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Institute
Unstetige Galerkin-Diskretisierung niedriger Ordnung in einem atmosphärischen Multiskalenmodell
(2014)
Die Dynamik der Atmosphäre der Erde umfasst einen Bereich von mikrophysikalischer Turbulenz über konvektive Prozesse und Wolkenbildung bis zu planetaren Wellenmustern. Für Wettervorhersage und zur Betrachtung des Klimas über Jahrzehnte und Jahrhunderte ist diese Gegenstand der Modellierung mit numerischen Verfahren. Mit voranschreitender Entwicklung der Rechentechnik sind Neuentwicklungen der dynamischen Kerne von Klimamodellen, die mit der feiner werdenden Auflösung auch entsprechende Prozesse auflösen können, notwendig. Der dynamische Kern eines Modells besteht in der Umsetzung (Diskretisierung) der grundlegenden dynamischen Gleichungen für die Entwicklung von Masse, Energie und Impuls, so dass sie mit Computern numerisch gelöst werden können. Die vorliegende Arbeit untersucht die Eignung eines unstetigen Galerkin-Verfahrens niedriger Ordnung für atmosphärische Anwendungen. Diese Eignung für Gleichungen mit Wirkungen von externen Kräften wie Erdanziehungskraft und Corioliskraft ist aus der Theorie nicht selbstverständlich. Es werden nötige Anpassungen beschrieben, die das Verfahren stabilisieren, ohne sogenannte „slope limiter” einzusetzen. Für das unmodifizierte Verfahren wird belegt, dass es nicht geeignet ist, atmosphärische Gleichgewichte stabil darzustellen. Das entwickelte stabilisierte Modell reproduziert eine Reihe von Standard-Testfällen der atmosphärischen Dynamik mit Euler- und Flachwassergleichungen in einem weiten Bereich von räumlichen und zeitlichen Skalen. Die Lösung der thermischen Windgleichung entlang der mit den Isobaren identischen charakteristischen Kurven liefert atmosphärische Gleichgewichtszustände mit durch vorgegebenem Grundstrom einstellbarer Neigung zu(barotropen und baroklinen)Instabilitäten, die für die Entwicklung von Zyklonen wesentlich sind. Im Gegensatz zu früheren Arbeiten sind diese Zustände direkt im z-System(Höhe in Metern)definiert und müssen nicht aus Druckkoordinaten übertragen werden.Mit diesen Zuständen, sowohl als Referenzzustand, von dem lediglich die Abweichungen numerisch betrachtet werden, und insbesondere auch als Startzustand, der einer kleinen Störung unterliegt, werden verschiedene Studien der Simulation von barotroper und barokliner Instabilität durchgeführt. Hervorzuheben ist dabei die durch die Formulierung von Grundströmen mit einstellbarer Baroklinität ermöglichte simulationsgestützte Studie des Grades der baroklinen Instabilität verschiedener Wellenlängen in Abhängigkeit von statischer Stabilität und vertikalem Windgradient als Entsprechung zu Stabilitätskarten aus theoretischen Betrachtungen in der Literatur.
The atmosphere over the Arctic Ocean is strongly influenced by the distribution of sea ice and open water. Leads in the sea ice produce strong convective fluxes of sensible and latent heat and release aerosol particles into the atmosphere. They increase the occurrence of clouds and modify the structure and characteristics of the atmospheric boundary layer (ABL) and thereby influence the Arctic climate.
In the course of this study aircraft measurements were performed over the western Arctic Ocean as part of the campaign PAMARCMIP 2012 of the Alfred Wegener Institute for Polar and Marine Research (AWI). Backscatter from aerosols and clouds within the lower troposphere and the ABL were measured with the nadir pointing Airborne Mobile Aerosol Lidar (AMALi) and dropsondes were launched to obtain profiles of meteorological variables. Furthermore, in situ measurements of aerosol properties, meteorological variables and turbulence were part of the campaign. The measurements covered a broad range of atmospheric and sea ice conditions.
In this thesis, properties of the ABL over Arctic sea ice with a focus on the influence of open leads are studied based on the data from the PAMARCMIP campaign. The height of the ABL is determined by different methods that are applied to dropsonde and AMALi backscatter profiles. ABL heights are compared for different flights representing different conditions of the atmosphere and of sea ice and open water influence. The different criteria for ABL height that are applied show large variation in terms of agreement among each other, depending on the characteristics of the ABL and its history. It is shown that ABL height determination from lidar backscatter by methods commonly used under mid-latitude conditions is applicable to the Arctic ABL only under certain conditions. Aerosol or clouds within the ABL are needed as a tracer for ABL height detection from backscatter. Hence an aerosol source close to the surface is necessary, that is typically found under the present influence of open water and therefore convective conditions. However it is not always possible to distinguish residual layers from the actual ABL. Stable boundary layers are generally difficult to detect.
To illustrate the complexity of the Arctic ABL and processes therein, four case studies are analyzed each of which represents a snapshot of the interplay between atmosphere and underlying sea ice or water surface. Influences of leads and open water on the aerosol and clouds within the ABL are identified and discussed. Leads are observed to cause the formation of fog and cloud layers within the ABL by humidity emission. Furthermore they decrease the stability and increase the height of the ABL and consequently facilitate entrainment of air and aerosol layers from the free troposphere.
Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous–infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.
Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.
The H.E.S.S. array is a third generation Imaging Atmospheric Cherenkov Telescope (IACT) array. It is located in the Khomas Highland in Namibia, and measures very high energy (VHE) gamma-rays. In Phase I, the array started data taking in 2004 with its four identical 13 m telescopes. Since then, H.E.S.S. has emerged as the most successful IACT experiment to date. Among the almost 150 sources of VHE gamma-ray radiation found so far, even the oldest detection, the Crab Nebula, keeps surprising the scientific community with unexplained phenomena such as the recently discovered very energetic flares of high energy gamma-ray radiation. During its most recent flare, which was detected by the Fermi satellite in March 2013, the Crab Nebula was simultaneously observed with the H.E.S.S. array for six nights. The results of the observations will be discussed in detail during the course of this work. During the nights of the flare, the new 24 m × 32 m H.E.S.S. II telescope was still being commissioned, but participated in the data taking for one night. To be able to reconstruct and analyze the data of the H.E.S.S. Phase II array, the algorithms and software used by the H.E.S.S. Phase I array had to be adapted. The most prominent advanced shower reconstruction technique developed by de Naurois and Rolland, the template-based model analysis, compares real shower images taken by the Cherenkov telescope cameras with shower templates obtained using a semi-analytical model. To find the best fitting image, and, therefore, the relevant parameters that describe the air shower best, a pixel-wise log-likelihood fit is done. The adaptation of this advanced shower reconstruction technique to the heterogeneous H.E.S.S. Phase II array for stereo events (i.e. air showers seen by at least two telescopes of any kind), its performance using MonteCarlo simulations as well as its application to real data will be described.
In dieser Arbeit werden nichtlineare Kopplungsmechanismen von akustischen Oszillatoren untersucht, die zu Synchronisation führen können. Aufbauend auf die Fragestellungen vorangegangener Arbeiten werden mit Hilfe theoretischer und experimenteller Studien sowie mit Hilfe numerischer Simulationen die Elemente der Tonentstehung in der Orgelpfeife und die Mechanismen der gegenseitigen Wechselwirkung von Orgelpfeifen identifiziert. Daraus wird erstmalig ein vollständig auf den aeroakustischen und fluiddynamischen Grundprinzipien basierendes nichtlinear gekoppeltes Modell selbst-erregter Oszillatoren für die Beschreibung des Verhaltens zweier wechselwirkender Orgelpfeifen entwickelt. Die durchgeführten Modellrechnungen werden mit den experimentellen Befunden verglichen. Es zeigt sich, dass die Tonentstehung und die Kopplungsmechanismen von Orgelpfeifen durch das entwickelte Oszillatormodell in weiten Teilen richtig beschrieben werden. Insbesondere kann damit die Ursache für den nichtlinearen Zusammenhang von Kopplungsstärke und Synchronisation des gekoppelten Zwei-Pfeifen Systems, welcher sich in einem nichtlinearen Verlauf der Arnoldzunge darstellt, geklärt werden. Mit den gewonnenen Erkenntnissen wird der Einfluss des Raumes auf die Tonentstehung bei Orgelpfeifen betrachtet. Dafür werden numerische Simulationen der Wechselwirkung einer Orgelpfeife mit verschiedenen Raumgeometrien, wie z. B. ebene, konvexe, konkave, und gezahnte Geometrien, exemplarisch untersucht. Auch der Einfluss von Schwellkästen auf die Tonentstehung und die Klangbildung der Orgelpfeife wird studiert. In weiteren, neuartigen Synchronisationsexperimenten mit identisch gestimmten Orgelpfeifen, sowie mit Mixturen wird die Synchronisation für verschiedene, horizontale und vertikale Pfeifenabstände in der Ebene der Schallabstrahlung, untersucht. Die dabei erstmalig beobachteten räumlich isotropen Unstetigkeiten im Schwingungsverhalten der gekoppelten Pfeifensysteme, deuten auf abstandsabhängige Wechsel zwischen gegen- und gleichphasigen Sychronisationsregimen hin. Abschließend wird die Möglichkeit dokumentiert, das Phänomen der Synchronisation zweier Orgelpfeifen durch numerische Simulationen, also der Behandlung der kompressiblen Navier-Stokes Gleichungen mit entsprechenden Rand- und Anfangsbedingungen, realitätsnah abzubilden. Auch dies stellt ein Novum dar.
Bacteria respond to changing environmental conditions by switching the global pattern of expressed genes. In response to specific environmental stresses the cell activates several stress-specific molecules such as sigma factors. They reversibly bind the RNA polymerase to form the so-called holoenzyme and direct it towards the appropriate stress response genes. In exponentially growing E. coli cells, the majority of the transcriptional activity is carried out by the housekeeping sigma factor, while stress responses are often under the control of alternative sigma factors. Different sigma factors compete for binding to a limited pool of RNA polymerase (RNAP) core enzymes, providing a mechanism for cross talk between genes or gene classes via the sharing of expression machinery. To quantitatively analyze the contribution of sigma factor competition to global changes in gene expression, we develop a thermodynamic model that describes binding between sigma factors and core RNAP at equilibrium, transcription, non-specific binding to DNA and the modulation of the availability of the molecular components.
Association of housekeeping sigma factor to RNAP is generally favored by its abundance and higher binding affinity to the core. In order to promote transcription by alternative sigma subunits, the bacterial cell modulates the transcriptional efficiency in a reversible manner through several strategies such as anti-sigma factors, 6S RNA and generally any kind of transcriptional regulators (e.g. activators or inhibitors). By shifting the outcome of sigma factor competition for the core, these modulators bias the transcriptional program of the cell. The model is validated by comparison with in vitro competition experiments, with which excellent agreement is found. We observe that transcription is affected via the modulation of the concentrations of the different types of holoenzymes, so saturated promoters are only weakly affected by sigma factor competition. However, in case of overlapping promoters or promoters recognized by two types of sigma factors, we find that even saturated promoters are strongly affected.
Active transcription effectively lowers the affinity between the sigma factor driving it and the core RNAP, resulting in complex cross talk effects and raising the question of how their in vitro measure is relevant in the cell. We also estimate that sigma factor competition is not strongly affected by non-specific binding of core RNAPs, sigma factors, and holoenzymes to DNA. Finally, we analyze the role of increased core RNAP availability upon the shut-down of ribosomal RNA transcription during stringent response. We find that passive up-regulation of alternative sigma-dependent transcription is not only possible, but also displays hypersensitivity based on the sigma factor competition. Our theoretical analysis thus provides support for a significant role of passive control during that global switch of the gene expression program and gives new insights into RNAP partitioning in the cell.
In the presented thesis, the most advanced photon reconstruction technique of ground-based γ-ray astronomy is adapted to the H.E.S.S. 28 m telescope. The method is based on a semi-analytical model of electromagnetic particle showers in the atmosphere. The properties of cosmic γ-rays are reconstructed by comparing the camera image of the telescope with the Cherenkov emission that is expected from the shower model. To suppress the dominant background from charged cosmic rays, events are selected based on several criteria. The performance of the analysis is evaluated with simulated events. The method is then applied to two sources that are known to emit γ-rays. The first of these is the Crab Nebula, the standard candle of ground-based γ-ray astronomy. The results of this source confirm the expected performance of the reconstruction method, where the much lower energy threshold compared to H.E.S.S. I is of particular importance. A second analysis is performed on the region around the Galactic Centre. The analysis results emphasise the capabilities of the new telescope to measure γ-rays in an energy range that is interesting for both theoretical and experimental astrophysics. The presented analysis features the lowest energy threshold that has ever been reached in ground-based γ-ray astronomy, opening a new window to the precise measurement of the physical properties of time-variable sources at energies of several tens of GeV.
During this work I built a four wave mixing setup for the time-resolved femtosecond spectroscopy of Raman-active lattice modes. This setup enables to study the selective excitation of phonon polaritons. These quasi-particles arise from the coupling of electro-magnetic waves and transverse optical lattice modes, the so-called phonons. The phonon polaritons were investigated in the optically non-linear, ferroelectric crystals LiNbO₃ and LiTaO₃.
The direct observation of the frequency shift of the scattered narrow bandwidth probe pulses proofs the role of the Raman interaction during the probe and excitation process of phonon polaritons. I compare this experimental method with the measurement where ultra-short laser pulses are used. The frequency shift remains obscured by the relative broad bandwidth of these laser pulses. In an experiment with narrow bandwidth probe pulses, the Stokes and anti-Stokes intensities are spectrally separated. They are assigned to the corresponding counter-propagating wavepackets of phonon polaritons. Thus, the dynamics of these wavepackets was separately studied. Based on these findings, I develop the mathematical description of the so-called homodyne detection of light for the case of light scattering from counter propagating phonon polaritons.
Further, I modified the broad bandwidth of the ultra-short pump pulses using bandpass filters to generate two pump pulses with non-overlapping spectra. This enables the frequency-selective excitation of polariton modes in the sample, which allows me to observe even very weak polariton modes in LiNbO₃ or LiTaO₃ that belong to the higher branches of the dispersion relation of phonon polaritons. The experimentally determined dispersion relation of the phonon polaritons could therefore be extended and compared to theoretical models. In addition, I determined the frequency-dependent damping of phonon polaritons.
Wir schlagen einen allgemein anwendbaren Algorithmus vor, der unter Verwendung des Skalarprodukts von Kraft und Weg zum richtigen Vorzeichen in den Gleichungen für die Arbeit und die Potentielle Energie bei reversiblen Prozessen (Druck-Volumen-Änderung, Dehnung, Elektrostatische Wechselwirkung, Hub)führt. Wir zeigen, dass es dabei möglich ist, systemimmanente oder externe Kräfte zu benutzen. Wir zeigen, dass bei Verwendung von systemimmanenten Kräften das Skalarprodukt mit negativem Vorzeichen anzusetzen ist. Zudem ist es sehr wichtig, nötige Vorzeichenwechsel bei den einzelnen Schritten zu beachten. Wir betonen dies, weil gelegentlich übersehen wird, dass ein Vorzeichenwechsel nötig ist, wenn das Wegdifferential ds durch das Höhendifferential dh beziehungsweise durch das Abstandsdifferential dx oder dr ersetzt werden muss.