Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows

The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an $L^p-L^q$-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases, the solution converges exponentially to an equilibrium in the natural state manifold

Vorhersage von reaktivem Stofftransport in porösen Medien auf Basis unabhängiger Beobachtungen mit X-Ray µ-CT

Der reaktive Transport und die Transformation von gelösten organischen Substanzen beeinflussen die Funktionen des Bodens in maßgeblicher Weise. Eine Einschätzung dieser Funktionen ist daher an ein quantitatives Verständnis der Transportprozesse gebunden, um die Ausbreitung von organischen Substanzen voraussagen zu können. Die hierfür geeigneten Modelle enthalten jedoch häufig eine Vielzahl unbekannter Parameter, die durch Modellinversion bestimmt werden. Diese Herangehensweise spiegelt nicht notwendigerweise eine physikalisch sinnvolle Parametrisierung wider und verhindert damit realistische Prognosen. Das Ziel dieser Studie ist die von Transportdaten unabhängige Bestimmung der reaktiven Transportparameter. Um Transport unter möglichst konstanten Randbedingungen beobachten zu können, führten wir Säulenversuche mit Schüttungen wohldefinierter Mineralzusammensetzung (Glas, Quarz und Goethit) durch. Teile der Oberflächen wurden dabei homogen mit Goethit beschichtet. Als Versuchslösungen kamen konservative Tracer (NaCl) zur Charakterisierung des Fließfeldes sowie reaktive Tracer (Phthalsäure) zur Veranschaulichung von Adsorption an der Festphase zum Einsatz. Der Porenraum und die Mineralverteilung der Säulen wurden mittels X-Ray µ-CT dreidimensional erfasst und relevante morphologische Parameter extrahiert (Porengrößenverteilung, Vernetzung, Oberfläche). Unter Verwendung dieser Parameter wurde anschließend ein Porennetzwerkmodell erstellt, welches die gleichen morphologischen Charakteristika aufweist wie der tatsächliche Porenraum. Auf diese Weise gelang die Vorhersage des konservativen Stofftransports bereits ohne die Verwendung eines kontinuumskaligen Dispersionsparameters. Im nächsten Schritt werden Interaktionsparameter der verwendeten Sorbat/Sorbenten-Mischung in Schüttelversuchen bestimmt und in die Modellierung mit einbezogen. Auf diesem Weg wird sich zeigen, ob auch der reaktive Transport unabhängig von Durchbruchsdaten nachzuvollziehen ist

The ℓs\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665

FACT -- the First Cherenkov Telescope using a G-APD Camera for TeV Gamma-ray Astronomy (HEAD 2010)

Geiger-mode Avalanche Photodiodes (G-APD) bear the potential to significantly improve the sensitivity of Imaging Air Cherenkov Telescopes (IACT). We are currently building the First G-APD Cherenkov Telescope (FACT) by refurbishing an old IACT with a mirror area of 9.5 square meters and construct a new, fine pixelized camera using novel G-APDs. The main goal is to evaluate the performance of a complete system by observing very high energy gamma-rays from the Crab Nebula. This is an important field test to check the feasibility of G-APD-based cameras to replace at some time the PMT-based cameras of planned future IACTs like AGIS and CTA. In this article, we present the basic design of such a camera as well as some important details to be taken into account.Comment: Poster shown at HEAD 2010, Big Island, Hawaii, March 1-4, 201

On thermodynamically consistent Stefan problems with variable surface energy

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv admin note: substantial text overlap with arXiv:1101.376

FACT -- The G-APD revolution in Cherenkov astronomy

Since two years, the FACT telescope is operating on the Canary Island of La Palma. Apart from its purpose to serve as a monitoring facility for the brightest TeV blazars, it was built as a major step to establish solid state photon counters as detectors in Cherenkov astronomy. The camera of the First G-APD Cherenkov Telesope comprises 1440 Geiger-mode avalanche photo diodes (G-APD), equipped with solid light guides to increase the effective light collection area of each sensor. Since no sense-line is available, a special challenge is to keep the applied voltage stable although the current drawn by the G-APD depends on the flux of night-sky background photons significantly varying with ambient light conditions. Methods have been developed to keep the temperature and voltage dependent response of the G-APDs stable during operation. As a cross-check, dark count spectra with high statistics have been taken under different environmental conditions. In this presentation, the project, the developed methods and the experience from two years of operation of the first G-APD based camera in Cherenkov astronomy under changing environmental conditions will be presented.Comment: Proceedings of the Nuclear Science Symposium and Medical Imaging Conference (IEEE-NSS/MIC), 201