Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and conductive heat transfer - a nonlinear parabolic PDE with a random field model for the thermal conductivity.Comment: 28 pages, 8 figures, 2 table

WIYN/Hydra Detection of Lithium Depletion in F Stars of the Young Open Cluster M35 and Implications for the Development of the Lithium Gap

We report discovery of significant depletion of Li on the surfaces of F dwarf stars in the 150-Myr-old open cluster M35, analagous to a feature in the 700-Myr-old Hyades cluster that has been referred to as the ``Li gap.'' We have caught the gap in the act of forming: using high resolution, high S/N, WIYN/Hydra observations, we detect Li in all but a few M35 F stars; the maximum depletion lies at least 0.6-0.8 dex below minimally depleted (or undepleted) stars. The M35 Li depletion region, a) is quite wide, with clear depletion seen from 6000K to 6700K or hotter; b) shows a significant dispersion in Li abundance at all T_eff, even with stars of the same T_eff; and c) contains undepleted stars (as well as depleted ones) in the (narrow) classical Hyades gap region, which itself shows no undepleted stars. All of these M35 Li depletion properties support rotationally-induced slow mixing as the primary physical mechanism that forms the gap, and argues against other proposed mechanisms, particularly diffusion and steady main sequence mass loss. When viewed in the context of the M35 Li depletion properties, the Hyades Li gap may well be wider than is usually recognized.Comment: 14 Pages, 3 figures. Accepted to ApJ Letter

WIYN Open Cluster Study XI: WIYN 3.5m Deep Photometry of M35 (NGC 2168)

We present deep BVI observations of the core of M35 and a nearby comparison field obtained at the WIYN 3.5m telescope under excellent seeing. These observations display the lower main sequence in BV and VI CMDs down to V = 23.3 and 24.6, respectively. At these faint magnitudes background field stars are far more numerous than the cluster stars, yet by using a smoothing technique and CMD density distribution subtraction we recover the cluster fiducial main sequence and luminosity function to V = 24.6. We find the location of the main sequence in these CMDs to be consistent with earlier work on other open clusters, specifically NGC 188, NGC 2420, and NGC 2477. We compare these open cluster fiducial sequences to stellar models by Baraffe et al. (1998), Siess et al. (2000), Girardi et al. (2000), and Yi et al. (2001) and find that the models are too blue in both B-V and V-I for stars below ~0.4 Mo. M35 contains stars to the limit of the extracted main sequence, at M ~ 0.10-0.15 Mo, suggesting that M35 may harbor a large number of brown dwarfs, which should be easy targets for near-IR instrumentation on 8-10m telescopes. We also identify a new candidate white dwarf in M35 at V = 21.36 +- 0.01. Depending on which WD models are used to interpret this cluster candidate, it is either a very high mass WD (1.05 +- 0.05 Mo) somewhat older (0.19-0.26 Gyr, 3-4 sigma) than our best isochrone age (150 Myr), or it is a modestly massive WD (0.67-0.78 Mo) much too old (0.42-0.83 Gyr) to belong to the cluster.Comment: 28 pages + 24 figures; to be published in the Sept, 2002 A

Length functions on currents and applications to dynamics and counting

The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use length functions to provide a proof of a folklore theorem which states that pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of projective geodesic currents with uniform north-south dynamics.Comment: 35pp, 2 figures, comments welcome! Second version: minor corrections. To appear as a chapter in the forthcoming book "In the tradition of Thurston" edited by V. Alberge, K. Ohshika and A. Papadopoulo

Anticipated Nostalgia: Looking Forward to Looking Back

Anticipated nostalgia is a new construct that has received limited empirical attention. It concerns the anticipation of having nostalgic feelings for one’s present and future experiences. In three studies, we assessed its prevalence, content, emotional profile, and implications for self-regulation and psychological functioning. Study 1 revealed that anticipated nostalgia most typically concerns interpersonal relationships, and also concerns goals, plans, current life, and culture. Further, it is affectively laden with happiness, sadness, bittersweetness, and sociality. Studies 2 and 3 assessed the implications of anticipated nostalgia for self-regulation and psychological functioning. In both studies, positive evaluation of a personal experience was linked to stronger anticipated nostalgia, and anticipated nostalgia was linked to savouring of the experience. In Study 3, anticipated nostalgia measured prior to an important life transition predicted nostalgia a few months after the transition, and post-transition nostalgia predicted heightened self-esteem, social connectedness, and meaning in life

BMQ

BMQ: Boston Medical Quarterly was published from 1950-1966 by the Boston University School of Medicine and the Massachusetts Memorial Hospitals. Pages 49-52, v17n2, provided courtesy of Howard Gotlieb Archival Research Center

Collective and independent-particle motion in two-electron artificial atoms

Investigations of the exactly solvable excitation spectra of two-electron quantum dots with a parabolic confinement, for different values of the parameter R_W expressing the relative magnitudes of the interelectron repulsion and the zero-point kinetic energy of the confined electrons, reveal for large R_W a remarkably well-developed ro-vibrational spectrum associated with formation of a linear trimeric rigid molecule composed of the two electrons and the infinitely heavy confining dot. This spectrum transforms to one characteristic of a "floppy" molecule for smaller values of R_W. The conditional probability distribution calculated for the exact two-electron wave functions allows for the identification of the ro-vibrational excitations as rotations and stretching/bending vibrations, and provides direct evidence pertaining to the formation of such molecules.Comment: Published version. Latex/Revtex, 5 pages with 2 postscript figures embedded in the text. For related papers, see http://www.prism.gatech.edu/~ph274c

The Evolution of Galactic Boron and the Production Site of the Light Elements

The Goddard High Resolution Spectrograph (GHRS) of the Hubble Space Telescope (HST) has been used to obtain spectra of the 2500 Å region in eight stars with metallicities ranging from [Fe/H] = -0.4 to -3.0, including the most metal-poor star ever observed for boron. Spectrum synthesis utilizing latest Kurucz model atmospheres has been used to determine the B abundance for each star, with particular attention paid to the errors of each point, to permit judgment of the quality of the fit of models of Galactic chemical evolution. Previous observations were combined with new ones, bringing the number of stars analyzed to 11