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One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.
Line driven winds are accelerated by the momentum transfer from photons to a plasma, by absorption and scattering in numerous spectral lines. Line driving is most efficient for ultraviolet radiation, and at plasma temperatures from 10^4 K to 10^5 K. Astronomical objects which show line driven winds include stars of spectral type O, B, and A, Wolf-Rayet stars, and accretion disks over a wide range of scales, from disks in young stellar objects and cataclysmic variables to quasar disks. It is not yet possible to solve the full wind problem numerically, and treat the combined hydrodynamics, radiative transfer, and statistical equilibrium of these flows. The emphasis in the present writing is on wind hydrodynamics, with severe simplifications in the other two areas. I consider three topics in some detail, for reasons of personal involvement. 1. Wind instability, as caused by Doppler de-shadowing of gas parcels. The instability causes the wind gas to be compressed into dense shells enclosed by strong shocks. Fast clouds occur in the space between shells, and collide with the latter. This leads to X-ray flashes which may explain the observed X-ray emission from hot stars. 2. Wind runaway, as caused by a new type of radiative waves. The runaway may explain why observed line driven winds adopt fast, critical solutions instead of shallow (or breeze) solutions. Under certain conditions the wind settles on overloaded solutions, which show a broad deceleration region and kinks in their velocity law. 3. Magnetized winds, as launched from accretion disks around stars or in active galactic nuclei. Line driving is assisted by centrifugal forces along co-rotating poloidal magnetic field lines, and by Lorentz forces due to toroidal field gradients. A vortex sheet starting at the inner disk rim can lead to highly enhanced mass loss rates.
The behaviour of an adhering cell is strongly influenced by the chemical, topographical and mechanical properties of the surface it attaches to. During recent years, it has been found experimentally that adhering cells actively sense the elastic properties of their environment by pulling on it through numerous sites of adhesion. The resulting build-up of force at sites of adhesion depends on the elastic properties of the environment and is converted into corresponding biochemical signals, which can trigger cellular programmes like growth, differentiation, apoptosis, and migration. In general, force is an important regulator of biological systems, for example in hearing and touch, in wound healing, and in rolling adhesion of leukocytes on vessel walls. In the habilitation thesis by Ulrich Schwarz, several theoretical projects are presented which address the role of forces and elasticity in cell adhesion. (1) A new method has been developed for calculating cellular forces exerted at sites of focal adhesion on micro-patterned elastic substrates. The main result is that cell-matrix contacts function as mechanosensors, converting internal force into protein aggregation. (2) A one-step master equation for the stochastic dynamics of adhesion clusters as a function of cluster size, rebinding rate and force has been solved both analytically and numerically. Moreover this model has been applied to the regulation of cell-matrix contacts, to dynamic force spectroscopy, and to rolling adhesion. (3) Using linear elasticity theory and the concept of force dipoles, a model has been introduced and solved which predicts the positioning and orientation of mechanically active cells in soft material, in good agreement with experimental observations for fibroblasts on elastic substrates and in collagen gels.
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.
Western Anatolia that represents the eastward lateral continuation of the Aegean domain is composed of several tectono-metamorphic units showing occurrences of high-pressure/low-temperature (HP-LT) rocks. While some of these metamorphic rocks are vestiges of the Pan-African or Cimmerian orogenies, others are the result of the more recent Alpine orogenesis. In southwest Turkey, the Menderes Massif occupies an extensive area tectonically overlain by nappe units of the Izmir-Ankara Suture Zone in the north, the Afyon Zone in the east, and the Lycian Nappes in the south. In the present study, investigations in the metasediments of the Lycian Nappes and underlying southern Menderes Massif revealed widespread occurrences of Fe-Mg-carpholite-bearing rocks. This discovery leads to the very first consideration that both nappe complexes recorded HP-LT metamorphic conditions during the Alpine orogenesis. P-T conditions for the HP metamorphic peak are about 10-12 kbar/400°C in the Lycian Nappes, and 12-14 kbar/470-500°C in the southern Menderes Massif, documenting a burial of at least 30 km during subduction and nappe stacking. Ductile deformation analysis in concert with multi-equilibrium thermobarometric calculations reveals that metasediments from the Lycian Nappes recorded distinct exhumation patterns after a common HP metamorphic peak. The rocks located far from the contact separating the Lycian Nappes and the Menderes Massif, where HP parageneses are well preserved, retained a single HP cooling path associated with top-to-the-NNE shearing related to the Akçakaya shear zone. This zone of strain localization is an intra-nappe contact that was active in the early stages of exhumation of HP rocks, within the stability field of Fe-Mg-carpholite. The rocks located close to the contact with the Menderes Massif, where HP parageneses are completely retrogressed into chlorite and mica, recorded warmer exhumation paths associated with top-to-the-E intense shearing. This deformation occurred after the southward emplacement of Lycian Nappes, and is contemporaneous with the reactivation of the ’Lycian Nappes-Menderes Massif′ contact as a major shear zone (the Gerit shear zone) that allowed late exhumation of HP parageneses under warmer conditions. The HP rocks from the southern Menderes Massif recorded a simple isothermal decompression at about 450°C during exhumation, and deformation during HP event and its exhumation is characterized by a severe N-S to NE-SW stretching. The age of the HP metamorphism recorded in the Lycian Nappes is assumed to range between the Latest Cretaceous (age of the youngest sediments in the Lycian allochthonous unit) and the Eocene (age of the Cycladic Blueschists). A probable Palaeocene age is suggested. The age of the HP metamorphism that affected the cover series of the Menderes Massif is constrained between the Middle Palaeocene (age of the uppermost metaolistostrome of the Menderes ’cover′) and the Middle Eocene (age of the HP metamorphism in the Dilek-Selçuk region that belongs to the Cycladic Complex). Apatite fission track data for the rocks on both sides of the ’Lycian Nappes/Menderes Massif’ contact suggest that these rocks were very close to the paleo-Earth surface in the Late Oligocene-Early Miocene time. This study in the Lycian Nappes and in the Menderes Massif establishes the existence of an extensive Alpine HP metamorphic belt in southwest Turkey. HP rocks were involved in the accretionary complex related to northward-verging subduction of the Neo-Tethys Ocean, Late Cretaceous obduction and subsequent Early Tertiary continental collision of the passive margin (Anatolide-Tauride block) beneath the active margin of the northern plate (Sakarya micro-continent). During the Eocene, the accretionary complex was made of three stacked HP units. The lowermost corresponds to the imbricated ’core′ and HP ’cover′ of the Menderes Massif, the intermediate one consists of the Cycladic Blueschist Complex (Dilek-Selçuk unit), and the uppermost unit is made of the HP Lycian Nappes. Whereas the basement units of both Aegean and Anatolian regions underwent a different pre-Mesozoic tectonic history, they were probably juxtaposed by the end of the Paleozoic and underwent a common Mesozoic history. Then, the basements and their cover, as well as the Cycladic Blueschists and the Lycian Nappes were involved in similar evolutional accretionary complexes during the Eocene and Oligocene times.
A polymer is a large molecule made up of many elementary chemical units, joined together by covalent bonds (for example, polyethylene). Polyelectrolytes (PELs) are polymer chains containing a certain amount of ionizable monomers. With their specific properties PELs acquire big importance in molecular and cell biology as well as in technology. Compared to neutral polymers the theory of PELs is less understood. In particular, this is valid for PELs in poor solvents. A poor solvent environment causes an effective attraction between monomers. Hence, for PELs in a poor solvent, there occurs a competition between attraction and repulsion. Strong or quenched PELs are completely dissociated at any accessible pH. The position of charges along the chain is fixed by chemical synthesis. On the other hand, in weak or annealed PELs dissociation of charges depends on solution pH. For the first time the simulation results have given direct evidence that at rather poor solvents an annealed PEL indeed undergoes a first-order phase transition when the chemical potential (solution pH) reaches at a certain value. The discontinuous transition occurs between a weakly charged compact globular structure and a strongly charged stretched configuration. At not too poor solvents theory predicts that globule would become unstable with respect to the formation of pearl-necklaces. The results show that pearl-necklaces exist in annealed PELs indeed. Furthermore, as predicted by theory, the simulation results have shown that annealed PELs display a sharp transition from a highly charged stretched state to a weakly charged globule at a critical salt concentration.
The dissertation examines aspects of the interlingual lexical processes of word recognition and word retrieval in Hungarian-German bilinguals learning English as a foreign language, with particular respect to the role of cognates. The purpose of the study is to describe the process of lexical activaton in a polyglot system and to model the mental lexicons and the ways entries in the lexicons are connected and activated (e.g. activation through direct word association or through concept mediation). Three dependent variables are studied in quantitative and qualitative analysis of empirical data taken from experiments: rate of accurate responses, response latencies and phonological interference. The results of the experiments are interpreted in the framework of a multiple language network model.
Die vorliegende Arbeit beschäftigt sich mit der Charakterisierung von Seismizität anhand von Erdbebenkatalogen. Es werden neue Verfahren der Datenanalyse entwickelt, die Aufschluss darüber geben sollen, ob der seismischen Dynamik ein stochastischer oder ein deterministischer Prozess zugrunde liegt und was daraus für die Vorhersagbarkeit starker Erdbeben folgt. Es wird gezeigt, dass seismisch aktive Regionen häufig durch nichtlinearen Determinismus gekennzeichent sind. Dies schließt zumindest die Möglichkeit einer Kurzzeitvorhersage ein. Das Auftreten seismischer Ruhe wird häufig als Vorläuferphaenomen für starke Erdbeben gedeutet. Es wird eine neue Methode präsentiert, die eine systematische raumzeitliche Kartierung seismischer Ruhephasen ermöglicht. Die statistische Signifikanz wird mit Hilfe des Konzeptes der Ersatzdaten bestimmt. Als Resultat erhält man deutliche Korrelationen zwischen seismischen Ruheperioden und starken Erdbeben. Gleichwohl ist die Signifikanz dafür nicht hoch genug, um eine Vorhersage im Sinne einer Aussage über den Ort, die Zeit und die Stärke eines zu erwartenden Hauptbebens zu ermöglichen.
Recent high-throughput technologies enable the acquisition of a variety of complementary data and imply regulatory networks on the systems biology level. A common approach to the reconstruction of such networks is the cluster analysis which is based on a similarity measure. We use the information theoretic concept of the mutual information, that has been originally defined for discrete data, as a measure of similarity and propose an extension to a commonly applied algorithm for its calculation from continuous biological data. We compare our approach to previously existing algorithms. We develop a performance optimised software package for the application of the mutual information to large-scale datasets. Furthermore, we design and implement a web-based service for the analysis of integrated data measured with different technologies. Application to biological data reveals biologically relevant groupings and reconstructed signalling networks show agreements with physiological findings.
Combining the magnetic properties of a given material with the tremendous advantages of colloids can exponentially increase the advantages of both systems. This thesis deals with the field of magnetic nanotechnology. Thus, the design and characterization of new magnetic colloids with fascinating properties compared with the bulk materials is presented. Ferrofluids are referred to either as water or organic stable dispersions of superparamagnetic nanoparticles which respond to the application of an external magnetic field but lose their magnetization in the absence of a magnetic field. In the first part of this thesis, a three-step synthesis for the fabrication of a novel water-based ferrofluid is presented. The encapsulation of high amounts of magnetite into polystyrene particles can efficiently be achieved by a new process including two miniemulsion processes. The ferrofluids consist of novel magnetite polystyrene nanoparticles dispersed in water which are obtained by three-step process including coprecipitation of magnetite, its hydrophobization and further surfactant coating to enable the redispersion in water and the posterior encapsulation into polystyrene by miniemulsion polymerization. It is a desire to take advantage of a potential thermodynamic control for the design of nanoparticles, and the concept of "nanoreactors" where the essential ingredients for the formation of the nanoparticles are already in the beginning. The formulation and application of polymer particles and hybrid particles composed of polymeric and magnetic material is of high interest for biomedical applications. Ferrofluids can for instance be used in medicine for cancer therapy and magnetic resonance imaging. Superparamagnetic or paramagnetic colloids containing iron or gadolinium are also used as magnetic resonance imaging contrast agent, for example as a important tool in the diagnosis of cancer, since they enhance the relaxation of the water of the neighbouring zones. New nanostructured composites by the thermal decomposition of iron pentacarbonyl in the monomer phase and thereafter the formation of paramagnetic nanocomposites by miniemulsion polymerization are discussed in the second part of this thesis. In order to obtain the confined paramagnetic nanocomposites a two-step process was used. In the first step, the thermal decomposition of the iron pentacarbonyl was obtained in the monomer phase using oleic acid as stabilizer. In the second step, this iron-containing monomer dispersion was used for making a miniemulsion polymerization thereof. The addition of lanthanide complexes to ester-containing monomers such as butyl acrylate and subsequent polymerization leading to the spontaneous formation of highly organized layered nanocomposites is presented in the final part of this thesis. By an one-step miniemulsion process, the formation of a lamellar structure within the polymer nanoparticles is achieved. The magnetization and the NMR relaxation measurements have shown these new layered nanocomposites to be very apt for application as contrast agent in magnetic resonance imaging.