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Stochastic information, to be understood as "information gained by the application of stochastic methods", is proposed as a tool in the assessment of changes in climate. This thesis aims at demonstrating that stochastic information can improve the consideration and reduction of uncertainty in the assessment of changes in climate. The thesis consists of three parts. In part one, an indicator is developed that allows the determination of the proximity to a critical threshold. In part two, the tolerable windows approach (TWA) is extended to a probabilistic TWA. In part three, an integrated assessment of changes in flooding probability due to climate change is conducted within the TWA. The thermohaline circulation (THC) is a circulation system in the North Atlantic, where the circulation may break down in a saddle-node bifurcation under the influence of climate change. Due to uncertainty in ocean models, it is currently very difficult to determine the distance of the THC to the bifurcation point. We propose a new indicator to determine the system's proximity to the bifurcation point by considering the THC as a stochastic system and using the information contained in the fluctuations of the circulation around the mean state. As the system is moved closer to the bifurcation point, the power spectrum of the overturning becomes "redder", i.e. more energy is contained in the low frequencies. Since the spectral changes are a generic property of the saddle-node bifurcation, the method is not limited to the THC, but it could also be applicable to other systems, e.g. transitions in ecosystems. In part two, a probabilistic extension to the tolerable windows approach (TWA) is developed. In the TWA, the aim is to determine the complete set of emission strategies that are compatible with so-called guardrails. Guardrails are limits to impacts of climate change or to climate change itself. Therefore, the TWA determines the "maneuvering space" humanity has, if certain impacts of climate change are to be avoided. Due to uncertainty it is not possible to definitely exclude the impacts of climate change considered, but there will always be a certain probability of violating a guardrail. Therefore the TWA is extended to a probabilistic TWA that is able to consider "probabilistic uncertainty", i.e. uncertainty that can be expressed as a probability distribution or uncertainty that arises through natural variability. As a first application, temperature guardrails are imposed, and the dependence of emission reduction strategies on probability distributions for climate sensitivities is investigated. The analysis suggests that it will be difficult to observe a temperature guardrail of 2°C with high probabilities of actually meeting the target. In part three, an integrated assessment of changes in flooding probability due to climate change is conducted. A simple hydrological model is presented, as well as a downscaling scheme that allows the reconstruction of the spatio-temporal natural variability of temperature and precipitation. These are used to determine a probabilistic climate impact response function (CIRF), a function that allows the assessment of changes in probability of certain flood events under conditions of a changed climate. The assessment of changes in flooding probability is conducted in 83 major river basins. Not all floods can be considered: Events that either happen very fast, or affect only a very small area can not be considered, but large-scale flooding due to strong longer-lasting precipitation events can be considered. Finally, the probabilistic CIRFs obtained are used to determine emission corridors, where the guardrail is a limit to the fraction of world population that is affected by a predefined shift in probability of the 50-year flood event. This latter analysis has two main results. The uncertainty about regional changes in climate is still very high, and even small amounts of further climate change may lead to large changes in flooding probability in some river systems.
Origin and symmetry of the observed global magnetic fields in galaxies are not fully understood. We intend to clarify the question of the magnetic field origin and investigate the global action of the magneto-rotational instability (MRI) in galactic disks with the help of 3D global magneto-hydrodynamical (MHD) simulations. The calculations were done with the time-stepping ZEUS 3D code using massive parallelization. The alpha-Omega dynamo is known to be one of the most efficient mechanisms to reproduce the observed global galactic fields. The presence of strong turbulence is a pre-requisite for the alpha-Omega dynamo generation of the regular magnetic fields. The observed magnitude and spatial distribution of turbulence in galaxies present unsolved problems to theoreticians. The MRI is known to be a fast and powerful mechanism to generate MHD turbulence and to amplify magnetic fields. We find that the critical wavelength increases with the increasing of magnetic fields during the simulation, transporting the energy from critical to larger scales. The final structure, if not disrupted by supernovae explosions, is the structure of `thin layers' of thickness of about 100 pcs. An important outcome of all simulations is the magnitude of the horizontal components of the Reynolds and Maxwell stresses. The result is that the MRI-driven turbulence is magnetic-dominated: its magnetic energy exceeds the kinetic energy by a factor of 4. The Reynolds stress is small and less than 1% of the Maxwell stress. The angular momentum transport is thus completely dominated by the magnetic field fluctuations. The volume-averaged pitch angle is always negative with a magnitude of about -30. The non-saturated MRI regime is lasting sufficiently long to fill the time between the galactic encounters, independently of strength and geometry of the initial field. Therefore, we may claim the observed pitch angles can be due to MRI action in the gaseous galactic disks. The MRI is also shown to be a very fast instability with e-folding time proportional to the time of one rotation. Steep rotation curves imply a stronger growth for the magnetic energy due to MRI. The global e-folding time is from 44 Myr to 100 Myr depending on the rotation profile. Therefore, MRI can explain the existence of rather large magnetic field in very young galaxies. We also have reproduced the observed rms values of velocities in the interstellar turbulence as it was observed in NGC 1058. We have shown with the simulations that the averaged velocity dispersion of about 5 km/s is a typical number for the MRI-driven turbulence in galaxies, which agrees with observations. The dispersion increases outside of the disk plane, whereas supernovae-driven turbulence is found to be concentrated within the disk. In our simulations the velocity dispersion increases a few times with the heights. An additional support to the dynamo alpha-effect in the galaxies is the ability of the MRI to produce a mix of quadrupole and dipole symmetries from the purely vertical seed fields, so it also solves the seed-fields problem of the galactic dynamo theory. The interaction of magneto-rotational instability and random supernovae explosions remains an open question. It would be desirable to run the simulation with the supernovae explosions included. They would disrupt the calm ring structure produced by global MRI, may be even to the level when we can no longer blame MRI to be responsible for the turbulence.
Wetting and phase transitions play a very important role our daily life. Molecularly thin films of long-chain alkanes at solid/vapour interfaces (e.g. C30H62 on silicon wafers) are very good model systems for studying the relation between wetting behaviour and (bulk) phase transitions. Immediately above the bulk melting temperature the alkanes wet partially the surface (drops). In this temperature range the substrate surface is covered with a molecularly thin ordered, solid-like alkane film ("surface freezing"). Thus, the alkane melt wets its own solid only partially which is a quite rare phenomenon in nature. The thesis treats about how the alkane melt wets its own solid surface above and below the bulk melting temperature and about the corresponding melting and solidification processes. Liquid alkane drops can be undercooled to few degrees below the bulk melting temperature without immediate solidification. This undercooling behaviour is quite frequent and theoretical quite well understood. In some cases, slightly undercooled drops start to build two-dimensional solid terraces without bulk solidification. The terraces grow radially from the liquid drops on the substrate surface. They consist of few molecular layers with the thickness multiple of all-trans length of the molecule. By analyzing the terrace growth process one can find that, both below and above the melting point, the entire substrate surface is covered with a thin film of mobile alkane molecules. The presence of this film explains how the solid terrace growth is feeded: the alkane molecules flow through it from the undercooled drops to the periphery of the terrace. The study shows for the first time the coexistence of a molecularly thin film ("precursor") with partially wetting bulk phase. The formation and growth of the terraces is observed only in a small temperature interval in which the 2D nucleation of terraces is more likely than the bulk solidification. The nucleation mechanisms for 2D solidification are also analyzed in this work. More surprising is the terrace behaviour above bulk the melting temperature. The terraces can be slightly overheated before they melt. The melting does not occur all over the surface as a single event; instead small drops form at the terrace edge. Subsequently these drops move on the surface "eating" the solid terraces on their way. By this they grow in size leaving behind paths from were the material was collected. Both overheating and droplet movement can be explained by the fact that the alkane melt wets only partially its own solid. For the first time, these results explicitly confirm the supposed connection between the absence of overheating in solid and "surface melting": the solids usually start to melt without an energetic barrier from the surface at temperatures below the bulk melting point. Accordingly, the surface freezing of alkanes give rise of an energetic barrier which leads to overheating.
Subject of this work is the study of applications of the Galactic Microlensing effect, where the light of a distant star (source) is bend according to Einstein's theory of gravity by the gravitational field of intervening compact mass objects (lenses), creating multiple (however not resolvable) images of the source. Relative motion of source, observer and lens leads to a variation of deflection/magnification and thus to a time dependant observable brightness change (lightcurve), a so-called microlensing event, lasting weeks to months. The focus lies on the modeling of binary-lens events, which provide a unique tool to fully characterize the lens-source system and to detect extra-solar planets around the lens star. Making use of the ability of genetic algorithms to efficiently explore large and intricate parameter spaces in the quest for the global best solution, a modeling software (Tango) for binary lenses is developed, presented and applied to data sets from the PLANET microlensing campaign. For the event OGLE-2002-BLG-069 the 2nd ever lens mass measurement has been achieved, leading to a scenario, where a G5III Bulge giant at 9.4 kpc is lensed by an M-dwarf binary with total mass of M=0.51 solar masses at distance 2.9 kpc. Furthermore a method is presented to use the absence of planetary lightcurve signatures to constrain the abundance of extra-solar planets.
Due to its relevance for global climate, the realistic representation of the Atlantic meridional overturning circulation (AMOC) in ocean models is a key task. In recent years, two paradigms have evolved around what are its driving mechanisms: diapycnal mixing and Southern Ocean winds. This work aims at clarifying what sets the strength of the Atlantic overturning components in an ocean general circulation model and discusses the role of spatially inhomogeneous mixing, numerical diffusion and winds. Furthermore, the relation of the AMOC with a key quantity, the meridional pressure difference is analyzed. Due to the application of a very low diffusive tracer advection scheme, a realistic Atlantic overturning circulation can be obtained that is purely wind driven. On top of the winddriven circulation, changes of density gradients are caused by increasing the parameterized eddy diffusion in the North Atlantic and Southern Ocean. The linear relation between the maximum of the Atlantic overturning and the meridional pressure difference found in previous studies is confirmed and it is shown to be due to one significant pressure gradient between the average pressure over high latitude deep water formation regions and a relatively uniform pressure between 30°N and 30°S, which can directly be related to a zonal flow through geostrophy. Under constant Southern Ocean windstress forcing, a South Atlantic outflow in the range of 6-16 Sv is obtained for a large variety of experiments. Overall, the circulation is winddriven but its strength not uniquely determined by the Southern Ocean windstress. The scaling of the Atlantic overturning components is linear with the background vertical diffusivity, not confirming the 2/3 power law for one-hemisphere models without wind forcing. The pycnocline depth is constant in the coarse resolution model with large vertical grid extends. It suggests the ocean model operates like the Stommel box model with a linear relation of the pressure difference and fixed vertical scale for the volume transport. However, this seems only valid for vertical diffusivities smaller 0.4 cm²/s, when the dominant upwelling within the Atlantic occurs along the boundaries. For larger vertical diffusivities, a significant amount of interior upwelling occurs. It is further shown that any localized vertical mixing in the deep to bottom ocean cannot drive an Atlantic overturning. However, enhanced boundary mixing at thermocline depths is potentially important. The numerical diffusion is shown to have a large impact on the representation of the Atlantic overturning in the model. While the horizontal numerical diffusion tends to destabilize the Atlantic overturning the verital numerical diffusion denotes an amplifying mechanism.
It is known that the efficiency of organic light-emitting devices (OLEDs) is strongly influenced by the ’quality′ of the thin films [1]. On the basis of this conviction, the work presented in this thesis aimed to obtain a better understanding of the structure of organic thin films of general interest in the field of organic light emitting devices by using scanning probe microscopies (SPMs). A not yet reported crystal structure of quaterthiophene film grown on potassium hydrogen (KHP) is determined by optical measurements, a simulation program, diffraction at both normal incidence and grazing angle and AFM. The crystal cell is triclinic with parameters a = 0.721 nm, b = 0.632 nm, c = 0.956 nm and a = 91°, b = 91.4°, g = 91° [2]. The morphologies of four organic thin films deposited on gold are characterized by ultra high vacuum scanning tunneling microscopy (UHV-STM). Terraces in an hexanethiol monolayer, lamellar structures in an azobenzenethiol monolayer, rods in a a poly(paraphenylenevinylene) oligomer film and a granular morphology in an oxadiazole film are shown. The topographies of a series of poly(3,4-ethylenedioxythiophene)/poly(styrenesulfonate) (PEDOT/PSS) films deposited on indium-tin oxide (ITO) and gold obtained from dispersions with PEDOT:PSS weight ratios of 1:20, 1:6 and 1:1 are investigated by AFM. It is demonstrated that the films show the same topography on gold and on ITO. It is shown that the PEDOT films eliminate the spike features of ITO. It is reported that PEDOT 1:20 and 1:6 appear indistinguishable between each other but different from PEDOT 1:1 (the most conductive). Coupling STM and I-d measurements, a not yet reported structural model of PEDOT 1:1 on gold is obtained [3]. In this model the surface presents grains and the bulk particles/domains rich in PEDOT embedded in a PEDOT-poor matrix. The equation of conductivity is derived. A STM investigation of four PEDOT films deposited on ITO obtained from dispersions with the same PEDOT:PSS weight ratio of 1:1 is carried out [4]. The films differ either for the presence of sorbitol or for a different synthetic route (and they present different conductivities). For the first time a quantitative and qualitative correlation between the nanometer-scale morphology of PEDOT films with and without sorbitol and their conductivity is established.
The topic of synchronization forms a link between nonlinear dynamics and neuroscience. On the one hand, neurobiological research has shown that the synchronization of neuronal activity is an essential aspect of the working principle of the brain. On the other hand, recent advances in the physical theory have led to the discovery of the phenomenon of phase synchronization. A method of data analysis that is motivated by this finding - phase synchronization analysis - has already been successfully applied to empirical data. The present doctoral thesis ties up to these converging lines of research. Its subject are methodical contributions to the further development of phase synchronization analysis, as well as its application to event-related potentials, a form of EEG data that is especially important in the cognitive sciences. The methodical contributions of this work consist firstly in a number of specialized statistical tests for a difference in the synchronization strength in two different states of a system of two oscillators. Secondly, in regard of the many-channel character of EEG data an approach to multivariate phase synchronization analysis is presented. For the empirical investigation of neuronal synchronization a classic experiment on language processing was replicated, comparing the effect of a semantic violation in a sentence context with that of the manipulation of physical stimulus properties (font color). Here phase synchronization analysis detects a decrease of global synchronization for the semantic violation as well as an increase for the physical manipulation. In the latter case, by means of the multivariate analysis the global synchronization effect can be traced back to an interaction of symmetrically located brain areas.<BR> The findings presented show that the method of phase synchronization analysis motivated by physics is able to provide a relevant contribution to the investigation of event-related potentials in the cognitive sciences.
In this thesis the magnetohydrodynamic jet formation and the effects of magnetic diffusion on the formation of axisymmetric protostellar jets have been investigated in three different simulation sets. The time-dependent numerical simulations have been performed, using the magnetohydrodynamic ZEUS-3D code.
Robotic telescopes & Doppler imaging : measuring differential rotation on long-period active stars
(2004)
The sun shows a wide variety of magnetic-activity related phenomena. The magnetic field responsible for this is generated by a dynamo process which is believed to operate in the tachocline, which is located at the bottom of the convection zone. This dynamo is driven in part by differential rotation and in part by magnetic turbulences in the convection zone. The surface differential rotation, one key ingredient of dynamo theory, can be measured by tracing sunspot positions.To extend the parameter space for dynamo theories, one can extend these measurements to other stars than the sun. The primary obstacle in this endeavor is the lack of resolved surface images on other stars. This can be overcome by the Doppler imaging technique, which uses the rotation-induced Doppler-broadening of spectral lines to compute the surface distribution of a physical parameter like temperature. To obtain the surface image of a star, high-resolution spectroscopic observations, evenly distributed over one stellar rotation period are needed. This turns out to be quite complicated for long period stars. The upcoming robotic observatory STELLA addresses this problem with a dedicated scheduling routine, which is tailored for Doppler imaging targets. This will make observations for Doppler imaging not only easier, but also more efficient.As a preview of what can be done with STELLA, we present results of a Doppler imaging study of seven stars, all of which show evidence for differential rotation, but unfortunately the errors are of the same order of magnitude as the measurements due to unsatisfactory data quality, something that will not happen on STELLA. Both, cross-correlation analysis and the sheared image technique where used to double check the results if possible. For four of these stars, weak anti-solar differential rotation was found in a sense that the pole rotates faster than the equator, for the other three stars weak differential rotation in the same direction as on the sun was found.Finally, these new measurements along with other published measurements of differential rotation using Doppler imaging, were analyzed for correlations with stellar evolution, binarity, and rotation period. The total sample of stars show a significant correlation with rotation period, but if separated into antisolar and solar type behavior, only the subsample showing anti-solar differential rotation shows this correlation. Additionally, there is evidence for binary stars showing less differential rotation as single stars, as is suggested by theory. All other parameter combinations fail to deliver any results due to the still small sample of stars available.
Adherent cells constantly collect information about the mechanical properties of their extracellular environment by actively pulling on it through cell-matrix contacts, which act as mechanosensors. In recent years, the sophisticated use of elastic substrates has shown that cells respond very sensitively to changes in effective stiffness in their environment, which results in a reorganization of the cytoskeleton in response to mechanical input. We develop a theoretical model to predict cellular self-organization in soft materials on a coarse grained level. Although cell organization in principle results from complex regulatory events inside the cell, the typical response to mechanical input seems to be a simple preference for large effective stiffness, possibly because force is more efficiently generated in a stiffer environment. The term effective stiffness comprises effects of both rigidity and prestrain in the environment. This observation can be turned into an optimization principle in elasticity theory. By specifying the cellular probing force pattern and by modeling the environment as a linear elastic medium, one can predict preferred cell orientation and position. Various examples for cell organization, which are of large practical interest, are considered theoretically: cells in external strain fields and cells close to boundaries or interfaces for different sample geometries and boundary conditions. For this purpose the elastic equations are solved exactly for an infinite space, an elastic half space and the elastic sphere. The predictions of the model are in excellent agreement with experiments for fibroblast cells, both on elastic substrates and in hydrogels. Mechanically active cells like fibroblasts could also interact elastically with each other. We calculate the optimal structures on elastic substrates as a function of material properties, cell density and the geometry of cell positioning, respectively, that allows each cell to maximize the effective stiffness in its environment due to the traction of all the other cells. Finally, we apply Monte Carlo simulations to study the effect of noise on cellular structure formation. The model not only contributes to a better understanding of many physiological situations. In the future it could also be used for biomedical applications to optimize protocols for artificial tissues with respect to sample geometry, boundary condition, material properties or cell density.
This work deals with the connection between two basic phenomena in Nonlinear Dynamics: synchronization of chaotic systems and recurrences in phase space. Synchronization takes place when two or more systems adapt (synchronize) some characteristic of their respective motions, due to an interaction between the systems or to a common external forcing. The appearence of synchronized dynamics in chaotic systems is rather universal but not trivial. In some sense, the possibility that two chaotic systems synchronize is counterintuitive: chaotic systems are characterized by the sensitivity ti different initial conditions. Hence, two identical chaotic systems starting at two slightly different initial conditions evolve in a different manner, and after a certain time, they become uncorrelated. Therefore, at a first glance, it does not seem to be plausible that two chaotic systems are able to synchronize. But as we will see later, synchronization of chaotic systems has been demonstrated. On one hand it is important to investigate the conditions under which synchronization of chaotic systems occurs, and on the other hand, to develop tests for the detection of synchronization. In this work, I have concentrated on the second task for the cases of phase synchronization (PS) and generalized synchronization (GS). Several measures have been proposed so far for the detection of PS and GS. However, difficulties arise with the detection of synchronization in systems subjected to rather large amounts of noise and/or instationarities, which are common when analyzing experimental data. The new measures proposed in the course of this thesis are rather robust with respect to these effects. They hence allow to be applied to data, which have evaded synchronization analysis so far. The proposed tests for synchronization in this work are based on the fundamental property of recurrences in phase space.
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.
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.
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.
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.
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.
This thesis presents new approaches to evolutions of binary black hole systems in numerical relativity. We analyze and compare evolutions from various physically motivated initial data sets, in particular presenting the first evolutions of Thin Sandwich data generated by the Meudon group. For the first time two different quasi-circular orbit initial data sequences are compared through fully 3d numerical evolutions: Puncture data and Thin Sandwich data (TSD) based on a helical killing vector ansatz. The two different sets are compared in terms of the physical quantities that can be measured from the numerical data, and in terms of their evolutionary behavior. The evolutions demonstrate that for the latter, "Meudon" datasets, the black holes do in fact orbit for a longer amount of time before they merge, in comparison with Puncture data from the same separation. This indicates they are potentially better estimates of quasi-circular orbit parameters. The merger times resulting from the numerical simulations are consistent with independent Post-Newtonian estimates that the final plunge phase of a black hole inspiral should take 60% of an orbit.
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.
This thesis describes the development and application of the impacts module of the ICLIPS model, a global integrated assessment model of climate change. The presentation of the technical aspects of this model component is preceded by a discussion of the sociopolitical context for model-based integrated assessments, which defines important requirements for the specification of the model. Integrated assessment of climate change comprises a broad range of scientific efforts to support the decision-making about objectives and measures for climate policy, whereby many different approaches have been followed to provide policy-relevant information about climate impacts. Major challenges in this context are the large diversity of the relevant spatial and temporal scales, the multifactorial causation of many climate impacts', considerable scientific uncertainties, and the ambiguity associated with unavoidable normative evaluations. A hierarchical framework is presented for structuring climate impact assessments that reflects the evolution of their practice and of the underlying theory. Integrated assessment models of climate change (IAMs) are scientific tools that contain simplified representations of the relevant components of the coupled society-climate system. The major decision-analytical frameworks for IAMs are evaluated according to their ability to address important aspects of the pertinent social decision problem. The guardrail approach is presented as an inverse' framework for climate change decision support, which aims to identify the whole set of policy strategies that are compatible with a set of normatively specified constraints (guardrails'). This approach combines, to a certain degree, the scientific rigour and objectivity typical of predictive approaches with the ability to consider virtually all decision options that is at the core of optimization approaches. The ICLIPS model is described as the first IAM that implements the guardrail approach. The representation of climate impacts is a key concern in any IAM. A review of existing IAMs reveals large differences in the coverage of impact sectors, in the choice of the impact numeraire(s), in the consideration of non-climatic developments, including purposeful adaptation, in the handling of uncertainty, and in the inclusion of singular events. IAMs based on an inverse approach impose specific requirements to the representation of climate impacts. This representation needs to combine a level of detail and reliability that is sufficient for the specification of impact guardrails with the conciseness and efficiency that allows for an exploration of the complete domain of plausible climate protection strategies. Large-scale singular events can often be represented by dynamic reduced-form models. This approach, however, is less appropriate for regular impacts where the determination of policy-relevant results generally needs to consider the heterogeneity of climatic, environmental, and socioeconomic factors at the local or regional scale. Climate impact response functions (CIRFs) are identified as the most suitable reduced-form representation of regular climate impacts in the ICLIPS model. A CIRF depicts the aggregated response of a climate-sensitive system or sector as simulated by a spatially explicit sectoral impact model for a representative subset of plausible futures. In the CIRFs presented here, global mean temperature and atmospheric CO2 concentration are used as predictors for global and regional impacts on natural vegetation, agricultural crop production, and water availability. Application of a pattern scaling technique makes it possible to consider the regional and seasonal patterns in the climate anomalies simulated by several general circulation models while ensuring the efficiency of the dynamic model components. Efforts to provide quantitative estimates of future climate impacts generally face a trade-off between the relevance of an indicator for stakeholders and the exactness with which it can be determined. A number of non-monetary aggregated impact indicators for the CIRFs is presented, which aim to strike the balance between these two conflicting goals while taking into account additional constraints of the ICLIPS modelling framework. Various types of impact diagrams are used for the visualization of CIRFs, each of which provides a different perspective on the impact result space. The sheer number of CIRFs computed for the ICLIPS model precludes their comprehensive presentation in this thesis. Selected results referring to changes in the distribution of biomes in different biogeographical regions, in the agricultural potential of various countries, and in the water availability in selected major catchments are discussed. The full set of CIRFs is accessible via the ICLIPS Impacts Tool, a graphical user interface that provides convenient access to more than 100,000 impact diagrams developed for the ICLIPS model. The technical aspects of the software are described as well as the accompanying database of CIRFs. The most important application of CIRFs is in inverse' mode, where they are used to translate impact guardrails into simultaneous constraints for variables from the optimizing ICLIPS climate-economy model. This translation is facilitated by algorithms for the computation of reachable climate domains and for the parameterized approximation of admissible climate windows derived from CIRFs. The comprehensive set of CIRFs, together with these algorithms, enables the ICLIPS model to flexibly explore sets of climate policy strategies that explicitly comply with impact guardrails specified in biophysical units. This feature is not found in any other intertemporally optimizing IAM. A guardrail analysis with the integrated ICLIPS model is described that applies selected CIRFs for ecosystem changes. So-called necessary carbon emission corridors' are determined for a default choice of normative constraints that limit global vegetation impacts as well as regional mitigation costs, and for systematic variations of these constraints. A brief discussion of recent developments in integrated assessment modelling of climate change connects the work presented here with related efforts.
In this thesis the gravitational lensing effect is used to explore a number of cosmological topics. We determine the time delay in the gravitationally lensed quasar system HE1104-1805 using different techniques. We obtain a time delay Delta_t(A-B) Delta_t(A-B) =-310 +- 20 days (2 sigma errors) between the two components. We also study the double quasar Q0957+561 during a three years monitoring campaign. The fluctuations we find in the difference light curves are completely consistent with noise and no microlensing is needed to explain these fluctuations. Microlensing is also studied in the quadruple quasar Q2237+0305 during the GLITP collaboration (Oct.1999-Feb.2000). We use the absence of a strong microlensing signal to obtain an upper limit of v=600 km/s for the effective transverse velocity of the lens galaxy (considering microlenses with 0.1 solar masses). The distribution of dark matter in galaxy clusters is also studied in the second part of the thesis. In the cluster of galaxies Cl0024+1654 we obtain a mass-to-light ratio of M/L = 200 M_sun/L_sun (within a radius of 3 arcminutes). In the galaxy cluster RBS380 we find a relatively low X-ray luminosity for a massive cluster of L =2*10^(44) erg/s, but a rich distribution of galaxies in the optical band.
The correlations between the chemical structures of the 2,5-diphenyl-1,3,4-oxadiazole compounds and their corresponding vapour deposited film structures on Si/SiO2 were systematically investigated with AFM, XSR and IR for the first time. The result shows that the film structure depends strongly on the substrate temperature (Ts). For the compounds with ether bridge group, the film periodicity depends linearly on the length of the aliphatic chain. The films based on those oxadiazols have ordered structure in the investigated substrate temperature region, while die amide bridged compounds form ordered film only at high Ts due to the formation of intermolecular H-bond. The tilt angle of most molecules is determined by the pi-pi complexes between the molecules. The intermolecular interaction between head groups leads to the structural transformation during the thermal treatment after deposition. All the ether bridged oxadiazoles form films with bilayer structure, while amide bridged oxadiazole form film bilayer structure only when the molecule has a head group.
This thesis deals with the encoding and transmission of information through a quantum channel. A quantum channel is a quantum mechanical system whose state is manipulated by a sender and read out by a receiver. The individual state of the channel represents the message. The two topics of the thesis comprise 1) the possibility of compressing a message stored in a quantum channel without loss of information and 2) the possibility to communicate a message directly from one party to another in a secure manner, that is, a third party is not able to eavesdrop the message without being detected. The main results of the thesis are the following. A general framework for variable-length quantum codes is worked out. These codes are necessary to make lossless compression possible. Due to the quantum nature of the channel, the encoded messages are in general in a superposition of different lengths. It is found to be impossible to compress a quantum message without loss of information if the message is not apriori known to the sender. In the other case it is shown that lossless quantum data compression is possible and a lower bound on the compression rate is derived. Furthermore, an explicit compression scheme is constructed that works for arbitrarily given source message ensembles. A quantum cryptographic protocol - the “ping-pong protocol” - is presented that realizes the secure direct communication of classical messages through a quantum channel. The security of the protocol against arbitrary eavesdropping attacks is proven for the case of an ideal quantum channel. In contrast to other quantum cryptographic protocols, the ping-pong protocol is deterministic and can thus be used to transmit a random key as well as a composed message. The protocol is perfectly secure for the transmission of a key, and it is quasi-secure for the direct transmission of a message. The latter means that the probability of successful eavesdropping exponentially decreases with the length of the message.
We study the effect on the elastic properties of lipid membranes induced by anchoring of long hydrophilic polymers. Theoretically, two limiting regimes for the membrane spontaneous curvature are expected : i) at low surface polymer concentration (mushroom regime) the spontaneous curvature should scale linearly with the surface density of anchored polymers; ii) at high coverage (brush regime) the dependence should be quadratic. We attempt to test the predictions for the brush regime by monitoring the morphological changes induced on giant vesicles. As long polymers we use fluorescently labeled λ-phage DNA molecules which are attached to biotinylated lipid vesicles with a biotin-avidin-biotin linkage. By varying the amount of biotinylated lipid in the membrane we control the surface concentration of the anchors. The amount of anchored DNA to the membrane is quantified with fluorescence measurements. Changes in the elastic properties of the membrane as DNA grafts to it are monitored via analysis of the vesicle fluctuations. The spontaneous curvature of the membrane increases as a function of the surface coverage. At higher grafting concentrations the vesicles bud. The size of the buds can also be used to assess the membrane curvature. The effect on the bending stiffness is a subject of further investigation.
The theory of atomic Boson-Fermion mixtures in the dilute limit beyond mean-field is considered in this thesis. Extending the formalism of quantum field theory we derived expressions for the quasi-particle excitation spectra, the ground state energy, and related quantities for a homogenous system to first order in the dilute gas parameter. In the framework of density functional theory we could carry over the previous results to inhomogeneous systems. We then determined to density distributions for various parameter values and identified three different phase regions: (i) a stable mixed regime, (ii) a phase separated regime, and (iii) a collapsed regime. We found a significant contribution of exchange-correlation effects in the latter case. Next, we determined the shift of the Bose-Einstein condensation temperature caused by Boson-Fermion interactions in a harmonic trap due to redistribution of the density profiles. We then considered Boson-Fermion mixtures in optical lattices. We calculated the criterion for stability against phase separation, identified the Mott-insulating and superfluid regimes both, analytically within a mean-field calculation, and numerically by virtue of a Gutzwiller Ansatz. We also found new frustrated ground states in the limit of very strong lattices. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2004 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.
Transport processes in and of cells are of major importance for the survival of the organism. Muscles have to be able to contract, chromosomes have to be moved to opposing ends of the cell during mitosis, and organelles, which are compartments enclosed by membranes, have to be transported along molecular tracks. Molecular motors are proteins whose main task is moving other molecules.For that purpose they transform the chemical energy released in the hydrolysis of ATP into mechanical work. The motors of the cytoskeleton belong to the three super families myosin, kinesin and dynein. Their tracks are filaments of the cytoskeleton, namely actin and the microtubuli. Here, we examine stochastic models which are used for describing the movements of these linear molecular motors. The scale of the movements comprises the regime of single steps of a motor protein up to the directed walk along a filament. A single step bridges around 10 nm, depending on the protein, and takes about 10 ms, if there is enough ATP available. Our models comprise M states or conformations the motor can attain during its movement along a one-dimensional track. At K locations along the track transitions between the states are possible. The velocity of the protein depending on the transition rates between the single states can be determined analytically. We calculate this velocity for systems of up to four states and locations and are able to derive a number of rules which are helpful in estimating the behaviour of an arbitrary given system. Beyond that we have a look at decoupled subsystems, i.e., one or a couple of states which have no connection to the remaining system. With a certain probability a motor undergoes a cycle of conformational changes, with another probability an independent other cycle. Active elements in real transport processes by molecular motors will not be limited to the transitions between the states. In distorted networks or starting from the discrete Master equation of the system, it is possible to specify horizontal rates, too, which furthermore no longer have to fulfill the conditions of detailed balance. Doing so, we obtain unique, complete paths through the respective network and rules for the dependence of the total current on all the rates of the system. Besides, we view the time evolutions for given initial distributions. In enzymatic reactions there is the idea of a main pathway these reactions follow preferably. We determine optimal paths and the maximal flow for given networks. In order to specify the dependence of the motor's velocity on its fuel ATP, we have a look at possible reaction kinetics determining the connection between unbalanced transitions rates and ATP-concentration. Depending on the type of reaction kinetics and the number of unbalanced rates, we obtain qualitatively different curves connecting the velocity to the ATP-concentration. The molecular interaction potentials the motor experiences on its way along its track are unknown. We compare different simple potentials and the effects the localization of the vertical rates in the network model has on the transport coefficients in comparison to other models.
Movements of processive cytoskeletal motors are characterized by an interplay between directed motion along filament and diffusion in the surrounding solution. In the present work, these peculiar movements are studied by modeling them as random walks on a lattice. An additional subject of our studies is the effect of motor-motor interactions on these movements. In detail, four transport phenomena are studied: (i) Random walks of single motors in compartments of various geometries, (ii) stationary concentration profiles which build up as a result of these movements in closed compartments, (iii) boundary-induced phase transitions in open tube-like compartments coupled to reservoirs of motors, and (iv) the influence of cooperative effects in motor-filament binding on the movements. All these phenomena are experimentally accessible and possible experimental realizations are discussed.
The present work investigates the structure formation and wetting in two dimensional (2D) Langmuir monolayer phases in local thermodynamic equilibrium. A Langmuir monolayer is an isolated 2D system of surfactants at the air/water interface. It exhibits crystalline, liquid crystalline, liquid and gaseous phases differing in positional and/or orientational order. Permanent electric dipole moments of the surfactants lead to a long range repulsive interaction and to the formation of mesoscopic patterns. An interaction model is used describing the structure formation as a competition between short range attraction (bare line tension) and long range repulsion (surface potentials) on a scale Delta. Delta has the meaning of a dividing length between the short and long range interaction. In the present work the thermodynamic equilibrium conditions for the shape of two phase boundary lines (Young-Laplace equation) and three phase intersection points (Young′s condition) are derived and applied to describe experimental data: The line tension is measured by pendant droplet tensiometry. The bubble shape and size of 2D foams is calculated numerically and compared to experimental foams. Contact angles are measured by fitting numerical solutions of the Young-Laplace equation on micron scale. The scaling behaviour of the contact angle allows to measure a lower limit for Delta. Further it is discussed, whether in biological membranes wetting transitions are a way in order to control reaction kinetics. Studies performed in our group are discussed with respect to this question in the framework of the above mentioned theory. Finally the apparent violation of Gibbs′ phase rule in Langmuir monolayers (non-horizontal plateau of the surface pressure/area-isotherm, extended three phase coexistence region in one component systems) is investigated quantitatively. It has been found that the most probable explanation are impurities within the system whereas finite size effects or the influence of the long range electrostatics can not explain the order of magnitude of the effect.
One of the rules-of-thumb of colloid and surface physics is that most surfaces are charged when in contact with a solvent, usually water. This is the case, for instance, in charge-stabilized colloidal suspensions, where the surface of the colloidal particles are charged (usually with a charge of hundreds to thousands of e, the elementary charge), monolayers of ionic surfactants sitting at an air-water interface (where the water-loving head groups become charged by releasing counterions), or bilayers containing charged phospholipids (as cell membranes). In this work, we look at some model-systems that, although being a simplified version of reality, are expected to capture some of the physical properties of real charged systems (colloids and electrolytes). We initially study the simple double layer, composed by a charged wall in the presence of its counterions. The charges at the wall are smeared out and the dielectric constant is the same everywhere. The Poisson-Boltzmann (PB) approach gives asymptotically exact counterion density profiles around charged objects in the weak-coupling limit of systems with low-valent counterions, surfaces with low charge density and high temperature (or small Bjerrum length). Using Monte Carlo simulations, we obtain the profiles around the charged wall and compare it with both Poisson-Boltzmann (in the low coupling limit) and the novel strong coupling (SC) theory in the opposite limit of high couplings. In the latter limit, the simulations show that the SC leads in fact to asymptotically correct density profiles. We also compare the Monte Carlo data with previously calculated corrections to the Poisson-Boltzmann theory. We also discuss in detail the methods used to perform the computer simulations. After studying the simple double layer in detail, we introduce a dielectric jump at the charged wall and investigate its effect on the counterion density distribution. As we will show, the Poisson-Boltzmann description of the double layer remains a good approximation at low coupling values, while the strong coupling theory is shown to lead to the correct density profiles close to the wall (and at all couplings). For very large couplings, only systems where the difference between the dielectric constants of the wall and of the solvent is small are shown to be well described by SC. Another experimentally relevant modification to the simple double layer is to make the charges at the plane discrete. The counterions are still assumed to be point-like, but we constraint the distance of approach between ions in the plane and counterions to a minimum distance D. The ratio between D and the distance between neighboring ions in the plane is, as we will see, one of the important quantities in determining the influence of the discrete nature of the charges at the wall over the density profiles. Another parameter that plays an important role, as in the previous case, is the coupling as we will demonstrate, systems with higher coupling are more subject to discretization effects than systems with low coupling parameter. After studying the isolated double layer, we look at the interaction between two double layers. The system is composed by two equally charged walls at distance d, with the counterions confined between them. The charge at the walls is smeared out and the dielectric constant is the same everywhere. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space, and the pressure is shown to be negative (attraction) at certain conditions. The simulations also show that the equilibrium plate separation (where the pressure changes from attractive to repulsive) exhibits a novel unbinding transition. We compare the Monte Carlo results with the strong-coupling theory, which is shown to describe well the bound states of systems with moderate and high couplings. The regime where the two walls are very close to each other is also shown to be well described by the SC theory. Finally, Using a field-theoretic approach, we derive the exact low-density ("virial") expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). The free energy obtained is valid for systems where the diameters d_+ and d_- and the charge valences q_+ and q_- of positive and negative ions are unconstrained, i.e., the same expression can be used to treat dilute salt solutions (where typically d_+ ~ d_- and q_+ ~ q_-) as well as colloidal suspensions (where the difference in size and valence between macroions and counterions can be very large). We also discuss some applications of our results.
Deep convection is an essential part of the circulation in the North Atlantic Ocean. It influences the northward heat transport achieved by the thermohaline circulation. Understanding its stability and variability is therefore necessary for assessing climatic changes in the area of the North Atlantic. This thesis aims at improving the conceptual understanding of the stability and variability of deep convection. Observational data from the Labrador Sea show phases with and without deep convection. A simple two-box model is fitted to these data. The results suggest that the Labrador Sea has two coexisting stable states, one with regular deep convection and one without deep convection. This bistability arises from a positive salinity feedback that is due to the net freshwater input into the surface layer. The convecting state can easily become unstable if the mean forcing shifts to warmer or less saline conditions. The weather-induced variability of the external forcing is included into the box model by adding a stochastic forcing term. It turns out that deep convection is then switched "on" and "off" frequently. The mean residence time in either state is a measure of its stochastic stability. The stochastic stability depends smoothly on the forcing parameters, in contrast to the deterministic (non-stochastic) stability which may change abruptly. The mean and the variance of the stochastic forcing both have an impact on the frequency of deep convection. For instance, a decline in convection frequency due to a surface freshening may be compensated for by an increased heat flux variability. With a further simplified box model some stochastic stability features are studied analytically. A new effect is described, called wandering monostability: even if deep convection is not a stable state due to changed forcing parameters, the stochastic forcing can still trigger convection events frequently. The analytical expressions explicitly show how wandering monostability and other effects depend on the model parameters. This dependence is always exponential for the mean residence times, but for the probability of long nonconvecting phases it is exponential only if this probability is small. It is to be expected that wandering monostability is relevant in other parts of the climate system as well. All in all, the results demonstrate that the stability of deep convection in the Labrador Sea reacts very sensitively to the forcing. The presence of variability is crucial for understanding this sensitivity. Small changes in the forcing can already significantly lower the frequency of deep convection events, which presumably strongly affects the regional climate. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2003 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.
Motivated by recent proposals on the experimental detectability of quantum gravity effects, the present thesis investigates assumptions and methods which might be used for the prediction of such effects within the framework of loop quantum gravity. To this end, a scalar field coupled to gravity is considered as a model system. Starting from certain assumptions about the dynamics of the coupled gravity-matter system, a quantum theory for the scalar field is proposed. Then, assuming that the gravitational field is in a semiclassical state, a "QFT on curved space-time limit" of this theory is defined. In contrast to ordinary quantum field theory on curved space-time however, in this limit the theory describes a quantum scalar field propagating on a (classical) random lattice. Then, methods to obtain the low energy limit of such a lattice theory, especially regarding the resulting modified dispersion relations, are discussed and applied to simple model systems. Finally, under certain simplifying assumptions, using the methods developed before as well as a specific class of semiclassical states, corrections to the dispersion relations for the scalar and the electromagnetic field are computed within the framework of loop quantum gravity. These calculations are of preliminary character, as many assumptions enter whose validity remains to be studied more thoroughly. However they exemplify the problems and possibilities of making predictions based on loop quantum gravity that are in principle testable by experiment.
Structural and spectroscopical study of crystals of 1,3,4-oxadiazole derivatives at high pressure
(2002)
In recent years the search for new materials of technological interest has given new impulses to the study of organic compounds. Organic substances possess a great number of advantages such as the possibility to adjust their properties for a given purpose by different chemical and physical techniques in the preparation process. Oxadiazole derivatives are interesting due to their use as material for light emitting diodes (LED) as well as scintillators. The physical properties of a solid depend on its structure. Different structures induce different intra- and intermolecular interactions. An advantageous method to modify the intra- as well as the intermolecular interactions of a given substance is the application of high pressure. Furthermore, using this method the chemical features of the compound are not influenced. We have investigated the influence of high pressure and high temperature on the super-molecular structure of several oxadiazole derivatives in crystalline state. From the results of this investigation an equation of state for these crystals was determined. Furthermore, the spectroscopical features of these materials under high pressure were characterized.
New polymers and low molecular compounds, suitable for organic light emitting devices and organic electronic applications, have been synthesised in this years in order to obtain electron transport characteristics compatible with requirements for applications in real plastic devices. However, despite of the technological importance and of the relevant progress in devices manufacture, fundamental physical properties of such class of materials are still not enough studied. In particular extensive presence of distributions of localised states inside the band gap has a deep impact on their electronic properties. Such presence of shallow traps as well as the influence of the sample preparation conditions on deep and shallow localised states have not been, until now, systematically explored. The thermal techniques are powerful tools in order to study localised levels in inorganic and organic materials. Thermally stimulated luminescence (TSL), thermally stimulated currents (TSC) and thermally stimulated depolarisation currents (TSDC) allow to deeply look to shallow and deep trap levels as well as they permit to study, in synergy with dielectric spectroscopy (DES), polarisation and depolarisation effects. We studied, by means of numerical simulations, the first and the second order kinetic equations characterised by negligible and strong re-trapping respectively. We included in the equations Gaussian, exponential and quasi-continuous distributions of localised states. The shapes of the theoretical peaks have been investigated by means of systematic variation of the two main parameters of the equations, i. e. the energy trap depth E and the frequency factor a and of the parameters regulating the distributions, in particular for a Gaussian distribution the distribution width s and the integration limits. The theoretical findings have been applied to experimental glow curves. Thin films of polymers and low molecular compounds. Polyphenylquinoxalines, trisphenylquinoxalines and oxadiazoles, studied because of their technological relevance, show complex thermograms, having several levels of localised states and depolarisation peaks. In particular well ordered films of an amphiphilic substituted 2-(p-nitrophenyl)-5-(p-undecylamidophenyl)-1,3,4-oxadiazole (NADPO) are characterised by rich TSL thermograms. A wide region of shallow traps, localised at Em = 4 meV, has been successfully fit by means of a first order kinetic equation having a Gaussian distribution of localised states. Two further peaks, having a different origin, have been characterised. The peaks at Tm = 221.5 K and Tm = 254.2 have activation energy of Em= 0.63 eV and Em = 0.66 eV, frequency factor s = 2.4x1012 s-1 and s = 1.85x1011 s-1, distribution width s = 0.045 eV and s = 0.088 eV respectively. Increasing the number of thermal cycle, a peak, probably connected with structural defects, appears at Tm = 197.7 K. The numerical analysis of this peak was performed by means of a first order equation containing a Gaussian distribution of traps. The activation energy of the trap level is centred at Em = 0.55 eV. The distribution is perfectly symmetric with a quite small width s = 0.028 eV. The frequency factor is s = 1.15 x 1012 s-1, resulting of the same order of magnitude of its neighbour peak at Tm = 221.5 K, having both, probably, the same origin. Furthermore the work demonstrates that the shape of the glow curves is strongly influenced by the excitation temperature and by the thermal cycles. For that reason Gaussian distributions of localised states can be confused with exponential distributions if the previous thermal history of the samples is not adequately considered.
Jets are highly collimated flows of matter. They are present in a large variety of astrophysical sources: young stars, stellar mass black holes (microquasars), galaxies with an active nucleus (AGN) and presumably also intense flashes of gamma-rays. In particular, the jets of microquasars, powered by accretion disks, are probably small-scale versions of the outflows from AGN. Beside observations of astrophysical jet sources, also theoretical considerations have shown that magnetic fields play an important role in jet formation, acceleration and collimation. Collimated jets seem to be systematically associated with the presence of an accretion disk around a star or a collapsed object. If the central object is a black hole, the surrounding accretion disk is the only possible location for a magnetic field generation. We are interested in the formation process of highly relativistic jets as observed from microquasars and AGN. We theoretically investigate the jet collimation region, whose physical dimensions are extremely tiny even compared to radio telescopes spatial resolution. Thus, for most of the jet sources, global theoretical models are, at the moment, the only possibility to gain information about the physical processes in the innermost jet region. For the first time, we determine the global two-dimensional field structure of stationary, axisymmetric, relativistic, strongly magnetized (force-free) jets collimating into an asymptotically cylindrical jet (taken as boundary condition) and anchored into a differentially rotating accretion disk. This approach allows for a direct connection between the accretion disk and the asymptotic collimated jet. Therefore, assuming that the foot points of the field lines are rotating with Keplerian speed, we are able to achieve a direct scaling of the jet magnetosphere in terms of the size of the central object. We find a close compatibility between the results of our model and radio observations of the M87 galaxy innermost jet. We also calculate the X-ray emission in the energy range 0.2--10.1\,keV from a microquasar relativistic jet close to its source of 5 solar masses. In order to do it, we apply the jet flow parameters (densities, velocities, temperatures of each volume element along the collimating jet) derived in the literature from the relativistic magnetohydrodynamic equations. We obtain theoretical thermal X-ray spectra of the innermost jet as composition of the spectral contributions of the single volume elements along the jet. Since relativistic effects as Doppler shift and Doppler boosting due to the motion of jets toward us might be important, we investigate how the spectra are affected by them considering different inclinations of the line of sight to the jet axis. Emission lines of highly ionized iron are clearly visible in our spectra, probably also observed in the Galactic microquasars GRS 1915+105 and XTE J1748-288. The Doppler shift of the emission lines is always evident. Due to the chosen geometry of the magnetohydrodynamic jet, the inner X-ray emitting part is not yet collimated. Ergo, depending on the viewing angle, the Doppler boosting does not play a major role in the total spectra. This is the first time that X-ray spectra have been calculated from the numerical solution of a magnetohydrodynamic jet.
Nonlinear multistable systems under the influence of noise exhibit a plethora of interesting dynamical properties. A medium noise level causes hopping between the metastable states. This attractorhopping process is characterized through laminar motion in the vicinity of the attractors and erratic motion taking place on chaotic saddles, which are embedded in the fractal basin boundary. This leads to noise-induced chaos. The investigation of the dissipative standard map showed the phenomenon of preference of attractors through the noise. It means, that some attractors get a larger probability of occurrence than in the noisefree system. For a certain noise level this prefernce achieves a maximum. Other attractors are occur less often. For sufficiently high noise they are completely extinguished. The complexity of the hopping process is examined for a model of two coupled logistic maps employing symbolic dynamics. With the variation of a parameter the topological entropy, which is used together with the Shannon entropy as a measure of complexity, rises sharply at a certain value. This increase is explained by a novel saddle merging bifurcation, which is mediated by a snapback repellor. Scaling laws of the average time spend on one of the formerly disconnected parts and of the fractal dimension of the connected saddle describe this bifurcation in more detail. If a chaotic saddle is embedded in the open neighborhood of the basin of attraction of a metastable state, the required escape energy is lowered. This enhancement of noise-induced escape is demonstrated for the Ikeda map, which models a laser system with time-delayed feedback. The result is gained using the theory of quasipotentials. This effect, as well as the two scaling laws for the saddle merging bifurcation, are of experimental relevance.
Subject of this work is the investigation of generic synchronization phenomena in interacting complex systems. These phenomena are observed, among all, in coupled deterministic chaotic systems. At very weak interactions between individual systems a transition to a weakly coherent behavior of the systems can take place. In coupled continuous time chaotic systems this transition manifests itself with the effect of phase synchronization, in coupled chaotic discrete time systems with the effect of non-vanishing macroscopic mean field. Transition to coherence in a chain of locally coupled oscillators described with phase equations is investigated with respect to the symmetries in the system. It is shown that the reversibility of the system caused by these symmetries results to non-trivial topological properties of trajectories so that the system constructed to be dissipative reveals in a whole parameter range quasi-Hamiltonian features, i.e. the phase volume is conserved on average and Lyapunov exponents come in symmetric pairs. Transition to coherence in an ensemble of globally coupled chaotic maps is described with the loss of stability of the disordered state. The method is to break the self-consistensy of the macroscopic field and to characterize the ensemble in analogy to an amplifier circuit with feedback with a complex linear transfer function. This theory is then generalized for several cases of theoretic interest.
Subject of this work is the investigation of universal scaling laws which are observed in coupled chaotic systems. Progress is made by replacing the chaotic fluctuations in the perturbation dynamics by stochastic processes. First, a continuous-time stochastic model for weakly coupled chaotic systems is introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck equation scaling relations are derived, which are confirmed by results of numerical simulations. Next, the new effect of avoided crossing of Lyapunov exponents of weakly coupled disordered chaotic systems is described, which is qualitatively similar to the energy level repulsion in quantum systems. Using the scaling relations obtained for the coupling sensitivity of chaos, an asymptotic expression for the distribution function of small spacings between Lyapunov exponents is derived and compared with results of numerical simulations. Finally, the synchronization transition in strongly coupled spatially extended chaotic systems is shown to resemble a continuous phase transition, with the coupling strength and the synchronization error as control and order parameter, respectively. Using results of numerical simulations and theoretical considerations in terms of a multiplicative noise partial differential equation, the universality classes of the observed two types of transition are determined (Kardar-Parisi-Zhang equation with saturating term, directed percolation).
Polymers at membranes
(2000)
The surface of biological cells consists of a lipid membrane and a large amount of various proteins and polymers, which are embedded in the membrane or attached to it. We investigate how membranes are influenced by polymers, which are anchored to the membrane by one end. The entropic pressure exerted by the polymer induces a curvature, which bends the membrane away from the polymer. The resulting membrane shape profile is a cone in the vicinity of the anchor segment and a catenoid far away from it. The perturbative calculations are confirmed by Monte-Carlo simulations. An additional attractive interaction between polymer and membrane reduces the entropically induced curvature. In the limit of strong adsorption, the polymer is localized directly on the membrane surface and does not induce any pressure, i.e. the membrane curvature vanishes. If the polymer is not anchored directly on the membrane surface, but in a non-vanishing anchoring distance, the membrane bends towards the polymer for strong adsorption. In the last part of the thesis, we study membranes under the influence of non-anchored polymers in solution. In the limit of pure steric interactions between the membrane and free polymers, the membrane curves towards the polymers (in contrast to the case of anchored polymers). In the limit of strong adsorption the membrane bends away from the polymers.
In this thesis we use the gravitational lensing effect as a tool to tackle two rather different cosmological topics: the nature of the dark matter in galaxy halos, and the rotation of the universe. Firstly, we study the microlensing effect in the gravitational lens systems Q0957+561 and Q2237+0305. In these systems the light from the quasar shines directly through the lensing galaxy. Due to the relative motion of the quasar, the lensing galaxy, and the observer compact objects in the galaxy or galaxy halo cause brightness fluctuations of the light from the background quasar. We compare light curve data from a monitoring program of the double quasar Q0957+561 at the 3.5m telescope at Apache Point Observatory from 1995 to 1998 (Colley, Kundic & Turner 2000) with numerical simulations to test whether the halo of the lensing galaxy consists of massive compact objects (MACHOs). This test was first proposed by Gott (1981). We can exclude MACHO masses from 10^-6 M_sun up to 10^-2 M_sun for quasar sizes of less than 3x10^14 h_60^-0.5 cm if the MACHOs make up at least 50% of the dark halo. Secondly, we present new light curve data for the gravitationally lensed quadruple quasar Q2237+0305 taken at the 3.5m telescope at Apache Point Observatory from June 1995 to January 1998. Although the images were taken under variable, often poor seeing conditions and with coarse pixel sampling, photometry is possible for the two brighter quasar images A and B with the help from HST observations. We find independent evidence for a brightness peak in image A of 0.4 to 0.5 mag with a duration of at least 100 days, which indicates that microlensing has taken place in the lensing galaxy. Finally, we use the weak gravitational lensing effect to put limits on a class of Goedel-type rotating cosmologies described by Korotky & Obukhov (1996). In weak lensing studies the shapes of thousands of background galaxies are measured and averaged to reveal coherent gravitational distortions of the galaxy shapes by foreground matter distributions, or by the large-scale structure of space-time itself. We calculate the predicted shear as a function of redshift in Goedel-type rotating cosmologies and compare this to the upper limit on cosmic shear gamma_limit of approximately 0.04 from weak lensing studies. We find that Goedel-type models cannot have larger rotations omega than H_0=6.1x10^-11 h_60/year if this shear limit is valid for the whole sky.
Encounters with neighbours
(2003)
In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications. Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed. Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots.