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

Biological hot spots and the accumulation of marine dissolved organic matter in a highly productive ocean margin

Concentrations of dissolved organic carbon (DOC) and major biochemicals (amino acids and carbohydrates) were measured during five cruises (2009–2010) to the Louisiana margin in the northern Gulf of Mexico. Concentrations of amino acids and carbohydrates were elevated at mid-salinities and were indicative of plankton production of dissolved organic matter (DOM) in surface waters. Hot spots of two compositionally distinct types of labile DOM were identified based on the relative abundances of amino acids and carbohydrates. Amino acid-rich hot spots occurred sporadically in regions of high phytoplankton biomass and were mostly observed between dusk and dawn, reflecting a grazing source. In contrast, carbohydrate-rich hot spots were more widespread and were often found in nutrient-poor waters, indicating the production of carbon-rich DOM associated with nutrient limitation. Major biochemical indicators and bioassay experiments indicated labile DOM comprised a relatively small fraction of the DOC. Most DOM was degraded and had a semi-labile nature. Substantial accumulations of marine (plankton-derived) DOC were observed in surface waters, particularly at mid-salinities during the summer. Microbial alteration of marine DOC and nutrient limitation of microbial utilization of carbon-rich DOM appeared largely responsible for the accumulation of DOC. The reservoir of accumulated marine DOC in the shelf surface mixed layer ranged from 0.11 Tg C to 0.23 Tg C, with the lowest and highest values occurring during winter and summer. Substantial cross-shelf export of semi-labile marine DOM occurred during the summer and provided a major carbon and energy subsidy to microbial food webs in offshore waters.We are grateful to Steven E. Lohrenz and Wei-Jun Cai for providing the opportunity to participate in the GulfCarbon cruises. We appreciate the sampling assistance by Leanne Powers and the crews of the R/V Cape Hatteras and the R/V Hugh Sharp. We thank the anonymous reviewers for their comments and suggestions. This research was funded by a grant from the U.S. National Science Foundation (0850653 to RB) and by the 111 Project of China (B13030 to SKL). (0850653 - U.S. National Science Foundation; B13030 - 111 Project of China

Diffusion of collaborative maps about accessibility

Recently, neogeography projects focused on collaborative mapping of localized accessibility knowledge have resulted in applications that are designed to collect ratings of how accessible certain venues (e.g., buildings) are for people who travel in wheelchairs, people with low to no hearing or vision and older adults. Each application is the product of different creators, yet there are striking similarities in their purpose and features. These applications are crowdsourcing systems for information sharing that allow users to add meaningful information to a personalized web map; however, little research has analyzed how these applications have been created and adopted overtime. This paper reviews several existing applications and presents a framework for analyzing their diffusion over time

Gaussian quadrature exponential sum modeling of near infrared methane laboratory spectra obtained at temperatures from 106 to 297 K

Transmission measurements made on near-infrared laboratory methane spectra have previously been fit using a Malkmus band model. The laboratory spectra were obtained in three groups at temperatures averaging 112, 188, and 295 K; band model fitting was done separately for each temperature group. These band model parameters cannot be used directly in scattering atmosphere model computations, so an exponential sum model is being developed which includes pressure and temperature fitting parameters. The goal is to obtain model parameters by least square fits at 10/cm intervals from 3800 to 9100/cm. These results will be useful in the interpretation of current planetary spectra and also NIMS spectra of Jupiter anticipated from the Galileo mission

Accelerating BST Methods for Model Reduction with Graphics Processors

Model order reduction of dynamical linear time-invariant system appears in many scientific and engineering applications. Numerically reliable SVD-based methods for this task require O(n3) floating-point arithmetic operations, with n being in the range 103 − 105 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems via Balanced Stochastic Truncation, by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach

Engineering yeast alcohol dehydrogenase. Replacing Trp54 by Leu broadens substrate specificity

Analysis of a crystal structure of alcohol dehydrogenase (Adh) from horse liver suggests that Trp54 in the homologous yeast alcohol dehydrogenase prevents the yeast enzyme from efficiently catalysing the oxidation of long-chain primary alcohols with branching at the 4 position (e.g. 4-methyl-1-pentanol, cinnamyl alcohol). This residue has been altered to Leu by site-directed mutagenesis. The alteration yields an enzyme that serves as an effective catalyst for both longer straight-chain primary alcohols and branched chain alcohol

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

Turbidity-Based Sediment Monitoring in Northern Thailand: Hysteresis, Variability, and Uncertainty

Annual total suspended solid (TSS) loads in the Mae Sa River in northern Thailand, determined with an automated, turbidity-based monitoring approach, were approximately 62,000, 33,000, and 14,000 Mg during the three years of observation. These loads were equivalent to basin yields of 839 (603-1170), 445 (217-462), and 192 (108-222) Mg km-2 for the 74.16-km2 catchment during 2006, 2007, and 2008, respectively. The yearly uncertainty ranges indicate our loads may be underestimated by 38-43% or overestimated by 28-33%. In determining the annual loads, discharge (Q) and turbidity (T) values were compared against 333 hand-sampled total suspended solid concentrations (TSS) measured during 18 runoff events and other flow conditions across the three-year period. Annual rainfall varied from 1632 to 1934 mm; and catchment runoff coefficients (annual runoff/annual rainfall) ranged from 0.25 to 0.41. Measured TSS ranged from 8-15,900 mg l-1; the low value was associated with dry-season base flow; the latter, a wet-season storm. Storm size and location played an important role in producing clockwise, anticlockwise, and complex hysteresis effects in the Q-TSS relationship. Turbidity alone was a good estimator for turbidity ranges of roughly 10-2800 NTU (or concentrations approximately 25-4000 mg l-1). However, owing to hysteresis and high sediment concentrations that surpass the detection limits of the turbidity sensor during many annual storms, TSS was estimated best using a complex multiple regression equation based on high/low ranges of turbidity and Q as independent variables. Turbidity was not a good predictor of TSS fractions \u3e 2000 μm. Hysteresis in the monthly Q-TSS relationship was generally clockwise over the course of the monsoon season, but infrequent large dry-season storms disrupted the pattern in some years. The large decrease in annual loads during the study was believed to be related to depletion of fine sediment delivered to the stream by several landslides occurring the year prior to the study. The study indicated the importance of monitoring Q and turbidity at fine resolutions (e.g., sub-hourly) to capture the TSS dynamics and to make accurate load estimations in this flashy headwater stream where hysteresis in the Q-TSS signature varied at several time scales

Deciphering and Predicting Spatial and Temporal Concentrations of Arsenic Within the Mekong Delta Aquifer

Unravelling the complex, coupled processes responsible for the spatial distribution of arsenic within groundwaters of South and South-East Asia remains challenging, limiting the ability to predict the subsurface spatial distribution of arsenic. Previous work illustrates that Himalayan-derived, near-surface (0 to 12 m) sediments contribute a substantial quantity of arsenic to groundwater, and that desorption from the soils and sediments is driven by the reduction of AsV and arsenic-bearing iron (hydr)oxides. However, the complexities of groundwater flow will ultimately dictate the distribution of arsenic within the aquifer, and these patterns will be influenced by inherent physical heterogeneity along with human alterations of the aquifer system. Accordingly, we present a unified biogeochemical and hydrologic description of arsenic release to the subsurface environment of an arsenic-afflicted aquifer in the Mekong Delta, Kandal Province, Cambodia, constructed from measured geochemical profiles and hydrologic parameters. Based on these measurements, we developed a simple yet dynamic reactive transport model to simulate one- and two-dimensional geochemical profiles of the near surface and aquifer environment to examine the effects of subsurface physical variation on the distribution of arsenic. Our results show that near-surface release (0–12 m) contributes enough arsenic to the aquifer to account for observed field values and that the spatial distribution of arsenic within the aquifer is strongly affected by variations in biogeochemical and physical parameters. Furthermore, infiltrating dissolved organic carbon and ample buried particulate organic carbon ensures arsenic release from iron (hydr)oxides will occur for hundreds to thousands of years