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

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

Control of VEGF-A transcriptional programs by pausing and genomic compartmentalization.

Vascular endothelial growth factor A (VEGF-A) is a master regulator of angiogenesis, vascular development and function. In this study we investigated the transcriptional regulation of VEGF-A-responsive genes in primary human aortic endothelial cells (HAECs) and human umbilical vein endothelial cells (HUVECs) using genome-wide global run-on sequencing (GRO-Seq). We demonstrate that half of VEGF-A-regulated gene promoters are characterized by a transcriptionally competent paused RNA polymerase II (Pol II). We show that transition into productive elongation is a major mechanism of gene activation of virtually all VEGF-regulated genes, whereas only ∼40% of the genes are induced at the level of initiation. In addition, we report a comprehensive chromatin interaction map generated in HUVECs using tethered conformation capture (TCC) and characterize chromatin interactions in relation to transcriptional activity. We demonstrate that sites of active transcription are more likely to engage in chromatin looping and cell type-specific transcriptional activity reflects the boundaries of chromatin interactions. Furthermore, we identify large chromatin compartments with a tendency to be coordinately transcribed upon VEGF-A stimulation. We provide evidence that these compartments are enriched for clusters of regulatory regions such as super-enhancers and for disease-associated single nucleotide polymorphisms (SNPs). Collectively, these findings provide new insights into mechanisms behind VEGF-A-regulated transcriptional programs in endothelial cells

An accurate measurement of electron beam induced displacement cross sections for single-layer graphene

We present an accurate measurement and a quantitative analysis of electron-beam induced displacements of carbon atoms in single-layer graphene. We directly measure the atomic displacement ("knock-on") cross section by counting the lost atoms as a function of the electron beam energy and applied dose. Further, we separate knock-on damage (originating from the collision of the beam electrons with the nucleus of the target atom) from other radiation damage mechanisms (e.g. ionization damage or chemical etching) by the comparison of ordinary (12C) and heavy (13C) graphene. Our analysis shows that a static lattice approximation is not sufficient to describe knock-on damage in this material, while a very good agreement between calculated and experimental cross sections is obtained if lattice vibrations are taken into account.Comment: 10 pages including supplementary inf

Strong anisotropy of superexchange in the copper-oxygen chains of La_{14-x}Ca_{x}Cu_{24}O_{41}

Electron spin resonance data of Cu^{2+} ions in La_{14-x}Ca_{x}Cu_{24}O_{41} crystals (x=9,11,12) reveal a very large width of the resonance line in the paramagnetic state. This signals an unusually strong anisotropy of ~10% of the isotropic Heisenberg superexchange in the Cu-O chains of this compound. The strong anisotropy can be explained by the specific geometry of two symmetrical 90 degree Cu-O-Cu bonds, which boosts the importance of orbital degrees of freedom. Our data show the apparent limitations of the applicability of an isotropic Heisenberg model to the low dimensional cuprates.Comment: 14 pages, 3 figures included, to be published in Phys. Rev. Let

Chaotic Waveguide-Based Resonators for Microlasers

We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as {\it open} resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasi bound states (QBS) which, in turn, propitiate the lasing mechanism. The energy values of the QBS are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.Comment: 5 pages, 5 figure

Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data

A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth?s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of10cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimatesimprove EGM2008 height anomaly differences by 10cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates thesefindings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTMomission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data

Distribution of calcifying and silicifying phytoplankton in relation to environmental and biogeochemical parameters during the late stages of the 2005 North East Atlantic Spring Bloom

The late stage of the North East Atlantic (NEA) spring bloom was investigated during June 2005 along a transect section from 45 to 66° N between 15 and 20° W in order to characterize the contribution of siliceous and calcareous phytoplankton groups and describe their distribution in relation to environmental factors. We measured several biogeochemical parameters such as nutrients, surface trace metals, algal pigments, biogenic silica (BSi), particulate inorganic carbon (PIC) or calcium carbonate, particulate organic carbon, nitrogen and phosphorus (POC, PON and POP, respectively), as well as transparent exopolymer particles (TEP). Results were compared with other studies undertaken in this area since the JGOFS NABE program. Characteristics of the spring bloom generally agreed well with the accepted scenario for the development of the autotrophic community. The NEA seasonal diatom bloom was in the late stages when we sampled the area and diatoms were constrained to the northern part of our transect, over the Icelandic Basin (IB) and Icelandic Shelf (IS). Coccolithophores dominated the phytoplankton community, with a large distribution over the Rockall-Hatton Plateau (RHP) and IB. The Porcupine Abyssal Plain (PAP) region at the southern end of our transect was the region with the lowest biomass, as demonstrated by very low Chl<i>a</i> concentrations and a community dominated by picophytoplankton. Early depletion of dissolved silicic acid (DSi) and increased stratification of the surface layer most likely triggered the end of the diatom bloom, leading to coccolithophore dominance. The chronic Si deficiency observed in the NEA could be linked to moderate Fe limitation, which increases the efficiency of the Si pump. TEP closely mirrored the distribution of both biogenic silica at depth and prymnesiophytes in the surface layer suggesting the sedimentation of the diatom bloom in the form of aggregates, but the relative contribution of diatoms and coccolithophores to carbon export in this area still needs to be resolved