimeter-wave interferometric images of accreting transition disks.Comment: 11 pages, 5 figures, accepted to A&

Observation of hypersonic phononic crystal effects in porous silicon superlattices

Brillouin light scattering experiments were carried out on porous silicon superlattices with modulation wavelengths in the range 37–167 nm. Phonon frequencies deduced from the Brillouin spectra show good agreement with those obtained from an elastic continuum model for a system with one-dimensional periodicity. Evidence for the existence of a hypersonic phononic bandgap and zone-folded longitudinal acoustic phonons is reported

Low lift-to-drag aero-assisted orbit transfer vehicles

The results of systems analysis conducted on low life drag ratio (L/D) aero-assisted orbit transfer vehicle (AOTV's) are presented. The objectives for this class of vehicle and formulate technology development plans and funding levels to bring the required technologies to readiness levels, as well as develop a credible decision data base encompassing the entire range of low L/D concepts for use in future NASA Aeroassist Orbit Transfer Vehicles studies. Each candidate low L/D concept, the aerobrake, the lifting brake, and the aeromaneuvering concept could be made to work with technologies achievable by the early 1990's. All concepts require flexible structure with flexible thermal protection system (TPS) to be successfully integrated into the shuttle orbiter for launch, all required improvements in guidance and control to fly the dispersed atmospheres at high altitude, and all concepts had potential to evolve from ground-based to space-based operations

Inverter ratio failure detector

A failure detector which detects the failure of a dc to ac inverter is disclosed. The inverter under failureless conditions is characterized by a known linear relationship of its input and output voltages and by a known linear relationship of its input and output currents. The detector includes circuitry which is responsive to the detector's input and output voltages and which provides a failure-indicating signal only when the monitored output voltage is less by a selected factor, than the expected output voltage for the monitored input voltage, based on the known voltages' relationship. Similarly, the detector includes circuitry which is responsive to the input and output currents and provides a failure-indicating signal only when the input current exceeds by a selected factor the expected input current for the monitored output current based on the known currents' relationship