Control system design using optimization techniques Final report

Optimization techniques for control of fuel valve systems for air breathing jet engines and 40-60 inlet control problem

Resummation of Nonalternating Divergent Perturbative Expansions

A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane. Nonperturbative imaginary contributions can be inferred from the purely real perturbative coefficients. A connection is drawn from the quantum field theoretic problem of resummation to divergent perturbative expansions in other areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman criterion added; version to appear in Phys. Rev.

Chemical Changes of Flattened Enamel Surfaces with in Vitro Weak Acid Demineralization

Infrared internal reflection spectroscopy (IRS) was used to study changes in surface chemistry of enamel after in vitro weak acid demineralization. Hypotheses that relate previous histomorphologic observations to current IRS findings are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68276/2/10.1177_00220345710500064001.pd

The effect of cusps in time-dependent quantum mechanics

Spatial cusps in initial wavefunctions can lead to non-analytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor-expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time-analytic.Comment: 5 pages, 1 figur

The Detection of Incipient Caries with Tracer Dyes

The purpose of this study was to determine the increase in color contrast produced by the use of a tracer dye in detection of incipient caries lesions with transillumination. Twenty four caries-free first premolars were immersed in an acid gelatin for production of artificial incipient caries lesions. After the lesions had developed, these teeth were photographed by transillumination. Two photographs were taken of each tooth. The first photograph showed the lesion without dye. A blue tracer dye was then added and absorbed by the lesion, and a second photograph was taken. The data on the color difference were obtained by use of a reflectance colorimeter and showed a four-fold increase between the lesion and surrounding area with the dye. A two-way analysis of variance was used for the statistical interpretation. The color difference between the lesion without the dye and then with the dye was significant. The use of the blue tracer dye, therefore, significantly increased the contrast in the images of the artificial incipient lesions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68289/2/10.1177_00220345890680021101.pd

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory

The present paper concerns the derivation of phase-integral quantization conditions for the two-centre Coulomb problem under the assumption that the two Coulomb centres are fixed. With this restriction we treat the general two-centre Coulomb problem according to the phase-integral method, in which one uses an {\it a priori} unspecified {\it base function}. We consider base functions containing three unspecified parameters $C, \tilde C$ and $\Lambda$. When the absolute value of the magnetic quantum number $m$ is not too small, it is most appropriate to choose $\Lambda=|m|\ne 0$. When, on the other hand, $|m|$ is sufficiently small, it is most appropriate to choose $\Lambda = 0$. Arbitrary-order phase-integral quantization conditions are obtained for these choices of $\Lambda$. The parameters $C$ and $\tilde C$ are determined from the requirement that the results of the first and the third order of the phase-integral approximation coincide, which makes the first-order approximation as good as possible. In order to make the paper to some extent self-contained, a short review of the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy

Structure and Composition of Two Transitional Circumstellar Disks in Corona Australis

The late stages of evolution of the primordial circumstellar disks surrounding young stars are poorly understood, yet vital to constrain theories of planet formation. We consider basic structural models for the disks around two ~10 Myr-old members of the nearby RCrA association, RX J1842.9-3532 and RX J1852.3-3700. We present new arcsecond-resolution maps of their 230 GHz continuum emission from the Submillimeter Array and unresolved CO(3-2) spectra from the Atacama Submillimeter Telescope Experiment. By combining these data with broadband fluxes from the literature and infrared fluxes and spectra from the catalog of the Formation and Evolution of Planetary Systems (FEPS) Legacy program on the Spitzer Space Telescope, we assemble a multiwavelength data set probing the gas and dust disks. Using the Monte Carlo radiative transfer code RADMC to model simultaneously the SED and millimeter continuum visibilities, we derive basic dust disk properties and identify an inner cavity of radius 16 AU in the disk around RX J1852.3-3700. We also identify an optically thin 5 AU cavity in the disk around RX J1842.9-3532, with a small amount of optically thick material close to the star. The molecular line observations suggest an intermediate disk inclination in RX J1842.9-3532, consistent with the continuum emission. In combination with the dust models, the molecular data allow us to derive a lower CO content than expected, suggesting that the process of gas clearing is likely underway in both systems, perhaps simultaneously with planet formation.Comment: 11 pages, 5 figures, accepted for publication in A