Institut für Physik und Astronomie
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Institute
This work incorporates three treatises which are commonly concerned with a stochastic theory of the Lyapunov exponents. With the help of this theory universal scaling laws are investigated which appear in coupled chaotic and disordered systems. First, two continuous-time stochastic models for weakly coupled chaotic systems are introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck formalism scaling relations are derived, which are confirmed by results of numerical simulations. Next, coupling sensitivity is shown to exist for coupled disordered chains, where it appears as a singular increase of the localization length. Numerical findings for coupled Anderson models are confirmed by analytic results for coupled continuous-space Schrödinger equations. The resulting scaling relation of the localization length resembles the scaling of the Lyapunov exponent of coupled chaotic systems. Finally, the statistics of the exponential growth rate of the linear oscillator with parametric noise are studied. It is shown that the distribution of the finite-time Lyapunov exponent deviates from a Gaussian one. By means of the generalized Lyapunov exponents the parameter range is determined where the non-Gaussian part of the distribution is significant and multiscaling becomes essential.
Concerns have been raised that anthropogenic climate change could lead to large-scale singular climate events, i.e., abrupt nonlinear climate changes with repercussions on regional to global scales. One central goal of this thesis is the development of models of two representative components of the climate system that could exhibit singular behavior: the Atlantic thermohaline circulation (THC) and the Indian monsoon. These models are conceived so as to fulfill the main requirements of integrated assessment modeling, i.e., reliability, computational efficiency, transparency and flexibility. The model of the THC is an interhemispheric four-box model calibrated against data generated with a coupled climate model of intermediate complexity. It is designed to be driven by global mean temperature change which is translated into regional fluxes of heat and freshwater through a linear down-scaling procedure. Results of a large number of transient climate change simulations indicate that the reduced-form THC model is able to emulate key features of the behavior of comprehensive climate models such as the sensitivity of the THC to the amount, regional distribution and rate of change in the heat and freshwater fluxes. The Indian monsoon is described by a novel one-dimensional box model of the tropical atmosphere. It includes representations of the radiative and surface fluxes, the hydrological cycle and surface hydrology. Despite its high degree of idealization, the model satisfactorily captures relevant aspects of the observed monsoon dynamics, such as the annual course of precipitation and the onset and withdrawal of the summer monsoon. Also, the model exhibits the sensitivity to changes in greenhouse gas and sulfate aerosol concentrations that are known from comprehensive models. A simplified version of the monsoon model is employed for the identification of changes in the qualitative system behavior against changes in boundary conditions. The most notable result is that under summer conditions a saddle-node bifurcation occurs at critical values of the planetary albedo or insolation. Furthermore, the system exhibits two stable equilibria: besides the wet summer monsoon, a stable state exists which is characterized by a weak hydrological cycle. These results are remarkable insofar, as they indicate that anthropogenic perturbations of the planetary albedo such as sulfur emissions and/or land-use changes could destabilize the Indian summer monsoon. The reduced-form THC model is employed in an exemplary integrated assessment application. Drawing on the conceptual and methodological framework of the tolerable windows approach, emissions corridors (i.e., admissible ranges of CO2- emissions) are derived that limit the risk of a THC collapse while considering expectations about the socio-economically acceptable pace of emissions reductions. Results indicate, for example, a large dependency of the width of the emissions corridor on climate and hydrological sensitivity: for low values of climate and/or hydrological sensitivity, the corridor boundaries are far from being transgressed by any plausible emissions scenario for the 21st century. In contrast, for high values of both quantities low non-intervention scenarios leave the corridor already in the early decades of the 21st century. This implies that if the risk of a THC collapse is to be kept low, business-as-usual paths would need to be abandoned within the next two decades. All in all, this thesis highlights the value of reduced-form modeling by presenting a number of applications of this class of models, ranging from sensitivity and bifurcation analysis to integrated assessment. The results achieved and conclusions drawn provide a useful contribution to the scientific and policy debate about the consequences of anthropogenic climate change and the long-term goals of climate protection. --- Anmerkung: Die Autorin ist Trägerin des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2003/2004.
We present the first separate spectra of both components of the small-separation double QSO HE 0512-3329 obtained with HST/STIS in the optical and near UV. The similarities especially of the emission line profiles and redshifts strongly suggest that this system really consists of two lensed images of one and the same source. The emission line flux ratios are assumed to be unaffected by microlensing and are used to study the differential extinction effects caused by the lensing galaxy. Fits of empirical laws show that the extinction properties seem to be different on both lines of sight. With our new results, HE 0512-3329 becomes one of the few extragalactic systems which show the 2175 Å absorption feature, although the detection is only marginal. We then correct the continuum flux ratio for extinction to obtain the differential microlensing signal. Since this may still be significantly affected by variability and time-delay effects, no detailled analysis of the microlensing is possible at the moment. This is the first time that differential extinction and microlensing could be separated unambiguously. We show that, at least in HE 0512-3329, both effects contribute significantly to the spectral differences and one cannot be analysed without taking into account the other. For lens modelling purposes, the flux ratios can only be used after correcting for both effects.
We present a determination of the optical/UV AGN luminosity function and its evolution, based on a large sample of faint (R < 24) QSOs identified in the COMBO-17 survey. Using multi-band photometry in 17 filters within 350 nm <~ lambdaobs <~ 930 nm, we could simultaneously determine photometric redshifts with an accuracy of sigmaz <0.03 and obtain spectral energy distributions. The redshift range covered by the sample is 1.2 < z < 4.8, which implies that even at z =~ 3, the sample reaches below luminosities corresponding to MB = -23, conventionally employed to distinguish between Seyfert galaxies and quasars. We clearly detect a broad plateau-like maximum of quasar activity around z =~ 2 and map out the smooth turnover between z =~ 1 and z =~ 4. The shape of the LF is characterised by some mild curvature, but no sharp ``break'' is present within the range of luminosities covered. Using only the COMBO-17 data, the evolving LF can be adequately described by either a pure density evolution (PDE) or a pure luminosity evolution (PLE) model. However, the absence of a strong L*-like feature in the shape of the LF inhibits a robust distinction between these modes. We present a robust estimate for the integrated UV luminosity generation by AGN as a function of redshift. We find that the LF continues to rise even at the lowest luminosities probed by our survey, but that the slope is sufficiently shallow that the contribution of low-luminosity AGN to the UV luminosity density is negligible. Although our sample reaches much fainter flux levels than previous data sets, our results on space densities and LF slopes are completely consistent with extrapolations from recent major surveys such as SDSS and 2QZ.
Integral-field spectrophotometry of the quadruple QSO HE 0435-1223 : Evidence for microlensing
(2003)
We present the first spatially resolved spectroscopic observations of the recently discovered quadruple QSO and gravitational lens HE 0435-1223. Using the Potsdam Multi-Aperture Spectrophotometer (PMAS), we show that all four QSO components have very similar but not identical spectra. In particular, the spectral slopes of components A, B, and D are indistinguishable, implying that extinction due to dust plays no major role in the lensing galaxy. While also the emission line profiles are identical within the error bars, as expected from lensing, the equivalent widths show significant differences between components. Most likely, microlensing is responsible for this phenomenon. This is also consistent with the fact that component D, which shows the highest relative continuum level, has brightened by 0.07 mag since Dec. 2001. We find that the emission line flux ratios between the components are in better agreement with simple lens models than broad band or continuum measurements, but that the discrepancies between model and data are still unacceptably large. Finally, we present a detection of the lensing galaxy, although this is close to the limits of the data. Comparing with a model galaxy spectrum, we obtain a redshift estimate of zlens=0.44+/- 0.02.
We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations
We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties
Multiple landslide clusters record quaternary climate changes in the northwestern Argentine andes
(2003)
The chronology of multiple landslide deposits and related lake sediments in the semi-arid eastern Argentine Cordillera suggests that major mass movements cluster in two time periods during the Quaternary, i.e. between 40 and 25 and after 5 14C kyr BP. These clusters may correspond to the Minchin (maximum at around 28-27 14C kyr BP) and Titicaca wet periods (after 3.9 14C kyr BP). The more humid conditions apparently caused enhanced landsliding in this environment. In contrast, no landslide-related damming and associated lake sediments occurred during the Coipasa (11.5- 10 14C yr BP) and Tauca wet periods (14.5-11 14C yr BP). The two clusters at 40-25 and after 5 14C kyr BP may correspond to periods where the El Niño-Southern Oscillation (ENSO) and Tropical Atlantic Sea Surface Temperature Variability (TAV) were active. This, however, was not the case during the Coipasa and Tauca wet periods. Lake-balance modelling of a landslide-dammed lake suggests a 10-15% increase in precipitation and a 3-4 ° C decrease in temperature at ~30 14C kyr BP as compared to the present. In addition, time-series analysis reveals a strong ENSO and TAV during that time. The landslide clusters in northwestern Argentina are therefore best explained by periods of more humid and more variable climates.
We present a detailed study of the effects of gravitational microlensing on compact and distant gamma-ray blazars. These objects have gamma-ray-emitting regions that are small enough to be affected by microlensing effects produced by stars lying in intermediate galaxies. We compute the gravitational magnification taking into account effects of the lensing and show that, whereas the innermost gamma-ray spheres can be significantly magnified, there is little magnification either for very high gamma-ray energies or for lower (radio) frequencies (because these wavelengths are emitted from larger regions). We analyse the temporal evolution of the gamma-ray magnification for sources moving in a caustic pattern field, where the combined effects of thousands of stars are taken into account using a numerical technique. We propose that some of the unidentified gamma-ray sources (particularly some of those lying at high galactic latitude with gamma-ray statistical properties that are very similar to detected gamma-ray blazars) are indeed the result of gravitational lensing magnification of background undetected active galactic nuclei (AGN). This is partly supported from a statistical point of view: we show herein as well, using the latest information from the third EGRET catalogue, that high-latitude gamma-ray sources have similar averaged properties to already detected gamma-ray AGN. Some differences between both samples, regarding the mean flux level, could also be understood within the lensing model. With an adequate selection of lensing parameters, it is possible to explain a variety of gamma-ray light curves with different time-scales, including non-variable sources. The absence of strong radio counterparts could be naturally explained by differential magnification in the extended source formalism.
Biochemical and genetic regulatory systems that involve low concentrations of molecules are inherently noisy. This intrinsic stochasticity, has received considerable interest recently, leading to new insights about the sources and consequences of noise in complex systems of genetic regulation. However, most prior work was devoted to the reduction of fluctuation and the robustness of cellular function with respect to intrinsic noise. Here, we focus on several scenarios in which the inherent molecular fluctuations are not merely a nuisance, but act constructively and bring about qualitative changes in the dynamics of the system. It will be demonstrated that in many typical situations biochemical and genetic regulatory systems may utilize intrinsic noise to their advantage. (C) 2002 Elsevier Ireland Ltd. All rights reserved
Correlations, as observed between the concentrations of metabolites in a biological sample, may be used to gain additional information about the physiological state of a given tissue. in this mini-review, we discuss the integration of these observed correlations into metabolomic networks and their relationships with the underlying biochemical pathways
Compact white-light source with an average output power of 2.4 W and 900 nm spectral bandwidth
(2003)
Due to their extremely small luminosity compared to the stars they orbit, planets outside our own Solar System are extraordinarily difficult to detect directly in optical light. Careful photometric monitoring of distant stars, however, can reveal the presence of exoplanets via the microlensing or eclipsing effects they induce. The international PLANET collaboration is performing such monitoring using a cadre of semi-dedicated telescopes around the world. Their results constrain the number of gas giants orbiting 1-7 AU from the most typical stars in the Galaxy. Upgrades in the program are opening regions of ''exoplanet discovery space'' - toward smaller masses and larger orbital radii - that are inaccessible to the Doppler velocity technique.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
In-situ Wachstumsuntersuchungen beim reaktiven Anlassen von Cu, In Schichten in elementarem Schwefel
(2003)
In dieser Arbeit wurde das reaktive Anlassen von dünnen Kupfer-Indium-Schichten in elementarem Schwefel mittels energiedispersiver Röntgenbeugung untersucht. Durch die simultane Aufnahme der Röntgenspektren und der Messung der diffusen Reflexion von Laserlicht der Wellenlänge 635 nm an der Oberfläche der Probe während des Schichtwachstums von CuInS<SUB>2</SUB> konnte eine Methode zur Prozesskontrolle für ein Herstellungsverfahren von CuInS<SUB>2</SUB> etabliert werden. Die Bildung von CuInS<SUB>2</SUB> aus Kupfer-Indium-Vorläuferschichten wird dominiert von Umwandlungen der intermetallischen Phasen. CuInS<SUB>2</SUB> wächst innerhalb der Aufheizperiode ab einer Temperatur von ca. 200°C aus der Phase Cu11In9. Jedoch zerfällt letztere metallische Phase in Cu16In9 und flüssiges Indium bei einer Temperatur von ca. 310°C. Das flüssige Indium reagiert im Falle von Kupferarmut mit dem Schwefel und führt zu einem zusätzlichen Reaktionspfad über InS zu CuIn5S8. Unter Präparationsbedingungen mit Kupferüberschuss wird das Indium in einer intermetallischen Phase gebunden.Erstmals konnte die Phase Digenite bei Temperaturen über 240°C beobachtet werden. Beim Abkühlen auf Raumtemperatur wandelt sich diese Phase unter dem Verbrauch von Schwefel in Covellite um.Für Proben mit Kupferüberschuss konnte eine Wachstumskinetik proportional zur Temperatur beobachtet werden. Dieses Verhalten wurde durch eine stress-induzierte Diffusion als dominierenden Reaktionsmechanismus interpretiert. Dabei werden während der Bildung von CuInS<SUB>2</SUB> durch unterschiedliche Ausdehnungen der metallischen und sulfidischen Schichten eine Spannung in der CuInS<SUB>2</SUB>-Schicht induziert, die nach Überschreiten einer Grenzspannung zu Rissen in der CuInS2-Schicht führt. Entlang dieser Risse findet ein schneller Transport der Metalle zur Oberfläche, wo diese mit dem Schwefel reagieren können, statt. Die Risse heilen durch die Bildung neuen Sulfids wieder aus.
Thin Layers of columns of an amphiphilic hexa-peri-hexabenzocoronene at silicon wafer surfaces
(2003)
This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient
The central star of the PN LMC-N66 showed an impressive outburst in 1993 - 1994, returning to its initial conditions about 8 years later. Its spectrum resembles that of a WN4.5 star, being the only confirmed central star of planetary nebulae showing such a spectral type. Recent analysis for the central star parameters, performed by Hamann et al. (2003) is presented. They have found that the bolometric luminosity increased by a factor larger than 6, during the outburst. We discuss the possible scenarios which have been proposed to explain the exceptional stellar parameters and the outburst mechanism. The stellar characteristics and the morphology and kinematics of the planetary nebula suggest the presence of binary system (massive star with a less massive companion or, a white dwarf accreting matter in a close- binary system). These cases pose the least severe contradictions with observational constraints.
The carbon-rich WC5 star WR 114 was not detected during a 15.9 ksec XMM-Newton observation, implying an upper limit to the X-ray luminosity of Lx < 2.5 x 1030 ergs-1 and to the X-ray to bolometric luminosity ratio of Lx/Lbol < 4 x 10-9. This confirms indications from earlier less sensitive measurements that there has been no convincing X-ray detection of any single WC star. This lack of detections is reinforced by XMM-Newton and CHANDRA observations of WC stars. Thus the conclusion has to be drawn that the stars with radiatively-driven stellar winds of this particular class are insignificant X-ray sources. We attribute this to photoelectronic absorption by the stellar wind. The high opacity of the metal-rich and dense winds from WC stars puts the radius of optical depth unity at hundreds or thousands of stellar radii for much of the X-ray band. We believe that the essential absence of hot plasma so far out in the wind exacerbated by the large distances and correspondingly high ISM column densities makes the WC stars too faint to be detectable with current technology. The result also applies to many WC stars in binary systems, of which only about 20 % are identified X-ray sources, presumably due to colliding winds.
Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26°S, 66°W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Niño/ Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.
Encounters with neighbours
(2003)
In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications. Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed. Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots.