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<img src="http://vg00.met.vgwort.de/na/806c85cec18906a64e06" width="1" height="1" alt=""> Subject of this work is the possibility to synchronize nonlinear systems via correlated noise and automatic control. The thesis is divided into two parts. The first part is motivated by field studies on feral sheep populations on two islands of the St. Kilda archipelago, which revealed strong correlations due to environmental noise. For a linear system the population correlation equals the noise correlation (Moran effect). But there exists no systematic examination of the properties of nonlinear maps under the influence of correlated noise. Therefore, in the first part of this thesis the noise-induced correlation of logistic maps is systematically examined. For small noise intensities it can be shown analytically that the correlation of quadratic maps in the fixed-point regime is always smaller than or equal to the noise correlation. In the period-2 regime a Markov model explains qualitatively the main dynamical characteristics. Furthermore, two different mechanisms are introduced which lead to a higher correlation of the systems than the environmental correlation. The new effect of "correlation resonance" is described, i. e. the correlation yields a maximum depending on the noise intensity. In the second part of the thesis an automatic control method is presented which synchronizes different systems in a robust way. This method is inspired by phase-locked loops and is based on a feedback loop with a differential control scheme, which allows to change the phases of the controlled systems. The effectiveness of the approach is demonstrated for controlled phase synchronization of regular oscillators and foodweb models.
Synchrotron-based angle-resolved time-of-flight electron spectroscopy for dynamics in dichalogenides
(2018)
Poly(vinylidene fluoride) (PVDF)-based homo-, co- and ter-polymers are well-known for their ferroelectric and relaxor-ferroelectric properties. Their semi-crystalline morphology consists of crystalline and amorphous phases, plus interface regions in between, and governs the relevant electro-active properties. In this work, the influence of chemical, thermal and mechanical treatments on the structure and morphology of PVDF-based polymers and on the related ferroelectric/relaxor-ferroelectric properties is investigated. Polymer films were prepared in different ways and subjected to various treatments such as annealing, quenching and stretching. The resulting changes in the transitions and relaxations of the polymer samples were studied by means of dielectric, thermal, mechanical and optical techniques. In particular, the origin(s) behind the mysterious mid-temperature transition (T_{mid}) that is observed in all PVDF-based polymers was assessed. A new hypothesis is proposed to describe the T_{mid} transition as a result of multiple processes taking place within the temperature range of the transition. The contribution of the individual processes to the observed overall transition depends on both the chemical structure of the monomer units and the processing conditions which also affect the melting transition. Quenching results in a decrease of the overall crystallinity and in smaller crystallites. On samples quenched after annealing, notable differences in the fractions of different crystalline phases have been observed when compared to samples that had been slowly cooled. Stretching of poly(vinylidene fluoride-tetrafluoroethylene) (P(VDF-TFE)) films causes an increase in the fraction of the ferroelectric β-phase with simultaneous increments in the melting point (T_m) and the crystallinity (\chi_c) of the copolymer. While an increase in the stretching temperature does not have a profound effect on the amount of the ferroelectric phase, its stability appears to improve.
Measurements of the non-linear dielectric permittivity \varepsilon_2^\prime in a poly(vinylidenefluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE- CFE)) relaxor-ferroelectric (R-F) terpolymer reveal peaks at 30 and 80 °C that cannot be identified in conventional dielectric spectroscopy. The former peak is associated with T_{mid}\ and may help to understand the non-zero \varepsilon_2^\prime values that are found for the paraelectric terpolymer phase. The latter peak can also be observed during cooling of P(VDF-TrFE) copolymer samples at 100 °C and is due to conduction processes and space-charge polarization as a result of the accumulation of real charges at the electrode-sample interface. Annealing lowers the Curie-transition temperature of the terpolymer as a consequence of its smaller ferroelectric-phase fraction, which by default exists even in terpolymers with relatively high CFE content. Changes in the transition temperatures are in turn related to the behavior of the hysteresis curves observed on differently heat-treated samples. Upon heating, the hysteresis curves evolve from those known for a ferroelectric to those of a typical relaxor-ferroelectric material. Comparing dielectric-hysteresis loops obtained at various temperatures, we find that annealed terpolymer films show higher electric-displacement values and lower coercive fields than the non-annealed samples − irrespective of the measurement temperature − and also exhibit ideal relaxor-ferroelectric behavior at ambient temperatures, which makes them excellent candidates for related applications at or near room temperature. However, non-annealed films − by virtue of their higher ferroelectric activity − show a larger and more stable remanent polarization at room temperature, while annealed samples need to be poled below 0 °C to induce a well-defined polarization. Overall, by modifying the three phases in PVDF-based polymers, it has been demonstrated how the preparation steps and processing conditions can be tailored to achieve the desired properties that are optimal for specific applications.
A huge number of applications require coherent radiation in the visible spectral range. Since diode lasers are very compact and efficient light sources, there exists a great interest to cover these applications with diode laser emission. Despite modern band gap engineering not all wavelengths can be accessed with diode laser radiation. Especially in the visible spectral range between 480 nm and 630 nm no emission from diode lasers is available, yet. Nonlinear frequency conversion of near-infrared radiation is a common way to generate coherent emission in the visible spectral range. However, radiation with extraordinary spatial temporal and spectral quality is required to pump frequency conversion. Broad area (BA) diode lasers are reliable high power light sources in the near-infrared spectral range. They belong to the most efficient coherent light sources with electro-optical efficiencies of more than 70%. Standard BA lasers are not suitable as pump lasers for frequency conversion because of their poor beam quality and spectral properties. For this purpose, tapered lasers and diode lasers with Bragg gratings are utilized. However, these new diode laser structures demand for additional manufacturing and assembling steps that makes their processing challenging and expensive. An alternative to BA diode lasers is the stripe-array architecture. The emitting area of a stripe-array diode laser is comparable to a BA device and the manufacturing of these arrays requires only one additional process step. Such a stripe-array consists of several narrow striped emitters realized with close proximity. Due to the overlap of the fields of neighboring emitters or the presence of leaky waves, a strong coupling between the emitters exists. As a consequence, the emission of such an array is characterized by a so called supermode. However, for the free running stripe-array mode competition between several supermodes occurs because of the lack of wavelength stabilization. This leads to power fluctuations, spectral instabilities and poor beam quality. Thus, it was necessary to study the emission properties of those stripe-arrays to find new concepts to realize an external synchronization of the emitters. The aim was to achieve stable longitudinal and transversal single mode operation with high output powers giving a brightness sufficient for efficient nonlinear frequency conversion. For this purpose a comprehensive analysis of the stripe-array devices was done here. The physical effects that are the origin of the emission characteristics were investigated theoretically and experimentally. In this context numerical models could be verified and extended. A good agreement between simulation and experiment was observed. One way to stabilize a specific supermode of an array is to operate it in an external cavity. Based on mathematical simulations and experimental work, it was possible to design novel external cavities to select a specific supermode and stabilize all emitters of the array at the same wavelength. This resulted in stable emission with 1 W output power, a narrow bandwidth in the range of 2 MHz and a very good beam quality with M²<1.5. This is a new level of brightness and brilliance compared to other BA and stripe-array diode laser systems. The emission from this external cavity diode laser (ECDL) satisfied the requirements for nonlinear frequency conversion. Furthermore, a huge improvement to existing concepts was made. In the next step newly available periodically poled crystals were used for second harmonic generation (SHG) in single pass setups. With the stripe-array ECDL as pump source, more than 140 mW of coherent radiation at 488 nm could be generated with a very high opto-optical conversion efficiency. The generated blue light had very good transversal and longitudinal properties and could be used to generate biphotons by parametric down-conversion. This was feasible because of the improvement made with the infrared stripe-array diode lasers due to the development of new physical concepts.
Mechanosensation is a fundamental biological process that provides the basis for sensing touch and pain as well as for hearing and proprioception. A special class of ion-channel proteins known as mechanosensitive proteins convert the mechanical stimuli into electrochemical signals to mediate this process. Mechanosensitive proteins undergo conformational changes in response to mechanical force, which eventually leads to the opening of the proteins' ion channel. Mammalian mechanosensitive proteins remained a long sought-after mystery until 2010 when a family of two proteins - Piezo1 and Piezo2 - was identifed as mechanosensors [1]. The cryo-EM structures of Piezo1 and Piezo2 protein were resolved in the last years and reveal a propeller-shaped homotrimer with 114 transmembrane helices [2, 3, 4, 5]. The protein structures are curved and have been suggested to deform the surrounding membrane into a nano-dome, which mechanically responds to membrane tension resulting from external forces [2]. In this thesis, the conformations of membrane-embedded Piezo1 and Piezo2 proteins and their tension-induced conformational changes are investigated using molecular dynamics simulations. Our coarse-grained molecular dynamics simulations show that the Piezo proteins induce curvature in the surrounding membrane and form a stable protein-membrane nano-dome in the tensionless membrane. These membrane-embedded Piezo proteins, however, adopt substantially less curved conformations in our simulations compared to the cryo-EM structures solved in detergent micelles, which agrees with recent experimental investigations of the overall Piezo nano-dome shape in membrane vesicles [6, 7, 8]. At high membrane tension, the Piezo proteins attain nearly planar conformations in our simulations. Our systematic investigation of Piezo proteins under different membrane tensions indicates a half-maximal conformational response at membrane tension values rather close to the experimentally suggested values of Piezo activation [9, 10]. In addition, our simulations indicate a widening of the Piezo1 ion channel at high membrane tension, which agrees with the channel widening observed in recent nearly flattened cryo-EM structures of Piezo1 in small membrane vesicles [11]. In contrast, the Piezo2 ion channel does not respond to membrane tension in our simulations. These different responses of the Piezo1 and Piezo2 ion channels in our simulations are in line with patch-clamp experiments, in which Piezo1, but not Piezo2, was shown to be activated by membrane tension alone [12].
Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes.
Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics
(2012)
Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples.
In normal everyday viewing, we perform large eye movements (saccades) and miniature or fixational eye movements. Most of our visual perception occurs while we are fixating. However, our eyes are perpetually in motion. Properties of these fixational eye movements, which are partly controlled by the brainstem, change depending on the task and the visual conditions. Currently, fixational eye movements are poorly understood because they serve the two contradictory functions of gaze stabilization and counteraction of retinal fatigue. In this dissertation, we investigate the spatial and temporal properties of time series of eye position acquired from participants staring at a tiny fixation dot or at a completely dark screen (with the instruction to fixate a remembered stimulus); these time series were acquired with high spatial and temporal resolution. First, we suggest an advanced algorithm to separate the slow phases (named drift) and fast phases (named microsaccades) of these movements, which are considered to play different roles in perception. On the basis of this identification, we investigate and compare the temporal scaling properties of the complete time series and those time series where the microsaccades are removed. For the time series obtained during fixations on a stimulus, we were able to show that they deviate from Brownian motion. On short time scales, eye movements are governed by persistent behavior and on a longer time scales, by anti-persistent behavior. The crossover point between these two regimes remains unchanged by the removal of microsaccades but is different in the horizontal and the vertical components of the eyes. Other analyses target the properties of the microsaccades, e.g., the rate and amplitude distributions, and we investigate, whether microsaccades are triggered dynamically, as a result of earlier events in the drift, or completely randomly. The results obtained from using a simple box-count measure contradict the hypothesis of a purely random generation of microsaccades (Poisson process). Second, we set up a model for the slow part of the fixational eye movements. The model is based on a delayed random walk approach within the velocity related equation, which allows us to use the data to determine control loop durations; these durations appear to be different for the vertical and horizontal components of the eye movements. The model is also motivated by the known physiological representation of saccade generation; the difference between horizontal and vertical components concurs with the spatially separated representation of saccade generating regions. Furthermore, the control loop durations in the model suggest an external feedback loop for the horizontal but not for the vertical component, which is consistent with the fact that an internal feedback loop in the neurophysiology has only been identified for the vertical component. Finally, we confirmed the scaling properties of the model by semi-analytical calculations. In conclusion, we were able to identify several properties of the different parts of fixational eye movements and propose a model approach that is in accordance with the described neurophysiology and described limitations of fixational eye movement control.
Arctic climate change is marked by intensified warming compared to global trends and a significant reduction in Arctic sea ice which can intricately influence mid-latitude atmospheric circulation through tropo- and stratospheric pathways. Achieving accurate simulations of current and future climate demands a realistic representation of Arctic climate processes in numerical climate models, which remains challenging.
Model deficiencies in replicating observed Arctic climate processes often arise due to inadequacies in representing turbulent boundary layer interactions that determine the interactions between the atmosphere, sea ice, and ocean. Many current climate models rely on parameterizations developed for mid-latitude conditions to handle Arctic turbulent boundary layer processes.
This thesis focuses on modified representation of the Arctic atmospheric processes and understanding their resulting impact on large-scale mid-latitude atmospheric circulation within climate models. The improved turbulence parameterizations, recently developed based on Arctic measurements, were implemented in the global atmospheric circulation model ECHAM6. This involved modifying the stability functions over sea ice and ocean for stable stratification and changing the roughness length over sea ice for all stratification conditions. Comprehensive analyses are conducted to assess the impacts of these modifications on ECHAM6's simulations of the Arctic boundary layer, overall atmospheric circulation, and the dynamical pathways between the Arctic and mid-latitudes.
Through a step-wise implementation of the mentioned parameterizations into ECHAM6, a series of sensitivity experiments revealed that the combined impacts of the reduced roughness length and the modified stability functions are non-linear. Nevertheless, it is evident that both modifications consistently lead to a general decrease in the heat transfer coefficient, being in close agreement with the observations.
Additionally, compared to the reference observations, the ECHAM6 model falls short in accurately representing unstable and strongly stable conditions.
The less frequent occurrence of strong stability restricts the influence of the modified stability functions by reducing the affected sample size. However, when focusing solely on the specific instances of a strongly stable atmosphere, the sensible heat flux approaches near-zero values, which is in line with the observations. Models employing commonly used surface turbulence parameterizations were shown to have difficulties replicating the near-zero sensible heat flux in strongly stable stratification.
I also found that these limited changes in surface layer turbulence parameterizations have a statistically significant impact on the temperature and wind patterns across multiple pressure levels, including the stratosphere, in both the Arctic and mid-latitudes. These significant signals vary in strength, extent, and direction depending on the specific month or year, indicating a strong reliance on the background state.
Furthermore, this research investigates how the modified surface turbulence parameterizations may influence the response of both stratospheric and tropospheric circulation to Arctic sea ice loss.
The most suitable parameterizations for accurately representing Arctic boundary layer turbulence were identified from the sensitivity experiments. Subsequently, the model's response to sea ice loss is evaluated through extended ECHAM6 simulations with different prescribed sea ice conditions.
The simulation with adjusted surface turbulence parameterizations better reproduced the observed Arctic tropospheric warming in vertical extent, demonstrating improved alignment with the reanalysis data. Additionally, unlike the control experiments, this simulation successfully reproduced specific circulation patterns linked to the stratospheric pathway for Arctic-mid-latitude linkages. Specifically, an increased occurrence of the Scandinavian-Ural blocking regime (negative phase of the North Atlantic Oscillation) in early (late) winter is observed. Overall, it can be inferred that improving turbulence parameterizations at the surface layer can improve the ECHAM6's response to sea ice loss.
The present work investigates the structure formation and wetting in two dimensional (2D) Langmuir monolayer phases in local thermodynamic equilibrium. A Langmuir monolayer is an isolated 2D system of surfactants at the air/water interface. It exhibits crystalline, liquid crystalline, liquid and gaseous phases differing in positional and/or orientational order. Permanent electric dipole moments of the surfactants lead to a long range repulsive interaction and to the formation of mesoscopic patterns. An interaction model is used describing the structure formation as a competition between short range attraction (bare line tension) and long range repulsion (surface potentials) on a scale Delta. Delta has the meaning of a dividing length between the short and long range interaction. In the present work the thermodynamic equilibrium conditions for the shape of two phase boundary lines (Young-Laplace equation) and three phase intersection points (Young′s condition) are derived and applied to describe experimental data: The line tension is measured by pendant droplet tensiometry. The bubble shape and size of 2D foams is calculated numerically and compared to experimental foams. Contact angles are measured by fitting numerical solutions of the Young-Laplace equation on micron scale. The scaling behaviour of the contact angle allows to measure a lower limit for Delta. Further it is discussed, whether in biological membranes wetting transitions are a way in order to control reaction kinetics. Studies performed in our group are discussed with respect to this question in the framework of the above mentioned theory. Finally the apparent violation of Gibbs′ phase rule in Langmuir monolayers (non-horizontal plateau of the surface pressure/area-isotherm, extended three phase coexistence region in one component systems) is investigated quantitatively. It has been found that the most probable explanation are impurities within the system whereas finite size effects or the influence of the long range electrostatics can not explain the order of magnitude of the effect.