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This dissertation contains theoretical investigations on the morphology and statistical mechanics of vesicles. The shapes of homogeneous fluid vesicles and inhomogeneous vesicles with fluid and solid membrane domains are calculated. The influence of thermal fluctuations is investigated. The obtained results are valid on mesoscopic length scales and are based on a geometrical membrane model, where the vesicle membrane is described as either a static or a thermal fluctuating surface. The thesis consists of three parts. In the first part, homogeneous vesicles are considered. The focus in this part is on the thermally induced morphological transition between vesicles with prolate and oblate shape. With the help of Monte Carlo simulations, the free energy profile of these vesicles is determined. It can be shown that the shape transformation between prolate and oblate vesicles proceeds continuously and is not hampered by a free energy barrier. The second and third part deal with inhomogeneous vesicles which contain intramembrane domains. These investigations are motivated by experimental results on domain formation in single or multicomponent vesicles, where phase separation occurs and different membrane phases coexist. The resulting domains differ with regard to their membrane structure (solid, fluid). The membrane structure has a distinct effect on the form of the domain and the morphology of the vesicle. In the second part, vesicles with coexisting solid and fluid membrane domains are studied, while the third part addresses vesicles with coexisting fluid domains. The equilibrium morphology of vesicles with simple and complex domain forms, derived through minimisation of the membrane energy, is determined as a function of material parameters. The results are summarised in morphology diagrams. These diagrams show previously unknown morphological transitions between vesicles with different domain shapes. The impact of thermal fluctuations on the vesicle and the form of the domains is investigated by means of Monte Carlo simulations.
The biological function and the technological applications of semiflexible polymers, such as DNA, actin filaments and carbon nanotubes, strongly depend on their rigidity. Semiflexible polymers are characterized by their persistence length, the definition of which is the subject of the first part of this thesis. Attractive interactions, that arise e.g.~in the adsorption, the condensation and the bundling of filaments, can change the conformation of a semiflexible polymer. The conformation depends on the relative magnitude of the material parameters and can be influenced by them in a systematic manner. In particular, the morphologies of semiflexible polymer rings, such as circular nanotubes or DNA, which are adsorbed onto substrates with three types of structures, are studied: (i) A topographical channel, (ii) a chemically modified stripe and (iii) a periodic pattern of topographical steps. The results are compared with the condensation of rings by attractive interactions. Furthermore, the bundling of two individual actin filaments, whose ends are anchored, is analyzed. This system geometry is shown to provide a systematic and quantitative method to extract the magnitude of the attraction between the filaments from experimentally observable conformations of the filaments.
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
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.
The role played by azobenzene polymers in the modern photonic, electronic and opto-mechanical applications cannot be underestimated. These polymers are successfully used to produce alignment layers for liquid crystalline fluorescent polymers in the display and semiconductor technology, to build waveguides and waveguide couplers, as data storage media and as labels in quality product protection. A very hot topic in modern research are light-driven artificial muscles based on azobenzene elastomers. The incorporation of azobenzene chromophores into polymer systems via covalent bonding or even by blending gives rise to a number of unusual effects under visible (VIS) and ultraviolet light irradiation. The most amazing effect is the inscription of surface relief gratings (SRGs) onto thin azobenzene polymer films. At least seven models have been proposed to explain the origin of the inscribing force but none of them describes satisfactorily the light induced material transport on the molecular level. In most models, to explain the mass transport over micrometer distances during irradiation at room temperature, it is necessary to assume a considerable degree of photoinduced softening, at least comparable with that at the glass transition. Contrary to this assumption, we have gathered a convincing evidence that there is no considerable softening of the azobenzene layers under illumination. Presently we can surely say that light induced softening is a very weak accompanying effect rather than a necessary condition for the formation of SRGs. This means that the inscribing force should be above the yield point of the azobenzene polymer. Hence, an appropriate approach to describe the formation and relaxation of SRGs is a viscoplastic theory. It was used to reproduce pulse-like inscription of SRGs as measured by VIS light scattering. At longer inscription times the VIS scattering pattern exhibits some peculiarities which can be explained by the appearance of a density grating that will be shown to arise due to the final compressibility of the polymer film. As a logical consequence of the aforementioned research, a thermodynamic theory explaining the light-induced deformation of free standing films and the formation of SRGs is proposed. The basic idea of this theory is that under homogeneous illumination an initially isotropic sample should stretch itself along the polarization direction to compensate the entropy decrease produced by the photoinduced reorientation of azobenzene chromophores. Finally, some ideas about further development of this controversial topic will be discussed.
We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
(2017)
We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.
We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a Lévy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of Lévy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter–controlled reactions in real systems are discussed.
Stochastic Wilson
(2015)
We consider a simple Markovian class of the stochastic Wilson–Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around −1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.
Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion
(2014)
The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.
Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus–Levich–Dogonadze(MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.
Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.
Organic-inorganic hybrids based on P3HT and mesoporous silicon for thermoelectric applications
(2024)
This thesis presents a comprehensive study on synthesis, structure and thermoelectric transport properties of organic-inorganic hybrids based on P3HT and porous silicon. The effect of embedding polymer in silicon pores on the electrical and thermal transport is studied. Morphological studies confirm successful polymer infiltration and diffusion doping with roughly 50% of the pore space occupied by conjugated polymer. Synchrotron diffraction experiments reveal no specific ordering of the polymer inside the pores. P3HT-pSi hybrids show improved electrical transport by five orders of magnitude compared to porous silicon and power factor values comparable or exceeding other P3HT-inorganic hybrids. The analysis suggests different transport mechanisms in both materials. In pSi, the transport mechanism relates to a Meyer-Neldel compansation rule. The analysis of hybrids' data using the power law in Kang-Snyder model suggests that a doped polymer mainly provides charge carriers to the pSi matrix, similar to the behavior of a doped semiconductor. Heavily suppressed thermal transport in porous silicon is treated with a modified Landauer/Lundstrom model and effective medium theories, which reveal that pSi agrees well with the Kirkpatrick model with a 68% percolation threshold. Thermal conductivities of hybrids show an increase compared to the empty pSi but the overall thermoelectric figure of merit ZT of P3HT-pSi hybrid exceeds both pSi and P3HT as well as bulk Si.
The cell interior is a highly packed environment in which biological macromolecules evolve and function. This crowded media has effects in many biological processes such as protein-protein binding, gene regulation, and protein folding. Thus, biochemical reactions that take place in such crowded conditions differ from diluted test tube conditions, and a considerable effort has been invested in order to understand such differences.
In this work, we combine different computationally tools to disentangle the effects of molecular crowding on biochemical processes. First, we propose a lattice model to study the implications of molecular crowding on enzymatic reactions. We provide a detailed picture of how crowding affects binding and unbinding events and how the separate effects of crowding on binding equilibrium act together. Then, we implement a lattice model to study the effects of molecular crowding on facilitated diffusion. We find that obstacles on the DNA impair facilitated diffusion. However, the extent of this effect depends on how dynamic obstacles are on the DNA. For the scenario in which crowders are only present in the bulk solution, we find that at some conditions presence of crowding agents can enhance specific-DNA binding. Finally, we make use of structure-based techniques to look at the impact of the presence of crowders on the folding a protein. We find that polymeric crowders have stronger effects on protein stability than spherical crowders. The strength of this effect increases as the polymeric crowders become longer. The methods we propose here are general and can also be applied to more complicated systems.
During this work I built a four wave mixing setup for the time-resolved femtosecond spectroscopy of Raman-active lattice modes. This setup enables to study the selective excitation of phonon polaritons. These quasi-particles arise from the coupling of electro-magnetic waves and transverse optical lattice modes, the so-called phonons. The phonon polaritons were investigated in the optically non-linear, ferroelectric crystals LiNbO₃ and LiTaO₃.
The direct observation of the frequency shift of the scattered narrow bandwidth probe pulses proofs the role of the Raman interaction during the probe and excitation process of phonon polaritons. I compare this experimental method with the measurement where ultra-short laser pulses are used. The frequency shift remains obscured by the relative broad bandwidth of these laser pulses. In an experiment with narrow bandwidth probe pulses, the Stokes and anti-Stokes intensities are spectrally separated. They are assigned to the corresponding counter-propagating wavepackets of phonon polaritons. Thus, the dynamics of these wavepackets was separately studied. Based on these findings, I develop the mathematical description of the so-called homodyne detection of light for the case of light scattering from counter propagating phonon polaritons.
Further, I modified the broad bandwidth of the ultra-short pump pulses using bandpass filters to generate two pump pulses with non-overlapping spectra. This enables the frequency-selective excitation of polariton modes in the sample, which allows me to observe even very weak polariton modes in LiNbO₃ or LiTaO₃ that belong to the higher branches of the dispersion relation of phonon polaritons. The experimentally determined dispersion relation of the phonon polaritons could therefore be extended and compared to theoretical models. In addition, I determined the frequency-dependent damping of phonon polaritons.
In the present dissertation paper we study problems related to synchronization phenomena in the presence of noise which unavoidably appears in real systems. One part of the work is aimed at investigation of utilizing delayed feedback to control properties of diverse chaotic dynamic and stochastic systems, with emphasis on the ones determining predisposition to synchronization. Other part deals with a constructive role of noise, i.e. its ability to synchronize identical self-sustained oscillators. First, we demonstrate that the coherence of a noisy or chaotic self-sustained oscillator can be efficiently controlled by the delayed feedback. We develop the analytical theory of this effect, considering noisy systems in the Gaussian approximation. Possible applications of the effect for the synchronization control are also discussed. Second, we consider synchrony of limit cycle systems (in other words, self-sustained oscillators) driven by identical noise. For weak noise and smooth systems we proof the purely synchronizing effect of noise. For slightly different oscillators and/or slightly nonidentical driving, synchrony becomes imperfect, and this subject is also studied. Then, with numerics we show moderate noise to be able to lead to desynchronization of some systems under certain circumstances. For neurons the last effect means “antireliability” (the “reliability” property of neurons is treated to be important from the viewpoint of information transmission functions), and we extend our investigation to neural oscillators which are not always limit cycle ones. Third, we develop a weakly nonlinear theory of the Kuramoto transition (a transition to collective synchrony) in an ensemble of globally coupled oscillators in presence of additional time-delayed coupling terms. We show that a linear delayed feedback not only controls the transition point, but effectively changes the nonlinear terms near the transition. A purely nonlinear delayed coupling does not affect the transition point, but can reduce or enhance the amplitude of collective oscillations.
Force plays a fundamental role in the regulation of biological processes. Cells can sense the mechanical properties of the extracellular matrix (ECM) by applying forces and transmitting mechanical signals. They further use mechanical information for regulating a wide range of cellular functions, including adhesion, migration, proliferation, as well as differentiation and apoptosis. Even though it is well understood that mechanical signals play a crucial role in directing cell fate, surprisingly little is known about the range of forces that define cell-ECM interactions at the molecular level.
Recently, synthetic molecular force sensor (MFS) designs have been established for measuring the molecular forces acting at the cell-ECM interface. MFSs detect the traction forces generated by cells and convert this mechanical input into an optical readout. They are composed of calibrated mechanoresponsive building blocks and are usually equipped with a fluorescence reporter system. Up to date, many different MFS designs have been introduced and successfully used for measuring forces involved in the adhesion of mammalian cells. These MFSs utilize different molecular building blocks, such as double-stranded deoxyribonucleic acid (dsDNA) molecules, DNA hairpins and synthetic polymers like polyethylene glycol (PEG). These currently available MFS designs lack ECM mimicking properties.
In this work, I introduce a new MFS building block for cell biology applications, derived from the natural ECM. It combines mechanical tunability with the ability to mimic the native cellular microenvironment. Inspired by structural ECM proteins with load bearing function, this new MFS design utilizes coiled coil (CC)-forming peptides. CCs are involved in structural and mechanical tasks in the cellular microenvironment and many of the key protein components of the cytoskeleton and the ECM contain CC structures. The well-known folding motif of CC structures, an easy synthesis via solid phase methods and the many roles CCs play in biological processes have inspired studies to use CCs as tunable model systems for protein design and assembly. All these properties make CCs ideal candidates as building blocks for MFSs. In this work, a series of heterodimeric CCs were designed, characterized and further used as molecular building blocks for establishing a novel, next-generation MFS prototype.
A mechanistic molecular understanding of their structural response to mechanical load is essential for revealing the sequence-structure-mechanics relationships of CCs. Here, synthetic heterodimeric CCs of different length were loaded in shear geometry and their mechanical response was investigated using a combination of atomic force microscope (AFM)-based single-molecule force spectroscopy (SMFS) and steered molecular dynamics (SMD) simulations. SMFS showed that the rupture forces of short heterodimeric CCs (3-5 heptads) lie in the range of 20-50 pN, depending on CC length, pulling geometry and the applied loading rate (dF/dt). Upon shearing, an initial rise in the force, followed by a force plateau and ultimately strand separation was observed in SMD simulations. A detailed structural analysis revealed that CC response to shear load depends on the loading rate and involves helix uncoiling, uncoiling-assisted sliding in the direction of the applied force and uncoiling-assisted dissociation perpendicular to the force axis.
The application potential of these mechanically characterized CCs as building blocks for MFSs has been tested in 2D cell culture applications with the goal of determining the threshold force for cell adhesion. Fully calibrated, 4- to 5-heptad long, CC motifs (CC-A4B4 and CC-A5B5) were used for functionalizing glass surfaces with MFSs. 3T3 fibroblasts and endothelial cells carrying mutations in a signaling pathway linked to cell adhesion and mechanotransduction processes were used as model systems for time-dependent adhesion experiments. A5B5-MFS efficiently supported cell attachment to the functionalized surfaces for both cell types, while A4B4-MFS failed to maintain attachment of 3T3 fibroblasts after the first 2 hours of initial cell adhesion. This difference in cell adhesion behavior demonstrates that the magnitude of cell-ECM forces varies depending on the cell type and further supports the application potential of CCs as mechanoresponsive and tunable molecular building blocks for the development of next-generation protein-based MFSs.This novel CC-based MFS design is expected to provide a powerful new tool for observing cellular mechanosensing processes at the molecular level and to deliver new insights into the mechanisms and forces involved. This MFS design, utilizing mechanically tunable CC building blocks, will not only allow for measuring the molecular forces acting at the cell-ECM interface, but also yield a new platform for the development of mechanically controlled materials for a large number of biological and medical applications.
Atmospheric circulation and the surface mass balance in a regional climate model of Antarctica
(2007)
Understanding the Earth's climate system and particularly climate variability presents one of the most difficult and urgent challenges in science. The Antarctic plays a crucial role in the global climate system, since it is the principal region of radiative energy deficit and atmospheric cooling. An assessment of regional climate model HIRHAM is presented. The simulations are generated with the HIRHAM model, which is modified for Antarctic applications. With a horizontal resolution of 55km, the model has been run for the period 1958-1998 creating long-term simulations from initial and boundary conditions provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA40 re-analysis. The model output is compared with observations from observation stations, upper air data, global atmospheric analyses and satellite data. In comparison with the observations, the evaluation shows that the simulations with the HIRHAM model capture both the large and regional scale circulation features with generally small bias in the modeled variables. On the annual time scale the largest errors in the model simulations are the overestimation total cloud cover and the colder near-surface temperature over the interior of the Antarctic plateau. The low-level temperature inversion as well as low-level wind jet is well captured by the model. The decadal scale processes were studied based on trend calculations. The long-term run was divided into two 20 years parts. The 2m temperature, 500 hPa temperature, MSLP, precipitation and net mass balance trends were calculated for both periods and over 1958 - 1998. During the last two decades the strong surface cooling was observed over the Eastern Antarctica, this result is in good agreement with the result of Chapman and Walsh (2005) who calculated the temperature trend based on the observational data. The MSLP trend reveals a big disparity between the first and second parts of the 40 year run. The overall trend shows the strengthening of the circumpolar vortex and continental anticyclone. The net mass balance as well as precipitation show a positive trend over the Antarctic Peninsula region, along Wilkes Land and in Dronning Maud Land. The Antarctic ice sheet grows over the Eastern part of Antarctica with small exceptions in Dronning Maud Land and Wilkes Land and sinks in the Antarctic Peninsula; this result is in good agreement with the satellite-measured altitude presented in Davis (2005) . To better understand the horizontal structure of MSLP, temperature and net mass balance trends the influence of the Southern Annual Mode (SAM) on the Antarctic climate was investigated. The main meteorological parameters during the positive and negative Antarctic Oscillation (AAO) phases were compared to each other. A positive/negative AAO index means strengthening/weakening of the circumpolar vortex, poleward/northward storm tracks and prevailing/weakening westerly winds. For detailed investigation of global teleconnection, two positive and one negative periods of AAO phase were chosen. The differences in MSLP and 2m temperature between positive and negative AAO years during the winter months partly explain the surface cooling during the last decades.
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.
Box-Simulationen von rotierender Magnetokonvektion im flüssigen Erdkern Numerische Simulationen der 3D-MHD Gleichungen sind mit Hilfe des Codes NIRVANA durchgeführt worden. Die Gleichungen für kompressible rotierende Magnetokonvektion wurden für erdähnliche Bedingungen numerisch in einer kartesischen Box gelöst. Charakteristische Eigenschaften mittlerer Größen, wie der Turbulenz-Intensität oder der turbulente Wärmefluss, die durch die kombinierte Wirkung kleinskaliger Fluktuationen entstehen, wurden bestimmt. Die Korrelationslänge der Turbulenz hängt signifikant von der Stärke und der Orientierung des Magnetfeldes ab, und das anisotrope Verhalten der Turbulenz aufgrund von Coriolis- und Lorentzkraft ist für schnellere Rotation wesentlich stärker ausgeprägt. Die Ausbildung eines isotropen Verhaltens auf kleinen Skalen unter dem Einfluss von Rotation alleine wird bereits durch ein schwaches Magnetfeld verhindert. Dies resultiert in einer turbulenten Strömung, die durch die vertikale Komponente dominiert wird. In Gegenwart eines horizontalen Magnetfeldes nimmt der vertikale turbulente Wärmefluss leicht mit zunehmender Feldstärke zu, so dass die Kühlung eines rotierenden Systems verbessert wird. Der horizontale Wärmetransport ist stets westwärts und in Richtung der Pole orientiert. Letzteres kann unter Umständen die Quelle für eine großskalige meridionale Strömung darstellen, während erstes in globalen Simulationen mit nicht axialsymmetrischen Randbedingungen für den Wärmefluss von Bedeutung ist. Die mittlere elektromotorische Kraft, die die Erzeugung von magnetischem Fluss durch die Turbulenz beschreibt, wurde unmittelbar aus den Lösungen für Geschwindigkeit und Magnetfeld berechnet. Hieraus konnten die entsprechenden α-Koeffizienten hergeleitet werden. Aufgrund der sehr schwachen Dichtestratifizierung ändert der α-Effekt sein Vorzeichen nahezu exakt in der Mitte der Box. Der α-Effekt ist positiv in der oberen Hälfte und negativ in der unteren Hälfte einer auf der Nordhalbkugel rotierenden Box. Für ein starkes Magnetfeld ergibt sich zudem eine deutliche abwärts orientierte Advektion von magnetischem Fluss. Ein Mean-Field Modell des Geodynamos wurde konstruiert, das auf dem α-Effekt basiert, wie er aus den Box-Simulationen berechnet wurde. Für eine äußerst beschränkte Klasse von radialen α-Profilen weist das lineare α^2-Modell Oszillationen auf einer Zeitskala auf, die durch die turbulente Diffusionszeit bestimmt wird. Die wesentlichen Eigenschaften der periodischen Lösungen werden präsentiert, und der Einfluss der Größe des inneren Kerns auf die Charakteristiken des kritischen Bereichs, innerhalb dessen oszillierende Lösungen auftreten, wurden untersucht. Reversals werden als eine halbe Oszillation interpretiert. Sie sind ein recht seltenes Ereignis, da sie lediglich dann stattfinden können, wenn das α-Profil ausreichend lange in dem periodische Lösungen erlaubenden Bereich liegt. Aufgrund starker Fluktuationen auf der konvektiven Zeitskala ist die Wahrscheinlichkeit eines solchen Reversals relativ klein. In einem einfachen nicht-linearen Mean-Field Modell mit realistischen Eingabeparametern, die auf den Box-Simulationen beruhen, konnte die Plausibilität des Reversal-Modells anhand von Langzeitsimulationen belegt werden.
Die Klangeigenschaften von Musikinstrumenten werden durch das Zusammenwirken der auf ihnen anregbaren akustischen Schwingungsmoden bestimmt, welche sich wiederum aus der geometrischen Struktur des Resonators in Kombination mit den verwendeten Materialien ergeben. In dieser Arbeit wurde das Schwingungsverhalten von Streichinstrumenten durch den Einsatz minimal-invasiver piezoelektrischer Polymerfilmsensoren untersucht. Die studierten Kopplungsphänomene umfassen den sogenannten Wolfton und Schwingungstilger, die zu dessen Abschwächung verwendet werden, sowie die gegenseitige Beeinflussung von Bogen und Instrument beim Spielvorgang. An Dielektrischen Elastomeraktormembranen wurde dagegen der Einfluss der elastischen Eigenschaften des Membranmaterials auf das akustische und elektromechanische Schwingungsverhalten gezeigt. Die Dissertation gliedert sich in drei Teile, deren wesentliche Ergebnisse im Folgenden zusammengefasst werden.
In Teil I wurde die Funktionsweise eines abstimmbaren Schwingungstilgers zur Dämpfung von Wolftönen auf Streichinstrumenten untersucht. Durch Abstimmung der Resonanzfrequenz des Schwingungstilgers auf die Wolftonfrequenz kann ein Teil der Saitenschwingungen absorbiert werden, so dass die zu starke Anregung der Korpusresonanz vermieden wird, die den Wolfton verursacht. Der Schwingungstilger besteht aus einem „Wolftöter“, einem Massestück, welches auf der Nachlänge der betroffenen Saite (zwischen Steg und Saitenhalter) installiert wird. Hier wurde gezeigt, wie die Resonanzen dieses Schwingungstilgers von der Masse des Wolftöters und von dessen Position auf der Nachlänge abhängen. Aber auch die Geometrie des Wolftöters stellte sich als ausschlaggebend heraus, insbesondere bei einem nicht-rotationssymmetrischen Wolftöter: In diesem Fall entsteht – basierend auf den zu erwartenden nicht-harmonischen Moden einer massebelasteten Saite – eine zusätzliche Mode, die von der Polarisationsrichtung der Saitenschwingung abhängt.
Teil II der Dissertation befasst sich mit Elastomermembranen, die als Basis von Dielektrischen Elastomeraktoren dienen, und die wegen der Membranspannung auch akustische Resonanzen aufweisen. Die Ansprache von Elastomeraktoren hängt unter anderem von der Geschwindigkeit der elektrischen Anregung ab. Die damit zusammenhängenden viskoelastischen Eigenschaften der hier verwendeten Elastomere, Silikon und Acrylat, wurden einerseits in einer frequenzabhängigen dynamisch-mechanischen Analyse des Elastomers erfasst, andererseits auch optisch an vollständigen Aktoren selbst gemessen. Die höhere Viskosität des Acrylats, das bei tieferen Frequenzen höhere Aktuationsdehnungen als das Silikon zeigt, führt zu einer Verminderung der Dehnungen bei höheren Frequenzen, so dass über etwa 40 Hertz mit Silikon größere Aktuationsdehnungen erreicht werden. Mit den untersuchten Aktoren konnte die Gitterkonstante weicher optischer Beugungsgitter kontrolliert werden, die als zusätzlicher Film auf der Membran installiert wurden. Über eine Messung der akustischen Resonanzfrequenz von Elastomermebranen aus Acrylat in 1Abhängigkeit von ihrer Vorstreckung konnte in Verbindung mit einer Modellierung des hyperelastischen Verhaltens des Elastomers (Ogden-Modell) der Schermodul bestimmt werden.
Schließlich wird in Teil III die Untersuchung von Geigen und ihrer Streichanregung mit Hilfe minimal-invasiver piezoelektrischer Polymerfilme geschildert. Es konnten am Bogen und am Steg von Geigen – unter den beiden Füßen des Stegs – jeweils zwei Filmsensoren installiert werden. Mit den beiden Sensoren am Steg wurden Frequenzgänge von Geigen gemessen, welche eine Bestimmung der frequenzabhängigen Stegbewegung erlaubten. Diese Methode ermöglicht damit auch eine umfassende Charakterisierung der Signaturmoden in Bezug auf die Stegdynamik. Die Ergebnisse der komplementären Methoden von Impulsanregung und natürlichem Spielen der Geigen konnten dank der Sensoren verglichen werden. Für die Nutzung der Sensoren am Bogen – insbesondere für eine Messung des Bogendrucks – wurde eine Kalibrierung des Bogen-Sensor-Systems mit Hilfe einer Materialprüfmaschine durchgeführt. Bei einer Messung während des natürlichen Spielens wurde mit den Sensoren am Bogen einerseits die Übertragung der Saitenschwingung auf den Bogen festgestellt. Dabei konnten außerdem longitudinale Bogenhaarresonanzen identifiziert werden, die von der Position der Saite auf dem Bogen abhängen. Aus der Analyse dieses Phänomens konnte die longitudinale Wellengeschwindigkeit der Bogenhaare bestimmt werden, die eine wichtige Größe für die Kopplung zwischen Saite und Bogen ist. Mit Hilfe des Systems aus Sensoren an Bogen und Steg werden auf Grundlage der vorliegenden Arbeit Studien an Streichinstrumenten vorgeschlagen, in denen die Bespielbarkeit der Instrumente zu den jeweils angeregten Steg- und Bogenschwingungen in Beziehung gesetzt werden kann. Damit könnte nicht zuletzt auch die bisher nicht vollständig geklärte Rolle des Bogens für Klang und Bespielbarkeit besser beurteilt werden
What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.
Nucleation and growth of unsubstituted metal phthalocyanine films from solution on planar substrates
(2012)
In den vergangenen Jahren wurden kosteneffiziente nasschemische Beschichtungsverfahren für die Herstellung organischer Dünnfilme für verschiedene opto-elektronische Anwendungen entdeckt und weiterentwickelt. Unter anderem wurden Phthalocyanin-Moleküle in photoaktiven Schichten für die Herstellung von Solarzellen intensiv erforscht. Aufgrund der kleinen bzw. unbekannten Löslichkeit wurden Phthalocyanin-Schichten durch Aufdampfverfahren im Vakuum hergestellt. Des Weiteren wurde die Löslichkeit durch chemische Synthese erhöht, was aber die Eigenschaften von Pc beeinträchtigte. In dieser Arbeit wurde die Löslichkeit, optische Absorption und Stabilität von 8 verschiedenen unsubstituierten Metall-Phthalocyaninen in 28 verschiedenen Lösungsmitteln quantitativ gemessen. Wegen ausreichender Löslichkeit, Stabilität und Anwendbarkeit in organischen Solarzellen wurde Kupferphthalocyanin (CuPc) in Trifluoressigsäure (TFA) für weitere Untersuchungen ausgewählt. Durch die Rotationsbeschichtung von CuPc aus TFA Lösung wurde ein dünner Film aus der verdampfenden Lösung auf dem Substrat platziert. Nach dem Verdampfen des Lösungsmittels, die Nanobändern aus CuPc bedecken das Substrat. Die Nanobänder haben eine Dicke von etwa ~ 1 nm (typische Dimension eines CuPc-Molekül) und variierender Breite und Länge, je nach Menge des Materials. Solche Nanobändern können durch Rotationsbeschichtung oder auch durch andere Nassbeschichtungsverfahren, wie Tauchbeschichtung, erzeugt werden. Ähnliche Fibrillen-Strukturen entstehen durch Nassbeschichtung von anderen Metall-Phthalocyaninen, wie Eisen- und Magnesium-Phthalocyanin, aus TFA-Lösung sowie auf anderen Substraten, wie Glas oder Indium Zinnoxid. Materialeigenschaften von aufgebrachten CuPc aus TFA Lösung und CuPc in der Lösung wurden ausführlich mit Röntgenbeugung, Spektroskopie- und Mikroskopie Methoden untersucht. Es wird gezeigt, dass die Nanobänder nicht in der Lösung, sondern durch Verdampfen des Lösungsmittels und der Übersättigung der Lösung entstehen. Die Rasterkraftmikroskopie wurde dazu verwendet, um die Morphologie des getrockneten Films bei unterschiedlicher Konzentration zu studieren. Der Mechanismus der Entstehung der Nanobändern wurde im Detail studiert. Gemäß der Keimbildung und Wachstumstheorie wurde die Entstehung der CuPc Nanobänder aus einer übersättigt Lösung diskutiert. Die Form der Nanobändern wurde unter Berücksichtigung der Wechselwirkung zwischen den Molekülen und dem Substrat diskutiert. Die nassverarbeitete CuPc-Dünnschicht wurde als Donorschicht in organischen Doppelschicht Solarzellen mit C60-Molekül, als Akzeptor eingesetzt. Die Effizienz der Energieumwandlung einer solchen Zelle wurde entsprechend den Schichtdicken der CuPc Schicht untersucht.
Selfsustained oscillations are some of the most commonly observed phenomena in biological systems. They emanate from non-linear systems in a heterogeneous environment and can be described by the theory of dynamical systems. Part of this theory considers reduced models of the oscillator dynamics by means of amplitudes and a phase variable. Such variables are highly attractive for theoretical and experimental studies. Theoretically these variables correspond to an integrable linearization of the generally non-linear system. Experimentally, there exist well established approaches to extract phases from oscillator signals. Notably, one can define phase models also for networks of oscillators. One highly active field examines effects of non-local coupling among oscillators, which is thought to play a key role in networks with strong coupling. The dissertation introduces and expands the knowledge about high-order phase coupling in networks of oscillators. Mathematical calculations consider the Stuart-Landau oscillator. A novel phase estimation scheme for direct observations of an oscillator dynamics is introduced based on numerics. A numerical study of high-order phase coupling applies a Fourier fit for the Stuart-Landau and for the van-der-Pol oscillator. The numerical approach is finally tested on observation-based phase estimates of the Morris-Lecar neuron. A popular approach for the construction of phases from signals is based on phase demodulation by means of the Hilbert transform. Generally, observations of oscillations contain a small and generic variation of their amplitude. The work presents a way to quantify how much the variations of signal amplitude spoil a phase demodulation procedure. For the ideal case of phase modulated signals, amplitude modulations vanish. However, the Hilbert transform produces artificial variations of the reconstructed amplitude even in this case. The work proposes a novel procedure called Iterative Hilbert Transform Embedding to obtain an optimal demodulation of signals. The text presents numerous examples and tests of application for the method, covering multicomponent signals, observables of highly stable limit cycle oscillations and noisy phase dynamics. The numerical results are supported by a spectral theory of convergence for weak phase modulations.
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.
Unter geeigneten Wachstumsbedingungen weisen Algenkulturen oft eine größere Produktivität der Zellen auf, als sie bei höheren Pflanzen zu beobachten ist. Chlamydomonas reinhardtii-Zellen sind vergleichsweise klein. So beträgt das Zellvolumen während des vegetativen Zellzyklus etwa 50–3500 µm³. Im Vergleich zu höheren Pflanzen ist in einer Algensuspension die Konzentration der Biomasse allerdings gering. So enthält beispielsweise 1 ml einer üblichen Konzentration zwischen 10E6 und 10E7 Algenzellen. Quantifizierungen von Metaboliten oder Makromolekülen, die zur Modellierung von zellulären Prozessen genutzt werden, werden meist im Zellensemble vorgenommen. Tatsächlich unterliegt jedoch jede Algenzelle einer individuellen Entwicklung, die die Identifizierung charakteristischer allgemeingültiger Systemparameter erschwert. Ziel dieser Arbeit war es, biochemisch relevante Messgrößen in-vivo und in-vitro mit Hilfe optischer Verfahren zu identifizieren und zu quantifizieren. Im ersten Teil der Arbeit wurde ein Puls-Amplituden-Modulation(PAM)-Fluorimetriemessplatz zur Messung der durch äußere Einflüsse bedingten veränderlichen Chlorophyllfluoreszenz an einzelnen Zellen vorgestellt. Die Verwendung eines kommerziellen Mikroskops, die Implementierung empfindlicher Nachweiselektronik und einer geeignete Immobilisierungsmethode ermöglichten es, ein Signal-zu-Rauschverhältnis zu erreichen, mit dem Fluoreszenzsignale einzelner lebender Chlamydomonas-Zellen gemessen werden konnten. Insbesondere wurden das Zellvolumen und der als Maß für die Effizienz des Photosyntheseapparats bzw. die Zellfitness geltende Chlorophyllfluoreszenzparameter Fv/Fm ermittelt und ein hohes Maß an Heterogenität dieser zellulären Parameter in verschiedenen Entwicklungsstadien der synchronisierten Chlamydomonas-Zellen festgestellt. Im zweiten Teil der Arbeit wurden die bildgebende Laser-Scanning-Mikroskopie und anschließende Bilddatenanalyse zur quantitativen Erfassung der wachstumsabhängigen zellulären Parameter angewandt. Ein kommerzielles konfokales Mikroskop wurde um die Möglichkeit der nichtlinearen Mikroskopie erweitert. Diese hat den Vorteil einer lokalisierten Anregung, damit verbunden einer höheren Ortsauflösung und insgesamt geringeren Probenbelastung. Weiterhin besteht neben der Signalgewinnung durch Fluoreszenzanregung die Möglichkeit der Erzeugung der Zweiten Harmonischen (SHG) an biophotonischen Strukturen, wie der zellulären Stärke. Anhand der Verteilungsfunktionen war es möglich mit Hilfe von modelltheoretischen Ansätzen zelluläre Parameter zu ermitteln, die messtechnisch nicht unmittelbar zugänglich sind. Die morphologischen Informationen der Bilddaten ermöglichten die Bestimmung der Zellvolumina und die Volumina subzellularer Strukturen, wie Nuclei, extranucleäre DNA oder Stärkegranula. Weiterhin konnte die Anzahl subzellulärer Strukturen innerhalb einer Zelle bzw. eines Zellverbunds ermittelt werden. Die Analyse der in den Bilddaten enthaltenen Signalintensitäten war Grundlage einer relativen Konzentrationsbestimmung von zellulären Komponenten, wie DNA bzw. Stärke. Mit dem hier vorgestellten Verfahren der nichtlinearen Mikroskopie und nachfolgender Bilddatenanalyse konnte erstmalig die Verteilung des zellulären Stärkegehalts in einer Chlamydomonas-Population während des Wachstums bzw. nach induziertem Stärkeabbau verfolgt werden. Im weiteren Verlauf wurde diese Methode auch auf Gefrierschnitte höherer Pflanzen, wie Arabidopsis thaliana, angewendet. Im Ergebnis wurde gezeigt, dass viele zelluläre Parameter, wie das Volumen, der zelluläre DNA- und Stärkegehalt bzw. die Anzahl der Stärkegranula durch eine Lognormalverteilung, mit wachstumsabhängiger Parametrisierung, beschrieben werden. Zelluläre Parameter, wie Stoffkonzentration und zelluläres Volumen, zeigen keine signifikanten Korrelationen zueinander, woraus geschlussfolgert werden muss, dass es ein hohes Maß an Heterogenität der zellulären Parameter innerhalb der synchronisierten Chlamydomonas-Populationen gibt. Diese Aussage gilt sowohl für die als homogenste Form geltenden Synchronkulturen von Chlamydomonas reinhardtii als auch für die gemessenen zellulären Parameter im intakten Zellverbund höherer Pflanzen. Dieses Ergebnis ist insbesondere für modelltheoretische Betrachtungen von Relevanz, die sich auf empirische Daten bzw. zelluläre Parameter stützen welche im Zellensemble gemessen wurden und somit nicht notwendigerweise den zellulären Status einer einzelnen Zelle repräsentieren.
Fluorination of organic spacer impacts on the structural and optical response of 2D perovskites
(2020)
Low-dimensional hybrid perovskites have triggered significant research interest due to their intrinsically tunable optoelectronic properties and technologically relevant material stability. In particular, the role of the organic spacer on the inherent structural and optical features in two-dimensional (2D) perovskites is paramount for material optimization. To obtain a deeper understanding of the relationship between spacers and the corresponding 2D perovskite film properties, we explore the influence of the partial substitution of hydrogen atoms by fluorine in an alkylammonium organic cation, resulting in (Lc)(2)PbI4 and (Lf)(2)PbI4 2D perovskites, respectively. Consequently, optical analysis reveals a clear 0.2 eV blue-shift in the excitonic position at room temperature. This result can be mainly attributed to a band gap opening, with negligible effects on the exciton binding energy. According to Density Functional Theory (DFT) calculations, the band gap increases due to a larger distortion of the structure that decreases the atomic overlap of the wavefunctions and correspondingly bandwidth of the valence and conduction bands. In addition, fluorination impacts the structural rigidity of the 2D perovskite, resulting in a stable structure at room temperature and the absence of phase transitions at a low temperature, in contrast to the widely reported polymorphism in some non-fluorinated materials that exhibit such a phase transition. This indicates that a small perturbation in the material structure can strongly influence the overall structural stability and related phase transition of 2D perovskites, making them more robust to any phase change. This work provides key information on how the fluorine content in organic spacer influence the structural distortion of 2D perovskites and their optical properties which possess remarkable importance for future optoelectronic applications, for instance in the field of light-emitting devices or sensors.
Coupling of the electrical, mechanical and optical response in polymer/liquid-crystal composites
(2010)
Micrometer-sized liquid-crystal (LC) droplets embedded in a polymer matrix may enable optical switching in the composite film through the alignment of the LC director along an external electric field. When a ferroelectric material is used as host polymer, the electric field generated by the piezoelectric effect can orient the director of the LC under an applied mechanical stress, making these materials interesting candidates for piezo-optical devices. In this work, polymer-dispersed liquid crystals (PDLCs) are prepared from poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) and a nematic liquid crystal (LC). The anchoring effect is studied by means of dielectric relaxation spectroscopy. Two dispersion regions are observed in the dielectric spectra of the pure P(VDF-TrFE) film. They are related to the glass transition and to a charge-carrier relaxation, respectively. In PDLC films containing 10 and 60 wt% LC, an additional, bias-field-dependent relaxation peak is found that can be attributed to the motion of LC molecules. Due to the anchoring effect of the LC molecules, this relaxation process is slowed down considerably, when compared with the related process in the pure LC. The electro-optical and piezo-optical behavior of PDLC films containing 10 and 60 wt% LCs is investigated. In addition to the refractive-index mismatch between the polymer matrix and the LC molecules, the interaction between the polymer dipoles and the LC molecules at the droplet interface influences the light-scattering behavior of the PDLC films. For the first time, it was shown that the electric field generated by the application of a mechanical stress may lead to changes in the transmittance of a PDLC film. Such a piezo-optical PDLC material may be useful e.g. in sensing and visualization applications. Compared to a non-polar matrix polymer, the polar matrix polymer exhibits a strong interaction with the LC molecules at the polymer/LC interface which affects the electro-optical effect of the PDLC films and prevents a larger increase in optical transmission.
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.
Proteine sind an praktisch allen Prozessen in lebenden Zellen maßgeblich beteiligt. Auch in der Biotechnologie werden Proteine in vielfältiger Weise eingesetzt.
Ein Protein besteht aus einer Kette von Aminosäuren. Häufig lagern sich mehrere dieser Ketten zu größeren Strukturen und Funktionseinheiten, sogenannten Proteinkomplexen,
zusammen. Kürzlich wurde gezeigt, dass eine Proteinkomplexbildung bereits während der Biosynthese der Proteine (co-translational) stattfinden kann
und nicht stets erst danach (post-translational) erfolgt. Da Fehlassemblierungen von Proteinen zu Funktionsverlusten und adversen Effekten führen, ist eine präzise und verlässliche Proteinkomplexbildung sowohl für zelluläre Prozesse als auch für biotechnologische Anwendungen essenziell. Mit experimentellen Methoden lassen sich zwar u.a. die Stöchiometrie und die Struktur von Proteinkomplexen bestimmen,
jedoch bisher nicht die Dynamik der Komplexbildung auf unterschiedlichen Zeitskalen. Daher sind grundlegende Mechanismen der Proteinkomplexbildung noch nicht vollständig verstanden. Die hier vorgestellte, auf experimentellen Erkenntnissen aufbauende, computergestützte Modellierung der Proteinkomplexbildung erlaubt eine umfassende Analyse des Einflusses physikalisch-chemischer Parameter
auf den Assemblierungsprozess. Die Modelle bilden möglichst realistisch die experimentellen Systeme der Kooperationspartner (Bar-Ziv, Weizmann-Institut, Israel; Bukau und Kramer, Universität Heidelberg) ab, um damit die Assemblierung von Proteinkomplexen einerseits in einem quasi-zweidimensionalen synthetischen Expressionssystem (in vitro) und andererseits im Bakterium Escherichia coli (in vivo) untersuchen zu können. Mit Hilfe eines vereinfachten Expressionssystems, in dem die Proteine nur an die Chip-Oberfläche, aber nicht aneinander binden können, wird das theoretische Modell parametrisiert. In diesem vereinfachten in-vitro-System durchläuft die Effizienz der Komplexbildung drei Regime – ein bindedominiertes Regime, ein Mischregime und ein produktionsdominiertes Regime. Ihr Maximum erreicht die Effizienz dabei kurz nach dem Übergang vom bindedominierten ins Mischregime und fällt anschließend monoton ab. Sowohl im nicht-vereinfachten in-vitro- als auch im in-vivo-System koexistieren je zwei konkurrierende Assemblierungspfade: Im in-vitro-System erfolgt die Komplexbildung entweder spontan in wässriger Lösung (Lösungsassemblierung) oder aber in einer definierten Schrittfolge an der Chip-Oberfläche (Oberflächenassemblierung); Im in-vivo-System konkurrieren hingegen die co- und die post-translationale Komplexbildung. Es zeigt sich, dass die Dominanz der Assemblierungspfade im in-vitro-System zeitabhängig ist und u.a. durch die Limitierung und Stärke der Bindestellen auf der Chip-Oberfläche beeinflusst werden kann. Im in-vivo-System hat der räumliche Abstand zwischen den Syntheseorten der beiden Proteinkomponenten nur dann einen Einfluss auf die Komplexbildung, wenn die Untereinheiten schnell degradieren. In diesem Fall dominiert die co-translationale Assemblierung auch auf kurzen Zeitskalen deutlich, wohingegen es bei stabilen Untereinheiten zu einem Wechsel von der Dominanz der post- hin zu einer geringen Dominanz der co-translationalen Assemblierung kommt. Mit den in-silico-Modellen lässt sich neben der Dynamik u.a. auch die Lokalisierung der Komplexbildung und -bindung darstellen, was einen Vergleich der theoretischen Vorhersagen mit experimentellen Daten und somit eine Validierung der Modelle ermöglicht. Der hier präsentierte in-silico Ansatz ergänzt die experimentellen Methoden, und erlaubt so, deren Ergebnisse zu interpretieren und neue Erkenntnisse davon abzuleiten.
Structural and spectroscopical study of crystals of 1,3,4-oxadiazole derivatives at high pressure
(2002)
In recent years the search for new materials of technological interest has given new impulses to the study of organic compounds. Organic substances possess a great number of advantages such as the possibility to adjust their properties for a given purpose by different chemical and physical techniques in the preparation process. Oxadiazole derivatives are interesting due to their use as material for light emitting diodes (LED) as well as scintillators. The physical properties of a solid depend on its structure. Different structures induce different intra- and intermolecular interactions. An advantageous method to modify the intra- as well as the intermolecular interactions of a given substance is the application of high pressure. Furthermore, using this method the chemical features of the compound are not influenced. We have investigated the influence of high pressure and high temperature on the super-molecular structure of several oxadiazole derivatives in crystalline state. From the results of this investigation an equation of state for these crystals was determined. Furthermore, the spectroscopical features of these materials under high pressure were characterized.
We present a setup combining a liquid flatjet sample delivery and a MHz laser system for time-resolved soft X-ray absorption measurements of liquid samples at the high brilliance undulator beamline UE52-SGM at Bessy II yielding unprecedented statistics in this spectral range. We demonstrate that the efficient detection of transient absorption changes in transmission mode enables the identification of photoexcited species in dilute samples. With iron(II)-trisbipyridine in aqueous solution as a benchmark system, we present absorption measurements at various edges in the soft X-ray regime. In combination with the wavelength tunability of the laser system, the set-up opens up opportunities to study the photochemistry of many systems at low concentrations, relevant to materials sciences, chemistry, and biology.
A key non-destructive technique for analysis, optimization and developing of new functional materials such as sensors, transducers, electro-optical and memory devices is presented. The Thermal-Pulse Tomography (TPT) provides high-resolution three-dimensional images of electric field and polarization distribution in a material. This thermal technique use a pulsed heating by means of focused laser light which is absorbed by opaque electrodes. The diffusion of the heat causes changes in the sample geometry, generating a short-circuit current or change in surface potential, which contains information about the spatial distribution of electric dipoles or space charges. Afterwards, a reconstruction of the internal electric field and polarization distribution in the material is possible via Scale Transformation or Regularization methods. In this way, the TPT was used for the first time to image the inhomogeneous ferroelectric switching in polymer ferroelectric films (candidates to memory devices). The results shows the typical pinning of electric dipoles in the ferroelectric polymer under study and support the previous hypotheses of a ferroelectric reversal at a grain level via nucleation and growth. In order to obtain more information about the impact of the lateral and depth resolution of the thermal techniques, the TPT and its counterpart called Focused Laser Intensity Modulation Method (FLIMM) were implemented in ferroelectric films with grid-shaped electrodes. The results from both techniques, after the data analysis with different regularization and scale methods, are in total agreement. It was also revealed a possible overestimated lateral resolution of the FLIMM and highlights the TPT method as the most efficient and reliable thermal technique. After an improvement in the optics, the Thermal-Pulse Tomography method was implemented in polymer-dispersed liquid crystals (PDLCs) films, which are used in electro-optical applications. The results indicated a possible electrostatic interaction between the COH group in the liquid crystals and the fluorinate atoms of the used ferroelectric matrix. The geometrical parameters of the LC droplets were partially reproduced as they were compared with Scanning Electron Microscopy (SEM) images. For further applications, it is suggested the use of a non-strong-ferroelectric polymer matrix. In an effort to develop new polymerferroelectrets and for optimizing their properties, new multilayer systems were inspected. The results of the TPT method showed the non-uniformity of the internal electric-field distribution in the shaped-macrodipoles and thus suggested the instability of the sample. Further investigation on multilayers ferroelectrets was suggested and the implementation of less conductive polymers layers too.
In dieser Arbeit werden nichtlineare Kopplungsmechanismen von akustischen Oszillatoren untersucht, die zu Synchronisation führen können. Aufbauend auf die Fragestellungen vorangegangener Arbeiten werden mit Hilfe theoretischer und experimenteller Studien sowie mit Hilfe numerischer Simulationen die Elemente der Tonentstehung in der Orgelpfeife und die Mechanismen der gegenseitigen Wechselwirkung von Orgelpfeifen identifiziert. Daraus wird erstmalig ein vollständig auf den aeroakustischen und fluiddynamischen Grundprinzipien basierendes nichtlinear gekoppeltes Modell selbst-erregter Oszillatoren für die Beschreibung des Verhaltens zweier wechselwirkender Orgelpfeifen entwickelt. Die durchgeführten Modellrechnungen werden mit den experimentellen Befunden verglichen. Es zeigt sich, dass die Tonentstehung und die Kopplungsmechanismen von Orgelpfeifen durch das entwickelte Oszillatormodell in weiten Teilen richtig beschrieben werden. Insbesondere kann damit die Ursache für den nichtlinearen Zusammenhang von Kopplungsstärke und Synchronisation des gekoppelten Zwei-Pfeifen Systems, welcher sich in einem nichtlinearen Verlauf der Arnoldzunge darstellt, geklärt werden. Mit den gewonnenen Erkenntnissen wird der Einfluss des Raumes auf die Tonentstehung bei Orgelpfeifen betrachtet. Dafür werden numerische Simulationen der Wechselwirkung einer Orgelpfeife mit verschiedenen Raumgeometrien, wie z. B. ebene, konvexe, konkave, und gezahnte Geometrien, exemplarisch untersucht. Auch der Einfluss von Schwellkästen auf die Tonentstehung und die Klangbildung der Orgelpfeife wird studiert. In weiteren, neuartigen Synchronisationsexperimenten mit identisch gestimmten Orgelpfeifen, sowie mit Mixturen wird die Synchronisation für verschiedene, horizontale und vertikale Pfeifenabstände in der Ebene der Schallabstrahlung, untersucht. Die dabei erstmalig beobachteten räumlich isotropen Unstetigkeiten im Schwingungsverhalten der gekoppelten Pfeifensysteme, deuten auf abstandsabhängige Wechsel zwischen gegen- und gleichphasigen Sychronisationsregimen hin. Abschließend wird die Möglichkeit dokumentiert, das Phänomen der Synchronisation zweier Orgelpfeifen durch numerische Simulationen, also der Behandlung der kompressiblen Navier-Stokes Gleichungen mit entsprechenden Rand- und Anfangsbedingungen, realitätsnah abzubilden. Auch dies stellt ein Novum dar.
In dieser Arbeit werden die Effekte der Synchronisation nichtlinearer, akustischer Oszillatoren am Beispiel zweier Orgelpfeifen untersucht. Aus vorhandenen, experimentellen Messdaten werden die typischen Merkmale der Synchronisation extrahiert und dargestellt. Es folgt eine detaillierte Analyse der Übergangsbereiche in das Synchronisationsplateau, der Phänomene während der Synchronisation, als auch das Austreten aus der Synchronisationsregion beider Orgelpfeifen, bei verschiedenen Kopplungsstärken. Die experimentellen Befunde werfen Fragestellungen nach der Kopplungsfunktion auf. Dazu wird die Tonentstehung in einer Orgelpfeife untersucht. Mit Hilfe von numerischen Simulationen der Tonentstehung wird der Frage nachgegangen, welche fluiddynamischen und aero-akustischen Ursachen die Tonentstehung in der Orgelpfeife hat und inwiefern sich die Mechanismen auf das Modell eines selbsterregten akustischen Oszillators abbilden lässt. Mit der Methode des Coarse Graining wird ein Modellansatz formuliert.
Anhand eines paradigmatischen Modellbeispiels werden die Konsequenzen der Koexistenz vieler Attraktoren auf die globale Dynamik schwach dissipativer Systeme studiert. Es wird gezeigt, dass diese Systeme eine sehr reichhaltige Dynamik besitzen und extrem sensitiv gegenüber Störungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilität ihres Verhaltens aus.
We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.
The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.
We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.
We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).
We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.
Particles in Saturn’s main rings range in size from dust to even kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q⋆ of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into “strength” and “gravity” regimes, and b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few meters, consistent with the maximum aggregate size observed in Saturn’s rings of about 10m.
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.
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 strong adhesion of sub-micron sized particles to surfaces is a nuisance, both for removing contaminating colloids from surfaces and for conscious manipulation of particles to create and test novel micro/nano-scale assemblies. The obvious idea of using detergents to ease these processes suffers from a lack of control: the action of any conventional surface-modifying agent is immediate and global. With photosensitive azobenzene containing surfactants we overcome these limitations. Such photo-soaps contain optical switches (azobenzene molecules), which upon illumination with light of appropriate wavelength undergo reversible trans-cis photo-isomerization resulting in a subsequent change of the physico-chemical molecular properties. In this work we show that when a spatial gradient in the composition of trans- and cis- isomers is created near a solid-liquid interface, a substantial hydrodynamic flow can be initiated, the spatial extent of which can be set, e.g., by the shape of a laser spot. We propose the concept of light induced diffusioosmosis driving the flow, which can remove, gather or pattern a particle assembly at a solid-liquid interface. In other words, in addition to providing a soap we implement selectivity: particles are mobilized and moved at the time of illumination, and only across the illuminated area.