Refine
Year of publication
Document Type
- Doctoral Thesis (550) (remove)
Language
- English (550) (remove)
Keywords
- Synchronisation (15)
- Klimawandel (10)
- data analysis (9)
- synchronization (9)
- Datenanalyse (8)
- Nichtlineare Dynamik (8)
- Spektroskopie (8)
- Synchronization (8)
- climate change (8)
- Astrophysik (7)
Institute
- Institut für Physik und Astronomie (550) (remove)
In recent decades, astronomy has seen a boom in large-scale stellar surveys of the Galaxy. The detailed information obtained about millions of individual stars in the Milky Way is bringing us a step closer to answering one of the most outstanding questions in astrophysics: how do galaxies form and evolve? The Milky Way is the only galaxy where we can dissect many stars into their high-dimensional chemical composition and complete phase space, which analogously as fossil records can unveil the past history of the genesis of the Galaxy. The processes that lead to large structure formation, such as the Milky Way, are critical for constraining cosmological models; we call this line of study Galactic archaeology or near-field cosmology.
At the core of this work, we present a collection of efforts to chemically and dynamically characterise the disks and bulge of our Galaxy. The results we present in this thesis have only been possible thanks to the advent of the Gaia astrometric satellite, which has revolutionised the field of Galactic archaeology by precisely measuring the positions, parallax distances and motions of more than a billion stars. Another, though not less important, breakthrough is the APOGEE survey, which has observed spectra in the near-infrared peering into the dusty regions of the Galaxy, allowing us to determine detailed chemical abundance patterns in hundreds of thousands of stars. To accurately depict the Milky Way structure, we use and develop the Bayesian isochrone fitting tool/code called StarHorse; this software can predict stellar distances, extinctions and ages by combining astrometry, photometry and spectroscopy based on stellar evolutionary models. The StarHorse code is pivotal to calculating distances where Gaia parallaxes alone cannot allow accurate estimates.
We show that by combining Gaia, APOGEE, photometric surveys and using StarHorse, we can produce a chemical cartography of the Milky way disks from their outermost to innermost parts. Such a map is unprecedented in the inner Galaxy. It reveals a continuity of the bimodal chemical pattern previously detected in the solar neighbourhood, indicating two populations with distinct formation histories. Furthermore, the data reveals a chemical gradient within the thin disk where the content of 𝛼-process elements and metals is higher towards the centre. Focusing on a sample in the inner MW we confirm the extension of the chemical duality to the innermost regions of the Galaxy. We find stars with bar shape orbits to show both high- and low-𝛼 abundances, suggesting the bar formed by secular evolution trapping stars that already existed. By analysing the chemical orbital space of the inner Galactic regions, we disentangle the multiple populations that inhabit this complex region. We reveal the presence of the thin disk, thick disk, bar, and a counter-rotating population, which resembles the outcome of a perturbed proto-Galactic disk. Our study also finds that the inner Galaxy holds a high quantity of super metal-rich stars up to three times solar suggesting it is a possible repository of old super-metal-rich stars found in the solar neighbourhood.
We also enter into the complicated task of deriving individual stellar ages. With StarHorse, we calculate the ages of main-sequence turn-off and sub-giant stars for several public spectroscopic surveys. We validate our results by investigating linear relations between chemical abundances and time since the 𝛼 and neutron capture elements are sensitive to age as a reflection of the different enrichment timescales of these elements. For further study of the disks in the solar neighbourhood, we use an unsupervised machine learning algorithm to delineate a multidimensional separation of chrono-chemical stellar groups revealing the chemical thick disk, the thin disk, and young 𝛼-rich stars. The thick disk is shown to have a small age dispersion indicating its fast formation contrary to the thin disk that spans a wide range of ages.
With groundbreaking data, this thesis encloses a detailed chemo-dynamical view of the disk and bulge of our Galaxy. Our findings on the Milky Way can be linked to the evolution of high redshift disk galaxies, helping to solve the conundrum of galaxy formation.
The Antarctic ice sheet is the largest freshwater reservoir worldwide. If it were to melt completely, global sea levels would rise by about 58 m. Calculation of projections of the Antarctic contribution to sea level rise under global warming conditions is an ongoing effort which
yields large ranges in predictions. Among the reasons for this are uncertainties related to the physics of ice sheet modeling. These
uncertainties include two processes that could lead to runaway ice retreat: the Marine Ice Sheet Instability (MISI), which causes rapid grounding line retreat on retrograde bedrock, and the Marine Ice Cliff Instability (MICI), in which tall ice cliffs become unstable and calve off, exposing even taller ice cliffs.
In my thesis, I investigated both marine instabilities (MISI and MICI) using the Parallel Ice Sheet Model (PISM), with a focus on MICI.
The field of gamma-ray astronomy opened a new window into the non-thermal universe that allows studying the acceleration sites of cosmic rays and the role of cosmic rays on evolutionary processes in galaxies. The detection of almost one hundred Galactic very-high-energy (VHE: 0.1−100TeV) gamma-ray sources in the Milky Way demonstrates that particle acceleration up to tens of TeV energies is a common phenomenon. Furthermore, the detection of VHE gamma rays from other galaxies has confirmed that cosmic rays are not exclusively accelerated in the Milky Way. The rapid development of gamma-ray astronomy in the past two decades has led to a transition from the detection and study of individual sources to source population studies. To answer the question, whether the VHE gamma-ray source population of the Milky Way is unique, observations of galaxies, for which individual sources can be resolved, are required. Such galaxies are the Magellanic Clouds, two satellite galaxies of the Milky Way, which have been surveyed by the H.E.S.S. experiment in the last decade. In this thesis, data from a total of 450 hours of H.E.S.S. observations towards the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) are presented. During the analysis of the data sets, special emphasis is put on the evaluation of systematic uncertainties of the experiment in order to assure an unbiased flux estimation of the potential VHE gamma-ray sources of the Magellanic Clouds. A detailed analysis of the survey data revealed the detection of the gamma-ray binary LMCP3, the most powerful gamma-ray binary known so far, that is located in the LMC, and thus, increases the number of known VHE gamma-ray sources in the LMC to four. No other VHE gamma-ray source is detected in the Magellanic Clouds and integral flux upper limits are estimated. These flux upper limits are used to perform a source population study based on known VHE source classes and existing multi-wavelength catalogues. A comparison of the source populations of the Magellanic Clouds and the Milky Way revealed that no other source in the Magellanic Clouds is as bright as the most luminous VHE gamma-ray source in the LMC: the pulsar wind nebula N 157B, and that one-third of the source population of the Magellanic Clouds is less luminous than the other known VHE gamma-ray sources in the LMC. For only a couple of sources luminosity levels of Galactic VHE sources, that are more than one order of magnitude fainter than the detected sources in the LMC, are constrained. Based on the flux upper limits, differences on the TeV source populations in the Magellanic Clouds and the Milky Way as well as the importance of the source environments will be discussed.
The aim of this thesis is to achieve a deep understanding of the working mechanism of polymer based solar cells and to improve the device performance. Two types of the polymer based solar cells are studied here: all-polymer solar cells comprising macromolecular donors and acceptors based on poly(p-phenylene vinylene) and hybrid cells comprising a PPV copolymer in combination with a novel small molecule electron acceptor. To understand the interplay between morphology and photovoltaic properties in all-polymer devices, I compared the photocurrent characteristics and excited state properties of bilayer and blend devices with different nano-morphology, which was fine tuned by using solvents with different boiling points. The main conclusion from these complementary measurements was that the performance-limiting step is the field-dependent generation of free charge carriers, while bimolecular recombination and charge extraction do not compromise device performance. These findings imply that the proper design of the donor-acceptor heterojunction is of major importance towards the goal of high photovoltaic efficiencies. Regarding polymer-small molecular hybrid solar cells I combined the hole-transporting polymer M3EH-PPV with a novel Vinazene-based electron acceptor. This molecule can be either deposited from solution or by thermal evaporation, allowing for a large variety of layer architectures to be realized. I then demonstrated that the layer architecture has a large influence on the photovoltaic properties. Solar cells with very high fill factors of up to 57 % and an open circuit voltage of 1V could be achieved by realizing a sharp and well-defined donor-acceptor heterojunction. In the past, fill factors exceeding 50 % have only been observed for polymers in combination with soluble fullerene-derivatives or nanocrystalline inorganic semiconductors as the electron-accepting component. The finding that proper processing of polymer-vinazene devices leads to similar high values is a major step towards the design of efficient polymer-based solar cells.
Supermassive black holes reside in the hearts of almost all massive galaxies. Their evolutionary path seems to be strongly linked to the evolution of their host galaxies, as implied by several empirical relations between the black hole mass (M BH ) and different host galaxy properties. The physical driver of this co-evolution is, however, still not understood. More mass measurements over homogeneous samples and a detailed understanding of systematic uncertainties are required to fathom the origin of the scaling relations.
In this thesis, I present the mass estimations of supermassive black holes in the nuclei of one late-type and thirteen early-type galaxies. Our SMASHING sample extends from the intermediate to the massive galaxy mass regime and was selected to fill in gaps in number of galaxies along the scaling relations. All galaxies were observed at high spatial resolution, making use of the adaptive-optics mode of integral field unit (IFU) instruments on state-of-the-art telescopes (SINFONI, NIFS, MUSE). I extracted the stellar kinematics from these observations and constructed dynamical Jeans and Schwarzschild models to estimate the mass of the central black holes robustly. My new mass estimates increase the number of early-type galaxies with measured black hole masses by 15%. The seven measured galaxies with nuclear light deficits (’cores’) augment the sample of cored galaxies with measured black holes by 40%. Next to determining massive black hole masses, evaluating the accuracy of black hole masses is crucial for understanding the intrinsic scatter of the black hole- host galaxy scaling relations. I tested various sources of systematic uncertainty on my derived mass estimates.
The M BH estimate of the single late-type galaxy of the sample yielded an upper limit, which I could constrain very robustly. I tested the effects of dust, mass-to-light ratio (M/L) variation, and dark matter on my measured M BH . Based on these tests, the typically assumed constant M/L ratio can be an adequate assumption to account for the small amounts of dark matter in the center of that galaxy. I also tested the effect of a variable M/L variation on the M BH measurement on a second galaxy. By considering stellar M/L variations in the dynamical modeling, the measured M BH decreased by 30%. In the future, this test should be performed on additional galaxies to learn how an as constant assumed M/L flaws the estimated black hole masses.
Based on our upper limit mass measurement, I confirm previous suggestions that resolving the predicted BH sphere-of-influence is not a strict condition to measure black hole masses. Instead, it is only a rough guide for the detection of the black hole if high-quality, and high signal-to-noise IFU data are used for the measurement. About half of our sample consists of massive early-type galaxies which show nuclear surface brightness cores and signs of triaxiality. While these types of galaxies are typically modeled with axisymmetric modeling methods, the effects on M BH are not well studied yet. The massive galaxies of our presented galaxy sample are well suited to test the effect of different stellar dynamical models on the measured black hole mass in evidently triaxial galaxies. I have compared spherical Jeans and axisymmetric Schwarzschild models and will add triaxial Schwarzschild models to this comparison in the future. The constructed Jeans and Schwarzschild models mostly disagree with each other and cannot reproduce many of the triaxial features of the galaxies (e.g., nuclear sub-components, prolate rotation). The consequence of the axisymmetric-triaxial assumption on the accuracy of M BH and its impact on the black hole - host galaxy relation needs to be carefully examined in the future.
In the sample of galaxies with published M BH , we find measurements based on different dynamical tracers, requiring different observations, assumptions, and methods. Crucially, different tracers do not always give consistent results. I have used two independent tracers (cold molecular gas and stars) to estimate M BH in a regular galaxy of our sample. While the two estimates are consistent within their errors, the stellar-based measurement is twice as high as the gas-based. Similar trends have also been found in the literature. Therefore, a rigorous test of the systematics associated with the different modeling methods is required in the future. I caution to take the effects of different tracers (and methods) into account when discussing the scaling relations.
I conclude this thesis by comparing my galaxy sample with the compilation of galaxies with measured black holes from the literature, also adding six SMASHING galaxies, which were published outside of this thesis. None of the SMASHING galaxies deviates significantly from the literature measurements. Their inclusion to the published early-type galaxies causes a change towards a shallower slope for the M BH - effective velocity dispersion relation, which is mainly driven by the massive galaxies of our sample. More unbiased and homogenous measurements are needed in the future to determine the shape of the relation and understand its physical origin.
The increasing number of known exoplanets raises questions about their demographics and the mechanisms that shape planets into how we observe them today. Young planets in close-in orbits are exposed to harsh environments due to the host star being magnetically highly active, which results in high X-ray and extreme UV fluxes impinging on the planet. Prolonged exposure to this intense photoionizing radiation can cause planetary atmospheres to heat up, expand and escape into space via a hydrodynamic escape process known as photoevaporation. For super-Earth and sub-Neptune-type planets, this can even lead to the complete erosion of their primordial gaseous atmospheres. A factor of interest for this particular mass-loss process is the activity evolution of the host star. Stellar rotation, which drives the dynamo and with it the magnetic activity of a star, changes significantly over the stellar lifetime. This strongly affects the amount of high-energy radiation received by a planet as stars age. At a young age, planets still host warm and extended envelopes, making them particularly susceptible to atmospheric evaporation. Especially in the first gigayear, when X-ray and UV levels can be 100 - 10,000 times higher than for the present-day sun, the characteristics of the host star and the detailed evolution of its high-energy emission are of importance.
In this thesis, I study the impact of stellar activity evolution on the high-energy-induced atmospheric mass loss of young exoplanets. The PLATYPOS code was developed as part of this thesis to calculate photoevaporative mass-loss rates over time. The code, which couples parameterized planetary mass-radius relations with an analytical hydrodynamic escape model, was used, together with Chandra and eROSITA X-ray observations, to investigate the future mass loss of the two young multiplanet systems V1298 Tau and K2-198. Further, in a numerical ensemble study, the effect of a realistic spread of activity tracks on the small-planet radius gap was investigated for the first time. The works in this thesis show that for individual systems, in particular if planetary masses are unconstrained, the difference between a young host star following a low-activity track vs. a high-activity one can have major implications: the exact shape of the activity evolution can determine whether a planet can hold on to some of its atmosphere, or completely loses its envelope, leaving only the bare rocky core behind. For an ensemble of simulated planets, an observationally-motivated distribution of activity tracks does not substantially change the final radius distribution at ages of several gigayears. My simulations indicate that the overall shape and slope of the resulting small-planet radius gap is not significantly affected by the spread in stellar activity tracks. However, it can account for a certain scattering or fuzziness observed in and around the radius gap of the observed exoplanet population.
Most of the matter in the universe consists of hydrogen. The hydrogen in the intergalactic medium (IGM), the matter between the galaxies, underwent a change of its ionisation state at the epoch of reionisation, at a redshift roughly between 6>z>10, or ~10^8 years after the Big Bang. At this time, the mostly neutral hydrogen in the IGM was ionised but the source of the responsible hydrogen ionising emission remains unclear. In this thesis I discuss the most likely candidates for the emission of this ionising radiation, which are a type of galaxy called Lyman alpha emitters (LAEs). As implied by their name, they emit Lyman alpha radiation, produced after a hydrogen atom has been ionised and recombines with a free electron. The ionising radiation itself (also called Lyman continuum emission) which is needed for this process inside the LAEs could also be responsible for ionising the IGM around those galaxies at the epoch of reionisation, given that enough Lyman continuum escapes. Through this mechanism, Lyman alpha and Lyman continuum radiation are closely linked and are both studied to better understand the properties of high redshift galaxies and the reionisation state of the universe.
Before I can analyse their Lyman alpha emission lines and the escape of Lyman continuum emission from them, the first step is the detection and correct classification of LAEs in integral field spectroscopic data, specifically taken with the Multi-Unit Spectroscopic Explorer (MUSE). After detecting emission line objects in the MUSE data, the task of classifying them and determining their redshift is performed with the graphical user interface QtClassify, which I developed during the work on this thesis. It uses the strength of the combination of spectroscopic and photometric information that integral field spectroscopy offers to enable the user to quickly identify the nature of the detected emission lines. The reliable classification of LAEs and determination of their redshifts is a crucial first step towards an analysis of their properties.
Through radiative transfer processes, the properties of the neutral hydrogen clouds in and around LAEs are imprinted on the shape of the Lyman alpha line. Thus after identifying the LAEs in the MUSE data, I analyse the properties of the Lyman alpha emission line, such as the equivalent width (EW) distribution, the asymmetry and width of the line as well as the double peak fraction. I challenge the common method of displaying EW distributions as histograms without taking the limits of the survey into account and construct a more independent EW distribution function that better reflects the properties of the underlying population of galaxies. I illustrate this by comparing the fraction of high EW objects between the two surveys MUSE-Wide and MUSE-Deep, both consisting of MUSE pointings (each with the size of one square arcminute) of different depths. In the 60 MUSE-Wide fields of one hour exposure time I find a fraction of objects with extreme EWs above EW_0>240A of ~20%, while in the MUSE-Deep fields (9 fields with an exposure time of 10 hours and one with an exposure time of 31 hours) I find a fraction of only ~1%, which is due to the differences in the limiting line flux of the surveys. The highest EW I measure is EW_0 = 600.63 +- 110A, which hints at an unusual underlying stellar population, possibly with a very low metallicity.
With the knowledge of the redshifts and positions of the LAEs detected in the MUSE-Wide survey, I also look for Lyman continuum emission coming from these galaxies and analyse the connection between Lyman continuum emission and Lyman alpha emission. I use ancillary Hubble Space Telescope (HST) broadband photometry in the bands that contain the Lyman continuum and find six Lyman continuum leaker candidates. To test whether the Lyman continuum emission of LAEs is coming only from those individual objects or the whole population, I select LAEs that are most promising for the detection of Lyman continuum emission, based on their rest-frame UV continuum and Lyman alpha line shape properties. After this selection, I stack the broadband data of the resulting sample and detect a signal in Lyman continuum with a significance of S/N = 5.5, pointing towards a Lyman continuum escape fraction of ~80%. If the signal is reliable, it strongly favours LAEs as the providers of the hydrogen ionising emission at the epoch of reionisation and beyond.
Most of the baryonic matter in the Universe resides in a diffuse gaseous phase in-between galaxies consisting mostly of hydrogen and helium. This intergalactic medium (IGM) is distributed in large-scale filaments as part of the overall cosmic web. The luminous extragalactic objects that we can observe today, such as galaxies and quasars, are surrounded by the IGM in the most dense regions within the cosmic web. The radiation of these objects contributes to the so-called ultraviolet background (UVB) which keeps the IGM highly ionized ever since the epoch of reionization.
Measuring the amount of absorption due to intergalactic neutral hydrogen (HI) against extragalactic background sources is a very useful tool to constrain the energy input of ionizing sources into the IGM. Observations suggest that the HI Lyman-alpha effective optical depth, τ_eff, decreases with decreasing redshift, which is primarily due to the expansion of the Universe. However, some studies find a smaller value of the effective optical depth than expected at the specific redshift z~3.2, possibly related to the complete reionization of helium in the IGM and a hardening of the UVB. The detection and possible cause of a decrease in τ_eff at z~3.2 is controversially debated in the literature and the observed features need further explanation.
To better understand the properties of the mean absorption at high redshift and to provide an answer for whether the detection of a τ_eff feature is real we study 13 high-resolution, high signal-to-noise ratio quasar spectra observed with the Ultraviolet and Visual Echelle Spectrograph (UVES) at the Very Large Telescope (VLT). The redshift evolution of the effective optical depth, τ_eff(z), is measured in the redshift range 2.7≤z≤3.6. The influence of metal absorption features is removed by performing a comprehensive absorption-line-fitting procedure.
In the first part of the thesis, a line-parameter analysis of the column density, N, and Doppler parameter, b, of ≈7500 individually fitted absorption lines is performed. The results are in good agreement with findings from previous surveys.
The second (main) part of this thesis deals with the analysis of the redshift evolution of the effective optical depth. The τ_eff measurements vary around the empirical power law τ_eff(z)~(1+z)^(γ+1) with γ=2.09±0.52. The same analysis as for the observed spectra is performed on synthetic absorption spectra. From a comparison between observed and synthetic spectral data it can be inferred that the uncertainties of the τ_eff values are likely underestimated and that the scatter is probably caused by high-column-density absorbers with column densities in the range 15≤logN≤17. In the real Universe, such absorbers are rarely observed, however. Hence, the difference in τ_eff from different observational data sets and absorption studies is most likely caused by cosmic variance. If, alternatively, the disagreement between such data is a result of an too optimistic estimate of the (systematic) errors, it is also possible that all τ_eff measurements agree with a smooth evolution within the investigated redshift range. To explore in detail the different analysis techniques of previous studies an extensive literature comparison to the results of this work is presented in this thesis.
Although a final explanation for the occurrence of the τ_eff deviation in different studies at z~3.2 cannot be given here, our study, which represents the most detailed line-fitting analysis of its kind performed at the investigated redshifts so far, represents another important benchmark for the characterization of the HI Ly-alpha effective optical depth at high redshift and its indicated unusual behavior at z~3.2.
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.
The High Energy Stereoscopic System (H.E.S.S.) is an array of five imaging atmospheric Cherenkov telescopes located in the Khomas Highland of Namibia. H.E.S.S. operates in a wide energy range from several tens of GeV to several tens of TeV, reaching the best sensitivity around 1 TeV or at lower energies. However, there are many important topics – such as the search for Galactic PeVatrons, the study of gamma-ray production scenarios for sources (hadronic vs. leptonic), EBL absorption studies – which require good sensitivity at energies above 10 TeV. This work aims at improving the sensitivity of H.E.S.S. and increasing the gamma-ray statistics at high energies. The study investigates an enlargement of the H.E.S.S. effective field of view using events with larger offset angles in the analysis. The greatest challenges in the analysis of large-offset events are a degradation of the reconstruction accuracy and a rise of the background rate as the offset angle increases. The more sophisticated direction reconstruction method (DISP) and improvements to the standard background rejection technique, which by themselves are effective ways to increase the gamma-ray statistics and improve the sensitivity of the analysis, are implemented to overcome the above-mentioned issues. As a result, the angular resolution at the preselection level is improved by 5 - 10% for events at 0.5◦ offset angle and by 20 - 30% for events at 2◦ offset angle. The background rate at large offset angles is decreased nearly to a level typical for offset angles below 2.5◦. Thereby, sensitivity improvements of 10 - 20% are achieved for the proposed analysis compared to the standard analysis at small offset angles. Developed analysis also allows for the usage of events at large offset angles up to approximately 4◦, which was not possible before. This analysis method is applied to the analysis of the Galactic plane data above 10 TeV. As a result, 40 sources out of the 78 presented in the H.E.S.S. Galactic plane survey (HGPS) are detected above 10 TeV. Among them are representatives of all source classes that are present in the HGPS catalogue; namely, binary systems, supernova remnants, pulsar wind nebulae and composite objects. The potential of the improved analysis method is demonstrated by investigating the more than 10 TeV emission for two objects: the region associated with the shell-type SNR HESS J1731−347 and the PWN candidate associated with PSR J0855−4644 that is coincident with Vela Junior (HESS J0852−463).
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.
The contribution of the warm-hot intergalactic medium to the CMB anisotropies and distortions
(2013)
The majority of baryons in the Universe is believed to reside in the intergalactic medium (IGM). This makes the IGM an important component in understanding cosmological structure formation. It is expected to trace the same dark matter distribution as galaxies, forming structures like filaments and clusters. However, whereas galaxies can be observed to be arranged along these large-scale structures, the spatial distribution of the diffuse IGM is not as easily unveiled. Absorption line studies of quasar (QSO) spectra can help with mapping the IGM, as well as the boundary layer between IGM and galaxies: the circumgalactic medium (CGM). By studying gas in the Local Group, as well as in the IGM, this study aims to get a better understanding of how the gas is linked to the large-scale structure of the local Universe and the galaxies residing in that structure.
Chapter 1 gives an introduction to the CGM and IGM, while the methods used in this study are explained in Chapter 2. Chapter 3 starts on a relatively small cosmological scale, namely that of our Local Group, which includes i.a. the Milky Way (MW) and the M31. Within the CGM of the MW, there exist denser clouds, some of which are infalling while others are moving away from the Galactic disc. To study these clouds, 29 QSO spectra obtained with the Cosmic Origins Spectrograph (COS) aboard the Hubble Space Telescope (HST) were analysed. Abundances of Si II, Si III, Si IV, C II, and C IV were measured for 69 HVCs belonging to two samples: one in the direction of the LG’s barycentre and the other in the anti-barycentre direction. Their velocities range from -100 ≥ vLSR ≥ -400 km/s for the barycentre sample and between +100 ≤ vLSR ≤ +300 km/s for the anti-barycentre sample. By using Cloudy models, these data could then be used to derive gas volume densities for the HVCs. Because of the relationship between density and pressure of the ambient medium, which is in turn determined by the Galactic radiation field, the distances of the HVCs could be estimated. From this, a subsample of absorbers located in the direction of M31 was found to exist outside of the MW’s virial radius, their low densities (log nH ≤ -3.54) making it likely for them to be part of the gas in between the MW and M31. No such low-density absorbers were found in the anti-barycentre sample. Our results thus hint at gas following the dark matter potential, which would be deeper between the MW and M31 as they are by far the most massive members of the LG.
From this bridge of gas in the LG, this study zooms out to the large-scale structure of the local Universe (z ~ 0) in Chapter 4. Galaxy data from the V8k catalogue and QSO spectra from COS were used to study the relation between the galaxies tracing large-scale filaments and the gas existing outside of those galaxies. This study used the filaments defined in Courtois et al. (2013). A total of 587 Lyman α (Lyα) absorbers were found in the 302 QSO spectra in the velocity range 1070 - 6700 km/s. After selecting sightlines passing through or close to these filaments, model spectra were made for 91 sightlines and 215 (227) Lyα absorbers (components) were measured in this sample. The velocity gradient along each filament was calculated and 74 absorbers were found within 1000 km/s of the nearest filament segment.
In order to find whether the absorbers are more tied to galaxies or to the large-scale structure, equivalent widths of the Lyα absorbers were plotted against both galaxy and filament impact parameters. While stronger absorbers do tend to be closer to either galaxies or filaments, there is a large scatter in this relation. Despite this large scatter, this study found that the absorbers do not follow a random distribution either. They cluster less strongly around filaments than galaxies, but stronger than random distributions, as confirmed by a Kolmogorov-Smirnov test.
Furthermore, the column density distribution function found in this study has a slope of -β = 1.63±0.12 for the total sample and -β =1.47±0.24 for the absorbers within 1000 km/s of a filament. The shallower slope for the latter subsample could indicate an excess of denser absorbers within the filament, but they are consistent within errors. These values are in agreement with values found in e.g. Lehner et al. (2007); Danforth et al. (2016).
The picture that emerges from this study regarding the relation between the IGM and the large-scale structure in the local Universe fits with what is found in other studies: while at least part of the gas traces the same filamentary structure as galaxies, the relation is complex. This study has shown that by taking a large sample of sightlines and comparing the data gathered from those with galaxy data, it is possible to study the gaseous large-scale structure. This approach can be used in the future together with simulations to get a better understanding of structure formation and evolution in the Universe.
Active Galactic Nuclei (AGN) are powered by gas accretion onto supermassive Black Holes (BH). The luminosity of AGN can exceed the integrated luminosity of their host galaxies by orders of magnitude, which are then classified as Quasi-Stellar Objects (QSOs). Some mechanisms are needed to trigger the nuclear activity in galaxies and to feed the nuclei with gas. Among several possibilities, such as gravitational interactions, bar instabilities, and smooth gas accretion from the environment, the dominant process has yet to be identified. Feedback from AGN may be important an important ingredient of the evolution of galaxies. However, the details of this coupling between AGN and their host galaxies remain unclear. In this work we aim to investigate the connection between the AGN and their host galaxies by studying the properties of the extendend ionised gas around AGN. Our study is based on observations of ~50 luminous, low-redshift (z<0.3) QSOs using the novel technique of integral field spectroscopy that combines imaging and spectroscopy. After spatially separating the emission of AGN-ionised gas from HII regions, ionised solely by recently formed massive stars, we demonstrate that the specific star formation rates in several disc-dominated AGN hosts are consistent with those of normal star forming galaxies, while others display no detectable star formation activity. Whether the star formation has been actively suppressed in those particular host galaxies by the AGN, or their gas content is intrinsically low, remains an open question. By studying the kinematics of the ionised gas, we find evidence for non-gravitational motions and outflows on kpc scales only in a few objects. The gas kinematics in the majority of objects however indicate a gravitational origin. It suggests that the importance of AGN feedback may have been overrated in theoretical works, at least at low redshifts. The [OIII] line is the strongest optical emission line for AGN-ionised gas, which can be extended over several kpc scales, usually called the Narrow-Line Region (NLR). We perform a systematic investigation of the NLR size and determine a NLR size-luminosity relation that is consistent with the scenario of a constant ionisation parameter throughout the NLR. We show that previous narrow-band imaging with the Hubble Space Telescope underestimated the NLR size by a factor of >2 and that the continuum AGN luminosity is better correlated with the NLR size than the [OIII] luminosity. These affects may account for the different NLR size-luminosity relations reported in previous studies. On the other hand, we do not detect extended NLRs around all QSOs, and demonstrate that the detection of extended NLRs goes along with radio emission. We employ emission line ratios as a diagnostic for the abundance of heavy elements in the gas, i.e. its metallicity, and find that the radial metallicity gradients are always flatter than in inactive disc-dominated galaxies. This can be interpreted as evidence for radial gas flows from the outskirts of these galaxies to the nucleus. Recent or ongoing galaxy interactions are likely responsible for this effect and may turn out to be a common prerequisite for QSO activity. The metallicity of bulge-dominated hosts are systematically lower than their disc-dominated counterparts, which we interpret as evidence for minor mergers, supported by our detailed study of the bulge-dominated host of the luminous QSO HE 1029-1401, or smooth gas accretion from the environment. In this line another new discovery is that HE 2158-0107 at z=0.218 is the most metal poor luminous QSO ever observed. Together with a large (30kpc) extended structure of low metallicity ionised gas, we propose smooth cold gas accretion as the most likely scenario. Theoretical studies suggested that this process is much more important at earlier epochs of the universe, so that HE 2158-0107 might be an ideal laboratory to study this mechanism of galaxy and BH growth at low redshift more detailed in the furture.
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.
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.
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].
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.
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.
Synchrotron-based angle-resolved time-of-flight electron spectroscopy for dynamics in dichalogenides
(2018)
<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.
Subject of this work is the investigation of generic synchronization phenomena in interacting complex systems. These phenomena are observed, among all, in coupled deterministic chaotic systems. At very weak interactions between individual systems a transition to a weakly coherent behavior of the systems can take place. In coupled continuous time chaotic systems this transition manifests itself with the effect of phase synchronization, in coupled chaotic discrete time systems with the effect of non-vanishing macroscopic mean field. Transition to coherence in a chain of locally coupled oscillators described with phase equations is investigated with respect to the symmetries in the system. It is shown that the reversibility of the system caused by these symmetries results to non-trivial topological properties of trajectories so that the system constructed to be dissipative reveals in a whole parameter range quasi-Hamiltonian features, i.e. the phase volume is conserved on average and Lyapunov exponents come in symmetric pairs. Transition to coherence in an ensemble of globally coupled chaotic maps is described with the loss of stability of the disordered state. The method is to break the self-consistensy of the macroscopic field and to characterize the ensemble in analogy to an amplifier circuit with feedback with a complex linear transfer function. This theory is then generalized for several cases of theoretic interest.
Synchronization of large ensembles of oscillators is an omnipresent phenomenon observed in different fields of science like physics, engineering, life sciences, etc. The most simple setup is that of globally coupled phase oscillators, where all the oscillators contribute to a global field which acts on all oscillators. This formulation of the problem was pioneered by Winfree and Kuramoto. Such a setup gives a possibility for the analysis of these systems in terms of global variables. In this work we describe nontrivial collective dynamics in oscillator populations coupled via mean fields in terms of global variables. We consider problems which cannot be directly reduced to standard Kuramoto and Winfree models.
In the first part of the thesis we adopt a method introduced by Watanabe and Strogatz. The main idea is that the system of identical oscillators of particular type can be described by a low-dimensional system of global equations. This approach enables us to perform a complete analytical analysis for a special but vast set of initial conditions. Furthermore, we show how the approach can be expanded for some nonidentical systems. We apply the Watanabe-Strogatz approach to arrays of Josephson junctions and systems of identical phase oscillators with leader-type coupling.
In the next parts of the thesis we consider the self-consistent mean-field theory method that can be applied to general nonidentical globally coupled systems of oscillators both with or without noise. For considered systems a regime, where the global field rotates uniformly, is the most important one. With the help of this approach such solutions of the self-consistency equation for an arbitrary distribution of frequencies and coupling parameters can be found analytically in the parametric form, both for noise-free and noisy cases.
We apply this method to deterministic Kuramoto-type model with generic coupling and an ensemble of spatially distributed oscillators with leader-type coupling. Furthermore, with the proposed self-consistent approach we fully characterize rotating wave solutions of noisy Kuramoto-type model with generic coupling and an ensemble of noisy oscillators with bi-harmonic coupling.
Whenever possible, a complete analysis of global dynamics is performed and compared with direct numerical simulations of large populations.
Oscillatory systems under weak coupling can be described by the Kuramoto model of phase oscillators. Kuramoto phase oscillators have diverse applications ranging from phenomena such as communication between neurons and collective influences of political opinions, to engineered systems such as Josephson Junctions and synchronized electric power grids. This thesis includes the author's contribution to the theoretical framework of coupled Kuramoto oscillators and to the understanding of non-trivial N-body dynamical systems via their reduced mean-field dynamics.
The main content of this thesis is composed of four parts. First, a partially integrable theory of globally coupled identical Kuramoto oscillators is extended to include pure higher-mode coupling. The extended theory is then applied to a non-trivial higher-mode coupled model, which has been found to exhibit asymmetric clustering. Using the developed theory, we could predict a number of features of the asymmetric clustering with only information of the initial state provided.
The second part consists of an iterated discrete-map approach to simulate phase dynamics. The proposed map --- a Moebius map --- not only provides fast computation of phase synchronization, it also precisely reflects the underlying group structure of the dynamics. We then compare the iterated-map dynamics and various analogous continuous-time dynamics. We are able to replicate known phenomena such as the synchronization transition of the Kuramoto-Sakaguchi model of oscillators with distributed natural frequencies, and chimera states for identical oscillators under non-local coupling.
The third part entails a particular model of repulsively coupled identical Kuramoto-Sakaguchi oscillators under common random forcing, which can be shown to be partially integrable. Via both numerical simulations and theoretical analysis, we determine that such a model cannot exhibit stationary multi-cluster states, contrary to the numerical findings in previous literature. Through further investigation, we find that the multi-clustering states reported previously occur due to the accumulation of discretization errors inherent in the integration algorithms, which introduce higher-mode couplings into the model. As a result, the partial integrability condition is violated.
Lastly, we derive the microscopic cross-correlation of globally coupled non-identical Kuramoto oscillators under common fluctuating forcing. The effect of correlation arises naturally in finite populations, due to the non-trivial fluctuations of the meanfield. In an idealized model, we approximate the finite-sized fluctuation by a Gaussian white noise. The analytical approximation qualitatively matches the measurements in numerical experiments, however, due to other periodic components inherent in the fluctuations of the mean-field there still exist significant inconsistencies.
This thesis analyses synchronization phenomena occurring in large ensembles of interacting oscillatory units. In particular, the effects of nonisochronicity (frequency dependence on the oscillator's amplitude) on the macroscopic transition to synchronization are studied in detail. The new phenomena found (Anomalous Synchronization) are investigated in populations of oscillators as well as between oscillator's ensembles.
In the present work synchronization phenomena in complex dynamical systems exhibiting multiple time scales have been analyzed. Multiple time scales can be active in different manners. Three different systems have been analyzed with different methods from data analysis. The first system studied is a large heterogenous network of bursting neurons, that is a system with two predominant time scales, the fast firing of action potentials (spikes) and the burst of repetitive spikes followed by a quiescent phase. This system has been integrated numerically and analyzed with methods based on recurrence in phase space. An interesting result are the different transitions to synchrony found in the two distinct time scales. Moreover, an anomalous synchronization effect can be observed in the fast time scale, i.e. there is range of the coupling strength where desynchronization occurs. The second system analyzed, numerically as well as experimentally, is a pair of coupled CO₂ lasers in a chaotic bursting regime. This system is interesting due to its similarity with epidemic models. We explain the bursts by different time scales generated from unstable periodic orbits embedded in the chaotic attractor and perform a synchronization analysis of these different orbits utilizing the continuous wavelet transform. We find a diverse route to synchrony of these different observed time scales. The last system studied is a small network motif of limit cycle oscillators. Precisely, we have studied a hub motif, which serves as elementary building block for scale-free networks, a type of network found in many real world applications. These hubs are of special importance for communication and information transfer in complex networks. Here, a detailed study on the mechanism of synchronization in oscillatory networks with a broad frequency distribution has been carried out. In particular, we find a remote synchronization of nodes in the network which are not directly coupled. We also explain the responsible mechanism and its limitations and constraints. Further we derive an analytic expression for it and show that information transmission in pure phase oscillators, such as the Kuramoto type, is limited. In addition to the numerical and analytic analysis an experiment consisting of electrical circuits has been designed. The obtained results confirm the former findings.
In nature one commonly finds interacting complex oscillators which by the coupling scheme form small and large networks, e.g. neural networks. Surprisingly, the oscillators can synchronize, still preserving the complex behavior. Synchronization is a fundamental phenomenon in coupled nonlinear oscillators. Synchronization can be enhanced at different levels, that is, the constraints on which the synchronization appears. Those can be in the trajectory amplitude, requiring the amplitudes of both oscillators to be equal, giving place to complete synchronization. Conversely, the constraint could also be in a function of the trajectory, e.g. the phase, giving place to phase synchronization (PS). In this case, one requires the phase difference between both oscillators to be finite for all times, while the trajectory amplitude may be uncorrelated. The study of PS has shown its relevance to important technological problems, e.g. communication, collective behavior in neural networks, pattern formation, Parkinson disease, epilepsy, as well as behavioral activities. It has been reported that it mediates processes of information transmission and collective behavior in neural and active networks and communication processes in the Human brain. In this work, we have pursed a general way to analyze the onset of PS in small and large networks. Firstly, we have analyzed many phase coordinates for compact attractors. We have shown that for a broad class of attractors the PS phenomenon is invariant under the phase definition. Our method enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether this set of points is localized. We have show that this approach is fruitful to analyze the onset of phase synchronization in chaotic attractors whose phases are not well defined, as well as, in networks of non-identical spiking/bursting neurons connected by chemical synapses. Moreover, we have also related the synchronization and the information transmission through the conditional observations. In particular, we have found that inside a network clusters may appear. These can be used to transmit more than one information, which provides a multi-processing of information. Furthermore, These clusters provide a multichannel communication, that is, one can integrate a large number of neurons into a single communication system, and information can arrive simultaneously at different places of the network.
This work deals with the connection between two basic phenomena in Nonlinear Dynamics: synchronization of chaotic systems and recurrences in phase space. Synchronization takes place when two or more systems adapt (synchronize) some characteristic of their respective motions, due to an interaction between the systems or to a common external forcing. The appearence of synchronized dynamics in chaotic systems is rather universal but not trivial. In some sense, the possibility that two chaotic systems synchronize is counterintuitive: chaotic systems are characterized by the sensitivity ti different initial conditions. Hence, two identical chaotic systems starting at two slightly different initial conditions evolve in a different manner, and after a certain time, they become uncorrelated. Therefore, at a first glance, it does not seem to be plausible that two chaotic systems are able to synchronize. But as we will see later, synchronization of chaotic systems has been demonstrated. On one hand it is important to investigate the conditions under which synchronization of chaotic systems occurs, and on the other hand, to develop tests for the detection of synchronization. In this work, I have concentrated on the second task for the cases of phase synchronization (PS) and generalized synchronization (GS). Several measures have been proposed so far for the detection of PS and GS. However, difficulties arise with the detection of synchronization in systems subjected to rather large amounts of noise and/or instationarities, which are common when analyzing experimental data. The new measures proposed in the course of this thesis are rather robust with respect to these effects. They hence allow to be applied to data, which have evaded synchronization analysis so far. The proposed tests for synchronization in this work are based on the fundamental property of recurrences in phase space.
In the present work, we use symbolic regression for automated modeling of dynamical systems. Symbolic regression is a powerful and general method suitable for data-driven identification of mathematical expressions. In particular, the structure and parameters of those expressions are identified simultaneously.
We consider two main variants of symbolic regression: sparse regression-based and genetic programming-based symbolic regression. Both are applied to identification, prediction and control of dynamical systems.
We introduce a new methodology for the data-driven identification of nonlinear dynamics for systems undergoing abrupt changes. Building on a sparse regression algorithm derived earlier, the model after the change is defined as a minimum update with respect to a reference model of the system identified prior to the change. The technique is successfully exemplified on the chaotic Lorenz system and the van der Pol oscillator. Issues such as computational complexity, robustness against noise and requirements with respect to data volume are investigated.
We show how symbolic regression can be used for time series prediction. Again, issues such as robustness against noise and convergence rate are investigated us- ing the harmonic oscillator as a toy problem. In combination with embedding, we demonstrate the prediction of a propagating front in coupled FitzHugh-Nagumo oscillators. Additionally, we show how we can enhance numerical weather predictions to commercially forecast power production of green energy power plants.
We employ symbolic regression for synchronization control in coupled van der Pol oscillators. Different coupling topologies are investigated. We address issues such as plausibility and stability of the control laws found. The toolkit has been made open source and is used in turbulence control applications.
Genetic programming based symbolic regression is very versatile and can be adapted to many optimization problems. The heuristic-based algorithm allows for cost efficient optimization of complex tasks.
We emphasize the ability of symbolic regression to yield white-box models. In contrast to black-box models, such models are accessible and interpretable which allows the usage of established tool chains.
This thesis is focused on a better understanding of the formation mechanism of bulk birefringence gratings (BBG) and a surface relief gratings (SRG) in photo-sensitive polymer films. A new set-up is developed enabling the in situ investigation how the polymer film is being structured during irradiation with modulated light. The new aspect of the equipment is that it combines several techniques such as a diffraction efficiency (DE) set-up, an atomic force microscope (AFM) and an optical set-up for controlled illumination of the sample. This enables the simultaneous acquiring and differentiation of both gratings (BBG and SRG), while changing the irradiation conditions in desired way.
The dissertation is based on five publications. The first publication (I) is focused on the description of the set-up and interpretation of the measured data. A fine structure within the 1st-order diffraction spot is observed, which is a result of the inhomogeneity of the inscribed gratings.
In the second publication (II) the interplay of BBG and SRG in the DE is discussed. It has been found, that, dependent on the polarization of a weak probe beam, the diffraction components of the SRG and BBG either interfere constructively or destructively in the DE, altering the appearance of the intensity distribution within the diffracted spot.
The third (III) and fourth (IV) publications describe the light-induced reconfiguration of surface structures. Special attention is payed to conditions influencing the erasure of topography and bulk gratings. This can be achieved via thermal treatment or illumination of the polymer film. Using the translation of the interference pattern (IP) in a controlled way, the optical erase speed is significantly increased. Additionally, a dynamic reconfigurable surface is generated, which could move surface attached objects by the continuous translation of the interference pattern during irradiation of the polymer films.
The fifth publication (V) deals with the understanding of polymer deformation under irradiation with SP-IP, which is the only IP generating a half-period topography grating (compared to the period of the IP) on the photo-sensitive polymer film. This mechanism is used, e.g. to generate a SRG below the diffraction limit of light. It also represents an easy way of changing the period of the surface grating just by a small change in polarization angle of the interfering beams without adjusting the optical pass of the two beams. Additionally, complex surface gratings formed in mixed polarization- and intensity interference patterns are shown.
I J. Jelken, C. Henkel and S. Santer, Applied Physics B, 125 (2019), 218
II J. Jelken, C. Henkel and S. Santer, Appl. Phys. Lett., 116 (2020), 051601
III J. Jelken and S. Santer, RSC Advances, 9 (2019), 20295
IV J. Jelken, M. Brinkjans, C. Henkel and S. Santer, SPIE Proceedings, 11367 (2020), 1136710
V J. Jelken, C. Henkel and S. Santer, Formation of Half-Period Surface Relief Gratings in Azobenzene Containing Polymer Films (submitted to Applied Physics B)
Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100Myr. The self-consistent numerical verification of such a “fast dynamo” is highly beneficial in explaining the observed strong magnetic fields in young galaxies. We, furthermore, highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field. This finding impressively confirms the classical picture of a dynamo based on cyclonic turbulence.
The mammalian brain is, with its numerous neural elements and structured complex connectivity, one of the most complex systems in nature. Recently, large-scale corticocortical connectivities, both structural and functional, have received a great deal of research attention, especially using the approach of complex networks. Here, we try to shed some light on the relationship between structural and functional connectivities by studying synchronization dynamics in a realistic anatomical network of cat cortical connectivity. We model the cortical areas by a subnetwork of interacting excitable neurons (multilevel model) and by a neural mass model (population model). With weak couplings, the multilevel model displays biologically plausible dynamics and the synchronization patterns reveal a hierarchical cluster organization in the network structure. We can identify a group of brain areas involved in multifunctional tasks by comparing the dynamical clusters to the topological communities of the network. With strong couplings of multilevel model and by using neural mass model, the dynamics are characterized by well-defined oscillations. The synchronization patterns are mainly determined by the node intensity (total input strengths of a node); the detailed network topology is of secondary importance. The biologically improved multilevel model exhibits similar dynamical patterns in the two regimes. Thus, the study of synchronization in a multilevel complex network model of cortex can provide insights into the relationship between network topology and functional organization of complex brain networks.