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In the last century, several astronomical measurements have supported that a significant percentage (about 22%) of the total mass of the Universe, on galactic and extragalactic scales, is composed of a mysterious ”dark” matter (DM). DM does not interact with the electromagnetic force; in other words it does not reflect, absorb or emit light. It is possible that DM particles are weakly interacting massive particles (WIMPs) that can annihilate (or decay) into Standard Model (SM) particles, and modern very- high-energy (VHE; > 100 GeV) instruments such as imaging atmospheric Cherenkov telescopes (IACTs) can play an important role in constraining the main properties of such DM particles, by detecting these products. One of the most privileged targets where to look for DM signal are dwarf spheroidal galaxies (dSphs), as they are expected to be high DM-dominated objects with a clean, gas-free environment. Some dSphs could be considered as extended sources, considering the angular resolution of IACTs; their angu- lar resolution is adequate to detect extended emission from dSphs. For this reason, we performed an extended-source analysis, by taking into account in the unbinned maximum likelihood estimation both the energy and the angular extension dependency of observed events. The goal was to set more constrained upper limits on the velocity-averaged cross-section annihilation of WIMPs with VERITAS data. VERITAS is an array of four IACTs, able to detect γ-ray photons ranging between 100 GeV and 30 TeV. The results of this extended analysis were compared against the traditional spectral analysis. We found that a 2D analysis may lead to more constrained results, depending on the DM mass, channel, and source. Moreover, in this thesis, the results of a multi-instrument project are presented too. Its goal was to combine already published 20 dSphs data from five different experiments, such as Fermi-LAT, MAGIC, H.E.S.S., VERITAS and HAWC, in order to set upper limits on the WIMP annihilation cross-section in the widest mass range ever reported.
Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.
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.
Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.
Pulsar wind nebulae (PWNe) are the most abundant TeV gamma-ray emitters in the Milky Way. The radiative emission of these objects is powered by fast-rotating pulsars, which donate parts of their rotational energy into winds of relativistic particles. This thesis presents an in-depth study of the detected population of PWNe at high energies. To outline general trends regarding their evolutionary behaviour, a time-dependent model is introduced and compared to the available data. In particular, this work presents two exceptional PWNe which protrude from the rest of the population, namely the Crab Nebula and N 157B. Both objects are driven by pulsars with extremely high rotational energy loss rates. Accordingly, they are often referred to as energetic twins. Modelling the non-thermal multi-wavelength emission of N157B gives access to specific properties of this object, like the magnetic field inside the nebula. Comparing the derived parameters to those of the Crab Nebula reveals large intrinsic differences between the two PWNe. Possible origins of these differences are discussed in context of the resembling pulsars.
Compared to the TeV gamma-ray regime, the number of detected PWNe is much smaller in the MeV-GeV gamma-ray range. In the latter range, the Crab Nebula stands out by the recent detection of gamma-ray flares. In general, the measured flux enhancements on short time scales of days to weeks were not expected in the theoretical understanding of PWNe. In this thesis, the variability of the Crab Nebula is analysed using data from the Fermi Large Area Telescope (Fermi-LAT). For the presented analysis, a new gamma-ray reconstruction method is used, providing a higher sensitivity and a lower energy threshold compared to previous analyses. The derived gamma-ray light curve of the Crab Nebula is investigated for flares and periodicity. The detected flares are analysed regarding their energy spectra, and their variety and commonalities are discussed. In addition, a dedicated analysis of the flare which occurred in March 2013 is performed. The derived short-term variability time scale is roughly 6h, implying a small region inside the Crab Nebula to be responsible for the enigmatic flares. The most promising theories explaining the origins of the flux eruptions and gamma-ray variability are discussed in detail.
In the technical part of this work, a new analysis framework is presented. The introduced software, called gammalib/ctools, is currently being developed for the future CTA observa- tory. The analysis framework is extensively tested using data from the H. E. S. S. experiment. To conduct proper data analysis in the likelihood framework of gammalib/ctools, a model describing the distribution of background events in H.E.S.S. data is presented. The software provides the infrastructure to combine data from several instruments in one analysis. To study the gamma-ray emitting PWN population, data from Fermi-LAT and H. E. S. S. are combined in the likelihood framework of gammalib/ctools. In particular, the spectral peak, which usually lies in the overlap energy regime between these two instruments, is determined with the presented analysis framework. The derived measurements are compared to the predictions from the time-dependent model. The combined analysis supports the conclusion of a diverse population of gamma-ray emitting PWNe.
In the presented thesis, the most advanced photon reconstruction technique of ground-based γ-ray astronomy is adapted to the H.E.S.S. 28 m telescope. The method is based on a semi-analytical model of electromagnetic particle showers in the atmosphere. The properties of cosmic γ-rays are reconstructed by comparing the camera image of the telescope with the Cherenkov emission that is expected from the shower model. To suppress the dominant background from charged cosmic rays, events are selected based on several criteria. The performance of the analysis is evaluated with simulated events. The method is then applied to two sources that are known to emit γ-rays. The first of these is the Crab Nebula, the standard candle of ground-based γ-ray astronomy. The results of this source confirm the expected performance of the reconstruction method, where the much lower energy threshold compared to H.E.S.S. I is of particular importance. A second analysis is performed on the region around the Galactic Centre. The analysis results emphasise the capabilities of the new telescope to measure γ-rays in an energy range that is interesting for both theoretical and experimental astrophysics. The presented analysis features the lowest energy threshold that has ever been reached in ground-based γ-ray astronomy, opening a new window to the precise measurement of the physical properties of time-variable sources at energies of several tens of GeV.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
Phase Space Reconstruction is a method that allows to reconstruct the phase space of a system using only an one dimensional time series as input. It can be used for calculating Lyapunov-exponents and detecting chaos. It helps to understand complex dynamics and their behavior. And it can reproduce datasets which were not measured. There are many different methods which produce correct reconstructions such as time-delay, Hilbert-transformation, derivation and integration. The most used one is time-delay but all methods have special properties which are useful in different situations. Hence, every reconstruction method has some situations where it is the best choice. Looking at all these different methods the questions are: Why can all these different looking methods be used for the same purpose? Is there any connection between all these functions? The answer is found in the frequency domain : Performing a Fourier transformation all these methods getting a similar shape: Every presented reconstruction method can be described as a multiplication in the frequency domain with a frequency-depending reconstruction function. This structure is also known as a filter. From this point of view every reconstructed dimension can be seen as a filtered version of the measured time series. It contains the original data but applies just a new focus: Some parts are amplified and other parts are reduced. Furthermore I show, that not every function can be used for reconstruction. In the thesis three characteristics are identified, which are mandatory for the reconstruction function. Under consideration of these restrictions one gets a whole bunch of new reconstruction functions. So it is possible to reduce noise within the reconstruction process itself or to use some advantages of already known reconstructions methods while suppressing unwanted characteristics of it.
During an unusually massive filament eruption on 7 June 2011, SDO/AIA imaged for the first time significant EUV emission around a magnetic reconnection region in the solar corona. The reconnection occurred between magnetic fields of the laterally expanding CME and a neighbouring active region. A pre-existing quasi-separatrix layer was activated in the process. This scenario is supported by data-constrained numerical simulations of the eruption. Observations show that dense cool filament plasma was re-directed and heated in situ, producing coronal-temperature emission around the reconnection region. These results provide the first direct observational evidence, supported by MHD simulations and magnetic modelling, that a large-scale re-configuration of the coronal magnetic field takes place during solar eruptions via the process of magnetic reconnection.
Understanding hydrological processes is of fundamental importance for the Vietnamese national food security and the livelihood of the population in the Vietnamese Mekong Delta (VMD). As a consequence of sparse data in this region, however, hydrologic processes, such as the controlling processes of precipitation, the interaction between surface and groundwater, and groundwater dynamics, have not been thoroughly studied. The lack of this knowledge may negatively impact the long-term strategic planning for sustainable groundwater resources management and may result in insufficient groundwater recharge and freshwater scarcity. It is essential to develop useful methods for a better understanding of hydrological processes in such data-sparse regions. The goal of this dissertation is to advance methodologies that can improve the understanding of fundamental hydrological processes in the VMD, based on the analyses of stable water isotopes and monitoring data. The thesis mainly focuses on the controlling processes of precipitation, the mechanism of surface–groundwater interaction, and the groundwater dynamics. These processes have not been fully addressed in the VMD so far. The thesis is based on statistical analyses of the isotopic data of Global Network of Isotopes in Precipitation (GNIP), of meteorological and hydrological data from Vietnamese agencies, and of the stable water isotopes and monitoring data collected as part of this work.
First, the controlling processes of precipitation were quantified by the combination of trajectory analysis, multi-factor linear regression, and relative importance analysis (hereafter, a model‐based statistical approach). The validity of this approach is confirmed by similar, but mainly qualitative results obtained in other studies. The total variation in precipitation isotopes (δ18O and δ2H) can be better explained by multiple linear regression (up to 80%) than single-factor linear regression (30%). The relative importance analysis indicates that atmospheric moisture regimes control precipitation isotopes rather than local climatic conditions. The most crucial factor is the upstream rainfall along the trajectories of air mass movement. However, the influences of regional and local climatic factors vary in importance over the seasons. The developed model‐based statistical approach is a robust tool for the interpretation of precipitation isotopes and could also be applied to understand the controlling processes of precipitation in other regions.
Second, the concept of the two-component lumped-parameter model (LPM) in conjunction with stable water isotopes was applied to examine the surface–groundwater interaction in the VMD. A calibration framework was also set up to evaluate the behaviour, parameter identifiability, and uncertainties of two-component LPMs. The modelling results provided insights on the subsurface flow conditions, the recharge contributions, and the spatial variation of groundwater transit time. The subsurface flow conditions at the study site can be best represented by the linear-piston flow distribution. The contributions of the recharge sources change with distance to the river. The mean transit time (mTT) of riverbank infiltration increases with the length of the horizontal flow path and the decreasing gradient between river and groundwater. River water infiltrates horizontally mainly via the highly permeable aquifer, resulting in short mTTs (<40 weeks) for locations close to the river (<200 m). The vertical infiltration from precipitation takes place primarily via a low‐permeable overlying aquitard, resulting in considerably longer mTTs (>80 weeks). Notably, the transit time of precipitation infiltration is independent of the distance to the river. All these results are hydrologically plausible and could be quantified by the presented method for the first time. This study indicates that the highly complex mechanism of surface–groundwater interaction at riverbank infiltration systems can be conceptualized by exploiting two‐component LPMs. It is illustrated that the model concept can be used as a tool to investigate the hydrological functioning of mixing processes and the flow path of multiple water components in riverbank infiltration systems.
Lastly, a suite of time series analysis approaches was applied to examine the groundwater dynamics in the VMD. The assessment was focused on the time-variant trends of groundwater levels (GWLs), the groundwater memory effect (representing the time that an aquifer holds water), and the hydraulic response between surface water and multi-layer alluvial aquifers. The analysis indicates that the aquifers act as low-pass filters to reduce the high‐frequency signals in the GWL variations, and limit the recharge to the deep groundwater. The groundwater abstraction has exceeded groundwater recharge between 1997 and 2017, leading to the decline of groundwater levels (0.01-0.55 m/year) in all considered aquifers in the VMD. The memory effect varies according to the geographical location, being shorter in shallow aquifers and flood-prone areas and longer in deep aquifers and coastal regions. Groundwater depth, season, and location primarily control the variation of the response time between the river and alluvial aquifers. These findings are important contributions to the hydrogeological literature of a little-known groundwater system in an alluvial setting. It is suggested that time series analysis can be used as an efficient tool to understand groundwater systems where resources are insufficient to develop a physical-based groundwater model.
This doctoral thesis demonstrates that important aspects of hydrological processes can be understood by statistical analysis of stable water isotope and monitoring data. The approaches developed in this thesis can be easily transferred to regions in similar tropical environments, particularly those in alluvial settings. The results of the thesis can be used as a baseline for future isotope-based studies and contribute to the hydrogeological literature of little-known groundwater systems in the VMD.