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On the effects of disorder on the ability of oscillatory or directional dynamics to synchronize
(2024)
In this thesis I present a collection of publications of my work, containing analytic results and observations in numerical experiments on the effects of various inhomogeneities, on the ability of coupled oscillators to synchronize their collective dynamics. Most of these works are concerned with the effects of Gaussian and non-Gaussian noise acting on the phase of autonomous oscillators (Secs. 2.1-2.4) or on the direction of higher dimensional state vectors (Secs. 2.5,2.6). I obtain exact and approximate solutions to the non-linear equations governing the distributions of phases, or perform linear stability analysis of the uniform distribution to obtain the transition point from a completely disordered state to partial order or more complicated collective behavior. Other inhomogeneities, that can affect synchronization of coupled oscillators, are irregular, chaotic oscillations or a complex, and possibly random structure in the coupling network. In Section 2.9 I present a new method to define the phase- and frequency linear response function for chaotic oscillators. In Sections 2.4, 2.7 and 2.8 I study synchronization in complex networks of coupled oscillators. Each section in Chapter 2 - Manuscripts, is devoted to one research paper and begins with a list of the main results, a description of my contributions to the work and a short account of the scientific context, i.e. the questions and challenges which started the research and the relation of the work to my other research projects. The manuscripts in this thesis are reproductions of the arXiv versions, i.e. preprints under the creative commons licence.
Synchronization of coupled oscillators manifests itself in many natural and man-made systems, including cyrcadian clocks, central pattern generators, laser arrays, power grids, chemical and electrochemical oscillators, only to name a few. The mathematical description of this phenomenon is often based on the paradigmatic Kuramoto model, which represents each oscillator by one scalar variable, its phase. When coupled, phase oscillators constitute a high-dimensional dynamical system, which exhibits complex behaviour, ranging from synchronized uniform oscillation to quasiperiodicity and chaos. The corresponding collective rhythms can be useful or harmful to the normal operation of various systems, therefore they have been the subject of much research.
Initially, synchronization phenomena have been studied in systems with all-to-all (global) and nearest-neighbour (local) coupling, or on random networks. However, in recent decades there has been a lot of interest in more complicated coupling structures, which take into account the spatially distributed nature of real-world oscillator systems and the distance-dependent nature of the interaction between their components. Examples of such systems are abound in biology and neuroscience. They include spatially distributed cell populations, cilia carpets and neural networks relevant to working memory. In many cases, these systems support a rich variety of patterns of synchrony and disorder with remarkable properties that have not been observed in other continuous media. Such patterns are usually referred to as the coherence-incoherence patterns, but in symmetrically coupled oscillator systems they are also known by the name chimera states.
The main goal of this work is to give an overview of different types of collective behaviour in large networks of spatially distributed phase oscillators and to develop mathematical methods for their analysis. We focus on the Kuramoto models for one-, two- and three-dimensional oscillator arrays with nonlocal coupling, where the coupling extends over a range wider than nearest neighbour coupling and depends on separation. We use the fact that, for a special (but still quite general) phase interaction function, the long-term coarse-grained dynamics of the above systems can be described by a certain integro-differential equation that follows from the mathematical approach called the Ott-Antonsen theory. We show that this equation adequately represents all relevant patterns of synchrony and disorder, including stationary, periodically breathing and moving coherence-incoherence patterns. Moreover, we show that this equation can be used to completely solve the existence and stability problem for each of these patterns and to reliably predict their main properties in many application relevant situations.
Intermolekulare Desaktivierung zwischen einem angeregten Fluorophor und einem Löscher durch Elektronenübertragung kann mit dynamischer und statischer Löschung beschrieben werden. Es wird vorgeschlagen den dynamischen Löschprozess in Transport- und Wechselwirkungsphase einzuteilen. Ergebnisse der Löschung der N-Heteroarene durch Naphthalen bei hohen Löscherkonzentrationen werden mit der statischen Löschung beschrieben. Außerdem werden CT-Systeme untersucht. Nach einem Überblick über statische Modelle zum Resonanzenergietransfer wird ein aus der Treffertheorie abgeleitetes Modell vorgestellt und an Beispielen getestet. Die Experimente sind computergesteuert.
The habilitation deals with the numerical analysis of the recurrence properties of geological and climatic processes. The recurrence of states of dynamical processes can be analysed with recurrence plots and various recurrence quantification options. In the present work, the meaning of the structures and information contained in recurrence plots are examined and described. New developments have led to extensions that can be used to describe the recurring patterns in both space and time. Other important developments include recurrence plot-based approaches to identify abrupt changes in the system's dynamics, to detect and investigate external influences on the dynamics of a system, the couplings between different systems, as well as a combination of recurrence plots with the methodology of complex networks. Typical problems in geoscientific data analysis, such as irregular sampling and uncertainties, are tackled by specific modifications and additions. The development of a significance test allows the statistical evaluation of quantitative recurrence analysis, especially for the identification of dynamical transitions. Finally, an overview of typical pitfalls that can occur when applying recurrence-based methods is given and guidelines on how to avoid such pitfalls are discussed. In addition to the methodological aspects, the application potential especially for geoscientific research questions is discussed, such as the identification and analysis of transitions in past climates, the study of the influence of external factors to ecological or climatic systems, or the analysis of landuse dynamics based on remote sensing data.
Ferroelectrets are internally charged polymer foams or cavity-containing polymer-_lm systems that combine large piezoelectricity with mechanical flexibility and elastic compliance. The term “ferroelectret” was coined based on the fact that it is a space-charge electret that also shows ferroic behavior. In this thesis, comprehensive work on ferroelectrets, and in particular on their preparation, their charging, their piezoelectricity and their applications is reported.
For industrial applications, ferroelectrets with well-controlled distributions or even uniform values of cavity size and cavity shape and with good thermal stability of the piezoelectricity are very desirable. Several types of such ferroelectrets are developed using techniques such as straightforward thermal lamination, sandwiching sticky templates with electret films, and screen printing. In particular, uoroethylenepropylene (FEP) _lm systems with tubular-channel openings, prepared by means of the thermal lamination technique, show piezoelectric d33 coefficients of up to 160 pC/N after charging through dielectric barrier discharges (DBDs) . For samples charged at suitable elevated temperatures, the piezoelectricity is stable at temperatures of at least 130°C. These preparation methods are easy to implement at laboratory or industrial scales, and are quite flexible in terms of material selection and cavity geometry design. Due to the uniform and well-controlled cavity structures, samples are also very suitable for fundamental studies on ferroelectrets.
Charging of ferroelectrets is achieved via a series of dielectric barrier discharges (DBDs) inside the cavities. In the present work, the DBD charging process is comprehensively studied by means of optical, electrical and electro-acoustic methods. The spectrum of the transient light from the DBDs in cellular polypropylene (PP) ferroelectrets directly confirms the ionization of molecular nitrogen, and allows the determination of the electric field in the discharge. Detection of the light emission reveals not only DBDs under high applied voltage but also back discharges when the applied voltage is reduced to sufficiently low values. Back discharges are triggered by the internally deposited charges, as the breakdown inside the cavities is controlled by the sum of the applied electric field and the electric field of the deposited charges. The remanent effective polarization is determined by the breakdown strength of the gas-filled cavities. These findings form the basis of more efficient charging techniques for ferroelectrets such as charging with high-pressure air, thermal poling and charging assisted by gas exchange. With the proposed charging strategies, the charging efficiency of ferroelectrets can be enhanced significantly.
After charging, the cavities can be considered as man-made macroscopic dipoles whose direction can be reversed by switching the polarity of the applied voltage. Polarization-versus-electric-field (P(E)) hysteresis loops in ferroelectrets are observed by means of an electro-acoustic method combined with dielectric resonance spectroscopy. P(E) hysteresis loops in ferrroelectrets are also obtained by more direct measurements using a modified Sawyer-Tower circuit. Hysteresis loops prove the ferroic behavior of ferroelectrets. However, repeated switching of the macroscopic dipoles involves complex physico-chemical processes. The DBD charging process generates a cold plasma with numerous active species and thus modifies the inner polymer surfaces of the cavities. Such treatments strongly affect the chargeability of the cavities. At least for cellular PP ferroelectrets, repeated DBDs in atmospheric conditions lead to considerable fatigue of the effective polarization and of the resulting piezoelectricity.
The macroscopic dipoles in ferroelectrets are highly compressible, and hence the piezoelectricity is essentially the primary effect. It is found that the piezoelectric d33 coefficient is proportional to the polarization and the elastic compliance of the sample, providing hints for developing materials with higher piezoelectric sensitivity in the future. Due to their outstanding electromechanical properties, there has been constant interest in the application of ferroelectrets. The antiresonance frequencies (fp) of ferroelectrets are sensitive to the boundary conditions during measurement. A tubular-channel FEP ferroelectret is conformably attached to a self-organized minimum-energy dielectric elastomer actuator (DEA). It turns out that the antiresonance frequency (fp) of the ferroelectret film changes noticeably with the bending angle of the DEA. Therefore, the actuation of DEAs can be used to modulate the fp value of ferroelectrets, but fp can also be exploited for in-situ diagnosis and for precise control of the actuation of the DEA. Combination of DEAs and ferroelectrets opens up various new possibilities for application.
Biological materials, in addition to having remarkable physical properties, can also change shape and volume. These shape and volume changes allow organisms to form new tissue during growth and morphogenesis, as well as to repair and remodel old tissues. In addition shape or volume changes in an existing tissue can lead to useful motion or force generation (actuation) that may even still function in the dead organism, such as in the well known example of the hygroscopic opening or closing behaviour of the pine cone. Both growth and actuation of tissues are mediated, in addition to biochemical factors, by the physical constraints of the surrounding environment and the architecture of the underlying tissue. This habilitation thesis describes biophysical studies carried out over the past years on growth and swelling mediated shape changes in biological systems. These studies use a combination of theoretical and experimental tools to attempt to elucidate the physical mechanisms governing geometry controlled tissue growth and geometry constrained tissue swelling. It is hoped that in addition to helping understand fundamental processes of growth and morphogenesis, ideas stemming from such studies can also be used to design new materials for medicine and robotics.
Die vorliegende Arbeit versammelt zwei einleitende Kapitel und zehn Essays, die sich als kritisch-konstruktive Beiträge zu einem "erlebenden Verstehen" (Buck) von Physik lesen lassen. Die traditionelle Anlage von Schulphysik zielt auf eine systematische Darstellung naturwissenschaftlichen Wissens, das dann an ausgewählten Beispielen angewendet wird: Schulexperimente beweisen die Aussagen der Systematik (oder machen sie wenigstens plausibel), ausgewählte Phänomene werden erklärt. In einem solchen Rahmen besteht jedoch leicht die Gefahr, den Bezug zur Lebenswirklichkeit oder den Interessen der Schüler zu verlieren. Diese Problematik ist seit mindestens 90 Jahren bekannt, didaktische Antworten - untersuchendes Lernen, Kontextualisierung, Schülerexperimente etc. - adressieren allerdings eher Symptome als Ursachen. Naturwissenschaft wird dadurch spannend, dass sie ein spezifisch investigatives Weltverhältnis stiftet: man müsste gleichsam nicht Wissen, sondern "Fragen lernen" (und natürlich auch, wie Antworten gefunden werden...). Doch wie kann dergleichen auf dem Niveau von Schulphysik aussehen, was für einen theoretischen Rahmen kann es hier geben? In den gesammelten Arbeiten wird einigen dieser Spuren nachgegangen: Der Absage an das zu modellhafte Denken in der phänomenologischen Optik, der Abgrenzung formal-mathematischen Denkens gegen wirklichkeitsnähere Formen naturwissenschaftlicher Denkbewegungen und Evidenz, dem Potential alternativer Interpretationen von "Physikunterricht", der Frage nach dem "Verstehen" u.a. Dabei werden nicht nur Bezüge zum modernen bildungstheoretischen Paradigma der Kompetenz sichtbar, sondern es wird auch versucht, eine ganze Reihe konkrete (schul-)physikalische Beispiele dafür zu geben, was passiert, wenn nicht schon gewusste Antworten Thema werden, sondern Expeditionen, die sich der physischen Welt widmen: Die Schlüsselbegriffe des Fachs, die Methoden der Datenerhebung und Interpretation, die Such- und Denkbewegungen kommen dabei auf eine Weise zur Sprache, die sich nicht auf die Fachsystematik abstützen möchte, sondern diese motivieren, konturieren und verständlich machen will.
Computational cosmology
(2008)
“Computational Cosmology” is the modeling of structure formation in the Universe by means of numerical simulations. These simulations can be considered as the only “experiment” to verify theories of the origin and evolution of the Universe. Over the last 30 years great progress has been made in the development of computer codes that model the evolution of dark matter (as well as gas physics) on cosmic scales and new research discipline has established itself. After a brief summary of cosmology we will introduce the concepts behind such simulations. We further present a novel computer code for numerical simulations of cosmic structure formation that utilizes adaptive grids to efficiently distribute the work and focus the computing power to regions of interests, respectively. In that regards we also investigate various (numerical) effects that influence the credibility of these simulations and elaborate on the procedure of how to setup their initial conditions. And as running a simulation is only the first step to modelling cosmological structure formation we additionally developed an object finder that maps the density field onto galaxies and galaxy clusters and hence provides the link to observations. Despite the generally accepted success of the cold dark matter cosmology the model still inhibits a number of deviations from observations. Moreover, none of the putative dark matter particle candidates have yet been detected. Utilizing both the novel simulation code and the halo finder we perform and analyse various simulations of cosmic structure formation investigating alternative cosmologies. These include warm (rather than cold) dark matter, features in the power spectrum of the primordial density perturbations caused by non-standard inflation theories, and even modified Newtonian dynamics. We compare these alternatives to the currently accepted standard model and highlight the limitations on both sides; while those alternatives may cure some of the woes of the standard model they also inhibit difficulties on their own. During the past decade simulation codes and computer hardware have advanced to such a stage where it became possible to resolve in detail the sub-halo populations of dark matter halos in a cosmological context. These results, coupled with the simultaneous increase in observational data have opened up a whole new window on the concordance cosmogony in the field that is now known as “Near-Field Cosmology”. We will present an in-depth study of the dynamics of subhaloes and the development of debris of tidally disrupted satellite galaxies.1 Here we postulate a new population of subhaloes that once passed close to the centre of their host and now reside in the outer regions of it. We further show that interactions between satellites inside the radius of their hosts may not be negliable. And the recovery of host properties from the distribution and properties of tidally induced debris material is not as straightforward as expected from simulations of individual satellites in (semi-)analytical host potentials.
Proteins are chain molecules built from amino acids. The precise sequence of the 20 different types of amino acids in a protein chain defines into which structure a protein folds, and the three-dimensional structure in turn specifies the biological function of the protein. The reliable folding of proteins is a prerequisite for their robust function. Misfolding can lead to protein aggregates that cause severe diseases, such as Alzheimer's, Parkinson's, or the variant Creutzfeldt-Jakob disease. Small single-domain proteins often fold without experimentally detectable metastable intermediate states. The folding dynamics of these proteins is thought to be governed by a single transition-state barrier between the unfolded and the folded state. The transition state is highly instable and cannot be observed directly. However, mutations in which a single amino acid of the protein is substituted by another one can provide indirect access. The mutations slightly change the transition-state barrier and, thus, the folding and unfolding times of the protein. The central question is how to reconstruct the transition state from the observed changes in folding times. In this habilitation thesis, a novel method to extract structural information on transition states from mutational data is presented. The method is based on (i) the cooperativity of structural elements such as alpha-helices and beta-hairpins, and (ii) on splitting up mutation-induced free-energy changes into components for these elements. By fitting few parameters, the method reveals the degree of structure formation of alpha-helices and beta-hairpins in the transition state. In addition, it is shown in this thesis that the folding routes of small single-domain proteins are dominated by loop-closure dependencies between the structural elements.
The role played by azobenzene polymers in the modern photonic, electronic and opto-mechanical applications cannot be underestimated. These polymers are successfully used to produce alignment layers for liquid crystalline fluorescent polymers in the display and semiconductor technology, to build waveguides and waveguide couplers, as data storage media and as labels in quality product protection. A very hot topic in modern research are light-driven artificial muscles based on azobenzene elastomers. The incorporation of azobenzene chromophores into polymer systems via covalent bonding or even by blending gives rise to a number of unusual effects under visible (VIS) and ultraviolet light irradiation. The most amazing effect is the inscription of surface relief gratings (SRGs) onto thin azobenzene polymer films. At least seven models have been proposed to explain the origin of the inscribing force but none of them describes satisfactorily the light induced material transport on the molecular level. In most models, to explain the mass transport over micrometer distances during irradiation at room temperature, it is necessary to assume a considerable degree of photoinduced softening, at least comparable with that at the glass transition. Contrary to this assumption, we have gathered a convincing evidence that there is no considerable softening of the azobenzene layers under illumination. Presently we can surely say that light induced softening is a very weak accompanying effect rather than a necessary condition for the formation of SRGs. This means that the inscribing force should be above the yield point of the azobenzene polymer. Hence, an appropriate approach to describe the formation and relaxation of SRGs is a viscoplastic theory. It was used to reproduce pulse-like inscription of SRGs as measured by VIS light scattering. At longer inscription times the VIS scattering pattern exhibits some peculiarities which can be explained by the appearance of a density grating that will be shown to arise due to the final compressibility of the polymer film. As a logical consequence of the aforementioned research, a thermodynamic theory explaining the light-induced deformation of free standing films and the formation of SRGs is proposed. The basic idea of this theory is that under homogeneous illumination an initially isotropic sample should stretch itself along the polarization direction to compensate the entropy decrease produced by the photoinduced reorientation of azobenzene chromophores. Finally, some ideas about further development of this controversial topic will be discussed.