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.

Color Gradients Detected in the HD 15115 Circumstellar Disk

We report HST/NICMOS coronagraphic images of the HD 15115 circumstellar disk at 1.1\micron. We find a similar morphology to that seen in the visible and at H band--an edge-on disk that is asymmetric in surface brightness. Several aspects of the 1.1\micron data are different, highlighting the need for multi-wavelength images of each circumstellar disk. We find a flattening to the western surface brightness profile at 1.1\micron interior to 2\arcsec (90 AU) and a warp in the western half of the disk. We measure the surface brightness profiles of the two disk lobes and create a measure of the dust scattering efficiency between 0.55-1.65\micron at 1\arcsec, 2\arcsec, and 3\arcsec. At 2\arcsec the western lobe has a neutral spectrum up to 1.1\micron and a strong absorption or blue spectrum $>$1.1\micron, while a blue trend is seen in the eastern lobe. At 1\arcsec the disk has a red F110W-H color in both lobes.Comment: 4 pages, 4 figures, emulateapj; accepted to ApJ

Brain choline concentrations may not be altered in euthymic bipolar disorder patients chronically treated with either lithium or sodium valproate

BACKGROUND: It has been suggested that lithium increases choline concentrations, although previous human studies examining this possibility using (1)H magnetic resonance spectroscopy ((1)H MRS) have had mixed results: some found increases while most found no differences. METHODS: The present study utilized (1)H MRS, in a 3 T scanner to examine the effects of both lithium and sodium valproate upon choline concentrations in treated euthymic bipolar patients utilizing two different methodologies. In the first part of the study healthy controls (n = 18) were compared with euthymic Bipolar Disorder patients (Type I and Type II) who were taking either lithium (n = 14) or sodium valproate (n = 11), and temporal lobe choline/creatine (Cho/Cr) ratios were determined. In the second part we examined a separate group of euthymic Bipolar Disorder Type I patients taking sodium valproate (n = 9) and compared these to controls (n = 11). Here we measured the absolute concentrations of choline in both temporal and frontal lobes. RESULTS: The results from the first part of the study showed that bipolar patients chronically treated with both lithium and sodium valproate had significantly reduced temporal lobe Cho/Cr ratios. In contrast, in the second part of the study, there were no effects of sodium valproate on either absolute choline concentrations or on Cho/Cr ratios in either temporal or frontal lobes. CONCLUSIONS: These findings suggest that measuring Cho/Cr ratios may not accurately reflect brain choline concentrations. In addition, the results do not support previous suggestions that either lithium or valproate increases choline concentrations in bipolar patients

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

Perturbative approach to the hydrogen atom in strong magnetic field

The states of hydrogen atom with principal quantum number n <= 3 and zero magnetic quantum number in constant homogeneous magnetic field H are considered. The perturbation theory series is summed with the help of Borel transformation and conformal mapping of the Borel variable. Convergence of approximate energy eigenvalues and their agreement with corresponding existing results are observed for external fields up to n^3 H ~ 5. The possibility of restoring the asymptotic behaviour of energy levels using perturbation theory coefficients is also discussed.Comment: LaTeX, 8 pages with 5 eps figure

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

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.