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Understanding stars, their magnetic activity phenomena and the underlying dynamo action is the foundation for understanding 'life, the universe and everything' - as stellar magnetic fields play a fundamental role for star and planet formation and for the terrestrial atmosphere and climate. Starspots are the fingerprints of magnetic field lines and thereby the most important sign of activity in a star's photosphere. However, they cannot be observed directly, as it is not (yet) possible to spacially resolve the surfaces of even the nearest neighbouring stars. Therefore, an indirect approach called 'Doppler imaging' is applied, which allows to reconstruct the surface spot distribution on rapidly rotating, active stars. In this work, data from 11 years of continuous spectroscopic observations of the active binary star EI Eridani are reduced and analysed. 34 Doppler maps are obtained and the problem of how to parameterise the information content of Doppler maps is discussed. Three approaches for parameter extraction are introduced and applied to all maps: average temperature, separated for several latitude bands; fractional spottedness; and, for the analysis of structural temperature distribution, longitudinal and latitudinal spot-occurrence functions. The resulting values do not show a distinct correlation with the proposed activity cycle as seen from photometric long-term observations, thereby suggesting that the photometric activity cycle is not accompanied by a spot cycle as seen on the Sun. The general morphology of the spot pattern on EI Eri remains persistent for the whole period of 11 years. In addition, a detailed parameter study is performed. Improved orbital parameters suggest that EI Eri might be complemented by a third star in a wide orbit of about 19 years. Preliminary differential rotation measurements are carried out, indicating an anti-solar orientation.
In this thesis, dynamical structures and manifolds in closed chaotic flows will be investigated. The knowledge about the dynamical structures (and manifolds) of a system is of importance, since they provide us first information about the dynamics of the system - means, with their help we are able to characterize the flow and maybe even to forecast it`s dynamics. The visualization of such structures in closed chaotic flows is a difficult and often long-lasting process. Here, the so-called 'Leaking-method' will be introduced, in examples of simple mathematical maps as the baker- or sine-map, with which we are able to visualize subsets of the manifolds of the system`s chaotic saddle. Comparisons between the visualized manifolds and structures traced out by chemical or biological reactions superimposed on the same flow will be done in the example of a kinematic model of the Gulf Stream. It will be shown that with the help of the leaking method dynamical structures can be also visualized in environmental systems. In the example of a realistic model of the Mediterranean Sea, the leaking method will be extended to the 'exchange-method'. The exchange method allows us to characterize transport between two regions, to visualize transport routes and their exchange sets and to calculate the exchange times. Exchange times and sets will be shown and calculated for a northern and southern region in the western basin of the Mediterranean Sea. Furthermore, mixing properties in the Earth mantle will be characterized and geometrical properties of manifolds in a 3dimensional mathematical model (ABC map) will be investigated.
In this work different approaches are undertaken to improve the understanding of the sucrose-to-starch pathway in developing potato tubers. At first an inducible gene expression system from fungal origin is optimised for the use of studying metabolism in the potato tuber. It is found that the alc system from Aspergillus nidulans responds more rapidly to acetaldehyde than ethanol, and that acetaldehyde has less side-effects on metabolism. The optimal induction conditions then are used to study the effects of temporally controlled cytosolic expression of a yeast invertase on metabolism of potato tubers. The observed differences between induced and constitutive expression of the invertase lead to the conclusion that glycolysis is induced after an ATP demand has been created by an increase in sucrose cycling. Furthermore, the data suggest that in the potato tuber maltose is a product of glucose condensation rather than starch degradation. In the second part of the work it is shown that the expression of a yeast invertase in the vacuole of potato tubers has similar effects on metabolism than the expression of the same enzyme in the apoplast. These observations give further evidence to the presence of a mechanism by which sucrose is taken up via endocytosis to the vacuole rather than via transporters directly to the cytosol. Finally, a kinetic in silico model of sucrose breakdown is presented that is able to simulate this part of potato tuber metabolism on a quantitative level. Furthermore, it can predict the metabolic effects of the introduction of a yeast invertase in the cytosol of potato tubers with an astonishing precision. In summary, these data prove that inducible gene expression and kinetic computer models of metabolic pathways are useful tools to greatly improve the understanding of plant metabolism.
Polymer optical fibers (POFs) are a rather new tool for high-speed data transfer by modulated light. They allow the transport of high amounts of data over distances up to about 100 m without be influenced by external electromagnetic fields. Due to organic chemical nature of POFs, they are sensitive to the climate of their environment and therefore the optical fiber properties are as well. Hence, the optical stability is a key issue for long-term applications of POFs. The causes for a loss of optical transmission due to climatic exposures (aging/degradation) are researched by means of chemical analytical tools such as chemiluminescence (CL) and Fourier transform infrared (FTIR) spectroscopy for five different (with respect to manufacturers) step-index multimode PMMA based POFs and for seven different climatic conditions. Three of the five POF samples are studied more in detail to realize the effects of individual parameters and for forecasting longterm optical stability by short-term exposure tests. At first, the unexposed POF components (core, cladding, and bare POF as combination of core and cladding) are characterized with respect to important physical and chemical properties. The glass transition temperature Tg, and the melting temperature Tm are in the region of 120 °C to 140 °C, the molecular weight (Mw) of cores is in the order of 105 g mol-1. POFs are found to have different chemical compositions of their claddings as could be detected by FTIR, but identical compositions of their cores. Two of the POFs are exposed as cables (core, cladding and jacket) for about 3300 hours to the climate 92 °C / 95 % relative humidity (RH) resulting in a different transmission decrease. Investigating the related unexposed and exposed bare POFs for degradation using CL, FTIR, thermogravimetry (TG), UV/visible transmittance and gel permeation chromatography (GPC) suggest that claddings of POFs are more affected than cores. Probably the observed loss of transmission is mainly due to increased light absorption and imperfections at the core-cladding boundary caused by a large degradation of claddings. Hence, it is highly possible that the optical transmission stability of POFs is governed mainly by the thermo-oxidative stability of the cladding and minor of the core. Three bare POFs (core and cladding only) are exposed for different duration of exposure time (30 hours to 4500 hours) to 92 °C / 95 %RH, 92 °C / 50 %RH, 50 °C / 95 %RH, 90 °C / low humidity, 100 °C / low humidity, 110 °C / low humidity and 120 °C / low humidity. In these climates their transmission variations are found to be different from each other, too. The outcomes strongly inform that under high temperature and high humid climates physical changes such as volume expansion, are the main sources for the loss of optical transmission. Also, the optical transmission stability of POFs is found to be dependent on chemical compositions of claddings. Under high temperature and low humid conditions, a loss of transmission at the early stages of the exposure is mainly caused by physical changes, presumable by corecladding interface imperfections. For the later stages of exposures it is proposed to an additional increase of light absorption by core and cladding owes to degradation. Optical simulation results obtained parallel by Mr. L. Jankowski (a PhD student of BAM) are found to confirm these results. For bare POFs, too, the optical stability of POFs seems to depend on their thermo-oxidative stability. Some short-term exposure tests are conducted to realize influences of individual climatic parameters on the transmission property of POFs. It is found that at stationary high temperature and variable humidity conditions POFs display to a certain amount a reversible transmission loss due to physically absorbed water. But in the case of varying temperature and constant high humidity such reversibility is hardly noticeable. However, at room temperature and varying humidity, POFs display fully reversible transmission loss. The whole research described above has to be regarded as a starting point for further investigations. The restricted distribution of fundamental POF data by the manufacturers and the time consuming aging by climatic exposures restrict the results more or less to the samples, investigated here. Significant general statements require for example additional information concerning the variation of POF properties due to production. Nevertheless the tests, described here, have the capability for approximating and forecasting the long-term optical transmission stability of POFs. -------------- Auch im Druck erschienen: Appajaiah, Anilkumar: Climatic stability of polymer optical fibers (POF) / Anilkumar Appajaiah. - Bremerhaven : Wirtschaftsverl. NW, Verl. für neue Wiss., 2005. - Getr. Zählung [ca. 175 S.]. : Ill., graph. Darst. - (BAM-Dissertationsreihe ; 9) ISBN 3-86509-302-7
This thesis discusses theoretical and practical aspects of modelling of light propagation in non-aged and aged step-index polymer optical fibres (POFs). Special attention has been paid in describing optical characteristics of non-ideal fibres, scattering and attenuation, and in combining application-oriented and theoretical approaches. The precedence has been given to practical issues, but much effort has been also spent on the theoretical analysis of basic mechanisms governing light propagation in cylindrical waveguides.As a result a practically usable general POF model based on the raytracing approach has been developed and implemented. A systematic numerical optimisation of its parameters has been performed to obtain the best fit between simulated and measured optical characteristics of numerous non-aged and aged fibre samples. The model was verified by providing good agreement, especially for the non-aged fibres. The relations found between aging time and optimal values of model parameters contribute to a better understanding of the aging mechanisms of POFs.
Modelling and simulation of light propagation in non-aged and aged step-index polymer optical fibres
(2004)
This thesis discusses theoretical and practical aspects of modelling of light propagation in non-aged and aged step-index polymer optical fibres (POFs). Special attention has been paid in describing optical characteristics of non-ideal fibres, scattering and attenuation, and in combining application-oriented and theoretical approaches. The precedence has been given to practical issues, but much effort has been also spent on the theoretical analysis of basic mechanisms governing light propagation in cylindrical waveguides. As a result a practically usable general POF model based on the raytracing approach has been developed and implemented. A systematic numerical optimisation of its parameters has been performed to obtain the best fit between simulated and measured optical characteristics of numerous non-aged and aged fibre samples. The model was verified by providing good agreement, especially for the non-aged fibres. The relations found between aging time and optimal values of model parameters contribute to a better understanding of the aging mechanisms of POFs.
Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.
One of the most striking features of ecological systems is their ability to undergo sudden outbreaks in the population numbers of one or a small number of species. The similarity of outbreak characteristics, which is exhibited in totally different and unrelated (ecological) systems naturally leads to the question whether there are universal mechanisms underlying outbreak dynamics in Ecology. It will be shown into two case studies (dynamics of phytoplankton blooms under variable nutrients supply and spread of epidemics in networks of cities) that one explanation for the regular recurrence of outbreaks stems from the interaction of the natural systems with periodical variations of their environment. Natural aquatic systems like lakes offer very good examples for the annual recurrence of outbreaks in Ecology. The idea whether chaos is responsible for the irregular heights of outbreaks is central in the domain of ecological modeling. This question is investigated in the context of phytoplankton blooms. The dynamics of epidemics in networks of cities is a problem which offers many ecological and theoretical aspects. The coupling between the cities is introduced through their sizes and gives rise to a weighted network which topology is generated from the distribution of the city sizes. We examine the dynamics in this network and classified the different possible regimes. It could be shown that a single epidemiological model can be reduced to a one-dimensional map. We analyze in this context the dynamics in networks of weighted maps. The coupling is a saturation function which possess a parameter which can be interpreted as an effective temperature for the network. This parameter allows to vary continously the network topology from global coupling to hierarchical network. We perform bifurcation analysis of the global dynamics and succeed to construct an effective theory explaining very well the behavior of the system.
This thesis analyses synchronization phenomena occurring in large ensembles of interacting oscillatory units. In particular, the effects of nonisochronicity (frequency dependence on the oscillator's amplitude) on the macroscopic transition to synchronization are studied in detail. The new phenomena found (Anomalous Synchronization) are investigated in populations of oscillators as well as between oscillator's ensembles.
We calculate the additional carbon emissions as a result of the conversion of natural land in a process of urbanisation; and the change of carbon flows by “urbanised” ecosystems, when the atmospheric carbon is exported to the neighboring territories, from 1980 till 2050 for the eight regions of the world. As a scenario we use combined UN and demographic model′s prognoses for regional total and urban population growth. The calculations of urban areas dynamics are based on two models: the regression model and the Gamma-model. The urbanised area is sub-divided on built-up, „green“ (parks, etc.) and informal settlements (favelas) areas. The next step is to calculate the regional and world dynamics of carbon emission and export, and the annual total carbon balance. Both models give similar results with some quantitative differences. In the first model, the world annual emissions attain a maximum of 205 MtC/year between 2020-2030. Emissions will then slowly decrease. The maximum contributions are given by China and the Asia and Pacific regions. In the second model, world annual emissions increase to 1.25 GtC in 2005, beginning to decrease afterwards. If we compare the emission maximum with the annual emission caused by deforestation, 1.36GtC per year, then we can say that the role of urbanised territories (UT) is of a comparable magnitude. Regarding the world annual export of carbon by UT, we observe its monotonous growth by three times, from 24 MtC to 66 MtC in the first model, and from 249 MtC to 505 MtC in the second one. The latter, is therefore comparable to the amount of carbon transported by rivers into the ocean (196-537 MtC). By estimating the total balance we find that urbanisation shifts the total balance towards a “sink” state. The urbanisation is inhibited in the interval 2020-2030, and by 2050 the growth of urbanised areas would almost stop. Hence, the total emission of natural carbon at that stage will stabilise at the level of the 1980s (80 MtC per year). As estimated by the second model, the total balance, being almost constant until 2000, then starts to decrease at an almost constant rate. We can say that by the end of the XXI century, the total carbon balance will be equal to zero, when the exchange flows are fully balanced, and may even be negative, when the system begins to take up carbon from the atmosphere, i.e., becomes a “sink”.
My thesis is concerned with several new noise-induced phenomena in excitable neural models, especially those with FitzHugh-Nagumo dynamics. In these effects the fluctuations intrinsically present in any complex neural network play a constructive role and improve functionality. I report the occurrence of Vibrational Resonance in excitable systems. Both in an excitable electronic circuit and in the FitzHugh-Nagumo model, I show that an optimal amplitude of high-frequency driving enhances the response of an excitable system to a low-frequency signal. Additionally, the influence of additive noise and the interplay between Stochastic and Vibrational Resonance is analyzed. Further, I study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies. I show that in such a system the effect of Stochastic Resonance can be amplified by an additional high-frequency signal which is in resonance with the oscillatory frequency. This amplification needs much lower noise intensities than for conventional Stochastic Resonance in excitable systems. I study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise-supported stochastic attractors. I show that the response of the coupled elements at different noise levels can be significantly enhanced or reduced by forcing some elements into resonance with these new frequencies which correspond to appropriate phase-relations. A noise-induced phase transition to excitability is reported in oscillatory media with FitzHugh-Nagumo dynamics. This transition takes place via noise-induced stabilization of a deterministically unstable fixed point of the local dynamics, while the overall phase-space structure of the system is maintained. The joint action of coupling and noise leads to a different type of phase transition and results in a stabilization of the system. The resulting noise-induced regime is shown to display properties characteristic of excitable media, such as Stochastic Resonance and wave propagation. This effect thus allows the transmission of signals through an otherwise globally oscillating medium. In particular, these theoretical findings suggest a possible mechanism for suppressing undesirable global oscillations in neural networks (which are usually characteristic of abnormal medical conditions such as Parkinson′s disease or epilepsy), using the action of noise to restore excitability, which is the normal state of neuronal ensembles.
Independent component analysis (ICA) is a tool for statistical data analysis and signal processing that is able to decompose multivariate signals into their underlying source components. Although the classical ICA model is highly useful, there are many real-world applications that require powerful extensions of ICA. This thesis presents new methods that extend the functionality of ICA: (1) reliability and grouping of independent components with noise injection, (2) robust and overcomplete ICA with inlier detection, and (3) nonlinear ICA with kernel methods.
For recombinant production of proteins for structural and functional analyses, the E. coli expression system is the most widely used due to high yields and straightforward processing. However, particularly the expression of eukaryotic proteins in E. coli is often problematic, e.g. when the protein is not folded correctly and is deposited in insoluble inclusion bodies. In some cases it is favourable to analyse deletion constructs of a protein or an individual protein domain instead of the full-length protein. This implies the generation of a set of expression constructs that need to be characterised. In this work methods to optimise and evaluate in vitro folding of inclusion body proteins as well as high-throughput characterisation of expression constructs were developed. Transferring inclusion body proteins to their native state involves two steps: (a) solubilisation with a chaotropic reagent or a strong ionic detergent and (b) folding of the protein by removal of the chaotrop accompanied by the transfer into an appropriate buffer. The yield of natively folded protein is often substantially reduced due to aggregation or misfolding; it may, however, be improved by certain additives to the folding buffer. These additives need to be identified empirically. In this thesis a screening procedure for folding conditions was developed. To reduce the number of possible combinations of screening additives, empirical observations documented in the literature as well as well known properties of certain screening additives were considered. To decrease the amount of protein and work invested, the screen was miniaturised and automated using a pipetting robot. Twenty rapid dilution conditions for the denatured protein are tested and two conditions for folding of proteins using the detergent/cyclodextrin protein folding system of Rozema et al. (1996). 100 µg protein is used per condition. In addition, eight conditions can be tested for folding of His-tagged proteins (approx. 200 µg) immobilised on metal chelate resins. The screen was successfully applied to fold a human protein, the p22 subunit of dynactin that is expressed in inclusion bodies in E. coli. For p22 dynactin – as is the case for many proteins – there was no biological assay available to assess the success of the folding screen. Protein solubility can not be used as a stringent criterion because beside natively folded protein, soluble misfolded species and microaggregates may occur. This work evaluates methods to detect small amounts of natively folded protein after automated folding screening. Before folding screening with p22 dynactin, two model enzymes, bovine carbonic anhydrase II (CAB) and pig heart mitochondrial malate dehydrogenase, were used for evaluation. Recovered activity after refolding was correlated to different biophysical methods. 8-anilino-1-naphtalenesulfonic acid binding-experiments gave no useful information when refolding CAB, due to low sensitivity and because misfolded protein could not be readily distinguished from native protein. Tryptophan fluorescence spectra of refolded CAB were used to assess the success of refolding. The shift of the intensity maximum to a shorter wavelength, compared to the denaturant unfolded protein, as well as the fluorescence intensity correlated to recovered enzymatic activity. For both model enzymes, analytical hydrophobic interaction chromatography (HIC) was useful to identify refolded samples that contain active enzyme. Compactly folded, active enzyme eluted in a distinct peak in a decreasing ammonium sulfate gradient. The detection limit of analytical HIC was approx. 5 µg. In case of CAB, tryptophan fluorescence spectroscopy and analytical HIC showed that both methods in combination can be useful to rule out false positives or false negatives obtained with one method. These two methods were also useful to identify conditions for folding of p22 dynactin. However, tryptophan fluorescence spectroscopy can lead to false positives because in some cases spectra of soluble microaggregates are not well distinguishable from spectra of natively folded protein. In summary, a fast and reliable screening procedure was developed to make inclusion body proteins accessible to structural or functional analyses. In a separate project, 88 different E. coli expression constructs for 17 human protein domains that had been identified by sequence analysis were analysed using high-throughput purification and folding analysis in order to obtain candidates suitable for structural analysis. After 96 deep-well microplate expression and automated protein purification, solubly expressed protein domains were directly analysed using 1D ¹H-NMR spectroscopy. It was found that isolated methyl group signals below 0.5 ppm are particularly sensitive and reliable probes for folded protein. In addition – similar to the evaluation of a folding screen – analytical HIC proved to be an efficient tool for identifying constructs that yield compactly folded protein. Both methods, 1D ¹H-NMR spectroscopy and analytical HIC, provided complementary results. Six constructs, representing two domains, could be quickly identified as targets that are well suitable for structural analysis. The structure of one of these domains was solved recently by co-workers, the other structure was published by another group during this project.
Highly collimated, high velocity streams of hot plasma – the jets – are observed as a general phenomenon being found in a variety of astrophysical objects regarding their size and energy output. Known as jet sources are protostellar objects (T Tauri stars, embedded IR sources), galactic high energy sources ("microquasars"), and active galactic nuclei (extragalactic radio sources and quasars). Within the last two decades our knowledge regarding the processes involved in astro-physical jet formation has condensed in a kind of standard model. This is the scenario of a magnetohydrodynamically accelerated and collimated jet stream launched from the innermost part of an accretion disk close to the central object. Traditionally, the problem of jet formation is divided in two categories. One is the question how to collimate and accelerate an uncollimated low velocity disk wind into a jet. The second is the question how to initiate that outflow from a disk, i.e. how to turn accretion of matter into an ejection as a disk wind. My own work is mainly related to the first question, the collimation and acceleration process. Due to the complexity of both, the physical processes believed to be responsible for the jet launching and also the spatial configuration of the physical components of the jet source, the enigma of jet formation is not yet completely understood. On the theoretical side, there has been a substantial advancement during the last decade from purely station-ary models to time-dependent simulations lead by the vast increase of computer power. Observers, on the other hand, do not yet have the instruments at hand in order to spatially resolve observe the very jet origin. It can be expected that also the next years will yield a substantial improvement on both tracks of astrophysical research. Three-dimensional magnetohydrodynamic simu-lations will improve our understanding regarding the jet-disk interrelation and the time-dependent character of jet formation, the generation of the magnetic field in the jet source, and the interaction of the jet with the ambient medium. Another step will be the combina-tion of radiation transfer computations and magnetohydrodynamic simulations providing a direct link to the observations. At the same time, a new generation of telescopes (VLT, NGST) in combination with new instrumental techniques (IR-interferometry) will lead to a "quantum leap" in jet observation, as the resolution will then be sufficient in order to zoom into the innermost region of jet formation.
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.
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.