Propellant grain for rocket motors Patent

Grain configuration for solid propellant rocket engine

Discrimination of form in images corrupted by speckle

The problem investigated is that of a human observer having to distinguish between certain specified geometrical forms corrupted by speckle-an idealization of the problem of a scientist studying a synthetic aperture radar map. Specifically, the cases of two simple alternative forms and of two and four orientations of a simple form have been considered. A theoretical model is developed for the observer's decision process by analogy with optimal receiver theory, and the probability of a correct decision is related to form parameters like size, contrast, and looks. These calculations are verified by psychophysical experiments using computer-simulated pictures

Induction probe determines levels of liquid metals

Mutual-inductance probe accurately measures liquid levels in a variety of liquid metals at elevated temperatures. It can be used in pyrochemical processes for the recovery of spent reactor fuel

Averages and moments associated to class numbers of imaginary quadratic fields

For any odd prime $\ell$, let $h_\ell(-d)$ denote the $\ell$-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\ell =3$; nontrivial upper bounds for averages of $h_\ell(-d)$ have previously been known only for $\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_\ell(-d)$ for all primes $\ell \geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geq 3$.Comment: 26 pages; minor edits to exposition and notation, to agree with published versio

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.Comment: 63 page

Helicopter rotor loads using discretized matched asymptotic expansions

The numerical practicality of a matched asymptotic expansion approach for the computation of unsteady three dimensional airloads on a helicopter rotor was improved. This effort utilizes a discretized repesentation of the doublet strength distribution and helical streamlines to decrease the computational requirements of the original analysis. The continuous variation of the doublet strength was approximated by piecewise constant or piecewise quadratic distributions, and the helical trajectory of a fluid particle was approximated by connected straight line segments. As a direct result of these simplified representations the computational time required for the execution of a typical flight condition was reduced by an order of magnitude with respect to the requirements of the original analysis. Airloads which were computed using the discretized method for a two bladed model rotor and a full scale four bladed rotor are in close agreement with measured results and airloads from the original asymptotic analysis. For conditions characterized by significant rotor/wake interaction the piecewise constant representation requires a reduced azimuth spacing to maintain acceptable accuracy