Entwicklung und Test eines massenerhaltenden semi-Lagrangschen Transportverfahrens auf der Kugel

In der vorliegenden Arbeit wird ein neues numerisches Verfahren entwickelt und getestet, das sogenannte semi-Lagrangsche Zelhntegrationsverfahren (SLZI). Die Idee besteht darin, ein lokales Schema zu entwickeln, welches globale Integralinvarianten, wie z.B. die Gesamtmasse der Atmosphäre, erhält und ansonsten die bekannten positiven Eigenschaften semi-Lagrangscher Methoden zeigt. Die Entwicklung verläuft sukzessive von eindimensio- nalen Untersuchungen, über Tests in ebenen kartesischen Koordinaten bis hin zu den spe- ziellen Bedingungen auf der Kugeloberfläche. In jedem Entwicklungsschritt wird am Ende ein Standardtest durchgeftihrt und die Ergebnisse mit der analytischen Lösung und mit einem traditionellen Verfahren verglichen. Neben den Experimenten mit analytisch lösba- ren Testsituationen wird auch ein Experiment mit realen Daten durchgeführt. Die Erweite- rung der Methode auf drei Dimensionen wird ebenso diskutiert wie die Kombination des SlZl-Verfahrens mit dem semi-impliziten Zeitschrittverfahren. Neben der Anwendung als Transportschema werden noch einige Überlegungen zur Ausdehnung der Methode auf den kompletten Satz der primitiven Gleichungen angestellt. Bei den Untersuchungen in einer Dimension liegt der Schwerpunkt zunächst in der konkre- ten Formulierung der neuen Methode. Dabei stellt sich heraus, daß man prinzipiell zwei Schritte unterscheiden kann. Zuerst wird in jeder Gitterzelle ein Polynom berechnet, wel- ches die Verteilung einer Variablen in dieser Zelle reprâsentiert und anschließend wird eine konservative Abbildung, bestehend aus Integralen über diese Polynome, zwischen dem Git- ter ntm alten und zum neuen Zeitpunkt durchgeführt. In dieser Arbeit werden als Polynome konstante, lineare und quadratische Funktionen verwendet und als Test wird zunächst der Transport eines Rechteck- bnv. Dreiecksignals analysiert. Es hat sich gezeig¡, daß die numerische Genauigkeit der Methode um so größer ist, je höher der Grad der verwendeten Polynome ist. Schränkt man die Polynome weiter ein, indem man etwa Positivitat oder gar Monotonie fordert, geht dies geringfrigig zu Lasten der Genauigkeit. Die Entwicklung des a¡reidimensionalen SlZl-Verfahrens in ebenen kartesischen Koordi- naten hat den Fokus die konservative Abbildung derart zu gestalten, daß sie die Eigenschaf- ten des eindimensionalen Verfahrens bestätigt und dabei möglichst effizient ist. Dabei hat sich gezeigt, daß eine sukzessive Anwendung von eindimensionalen Integrationen in Rich- tung der zwei Koordinatenachsen die Forderungen erfüllen kann. Als Testobjekt dient die gleichftirmige Rotation eines Zylinderc um den Mittelpunkt des Integrationsgebietes. Die Lösung ist dabei unabhängig von der V/ahl der Koordinatenrichtung in welche zuerst inte- griert wird. V/ie bei den eindimensionalen Tests hat sich bestätigt, daß die Verwendunglinearer Funktionen zu ähnlichen Eigenschaften flihrt wie die klassische semi-Lagrangsche bikubische Interpolation. Auf der Kugeloberfläche wird der Standardtest, die Advekfion einer kosinusftirmigen Glok- kenfunktion direkt über den Pol, entlang des Aquators und in kleinen Abweichungen von diesen Extremen, untersucht. Insbesondere die Advektion direkt über den Pol zeigt, daß hier mit neuen Problemen zu rechnen ist. Die starke Krümmung und Drängung der Koordinaten- linien erfordert eine Modifikation des bisher entwickelten Schemas. Die Änderung beinhal- tet im Wesentlichen die Berechnung von zusätzlichen Punkten, um die Fläche der Gitterzellen in Polnähe zum alten Zeitpurktkorrekt wiederzugeben. Die Verwendung eines Polfilters ftihrt dann schließlich auch zu quantitativ zufriedenstellenden Resultaten. Gerade die besondere Behandlung der Gitterpunkte in der Nähe der Pole bietet aber auch Ansatz- punkte für weitere Verbesserungen. Experimente mit verschiedenen Auflösungen ergaben, daß mit höherer Gitterauflösung die SLZI-Methode, wie zu erwarten, eine genauere Lösung liefert. Die wichtige Frage nach der Effizienz des Verfahrens wird an dieser Stelle auch beantwortet. Dabei kam heraus, daß die Verwendung linearer Funktionen im SLZI-Schema zrrar geringfügig aufwendiger ist als bikubische semi-Lagrangsche Interpolation, aber den zusätzlichen Vorteil der Massenerhaltung bietet. V/ill man höhere Genauigkeit erzielen, so kann dies durch quadratische Funktionen erreicht werden, wodurch die Methode etwa um den Faktor 1,6 mehr Rechenzeit benötigt. Um das Verfahren mit realen Daten zu testen, mußte eine Situation gefunden werden, die über einen längeren Zeitraum annähernd nveidimensionale Strömungsverhältnisse bietet. Die Advektion potentieller Vorticity im Zeitram 16-28 Januar 1992 auf der 450 K Isentro- penfläche konnte diese Anforderungen erfüllen. Neben der Bestätigung der bis dahin gewonnenen Ergebnisse wird deutlich, daß die genauere SLZI-Methode mit quadratischen Funktionen viel besser kleinskalige Strukturen simuliert als die bikubische semi-Lagrange Interpolation.In the present study, a new numerical method is developed and tested, the so-called cell- integrated semi-Lagrangian scheme (CISL). The basic idea is to develop a local scheme which shows the well-known solid properties of semi-Lagrangian schemes and additionally conserves some global integral invariants. The development proceeds continuously from simple one-dimensional investigation and tests in the cartesian plane up to the special con- ditions on the sphere. At the end of every step a standard test is carried out and the results are compared with the analytical solution and a traditional method. Besides the experiments with analytical test cases an integration with realistic data is performed. The extension to a three-dimensional scheme is discussed as well as the combination of the CISL method with the semi-implicit time stepping. Additional to the design as a transport scheme some ideas to apply the method to the full set of primitive equations are presented. The one-dimensional investigations concentrate above all on the practical formulation of the scheme. It turned out that in principle the new method could be divided in two steps. At first a polynomial which describes the spatial distribution of the variable is computed in every grid cell and subsequently a conservative remapping between the grid at previous time level and the grid at next time level is carried out using integrals over these polynomi- als. In the present paper constant, linear and parabolic functions are used and the first test case is the transport of a rectangular and a triangular wave. The experiments show that with higher degree of the polynomials a more accurate solution is achieved. Implying additional conditions on the functions like positivity o. monotonicity the accuracy is slightly smaller. The focus of the tests in two-dimensional cartesian coordinates is to develop an efficient conservative remapping which maintains the properties from the one-dimensional experi- ments. It turned out that a cascade of one-dimensional integrations parallel to the coordinate lines might fit these requirements. The test case here is the solid body rotation of a cylinder and it ends up that the solution is independent of the sequence of integrations. Similar to the one-dimensional results the use of linear functions within the CISL scheme is comparable to the traditional semi-Lagrangian bicubic interpolation. On the sphere the standard test, the advection of a cosine bell directly over the poles, around the equator and minor shifts from these two orientations, is performed. Especially the advection over the poles shows new problems under the conditions of spherical geometry. The strong curvature and the crowded coordinate lines near the poles require a modification of the scheme developed until now. The main changes are the calculation of additional points in order to reflect the area of the grid cell at previous time level more conect. Finally, the application of a pole filter leeds to quantitatively sufficient results. But the specific treat-ment of near pole grid points shows some promise for further improvements. Experiments with different grid resolutions result in more accurate solutions with CISL as the resolution increases. The important question of efficiency has been regarded now. CISL scheme with linear functions is slightly more expensive than semi-Lagrangian bicubic interpolation, but besides the same numerical properties the new method offers the additional advantage of the exact conservation of total mass. Higher accuracy can achieved using parabolic func- tions which need a factor of 1,6 more computer time. In order to test the method with realistic data a situation with an almost two-dimensional flow over a longer period has to be found. This is the case for the advection of potential vor- ticity during the period 16-28 january 1992 on the 450 K isentropic surface. Besides the confirmation of previous results the more accurate CISL scheme with parabolic functions simulates the small scale structures slightly better than the semi-Lagrangian bicubic inter- polation

Universal Features of Quantized Thermal Conductance of Carbon Nanotubes

The universal features of quantized thermal conductance of carbon nanotubes (CNTs) are revealed through theoretical analysis based on the Landauer theory of heat transport. The phonon-derived thermal conductance of semiconducting CNTs exhibits a universal quantization in the low temperature limit, independent of the radius or atomic geometry. The temperature dependence follows a single curve given in terms of temperature scaled by the phonon energy gap. The thermal conductance of metallic CNTs has an additional contribution from electronic states, which also exhibits quantized behavior up to room temperature.Comment: 4 pages, 5 figures. accepted for publication in Phys. Rev. Let

Using Humic Fractions to Understand Natural Organic Matter Processes in Soil and Water: Selected Studies and Applications

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Structural investigation of Fe silicide films grown by pulsed laser deposition

Pulsed laser deposition was used to grow epitaxial β‐FeSi2 films on Si(111) (1×1) and Si(111) (7×7) with the following epitaxial orientations: β‐FeSi2(001)//Si(111) with β‐FeSi2[010]//Si〈110〉 and three rotational variants. Silicide growth was influenced by substrate temperature and deposition rate, but not by the structure of the starting surface. Films containing both β‐FeSi2 and FeSi were formed at low substrate temperatures and high deposition rates, while films containing only β‐FeSi2 were formed at higher substrate temperatures and lower deposition rates. FeSi grains had the following epitaxial relationship to the Si substrate, FeSi(111)//Si(111) with FeSi(110)//Si(112). The microstructure of the silicide films varied with film thickness, as did the roughness at the silicide/Si interface. These results suggest that an Fe‐rich environment was created during the growth of the silicide films.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70762/2/JAPIAU-76-4-2202-1.pd

Driving vascular endothelial cell fate of human multipotent Isl1 + heart progenitors with VEGF modified mRNA

published_or_final_versio

Chondrogenic differentiation of growth factor-stimulated precursor cells in cartilage repair tissue is associated with increased HIF-1α activity

SummaryObjectiveTo investigate the chondrogenic potential of growth factor-stimulated periosteal cells with respect to the activity of Hypoxia-inducible Factor 1α (HIF-1α).MethodsScaffold-bound autologous periosteal cells, which had been activated by Insulin-like Growth Factor 1 (IGF-1) or Bone Morphogenetic Protein 2 (BMP-2) gene transfer using both adeno-associated virus (AAV) and adenoviral (Ad) vectors, were applied to chondral lesions in the knee joints of miniature pigs. Six weeks after transplantation, the repair tissues were investigated for collagen type I and type II content as well as for HIF-1α expression. The functional role of phosphatidylinositol 3-kinase (PI3K)/mammalian target of rapamycin (mTOR) and mitogen-activated protein kinase (MEK)/extracellular signal-regulated kinase (ERK) signaling on BMP-2/IGF-1-induced HIF-1α expression was assessed in vitro by employing specific inhibitors.ResultsUnstimulated periosteal cells formed a fibrous extracellular matrix in the superficial zone and a fibrocartilaginous matrix in deep zones of the repair tissue. This zonal difference was reflected by the absence of HIF-1α staining in superficial areas, but moderate HIF-1α expression in deep zones. In contrast, Ad/AAVBMP-2-stimulated periosteal cells, and to a lesser degree Ad/AAVIGF-1-infected cells, adopted a chondrocyte-like phenotype with strong intracellular HIF-1α staining throughout all zones of the repair tissue and formed a hyaline-like matrix. In vitro, BMP-2 and IGF-1 supplementation increased HIF-1α protein levels in periosteal cells, which was based on posttranscriptional mechanisms rather than de novo mRNA synthesis, involving predominantly the MEK/ERK pathway.ConclusionThis pilot experimental study on a relatively small number of animals indicated that chondrogenesis by precursor cells is facilitated in deeper hypoxic zones of cartilage repair tissue and is stimulated by growth factors which enhance HIF-1α activity

Metallpartikel erhellen die Nanowelt: Optische Nahfeldmikroskopie an organischen Fluoreszenzmolekülen

Modern optical microscopy is gaining deeper and deeper insight into the nanoworld. Conventional microscopy faces restrictions by both the diffraction limit and its sensitivity concerning the low intensities of nanoscale light sources. To be able to circumvent these drawbacks, scanning near-field optical microscopy (SNOM) has been implemented at the Institute of Applied Photophysics at the TU Dresden by applying optically active scanning probes in order to constitute interfaces between the macroscopic and the nanoscopic world. New probes functionalised with metal nanoparticles can resolve structures which are unreachable by traditional methods (~ 50 nm). Our work has led to inexpensive and fast fabrication of such probes allowing an unprecedented views of the nanoworld.Die moderne optische Mikroskopie erlaubt es, der Nanowelt immer neue spannende Erkenntnisse zu entlocken. Jedoch ist die herkömmliche Lichtmikroskopie in ihrer Auflösung begrenzt und im Hinblick auf die geringe Intensität nanoskopischer Lichtquellen häufig nicht empfindlich genug. Um diese Probleme zu umgehen, wird am Institut für Angewandte Photophysik (IAPP) der TU Dresden die sogenannte optische Nahfeldmikroskopie eingesetzt. Hierbei dienen optisch aktive Sonden als Schnittstelle zwischen makroskopischer und nanoskopischer Welt. Diese am IAPP entwickelten neuartigen Sonden sind mit metallischen Nanopartikeln besetzt. Das Nahfeldmikroskop erlangt mit derartigen Sonden ein Auflösungsvermögen, welches weit jenseits der Möglichkeiten konventioneller Mikroskope liegt. Die Sonden können einfach und schnell hergestellt werden und erlauben der Nahfeldmikroskopie bisher unerreichte Einblicke in die Nanowelt

The effect of rotation, tillage, and fertility on rice grain yields and nutrient flows

ABSTRACT Rice is one of the most intensively cultivated row crops in America. In order to move away from current tillage practices it will be necessary to maintain current yield levels. A key to successful no-till rice production will be to maintain plant fertilizer efficiency in a system that is flooded much of the growing season and not increase nutrient runoff. A study was established in 2000 that compares fertility, variety, and conventional-and no-till rice rotations. Rice grain yields, across all treatments, were between 140 and 195 bu a -1 . Yields were most affected by rotation and tillage. Continuous rice grain yields averaged 34 bu a -1 lower than a rice-soybean rotation. Plant P and K uptake varied significantly between rotation treatments but not between tillage, fertility, or variety treatments. Phosphorus concentrations in run off liquid were significantly higher in the no-till plots. Total P in runoff was lower in the no-till plots because of reduced P being carried in solids. Total nitrogen uptake was lower in the continuous rice rotation compared to the rice-soybean rotation with soil N uptake higher for the no-till compared to conventional-till in both rotations. MATERIALS AND METHODS Field #8 at the University of Arkansas Rice Research and Extension Center was selected for this study and cut to a 0.15% slope in February, 1999. This site had not been previously used for rice research because irrigation water was not available. Soil at the site is referred to as a Stuttgart silt loam and classified as a fine, smectitic, thermic Albaqultic Hapludolf. Initial soil samples showed a pH range of 5.6 to 6.2 with carbon content averaging 0.84% and nitrogen 0.08%. Plots measuring 250' x 40' were laid out in a north-south direction. These plots were then divided in half east-west with each side randomized as conventional or no-till treatments. Each tillage treatment was then split into a standard and high fertility treatment. For rice, 'standard' fertility consisted of a single preflood N application of 100 lbs urea a -1 plus 40 lbs a -1 P 2 O 5 , and 60 lbs a -1 K 2 O applied prior to planting. Rates increased to 150 lbs a -1 N, 60 lbs a -1 P 2 O 5 , and 90 lbs a -1 K 2 O for the 'enhanced' treatment with application times remaining the same. Two varieties of each crop species were planted in a continuous strip across the conventional-and no-till treatments. In March, soil samples were collected for fertility evaluations. Soil samples were ground and dried. Phosphorus and potassium determinations were made using a Melich III extraction at a 1:10 extraction ratio. Plant samples were collected following physiological maturity but before leaf senescence for nutrient determinations in 1999, 2000, and 2001. Plants were divided into grain, leaf, and stem portions for analysis. Plant analysis was completed using a HNO 3 digest and read with a ICP (Spectro Model D). The following rotations were started in 1999: 1) continuous rice, 2) ricesoybean, 3) soybean-rice, 4) rice-corn, 5) corn-rice, 6) rice (wheat) rice (wheat), 7) rice (wheat)-soybeans (wheat), 8) soybeans (wheat)-rice (wheat), 9) rice-corn-soybeans, 10) rice-corn (wheat)-soybeans. Yield data and nutrient uptake will be presented for the continuous rice and rice-soybean rotations. 2