Institut für Physik und Astronomie
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In dieser Arbeit werden Konzepte für die Diagnostik der großskaligen Zirkulation in der Troposphäre und Stratosphäre entwickelt. Der Fokus liegt dabei auf dem Energiehaushalt, auf der Wellenausbreitung und auf der Interaktion der atmosphärischen Wellen mit dem Grundstrom. Die Konzepte werden hergeleitet, wobei eine neue Form des lokalen Eliassen-Palm-Flusses unter Einbeziehung der Feuchte eingeführt wird. Angewendet wird die Diagnostik dann auf den Reanalysedatensatz ERA-Interim und einen durch beobachtete Meerestemperatur- und Eisdaten angetriebenen Lauf des ECHAM6 Atmosphärenmodells. Die diagnostischen Werkzeuge zur Analyse der großskaligen Zirkulation sind einerseits nützlich, um das Verständnis der Dynamik des Klimasystems weiter zu fördern. Andererseits kann das gewonnene Verständnis des Zusammenhangs von Energiequellen und -senken sowie deren Verknüpfung mit synoptischen und planetaren Wellensystemen und dem resultierenden Antrieb des Grundstroms auch verwendet werden, um Klimamodelle auf die korrekte Wiedergabe dieser Beobachtungen zu prüfen. Hier zeigt sich, dass die Abweichungen im untersuchten ECHAM6-Modelllauf bezüglich des Energiehaushalts klein sind, jedoch teils starke Abweichungen bezüglich der Ausbreitung von atmosphärischen Wellen existieren. Planetare Wellen zeigen allgemein zu große Intensitäten in den Eliassen-Palm-Flüssen, während innerhalb der Strahlströme der oberen Troposphäre der Antrieb des Grundstroms durch synoptische Wellen verfälscht ist, da deren vertikale Ausbreitung gegenüber den Beobachtungen verschoben ist. Untersucht wird auch der Einfluss von arktischen Meereisänderungen ausgehend vom Bedeckungsminimum im August/September bis in den Winter. Es werden starke positive Temperaturanomalien festgestellt, welche an der Oberfläche am größten sind. Diese führen vor allem im Herbst zur Intensivierung von synoptischen Systemen in den arktischen Breiten, da die Stabilität der troposphärischen Schichtung verringert ist. Im darauffolgenden Winter stellen sich barotrope bis in die Stratosphäre reichende Änderungen der großskaligen Zirkulation ein, welche auf Meereisänderungen zurückzuführen sind. Der meridionale Druckgradient sinkt und führt so zu einem Muster ähnlich einer negativen Phase der arktischen Oszillation in der Troposphäre und einem geschwächten Polarwirbel in der Stratosphäre. Diese Zusammenhänge werden ebenfalls in einem ECHAM6-Modelllauf untersucht, wobei vor allem der Erwärmungstrend in der Arktis zu gering ist. Die großskaligen Veränderungen im Winter können zum Teil auch im Modelllauf festgestellt werden, jedoch zeigen sich insbesondere in der Stratosphäre Abweichungen für die Periode mit der geringsten Eisausdehnung. Die vertikale Ausbreitung planetarer Wellen von der Troposphäre in die Stratosphäre ist in ECHAM6 mit sehr großen Abweichungen wiedergegeben. Somit stellt die Wellenausbreitung insgesamt den größten in dieser Arbeit festgestellten Mangel in ECHAM6 dar.
Within the course of this thesis, I have investigated the complex interplay between electron and lattice dynamics in nanostructures of perovskite oxides. Femtosecond hard X-ray pulses were utilized to probe the evolution of atomic rearrangement directly, which is driven by ultrafast optical excitation of electrons. The physics of complex materials with a large number of degrees of freedom can be interpreted once the exact fingerprint of ultrafast lattice dynamics in time-resolved X-ray diffraction experiments for a simple model system is well known. The motion of atoms in a crystal can be probed directly and in real-time by femtosecond pulses of hard X-ray radiation in a pump-probe scheme. In order to provide such ultrashort X-ray pulses, I have built up a laser-driven plasma X-ray source. The setup was extended by a stable goniometer, a two-dimensional X-ray detector and a cryogen-free cryostat. The data acquisition routines of the diffractometer for these ultrafast X-ray diffraction experiments were further improved in terms of signal-to-noise ratio and angular resolution. The implementation of a high-speed reciprocal-space mapping technique allowed for a two-dimensional structural analysis with femtosecond temporal resolution. I have studied the ultrafast lattice dynamics, namely the excitation and propagation of coherent phonons, in photoexcited thin films and superlattice structures of the metallic perovskite SrRuO3. Due to the quasi-instantaneous coupling of the lattice to the optically excited electrons in this material a spatially and temporally well-defined thermal stress profile is generated in SrRuO3. This enables understanding the effect of the resulting coherent lattice dynamics in time-resolved X-ray diffraction data in great detail, e.g. the appearance of a transient Bragg peak splitting in both thin films and superlattice structures of SrRuO3. In addition, a comprehensive simulation toolbox to calculate the ultrafast lattice dynamics and the resulting X-ray diffraction response in photoexcited one-dimensional crystalline structures was developed in this thesis work. With the powerful experimental and theoretical framework at hand, I have studied the excitation and propagation of coherent phonons in more complex material systems. In particular, I have revealed strongly localized charge carriers after above-bandgap femtosecond photoexcitation of the prototypical multiferroic BiFeO3, which are the origin of a quasi-instantaneous and spatially inhomogeneous stress that drives coherent phonons in a thin film of the multiferroic. In a structurally imperfect thin film of the ferroelectric Pb(Zr0.2Ti0.8)O3, the ultrafast reciprocal-space mapping technique was applied to follow a purely strain-induced change of mosaicity on a picosecond time scale. These results point to a strong coupling of in- and out-of-plane atomic motion exclusively mediated by structural defects.
We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems.
In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.
A novel atomic beam splitter, using reflection of atoms off an evanescent light wave, is investigated theoretically. The intensity or frequency of the light is modulated in order to create sidebands on the reflected de Broglie wave. The weights and phases of the various sidevands are calculated using three different approaches: the Born approximation, a semiclassical path integral approach, and a numerical solution of the time-dependent Schrdinger equation. We show how this modulated mirror could be used to build practical atomic interferometers.
We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed.
Das Strahlungsfeld in einem absorbierenden, periodischen Dielektrikum ist kanonisch quantisiert worden. Dabei wurde ein eindimensionales Modell mit punktförmigen Streuern betrachtet, deren Polarisierbarkeit den Kramers-Kronig Relationen gehorcht. Es wurde ein Quantisierungsverfahren nach Knöll, Scheel und Welsch [1] verwendet, das als eine Ergänzung zum mikroskopischen Huttner-Barnett Schema [2] aufgefaßt werden kann und in dem auf der Basis der phänomenologischen Maxwell Gleichungen eine bosonische Rauschpolarisation als die Quelle des Feldes auftritt. Das Problem reduziert sich dabei auf die Bestimmung der klassischenGreens Funktion. Die Kramers-Kronig Relationen der komplexen Polarisierbarkeit der Punktstreuer sichert die korrekte Verknüpfung zwischen Dispersion und Absorption. Der Punktstreuer ist dabei ein idealisiertes Modell, um periodische Hintergrundmedien, denen das Strahlungsfeld ausgesetzt ist, zu beschreiben. Er bedarf jedoch eines Kompromisses, um die entsprechenden Rauschquellen zu konstruieren. Es konnte gezeigt werden, daß der Punktstreuer dasselbe Streuverhalten wie eine dünne Potentialschwelle besitzt und damit die technischen Schwierigkeiten für den Fall eines absorptiven Punktstreuers überwunden werden können. An Hand dieses Beispiels konnte das Quantisierungsschema nach Knöll, Scheel und Welsch auf periodische und absorbierende Strukturen angewendet werden. Es ist bekannt, daß die Bestimmung der Modenstruktur für den Fall der Modenzerlegung des Strahlungsfeldes ein rein klassisches Problem darstellt. Mit Ausnahme des Vakuums ist eine zweckmäßige Modenzerlegung nur dann durchführbar, wenn mit einer reellen Polarisierbarkeit die Absorption vernachlässigt werden kann. Aus den Kramers-Kronig Relationen wird klar, daß solch eine Annahme nur in bestimmten Intervallen des Frequenzspektrums gerechtfertigt werden kann. Es wurde gezeigt, daß auch das quantisierte Strahlungsfeld in Anwesenheit der Punktstreuer in eben solchen Intervallen in Quasimoden entwickelt werden kann, wenn man neue Quasioperatoren als Erzeuger und Vernichter einführt. Die bosonischen Vertauschungsrelationen dieser Operatoren konnten bestätigt werden. Die allgemeine Vertauschungsrelation kanonisch konjugierter Variablen im Sinne der kanonischen Quantisierung kann für das elektrische Feld und das Vektorpotential beibehalten werden. In der Greens Funktion sind sämtliche Informationen über die dispersiven und absorptiven Eigenschaften des Dielektrikums sowie über die räumliche Struktur enthalten. Die wesentlichen Merkmale werden dabei durch den Reflexionskoeffizienten nach Boedecker und Henkel [3] bestimmt, der das Reflexionsverhalten an einem unendlich ausgedehnten Halbraum aus periodisch angeordneten Punktstreuern beschreibt. Mit Hilfe des Transfermatrixformalismus war es möglich einen allgemeinen Zugang zum Reflexionsverhalten zunächst endlicher Strukturen zu erhalten. Die Ausdehnung auf den Halbraum mit Hilfe der Klassifizierung in Untergruppen der Transfermatrizen nach ermöglichte es, den Reflexionskoeffizienten nach Boedecker und Henkel [3] auch geometrisch plausibel zu machen. Ein wesentlicher Aspekt von periodischen Systemen ist die Translationssymmetrie, die im Fall unendlich ausgedehnter, verlustfreier Systeme auf eine ideale Bandstruktur führt. Mit Hilfe der Untergruppenklassifizierung kann im verlustfreien Fall die Geometrie der Anordnung indirekt mit der Bandstruktur verknüpft werden. Es konnte nachgewiesen werden, daß auch der einzelne Punktstreuer immer in einer dieser Untergruppen zu finden ist. Dabei besitzt die Bandstruktur der unendlich periodischen Anordnung dieser Streuer immer eine von der Polarisierbarkeit abhängige Bandkante und eine von der Polarisierbarkeit unabhängige Bandkante. Die Bandstruktur, die mit den verlustbehafteten Feldern einhergeht, ist eine doppelt komplexe. Alternativ zu dieser nur schwer zu interpretierenden Bandstruktur wurden die Feldfluktuationen selektiv nach reellen Frequenzen und Wellenzahlen sondiert. Es zeigt sich, daß Absorption besonders in der Nähe der Bandkanten die Bänder verbreitert. Die Ergebnisse, die mit Hilfe der lokalen Zustandsdichtefunktion gewonnen wurden, konnten dabei bestätigt werden. [1] S. Scheel, L. Knöll and D. G. Welsch, Phys.Rev. A 58, 700 (1998). [2] B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992). [3] G. Boedecker and C. Henkel, OPTICS EXPRESS 11, 1590 (2003).
In Allefeld & Kurths [2004], we introduced an approach to multivariate phase synchronization analysis in the form of a Synchronization Cluster Analysis (SCA). A statistical model of a synchronization cluster was described, and an abbreviated instruction on how to apply this model to empirical data was given, while an implementation of the corresponding algorithm was (and is) available from the authors. In this letter, the complete details on how the data analysis algorithm is to be derived from the model are filled in.
In order to investigate the temporal characteristics of cognitive processing, we apply multivariate phase synchronization analysis to event-related potentials. The experimental design combines a semantic incongruity in a sentence context with a physical mismatch (color change). In the ERP average, these result in an N400 component and a P300-like positivity, respectively. The synchronization analysis shows an effect of global desynchronization in the theta band around 288ms after stimulus presentation for the semantic incongruity, while the physical mismatch elicits an increase of global synchronization in the alpha band around 204ms. Both of these effects clearly precede those in the ERP average. Moreover, the delay between synchronization effect and ERP component correlates with the complexity of the cognitive processes.
Phase synchronization analysis, including our recently introduced multivariate approach, is applied to event-related EEG data from an experiment on language processing, following a classic psycholinguistic paradigm. For the two types of experimental manipulation distinct effects in overall synchronization are found; for one of them they can also be localized. The synchronization effects occur earlier than those found by the conventional analysis method, indicating that the new approach provides additional information on the underlying neuronal process.
A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.
We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.
X-ray spectroscopy is a sensitive probe of stellar winds. X-rays originate from optically thin shock-heated plasma deep inside the wind and propagate outwards throughout absorbing cool material. Recent analyses of the line ratios from He-like ions in the X-ray spectra of O-stars highlighted problems with this general paradigm: the measured line ratios of highest ions are consistent with the location of the hottest X-ray emitting plasma very close to the base of the wind, perhaps indicating the presence of a corona, while measurements from lower ions conform with the wind-embedded shock model. Generally, to correctly model the emerging Xray spectra, a detailed knowledge of the cool wind opacities based on stellar atmosphere models is prerequisite. A nearly grey stellar wind opacity for the X-rays is deduced from the analyses of high-resolution X-ray spectra. This indicates that the stellar winds are strongly clumped. Furthermore, the nearly symmetric shape of X-ray emission line profiles can be explained if the wind clumps are radially compressed. In massive binaries the orbital variations of X-ray emission allow to probe the opacity of the stellar wind; results support the picture of strong wind clumping. In high-mass X-ray binaries, the stochastic X-ray variability and the extend of the stellar-wind part photoionized by X-rays provide further strong evidence that stellar winds consist of dense clumps.
Clumps in hot star winds can originate from shock compression due to the line driven instability. One-dimensional hydrodynamic simulations reveal a radial wind structure consisting of highly compressed shells separated by voids, and colliding with fast clouds. Two-dimensional simulations are still largely missing, despite first attempts. Clumpiness dramatically affects the radiative transfer and thus all wind diagnostics in the UV, optical, and in X-rays. The microturbulence approximation applied hitherto is currently superseded by a more sophisticated radiative transfer in stochastic media. Besides clumps, i.e. jumps in the density stratification, so-called kinks in the velocity law, i.e. jumps in dv/dr, play an eminent role in hot star winds. Kinks are a new type of radiative-acoustic shock, and propagate at super-Abbottic speed.
We investigate the effect of wind clumping on the dynamics of Wolf-Rayet winds, by means of the Potsdam Wolf-Rayet (PoWR) hydrodynamic atmosphere models. In the limit of microclumping the radiative acceleration is generally enhanced. We examine the reasons for this effect and show that the resulting wind structure depends critically on the assumed radial dependence of the clumping factor D(r). The observed terminal wind velocities for WR stars imply that D(r) increases to very large values in the outer part of the wind, in agreement with the assumption of detached expanding shells.
Mass accretion onto compact objects through accretion disks is a common phenomenon in the universe. It is seen in all energy domains from active galactic nuclei through cataclysmic variables (CVs) to young stellar objects. Because CVs are fairly easy to observe, they provide an ideal opportunity to study accretion disks in great detail and thus help us to understand accretion also in other energy ranges. Mass accretion in these objects is often accompanied by mass outflow from the disks. This accretion disk wind, at least in CVs, is thought to be radiatively driven, similar to O star winds. WOMPAT, a 3-D Monte Carlo radiative transfer code for accretion disk winds of CVs is presented.
Modeling expanding atmospheres is a difficult task because of the extreme non-LTE situation, the need to account for complex model atoms, especially for the iron-group elements with their millions of lines, and because of the supersonic expansion. Adequate codes have been developed e.g. by Hillier (CMFGEN), the Munich group (Puls, Pauldrach), and in Potsdam (PoWR code, Hamann et al.). While early work was based on the assumption of a smooth and homogeneous spherical stellar wind, the need to account for clumping became obvious about ten years ago. A relatively simple first-order clumping correction was readily implemented into the model codes. However, its simplifying assumptions are severe. Most importantly, the clumps are taken to be optically thin at all frequencies (”microclumping”). We discuss the consequences of this approximation and describe an approach to account for optically thick clumps (“macroclumping”). First results demonstrate that macroclumping can generally reduce the strength of spectral features, depending on their optical thickness. The recently reported discrepancy between the Hα diagnostic and the Pv resonance lines in O star spectra can be resolved without decreasing the mass-loss rates, when macroclumping is taken into account.
While there is strong evidence for clumping in the winds of massive hot stars, very little is known about clumping in the winds from Central Stars. We have checked [WC]-type CSPN winds for clumping by inspecting the electron-scattering line wings. At least for three stars we found indications for wind inhomogeneities.