TAU Hyperflex Report

Computational meshes used in practical aerodynamic applications may possess various properties. For example, structured or unstructured ordering may be used to utilize efficient data structures or simplify mesh generation; high-aspect-ratio cells may be used to resolve boundary layers of high-Reynoldsnumber flows; the cell orientation may align with specific flow directions to maximize benefits of certain discretization techniques, such as approximated Riemann solvers. The HyperFlex version of the DLR TAU-code provides a suit of computational algorithms and solution techniques that can be canonically switched depending on mesh characteristics to optimize accuracy, efficiency, and robustness of flow solutions. The current HyperFlex implementation derives from experiences gained during previous efforts concerned with enabling structured data and algorithms in an unstructured code environment, developing an hierarchy of preconditioning techniques embedded into a multistage Runge-Kutta method, and implementing alternative multigrid techniques. The practical aspects of code design, such as maintainability and expendability, are also taken into account

Finite Element Approximation auf der Basis geometrischer Zellen

Die Methode der Finiten Elemente ist ein numerisches Verfahren zur Interpolation vorgegebener Werte und zur numerischen Approximation von Lösungen stationärer oder instationärer partieller Differentialgleichungen bzw. Systemen partieller Differentialgleichungen. Grundlage dieser Verfahren ist die Formulierung geeigneter Finiter Elemente und Finiter Element Zerlegungen. Finite Elemente besitzen in der Regel eine geometrische Basis bestehend aus Strecken im eindimensionalen, Drei- oder Vierecken im zweidimensionalen und Tetra- oder Hexaedern im dreidimensionalen euklidischen Raum, eine Menge von Freiheitsgraden und eine Basis von Funktionen. Die geometrische Basis eines Finiten Elements wird verallgemeinert als geometrische Zelle formuliert. Diese geschlossene geometrische Formulierung führt zu einer geometrieunabhängigen Definition der Basisfunktionen eines Finiten Elements in den Zellkoordinaten der geometrischen Zelle. Finite Elemente auf der Basis geometrischer Zellen werden als Bestandteile Finiter Element Zerlegungen in Finiten Element Interpolationen und Finiten Element Approximationen verwendet. Die Finiten Element Approximationen werden am Beispiel der 2-dimensionalen Diffusionsgleichung über das Standard-Galerkin-Verfahren ermittelt

Finite Cell-Elements of Higher Order

The method of the finite elements is an adaptable numerical procedure for interpolation as well as for the numerical approximation of solutions of partial differential equations. The basis of these procedure is the formulation of suitable finite elements and element decompositions of the solution space. Classical finite elements are based on triangles or quadrangles in the two-dimensional space and tetrahedron or hexahedron in the threedimensional space. The use of arbitrary-dimensional convex and non-convex polyhedrons as the geometrical basis of finite elements increases the flexibility of generating finite element decompositions substantially and is sometimes the only way to get a clear decomposition..

Modification of Daunorubicin-GnRH-III Bioconjugates With Oligoethylene Glycol Derivatives to Improve Solubility and Bioavailability for Targeted Cancer Chemotherapy

Daunorubicin-GnRH-III bioconjugates have recently been developed as drug delivery systems with potential applications in targeted cancer chemotherapy. In order to improve their biochemical properties, several strategies have been pursued: (1) incorporation of an enzymatic cleavable spacer between the anticancer drug and the peptide-based targeting moiety, (2) peptide modification by short chain fatty acids or (3) attachment of two anticancer drugs to the same GnRH-III derivative. Although these modifications led to more potent bioconjugates, a decrease in their solubility was observed. Here we report on the design, synthesis and biochemical characterization of daunorubicin-GnRH-III bioconjugates with increased solubility, which could be achieved by incorporating oligoethylene glycol-based spacers in their structure. First, we have evaluated the effect of an oligoethylene glycol-based spacer on the solubility, enzymatic stability/degradation, cellular uptake and in vitro cytostatic effect of a bioconjugate containing only one daunorubicin attached through a GFLG tetrapeptide spacer to the GnRH-III targeting moiety. Thereafter, more complex compounds containing two copies of daunorubicin, GFLG spacers as well as Lys(nBu) in position 4 of GnRH-III were synthesized and biochemically characterized. Our results indicated that all synthesized oligoethylene glycol-containing bioconjugates had higher solubility in cell culture medium than the unmodified analogs. They were degraded in the presence of rat liver lysosomal homogenate leading to the formation of small drug containing metabolites. In the case of bioconjugates containing two copies of daunorubicin, the incorporation of oligoethylene glycol-based spacers led to increased in vitro cytostatic effect on MCF-7 human breast cancer cells

The Origin and Development of the Geometrical Ideas in Arabic Mathematics : The Synopsis of the Geometrical Works of al-Quhi

Arabic Mathematics has been characterized as algebra. Compared with this, Arabic geometry had not influence on the later mathematics, and has not been studied so much. However without this geometry, no solution of cubic equations has not completed in Arabic mathematics. We sketch here the synopsis of the geometrical works of Abu Sahl al-Quhl (second half of the tenth century), 'one of the most eminent mathematicians in Iraq', and investigate the origin and development of his geometrical ideas. Thirty three mathematical works are attributed to him, and almost of them are geometrical. His ideas were from Archimedes, Euclid and Apollonius. The opus magnum of the last one is indispensable for al-Quhl's works, and in the field of conic sections he contributed much. He completed the lacuna of the Greek mathematics, and developed it further. For showing this aspect four treatises are presented with partial translations. 'On Tangent Circles' investigated Apollonian circle problems further, and 'On the Trisection of Angle' solved the famous problem by Apollonian conic sections. 'On the Motion' was a unique treatise in Arabic mathematics, for it dealt with infinity which had been avoided in Greek mathematics. 'On the Perfect Compass (an instrument to draw conies by continuous moving)' gave an idea on the new classification of curves, which anticipates the seventeenth-century European mathematics. The problems and method which he used seems to be analytical and purely Greek, and he might be called as the last Greek-style mathematician. The atmosphere where he studied shows that Arabic science developed under a kind of patronage, and the manuscripts containing his treatises shows that Greek geometry was well established at his times. In conclusion, geometry flourished in Arabic world of the tenth century, and its results were over the Greek ones, and might be compared to the early modern mathematics in Europe

Nanoparticles that communicate in vivo to amplify tumour targeting

Author Manuscript: 2012 May 29Nanomedicines have enormous potential to improve the precision of cancer therapy, yet our ability to efficiently home these materials to regions of disease in vivo remains very limited. Inspired by the ability of communication to improve targeting in biological systems, such as inflammatory-cell recruitment to sites of disease, we construct systems where synthetic biological and nanotechnological components communicate to amplify disease targeting in vivo. These systems are composed of ‘signalling’ modules (nanoparticles or engineered proteins) that target tumours and then locally activate the coagulation cascade to broadcast tumour location to clot-targeted ‘receiving’ nanoparticles in circulation that carry a diagnostic or therapeutic cargo, thereby amplifying their delivery. We show that communicating nanoparticle systems can be composed of multiple types of signalling and receiving modules, can transmit information through multiple molecular pathways in coagulation, can operate autonomously and can target over 40 times higher doses of chemotherapeutics to tumours than non-communicating controls.National Cancer Institute (U.S.) (SBMRI Cancer Center Support Grant 5 P30 CA30199-28)National Cancer Institute (U.S.) (MIT CCNE Grant U54 CA119349)National Cancer Institute (U.S.) (Bioengineering Research Partnership Grant 5-R01-CA124427)National Cancer Institute (U.S.) (UCSD CCNE Grant U54 CA 119335)National Science Foundation (U.S.) (Whitaker Graduate Fellowship