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Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of the observations. Unraveling such transitions yields essential information for the understanding of the observed system’s intrinsic evolution and potential external influences. A precise detection of multiple changes is therefore of great importance for various research disciplines, such as environmental sciences, bioinformatics and economics. The primary purpose of the detection approach introduced in this thesis is the investigation of transitions underlying direct or indirect climate observations. In order to develop a diagnostic approach capable to capture such a variety of natural processes, the generic statistical features in terms of central tendency and dispersion are employed in the light of Bayesian inversion. In contrast to established Bayesian approaches to multiple changes, the generic approach proposed in this thesis is not formulated in the framework of specialized partition models of high dimensionality requiring prior specification, but as a robust kernel-based approach of low dimensionality employing least informative prior distributions.
First of all, a local Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of a single transition. The analysis of synthetic time series comprising changes of different observational evidence, data loss and outliers validates the performance, consistency and sensitivity of the inference algorithm. To systematically investigate time series for multiple changes, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the weighted kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. The detection approach is applied to environmental time series from the Nile river in Aswan and the weather station Tuscaloosa, Alabama comprising documented changes. The method’s performance confirms the approach as a powerful diagnostic tool to decipher multiple changes underlying direct climate observations.
Finally, the kernel-based Bayesian inference approach is used to investigate a set of complex terrigenous dust records interpreted as climate indicators of the African region of the Plio-Pleistocene period. A detailed inference unravels multiple transitions underlying the indirect climate observations, that are interpreted as conjoint changes. The identified conjoint changes coincide with established global climate events. In particular, the two-step transition associated to the establishment of the modern Walker-Circulation contributes to the current discussion about the influence of paleoclimate changes on the environmental conditions in tropical and subtropical Africa at around two million years ago.
Thermophony in real gases
(2016)
A thermophone is an electrical device for sound generation. The advantages of thermophones over conventional sound transducers such as electromagnetic, electrostatic or piezoelectric transducers are their operational principle which does not require any moving parts, their resonance-free behavior, their simple construction and their low production costs.
In this PhD thesis, a novel theoretical model of thermophonic sound generation in real gases has been developed. The model is experimentally validated in a frequency range from 2 kHz to 1 MHz by testing more then fifty thermophones of different materials, including Carbon nano-wires, Titanium, Indium-Tin-Oxide, different sizes and shapes for sound generation in gases such as air, argon, helium, oxygen, nitrogen and sulfur hexafluoride.
Unlike previous approaches, the presented model can be applied to different kinds of thermophones and various gases, taking into account the thermodynamic properties of thermophone materials and of adjacent gases, degrees of freedom and the volume occupied by the gas atoms and molecules, as well as sound attenuation effects, the shape and size of the thermophone surface and the reduction of the generated acoustic power due to photonic emission. As a result, the model features better prediction accuracy than the existing models by a factor up to 100. Moreover, the new model explains previous experimental findings on thermophones which can not be explained with the existing models.
The acoustic properties of the thermophones have been tested in several gases using unique, highly precise experimental setups comprising a Laser-Doppler-Vibrometer combined with a thin polyethylene film which acts as a broadband and resonance-free sound-pressure detector. Several outstanding properties of the thermophones have been demonstrated for the first time, including the ability to generate arbitrarily shaped acoustic signals, a greater acoustic efficiency compared to conventional piezoelectric and electrostatic airborne ultrasound transducers, and applicability as powerful and tunable sound sources with a bandwidth up to the megahertz range and beyond.
Additionally, new applications of thermophones such as the study of physical properties of gases, the thermo-acoustic gas spectroscopy, broad-band characterization of transfer functions of sound and ultrasound detection systems, and applications in non-destructive materials testing are discussed and experimentally demonstrated.
This thesis is focussed on the electronic properties of the new material class named topological insulators. Spin and angle resolved photoelectron spectroscopy have been applied to reveal several unique properties of the surface state of these materials. The first part of this thesis introduces the methodical background of these quite established experimental techniques.
In the following chapter, the theoretical concept of topological insulators is introduced. Starting from the prominent example of the quantum Hall effect, the application of topological invariants to classify material systems is illuminated. It is explained how, in presence of time reversal symmetry, which is broken in the quantum Hall phase, strong spin orbit coupling can drive a system into a topologically non trivial phase. The prediction of the spin quantum Hall effect in two dimensional insulators an the generalization to the three dimensional case of topological insulators is reviewed together with the first experimental realization of a three dimensional topological insulator in the Bi1-xSbx alloys given in the literature.
The experimental part starts with the introduction of the Bi2X3 (X=Se, Te) family of materials. Recent theoretical predictions and experimental findings on the bulk and surface electronic structure of these materials are introduced in close discussion to our own experimental results. Furthermore, it is revealed, that the topological surface state of Bi2Te3 shares its orbital symmetry with the bulk valence band and the observation of a temperature induced shift of the chemical potential is to a high probability unmasked as a doping effect due to residual gas adsorption.
The surface state of Bi2Te3 is found to be highly spin polarized with a polarization value of about 70% in a macroscopic area, while in Bi2Se3 the polarization appears reduced, not exceeding 50%. We, however, argue that the polarization is most likely only extrinsically limited in terms of the finite angular resolution and the lacking detectability of the out of plane component of the electron spin. A further argument is based on the reduced surface quality of the single crystals after cleavage and, for Bi2Se3 a sensitivity of the electronic structure to photon exposure.
We probe the robustness of the topological surface state in Bi2X3 against surface impurities in Chapter 5. This robustness is provided through the protection by the time reversal symmetry. Silver, deposited on the (111) surface of Bi2Se3 leads to a strong electron doping but the surface state is observed up to a deposited Ag mass equivalent to one atomic monolayer. The opposite sign of doping, i.e., hole-like, is observed by exposing oxygen to Bi2Te3. But while the n-type shift of Ag on Bi2Se3 appears to be more or less rigid, O2 is lifting the Dirac point of the topological surface state in Bi2Te3 out of the valence band minimum at $\Gamma$. After increasing the oxygen dose further, it is possible to shift the Dirac point to the Fermi level, while the valence band stays well beyond. The effect is found reversible, by warming up the samples which is interpreted in terms of physisorption of O2.
For magnetic impurities, i.e., Fe, we find a similar behavior as for the case of Ag in both Bi2Se3 and Bi2Te3. However, in that case the robustness is unexpected, since magnetic impurities are capable to break time reversal symmetry which should introduce a gap in the surface state at the Dirac point which in turn removes the protection. We argue, that the fact that the surface state shows no gap must be attributed to a missing magnetization of the Fe overlayer. In Bi2Te3 we are able to observe the surface state for deposited iron mass equivalents in the monolayer regime. Furthermore, we gain control over the sign of doping through the sample temperature during deposition.
Chapter6 is devoted to the lifetime broadening of the photoemission signal from the topological surface states of Bi2Se3 and Bi2Te3. It is revealed that the hexagonal warping of the surface state in Bi2Te3 introduces an anisotropy for electrons traveling along the two distinct high symmetry directions of the surface Brillouin zone, i.e., $\Gamma$K and $\Gamma$M. We show that the phonon coupling strength to the surface electrons in Bi2Te3 is in nice agreement with the theoretical prediction but, nevertheless, higher than one may expect. We argue that the electron-phonon coupling is one of the main contributions to the decay of photoholes but the relatively small size of the Fermi surface limits the number of phonon modes that may scatter off electrons. This effect is manifested in the energy dependence of the imaginary part of the electron self energy of the surface state which shows a decay to higher binding energies in contrast to the monotonic increase proportional to E$^2$ in the Fermi liquid theory due to electron-electron interaction.
Furthermore, the effect of the surface impurities of Chapter 5 on the quasiparticle life- times is investigated. We find that Fe impurities have a much stronger influence on the lifetimes as compared to Ag. Moreover, we find that the influence is stronger independently of the sign of the doping. We argue that this observation suggests a minor contribution of the warping on increased scattering rates in contrast to current belief. This is additionally confirmed by the observation that the scattering rates increase further with increasing silver amount while the doping stays constant and by the fact that clean Bi2Se3 and Bi2Te3 show very similar scattering rates regardless of the much stronger warping in Bi2Te3.
In the last chapter we report on a strong circular dichroism in the angle distribution of the photoemission signal of the surface state of Bi2Te3. We show that the color pattern obtained by calculating the difference between photoemission intensities measured with opposite photon helicity reflects the pattern expected for the spin polarization. However, we find a strong influence on strength and even sign of the effect when varying the photon energy. The sign change is qualitatively confirmed by means of one-step photoemission calculations conducted by our collaborators from the LMU München, while the calculated spin polarization is found to be independent of the excitation energy. Experiment and theory together unambiguously uncover the dichroism in these systems as a final state effect and the question in the title of the chapter has to be negated: Circular dichroism in the angle distribution is not a new spin sensitive technique.
This publications-based thesis summarizes my contribution to the scientific field of ultrafast structural dynamics. It consists of 16 publications, about the generation, detection and coupling of coherent gigahertz longitudinal acoustic phonons, also called hypersonic waves. To generate such high frequency phonons, femtosecond near infrared laser pulses were used to heat nanostructures composed of perovskite oxides on an ultrashort timescale. As a consequence the heated regions of such a nanostructure expand and a high frequency acoustic phonon pulse is generated. To detect such coherent acoustic sound pulses I use ultrafast variants of optical Brillouin and x-ray scattering. Here an incident optical or x-ray photon is scattered by the excited sound wave in the sample. The scattered light intensity measures the occupation of the phonon modes.
The central part of this work is the investigation of coherent high amplitude phonon wave packets which can behave nonlinearly, quite similar to shallow water waves which show a steepening of wave fronts or solitons well known as tsunamis. Due to the high amplitude of the acoustic wave packets in the solid, the acoustic properties can change significantly in the vicinity of the sound pulse. This may lead to a shape change of the pulse. I have observed by time-resolved Brillouin scattering, that a single cycle hypersound pulse shows a wavefront steepening. I excited hypersound pulses with strain amplitudes until 1% which I have calibrated by ultrafast x-ray diffraction (UXRD).
On the basis of this first experiment we developed the idea of the nonlinear mixing of narrowband phonon wave packets which we call "nonlinear phononics" in analogy with the nonlinear optics, which summarizes a kaleidoscope of surprising optical phenomena showing up at very high electric fields. Such phenomena are for instance Second Harmonic Generation, four-wave-mixing or solitons. But in case of excited coherent phonons the wave packets have usually very broad spectra which make it nearly impossible to look at elementary scattering processes between phonons with certain momentum and energy.
For that purpose I tested different techniques to excite narrowband phonon wave packets which mainly consist of phonons with a certain momentum and frequency. To this end epitaxially grown metal films on a dielectric substrate were excited with a train of laser pulses. These excitation pulses drive the metal film to oscillate with the frequency given by their inverse temporal displacement and send a hypersonic wave of this frequency into the substrate. The monochromaticity of these wave packets was proven by ultrafast optical Brillouin and x-ray scattering.
Using the excitation of such narrowband phonon wave packets I was able to observe the Second Harmonic Generation (SHG) of coherent phonons as a first example of nonlinear wave mixing of nanometric phonon wave packets.
Semi-empirical sea-level models (SEMs) exploit physically motivated empirical relationships between global sea level and certain drivers, in the following global mean temperature. This model class evolved as a supplement to process-based models (Rahmstorf (2007)) which were unable to fully represent all relevant processes. They thus failed to capture past sea-level change (Rahmstorf et al. (2012)) and were thought likely to underestimate future sea-level rise. Semi-empirical models were found to be a fast and useful tool for exploring the uncertainties in future sea-level rise, consistently giving significantly higher projections than process-based models.
In the following different aspects of semi-empirical sea-level modelling have been studied. Models were first validated using various data sets of global sea level and temperature. SEMs were then used on the glacier contribution to sea level, and to infer past global temperature from sea-level data via inverse modelling. Periods studied encompass the instrumental period, covered by tide gauges (starting 1700 CE (Common Era) in Amsterdam) and satellites (first launched in 1992 CE), the era from 1000 BCE (before CE) to present, and the full length of the Holocene (using proxy data). Accordingly different data, model formulations and implementations have been used. It could be shown in Bittermann et al. (2013) that SEMs correctly predict 20th century sea-level when calibrated with data until 1900 CE. SEMs also turned out to give better predictions than the Intergovernmental Panel on Climate Change (IPCC) 4th assessment report (AR4, IPCC (2007)) models, for the period from 1961–2003 CE.
With the first multi-proxy reconstruction of global sea-level as input, estimate of the human-induced component of modern sea-level change and projections of future sea-level rise were calculated (Kopp et al. (2016)). It turned out with 90% confidence that more than 40 % of the observed 20th century sea-level rise is indeed anthropogenic. With the new semi-empirical and IPCC (2013) 5th assessment report (AR5) projections the gap between SEM and process-based model projections closes, giving higher credibility to both. Combining all scenarios, from strong mitigation to business as usual, a global sea-level rise of 28–131 cm relative to 2000 CE, is projected with 90% confidence. The decision for a low carbon pathway could halve the expected global sea-level rise by 2100 CE.
Present day temperature and thus sea level are driven by the globally acting greenhouse-gas forcing. Unlike that, the Milankovich forcing, acting on Holocene timescales, results mainly in a northern-hemisphere temperature change. Therefore a semi-empirical model can be driven with northernhemisphere temperatures, which makes it possible to model the main subcomponent of sea-level change over this period. It showed that an additional positive constant rate of the order of the estimated Antarctic sea-level contribution is then required to explain the sea-level evolution over the Holocene. Thus the global sea level, following the climatic optimum, can be interpreted as the sum of a temperature induced sea-level drop and a positive long-term contribution, likely an ongoing response to deglaciation coming from Antarctica.
Changes in extratropical storm track activity and their implications for extreme weather events
(2016)
In this thesis, the two prototype catalysts Fe(CO)₅ and Cr(CO)₆ are investigated with time-resolved photoelectron spectroscopy at a high harmonic setup. In both of these metal carbonyls, a UV photon can induce the dissociation of one or more ligands of the complex. The mechanism of the dissociation has been debated over the last decades. The electronic dynamics of the first dissociation occur on the femtosecond timescale.
For the experiment, an existing high harmonic setup was moved to a new location, was extended, and characterized. The modified setup can induce dynamics in gas phase samples with photon energies of 1.55eV, 3.10eV, and 4.65eV. The valence electronic structure of the samples can be probed with photon energies between 20eV and 40eV. The temporal resolution is 111fs to 262fs, depending on the combination of the two photon energies.
The electronically excited intermediates of the two complexes, as well as of the reaction product Fe(CO)₄, could be observed with photoelectron spectroscopy in the gas phase for the first time. However, photoelectron spectroscopy gives access only to the final ionic states. Corresponding calculations to simulate these spectra are still in development. The peak energies and their evolution in time with respect to the initiation pump pulse have been determined, these peaks have been assigned based on literature data. The spectra of the two complexes show clear differences. The dynamics have been interpreted with the assumption that the motion of peaks in the spectra relates to the movement of the wave packet in the multidimensional energy landscape. The results largely confirm existing models for the reaction pathways. In both metal carbonyls, this pathway involves a direct excitation of the wave packet to a metal-to-ligand charge transfer state and the subsequent crossing to a dissociative ligand field state. The coupling of the electronic dynamics to the nuclear dynamics could explain the slower dissociation in Fe(CO)₅ as compared to Cr(CO)₆.
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.