Quantales of open groupoids

It is well known that inverse semigroups are closely related to \'etale groupoids. In particular, it has recently been shown that there is a (non-functorial) equivalence between localic \'etale groupoids, on one hand, and complete and infinitely distributive inverse semigroups (abstract complete pseudogroups), on the other. This correspondence is mediated by a class of quantales, known as inverse quantal frames, that are obtained from the inverse semigroups by a simple join completion that yields an equivalence of categories. Hence, we can regard abstract complete pseudogroups as being essentially ``the same'' as inverse quantal frames, and in this paper we exploit this fact in order to find a suitable replacement for inverse semigroups in the context of open groupoids that are not necessarily \'etale. The interest of such a generalization lies in the importance and ubiquity of open groupoids in areas such as operator algebras, differential geometry and topos theory, and we achieve it by means of a class of quantales, called open quantal frames, which generalize inverse quantal frames and whose properties we study in detail. The resulting correspondence between quantales and open groupoids is not a straightforward generalization of the previous results concerning \'etale groupoids, and it depends heavily on the existence of inverse semigroups of local bisections of the quantales involved.Comment: 55 page

Uncertainty Quantification for Airfoil Icing using Polynomial Chaos Expansions

The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a large amount of uncertainty in aerodynamic performance metrics (e.g., stall angle of attack). The main focus of this work concerns using the techniques of Polynomial Chaos Expansions (PCE) to quantify icing uncertainty much more quickly than traditional methods (e.g., Monte Carlo). First, we present a brief survey of the literature concerning the physics of wing icing, with the intention of giving a certain amount of intuition for the physical process. Next, we give a brief overview of the background theory of PCE. Finally, we compare the results of Monte Carlo simulations to PCE-based uncertainty quantification for several different airfoil icing scenarios. The results are in good agreement and confirm that PCE methods are much more efficient for the canonical airfoil icing uncertainty quantification problem than Monte Carlo methods.Comment: Submitted and under review for the AIAA Journal of Aircraft and 2015 AIAA Conferenc

State-space model identification and feedback control of unsteady aerodynamic forces

Unsteady aerodynamic models are necessary to accurately simulate forces and develop feedback controllers for wings in agile motion; however, these models are often high dimensional or incompatible with modern control techniques. Recently, reduced-order unsteady aerodynamic models have been developed for a pitching and plunging airfoil by linearizing the discretized Navier-Stokes equation with lift-force output. In this work, we extend these reduced-order models to include multiple inputs (pitch, plunge, and surge) and explicit parameterization by the pitch-axis location, inspired by Theodorsen's model. Next, we investigate the na\"{\i}ve application of system identification techniques to input--output data and the resulting pitfalls, such as unstable or inaccurate models. Finally, robust feedback controllers are constructed based on these low-dimensional state-space models for simulations of a rigid flat plate at Reynolds number 100. Various controllers are implemented for models linearized at base angles of attack $\alpha_0=0^\circ, \alpha_0=10^\circ$, and $\alpha_0=20^\circ$. The resulting control laws are able to track an aggressive reference lift trajectory while attenuating sensor noise and compensating for strong nonlinearities.Comment: 20 pages, 13 figure

Augmentation of Water Resources Through Pollution Abatement

Author Institution: U.S. Department of Health, Education, and Welfare, Public Health Service, Robert A. Taft Sanitary Engineering Center, Cincinnati, Ohi

The influence of grazing on surface climatological variables of tallgrass prairie

Mass and energy exchange between most grassland canopies and the atmosphere are mediated by grazing activities. Ambient temperatures can be increased or decreased by grazers. Data have been assembled from simulated grazing experiments on Konza Prairie Research Natural Area and observations on adjacent pastures grazed by cattle show significant changes in primary production, nutrient content, and bidirectional reflectance characteristics as a function of grazing intensity. The purpose of this research was to provide algorithms that would allow incorporation of grazing effects into models of energy budgets using remote sensing procedures. The approach involved: (1) linking empirical measurements of plant biomass and grazing intensities to remotely sensed canopy reflectance, and (2) using a higher resolution, mechanistic grazing model to derive plant ecophysiological parameters that influence reflectance and other surface climatological variables

Affirmative Action: Problems and Perspectives

If I sound a little bit incoherent it is because I have only been in California for ten hours in the last three weeks, and that was just to change clothes and change bags and hug my little six-year-old tight and spend some time with my wife. I got back in last Tuesday night from a trip to the East Coast by way of Salt Lake City and got up at 2:00 a.m. to be at a local television show to be able to be on the CBS Morning News. My options were slim-either go to New York and do it or stay in California and do it. Whichever one you take, you have to get up early in the morning so those of you on the East Coast can see what goes on at 7:00 a.m. live. Getting up for five or seven minutes of television is not the most profitable thing in the world. I got back on a plane yesterday afternoon and got to New York this morning at 2:00. I was up at 7:00 and am here now. So ifyou will pardon me, I will do the best that I possibly can under the circumstances. The reason I am tired, as you know, is that tomorrow morning the Civil Rights Commission will consider a staff recommendation with respect to the Minority Set-Aside Program in the federal government-those three programs that are ongoing. There is a lot of attention on that. I just want to say to you that the commission\u27s concerns are not to put people out of business. The commission\u27s concerns for the most part-the majority of the commission\u27s, I think-are that, if there are going to be small business programs, they should be available to all Americans and not be based on ethnicity or gender and that, if there are going to be remedies for discrimination, they should be given to those who are victims of discrimination; and people should understand that there can be beneficiaries and victims on both sides of the ledger. It is a kind of affirmative action program