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Moving spiral wave chimeras
(2021)
We consider a two-dimensional array of heterogeneous nonlocally coupled phase oscillators on a flat torus and study the bound states of two counter-rotating spiral chimeras, shortly two-core spiral chimeras, observed in this system. In contrast to other known spiral chimeras with motionless incoherent cores, the two-core spiral chimeras typically show a drift motion. Due to this drift, their incoherent cores become spatially modulated and develop specific fingerprint patterns of varying synchrony levels. In the continuum limit of infinitely many oscillators, the two-core spiral chimeras can be studied using the Ott-Antonsen equation. Numerical analysis of this equation allows us to reveal the stability region of different spiral chimeras, which we group into three main classes-symmetric, asymmetric, and meandering spiral chimeras.
We demonstrate a tilted pulse-front transient grating (TG) technique that allows to optimally utilize time resolution as well as TG line density while probing under grazing incidence as typically done in extreme ultraviolet (EUV) or soft x-ray (SXR) experiments. Our optical setup adapts the pulse front tilt of the two pulses that create the TG to the grazing incident pulse. We demonstrate the technique using all 800 nm femtosecond laser pulses for TG generation on a vanadium dioxide film. We probe that grating via diffraction of a third 800 nm pulse. The time resolution of 90 fs is an improvement by a factor of 30 compared to our previous experiments on the same system. The scheme paves the way for EUV and SXR probing of optically induced TGs on any material.
Diffusion of finite-size particles in two-dimensional channels with random wall configurations
(2014)
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick–Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].
Diffusion of finite-size particles in two-dimensional channels with random wall configurations
(2014)
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick–Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].
We consider the behavior of spherically symmetric Einasto halos composed of gravitating particles in the Fokker-Planck approximation. This approach allows us to consider the undesirable influence of close encounters in the N-body simulations more adequately than the generally accepted criteria. The Einasto profile with index n approximate to 6 is a stationary solution of the Fokker-Planck equation in the halo center. There are some reasons to believe that the solution is an attractor. Then the Fokker-Planck diffusion tends to transform a density profile to the equilibrium one with the Einasto index n approximate to 6. We suggest this effect as a possible reason why the Einasto index n approximate to 6 occurs so frequently in the interpretation of N-body simulation results. The results obtained cast doubt on generally accepted criteria of N-body simulation convergence.
We present a survey for metal absorption systems traced by neutral oxygen over 3.2 < z < 6.5. Our survey uses Keck/ESI and VLT/X-Shooter spectra of 199 QSOs with redshifts up to 6.6. In total, we detect 74 OI absorbers, of which 57 are separated from the background QSO by more than 5000 km s(-1). We use a maximum likelihood approach to fit the distribution of OI lambda 1302 equivalent widths in bins of redshift and from this determine the evolution in number density of absorbers with W-1302 > 0.05 angstrom, of which there are 49 nonproximate systems in our sample. We find that the number density does not monotonically increase with decreasing redshift, as would naively be expected from the buildup of metal-enriched circumgalactic gas with time. The number density over 4.9 < z < 5.7 is a factor of 1.7-4.1 lower (68% confidence) than that over 5.7 < z < 6.5, with a lower value at z < 5.7 favored with 99% confidence. This decrease suggests that the fraction of metals in a low-ionization phase is larger at z similar to 6 than at lower redshifts. Absorption from highly ionized metals traced by CIV is also weaker in higher-redshift OI systems, supporting this picture. The evolution of OI absorbers implies that metal-enriched circumgalactic gas at z similar to 6 is undergoing an ionization transition driven by a strengthening ultraviolet background. This in turn suggests that the reionization of the diffuse intergalactic medium may still be ongoing at or only recently ended by this epoch.
A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.
We report on the multiple response of microgels triggered by a single optical stimulus. Under irradiation, the volume of the microgels is reversibly switched by more than 20 times. The irradiation initiates two different processes: photo-isomerization of the photo-sensitive surfactant, which forms a complex with the anionic microgel, rendering it photo-responsive; and local heating due to a thermo-plasmonic effect within the structured gold layer on which the microgel is deposited. The photo-responsivity is related to the reversible accommodation/release of the photo-sensitive surfactant depending on its photo-isomerization state, while the thermo-sensitivity is intrinsically built in. We show that under exposure to green light, the thermo-plasmonic effect generates a local hot spot in the gold layer, resulting in the shrinkage of the microgel. This process competes with the simultaneous photo-induced swelling. Depending on the position of the laser spot, the spatiotemporal control of reversible particle shrinking/swelling with a predefined extent on a per-second base can be implemented.
The angular size of a star is a critical factor in determining its basic properties1. Direct measurement of stellar angular diameters is difficult: at interstellar distances stars are generally too small to resolve by any individual imaging telescope. This fundamental limitation can be overcome by studying the diffraction pattern in the shadow cast when an asteroid occults a star2, but only when the photometric uncertainty is smaller than the noise added by atmospheric scintillation3. Atmospheric Cherenkov telescopes used for particle astrophysics observations have not generally been exploited for optical astronomy due to the modest optical quality of the mirror surface. However, their large mirror area makes them well suited for such high-time-resolution precision photometry measurements4. Here we report two occultations of stars observed by the Very Energetic Radiation Imaging Telescope Array System (VERITAS)5 Cherenkov telescopes with millisecond sampling, from which we are able to provide a direct measurement of the occulted stars’ angular diameter at the ≤0.1 mas scale. This is a resolution never achieved before with optical measurements and represents an order of magnitude improvement over the equivalent lunar occultation method6. We compare the resulting stellar radius with empirically derived estimates from temperature and brightness measurements, confirming the latter can be biased for stars with ambiguous stellar classifications.
Organic solar cells demonstrate external quantum efficiencies and fill factors approaching those of conventional photovoltaic technologies. However, as compared with the optical gap of the absorber materials, their open-circuit voltage is much lower, largely due to the presence of significant non-radiative recombination. Here, we study a large data set of published and new material combinations and find that non-radiative voltage losses decrease with increasing charge-transfer-state energies. This observation is explained by considering non-radiative charge-transfer-state decay as electron transfer in the Marcus inverted regime, being facilitated by a common skeletal molecular vibrational mode. Our results suggest an intrinsic link between non-radiative voltage losses and electron-vibration coupling, indicating that these losses are unavoidable. Accordingly, the theoretical upper limit for the power conversion efficiency of single-junction organic solar cells would be reduced to about 25.5% and the optimal optical gap increases to (1.45-1.65) eV, that is, (0.2-0.3) eV higher than for technologies with minimized non-radiative voltage losses.
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.
We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in Hollander (Isr. J. Math. 163:93-124, 2008), which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BG (con).
Cargo transport by molecular motors is ubiquitous in all eukaryotic cells and is typically driven cooperatively by several molecular motors, which may belong to one or several motor species like kinesin, dynein or myosin. These motor proteins transport cargos such as RNAs, protein complexes or organelles along filaments, from which they unbind after a finite run length. Understanding how these motors interact and how their movements are coordinated and regulated is a central and challenging problem in studies of intracellular transport. In this thesis, we describe a general theoretical framework for the analysis of such transport processes, which enables us to explain the behavior of intracellular cargos based on the transport properties of individual motors and their interactions. Motivated by recent in vitro experiments, we address two different modes of transport: unidirectional transport by two identical motors and cooperative transport by actively walking and passively diffusing motors. The case of cargo transport by two identical motors involves an elastic coupling between the motors that can reduce the motors’ velocity and/or the binding time to the filament. We show that this elastic coupling leads, in general, to four distinct transport regimes. In addition to a weak coupling regime, kinesin and dynein motors are found to exhibit a strong coupling and an enhanced unbinding regime, whereas myosin motors are predicted to attain a reduced velocity regime. All of these regimes, which we derive both by analytical calculations and by general time scale arguments, can be explored experimentally by varying the elastic coupling strength. In addition, using the time scale arguments, we explain why previous studies came to different conclusions about the effect and relevance of motor-motor interference. In this way, our theory provides a general and unifying framework for understanding the dynamical behavior of two elastically coupled molecular motors. The second mode of transport studied in this thesis is cargo transport by actively pulling and passively diffusing motors. Although these passive motors do not participate in active transport, they strongly enhance the overall cargo run length. When an active motor unbinds, the cargo is still tethered to the filament by the passive motors, giving the unbound motor the chance to rebind and continue its active walk. We develop a stochastic description for such cooperative behavior and explicitly derive the enhanced run length for a cargo transported by one actively pulling and one passively diffusing motor. We generalize our description to the case of several pulling and diffusing motors and find an exponential increase of the run length with the number of involved motors.
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.
Am Beispiel der Orgelpfeife wurde der Einfluss der Wandungsgeometrie des akustischen Wellenleiters auf die Schallabstrahlung untersucht. Für verschiedene Metalllegierungen wurden unterschiedliche Profile der Orgelpfeifenwandung verglichen: ein konisches Wandungsprofil mit zur Mündung hin abnehmender Wandungsstärke und ein paralleles Wandungsprofil mit konstanter Wandungsstärke. Für eine hohe statistische Sicherheit der Ergebnisse wurden sämtliche Untersuchungen an vier mal zehn Testpfeifen durchgeführt. Mit Ausnahme der beschriebenen Unterschiede sind die Pfeifen von gleichen Abmessungen und auf gleichen Klang intoniert. Die Überprüfung der Wandungseinflüsse auf den Klang besteht aus drei verschiedenen Untersuchungen: Erstens, einer subjektiven Hinterfragung der Wahrnehmbarkeit in einem Hörtest. Zweitens wurde der abgestrahlte Luftschall objektiv gemessen und das Spektrum der Pfeifen in seinen Komponenten (Teiltöne, Grundfrequenz) verglichen. Drittens wurde mit einer neuartigen Messtechnik die Oszillation des Pfeifenkörpers (ein einem akustischen Monopol entsprechendes "Atmen" des Querschnitts) untersucht. Die Ergebnisse belegen die Wahrnehmbarkeit unterschiedlicher Wandungsprofile als auch klare objektive Differenzen zwischen den emittierten Schallspektren. Ein Atmen mit guter Korrelation zur inneren Druckanregung bestätigt den Einfluss wandungsprofilabhängiger Oszillationen auf den Klang der Orgelpfeife. Schließlich wurde die Interaktion zweier in Abstand und Grundfrequenz nah beieinander liegender Orgelpfeifen überprüft. Als Ursache des dabei wahrnehmbaren Oktavsprung des Orgeltons konnte eine gegenphasiger Oszillation des Grundtons beider Pfeifen nachgewiesen werden.
Most image restoration methods in astronomy rely upon probabilistic tools that infer the best solution for a deconvolution problem. They achieve good performances when the point spread function (PSF) is spatially invariant in the image plane.
However, this condition is not always satisfied in real optical systems. We propose a new method for the restoration of images affected by static and anisotropic aberrations using Deep Neural Networks that can be directly applied to sky images.
The network is trained using simulated sky images corresponding to the T80-S Telescope optical model, a 80-cm survey imager at Cerro Tololo (Chile), which are synthesized using a Zernike polynomial representation of the optical system.
Once trained, the network can be used directly on sky images, outputting a corrected version of the image that has a constant and known PSF across its field of view. The method is to be tested on the T80-S Telescope.
We present the method and results on synthetic data.
Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of the observations. Unraveling such transitions yields essential information for the understanding of the observed system’s intrinsic evolution and potential external influences. A precise detection of multiple changes is therefore of great importance for various research disciplines, such as environmental sciences, bioinformatics and economics. The primary purpose of the detection approach introduced in this thesis is the investigation of transitions underlying direct or indirect climate observations. In order to develop a diagnostic approach capable to capture such a variety of natural processes, the generic statistical features in terms of central tendency and dispersion are employed in the light of Bayesian inversion. In contrast to established Bayesian approaches to multiple changes, the generic approach proposed in this thesis is not formulated in the framework of specialized partition models of high dimensionality requiring prior specification, but as a robust kernel-based approach of low dimensionality employing least informative prior distributions.
First of all, a local Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of a single transition. The analysis of synthetic time series comprising changes of different observational evidence, data loss and outliers validates the performance, consistency and sensitivity of the inference algorithm. To systematically investigate time series for multiple changes, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the weighted kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. The detection approach is applied to environmental time series from the Nile river in Aswan and the weather station Tuscaloosa, Alabama comprising documented changes. The method’s performance confirms the approach as a powerful diagnostic tool to decipher multiple changes underlying direct climate observations.
Finally, the kernel-based Bayesian inference approach is used to investigate a set of complex terrigenous dust records interpreted as climate indicators of the African region of the Plio-Pleistocene period. A detailed inference unravels multiple transitions underlying the indirect climate observations, that are interpreted as conjoint changes. The identified conjoint changes coincide with established global climate events. In particular, the two-step transition associated to the establishment of the modern Walker-Circulation contributes to the current discussion about the influence of paleoclimate changes on the environmental conditions in tropical and subtropical Africa at around two million years ago.
X-ray free-electron lasers have, over the past decade, opened up the possibility of understanding the ultrafast response of matter to intense X-ray pulses. In earlier research on atoms and small molecules, new aspects of this response were uncovered, such as rapid sequences of inner-shell photoionization and Auger ionization. Here, we studied a larger molecule, buckminsterfullerene (C-60), exposed to 640 eV X-rays, and examined the role of chemical effects, such as chemical bonds and charge transfer, on the fragmentation following multiple ionization of the molecule. To provide time resolution, we performed femtosecond-resolved X-ray pump/X-ray probe measurements, which were accompanied by advanced simulations. The simulations and experiment reveal that despite substantial ionization induced by the ultrashort (20 fs) X-ray pump pulse, the fragmentation of C-60 is considerably delayed. This work uncovers the persistence of the molecular structure of C-60, which hinders fragmentation over a timescale of hundreds of femtoseconds. Furthermore, we demonstrate that a substantial fraction of the ejected fragments are neutral carbon atoms. These findings provide insights into X-ray free-electron laser-induced radiation damage in large molecules, including biomolecules.
Dynamic processes in living cells are highly organized in space and time. Unraveling the underlying molecular mechanisms of spatiotemporal pattern formation remains one of the outstanding challenges at the interface between physics and biology. A fundamental recurrent pattern found in many different cell types is that of self-sustained oscillations. They are involved in a wide range of cellular functions, including second messenger signaling, gene expression, and cytoskeletal dynamics. Here, we review recent developments in the field of cellular oscillations and focus on cases where concepts from physics have been instrumental for understanding the underlying mechanisms. We consider biochemical and genetic oscillators as well as oscillations that arise from chemo-mechanical coupling. Finally, we highlight recent studies of intracellular waves that have increasingly moved into the focus of this research field.
In addition to (bacterio)chlorophylls, (B)Chls, light-harvesting complexes (LHCs) bind carotenoids, and/or their oxygen derivatives, xanthophylls. Xanthophylls/carotenoids have pivotal functions in LHCs: in stabilization of the structure, as accessory light-harvesting pigments and, probably most importantly, in photoprotection. Xanthophylls are assumed to be involved in the not yet fully understood mechanism of energy-dependent (qE) non-photochemical quenching of Chl fluorescence (NPQ) in higher plants and algae. The so called "xanthophyll cycle" appears to be crucial in this regard. The molecular mechanism(s) of xanthophyll involvement in qE/NPQ have not been established, yet. Moreover, excitation energy transfer (EET) processes involving carotenoids are also difficult to study, due to the fact that transitions between the ground state (S-0, 1(1)A(g)(-)) and the lowest excited singlet state (S-1, 2(1)A(g)(-)) of carotenoids are optically one-photon forbidden ("dark"). Two-photon excitation spectroscopic techniques have been used for more than two decades to study one-photon forbidden states of carotenoids. In the current study, two-photon excitation profiles of LHCII samples containing different xanthophyll complements were measured in the presumed 1(1)A(g)(-) -> 2(1)A(g)(-) (S-0 -> S-1) transition spectral region of the xanthophylls, as well as for isolated chlorophylls a and b in solution. The results indicate that direct two-photon excitation of Chls in this spectral region is dominant over that by xanthophylls. Implications of the results for proposed mechanism(s) of qE/NPQ will be discussed.
In the living cell, the organization of the complex internal structure relies to a large extent on molecular motors. Molecular motors are proteins that are able to convert chemical energy from the hydrolysis of adenosine triphosphate (ATP) into mechanical work. Being about 10 to 100 nanometers in size, the molecules act on a length scale, for which thermal collisions have a considerable impact onto their motion. In this way, they constitute paradigmatic examples of thermodynamic machines out of equilibrium. This study develops a theoretical description for the energy conversion by the molecular motor myosin V, using many different aspects of theoretical physics. Myosin V has been studied extensively in both bulk and single molecule experiments. Its stepping velocity has been characterized as a function of external control parameters such as nucleotide concentration and applied forces. In addition, numerous kinetic rates involved in the enzymatic reaction of the molecule have been determined. For forces that exceed the stall force of the motor, myosin V exhibits a 'ratcheting' behaviour: For loads in the direction of forward stepping, the velocity depends on the concentration of ATP, while for backward loads there is no such influence. Based on the chemical states of the motor, we construct a general network theory that incorporates experimental observations about the stepping behaviour of myosin V. The motor's motion is captured through the network description supplemented by a Markov process to describe the motor dynamics. This approach has the advantage of directly addressing the chemical kinetics of the molecule, and treating the mechanical and chemical processes on equal grounds. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor behaviour is governed by several chemomechanical motor cycles. In addition, we investigate the functional dependence of stepping rates on force by deducing the motor's response to external loads via an appropriate Fokker-Planck equation. For substall forces, the dominant pathway of the motor network is profoundly different from the one for superstall forces, which leads to a stepping behaviour that is in agreement with the experimental observations. The extension of our analysis to Markov processes with absorbing boundaries allows for the calculation of the motor's dwell time distributions. These reveal aspects of the coordination of the motor's heads and contain direct information about the backsteps of the motor. Our theory provides a unified description for the myosin V motor as studied in single motor experiments.
Adherent cells constantly collect information about the mechanical properties of their extracellular environment by actively pulling on it through cell-matrix contacts, which act as mechanosensors. In recent years, the sophisticated use of elastic substrates has shown that cells respond very sensitively to changes in effective stiffness in their environment, which results in a reorganization of the cytoskeleton in response to mechanical input. We develop a theoretical model to predict cellular self-organization in soft materials on a coarse grained level. Although cell organization in principle results from complex regulatory events inside the cell, the typical response to mechanical input seems to be a simple preference for large effective stiffness, possibly because force is more efficiently generated in a stiffer environment. The term effective stiffness comprises effects of both rigidity and prestrain in the environment. This observation can be turned into an optimization principle in elasticity theory. By specifying the cellular probing force pattern and by modeling the environment as a linear elastic medium, one can predict preferred cell orientation and position. Various examples for cell organization, which are of large practical interest, are considered theoretically: cells in external strain fields and cells close to boundaries or interfaces for different sample geometries and boundary conditions. For this purpose the elastic equations are solved exactly for an infinite space, an elastic half space and the elastic sphere. The predictions of the model are in excellent agreement with experiments for fibroblast cells, both on elastic substrates and in hydrogels. Mechanically active cells like fibroblasts could also interact elastically with each other. We calculate the optimal structures on elastic substrates as a function of material properties, cell density and the geometry of cell positioning, respectively, that allows each cell to maximize the effective stiffness in its environment due to the traction of all the other cells. Finally, we apply Monte Carlo simulations to study the effect of noise on cellular structure formation. The model not only contributes to a better understanding of many physiological situations. In the future it could also be used for biomedical applications to optimize protocols for artificial tissues with respect to sample geometry, boundary condition, material properties or cell density.
Semi-empirical sea-level models (SEMs) exploit physically motivated empirical relationships between global sea level and certain drivers, in the following global mean temperature. This model class evolved as a supplement to process-based models (Rahmstorf (2007)) which were unable to fully represent all relevant processes. They thus failed to capture past sea-level change (Rahmstorf et al. (2012)) and were thought likely to underestimate future sea-level rise. Semi-empirical models were found to be a fast and useful tool for exploring the uncertainties in future sea-level rise, consistently giving significantly higher projections than process-based models.
In the following different aspects of semi-empirical sea-level modelling have been studied. Models were first validated using various data sets of global sea level and temperature. SEMs were then used on the glacier contribution to sea level, and to infer past global temperature from sea-level data via inverse modelling. Periods studied encompass the instrumental period, covered by tide gauges (starting 1700 CE (Common Era) in Amsterdam) and satellites (first launched in 1992 CE), the era from 1000 BCE (before CE) to present, and the full length of the Holocene (using proxy data). Accordingly different data, model formulations and implementations have been used. It could be shown in Bittermann et al. (2013) that SEMs correctly predict 20th century sea-level when calibrated with data until 1900 CE. SEMs also turned out to give better predictions than the Intergovernmental Panel on Climate Change (IPCC) 4th assessment report (AR4, IPCC (2007)) models, for the period from 1961–2003 CE.
With the first multi-proxy reconstruction of global sea-level as input, estimate of the human-induced component of modern sea-level change and projections of future sea-level rise were calculated (Kopp et al. (2016)). It turned out with 90% confidence that more than 40 % of the observed 20th century sea-level rise is indeed anthropogenic. With the new semi-empirical and IPCC (2013) 5th assessment report (AR5) projections the gap between SEM and process-based model projections closes, giving higher credibility to both. Combining all scenarios, from strong mitigation to business as usual, a global sea-level rise of 28–131 cm relative to 2000 CE, is projected with 90% confidence. The decision for a low carbon pathway could halve the expected global sea-level rise by 2100 CE.
Present day temperature and thus sea level are driven by the globally acting greenhouse-gas forcing. Unlike that, the Milankovich forcing, acting on Holocene timescales, results mainly in a northern-hemisphere temperature change. Therefore a semi-empirical model can be driven with northernhemisphere temperatures, which makes it possible to model the main subcomponent of sea-level change over this period. It showed that an additional positive constant rate of the order of the estimated Antarctic sea-level contribution is then required to explain the sea-level evolution over the Holocene. Thus the global sea level, following the climatic optimum, can be interpreted as the sum of a temperature induced sea-level drop and a positive long-term contribution, likely an ongoing response to deglaciation coming from Antarctica.
Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey(1-4). However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods(5-8) and experimental studies indicate that oscillations may be short-lived without external stabilizing factors(9-19). Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events.
Der Einfluss der Dynamik auf die stratosphärische Ozonvariabilität über der Arktis im Frühwinter
(2010)
Der frühwinterliche Ozongehalt ist ein Indikator für den Ozongehalt im Spätwinter/Frühjahr. Jedoch weist dieser aufgrund von Absinkprozessen, chemisch bedingten Ozonabbau und Wellenaktivität von Jahr zu Jahr starke Schwankungen auf. Die vorliegende Arbeit zeigt, dass diese Variabilität weitestgehend auf dynamische Prozesse während der Wirbelbildungsphase des arktischen Polarwirbels zurückgeht. Ferner wird der bisher noch ausstehende Zusammenhang zwischen dem früh- und spätwinterlichen Ozongehalt bezüglich Dynamik und Chemie aufgezeigt. Für die Untersuchung des Zusammenhangs zwischen der im Polarwirbel eingeschlossenen Luftmassenzusammensetzung und Ozonmenge wurden Beobachtungsdaten von Satellitenmessinstrumenten und Ozonsonden sowie Modellsimulationen des Lagrangschen Chemie/Transportmodells ATLAS verwandt. Die über die Fläche (45–75°N) und Zeit (August-November) gemittelte Vertikalkomponente des Eliassen-Palm-Flussvektors durch die 100hPa-Fläche zeigt eine Verbindung zwischen der frühwinterlichen wirbelinneren Luftmassenzusammensetzung und der Wirbelbildungsphase auf. Diese ist jedoch nur für die untere Stratosphäre gültig, da die Vertikalkomponente die sich innerhalb der Stratosphäre ändernden Wellenausbreitungsbedingungen nicht erfasst. Für eine verbesserte Höhendarstellung des Signals wurde eine neue integrale auf der Wellenamplitude und dem Charney-Drazin-Kriterium basierende Größe definiert. Diese neue Größe verbindet die Wellenaktivität während der Wirbelbildungsphase sowohl mit der Luftmassenzusammensetzung im Polarwirbel als auch mit der Ozonverteilung über die Breite. Eine verstärkte Wellenaktivität führt zu mehr Luft aus niedrigeren ozonreichen Breiten im Polarwirbel. Aber im Herbst und Frühwinter zerstören chemische Prozesse, die das Ozon ins Gleichgewicht bringen, die interannuale wirbelinnere Ozonvariablität, die durch dynamische Prozesse während der arktischen Polarwirbelbildungsphase hervorgerufen wird. Eine Analyse in Hinblick auf den Fortbestand einer dynamisch induzierten Ozonanomalie bis in den Mittwinter ermöglicht eine Abschätzung des Einflusses dieser dynamischen Prozesse auf den arktischen Ozongehalt. Zu diesem Zweck wurden für den Winter 1999–2000 Modellläufe mit dem Lagrangesche Chemie/Transportmodell ATLAS gerechnet, die detaillierte Informationen über den Erhalt der künstlichen Ozonvariabilität hinsichtlich Zeit, Höhe und Breite liefern. Zusammengefasst, besteht die dynamisch induzierte Ozonvariabilität während der Wirbelbildungsphase länger im Inneren als im Äußeren des Polarwirbels und verliert oberhalb von 750K potentieller Temperatur ihre signifikante Wirkung auf die mittwinterliche Ozonvariabilität. In darunterliegenden Höhenbereichen ist der Anteil an der ursprünglichen Störung groß, bis zu 90% auf der 450K. Innerhalb dieses Höhenbereiches üben die dynamischen Prozesse während der Wirbelbildungsphase einen entscheidenden Einfluss auf den Ozongehalt im Mittwinter aus.
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient D(t)∼tα−1 with α>0 (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. In the present work we discuss the situation in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of the coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series [A. S. Bodrova et al., Phys. Rev. E 100, 012119 (2019)]. We show that the properties of the probability densities in such processes (erasing or retaining the memory on the diffusion coefficient) are vastly different. In addition we discuss the first-passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.
We investigate an intermittent stochastic process in which diffusive motion with a time-dependent diffusion coefficient, D(t)∼tα−1, α>0 (scaled Brownian motion), is stochastically reset to its initial position and starts anew. The resetting follows a renewal process with either an exponential or a power-law distribution of the waiting times between successive renewals. The resetting events, however, do not affect the time dependence of the diffusion coefficient, so that the whole process appears to be a nonrenewal one. We discuss the mean squared displacement of a particle and the probability density function of its positions in this process. We show that scaled Brownian motion with resetting demonstrates rich behavior whose properties essentially depend on the interplay of the parameters of the resetting process and the particle's displacement infree motion. The motion of particles can remain almost unaffected by resetting but can also get slowed down or even be completely suppressed. Especially interesting are the nonstationary situations in which the mean squared displacement stagnates but the distribution of positions does not tend to any steady state. This behavior is compared to the situation [discussed in the companion paper; A. S. Bodrova et al., Phys. Rev. E 100, 012120 (2019)] in which the memory of the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. We show that the properties of the probability densities in such processes (erasing or retaining the memory on the diffusion coefficient) are vastly different.
The problem under consideration in the thesis is a two level atom in a photonic crystal and a pumping laser. The photonic crystal provides an environment for the atom, that modifies the decay of the exited state, especially if the atom frequency is close to the band gap. The population inversion is investigated als well as the emission spectrum. The dynamics is analysed in the context of open quantum systems. Due to the multiple reflections in the photonic crystal, the system has a finite memory that inhibits the Markovian approximation. In the Heisenberg picture the equations of motion for the system variables form a infinite hierarchy of integro-differential equations. To get a closed system, approximations like a weak coupling approximation are needed. The thesis starts with a simple photonic crystal that is amenable to analytic calculations: a one-dimensional photonic crystal, that consists of alternating layers. The Bloch modes inside and the vacuum modes outside a finite crystal are linked with a transformation matrix that is interpreted as a transfer matrix. Formulas for the band structure, the reflection from a semi-infinite crystal, and the local density of states in absorbing crystals are found; defect modes and negative refraction are discussed. The quantum optics section of the work starts with the discussion of three problems, that are related to the full resonance fluorescence problem: a pure dephasing model, the driven atom and resonance fluorescence in free space. In the lowest order of the system-environment coupling, the one-time expectation values for the full problem are calculated analytically and the stationary states are discussed for certain cases. For the calculation of the two time correlation functions and spectra, the additional problem of correlations between the two times appears. In the Markovian case, the quantum regression theorem is valid. In the general case, the fluctuation dissipation theorem can be used instead. The two-time correlation functions are calculated by the two different methods. Within the chosen approximations, both methods deliver the same result. Several plots show the dependence of the spectrum on the parameters. Some examples for squeezing spectra are shown with different approximations. A projection operator method is used to establish two kinds of Markovian expansion with and without time convolution. The lowest order is identical with the lowest order of system environment coupling, but higher orders give different results.
We explore electron preacceleration at high-Mach-number nonrelativistic perpendicular shocks at, e.g., young supernova remnants, which are a prerequisite of further acceleration to very high energies via diffusive shock acceleration. Using fully kinetic particle-in-cell simulations of shocks and electron dynamics in them, we investigate the influence of shock-surfing acceleration (SSA) at the shock foot on the nonthermal population of electrons downstream of the shock. The SSA is followed by further energization at the shock ramp where the Weibel instability spawns a type of second-order Fermi acceleration. The combination of these two processes leads to the formation of a nonthermal electron population, but the importance of SSA becomes smaller for larger ion-to-electron mass ratios in the simulation. We discuss the resulting electron spectra and the relevance of our results to the physics of systems with real ion-to-electron mass ratios and fully three-dimensional behavior.
This publications-based thesis summarizes my contribution to the scientific field of ultrafast structural dynamics. It consists of 16 publications, about the generation, detection and coupling of coherent gigahertz longitudinal acoustic phonons, also called hypersonic waves. To generate such high frequency phonons, femtosecond near infrared laser pulses were used to heat nanostructures composed of perovskite oxides on an ultrashort timescale. As a consequence the heated regions of such a nanostructure expand and a high frequency acoustic phonon pulse is generated. To detect such coherent acoustic sound pulses I use ultrafast variants of optical Brillouin and x-ray scattering. Here an incident optical or x-ray photon is scattered by the excited sound wave in the sample. The scattered light intensity measures the occupation of the phonon modes.
The central part of this work is the investigation of coherent high amplitude phonon wave packets which can behave nonlinearly, quite similar to shallow water waves which show a steepening of wave fronts or solitons well known as tsunamis. Due to the high amplitude of the acoustic wave packets in the solid, the acoustic properties can change significantly in the vicinity of the sound pulse. This may lead to a shape change of the pulse. I have observed by time-resolved Brillouin scattering, that a single cycle hypersound pulse shows a wavefront steepening. I excited hypersound pulses with strain amplitudes until 1% which I have calibrated by ultrafast x-ray diffraction (UXRD).
On the basis of this first experiment we developed the idea of the nonlinear mixing of narrowband phonon wave packets which we call "nonlinear phononics" in analogy with the nonlinear optics, which summarizes a kaleidoscope of surprising optical phenomena showing up at very high electric fields. Such phenomena are for instance Second Harmonic Generation, four-wave-mixing or solitons. But in case of excited coherent phonons the wave packets have usually very broad spectra which make it nearly impossible to look at elementary scattering processes between phonons with certain momentum and energy.
For that purpose I tested different techniques to excite narrowband phonon wave packets which mainly consist of phonons with a certain momentum and frequency. To this end epitaxially grown metal films on a dielectric substrate were excited with a train of laser pulses. These excitation pulses drive the metal film to oscillate with the frequency given by their inverse temporal displacement and send a hypersonic wave of this frequency into the substrate. The monochromaticity of these wave packets was proven by ultrafast optical Brillouin and x-ray scattering.
Using the excitation of such narrowband phonon wave packets I was able to observe the Second Harmonic Generation (SHG) of coherent phonons as a first example of nonlinear wave mixing of nanometric phonon wave packets.
We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott - Antonsen approach, the problem is formulated as a system of partial derivative equations for the local complex order parameter. In this framework, we investigate the existence and stability of twisted states. Both fully coherent and partially coherent stable twisted states were found (the latter ones for the first time for identical oscillators). We show that twisted states can be stable starting from a certain critical value of the medium length, or on a length segment. The analytical results are confirmed with direct numerical simulations in finite ensembles.
Synchronization regimes in an ensemble of phase oscillators coupled through a diffusion field
(2022)
We consider an ensemble of identical phase oscillators coupled through a common diffusion field. Using the Ott-Antonsen reduction, we develop dynamical equations for the complex local order parameter and the mean field. The regions of the existence and stability are determined for the totally synchronous, partially synchronous, and asynchronous spatially homogeneous states. A procedure of searching for inhomogeneous states as periodic trajectories of an auxiliary system of the ordinary differential equations is demonstrated. A scenario of emergence of chimera structures from homogeneous synchronous solutions is described.
We consider the spatiotemporal states of an ensemble of nonlocally coupled nonidentical phase oscillators, which correspond to different regimes of the long-term evolution of such a system. We have obtained homogeneous, twisted, and nonhomogeneous stationary solutions to the Ott-Antonsen equations corresponding to key variants of the realized collective rotational motion of elements of the medium in question with nonzero mesoscopic characteristics determining the degree of coherence of the dynamics of neighboring particles. We have described the procedures of the search for the class of nonhomogeneous solutions as stationary points of the auxiliary point map and of determining the stability based on analysis of the eigenvalue spectrum of the composite operator. Static and breather cluster regimes have been demonstrated and described, as well as the regimes with an irregular behavior of averaged complex fields including, in particular, the local order parameter.
We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. In terms of a local coarse-grained complex order parameter, the problem of finding stationary rotating nonhomogeneous solutions reduces to a third-order ordinary differential equation. This allows finding chimera-type and other inhomogeneous states as periodic orbits of this equation. Stability calculations reveal that only some of these states are stable. We demonstrate that an oscillatory instability leads to a breathing chimera, for which the synchronous domain splits into subdomains with different mean frequencies. Further development of instability leads to turbulent chimeras. Published by AIP Publishing.
Chimera states consisting of synchronous and asynchronous domains in a medium of nonlinearly coupled phase oscillators have been considered. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. The direct numerical simulation has shown that these structures under certain conditions are transformed to oscillatory (breathing) chimera regimes because of the development of instability.
We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. Stability calculations reveal that only some of these states are stable. The direct numerical simulation has shown that these structures under certain conditions are transformed to breathing chimera regimes because of the development of instability. Further development of instability leads to turbulent chimeras.
In recent years, gravitational-wave astronomy has motivated increasingly accurate perturbative studies of gravitational dynamics in compact binaries. This in turn has enabled more detailed analyses of the dynamical black holes in these systems. For example, Pound et al. [Phys. Rev. Lett. 124, 021101 (2020)] recently computed the surface area of a Schwarzschild black hole's apparent horizon, perturbed by an orbiting body, to second order in the binary's mass ratio. In this paper, we take that as the starting point for a comprehensive study of a perturbed Schwarzschild black hole's apparent and event horizon at second perturbative order, deriving generic formulas for the first- and second-order corrections to the horizons' radial profiles, surface areas, Hawking masses, and intrinsic curvatures. We find that the two horizons are remarkably similar, and that any teleological behavior of the event horizon is suppressed in several ways. Critically, we establish that at all orders, the perturbed event horizon in a small-mass-ratio binary is effectively localized in time. Even more pointedly, the event horizon is identical to the apparent horizon at linear order regardless of the source of perturbation, implying that the seemingly teleological "tidal lead," previously observed in linearly perturbed event horizons, is not genuinely teleological in origin. The two horizons do generically differ at second order, but their Hawking masses remain identical, implying that the event horizon obeys the same energy-flux balance law as the apparent horizon. At least in the case of a binary system, the difference between their surface areas remains extremely small even in the late stages of inspiral. In the course of our analysis, we also numerically illustrate puzzling behavior in the black hole's motion around the binary's center of mass.
Any physical system can be described on the level of interacting particles, thus it is of fundamental importance to improve the scientific understanding of interacting many-body systems. This thesis experimentally addresses specific quasi-particle interactions, namely interactions be- tween electrons and between electrons and phonons. It describes the consequential effects of those processes on the electronic structure and the core-hole relaxation pathways in 3d metals. Despite the great amount of experimental and theoretical studies of these interactions and their impact on the behavior of solid-state matter, there are still open questions concerning the cor- responding physical, chemical and mechanical properties of solid-state matter. Especially, the study of 3d metals and their compounds is a great experimental challenge, since those exhibit a variety of spectral features originating from many-body effects such as multiplet splitting, shake up/off satellites, vibrationally excited states or more complex effects like superconductivity and ultrafast demagnetization. In X-ray spectroscopy, these effects often produce overlapping fea- tures, complicating the analysis and limiting the understanding. In this thesis, to overcome the limitations set by conventional X-ray spectroscopy, two different experimental approaches were successfully refined, namely Auger electron photoelectron coincidence spectroscopy (APECS) and temperature-dependent X-ray emission spectroscopy (tXES), which enabled the separation of different core-hole relaxation pathways and the isolation of the impact of specific many-body interactions in the experimental spectra. APECS was utilized at the new Coincidence electron spectroscopy for chemical analysis (Co- ESCA) station at BESSY II to study the core-hole decay and electron-correlation effects in single- crystal Ni, Cu and Co. The observation of photoelectrons in coincidence with Auger electrons allows for the separation of the initial and final state effects in the Auger electron spectra. The results show that a Cu LV V Auger spectrum can be represented by broadened atomic multiplets confirming the localized nature of the intermediate core-hole states. In contrast, the Co LV V Auger spectrum is band-like and can be represented by the self-convolution of the valence band. Ni behaves mixed, localized and itinerant. Thus, the Ni Auger spectrum can only be represented by a mixture of atomic multiplet peaks and the self-convoluted valence band. In the case of Ni, the LV V Auger electrons in coincidence with the 6 eV satellite photoelectrons were also stud- ied. Utilizing the core-hole clock method, the lifetime of the localized double-hole intermediate 2 p53d9 states of 1.8 fs could be determined. However, a fraction of these states delocalizes before the Auger decay contributing to the main peak. A similar delocalization was observed for the double-hole states produced by the L2L3M4,5 Coster-Kronig process. Additionally, the influence of surface oxidation on the Ni(111) 3p levels was studied with APECS. The Ni 3p PES spectrum is broad and featureless, due to overlapping many-body effects and gives little chance for exact analysis using conventional photoelectron spectroscopy. Utilizing APECS or precisely the final state selectivity of the method, the spectral width of the 3p levels could be narrowed and their positions and the spin-orbit splitting were determined. Moreover, due to the surface sensitivity of the method, the chemically shifted 3p photoelectron peaks originating from the oxidized surface and the bulk Ni were disentangled. For the study of the atomic electron-phonon spin-flip scattering in 3d metals as a spin-relaxation channel, the tXES method at the SolidFlexRIXS station was developed. The atomic spin-flip scat- tering was studied in single-crystal Ni, Cu, Co and in FeNi alloys, which show considerable dif- ferences in their behavior. The scattering rate in Ni increases with temperature, whereas the rate in Cu and Co remains constant within the measured temperature range up to 1000 K. In FeNi alloys, our results reveal that the spin-flip scattering is restricted by sublattice exchange energies J. The electron-phonon scattering driven spin-flips only appear in the case where the thermal energy ex- ceeds the exchange energy kT > J. This thresholding is an important microscopic process for the description of the sublattice dynamics in alloys, but as shown also relevant for elemental magnetic systems. Overall, the results strongly indicate that the spin-flip probability is correlated with the exchange energy, which might become an important parameter in the ultrafast demagnetization debate. Taken together, the applied experimental approaches allowed to study complex many-body effects in 3d metals. The results show that utilizing APECS enabled the distinction and clear assignment of otherwise overlapping features in AES or PES spectra of Ni, Cu, Co and NiO. This is of fundamental importance for the basic understanding of photoionization and core-hole decay processes but also for the chemical analysis in applied science. The measurement of the atomic electron-phonon spin-flip scattering rate utilizing tXES shows that the electron-phonon spin-flip scattering is a relevant atomic process for the macroscopic demagnetization process. Additionally, a temperature-dependent thresholding mechanism was discovered, which introduces an important dynamic factor into the electron-phonon spin-flip model.
How different microscopic mechanisms of ultrafast spin dynamics coexist and interplay is not only relevant for the development of spintronics but also for the thorough description of physical systems out-of-equilibrium. In pure crystalline ferromagnets, one of the main microscopic mechanism of spin relaxation is the electron-phonon (el-ph) driven spin-flip, or Elliott-Yafet, scattering. Unexpectedly, recent experiments with ferro- and ferrimagnetic alloys have shown different dynamics for the different sublattices. These distinct sublattice dynamics are contradictory to the Elliott-Yafet scenario. In order to rationalize this discrepancy, it has been proposed that the intra- and intersublattice exchange interaction energies must be considered in the microscopic demagnetization mechanism, too. Here, using a temperature-dependent x-ray emission spectroscopy (XES) method, we address experimentally the element specific el-ph angular momentum transfer rates, responsible for the spin-flips in the respective (sub)lattices of Fe20Ni80, Fe50Ni50 and pure nickel single crystals. We establish how the deduced rate evolution with the temperature is linked to the exchange coupling constants reported for different alloy stoichiometries and how sublattice exchange energies threshold the related el-ph spin-flip channels. Thus, these results evidence that the Elliott-Yafet spin-flip scattering, thresholded by sublattice exchange energies, is the relevant microscopic process to describe sublattice dynamics in alloys and elemental magnetic systems.
Auger-photoelectron coincidence spectroscopy (APECS) has been used to examine the electron correlation and itinerance effects in transition metals Cu, Ni and Co.
It is shown that the LVV Auger, in coincidence with 2p photoelectrons, spectra can be represented using atomic multiplet positions if the 3d-shell is localized (atomic-like) and with a self-convoluted valence band for band-like (itinerant) materials as explained using the Cini-Sawatzky model.
For transition metals, the 3d band changes from band-like to localized with increasing atomic number, with the possibility of a mixed behavior.
Our result shows that the LVV spectra of Cu can be represented by atomic multiplet calculations, those of Co resemble the self-convolution of the valence band and those of Ni are a mixture of both, consistent with the Cini-Sawatzky model.
This work explores the equilibrium structure and thermodynamic phase behavior of complexes formed by charged polymer chains (polyelectrolytes) and oppositely charged spheres (macroions). Polyelectrolyte-macroion complexes form a common pattern in soft-matter physics, chemistry and biology, and enter in numerous technological applications as well. From a fundamental point of view, such complexes are interesting in that they combine the subtle interplay between electrostatic interactions and elastic as well as entropic effects due to conformational changes of the polymer chain, giving rise to a wide range of structural properties. This forms the central theme of theoretical studies presented in this thesis, which concentrate on a number of different problems involving strongly coupled complexes, i.e. complexes that are characterized by a large adsorption energy and small chain fluctuations. In the first part, a global analysis of the structural phase behavior of a single polyelectrolyte-macroion complex is presented based on a dimensionless representation, yielding results that cover a wide range of realistic system parameters. Emphasize is made on the interplay between the effects due to the polyelectrolytes chain length, salt concentration and the macroion charge as well as the mechanical chain persistence length. The results are summarized into generic phase diagrams characterizing the wrapping-dewrapping behavior of a polyelectrolyte chain on a macroion. A fully wrapped chain state is typically obtained at intermediate salt concentrations and chain lengths, where the amount of polyelectrolyte charge adsorbed on the macroion typically exceeds the bare macroion charge leading thus to a highly overcharged complex. Perhaps the most striking features occur when a single long polyelectrolyte chain is complexed with many oppositely charged spheres. In biology, such complexes form between DNA (which carries the cell's genetic information) and small oppositely charged histone proteins serving as an efficient mechanism for packing a huge amount of DNA into the micron-size cell nucleus in eucaryotic cells. The resultant complex fiber, known as the chromatin fiber, appears with a diameter of 30~nm under physiological conditions. Recent experiments indicate a zig-zag spatial arrangement for individual DNA-histone complexes (nucleosome core particles) along the chromatin fiber. A numerical method is introduced in this thesis based on a simple generic chain-sphere cell model that enables one to investigate the mechanism of fiber formation on a systematic level by incorporating electrostatic and elastic contributions. As will be shown, stable complex fibers exhibit an impressive variety of structures including zig-zag, solenoidal and beads-on-a-string patterns, depending on system parameters such as salt concentration, sphere charge as well as the chain contour length (per sphere). The present results predict fibers of compact zig-zag structure within the physiologically relevant regime with a diameter of about 30~nm, when DNA-histone parameters are adopted. In the next part, a numerical method is developed in order to investigate the role of thermal fluctuations on the structure and thermodynamic phase behavior of polyelectrolyte-macroion complexes. This is based on a saddle-point approximation, which allows to describe the experimentally observed reaction (or complexation) equilibrium in a dilute solution of polyelectrolytes and macroions on a systematic level. This equilibrium is determined by the entropy loss a single polyelectrolyte chain suffers as it binds to an oppositely charged macroion. This latter quantity can be calculated from the spectrum of polyelectrolyte fluctuations around a macroion, which is determined by means of a normal-mode analysis. Thereby, a stability phase diagram is obtained, which exhibits qualitative agreement with experimental findings. At elevated complex concentrations, one needs to account for the inter-complex interactions as well. It will be shown that at small separations, complexes undergo structural changes in such a way that positive patches from one complex match up with negative patches on the other. Furthermore, one of the polyelectrolyte chains may bridge between the two complexes. These mechanisms lead to a strong inter-complex attraction. As a result, the second virial coefficient associated with the inter-complex interaction becomes negative at intermediate salt concentrations in qualitative agreement with recent experiments on solutions of nucleosome core particles.
This thesis deals with the encoding and transmission of information through a quantum channel. A quantum channel is a quantum mechanical system whose state is manipulated by a sender and read out by a receiver. The individual state of the channel represents the message. The two topics of the thesis comprise 1) the possibility of compressing a message stored in a quantum channel without loss of information and 2) the possibility to communicate a message directly from one party to another in a secure manner, that is, a third party is not able to eavesdrop the message without being detected. The main results of the thesis are the following. A general framework for variable-length quantum codes is worked out. These codes are necessary to make lossless compression possible. Due to the quantum nature of the channel, the encoded messages are in general in a superposition of different lengths. It is found to be impossible to compress a quantum message without loss of information if the message is not apriori known to the sender. In the other case it is shown that lossless quantum data compression is possible and a lower bound on the compression rate is derived. Furthermore, an explicit compression scheme is constructed that works for arbitrarily given source message ensembles. A quantum cryptographic protocol - the “ping-pong protocol” - is presented that realizes the secure direct communication of classical messages through a quantum channel. The security of the protocol against arbitrary eavesdropping attacks is proven for the case of an ideal quantum channel. In contrast to other quantum cryptographic protocols, the ping-pong protocol is deterministic and can thus be used to transmit a random key as well as a composed message. The protocol is perfectly secure for the transmission of a key, and it is quasi-secure for the direct transmission of a message. The latter means that the probability of successful eavesdropping exponentially decreases with the length of the message.
We discuss the effect of molecular symmetry on coherent tunneling in symmetric double-well potentials whose two molecular equilibrium configurations are interconverted by nuclear permutations. This is illustrated with vibrational tunneling in ammonia molecules, electronic tunneling in the dihydrogen cation, and laser-induced rotational tunneling of homonuclear diatomics. In this contribution, we reexamine the textbook picture of coherent tunneling in such potentials, which is depicted with a wavepacket shuttling back and forth between the two potential-wells. We show that the common application of this picture to the aforementioned molecules contravenes the principle of the indistinguishability of identical particles. This conflict originates from the sole consideration of the dynamics of the tunneling-mode, connecting the double-well energy minima, and complete omission of all the remaining molecular degrees of freedom. This gives rise to double-well wavepackets that are nonsymmetric under nuclear permutations. To obey quantum statistics, we show that the double-well eigenstates composing these wavepackets must be entangled with the wavefunctions that describe all the omitted molecular modes. These wavefunctions have compensating and opposite nuclear permutation symmetry. This in turn leads to complete quenching of interference effects behind localization in one potential-well or another. Indeed, we demonstrate that the reduced density of probability of the symmetrized molecular wavefunction, where all the molecular coordinates but the tunneling-mode are integrated out, is symmetrically distributed over the two potential-wells, at all times. This applies to any multilevel wavepacket of isotropic or fully aligned symmetric double-well achiral molecules. However, in the case of coherent electronic or vibrational tunneling, fully aligned molecules may exhibit dynamical localization in the space-fixed frame, where the tunneling-mode density shuttles between the opposite directions of the alignment axis. This dynamical spatial-localization results from linear combinations of molecular states that have opposite parity. In summary, this study shows that dynamical localization of the tunneling-mode density on either of the two indistinguishable molecular equilibrium configurations of symmetric double-well achiral molecules is forbidden by quantum statistics, whereas its dynamical localization in the space-fixed frame is allowed by parity. The subtle distinction between these two types of localization has far-reaching implications in the interpretation of many ultrafast molecular dynamics experiments.
In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H–Si and D–Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D–Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H–Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D–Si system and both one- and two-phonon interaction terms in the case of H–Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi’s golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D–Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H–Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude—a few hundred fs for D–Si and a couple of ps for H–Si—, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H–Si initial vibrational state, allowing an easy extraction of the bending mode “lifetime.” This is in contrast with the D–Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D–Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H–Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation.
Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles. Published under an exclusive license by AIP Publishing.
We present a general analysis of the cooling produced by losses on condensates or quasi-condensates. We study how the occupations of the collective phonon modes evolve in time, assuming that the loss process is slow enough so that each mode adiabatically follows the decrease of the mean density. The theory is valid for any loss process whose rate is proportional to the jth power of the density, but otherwise spatially uniform. We cover both homogeneous gases and systems confined in a smooth potential. For a low-dimensional gas, we can take into account the modified equation of state due to the broadening of the cloud width along the tightly confined directions, which occurs for large interactions. We find that at large times, the temperature decreases proportionally to the energy scale mc2, where m is the mass of the particles and c the sound velocity. We compute the asymptotic ratio of these two quantities for different limiting cases: a homogeneous gas in any dimension and a one-dimensional gas in a harmonic trap.
We present a general analysis of the cooling produced by losses on condensates or quasi-condensates. We study how the occupations of the collective phonon modes evolve in time, assuming that the loss process is slow enough so that each mode adiabatically follows the decrease of the mean density. The theory is valid for any loss process whose rate is proportional to the jth power of the density, but otherwise spatially uniform. We cover both homogeneous gases and systems confined in a smooth potential. For a low-dimensional gas, we can take into account the modified equation of state due to the broadening of the cloud width along the tightly confined directions, which occurs for large interactions. We find that at large times, the temperature decreases proportionally to the energy scale mc(2), where m is the mass of the particles and c the sound velocity. We compute the asymptotic ratio of these two quantities for different limiting cases: a homogeneous gas in any dimension and a one-dimensional gas in a harmonic trap.
Aims. We investigated the ionisation conditions and distances of Galactic high-velocity clouds (HVCs) in the Galactic halo and beyond in the direction of the Local Group (LG) barycentre and anti-barycentre, by studying spectral data of 29 extragalactic background sources obtained with the Cosmic Origins Spectropgraph (COS) installed on the Hubble Space Telescope (HST). Methods. We model column-densities of low, intermediate, and high ions such as Si ii, C ii, Si iii, Si vi, and C iv, and use these data to construct a set of Cloudy ionisation models. Results. In total, we found 69 high-velocity absorption components along the 29 lines of sight. The components in the direction of the LG barycentre span the entire range of studied velocities, 100 less than or similar to vertical bar nu(LSR)vertical bar less than or similar to 400 km s(-1), while those in the anti-barycentre sample have velocities up to about 300 km s(-1). For 49 components, we infer the gas densities. In the direction of the LG barycentre, the gas densities exhibit a wide range from log nH = -3.96 to -2.55, while in the anti-barycentre direction the densities are systematically higher, log nH > -3.25. The barycentre absorbers can be split into two groups based on their density: a high-density group with log nH > -3.54, which can be affected by the Milky Way radiation field, and a low-density group (log nH <= -3.54). The latter has very low thermal pressures of P/k < 7.3 Kcm(-3). Conclusions. Our study shows that part of the absorbers in the LG barycentre direction trace gas at very low gas densities and thermal pressures. These properties indicate that the absorbers are located beyond the virial radius of the Milky Way. Our study also confirms results from earlier, single-sightline studies, suggesting the presence of a metal-enriched intragroup medium filling the LG near its barycentre.
In der vorliegenden Arbeit werden Methoden der Erdsystemanalyse auf die Untersuchung der Habitabilität terrestrischer Exoplaneten angewandt. Mit Hilfe eines parametrisierten Konvektionsmodells für die Erde wird die thermische Evolution von terrestrischen Planeten berechnet. Bei zunehmender Leuchtkraft des Zentralsterns wird über den globalen Karbonat-Silikat-Kreislauf das planetare Klima stabilisiert. Für eine photosynthetisch-aktive Biosphäre, die in einem bestimmten Temperaturbereich bei hinreichender CO2-Konzentration existieren kann, wird eine Überlebenspanne abgeschätzt. Der Abstandsbereich um einen Stern, in dem eine solche Biosphäre produktiv ist, wird als photosynthetisch-aktive habitable Zone (pHZ) definiert und berechnet. Der Zeitpunkt, zu dem die pHZ in einem extrasolaren Planetensystem endgültig verschwindet, ist die maximale Lebenspanne der Biosphäre. Für Supererden, massereiche terrestrische Planeten, ist sie umso länger, je massereicher der Planet ist und umso kürzer, je mehr er mit Kontinenten bedeckt ist. Für Supererden, die keine ausgeprägten Wasser- oder Landwelten sind, skaliert die maximale Lebenspanne mit der Planetenmasse mit einem Exponenten von 0,14. Um K- und M-Sterne ist die Überlebensspanne einer Biosphäre auf einem Planeten immer durch die maximale Lebensspanne bestimmt und nicht durch das Ende der Hauptreihenentwicklung des Zentralsterns limitiert. Das pHZ-Konzept wird auf das extrasolare Planetensystem Gliese 581 angewandt. Danach könnte die 8-Erdmassen-Supererde Gliese 581d habitabel sein. Basierend auf dem vorgestellten pHZ-Konzept wird erstmals die von Ward und Brownlee 1999 aufgestellte Rare-Earth-Hypothese für die Milchstraße quantifiziert. Diese Hypothese besagt, dass komplexes Leben im Universum vermutlich sehr selten ist, wohingegen primitives Leben weit verbreitet sein könnte. Unterschiedliche Temperatur- und CO2-Toleranzen sowie ein unterschiedlicher Einfluss auf die Verwitterung für komplexe und primitive Lebensformen führt zu unterschiedlichen Grenzen der pHZ und zu einer unterschiedlichen Abschätzung für die Anzahl der Planeten, die mit den entsprechenden Lebensformen besiedelt sein könnten. Dabei ergibt sich, dass komplex besiedelte Planeten heute etwa 100-mal seltener sein müssten als primitiv besiedelte.
In dieser Arbeit wurde die Variabilität der Atmosphäre in einem neuen gekoppelten Klimamodell (ECHO-GiSP) untersucht, welches eine vereinfachte Stratosphärenchemie (bis 80 km Höhe) enthält. Es wurden 2 Simulationen über 150 Jahre durchgeführt. In einer der Simulationen wurde die atmosphärische Chemie modelliert, hatte aber keinen Einfluß auf die Dynamik des Klimamodelles. In der zweiten Simulation wurde hingegen die Wirkung der Chemie auf die Klimadynamik explizit berücksichtigt, die über die Strahlungsbilanz des Modelles erfolgt. Dies ist die erste Langzeitsimulation mit einem voll gekoppelten globalen Klimamodell mit interaktiver Chemie. Die Simulation mit rückgekoppelter Chemie zeigt eine Abschwächung des atmosphärischen Variabilitätsmusters der Arktischen Oszillation (AO). Zudem kommt es in der Troposphäre zu einer Reduzierung der mittleren Windgeschwindigkeiten der gemäßigten Breiten aufgrund verringerter Temperaturgegensätze zwischen den Tropen und den Polargebieten. Auch in der Stratosphäre ergibt sich eine Abschwächung und Erwärmung des Polarwirbels. Diese Auswirkungen der Kopplung zwischen der atmosphärischen Chemie und der Dynamik des Klimamodelles sind eine wichtige Erkenntnis, da in früheren Klimasimulationen die Variabilität der AO oft zu stark ausgeprägt war. In der Stratosphäre reduziert sich infolge des abgeschwächten Polarwirbels auch die großräumige Zirkulation zwischen den beiden Hemisphären der Erde. In der Troposphäre werden hingegen die allgemeine Zirkulation, und damit auch die subtropischen Strahlströme des Windes verstärkt. Zudem kommt es in den Tropen zu Temperaturänderungen durch stratosphärische Ozonschwankungen in Abhängigkeit von der AO. Allgemein verändert sich die Kopplung zwischen Troposphäre und Stratosphäre, einschließlich des durch die Anregung von langen atmosphärischen Wellen erfolgenden vertikalen Energieübertrages aus der Troposphäre in die Stratosphäre.
We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.
We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.
We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.
Recurrences in past climates
(2023)
Our ability to predict the state of a system relies on its tendency to recur to states it has visited before. Recurrence also pervades common intuitions about the systems we are most familiar with: daily routines, social rituals and the return of the seasons are just a few relatable examples. To this end, recurrence plots (RP) provide a systematic framework to quantify the recurrence of states. Despite their conceptual simplicity, they are a versatile tool in the study of observational data. The global climate is a complex system for which an understanding based on observational data is not only of academical relevance, but vital for the predurance of human societies within the planetary boundaries. Contextualizing current global climate change, however, requires observational data far beyond the instrumental period. The palaeoclimate record offers a valuable archive of proxy data but demands methodological approaches that adequately address its complexities. In this regard, the following dissertation aims at devising novel and further developing existing methods in the framework of recurrence analysis (RA). The proposed research questions focus on using RA to capture scale-dependent properties in nonlinear time series and tailoring recurrence quantification analysis (RQA) to characterize seasonal variability in palaeoclimate records (‘Palaeoseasonality’).
In the first part of this thesis, we focus on the methodological development of novel approaches in RA. The predictability of nonlinear (palaeo)climate time series is limited by abrupt transitions between regimes that exhibit entirely different dynamical complexity (e.g. crossing of ‘tipping points’). These possibly depend on characteristic time scales. RPs are well-established for detecting transitions and capture scale-dependencies, yet few approaches have combined both aspects. We apply existing concepts from the study of self-similar textures to RPs to detect abrupt transitions, considering the most relevant time scales. This combination of methods further results in the definition of a novel recurrence based nonlinear dependence measure. Quantifying lagged interactions between multiple variables is a common problem, especially in the characterization of high-dimensional complex systems. The proposed ‘recurrence flow’ measure of nonlinear dependence offers an elegant way to characterize such couplings. For spatially extended complex systems, the coupled dynamics of local variables result in the emergence of spatial patterns. These patterns tend to recur in time. Based on this observation, we propose a novel method that entails dynamically distinct regimes of atmospheric circulation based on their recurrent spatial patterns. Bridging the two parts of this dissertation, we next turn to methodological advances of RA for the study of Palaeoseasonality. Observational series of palaeoclimate ‘proxy’ records involve inherent limitations, such as irregular temporal sampling. We reveal biases in the RQA of time series with a non-stationary sampling rate and propose a correction scheme.
In the second part of this thesis, we proceed with applications in Palaeoseasonality. A review of common and promising time series analysis methods shows that numerous valuable tools exist, but their sound application requires adaptions to archive-specific limitations and consolidating transdisciplinary knowledge. Next, we study stalagmite proxy records from the Central Pacific as sensitive recorders of mid-Holocene El Niño-Southern Oscillation (ENSO) dynamics. The records’ remarkably high temporal resolution allows to draw links between ENSO and seasonal dynamics, quantified by RA. The final study presented here examines how seasonal predictability could play a role for the stability of agricultural societies. The Classic Maya underwent a period of sociopolitical disintegration that has been linked to drought events. Based on seasonally resolved stable isotope records from Yok Balum cave in Belize, we propose a measure of seasonal predictability. It unveils the potential role declining seasonal predictability could have played in destabilizing agricultural and sociopolitical systems of Classic Maya populations.
The methodological approaches and applications presented in this work reveal multiple exciting future research avenues, both for RA and the study of Palaeoseasonality.
We report on the formation of wrinkle-patterned surface morphologies in cesium formamidinium-based Cs(x)FA(1-y)Pb(I1-yBry)(3) perovskite compositions with x = 0-0.3 and y = 0-0.3 under various spin-coating conditions. By varying the Cs and Br contents, the perovskite precursor solution concentration and the spin-coating procedure, the occurrence and characteristics of the wrinkle-shaped morphology can be tailored systematically. Cs(0.17)FA(0.83)Pb(I0.83Br0.17)(3) perovskite layers were analyzed regarding their surface roughness, microscopic structure, local and overall composition, and optoelectronic properties. Application of these films in p-i-n perovskite solar cells (PSCs) with indium-doped tin oxide/NiOx/perovskite/C-60/bathocuproine/Cu architecture resulted in up to 15.3 and 17.0% power conversion efficiency for the flat and wrinkled morphology, respectively. Interestingly, we find slightly red-shifted photoluminescence (PL) peaks for wrinkled areas and we are able to directly correlate surface topography with PL peak mapping. This is attributed to differences in the local grain size, whereas there is no indication for compositional demixing in the films. We show that the perovskite composition, crystallization kinetics, and layer thickness strongly influence the formation of wrinkles which is proposed to be related to the release of compressive strain during perovskite crystallization. Our work helps us to better understand film formation and to further improve the efficiency of PSCs with widely used mixed-perovskite compositions.
Polymers at membranes
(2000)
The surface of biological cells consists of a lipid membrane and a large amount of various proteins and polymers, which are embedded in the membrane or attached to it. We investigate how membranes are influenced by polymers, which are anchored to the membrane by one end. The entropic pressure exerted by the polymer induces a curvature, which bends the membrane away from the polymer. The resulting membrane shape profile is a cone in the vicinity of the anchor segment and a catenoid far away from it. The perturbative calculations are confirmed by Monte-Carlo simulations. An additional attractive interaction between polymer and membrane reduces the entropically induced curvature. In the limit of strong adsorption, the polymer is localized directly on the membrane surface and does not induce any pressure, i.e. the membrane curvature vanishes. If the polymer is not anchored directly on the membrane surface, but in a non-vanishing anchoring distance, the membrane bends towards the polymer for strong adsorption. In the last part of the thesis, we study membranes under the influence of non-anchored polymers in solution. In the limit of pure steric interactions between the membrane and free polymers, the membrane curves towards the polymers (in contrast to the case of anchored polymers). In the limit of strong adsorption the membrane bends away from the polymers.
Binary III-V nitrides such as AlN, GaN and InN in the wurtzite-type structure have long been considered as potent semiconducting materials because of their optoelectronic properties, amongst others. With rising concerns over the utilization of scarce elements, a replacement of the trivalent cations by others in ternary and multinary nitrides has led to the development of different variants of nitrides and oxide nitrides crystallizing in lower-symmetry variants of wurtzite. This work presents the symmetry relationships between these structural types specific to nitrides and oxide nitrides and updates some prior work on this matter. The non-existence of compounds crystallizing in Pmc2(1), formally the highest subgroup of the wurtzite type fulfilling Pauling's rules for 1:1:2 stoichiometries, has been puzzling scientists for a while; a rationalization is given, from a crystallographic basis, of why this space group is unlikely to be adopted.
Halide perovskites
(2021)
The cytoskeleton is an essential component of living cells. It is composed of different types of protein filaments that form complex, dynamically rearranging, and interconnected networks. The cytoskeleton serves a multitude of cellular functions which further depend on the cell context. In animal cells, the cytoskeleton prominently shapes the cell's mechanical properties and movement. In plant cells, in contrast, the presence of a rigid cell wall as well as their larger sizes highlight the role of the cytoskeleton in long-distance intracellular transport. As it provides the basis for cell growth and biomass production, cytoskeletal transport in plant cells is of direct environmental and economical relevance. However, while knowledge about the molecular details of the cytoskeletal transport is growing rapidly, the organizational principles that shape these processes on a whole-cell level remain elusive.
This thesis is devoted to the following question: How does the complex architecture of the plant cytoskeleton relate to its transport functionality? The answer requires a systems level perspective of plant cytoskeletal structure and transport. To this end, I combined state-of-the-art confocal microscopy, quantitative digital image analysis, and mathematically powerful, intuitively accessible graph-theoretical approaches.
This thesis summarizes five of my publications that shed light on the plant cytoskeleton as a transportation network: (1) I developed network-based frameworks for accurate, automated quantification of cytoskeletal structures, applicable in, e.g., genetic or chemical screens; (2) I showed that the actin cytoskeleton displays properties of efficient transport networks, hinting at its biological design principles; (3) Using multi-objective optimization, I demonstrated that different plant cell types sustain cytoskeletal networks with cell-type specific and near-optimal organization; (4) By investigating actual transport of organelles through the cell, I showed that properties of the actin cytoskeleton are predictive of organelle flow and provided quantitative evidence for a coordination of transport at a cellular level; (5) I devised a robust, optimization-based method to identify individual cytoskeletal filaments from a given network representation, allowing the investigation of single filament properties in the network context. The developed methods were made publicly available as open-source software tools.
Altogether, my findings and proposed frameworks provide quantitative, system-level insights into intracellular transport in living cells. Despite my focus on the plant cytoskeleton, the established combination of experimental and theoretical approaches is readily applicable to different organisms. Despite the necessity of detailed molecular studies, only a complementary, systemic perspective, as presented here, enables both understanding of cytoskeletal function in its evolutionary context as well as its future technological control and utilization.
From dawn till dusk
(2020)
Supernova remnants are believed to be the source of cosmic rays with energies up to 10^15 eV that are produced within our Galaxy. The acceleration mechanism associated with the collision-less shocks in supernova remnants - diffusive shock acceleration - predicts a spectral index of the accelerated non-thermal particles of s = 2. However, measurements of non-thermal emission in radio, X-rays and gamma-rays reveal significant deviations of the particles spectral index from the canonical value of s = 2.
The youngest Galactic supernova remnant G1.9+0.3 is an interesting target for next-generation gamma-ray observatories. So far, the remnant is only detected in the radio and the X-ray bands, but its young age of ≈100 yrs and inferred shock speed of ≈ 14, 000 km/s could make it an efficient particle accelerator.
I performed spherical symmetric 1D simulations with the RATPaC code, in which I simultaneously solved the transport equation for cosmic rays, the transport equation for magnetic turbulence, and the hydro-dynamical equations for the gas flow. Separately computed distributions of the particles accelerated at the forward and the reverse shock were then used to calculate the spectra of synchrotron, inverse Compton, and Pion-decay radiation from the source.
The emission from G1.9+0.3 can be self-consistently explained within the test-particle limit. I find that the X-ray flux is dominated by emission from the forward shock while most of the radio emission originates near the reverse shock, which makes G1.9+0.3 the first remnant with non-thermal radiation detected from the reverse shock. The flux of very-high-energy gamma-ray emission from G1.9+0.3 is expected to be close to the sensitivity threshold of the Cherenkov Telescope Array. The limited time available to grow large-scale turbulence limits the maximum energy of particles to values below 100 TeV, hence G1.9+0.3 is not a PeVatron.
Although there are many models for the acceleration of cosmic rays in Supernova remnants, the escape of cosmic rays from these sources is yet understudied.
I use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic Supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. My simulations span 100,000 years, thus covering the free-expansion, the Sedov-Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution.
At later stages of the evolution cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration and feature breaks in the 10 - 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. I further find the gamma-ray luminosity to peak around an age of 4,000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media emit generally more inverse-Compton radiation matching the fact that the brightest known supernova remnants - RCW86, Vela Jr, HESSJ1721-347 and RXJ1713.7-3946 - are all expanding in low density environments.
The importance of feedback from the cosmic-rays on the hydrodynamical evolution of the remnants is debated as a possibility to obtain soft cosmic-ray spectra at low energies.
I performed spherically symmetric 1-D simulations with a modified version of the RATPaC code, in which I simultaneously solve the transport equation for cosmic rays and the hydrodynamical equations, including the back-reaction of the cosmic-ray pressure on the flow profiles.
Besides the known modification of the flow profiles and the consequently curved cosmic-ray spectra, steady-state models for non-linear diffusive shock acceleration overpredict the total compression ratio that can be reached with cosmic-ray feedback, as there is limited time for building these modifications. Further, I find modifications to the downstream flow structure that change the evolutionary behavior of the remnant and trigger a cosmic-ray-induced instability close to the contact discontinuity, if and when the cosmic-ray pressure becomes dominant there.
Nonthermal emission from the reverse shock of the youngest galactic supernova remnant G1.9+0.3
(2019)
Context. The youngest Galactic supernova remnant G1.9+0.3 is an interesting target for next-generation gamma-ray observatories. So far, the remnant is only detected in the radio and the X-ray bands, but its young age of approximate to 100 yr and inferred shock speed of approximate to 14 000 km s(-1) could make it an efficient particle accelerator. Aims. We aim to model the observed radio and X-ray spectra together with the morphology of the remnant. At the same time, we aim to estimate the gamma-ray flux from the source and evaluate the prospects of its detection with future gamma-ray experiments. Methods. We performed spherical symmetric 1D simulations with the RATPaC code, in which we simultaneously solved the transport equation for cosmic rays, the transport equation for magnetic turbulence, and the hydro-dynamical equations for the gas flow. Separately computed distributions of the particles accelerated at the forward and the reverse shock were then used to calculate the spectra of synchrotron, inverse Compton, and pion-decay radiation from the source. Results. The emission from G1.9+0.3 can be self-consistently explained within the test-particle limit. We find that the X-ray flux is dominated by emission from the forward shock while most of the radio emission originates near the reverse shock, which makes G1.9+0.3 the first remnant with nonthermal radiation detected from the reverse shock. The flux of very-high-energy gamma-ray emission from G1.9+0.3 is expected to be close to the sensitivity threshold of the Cherenkov Telescope Array. The limited time available to grow large-scale turbulence limits the maximum energy of particles to values below 100 TeV, hence G1.9+0.3 is not a PeVatron.
The evolution of life on Earth has been driven by disturbances of different types and magnitudes over the 4.6 million years of Earth’s history (Raup, 1994, Alroy, 2008). One example for such disturbances are mass extinctions which are characterized by an exceptional increase in the extinction rate affecting a great number of taxa in a short interval of geologic time (Sepkoski, 1986). During the 541 million years of the Phanerozoic, life on Earth suffered five exceptionally severe mass extinctions named the “Big Five Extinctions”. Many mass extinctions are linked to changes in climate
(Feulner, 2009). Hence, the study of past mass extinctions is not only intriguing, but can also provide insights into the complex nature of the Earth system. This thesis aims at deepening our understanding of the triggers of mass extinctions and how they affected life. To accomplish this, I investigate changes in climate during two of the Big Five extinctions using a coupled climate model.
During the Devonian (419.2–358.9 million years ago) the first vascular plants and vertebrates evolved on land while extinction events occurred in the ocean (Algeo et al., 1995). The causes of these formative changes, their interactions and their links to changes in climate are still poorly understood. Therefore, we explore the sensitivity of the Devonian climate to various boundary conditions using an intermediate-complexity climate model (Brugger et al., 2019). In contrast to Le Hir et al. (2011), we find only a minor biogeophysical effect of changes in vegetation cover due to unrealistically high soil albedo values used in the earlier study. In addition, our results cannot support the strong influence of orbital parameters on the Devonian climate, as simulated with a climate model with a strongly simplified ocean model (De Vleeschouwer et al., 2013, 2014, 2017). We can only reproduce the changes in Devonian climate suggested by proxy data by decreasing atmospheric CO2. Still, finding agreement between the evolution of sea surface temperatures reconstructed from proxy data (Joachimski et al., 2009) and our simulations remains challenging and suggests a lower δ18O ratio of Devonian seawater. Furthermore, our study of the sensitivity of the Devonian climate reveals a prevailing mode of climate variability on a timescale of decades to centuries. The quasi-periodic ocean temperature fluctuations are linked to a physical mechanism of changing sea-ice cover, ocean convection and overturning in high northern latitudes.
In the second study of this thesis (Dahl et al., under review) a new reconstruction of atmospheric CO2 for the Devonian, which is based on CO2-sensitive carbon isotope fractionation in the earliest vascular plant fossils, suggests a much earlier drop of atmo- spheric CO2 concentration than previously reconstructed, followed by nearly constant CO2 concentrations during the Middle and Late Devonian. Our simulations for the Early Devonian with identical boundary conditions as in our Devonian sensitivity study (Brugger et al., 2019), but with a low atmospheric CO2 concentration of 500 ppm, show no direct conflict with available proxy and paleobotanical data and confirm that under the simulated climatic conditions carbon isotope fractionation represents a robust proxy for atmospheric CO2. To explain the earlier CO2 drop we suggest that early forms of vascular land plants have already strongly influenced weathering. This new perspective on the Devonian questions previous ideas about the climatic conditions and earlier explanations for the Devonian mass extinctions.
The second mass extinction investigated in this thesis is the end-Cretaceous mass extinction (66 million years ago) which differs from the Devonian mass extinctions in terms of the processes involved and the timescale on which the extinctions occurred. In the two studies presented here (Brugger et al., 2017, 2021), we model the climatic effects of the Chicxulub impact, one of the proposed causes of the end-Cretaceous extinction, for the first millennium after the impact. The light-dimming effect of stratospheric sulfate aerosols causes severe cooling, with a decrease of global annual mean surface air temperature of at least 26◦C and a recovery to pre-impact temperatures after more than 30 years. The sudden surface cooling of the ocean induces deep convection which brings nutrients from the deep ocean via upwelling to the surface ocean. Using an ocean biogeochemistry model we explore the combined effect of ocean mixing and iron-rich dust originating from the impactor on the marine biosphere. As soon as light levels have recovered, we find a short, but prominent peak in marine net primary productivity. This newly discovered mechanism could result in toxic effects for marine near-surface ecosystems. Comparison of our model results to proxy data (Vellekoop et al., 2014, 2016, Hull et al., 2020) suggests that carbon release from the terrestrial biosphere is required in addition to the carbon dioxide which can be attributed to the target material. Surface ocean acidification caused by the addition of carbon dioxide and sulfur is only moderate. Taken together, the results indicate a significant contribution of the Chicxulub impact to the end-Cretaceous mass extinction by triggering multiple stressors for the Earth system.
Although the sixth extinction we face today is characterized by human intervention in nature, this thesis shows that we can gain many insights into future extinctions from studying past mass extinctions, such as the importance of the rate of change (Rothman, 2017), the interplay of multiple stressors (Gunderson et al., 2016), and changes in the carbon cycle (Rothman, 2017, Tierney et al., 2020).
The stress-strain behavior of microcracked polycrystalline materials (such as ceramics or rocks) under conditions of tensile, displacement-controlled, loading is discussed. Micromechanical explanation and modeling of the basic features, such as non-linearity and hysteresis in stress-strain curves, is developed, with stable microcrack propagation and "roughness" of intergranular cracks playing critical roles. Experiments involving complex loading histories were done on large- and medium grain size beta-eucryptite ceramic. The model is shown to reproduce the basic features of the observed stress-strain curves. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
A numerical framework is developed to study the hysteresis of elastic properties of porous ceramics as a function of temperature. The developed numerical model is capable of employing experimentally measured crystallographic orientation distribution and coefficient of thermal expansion values. For realistic modeling of the microstructure, Voronoi polygons are used to generate polycrystalline grains. Some grains are considered as voids, to simulate the material porosity. To model intercrystalline cracking, cohesive elements are inserted along grain boundaries. Crack healing (recovery of the initial properties) upon closure is taken into account with special cohesive elements implemented in the commercial code ABAQUS. The numerical model can be used to estimate fracture properties governing the cohesive behavior through inverse analysis procedure. The model is applied to a porous cordierite ceramic. The obtained fracture properties are further used to successfully simulate general non-linear macroscopic stress-strain curves of cordierite, thereby validating the model.
The simultaneous detection of gravitational waves and light from the binary neutron star merger GW170817 led to independent measurements of distance and redshift, providing a direct estimate of the Hubble constant H-0 that does not rely on a cosmic distance ladder, nor assumes a specific cosmological model.
By using gravitational waves as "standard sirens", this approach holds promise to arbitrate the existing tension between the H-0 value inferred from the cosmic microwave background and those obtained from local measurements.
However, the known degeneracy in the gravitational-wave analysis between distance and inclination of the source led to a H-0 value from GW170817 that was not precise enough to resolve the existing tension.
In this review, we summarize recent works exploiting the viewing-angle dependence of the electromagnetic signal, namely the associated short gamma-ray burst and kilonova, to constrain the system inclination and improve on H-0.
We outline the key ingredients of the different methods, summarize the results obtained in the aftermath of GW170817 and discuss the possible systematics introduced by each of these methods.
Over the last decades, the percentage of the age group choosing to pursue university studies has increased significantly across the world. At the same time, there are university teachers who believe that the standards have fallen. There is little research on whether students nowadays demonstrate knowledge or abilities similar to that of the preceding cohorts. However, in times of educational expansion, empirical evidence on student test performance is extremely helpful in evaluating how well educational systems cope with the increasing numbers of students. In this study, we compared a sample of 2322 physics freshmen from 2013 with another sample of 2718 physics freshmen from 1978 at universities in Germany with regard to their physics knowledge based on their results in the same entrance test. Previous results on mathematics knowledge and abilities in the same sample of students indicated that there was no severe decline in their average achievement. This paper compares the physics knowledge of the same two samples of students. Contrary to their mathematics results, their physics results showed a substantial decrease in physics knowledge as measured by the test.
Observational studies have revealed that galaxy pairs tend to have lower gas-phase metallicity than isolated galaxies. This metallicity deficiency can be caused by inflows of low-metallicity gas due to the tidal forces and gravitational torques associated with galaxy mergers, diluting the metal content of the central region. In this work we demonstrate that such metallicity dilution occurs in state-of-the-art cosmological simulations of galaxy formation. We find that the dilution is typically 0.1 dex for major mergers, and is noticeable at projected separations smaller than 40 kpc. For minor mergers the metallicity dilution is still present, even though the amplitude is significantly smaller. Consistent with previous analysis of observed galaxies we find that mergers are outliers from the fundamental metallicity relation, with deviations being larger than expected for a Gaussian distribution of residuals. Our large sample of mergers within full cosmological simulations also makes it possible to estimate how the star formation rate enhancement and gas consumption timescale behave as a function of the merger mass ratio. We confirm that strong starbursts are likely to occur in major mergers, but they can also arise in minor mergers if more than two galaxies are participating in the interaction, a scenario that has largely been ignored in previous work based on idealised isolated merger simulations.
The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
Self-propelled rods
(2019)
A wide range of experimental systems including gliding, swarming and swimming bacteria, in vitro motility assays, and shaken granular media are commonly described as self-propelled rods. Large ensembles of those entities display a large variety of self-organized, collective phenomena, including the formation of moving polar clusters, polar and nematic dynamic bands, mobility-induced phase separation, topological defects, and mesoscale turbulence, among others. Here, we give a brief survey of experimental observations and review the theoretical description of self-propelled rods. Our focus is on the emergent pattern formation of ensembles of dry self-propelled rods governed by short-ranged, contact mediated interactions and their wet counterparts that are also subject to long-ranged hydrodynamic flows. Altogether, self-propelled rods provide an overarching theme covering many aspects of active matter containing well-explored limiting cases. Their collective behavior not only bridges the well-studied regimes of polar selfpropelled particles and active nematics, and includes active phase separation, but also reveals a rich variety of new patterns.
The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.
The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.
The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information.
In this thesis, the dependencies of charge localization and itinerance in two classes of aromatic molecules are accessed: pyridones and porphyrins. The focus lies on the effects of isomerism, complexation, solvation, and optical excitation, which are concomitant with different crucial biological applications of specific members of these groups of compounds. Several porphyrins play key roles in the metabolism of plants and animals. The nucleobases, which store the genetic information in the DNA and RNA are pyridone derivatives. Additionally, a number of vitamins are based on these two groups of substances.
This thesis aims to answer the question of how the electronic structure of these classes of molecules is modified, enabling the versatile natural functionality. The resulting insights into the effect of constitutional and external factors are expected to facilitate the design of new processes for medicine, light-harvesting, catalysis, and environmental remediation.
The common denominator of pyridones and porphyrins is their aromatic character. As aromaticity was an early-on topic in chemical physics, the overview of relevant theoretical models in this work also mirrors the development of this scientific field in the 20th century. The spectroscopic investigation of these compounds has long been centered on their global, optical transition between frontier orbitals.
The utilization and advancement of X-ray spectroscopic methods characterizing the local electronic structure of molecular samples form the core of this thesis. The element selectivity of the near-edge X-ray absorption fine structure (NEXAFS) is employed to probe the unoccupied density of states at the nitrogen site, which is key for the chemical reactivity of pyridones and porphyrins. The results contribute to the growing database of NEXAFS features and their interpretation, e.g., by advancing the debate on the porphyrin N K-edge through systematic experimental and theoretical arguments. Further, a state-of-the-art laser pump – NEXAFS probe scheme is used to characterize the relaxation pathway of a photoexcited porphyrin on the atomic level.
Resonant inelastic X-ray scattering (RIXS) provides complementary results by accessing the highest occupied valence levels including symmetry information. It is shown that RIXS is an effective experimental tool to gain detailed information on charge densities of individual species in tautomeric mixtures. Additionally, the hRIXS and METRIXS high-resolution RIXS spectrometers, which have been in part commissioned in the course of this thesis, will gain access to the ultra-fast and thermal chemistry of pyridones, porphyrins, and many other compounds.
With respect to both classes of bio-inspired aromatic molecules, this thesis establishes that even though pyridones and porphyrins differ largely by their optical absorption bands and hydrogen bonding abilities, they all share a global stabilization of local constitutional changes and relevant external perturbation. It is because of this wide-ranging response that pyridones and porphyrins can be applied in a manifold of biological and technical processes.
Steric hindrance of hydration and hydrogen bond enhancement by localized charges have been identified as key factors for the massive chemical differences between the hydroxypyridine/pyridone isomers in aqueous solution. While all isomers occur mainly in the hydroxypyridine form in the gas phase, they differ by more than 3 orders of magnitude both in their acidity and tautomeric equilibrium constants upon hydration. By monitoring the electronic and solvation structures as a function of the protonation state and the O- substitution position on the pyridine ring, the amplification of the isomeric differences in aqueous solution has been investigated. Near-edge X-ray absorption fine structure (NEXAFS) measurements at the N K-edge served as the probe of the chemical state. The combination of molecular dynamics simulations, complete active space self-consistent field (CASSCF), and time-dependent density functional theory (TD-DFT) spectral calculations contributes to unraveling the principles of tautomerism and acidity in multiple biochemical systems based on tautomerism.
In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining aformal proofshowing that the answer sets of a given (non-ground) logic programPcorrectly correspond to the solutions to the problem encoded byP, regardless of the problem instance. To this aim, we use a formal specification language based on ASP modules, so that each module can be proved to capture some informal aspect of the problem in an isolated way. This specification language relies on a novel definition of (possibly nested, first order)program modulesthat may incorporate local hidden atoms at different levels. Then,verifyingthe logic programPamounts to prove some kind of equivalence betweenPand its modular specification.
In order to provide further evidence of damage mechanisms predicted by the recent solid-state transformation creep (SSTC) model, direct observation of damage accumulation during creep of Al-3.85Mg was made using synchrotron X-ray refraction. X-ray refraction techniques detect the internal specific surface (i.e. surface per unit volume) on a length scale comparable to the specimen size, but with microscopic sensitivity. A significant rise in the internal specific surface with increasing creep time was observed, providing evidence for the creation of a fine grain substructure, as predicted by the SSTC model. This substructure was also observed by scanning electron microscopy.
The Atlantic Meridional Overturning Circulation (AMOC) is likely the most well-known system of ocean currents on Earth, redistributing heat, nutrients and carbon over a large part of the Earth’s surface and affecting global climate as a result. Due to enhanced freshwater fluxes into the subpolar North Atlantic as a response to global warming, the AMOC is expected, and may have already started, to weaken and these changes will likely have global impacts. It is therefore of considerable relevance to improve our understanding of past and future AMOC changes. My thesis tries to answer some of the open questions in this field by giving strong evidence that the AMOC has already weakened over the last century, by narrowing future projections of this slowdown and
by studying the impacts on global surface warming.
While there have been various studies trying to reconstruct the strength of the overturning circulation in the past, often based on model simulations in combination with observations (Jackson et al., 2016, Kanzow et al., 2010) or proxies (Frajka-Williams, 2015, Latif et al., 2006), the results so far, due to lack of direct measurements, have been inconclusive. In the first paper I build on previous work that links the anomalously low sea surface temperatures (SSTs) in the North Atlantic with the reduced meridional heat transport due to a weaker AMOC. Using the output of a high-resolution global climate model, I derive a characteristic spatial and seasonal SST fingerprint of an AMOC slowdown and an improved SST-based AMOC index. The same fingerprint is seen in
the observational SSTs since the late 19th Century, giving strong evidence that since then the AMOC has slowed down. In addition, the reconstruction of the historical overturning strength with the new AMOC index agrees well with and extends the results of earlier studies as well as the direct measurements from the RAPID project and shows a strong decline of the AMOC by about 15% (3±1 Sv) since the mid-20th Century (Caesar et al., 2018).
The reconstruction of the historical overturning strength with the AMOC index enables us to weight future AMOC projections based on their skill in modeling the historical AMOC as described in the second paper of this thesis (Olson et al., 2018). Using Bayesian model averaging we considerably narrow the projections of the CMIP5 ensemble to a decrease of -4.0 Sv and -6.8 Sv between the years 1960-1999 and 2060-2099 for the RCP4.5 and RCP8.5 emission scenarios, respectively. These values fit to, yet are at the lower end of, previously published estimates.
In the third paper I examine how the AMOC slowdown affects the global mean surface temperature (GMST) with a focus on how it will change the ocean heat uptake (OHC). Accounting for the effect of changes in the radiative forcing on the GMST, I test how AMOC variations correlate with the residual part of surface temperature changes in the past. I find that the correlation is positive which fits the understanding that the deep-water formation that is important in driving the AMOC cools the deep ocean and therefore warms the surface (Caesar et al., 2019). The future weakening of the overturning circulation could therefore delay global surface warming.
Due to nonlinear behavior and scale specific changes it can be difficult to study the dominant processes and modes that drive climate variability. In the fourth paper we develop and test a new technique based on the wavelet multiscale correlation (WMC) similarity measure to study climate variability on different temporal and spatial scales (Agarwal et al., 2018). In a fifth contribution to my thesis this method is applied to the observed sea surface temperatures. The results reconfirm well-known relations between SST anomalies such as the El Niño-Southern Oscillation (ENSO) and the Pacific Decadal Oscillation (PDO) on inter-annual and decadal timescales, respectively. They
furthermore give new insights into the characteristics and origins of long-range teleconnections, for example, that the teleconnection between ENSO and Indian Ocean dipole exist mainly between the northern part of the ENSO tongue and the equatorial Indian Ocean, and provides therefore valuable knowledge about the regions that are necessary to include when modeling regional climate variability at a certain scale (Agarwal et al., 2019).
In summary, my PhD thesis investigates past and future AMOC variability and its effects on global mean surface temperature by utilizing a combination of observational sea surface data and the output of historical and future climate model simulations from both the high-resolution CM2.6 model as well as the CMIP5 ensemble. It further includes the development and validation of a new method to study climate variability, that, applied to the observed sea surface temperatures, gives new insight about teleconnections in the Earth System. My findings provide evidence that the AMOC has already slowed down, will continue to do so in the future, and will impact the global mean temperature. Further impacts of an AMOC slowdown may include increased sea-level rise at the U.S. east coast (Ezer, 2015), heat extremes in Europe (Duchez et al., 2016) and increased storm activity in the North Atlantic region (Jackson et al., 2015), all of which have significant socio-economic implications.
In their comment on our paper (Caesar et al 2020 Environ. Res. Lett. 15 024003), Chen and Tung (hereafter C&T) argue that our analysis, showing that over the last decades Atlantic meridional overturning circulation (AMOC) strength and global mean surface temperature (GMST) were positively correlated, is incorrect. Their claim is mainly based on two arguments, neither of which is justified: first, C&T claim that our analysis is based on 'established evidence' that was only true for preindustrial conditions-this is not the case. Using data from the modern period (1947-2012), we show that the established understanding (i.e. deep-water formation in the North Atlantic cools the deep ocean and warms the surface) is correct, but our analysis is not based on this fact. Secondly, C&T claim that our results are based on a statistical analysis of only one cycle of data which was furthermore incorrectly detrended. This, too, is not true. Our conclusion that a weaker AMOC delays the current surface warming rather than enhances it, is based on several independent lines of evidence. The data we show to support this covers more than one cycle and the detrending (which was performed to avoid spurious correlations due to a common trend) does not affect our conclusion: the correlation between AMOC strength and GMST is positive. We do not claim that this is strong evidence that the two time series are in phase, but rather that this means that the two time series are not anti-correlated.
According to established understanding, deep-water formation in the North Atlantic and Southern Ocean keeps the deep ocean cold, counter-acting the downward mixing of heat from the warmer surface waters in the bulk of the world ocean. Therefore, periods of strong Atlantic meridional overturning circulation (AMOC) are expected to coincide with cooling of the deep ocean and warming of the surface waters. It has recently been proposed that this relation may have reversed due to global warming, and that during the past decades a strong AMOC coincides with warming of the deep ocean and relative cooling of the surface, by transporting increasingly warmer waters downward. Here we present multiple lines of evidence, including a statistical evaluation of the observed global mean temperature, ocean heat content, and different AMOC proxies, that lead to the opposite conclusion: even during the current ongoing global temperature rise a strong AMOC warms the surface. The observed weakening of the AMOC has therefore delayed global surface warming rather than enhancing it.
Social Media Abstract:
The overturning circulation in the Atlantic Ocean has weakened in response to global warming, as predicted by climate models. Since it plays an important role in transporting heat, nutrients and carbon, a slowdown will affect global climate processes and the global mean temperature. Scientists have questioned whether this slowdown has worked to cool or warm global surface temperatures. This study analyses the overturning strength and global mean temperature evolution of the past decades and shows that a slowdown acts to reduce the global mean temperature. This is because a slower overturning means less water sinks into the deep ocean in the subpolar North Atlantic. As the surface waters are cold there, the sinking normally cools the deep ocean and thereby indirectly warms the surface, thus less sinking implies less surface warming and has a cooling effect. For the foreseeable future, this means that the slowing of the overturning will likely continue to slightly reduce the effect of the general warming due to increasing greenhouse gas concentrations.
According to established understanding, deep-water formation in the North Atlantic and Southern Ocean keeps the deep ocean cold, counter-acting the downward mixing of heat from the warmer surface waters in the bulk of the world ocean. Therefore, periods of strong Atlantic meridional overturning circulation (AMOC) are expected to coincide with cooling of the deep ocean and warming of the surface waters. It has recently been proposed that this relation may have reversed due to global warming, and that during the past decades a strong AMOC coincides with warming of the deep ocean and relative cooling of the surface, by transporting increasingly warmer waters downward. Here we present multiple lines of evidence, including a statistical evaluation of the observed global mean temperature, ocean heat content, and different AMOC proxies, that lead to the opposite conclusion: even during the current ongoing global temperature rise a strong AMOC warms the surface. The observed weakening of the AMOC has therefore delayed global surface warming rather than enhancing it.
Social Media Abstract:
The overturning circulation in the Atlantic Ocean has weakened in response to global warming, as predicted by climate models. Since it plays an important role in transporting heat, nutrients and carbon, a slowdown will affect global climate processes and the global mean temperature. Scientists have questioned whether this slowdown has worked to cool or warm global surface temperatures. This study analyses the overturning strength and global mean temperature evolution of the past decades and shows that a slowdown acts to reduce the global mean temperature. This is because a slower overturning means less water sinks into the deep ocean in the subpolar North Atlantic. As the surface waters are cold there, the sinking normally cools the deep ocean and thereby indirectly warms the surface, thus less sinking implies less surface warming and has a cooling effect. For the foreseeable future, this means that the slowing of the overturning will likely continue to slightly reduce the effect of the general warming due to increasing greenhouse gas concentrations.
Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption-the phase-separation curve between the adsorbed and desorbed states of the PEs-as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE-SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption-desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.
In view of the importance of charge storage in polymer electrets for electromechanical transducer applications, the aim of this work is to contribute to the understanding of the charge-retention mechanisms. Furthermore, we will try to explain how the long-term storage of charge carriers in polymeric electrets works and to identify the probable trap sites. Charge trapping and de-trapping processes were investigated in order to obtain evidence of the trap sites in polymeric electrets. The charge de-trapping behavior of two particular polymer electrets was studied by means of thermal and optical techniques. In order to obtain evidence of trapping or de-trapping, charge and dipole profiles in the thickness direction were also monitored. In this work, the study was performed on polyethylene terephthalate (PETP) and on cyclic-olefin copolymers (COCs). PETP is a photo-electret and contains a net dipole moment that is located in the carbonyl group (C = O). The electret behavior of PETP arises from both the dipole orientation and the charge storage. In contrast to PETP, COCs are not photo-electrets and do not exhibit a net dipole moment. The electret behavior of COCs arises from the storage of charges only. COC samples were doped with dyes in order to probe their internal electric field. COCs show shallow charge traps at 0.6 and 0.11 eV, characteristic for thermally activated processes. In addition, deep charge traps are present at 4 eV, characteristic for optically stimulated processes. PETP films exhibit a photo-current transient with a maximum that depends on the temperature with an activation energy of 0.106 eV. The pair thermalization length (rc) calculated from this activation energy for the photo-carrier generation in PETP was estimated to be approx. 4.5 nm. The generated photo-charge carriers can recombine, interact with the trapped charge, escape through the electrodes or occupy an empty trap. PETP possesses a small quasi-static pyroelectric coefficient (QPC): ~0.6 nC/(m²K) for unpoled samples, ~60 nC/(m²K) for poled samples and ~60 nC/(m²K) for unpoled samples under an electric bias (E ~10 V/µm). When stored charges generate an internal electric field of approx. 10 V/µm, they are able to induce a QPC comparable to that of the oriented dipoles. Moreover, we observe charge-dipole interaction. Since the raw data of the QPC-experiments on PETP samples is noisy, a numerical Fourier-filtering procedure was applied. Simulations show that the data analysis is reliable when the noise level is up to 3 times larger than the calculated pyroelectric current for the QPC. PETP films revealed shallow traps at approx. 0.36 eV during thermally-stimulated current measurements. These energy traps are associated with molecular dipole relaxations (C = O). On the other hand, photo-activated measurements yield deep charge traps at 4.1 and 5.2 eV. The observed wavelengths belong to the transitions in PETP that are analogous to the π - π* benzene transitions. The observed charge de-trapping selectivity in the photocharge decay indicates that the charge detrapping is from a direct photon-charge interaction. Additionally, the charge de-trapping can be facilitated by photo-exciton generation and the interaction of the photo-excitons with trapped charge carriers. These results indicate that the benzene rings (C6H4) and the dipolar groups (C = O) can stabilize and share an extra charge carrier in a chemical resonance. In this way, this charge could be de-trapped in connection with the photo-transitions of the benzene ring and with the dipole relaxations. The thermally-activated charge release shows a difference in the trap depth to its optical counterpart. This difference indicates that the trap levels depend on the de-trapping process and on the chemical nature of the trap site. That is, the processes of charge detrapping from shallow traps are related to secondary forces. The processes of charge de-trapping from deep traps are related to primary forces. Furthermore, the presence of deep trap levels causes the stability of the charge for long periods of time.
In the frame of a world fighting a dramatic global warming caused by human-related activities, research towards the development of renewable energies plays a crucial role. Solar energy is one of the most important clean energy sources and its role in the satisfaction of the global energy demand is set to increase. In this context, a particular class of materials captured the attention of the scientific community for its attractive properties: halide perovskites. Devices with perovskite as light-absorber saw an impressive development within the last decade, reaching nowadays efficiencies comparable to mature photovoltaic technologies like silicon solar cells. Yet, there are still several roadblocks to overcome before a wide-spread commercialization of this kind of devices is enabled. One of the critical points lies at the interfaces: perovskite solar cells (PSCs) are made of several layers with different chemical and physical features. In order for the device to function properly, these properties have to be well-matched.
This dissertation deals with some of the challenges related to interfaces in PSCs, with a focus on the interface between the perovskite material itself and the subsequent charge transport layer. In particular, molecular assemblies with specific properties are deposited on the perovskite surface to functionalize it. The functionalization results in energy level alignment adjustment, interfacial losses reduction, and stability improvement.
First, a strategy to tune the perovskite’s energy levels is introduced: self-assembled monolayers of dipolar molecules are used to functionalize the surface, obtaining simultaneously a shift in the vacuum level position and a saturation of the dangling bonds at the surface. A shift in the vacuum level corresponds to an equal change in work function, ionization energy, and electron affinity. The direction of the shift depends on the direction of the collective interfacial dipole. The magnitude of the shift can be tailored by controlling the deposition parameters, such as the concentration of the solution used for the deposition. The shift for different molecules is characterized by several non-invasive techniques, including in particular Kelvin probe. Overall, it is shown that it is possible to shift the perovskite energy levels in both directions by several hundreds of meV. Moreover, interesting insights on the molecules deposition dynamics are revealed.
Secondly, the application of this strategy in perovskite solar cells is explored. Devices with different perovskite compositions (“triple cation perovskite” and MAPbBr3) are prepared. The two resulting model systems present different energetic offsets at the perovskite/hole-transport layer interface. Upon tailored perovskite surface functionalization, the devices show a stabilized open circuit voltage (Voc) enhancement of approximately 60 meV on average for devices with MAPbBr3, while the impact is limited on triple-cation solar cells. This suggests that the proposed energy level tuning method is valid, but its effectiveness depends on factors such as the significance of the energetic offset compared to the other losses in the devices.
Finally, the above presented method is further developed by incorporating the ability to interact with the perovskite surface directly into a novel hole-transport material (HTM), named PFI. The HTM can anchor to the perovskite halide ions via halogen bonding (XB). Its behaviour is compared to that of another HTM (PF) with same chemical structure and properties, except for the ability of forming XB. The interaction of perovskite with PFI and PF is characterized through UV-Vis, atomic force microscopy and Kelvin probe measurements combined with simulations. Compared to PF, PFI exhibits enhanced resilience against solvent exposure and improved energy level alignment with the perovskite layer. As a consequence, devices comprising PFI show enhanced Voc and operational stability during maximum-power-point tracking, in addition to hysteresis reduction. XB promotes the formation of a high-quality interface by anchoring to the halide ions and forming a stable and ordered interfacial layer, showing to be a particularly interesting candidate for the development of tailored charge transport materials in PSCs.
Overall, the results exposed in this dissertation introduce and discuss a versatile tool to functionalize the perovskite surface and tune its energy levels. The application of this method in devices is explored and insights on its challenges and advantages are given. Within this frame, the results shed light on XB as ideal interaction for enhancing stability and efficiency in perovskite-based devices.
Fires are a fundamental part of the Earth System. In the last decades, they have been altering ecosystem structure, biogeochemical cycles and atmospheric composition with unprecedented rapidity. In this study, we implement a complex networks-based methodology to track individual fires over space and time. We focus on extreme fires-the 5% most intense fires-in the tropical forests of the Brazilian Legal Amazon over the period 2002-2019. We analyse the interannual variability in the number and spatial patterns of extreme forest fires in years with diverse climatic conditions and anthropogenic pressure to examine potential synergies between climate and anthropogenic drivers. We observe that major droughts, that increase forest flammability, co-occur with high extreme fire years but also that it is fundamental to consider anthropogenic activities to understand the distribution of extreme fires. Deforestation fires, fires escaping from managed lands, and other types of forest degradation and fragmentation provide the ignition sources for fires to ignite in the forests. We find that all extreme forest fires identified are located within a 0.5-km distance from forest edges, and up to 56% of them are within a 1-km distance from roads (which increases to 73% within 5 km), showing a strong correlation that defines spatial patterns of extreme fires.
Electromagnetic ion cyclotron waves have long been recognized to play a crucial role in the dynamic loss of ring current protons. While the field-aligned propagation approximation of electromagnetic ion cyclotron waves was widely used to quantify the scattering loss of ring current protons, in this study, we find that the wave normal distribution strongly affects the pitch angle scattering efficiency of protons. Increase of peak normal angle or angular width can considerably reduce the scattering rates of <= 10 keV protons. For >10 keV protons, the field-aligned propagation approximation results in a pronounced underestimate of the scattering of intermediate equatorial pitch angle protons and overestimates the scattering of high equatorial pitch angle protons by orders of magnitude. Our results suggest that the wave normal distribution of electromagnetic ion cyclotron waves plays an important role in the pitch angle evolution and scattering loss of ring current protons and should be incorporated in future global modeling of ring current dynamics.
The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.
The incorporation of even small amounts of strontium (Sr) into lead-base hybrid quadruple cation perovskite solar cells results in a systematic increase of the open circuit voltage (V-oc) in pin-type perovskite solar cells. We demonstrate via absolute and transient photoluminescence (PL) experiments how the incorporation of Sr significantly reduces the non-radiative recombination losses in the neat perovskite layer. We show that Sr segregates at the perovskite surface, where it induces important changes of morphology and energetics. Notably, the Sr-enriched surface exhibits a wider band gap and a more n-type character, accompanied with significantly stronger surface band bending. As a result, we observe a significant increase of the quasi-Fermi level splitting in the neat perovskite by reduced surface recombination and more importantly, a strong reduction of losses attributed to non-radiative recombination at the interface to the C-60 electron-transporting layer. The resulting solar cells exhibited a V-oc of 1.18 V, which could be further improved to nearly 1.23 V through addition of a thin polymer interlayer, reducing the non-radiative voltage loss to only 110 meV. Our work shows that simply adding a small amount of Sr to the precursor solutions induces a beneficial surface modification in the perovskite, without requiring any post treatment, resulting in high efficiency solar cells with power conversion efficiency (PCE) up to 20.3%. Our results demonstrate very high V-oc values and efficiencies in Sr-containing quadruple cation perovskite pin-type solar cells and highlight the imperative importance of addressing and minimizing the recombination losses at the interface between perovskite and charge transporting layer.
With the advent of big data and data lakes, data are often integrated from multiple sources. Such integrated data are often of poor quality, due to inconsistencies, errors, and so forth. One way to check the quality of data is to infer functional dependencies (fds). However, in many modern applications it might be necessary to extract properties and relationships that are not captured through fds, due to the necessity to admit exceptions, or to consider similarity rather than equality of data values. Relaxed fds (rfds) have been introduced to meet these needs, but their discovery from data adds further complexity to an already complex problem, also due to the necessity of specifying similarity and validity thresholds. We propose Domino, a new discovery algorithm for rfds that exploits the concept of dominance in order to derive similarity thresholds of attribute values while inferring rfds. An experimental evaluation on real datasets demonstrates the discovery performance and the effectiveness of the proposed algorithm.
Simulations of the inner magnetospheric energetic electrons using the IMPTAM-VERB coupled model
(2019)
In this study, we present initial results of the coupling between the Inner Magnetospheric Particle Transport and Acceleration Model (IMPTAM) and the Versatile Electron Radiation Belt (VERB-3D) code. IMPTAM traces electrons of 10-100 keV energies from the plasma sheet (L = 9 Re) to inner L-shell regions. The flux evolution modeled by IMPTAM is used at the low energy and outer L* computational boundaries of the VERB code (assuming a dipole approximation) to perform radiation belt simulations of energetic electrons. The model was tested on the March 17th, 2013 storm, for a six-day period. Four different simulations were performed and their results compared to satellites observations from Van Allen probes and GOES. The coupled IMPTAM-VERB model reproduces evolution and storm-time features of electron fluxes throughout the studied storm in agreement with the satellite data (within similar to 0.5 orders of magnitude). Including dynamics of the low energy population at L* = 6.6 increases fluxes closer to the heart of the belt and has a strong impact in the VERB simulations at all energies. However, inclusion of magnetopause losses leads to drastic flux decreases even below L* = 3. The dynamics of low energy electrons (max. 10s of keV) do not affect electron fluxes at energies >= 900 keV. Since the IMPTAM-VERB coupled model is only driven by solar wind parameters and the Dst and Kp indexes, it is suitable as a forecasting tool. In this study, we demonstrate that the estimation of electron dynamics with satellite-data-independent models is possible and very accurate.
A reliable inference of networks from data is of key interest in many scientific fields. Several methods have been suggested in the literature to reliably determine links in a network. These techniques rely on statistical methods, typically controlling the number of false positive links, but not considering false negative links. In this thesis new methodologies to improve network inference are suggested. Initial analyses demonstrate the impact of falsepositive and false negative conclusions about the presence or absence of links on the resulting inferred network. Consequently, revealing the importance of making well-considered choices leads to suggest new approaches to enhance existing network reconstruction methods.
A simulation study, presented in Chapter 3, shows that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. The existence of type I and type II errors in the reconstructed network, also called biased network, is accepted. Consequently, an analytic method that describes the influence of these two errors on the network structure is explored. As a result of this analysis, an analytic formula of the density of the biased vertex degree distribution is found (Chapter 4).
In the inverse problem, the vertex degree distribution of the true underlying network is analytically reconstructed, assuming the probabilities of type I and type II errors. Chapters 4-5 show that the method is robust to incorrect estimates of α and β within reasonable limits. In Chapter 6, an iterative procedure to enhance this method is presented in the case of large errors on the estimates of α and β.
The investigations presented so far focus on the influence of false positive and false negative links on the network characteristics. In Chapter 7, the analysis is reversed - the study focuses on the influence of network characteristics on the probability of type I and type II errors, in the case of networks of coupled oscillators. The probabilities of α and β are influenced by the shortest path length and the detour degree, respectively. These results have been used to improve the network reconstruction, when the true underlying network is not known a priori, introducing a novel and advanced concept of threshold.
When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is analytically analyzed. Moreover, an analytic formula of the density of the biased vertex degree distribution is found. In the inverse problem, we find a reliable procedure to reconstruct analytically the density of the vertex degree distribution of any network based on the inferred network and estimates for the false positive and false negative errors based on, e.g., simulation studies.
Improving network inference
(2018)
Background: A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely on statistical inference, typically controlling the number of false positives, paying little attention to false negatives. New method: In this paper, by means of a comprehensive simulation study, we analyse the influence of false positive and false negative conclusions about the presence or absence of links in a network on the network topology. We show that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. We propose to run careful simulation studies prior to making potentially erroneous conclusion about the network topology. Results: Our analysis shows that optimal values to balance false positive and false negative conclusions about links depend on the network topology and characteristic of interest. Comparison with existing methods: Existing methods rely on a choice of the rate for false positive conclusions. They aim to be sure about individual links rather than the entire network. The rate of false negative conclusions is typically not investigated. Conclusions: Our investigation shows that the balance of false positive and false negative conclusions about links in a network has to be tuned for any network topology that is to be estimated. Moreover, within the same network topology, the results are qualitatively the same for each network characteristic, but the actual values leading to reliable estimates of the characteristics are different.