A High Order Finite Volume Scheme for the 2D Shallow Water Equations Including Topography

Inhalt dieser Arbeit ist ein Verfahren zur numerischen Lösung der zweidimensionalen Flachwassergleichung, welche das Fließverhalten von Gewässern, deren Oberflächenausdehnung wesentlich größer als deren Tiefe ist, modelliert. Diese Gleichung beschreibt die gravitationsbedingte zeitliche Änderung eines gegebenen Anfangszustandes bei Gewässern mit freier Oberfläche. Diese Klasse beinhaltet Probleme wie das Verhalten von Wellen an flachen Stränden oder die Bewegung einer Flutwelle in einem Fluss. Diese Beispiele zeigen deutlich die Notwendigkeit, den Einfluss von Topographie sowie die Behandlung von Nass/Trockenübergängen im Verfahren zu berücksichtigen. In der vorliegenden Dissertation wird ein, in Gebieten mit hinreichender Wasserhöhe, hochgenaues Finite-Volumen-Verfahren zur numerischen Bestimmung des zeitlichen Verlaufs der Lösung der zweidimensionalen Flachwassergleichung aus gegebenen Anfangs- und Randbedingungen auf einem unstrukturierten Gitter vorgestellt, welches in der Lage ist, den Einfluss topographischer Quellterme auf die Strömung zu berücksichtigen, sowie in sogenannten \glqq lake at rest\grqq-stationären Zuständen diesen Einfluss mit den numerischen Flüssen exakt auszubalancieren. Basis des Verfahrens ist ein Finite-Volumen-Ansatz erster Ordnung, welcher durch eine WENO Rekonstruktion unter Verwendung der Methode der kleinsten Quadrate und eine sogenannte Space Time Expansion erweitert wird mit dem Ziel, ein Verfahren beliebig hoher Ordnung zu erhalten. Die im Verfahren auftretenden Riemannprobleme werden mit dem Riemannlöser von Chinnayya, LeRoux und Seguin von 1999 gelöst, welcher die Einflüsse der Topographie auf den Strömungsverlauf mit berücksichtigt. Es wird in der Arbeit bewiesen, dass die Koeffizienten der durch das WENO-Verfahren berechneten Rekonstruktionspolynome die räumlichen Ableitungen der zu rekonstruierenden Funktion mit einem zur Verfahrensordnung passenden Genauigkeitsgrad approximieren. Ebenso wird bewiesen, dass die Koeffizienten des aus der Space Time Expansion resultierenden Polynoms die räumlichen und zeitlichen Ableitungen der Lösung des Anfangswertproblems approximieren. Darüber hinaus wird die wohlbalanciertheit des Verfahrens für beliebig hohe numerische Ordnung bewiesen. Für die Behandlung von Nass/Trockenübergangen wird eine Methode zur Ordnungsreduktion abhängig von Wasserhöhe und Zellgröße vorgeschlagen. Dies ist notwendig, um in der Rechnung negative Werte für die Wasserhöhe, welche als Folge von Oszillationen des Raum-Zeit-Polynoms auftreten können, zu vermeiden. Numerische Ergebnisse die die theoretische Verfahrensordnung bestätigen werden ebenso präsentiert wie Beispiele, welche die hervorragenden Eigenschaften des Gesamtverfahrens in der Berechnung herausfordernder Probleme demonstrieren.

2D-3D Rigid-Body Registration of X-Ray Fluoroscopy and CT Images

The registration of pre-operative volumetric datasets to intra- operative two-dimensional images provides an improved way of verifying patient position and medical instrument loca- tion. In applications from orthopedics to neurosurgery, it has a great value in maintaining up-to-date information about changes due to intervention. We propose a mutual information- based registration algorithm to establish the proper align- ment. For optimization purposes, we compare the perfor- mance of the non-gradient Powell method and two slightly di erent versions of a stochastic gradient ascent strategy: one using a sparsely sampled histogramming approach and the other Parzen windowing to carry out probability density approximation. Our main contribution lies in adopting the stochastic ap- proximation scheme successfully applied in 3D-3D registra- tion problems to the 2D-3D scenario, which obviates the need for the generation of full DRRs at each iteration of pose op- timization. This facilitates a considerable savings in compu- tation expense. We also introduce a new probability density estimator for image intensities via sparse histogramming, de- rive gradient estimates for the density measures required by the maximization procedure and introduce the framework for a multiresolution strategy to the problem. Registration results are presented on uoroscopy and CT datasets of a plastic pelvis and a real skull, and on a high-resolution CT- derived simulated dataset of a real skull, a plastic skull, a plastic pelvis and a plastic lumbar spine segment.

Correlación y concordancia entre ecocardiografía y cateterismo cardiaco derecho para determinación de la presión sistólica de arteria pulmonar

Introducción. El cateterismo cardiaco derecho representa el estándar de referencia para el diagnóstico de hipertensión pulmonar, sin embargo el rendimiento de la ecocardiografía como estudio inicial ha mostrado buena correlación con las variables medidas por cateterismo. El presente estudio pretende describir el grado de correlación y concordancia entre la ecocardiografía y el cateterismo cardiaco derecho para la medición de la presión sistólica de la arteria pulmonar. Materiales y métodos. Se realizó un estudio observacional retrospectivo de los pacientes sometidos a cateterismo cardiaco derecho entre los años 2009 a 2014 y se compararon con los datos de ecocardiograma más cercano a este cateterismo, teniendo en cuenta la presión sistólica de la arteria pulmonar (PSAP) en las dos modalidades diagnósticas mediante correlación y concordancia estadística según los coeficientes de Pearson y el índice de Lin respectivamente. Resultados. Se recolectaron un total de 169 pacientes con un índice de correlación (r) obtenido para la medición de PSAP del total de la muestra de 0.73 p < 0.0001 mostrando un grado de correlación alto para toda la muestra evaluada. El análisis de concordancia obtenido para toda la población a partir del índice de Lin fue de 0.71 lo que determinó una pobre concordancia. Discusión. Se encontró buena correlación entre ecocardiografía y cateterismo cardiaco derecho para la medición de la PSAP, sin embargo la concordancia entre los métodos diagnósticos es pobre, por tanto el ecocardiograma no reemplaza al cateterismo cardiaco derecho como estudio de elección para diagnóstico y seguimiento de pacientes con hipertensión pulmonar.

Benchmarking 2D hydraulic models for urban flooding

This paper describes benchmark testing of six two-dimensional (2D) hydraulic models (DIVAST, DIVASTTVD, TUFLOW, JFLOW, TRENT and LISFLOOD-FP) in terms of their ability to simulate surface flows in a densely urbanised area. The models are applied to a 1·0 km × 0·4 km urban catchment within the city of Glasgow, Scotland, UK, and are used to simulate a flood event that occurred at this site on 30 July 2002. An identical numerical grid describing the underlying topography is constructed for each model, using a combination of airborne laser altimetry (LiDAR) fused with digital map data, and used to run a benchmark simulation. Two numerical experiments were then conducted to test the response of each model to topographic error and uncertainty over friction parameterisation. While all the models tested produce plausible results, subtle differences between particular groups of codes give considerable insight into both the practice and science of urban hydraulic modelling. In particular, the results show that the terrain data available from modern LiDAR systems are sufficiently accurate and resolved for simulating urban flows, but such data need to be fused with digital map data of building topology and land use to gain maximum benefit from the information contained therein. When such terrain data are available, uncertainty in friction parameters becomes a more dominant factor than topographic error for typical problems. The simulations also show that flows in urban environments are characterised by numerous transitions to supercritical flow and numerical shocks. However, the effects of these are localised and they do not appear to affect overall wave propagation. In contrast, inertia terms are shown to be important in this particular case, but the specific characteristics of the test site may mean that this does not hold more generally.

An X-ray micro-tomography system optimised for the low-dose study of living organisms

An X-ray micro-tomography system has been designed that is dedicated to the low-dose imaging of radiation sensitive living organisms and has been used to image the early development of the first few days of plant development immediately after germination. The system is based on third-generation X-ray micro-tomography system and consists of an X-ray tube, two-dimensional X-ray detector and a mechanical sample manipulation stage. The X-ray source is a 50 kVp X-ray tube with a silver target with a filter to centre the X-ray spectrum on 22 keV.A 100 mm diameter X-ray image intensifier (XRII) is used to collect the two-dimensional projection images. The rotation tomography table incorporates a linear translation mechanism to eliminate ring artefact that is commonly associated with third-generation tomography systems' Developing maize seeds (Triticum aestivum) have been imaged using the system with a cubic voxel linear dimension of 100 mum, over a diameter of 25 mm and the root lengths and volumes measured. The X-ray dose to the plants was also assessed and found to have no effect on the plant root development. (C) 2003 Elsevier Science Ltd. All rights reserved.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

In vivo transformations of dihydroartemisinic acid in Artemisia annua plants

[15-(CH3)-C-13-H-2]-dihydroartemisinic acid (2a) and [15-(CH3)-H-2]-dihydroartemisinic acid (2b) have been fed via the root to intact Artemisia annua plants and their transformations studied in vivo by one-dimensional H-2 NMR spectroscopy and two-dimensional, C-13-H-2 correlation NMR spectroscopy (C-13-(2) H COSY). Labelled dihydroartemisinic acid was transformed into 16 12-carboxy-amorphane and cadinane sesquiterpenes within a few days in the aerial parts of A. annua, although transformations in the root were much slower and more limited. Fifteen of these 16 metabolites have been reported previously as natural products from A. annua. Evidence is presented that the first step in the transformation of dihydroartemisinic acid in vivo is the formation of allylic hydroperoxides by the reaction of molecular oxygen with the Delta(4,5)-double bond in this compound. The origin of all 16 secondary metabolites might then be explained by the known further reactions of such hydroperoxides. The qualitative pattern for the transformations of dihydroartemisinic acid in vivo was essentially unaltered when a comparison was made between plants, which had been kept alive and plants which were allowed to die after feeding of the labelled precursor. This, coupled with the observation that the pattern of transformations of 2 in vivo demonstrated very close parallels with the spontaneous autoxidation chemistry for 2, which we have recently demonstrated in vitro, has lead us to conclude that the main 'metabolic route' for dihydroartemisinic acid in A. annua involves its spontaneous autoxidation and the subsequent spontaneous reactions of allylic hydroperoxides which are derived from 2. There may be no need to invoke the participation of enzymes in any of the later biogenetic steps leading to all 16 of the labelled 11,13-dihydro-amorphane sesquiterpenes which are found in A. annua as natural products. (C) 2003 Elsevier Ltd. All rights reserved.

Orientational ordering in the nematic phase of a polyethylene glycol-peptide conjugate in aqueous solution

The orientational ordering of the nematic phase of a polyethylene glycol (PEG)-peptide block copolymer in aqueous solution is probed by small-angle neutron scattering (SANS), with the sample subjected to steady shear in a Couette cell. The PEG-peptide conjugate forms fibrils that behave as semiflexible rodlike chains. The orientational order parameters (P) over bar (2) and (P) over bar (4) are obtained by modeling the data using a series expansion approach to the form factor of uniform cylinders. The method used is independent of assumptions on the form of the singlet orientational distribution function. Good agreement with the anisotropic two-dimensional SANS patterns is obtained. The results show shear alignment starting at very low shear rates, and the orientational order parameters reach a plateau at higher shear rates with a pseudologarithmic dependence on shear rate. The most probable distribution functions correspond to fibrils parallel to the flow direction under shear, but a sample at rest shows a bimodal distribution with some of the rodlike peptide fibrils oriented perpendicular to the flow direction.

Observational tracking of the 2D structure of coronal mass ejections between the sun and 1 AU

The Solar TErrestrial RElations Observatory (STEREO) provides high cadence and high resolution images of the structure and morphology of coronal mass ejections (CMEs) in the inner heliosphere. CME directions and propagation speeds have often been estimated through the use of time-elongation maps obtained from the STEREO Heliospheric Imager (HI) data. Many of these CMEs have been identified by citizen scientists working within the SolarStormWatch project ( www.solarstormwatch.com ) as they work towards providing robust real-time identification of Earth-directed CMEs. The wide field of view of HI allows scientists to directly observe the two-dimensional (2D) structures, while the relative simplicity of time-elongation analysis means that it can be easily applied to many such events, thereby enabling a much deeper understanding of how CMEs evolve between the Sun and the Earth. For events with certain orientations, both the rear and front edges of the CME can be monitored at varying heliocentric distances (R) between the Sun and 1 AU. Here we take four example events with measurable position angle widths and identified by the citizen scientists. These events were chosen for the clarity of their structure within the HI cameras and their long track lengths in the time-elongation maps. We show a linear dependency with R for the growth of the radial width (W) and the 2D aspect ratio (χ) of these CMEs, which are measured out to ≈ 0.7 AU. We estimated the radial width from a linear best fit for the average of the four CMEs. We obtained the relationships W=0.14R+0.04 for the width and χ=2.5R+0.86 for the aspect ratio (W and R in units of AU).

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

Host–guest supramolecular interactions in the coordination compounds of 4,4′-azobis(pyridine) with MnX2(X = NCS–, NCNCN–, and PF6–): structural analyses and theoretical study

Three new Mn(II) coordination compounds {[Mn(NCNCN)2(azpy)]·0.5azpy}n (1), {[Mn(NCS)2(azpy)(CH3OH)2]·azpy}n (2), and [Mn(azpy)2(H2O)4][Mn(azpy)(H2O)5]·4PF6·H2O·5.5azpy (3) (where azpy = 4,4'-azobis-(pyridine)) have been synthesized by self-assembly of the primary ligands, dicyanamide, thiocyanate, and hexafluorophosphate, respectively, together with azpy as the secondary spacer. All three complexes were characterized by elemental analyses, IR spectroscopy, thermal analyses, and single crystal X-ray crystallography. The structural analyses reveal that complex 1 forms a two-dimensional (2D) grid sheet motif These sheets assemble to form a microporous framework that incorporates coordination-free azpy by host-guest pi center dot center dot center dot pi. and C-H center dot center dot center dot N hydrogen bonding interactions. Complex 2 features azpy bridged one-dimensional (ID) chains of centrosymmetric [Mn(NCS)(2)(CH3OH)(2)} units which form a 2D porous sheet via a CH3 center dot center dot center dot pi supramolecular interaction. A guest azpy molecule is incorporated within the pores by strong H-bonding interactions. Complex 3 affords a 0-D motif with two monomeric Mn(II) units in the asymmetric unit. There exist pi center dot center dot center dot pi, anion center dot center dot center dot pi, and strong hydrogen bonding interactions between the azpy, water, and the anions. Density functional theory (DFT) calculations, at the M06/6-31+G* level of theory, are used to characterize a great variety of interactions that explicitly show the importance of host-guest supramolecular interactions for the stabilization of coordination compounds and creation of the fascinating three-dimensional (3D) architecture of the title compounds.

Temporal coupling between stimulus-evoked neural activity and hemodynamic responses from individual cortical columns

Using previously published data from the whisker barrel cortex of anesthetized rodents (Berwick et al 2008 J. Neurophysiol. 99 787–98) we investigated whether highly spatially localized stimulus-evoked cortical hemodynamics responses displayed a linear time-invariant (LTI) relationship with neural activity. Presentation of stimuli to individual whiskers of 2 s and 16 s durations produced hemodynamics and neural activity spatially localized to individual cortical columns. Two-dimensional optical imaging spectroscopy (2D-OIS) measured hemoglobin responses, while multi-laminar electrophysiology recorded neural activity. Hemoglobin responses to 2 s stimuli were deconvolved with underlying evoked neural activity to estimate impulse response functions which were then convolved with neural activity evoked by 16 s stimuli to generate predictions of hemodynamic responses. An LTI system more adequately described the temporal neuro-hemodynamics coupling relationship for these spatially localized sensory stimuli than in previous studies that activated the entire whisker cortex. An inability to predict the magnitude of an initial 'peak' in the total and oxy- hemoglobin responses was alleviated when excluding responses influenced by overlying arterial components. However, this did not improve estimation of the hemodynamic responses return to baseline post-stimulus cessation.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Human neural stem cell-derived cultures in three- dimensional substrates form spontaneously functional neuronal networks

Differentiated human neural stem cells were cultured in an inert three-dimensional (3D) scaffold and, unlike two-dimensional (2D) but otherwise comparable monolayer cultures, formed spontaneously active, functional neuronal networks that responded reproducibly and predictably to conventional pharmacological treatments to reveal functional, glutamatergic synapses. Immunocytochemical and electron microscopy analysis revealed a neuronal and glial population, where markers of neuronal maturity were observed in the former. Oligonucleotide microarray analysis revealed substantial differences in gene expression conferred by culturing in a 3D vs a 2D environment. Notable and numerous differences were seen in genes coding for neuronal function, the extracellular matrix and cytoskeleton. In addition to producing functional networks, differentiated human neural stem cells grown in inert scaffolds offer several significant advantages over conventional 2D monolayers. These advantages include cost savings and improved physiological relevance, which make them better suited for use in the pharmacological and toxicological assays required for development of stem cell-based treatments and the reduction of animal use in medical research.

Neuronal-glial populations form functional networks in a biocompatible 3D scaffold

Monolayers of neurons and glia have been employed for decades as tools for the study of cellular physiology and as the basis for a variety of standard toxicological assays. A variety of three dimensional (3D) culture techniques have been developed with the aim to produce cultures that recapitulate desirable features of intact. In this study, we investigated the effect of preparing primary mouse mixed neuron and glial cultures in the inert 3D scaffold, Alvetex. Using planar multielectrode arrays, we compared the spontaneous bioelectrical activity exhibited by neuroglial networks grown in the scaffold with that seen in the same cells prepared as conventional monolayer cultures. Two dimensional (monolayer; 2D) cultures exhibited a significantly higher spike firing rate than that seen in 3D cultures although no difference was seen in total signal power (<50 Hz) while pharmacological responsiveness of each culture type to antagonism of GABAAR, NMDAR and AMPAR was highly comparable. Interestingly, correlation of burst events, spike firing and total signal power (<50 Hz) revealed that local field potential events were associated with action potential driven bursts as was the case for 2D cultures. Moreover, glial morphology was more physiologically normal in 3D cultures. These results show that 3D culture in inert scaffolds represents a more physiologically normal preparation which has advantages for physiological, pharmacological, toxicological and drug development studies, particularly given the extensive use of such preparations in high throughput and high content systems.