An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations

We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al. '16] to a class of descriptor systems in an efficient and reliable way. Recently, it has been shown in the case of linear or bilinear systems that a direct extension of interpolation-based model reduction techniques to descriptor systems, without any modifications, may lead to poor reduced-order systems. Therefore, for the analysis, we aim at transforming the considered QB descriptor system into an equivalent QBODE system by means of projectors for which standard model reduction techniques for QBODEs can be employed, including aforementioned interpolation scheme. Subsequently, we discuss related computational issues, thus resulting in a modified algorithm that allows us to construct \emph{near}--optimal reduced-order systems without explicitly computing the projectors used in the analysis. The efficiency of the proposed algorithm is illustrated by means of a numerical example, obtained via semi-discretization of the Navier-Stokes equations

The Fallacy of An Expensive Standard of Living

Our social reformers and professional uplifters have been so constantly talking about the necessitty for \u27the masses to maintain a high standard of living that some very deterimental economic fallacies are becoming very popular and quite wide spread among certain classes of our people. It is a noteworthy fact that in many circles the free and careless spender is commended instead of the cautious buyer. The frugal saver, who in his endeavors to build up a little capital, abstains from some of the current foolish expenditures is too often pointed out as the undesirable citizen while his spendthrift neighbor is selected as a model, progressive, up-to-date man

Overview of SERI's high efficiency solar cell research

The bulk of the research efforts supported by the Solar Energy Research Institute (SERI) High Efficiency Concepts area has been directed towards establishing the feasibility of achieving very high efficiencies, 30% for concentrator and more than 20% for thin film flat plate, in solar cell designs which could possibly be produced competitively. The research has accomplished a great deal during the past two years. Even though the desired performance levels have not yet been demonstrated, based on the recent progress, a greater portion of the terrestrial photovoltaics community believes that these efficiencies are attainable. The program will now allocate a larger portion of resources to low cost, large area deposition technology. The program is currently shifting greater emphasis on to the study of crystal growth in order to provide the understanding and tools needed to design a large area process

Gatekeeping after Gilbert: How Lawyers Should Address the Court\u27s New Emphasis

In the world of modern trials, expert witnesses are the coin of the realm. Lawyers know that most of the time, experts are case-breakers. Their demeanor, knowledge, and presentation ability are key qualities. Accordingly, their persuasive effect on modern lay jurors makes it incumbent on judges to ensure that an expert\u27s opinions are appropriately directed. That means not allowing an economist to testify about the medical dynamics of bone disease, for example

Should Michigan Rule of Evidence 703 Be Revised?

Technical witnesses regularly assist the fact-finding process in Michigan trials. Jury or bench trials in federal and state courts routinely feature the appearance of experts. Properly policed by our courts, few forms of testimony hold more promise for advancing the truth-seeking function of American litigation. The expanding presence of experts raises hard questions. Are the Michigan rules in turn with modern needs? Should the state rule controlling the basis for expert opinion be aligned with the federal pattern? If Michigan Rule of Evidence 703 could stand revision, does proper alteration require significant additions not presently contained in either state or federal rules? This article addresses these important issues affecting the scope of expert opinion in modern trials

Sources, Distributions, and Dynamics of Dissolved Organic Matter in the Canada and Makarov Basins

A comprehensive survey of dissolved organic carbon (DOC) and chromophoric dissolved organic matter (CDOM) was conducted in the Canada and Makarov Basins and adjacent seas during 2010–2012 to investigate the dynamics of dissolved organic matter (DOM) in the Arctic Ocean. Sources and distributions of DOM in polar surface waters were very heterogeneous and closely linked to hydrological conditions. Canada Basin surface waters had relatively low DOC concentrations (69 ± 6 μmol L−1), CDOM absorption (a325: 0.32 ± 0.07 m−1) and CDOM-derived lignin phenols (3 ± 0.4 nmol L−1), and high spectral slope values (S275–295: 31.7 ± 2.3 μm−1), indicating minor terrigenous inputs and evidence of photochemical alteration in the Beaufort Gyre. By contrast, surface waters of the Makarov Basin had elevated DOC (108 ± 9 μmol L−1) and lignin phenol concentrations (15 ± 3 nmol L−1), high a325 values (1.36 ± 0.18 m−1), and low S275–295 values (22.8 ± 0.8 μm−1), indicating pronounced Siberian river inputs associated with the Transpolar Drift and minor photochemical alteration. Observations near the Mendeleev Plain suggested limited interactions of the Transpolar Drift with Canada Basin waters, a scenario favoring export of Arctic DOM to the North Atlantic. The influence of sea-ice melt on DOM was region-dependent, resulting in an increase (Beaufort Sea), a decrease (Bering-Chukchi Seas), and negligible change (deep basins) in surface DOC concentrations and a325 values. Halocline structures differed between basins, but the Canada Basin upper halocline and Makarov Basin halocline were comparable in their average DOC (65–70 μmol L−1) and lignin phenol concentrations (3–4 nmol L−1) and S275–295 values (22.9–23.7 μm−1). Deep-water DOC concentrations decreased by 6–8 μmol L−1 with increasing depth, water mass age, nutrient concentrations, and apparent oxygen utilization. Maximal estimates of DOC degradation rates (0.036–0.039 μmol L−1 yr−1) in the deep Arctic were lower than those in other ocean basins, possibly due to low water temperatures. DOC concentrations in bottom waters (\u3e2500 m; 46 ± 2 μmol L−1) of the Canada and Makarov Basins were slightly lower than those reported for deep waters of the Eurasian Basin and Nordic Seas. Elevated a325 values (by 10–20%) were observed near the seafloor, indicating biological activity in Arctic basin sediments