Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, U-res bundles and other examples motivated by considerations from quantum field theory.Comment: 28 pages, latex, no figures, uses amsmath, amsthm, amsfonts. Revised version - only change a lot of irritating typos remove

The Decline of U.S. Manufacturing: Empirical Evidence and Policy Implications

This paper focuses on output as a prime indicator of the economic performance of business firms. Decline in the labor force does not necessarily mean that overall productivity is declining as well, due to factors such as improved technology.https://openscholarship.wustl.edu/mlw_papers/1188/thumbnail.jp

The Revival of the Rust Belt

The author questions whether there really is a decline in low-tech industries, and shows a comparison in their growth alongside that of high-tech industries.https://openscholarship.wustl.edu/mlw_papers/1061/thumbnail.jp

Toward a Healthier Environment and a Stronger Economy: How to Achieve Common Ground

Economic and environmental interests are typically opponents in the public arena. Most efforts to bridge intellectual differences involve economists trying to get environmentalists to develop an economic way of thinking while conversely, ecologists attempt to sway economists toward kinder environmental values. It is time for a new approach to public policy that takes advantage of the middle ground between these two ideologies. This study presents six specific reforms that make both sound economic and environmental sense. These reforms occur within selected government spending programs, special federal tax provisions, and particular regulatory requirements.https://openscholarship.wustl.edu/mlw_papers/1166/thumbnail.jp

Pattern Formation by Boundary Forcing in Convectively Unstable, Oscillatory Media With and Without Differential Transport

Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or periodic forcing at the upstream boundary. Such boundary-controlled pattern selection is a generalization of the flow-distributed oscillation (FDO) mechanism that can include Turing or differential flow instability (DIFI) modes. Our goal is to clarify the relationships among these mechanisms in the general case where there is differential flow as well as differential diffusion. We do so by analyzing the dispersion relation for linear perturbations and showing how its solutions are affected by differential transport. We find a close relationship between DIFI and FDO, while the Turing mechanism gives rise to a distinct set of unstable modes. Finally, we illustrate the relevance of the dispersion relations using nonlinear simulations and we discuss the experimental implications of our results.Comment: Revised version with added content (new section and figures added), changes to wording and organizatio

On The Nature of Variations in the Measured Star Formation Efficiency of Molecular Clouds

Measurements of the star formation efficiency (SFE) of giant molecular clouds (GMCs) in the Milky Way generally show a large scatter, which could be intrinsic or observational. We use magnetohydrodynamic simulations of GMCs (including feedback) to forward-model the relationship between the true GMC SFE and observational proxies. We show that individual GMCs trace broad ranges of observed SFE throughout collapse, star formation, and disruption. Low measured SFEs (<<1%) are "real" but correspond to early stages, the true "per-freefall" SFE where most stars actually form can be much larger. Very high (>>10%) values are often artificially enhanced by rapid gas dispersal. Simulations including stellar feedback reproduce observed GMC-scale SFEs, but simulations without feedback produce 20x larger SFEs. Radiative feedback dominates among mechanisms simulated. An anticorrelation of SFE with cloud mass is shown to be an observational artifact. We also explore individual dense "clumps" within GMCs and show that (with feedback) their bulk properties agree well with observations. Predicted SFEs within the dense clumps are ~2x larger than observed, possibly indicating physics other than feedback from massive (main sequence) stars is needed to regulate their collapse.Comment: Fixed typo in the arXiv abstrac

Holonomy on D-Branes

This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action.Comment: Corrections made and some typographical errors remove

Star Formation at z=2.481 in the Lensed Galaxy SDSS J1110+6459, I: Lens Modeling and Source Reconstruction

Using the combined resolving power of the Hubble Space Telescope and gravitational lensing, we resolve star-forming structures in a z~2.5 galaxy on scales much smaller than the usual kiloparsec diffraction limit of HST. SGAS J111020.0+645950.8 is a clumpy, star forming galaxy lensed by the galaxy cluster SDSS J1110+6459 at z = 0.659, with a total magnification ~30x across the entire arc. We use a hybrid parametric/non-parametric strong lensing mass model to compute the deflection and magnification of this giant arc, reconstruct the light distribution of the lensed galaxy in the source plane, and resolve the star formation into two dozen clumps. We develop a forward-modeling technique to model each clump in the source plane. We ray trace the model to the image plane, convolve with the instrumental point spread function (PSF), and compare with the GALFIT model of the clumps in the image plane, which decomposes clump structure from more extended emission. This technique has the advantage, over ray tracing, by accounting for the asymmetric lensing shear of the galaxy in the image plane and the instrument PSF. At this resolution, we can begin to study star formation on a clump-by-clump basis, toward the goal of understanding feedback mechanisms and the buildup of exponential disks at high redshift.Comment: 19 pages, 12 figures, accepted to Ap