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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.
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.
Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced.
Acclimatization
(2003)
Together with their wives Otto and Richard Schomburgk arrived in Port Adelaide (South Australia) on August 16th 1849. The essay looks at how these two brothers, who had received their scientific training and promotion in the circle surrounding Alexander von Humboldt, reacted to the unfamiliar conditions in the young British colony. Some indication will be given as to the differences between the Schomburgk brothers treatment of the natural resources of the new colony and that of the English colonists of the time.
Interpretation of and reasoning with conditionals : probabilities, mental models, and causality
(2003)
In everyday conversation "if" is one of the most frequently used conjunctions. This dissertation investigates what meaning an everyday conditional transmits and what inferences it licenses. It is suggested that the nature of the relation between the two propositions in a conditional might play a major role for both questions. Thus, in the experiments reported here conditional statements that describe a causal relationship (e.g., "If you touch that wire, you will receive an electric shock") were compared to arbitrary conditional statements in which there is no meaningful relation between the antecedent and the consequent proposition (e.g., "If Napoleon is dead, then Bristol is in England"). Initially, central assumptions from several approaches to the meaning and the reasoning from causal conditionals will be integrated into a common model. In the model the availability of exceptional situations that have the power to generate exceptions to the rule described in the conditional (e.g., the electricity is turned off), reduces the subjective conditional probability of the consequent, given the antecedent (e.g., the probability of receiving an electric shock when touching the wire). This conditional probability determines people's degree of belief in the conditional, which in turn affects their willingness to accept valid inferences (e.g., "Peter touches the wire, therefore he receives an electric shock") in a reasoning task. Additionally to this indirect pathway, the model contains a direct pathway: Cognitive availability of exceptional situations directly reduces the readiness to accept valid conclusions. The first experimental series tested the integrated model for conditional statements embedded in pseudo-natural cover stories that either established a causal relation between the antecedent and the consequent event (causal conditionals) or did not connect the propositions in a meaningful way (arbitrary conditionals). The model was supported for the causal, but not for the arbitrary conditional statements. Furthermore, participants assigned lower degrees of belief to arbitrary than to causal conditionals. Is this effect due to the presence versus absence of a semantic link between antecedent and consequent in the conditionals? This question was one of the starting points for the second experimental series. Here, the credibility of the conditionals was manipulated by adding explicit frequency information about possible combinations of presence or absence of antecedent and consequent events to the problems (i.e., frequencies of cases of 1. true antecedent with true consequent, 2. true antecedent with false consequent, 3. false antecedent with true consequent, 4. false antecedent with false consequent). This paradigm allows testing different approaches to the meaning of conditionals (Experiment 4) as well as theories of conditional reasoning against each other (Experiment 5). The results of Experiment 4 supported mainly the conditional probability approach to the meaning of conditionals (Edgington, 1995) according to which the degree of belief a listener has in a conditional statement equals the conditional probability that the consequent is true given the antecedent (e.g., the probability of receiving an electric shock when touching the wire). Participants again assigned lower degrees of belief to the arbitrary than the causal conditionals, although the conditional probability of the consequent given the antecedent was held constant within every condition of explicit frequency information. This supports the hypothesis that the mere presence of a causal link enhances the believability of a conditional statement. In Experiment 5 participants solved conditional reasoning tasks from problems that contained explicit frequency information about possible relevant cases. The data favored the probabilistic approach to conditional reasoning advanced by Oaksford, Chater, and Larkin (2000). The two experimental series reported in this dissertation provide strong support for recent probabilistic theories: for the conditional probability approach to the meaning of conditionals by Edgington (1995) and the probabilistic approach to conditional reasoning by Oaksford et al. (2000). In the domain of conditional reasoning, there was additionally support for the modified mental model approaches by Markovits and Barrouillet (2002) and Schroyens and Schaeken (2003). Probabilistic and mental model approaches could be reconciled within a dual-process-model as suggested by Verschueren, Schaeken, and d'Ydewalle (2003).
Counting Markedness
(2003)
This paper reports the results of a corpus investigation on case conflicts in German argument free relative constructions. We investigate how corpus frequencies reflect the relative markedness of free relative and correlative constructions, the relative markedness of different case conflict configurations, and the relative markedness of different conflict resolution strategies. Section 1 introduces the conception of markedness as used in Optimality Theory. Section 2 introduces the facts about German free relative clauses, and section 3 presents the results of the corpus study. By and large, markedness and frequency go hand in hand. However, configurations at the highest end of the markedness scale rarely show up in corpus data, and for the configuration at the lowest end we found an unexpected outcome: the more marked structure is preferred.
During the past several decades polymer materials become widely used as components of medical devices and implants such as hemodialysers, bioartificial organs as well as vascular and recombinant surgery. Most of the devices cannot avoid the blood contact in their use. When the polymer materials come in contact with blood they can cause different undesired host responses like thrombosis, inflammatory reactions and infections. Thus the materials must be hemocompatible in order to minimize these undesired body responses. The earliest and one of the main problems in the use of blood-contacting biomaterials is the surface induced thrombosis. The sequence of the thrombus formation on the artificial surfaces has been well established. The first event, which occurs, after exposure of biomaterials to blood, is the adsorption of blood proteins. Surface physicochemical properties of the materials as wettability greatly influence the amount and conformational changes of adsorbed proteins. In turn the type, amount and conformational state of the adsorbed protein layer determines whether platelets will adhere and become activated or not on the artificial surface and thus to complete the thrombus formation. The adsorption of fibrinogen (FNG), which is present in plasma, has been shown to be closely related to surface induced thrombosis by participating in all processes of the thrombus formation such as fibrin formation, platelet adhesion and aggregation. Therefore study the FNG adsorption to artificial surfaces could contribute to better understanding of the mechanisms of platelet adhesion and activation and thus to controlling the surface induced thrombosis. Endothelization of the polymer surfaces is one of the strategies for improving the materials hemocompatibility, which is believed to be the most ideal solution for making truly blood-compatible materials. Since at physiological conditions proteins such as FNG and fibronectin (FN) are the usual extracellular matrix (ECM) for endothelial cells (EC) adhesion, precoating of the materials with these proteins has been shown to improve EC adhesion and growth in vitro. ECM proteins play an essential role not only like a structural support for cell adhesion and spreading, but also they are important factor in transmitting signals for different cell functions. The ability of cells to remodel plasma proteins such as FNG and FN in matrix-like structures together with the classical cell parameters such as actin cytoskeleton and focal adhesion formation could be used as an criteria for proper cell functioning. The establishment and the maintaining of delicate balance between cell-cell and cell-substrate contacts is another important factor for better EC colonization of the implants. The functionality of newly established endothelium in order to produce antithromotic substances should be always considered when EC seeding is used for improving the hemocompatibility of the polymer materials. Controlling the polymer surface properties such as surface wettability represents a versatile approach to manipulate the above cellular responses and therefore can be used in biomaterial and tissue engineering applications for producing better hemocompatible materials.
This paper argues that the texts surviving from the Old English period do not reflect the spoken language of the bulk of the population under Anglo-Saxon elite domination. While the Old English written documents suggest that the language was kept remarkably unchanged, i.e. was strongly monitored during the long OE period (some 500 years!), the spoken and "real Old English" is likely to have been very different and much more of the type of Middle English than the written texts. "Real Old Engish", i.e. of course only appeared in writing after the Norman Conquest. Middle English is therefore claimed to have begun with the 'late British' speaking shifters to Old English. The shift patterns must have differed in the various part of the island of Britain, as the shifters became exposed to further language contact with the Old Norse adstrate in the Danelaw areas and the Norman superstrate particularly in the South East, the South West having been least exposed to language contact after the original shift from 'Late British' to Old English. This explains why the North was historically the most innovative zone. This also explains the conservatism of the present day dialects in the South West. It is high time that historical linguists acknowledge the arcane character of the Old English written texts.
Studies of the role of disturbance in vegetation or ecosystems showed that disturbances are an essential and intrinsic element of ecosystems that contribute substantially to ecosystem health, to structural diversity of ecosystems and to nutrient cycling at the local as well as global level. Fire as a grassland, bush or forest fire is a special disturbance agent, since it is caused by biotic as well abiotic environmental factors. Fire affects biogeochemical cycles and plays an important role in atmospheric chemistry by releasing climate-sensitive trace gases and aerosols, and thus in the global carbon cycle by releasing approximately 3.9 Gt C p.a. through biomass burning. A combined model to describe effects and feedbacks between fire and vegetation became relevant as changes in fire regimes due to land use and land management were observed and the global dimension of biomass burnt as an important carbon flux to the atmosphere, its influence on atmospheric chemistry and climate as well as vegetation dynamics were emphasized. The existing modelling approaches would not allow these investigations. As a consequence, an optimal set of variables that best describes fire occurrence, fire spread and its effects in ecosystems had to be defined, which can simulate observed fire regimes and help to analyse interactions between fire and vegetation dynamics as well as to allude to the reasons behind changing fire regimes. Especially, dynamic links between vegetation, climate and fire processes are required to analyse dynamic feedbacks and effects of changes of single environmental factors. This led us to the point, where new fire models had to be developed that would allow the investigations, mentioned above, and could help to improve our understanding of the role of fire in global ecology. In conclusion of the thesis, one can state that moisture conditions, its persistence over time and fuel load are the important components that describe global fire pattern. If time series of a particular region are to be reproduced, specific ignition sources, fire-critical climate conditions and vegetation composition become additional determinants. Vegetation composition changes the level of fire occurrence and spread, but has limited impact on the inter-annual variability of fire. The importance to consider the full range of major fire processes and links to vegetation dynamics become apparent under climate change conditions. Increases in climate-dependent length of fire season does not automatically imply increases in biomass burnt, it can be buffered or accelerated by changes in vegetation productivity. Changes in vegetation composition as well as enhanced vegetation productivity can intensify changes in fire and lead to even more fire-related emissions. --- Anmerkung: Die Autorin ist Trägerin des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2002/2003.