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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.
In dieser Arbeit wird den verschiedenen Thesen, die das Wahlverhalten in Ostdeutschland begründen, nachgegangen. Der Einbezug der politischen Kultur scheint als Erweiterung des sozialpsychologischen Ansatzes notwendig, um das Wählerverhalten in den neuen Bundesländern angemessen zu modellieren. Für die Analyse der Parteiaffinitäten werden die in den ersten beiden Kapiteln ausgearbeiteten Deutungen zu empirisch überprüfbaren Hypothesen verdichtet und anhand der im empirischen Teil der Arbeit aufgestellten Regressionsmodelle getestet. Inhalt: Die politische Kultur in Ostdeutschland - Besonderheiten politischer Einstellungen: Einstellungen zur Demokratie, Identitätsabgrenzung - Problemwahrnehmungen und Kompetenzzuweisungen Ostdeutsches Wahlverhalten - Thesen - Politisierung der Sozialstruktur - Anwendbarkeit des Konzeptes Parteiidentifikation - Parteiidentifikation und Sozialstruktur - Sachthemen und Kandidaten Empirischer Test - Daten und Methode: Kausalmodell - Hypothesen - Ergebnisse für die einzelnen Parteien: CDU, SPD, PDS - Relatives Gewicht lang- und kurzfristiger Faktoren Fazit - Diskussion der Ergebnisse
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.
Der Beitrag “Humboldteanisierung des Westens? Die Bedeutung der Reise Humboldts für Europa und Lateinamerika” behandelt der preußischen emprischen Universalgelehrten, in Übereinstimmung mit dem von Ottmar Ette entwickelten Konzept, als einen, wenn nicht den wichtigsten Begründer der westlichen Moderne. Im Gegensatz zu den bekannten Gründern der Moderne (Descartes, Kant, Buffon, Schiller, Hegel, Marx ... etc.) war Humboldt Empiriker und Globaldenker und er tat dies auf transkulturelle Weise, manchmal auch schon auf interkulturelle Weise; allerdings meist auf Basis der römisch-klassizistischen Denktradition und Ästhetik Europas. Der Beitrag arbeitet drei Wissenstypen Humboldts heraus und versucht zu zeigen, dass der Universalismus Humboldt wichtige interkulturelle Grundlagen in der Kommunikation mit amerikanischen Gelehrten und im amerikanischen Empirismus (“lokales Wissen”) hat. Die Bedeutung einer solchen Konzeption der Humboldt-Reise zeigt sich – in der Negierung – in den gegenwärtigen Debatten um Diasporas und “Race” im atlantischen Westen (“Black Atlantic”). Humboldt Kenntnisse der amerikanischen Sklavereien und seine absolute Verurteilung der Sklaverei ist dabei nicht präsent.
Im zweiten Teil zeigt der Beitrag mögliche Lesarten der Humboldt-Tagebücher, indem er “imaginäre Humboldt-Essays” konstruiert.
Ecological and evolutionary dynamics can occur on similar timescales. However, theoretical predictions of how rapid evolution can affect ecological dynamics are inconclusive and often depend on untested model assumptions. Here we report that rapid prey evolution in response to oscillating predator density affects predator-prey (rotifer-algal) cycles in laboratory microcosms. Our experiments tested explicit predictions from a model for our system that allows prey evolution. We verified the predicted existence of an evolutionary tradeoff between algal competitive ability and defence against consumption, and examined its effects on cycle dynamics by manipulating the evolutionary potential of the prey population. Single-clone algal cultures (lacking genetic variability) produced short cycle periods and typical quarter-period phase lags between prey and predator densities, whereas multi-clonal (genetically variable) algal cultures produced long cycles with prey and predator densities nearly out of phase, exactly as predicted. These results confirm that prey evolution can substantially alter predator-prey dynamics, and therefore that attempts to understand population oscillations in nature cannot neglect potential effects from ongoing rapid evolution.
From the stem bark of Erythrina burttii, a new isoflavone, 5,2',4'-trihydroxy-7-methoxy-6-(3- methylbut-2-enyl)isoflavone (trivial name, 7-O-methylluteone) and a new flavanone, 5,7-dihydroxy-4'-methoxy- 3'-(3-methylbutadienyl)-5'-(3-methylbut-2-enyl)flavanone (trivial name, burttinonedehydrate) along with three known isoflavonoids (8-prenylluteone, 3-O-methylcalopocarpin and genistein) were isolated. The structures were detd. on the basis of spectroscopic evidence.