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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.
Die Fusion von Membranen ist ein entscheidender Prozeß bei der Entwicklung von Zellen im Körper. Beispielsweise ist sie eine der Voraussetzungen bei der Befruchtung einer Eizelle durch ein Spermium oder für das Eindringen von Viren in eine Zelle. Membranfusion ist auch notwendig für den Stofftransport in die Zelle hinein oder aus ihr heraus. Die Membranfusion ist daher auch von praktischen Interesse auf den Gebieten der Pharmazeutik und des 'Bioengineering'. Oft muss eine Membran mit der infiziertin Zelle fusionieren, um ein Medikament an sein Zeil zu bringen. Deshalb ist ein Verständnis der Membranfusion von großem Interesse für die Entwicklung von gezielten und effizienten Methoden des 'drug delivery'. Dasselbe gilt für die gezielte Zufuhr von Genen bei der Gentherapie. Obwohl die Membranfusion schon vor nahezu 200 Jahren von dem deutschen Biologen und Mediziner Johannes Müller beobachtet wurde, liegt ein vollständiges Verständnis des Fusionsprozesses von Zellen und (Modell-) Membranen auch heute noch in weiter Ferne. Allerdings hat im letzten Jahrzehnt das Interesse für dieses Forschungsgebiet stark zugenommen. Wissenschaftler der unterschiedlichsten Disziplinen arbeiten daran, die Mechanismen der Membranfusion aufzudecken. Biologen untersuchen Proteine, die die Fusion auslösen, Chemiker entwickeln Moleküle, die die Fusion erleichtern, und Physiker versuchen die Antriebsmechanismen der Membranfusion zu verstehen. Neue Mikroskopietechniken und die hohe Rechenleistung moderner Computer helfen die molekulare und die makroskopische Welt der Membranfusion in einem Bild zusammenzufügen. Für unsere Untersuchungen haben wir Modellmembranen, die aus Lipiddoppelschichten bestehen, benutzt. Diese Membranen formen sogenannte Vesikel oder Liposomen, abgeschlossene Membrane, in denen eine bestimmte Menge an Flüssigkeit enthalten ist. Indem wir Rezeptoren in die Membran einbringen, schaffen wir funkionalisierte Vesikel, die sich differenzieren, kooperieren und selektiv reagieren können. Wir benutzen positiv geladene wasserlösliche Ionen, um Wechselwirkungen zwischen den Vesikeln zu vermitteln, und lassen die Rezeptoren und die Ionen den Fusionsprozess auslösen. Die Wechselwirkungen werden unter dem Mikroskop durch spezielle Mikromechanischn Gerätz Mikromechinerien kontrolliert. Mit Hilfe einer sehr schnellen digitale Bildaufnahmetechnik ist es uns gelungen, die Fusion unserer Modellmembranen aufzunehmen und in Echtzeit zu dokumentieren mit einer Auflösung von 50 µs. Unsere Messungen können vergleichen werden mit Computersimulationen des Fusionsprozesses. Diese Simulationen untersuchen Prozesse, die zwischen 0.1 und 1 Mikrosekunde dauern. Eine Herausforderung für die Zukunft wird es sein, die Lücke zwischen den in Experimenten (50µs) und den in Simulationen zugänglichen Zeitskalen von beiden Seiten her zu schließen.
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.
It has been known for several years that under certain conditions electrons can be confined within thin layers even if these layers consist of metal and are supported by a metal substrate. In photoelectron spectra, these layers show characteristic discrete energy levels and it has turned out that these lead to large effects like the oscillatory magnetic coupling technically exploited in modern hard disk reading heads. The current work asks in how far the concepts underlying quantization in two-dimensional films can be transferred to lower dimensionality. This problem is approached by a stepwise transition from two-dimensional layers to one-dimensional nanostructures. On the one hand, these nanostructures are represented by terraces on atomically stepped surfaces, on the other hand by atom chains which are deposited onto these terraces up to complete coverage by atomically thin nanostripes. Furthermore, self organization effects are used in order to arrive at perfectly one-dimensional atomic arrangements at surfaces. Angle-resolved photoemission is particularly suited as method of investigation because is reveals the behavior of the electrons in these nanostructures in dependence of the spacial direction which distinguishes it from, e. g., scanning tunneling microscopy. With this method intense and at times surprisingly large effects of one-dimensional quantization are observed for various exemplary systems, partly for the first time. The essential role of bandgaps in the substrate known from two-dimensional systems is confirmed for nanostructures. In addition, we reveal an ambiguity without precedent in two-dimensional layers between spacial confinement of electrons on the one side and superlattice effects on the other side as well as between effects caused by the sample and by the measurement process. The latter effects are huge and can dominate the photoelectron spectra. Finally, the effects of reduced dimensionality are studied in particular for the d electrons of manganese which are additionally affected by strong correlation effects. Surprising results are also obtained here. ---------------------------- Die Links zur jeweiligen Source der im Appendix beigefügten Veröffentlichungen befinden sich auf Seite 83 des Volltextes.
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.
Die Frage nach der Herkunft und der dynamischen Entwicklung langlebiger kosmischer Magnetfelder ist in vielen Details noch unbeantwortet. Es besteht zwar kein Zweifel daran, dass das Magnetfeld der Erde und anderer kosmischer Objekte durch den sogenannten Dynamoeffekt verursacht werden, der genaue Mechanismus als auch die notwendigen Voraussetzungen und Randbedingungen der zugrundeliegenden Strömungen sind aber weitgehend unbekannt. Die für einen Dynamo interessanten Strömungsmuster, die im Inneren von Himmelskörpern durch Konvektion und differentielle Rotation entstehen, sind Konvektionsrollen parallel zur Rotationsachse. Auf einer Strömung mit eben solcher Geometrie, der sogenannten Roberts-Strömung, basieren die in der vorliegenden Arbeit untersuchten Dynamomodelle. Mit Methoden der nichtlinearen Dynamik wird versucht, das Systemverhalten bei Änderung der Systemparamter genauer zu charakterisieren. Die numerischen Untersuchungen beginnen mit einer Analyse der Dynamoaktivität der Roberts-Strömung in Abhängigkeit von den zwei freien Parametern in den Modellgleichungen, der magnetischen Prandtl-Zahl und der Stärke des Energieinputs. Gefunden werden verschiedene Lösungstypen die von einem stationären Magnetfeld über periodische bis zu chaotischen Zuständen reichen. Die yugrundeliegenden Symmetrien werden beschrieben und die Bifurkationen, die zum Wechsel der Lösungstypen führen, charakterisiert. Zusätzlich gibt es Bereiche bei sehr kleinen Prandtl-Zahlen, in denen überhaupt kein Dynamo existiert. Dieses Verhalten wird in der Literatur auch für viele andere numerisch ausgewertete Modelle beschrieben. Im Übergangsbereich zwischen dynamoaktivem und dynamoinaktivem Bereich wird das Auftreten einer sogenannten Blowout-Bifurkation gefunden. Desweiteren beschäftigt sich die Arbeit mit der Frage, inwiefern Helizität, also eine schraubenförmige Bewegung, der Strömung den Dynamoeffekt beeinflusst. Dazu werden ähnliche Strömungstypen verglichen, die sich hauptsächlich in ihrem Helizitätswert unterscheiden. Es wird gefunden, dass ein bestimmter Wert der Helizität nicht unterschritten werden darf, um einen stabilen Roberts-Dynamo zu erhalten.
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.
Eine Nutzung der optischen Anisotropie dünner Schichten ist vor allem für die Displaytechnologie, die optische Datenspeicherung und für optische Sicherheitselemente von hoher Bedeutung. Diese Doktorarbeit befasst sich mit theoretischen und experimentellen Untersuchung von dreidimensionaler Anisotropie und dabei insbesondere mit der Untersuchung von lichtinduzierter dreidimensionaler Anisotropie in organischen dünnen Polymer-Schichten. Die gewonnenen Erkentnisse und entwickelten Methoden können wertvolle Beiträge für Optimierungsprozesse, wie bei der Kompensation der Blickwinkelabhängigkeit von Flüssigkristall-Displays, liefern. Die neue Methode der Immersions-Transmissions-Ellipsometrie (ITE) zur Untersuchung von dünneren Schichten wurde im Rahmen dieser Dissertation entwickelt. Diese Methode gestattet es, in Kombination mit konventioneller Reflexions- und Transmissionsellipsometrie, die absoluten dreidimensionalen Brechungsindices einer biaxialen Schicht zu bestimmen. Erstmals gelang es damit, das dreidimensionale Brechungsindexellipsoid von transparenten, dünneren (150 nm) Filmen hochgenau (drei Stellen hinter dem Komma) zu bestimmen. Die ITE-Methode hat demzufolge das Potential, auch bei noch dünneren Schichten mit Gewinn eingesetzt werden zu können. Die lichtinduzierte Generierung von dreidimensionaler Anisotropie wurde in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen, amorphen und flüssig-kristallinen Homo- und Copolymeren untersucht. Erstmals wurden quantitative Untersuchungen zur Änderung von lichtinduzierten, dreidimensionalen Anisotropien in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen Polymeren bei Tempern oberhalb der Glastemperatur durchgeführt. Bei vielen der untersuchten Polymere war die dreidimensionale Ordnung nach dem Bestrahlen mit polarisiertem Licht und anschließendem Tempern oberhalb der Glastemperatur scheinbar von der Schichtdicke abhängig. Die Ursache liegt wohl in der, mit der neuentwickelten ITE-Methode detektierten, planaren Ausgangsorientierung der aufgeschleuderten dünneren Schichten. Um Verkippungs-Gradienten in dickeren Polymerschichten in ihrem Verlauf zu bestimmen, wurde eine spezielle Methode unter Benutzung der Wellenleitermoden-Spektroskopie entwickelt. Quantenchemisch bestimmte, maximal induzierbare Doppelbrechungen in flüssig-kristallinen Polymeren wurden mit den experimentell gefundenen Ordnungen verglichen.
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.
Die Untersuchung mikrogelinster astronomischer Objekte ermöglicht es, Informationen über die Größe und Struktur dieser Objekte zu erhalten. Im ersten Teil dieser Arbeit werden die Spektren von drei gelinsten Quasare, die mit dem Potsdamer Multi Aperture Spectrophotometer (PMAS) erhalten wurden, auf Anzeichen für Mikrolensing untersucht. In den Spektren des Vierfachquasares HE 0435-1223 und des Doppelquasares HE 0047-1756 konnten Hinweise für Mikrolensing gefunden werden, während der Doppelquasar UM 673 (Q 0142--100) keine Anzeichen für Mikrolensing zeigt. Die Invertierung der Lichtkurve eines Mikrolensing-Kausik-Crossing-Ereignisses ermöglicht es, das eindimensionale Helligkeitsprofil der gelinsten Quelle zu rekonstruieren. Dies wird im zweiten Teil dieser Arbeit untersucht. Die mathematische Beschreibung dieser Aufgabe führt zu einer Volterra'schen Integralgleichung der ersten Art, deren Lösung ein schlecht gestelltes Problem ist. Zu ihrer Lösung wird in dieser Arbeit ein lokales Regularisierungsverfahren angewendet, das an die kausale Strukture der Volterra'schen Gleichung besser angepasst ist als die bisher verwendete Tikhonov-Phillips-Regularisierung. Es zeigt sich, dass mit dieser Methode eine bessere Rekonstruktion kleinerer Strukturen in der Quelle möglich ist. Weiterhin wird die Anwendbarkeit der Regularisierungsmethode auf realistische Lichtkurven mit irregulärem Sampling bzw. größeren Lücken in den Datenpunkten untersucht.
Highly collimated, high velocity streams of hot plasma – the jets – are observed as a general phenomenon being found in a variety of astrophysical objects regarding their size and energy output. Known as jet sources are protostellar objects (T Tauri stars, embedded IR sources), galactic high energy sources ("microquasars"), and active galactic nuclei (extragalactic radio sources and quasars). Within the last two decades our knowledge regarding the processes involved in astro-physical jet formation has condensed in a kind of standard model. This is the scenario of a magnetohydrodynamically accelerated and collimated jet stream launched from the innermost part of an accretion disk close to the central object. Traditionally, the problem of jet formation is divided in two categories. One is the question how to collimate and accelerate an uncollimated low velocity disk wind into a jet. The second is the question how to initiate that outflow from a disk, i.e. how to turn accretion of matter into an ejection as a disk wind. My own work is mainly related to the first question, the collimation and acceleration process. Due to the complexity of both, the physical processes believed to be responsible for the jet launching and also the spatial configuration of the physical components of the jet source, the enigma of jet formation is not yet completely understood. On the theoretical side, there has been a substantial advancement during the last decade from purely station-ary models to time-dependent simulations lead by the vast increase of computer power. Observers, on the other hand, do not yet have the instruments at hand in order to spatially resolve observe the very jet origin. It can be expected that also the next years will yield a substantial improvement on both tracks of astrophysical research. Three-dimensional magnetohydrodynamic simu-lations will improve our understanding regarding the jet-disk interrelation and the time-dependent character of jet formation, the generation of the magnetic field in the jet source, and the interaction of the jet with the ambient medium. Another step will be the combina-tion of radiation transfer computations and magnetohydrodynamic simulations providing a direct link to the observations. At the same time, a new generation of telescopes (VLT, NGST) in combination with new instrumental techniques (IR-interferometry) will lead to a "quantum leap" in jet observation, as the resolution will then be sufficient in order to zoom into the innermost region of jet formation.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.
Line driven winds are accelerated by the momentum transfer from photons to a plasma, by absorption and scattering in numerous spectral lines. Line driving is most efficient for ultraviolet radiation, and at plasma temperatures from 10^4 K to 10^5 K. Astronomical objects which show line driven winds include stars of spectral type O, B, and A, Wolf-Rayet stars, and accretion disks over a wide range of scales, from disks in young stellar objects and cataclysmic variables to quasar disks. It is not yet possible to solve the full wind problem numerically, and treat the combined hydrodynamics, radiative transfer, and statistical equilibrium of these flows. The emphasis in the present writing is on wind hydrodynamics, with severe simplifications in the other two areas. I consider three topics in some detail, for reasons of personal involvement. 1. Wind instability, as caused by Doppler de-shadowing of gas parcels. The instability causes the wind gas to be compressed into dense shells enclosed by strong shocks. Fast clouds occur in the space between shells, and collide with the latter. This leads to X-ray flashes which may explain the observed X-ray emission from hot stars. 2. Wind runaway, as caused by a new type of radiative waves. The runaway may explain why observed line driven winds adopt fast, critical solutions instead of shallow (or breeze) solutions. Under certain conditions the wind settles on overloaded solutions, which show a broad deceleration region and kinks in their velocity law. 3. Magnetized winds, as launched from accretion disks around stars or in active galactic nuclei. Line driving is assisted by centrifugal forces along co-rotating poloidal magnetic field lines, and by Lorentz forces due to toroidal field gradients. A vortex sheet starting at the inner disk rim can lead to highly enhanced mass loss rates.
The behaviour of an adhering cell is strongly influenced by the chemical, topographical and mechanical properties of the surface it attaches to. During recent years, it has been found experimentally that adhering cells actively sense the elastic properties of their environment by pulling on it through numerous sites of adhesion. The resulting build-up of force at sites of adhesion depends on the elastic properties of the environment and is converted into corresponding biochemical signals, which can trigger cellular programmes like growth, differentiation, apoptosis, and migration. In general, force is an important regulator of biological systems, for example in hearing and touch, in wound healing, and in rolling adhesion of leukocytes on vessel walls. In the habilitation thesis by Ulrich Schwarz, several theoretical projects are presented which address the role of forces and elasticity in cell adhesion. (1) A new method has been developed for calculating cellular forces exerted at sites of focal adhesion on micro-patterned elastic substrates. The main result is that cell-matrix contacts function as mechanosensors, converting internal force into protein aggregation. (2) A one-step master equation for the stochastic dynamics of adhesion clusters as a function of cluster size, rebinding rate and force has been solved both analytically and numerically. Moreover this model has been applied to the regulation of cell-matrix contacts, to dynamic force spectroscopy, and to rolling adhesion. (3) Using linear elasticity theory and the concept of force dipoles, a model has been introduced and solved which predicts the positioning and orientation of mechanically active cells in soft material, in good agreement with experimental observations for fibroblasts on elastic substrates and in collagen gels.
Concerns have been raised that anthropogenic climate change could lead to large-scale singular climate events, i.e., abrupt nonlinear climate changes with repercussions on regional to global scales. One central goal of this thesis is the development of models of two representative components of the climate system that could exhibit singular behavior: the Atlantic thermohaline circulation (THC) and the Indian monsoon. These models are conceived so as to fulfill the main requirements of integrated assessment modeling, i.e., reliability, computational efficiency, transparency and flexibility. The model of the THC is an interhemispheric four-box model calibrated against data generated with a coupled climate model of intermediate complexity. It is designed to be driven by global mean temperature change which is translated into regional fluxes of heat and freshwater through a linear down-scaling procedure. Results of a large number of transient climate change simulations indicate that the reduced-form THC model is able to emulate key features of the behavior of comprehensive climate models such as the sensitivity of the THC to the amount, regional distribution and rate of change in the heat and freshwater fluxes. The Indian monsoon is described by a novel one-dimensional box model of the tropical atmosphere. It includes representations of the radiative and surface fluxes, the hydrological cycle and surface hydrology. Despite its high degree of idealization, the model satisfactorily captures relevant aspects of the observed monsoon dynamics, such as the annual course of precipitation and the onset and withdrawal of the summer monsoon. Also, the model exhibits the sensitivity to changes in greenhouse gas and sulfate aerosol concentrations that are known from comprehensive models. A simplified version of the monsoon model is employed for the identification of changes in the qualitative system behavior against changes in boundary conditions. The most notable result is that under summer conditions a saddle-node bifurcation occurs at critical values of the planetary albedo or insolation. Furthermore, the system exhibits two stable equilibria: besides the wet summer monsoon, a stable state exists which is characterized by a weak hydrological cycle. These results are remarkable insofar, as they indicate that anthropogenic perturbations of the planetary albedo such as sulfur emissions and/or land-use changes could destabilize the Indian summer monsoon. The reduced-form THC model is employed in an exemplary integrated assessment application. Drawing on the conceptual and methodological framework of the tolerable windows approach, emissions corridors (i.e., admissible ranges of CO2- emissions) are derived that limit the risk of a THC collapse while considering expectations about the socio-economically acceptable pace of emissions reductions. Results indicate, for example, a large dependency of the width of the emissions corridor on climate and hydrological sensitivity: for low values of climate and/or hydrological sensitivity, the corridor boundaries are far from being transgressed by any plausible emissions scenario for the 21st century. In contrast, for high values of both quantities low non-intervention scenarios leave the corridor already in the early decades of the 21st century. This implies that if the risk of a THC collapse is to be kept low, business-as-usual paths would need to be abandoned within the next two decades. All in all, this thesis highlights the value of reduced-form modeling by presenting a number of applications of this class of models, ranging from sensitivity and bifurcation analysis to integrated assessment. The results achieved and conclusions drawn provide a useful contribution to the scientific and policy debate about the consequences of anthropogenic climate change and the long-term goals of climate protection. --- Anmerkung: Die Autorin ist Trägerin des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2003/2004.
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.
Diese Arbeit beschäftigt sich mit der Annahme, dass den Erdbeben ein selbstorganisiert kritischer Zustand der Erdkruste zugrunde liegt. Mit Hilfe einer Erweiterung bisheriger Modelle wird gezeigt, dass ein solcher Zustand nicht nur für die Grössenverteilung der Erdbeben (Gutenberg-Richter Gesetz), sondern auch für das beobachtete raumzeitliche Auftreten, z.B. für das Omori-Gesetz für Nachbebenserien, verantwortlich sein kann. Desweiteren wird die Frage nach der Vorhersagbarkeit grosser Erdbeben in solchen Modellsimulationen untersucht.
We theoretically discuss the interaction of neutral particles (atoms, molecules) with surfaces in the regime where it is mediated by the electromagnetic field. A thorough characterization of the field at sub-wavelength distances is worked out, including energy density spectra and coherence functions. The results are applied to typical situations in integrated atom optics, where ultracold atoms are coupled to a thermal surface, and to single molecule probes in near field optics, where sub-wavelength resolution can be achieved.
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.
In-situ Wachstumsuntersuchungen beim reaktiven Anlassen von Cu, In Schichten in elementarem Schwefel
(2003)
In dieser Arbeit wurde das reaktive Anlassen von dünnen Kupfer-Indium-Schichten in elementarem Schwefel mittels energiedispersiver Röntgenbeugung untersucht. Durch die simultane Aufnahme der Röntgenspektren und der Messung der diffusen Reflexion von Laserlicht der Wellenlänge 635 nm an der Oberfläche der Probe während des Schichtwachstums von CuInS<SUB>2</SUB> konnte eine Methode zur Prozesskontrolle für ein Herstellungsverfahren von CuInS<SUB>2</SUB> etabliert werden. Die Bildung von CuInS<SUB>2</SUB> aus Kupfer-Indium-Vorläuferschichten wird dominiert von Umwandlungen der intermetallischen Phasen. CuInS<SUB>2</SUB> wächst innerhalb der Aufheizperiode ab einer Temperatur von ca. 200°C aus der Phase Cu11In9. Jedoch zerfällt letztere metallische Phase in Cu16In9 und flüssiges Indium bei einer Temperatur von ca. 310°C. Das flüssige Indium reagiert im Falle von Kupferarmut mit dem Schwefel und führt zu einem zusätzlichen Reaktionspfad über InS zu CuIn5S8. Unter Präparationsbedingungen mit Kupferüberschuss wird das Indium in einer intermetallischen Phase gebunden.Erstmals konnte die Phase Digenite bei Temperaturen über 240°C beobachtet werden. Beim Abkühlen auf Raumtemperatur wandelt sich diese Phase unter dem Verbrauch von Schwefel in Covellite um.Für Proben mit Kupferüberschuss konnte eine Wachstumskinetik proportional zur Temperatur beobachtet werden. Dieses Verhalten wurde durch eine stress-induzierte Diffusion als dominierenden Reaktionsmechanismus interpretiert. Dabei werden während der Bildung von CuInS<SUB>2</SUB> durch unterschiedliche Ausdehnungen der metallischen und sulfidischen Schichten eine Spannung in der CuInS<SUB>2</SUB>-Schicht induziert, die nach Überschreiten einer Grenzspannung zu Rissen in der CuInS2-Schicht führt. Entlang dieser Risse findet ein schneller Transport der Metalle zur Oberfläche, wo diese mit dem Schwefel reagieren können, statt. Die Risse heilen durch die Bildung neuen Sulfids wieder aus.
Die heutige optische Informationsverarbeitung erfordert neue Materialien, die Licht effektiv verarbeiten, steuern und speichern können. Photorefraktive (PR) Materialien sind dafür sehr interessant. In diesen Materialien entsteht bei inhomogener Beleuchtung (z.B. mit einem Intererenzmuster) über Ladungsträgergenerierung und Einfang der Ladungsträger in Fallen ein Raumladungsfeld. Dieses wird über den elektrooptischen Effekt in eine räumliche Modulation des Brechungsindex umgesetzt. Letztendlich führt somit die inhomogene Beleuchtung eines PR-Materials zu einer räumlich variierenden Änderung des Brechungsindex. Vor ca. 10 Jahren wurde entdeckt, dass auch Polymere einen PR-Effekt aufweisen können. Die Ansprechzeit dieser Materialien wird dabei wesentlich durch die Dynamik der Ladungsträger (bestimmt durch Erzeugung, Transport, Einfang in Fallen etc.) begrenzt. Bis zu Beginn dieser Arbeit war es noch nicht gelungen, einen quantitativen Zusammenhang zwischen der Ladungsträgerdynamik und der Ansprechzeit des PR-Effekts experimentell nachzuweisen. In dieser Arbeit wird ein Weg aufgezeigt, durch photophysikalische Experimente unter verschiedenen Beleuchtungsbedingungen alle photophysikalischen Größen experimentell zu bestimmen, die den Aufbau des Raumladungsfelds in organischen photorefraktiven Materialien bestimmen. So konnte durch Experimente unter Beleuchtung mit kurzen Einzelpulsen sowohl die Beweglichkeit der freien Ladungsträger als auch die charakteristischen Parameter flacher Fallen ermittelt werden. Zur Bestimmung der Dichte tiefer Fallen wurde die Intensitätsabhängigkeit des stationären Photostroms untersucht. Durch die analytische Lösung des bestimmenden Gleichungssystems konnte gezeigt werden, dass die Sublinearität der Intensitätsabhängigkeit des Photostroms primär mit dem Verhältnis zwischen Entleerungs- und Einfangkoeffizienten tiefer Fallen korreliert. Zur unabhängigen Bestimmung des Entleerungskoeffizienten der tiefen Fallen wurden Doppelpulsexperimente mit variabler Verzögerungszeit zwischen den Pulsen verwendet. Mit den erhaltenen Parametern konnte dann das untere Limit der zum Aufbau des Raumladungsfelds notwendigen Zeit abgeschätzt werden. Diese Werte wurden mit den gemessenen photorefraktiven Ansprechzeiten verglichen. Es zeigt sich, dass weder die Photogeneration noch der Transport der Ladungsträger die Geschwindigkeit des Aufbaus des Raumladungsfeldes limitiert. Stattdessen konnte erstmals quantitativ nachgewiesen werden, dass die Dynamik des Raumladungsfelds in den hier untersuchten PR-Materialien durch das Füllen tiefer Fallen mit photogenerierten Ladungsträgern bestimmt wird. Dabei spielt das Verhältnis zwischen dem Einfang- und dem Rekombinationskoeffizienten eine wesentliche Rolle. Weiterhin wurde die Dynamik des Aufbaus des Raumladungsfelds bei unterschiedlichen Vorbeleuchtungsbedingungen quantitativ simuliert und mit den experimentellen PR-Transienten verglichen. Die gute Übereinstimmung zwischen den simulierten und gemessenen Transienten erlaubte es abschließend, die kritischen Parameter, die die Dynamik des PR-Effekts in den untersuchten Polymeren begrenzen, zu identifizieren.
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.
Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift. Recently, however, both observational and numerical work has begun to suggest that supersonic interstellar turbulence rather than magnetic fields controls star formation. This review begins with a historical overview of the successes and problems of both the classical dynamical theory of star formation, and the standard theory of magnetostatic support from both observational and theoretical perspectives. We then present the outline of a new paradigm of star formation based on the interplay between supersonic turbulence and self-gravity. Supersonic turbulence can provide support against gravitational collapse on global scales, while at the same time it produces localized density enhancements that allow for collapse on small scales. The efficiency and timescale of stellar birth in Galactic gas clouds strongly depend on the properties of the interstellar turbulent velocity field, with slow, inefficient, isolated star formation being a hallmark of turbulent support, and fast, efficient, clustered star formation occurring in its absence. After discussing in detail various theoretical aspects of supersonic turbulence in compressible self-gravitating gaseous media relevant for star forming interstellar clouds, we explore the consequences of the new theory for both local star formation and galactic scale star formation. The theory predicts that individual star-forming cores are likely not quasi-static objects, but dynamically evolving. Accretion onto these objects will vary with time and depend on the properties of the surrounding turbulent flow. This has important consequences for the resulting stellar mass function. Star formation on scales of galaxies as a whole is expected to be controlled by the balance between gravity and turbulence, just like star formation on scales of individual interstellar gas clouds, but may be modulated by additional effects like cooling and differential rotation. The dominant mechanism for driving interstellar turbulence in star-forming regions of galactic disks appears to be supernovae explosions. In the outer disk of our Milky Way or in low-surface brightness galaxies the coupling of rotation to the gas through magnetic fields or gravity may become important.
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.
In festen azobenzenhaltigen Polymeren wurde bei Bestrahlung mit blauem Licht ein makroskopischer Materialtransport beobachtet. Um die Dynamik der Gitterentstehung zu verfolgen, wurde am Speicherring für Synchrotronstrahlung ein Gitterschreibaufbau errichtet. Damit konnte erstmals in dieser Arbeit die Gitterbildungsgeschwindigkeit in-situ simultan mit Röntgen- und Lichtstreuung untersucht werden. Mit Hilfe einer speziellen Anpassung der Röntgenstreutheorie konnten sehr gute Übereinstimmungen von theoretischen Berechnungen mit den Messergebnissen erzielt werden. Dabei konnte nachgewiesen werden, dass sich zeitgleich mit einem Oberflächengitter auch ein Dichtegitter entwickelt. Durch die Trennung beider Streuanteile ließ sich die Dynamik der Strukturentstehungen bestimmen. Des weiteren konnte erstmals mit Hilfe der Photoelektronenspektroskopie die molekulare Orientierung an der Oberfläche eines Oberflächengitters nachgewiesen werden. Die Bewegungsursache kann auf einen Impulsübertrag während der Isomerisierung zurückgeführt werden, während die Bewegungsrichtung durch den elektrischen Feldvektor festgelegt wird. Die Theorie der Gitterentstehung konnte verbessert werden.
Eine Nutzung der optischen Anisotropie dünner Schichten ist vor allem für die Displaytechnologie, die optische Datenspeicherung und für optische Sicherheitselemente von hoher Bedeutung. Diese Doktorarbeit befasst sich mit theoretischen und experimentellen Untersuchung von dreidimensionaler Anisotropie und dabei insbesondere mit der Untersuchung von lichtinduzierter dreidimensionaler Anisotropie in organischen dünnen Polymer-Schichten. Die gewonnenen Erkentnisse und entwickelten Methoden können wertvolle Beiträge für Optimierungsprozesse, wie bei der Kompensation der Blickwinkelabhängigkeit von Flüssigkristall-Displays, liefern. Die neue Methode der Immersions-Transmissions-Ellipsometrie (ITE) zur Untersuchung von dünneren Schichten wurde im Rahmen dieser Dissertation entwickelt. Diese Methode gestattet es, in Kombination mit konventioneller Reflexions- und Transmissionsellipsometrie, die absoluten dreidimensionalen Brechungsindices einer biaxialen Schicht zu bestimmen. Erstmals gelang es damit, das dreidimensionale Brechungsindexellipsoid von transparenten, dünneren (150 nm) Filmen hochgenau (drei Stellen hinter dem Komma) zu bestimmen. Die ITE-Methode hat demzufolge das Potential, auch bei noch dünneren Schichten mit Gewinn eingesetzt werden zu können. Die lichtinduzierte Generierung von dreidimensionaler Anisotropie wurde in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen, amorphen und flüssig-kristallinen Homo- und Copolymeren untersucht. Erstmals wurden quantitative Untersuchungen zur Änderung von lichtinduzierten, dreidimensionalen Anisotropien in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen Polymeren bei Tempern oberhalb der Glastemperatur durchgeführt. Bei vielen der untersuchten Polymere war die dreidimensionale Ordnung nach dem Bestrahlen mit polarisiertem Licht und anschließendem Tempern oberhalb der Glastemperatur scheinbar von der Schichtdicke abhängig. Die Ursache liegt wohl in der, mit der neuentwickelten ITE-Methode detektierten, planaren Ausgangsorientierung der aufgeschleuderten dünneren Schichten. Um Verkippungs-Gradienten in dickeren Polymerschichten in ihrem Verlauf zu bestimmen, wurde eine spezielle Methode unter Benutzung der Wellenleitermoden-Spektroskopie entwickelt. Quantenchemisch bestimmte, maximal induzierbare Doppelbrechungen in flüssig-kristallinen Polymeren wurden mit den experimentell gefundenen Ordnungen verglichen.
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.
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences.
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.