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The occurrence of earthquakes is characterized by a high degree of spatiotemporal complexity. Although numerous patterns, e.g. fore- and aftershock sequences, are well-known, the underlying mechanisms are not observable and thus not understood. Because the recurrence times of large earthquakes are usually decades or centuries, the number of such events in corresponding data sets is too small to draw conclusions with reasonable statistical significance. Therefore, the present study combines both, numerical modeling and analysis of real data in order to unveil the relationships between physical mechanisms and observational quantities. The key hypothesis is the validity of the so-called "critical point concept" for earthquakes, which assumes large earthquakes to occur as phase transitions in a spatially extended many-particle system, similar to percolation models. New concepts are developed to detect critical states in simulated and in natural data sets. The results indicate that important features of seismicity like the frequency-size distribution and the temporal clustering of earthquakes depend on frictional and structural fault parameters. In particular, the degree of quenched spatial disorder (the "roughness") of a fault zone determines whether large earthquakes occur quasiperiodically or more clustered. This illustrates the power of numerical models in order to identify regions in parameter space, which are relevant for natural seismicity. The critical point concept is verified for both, synthetic and natural seismicity, in terms of a critical state which precedes a large earthquake: a gradual roughening of the (unobservable) stress field leads to a scale-free (observable) frequency-size distribution. Furthermore, the growth of the spatial correlation length and the acceleration of the seismic energy release prior to large events is found. The predictive power of these precursors is, however, limited. Instead of forecasting time, location, and magnitude of individual events, a contribution to a broad multiparameter approach is encouraging.
One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences.
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.
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.
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.
The behaviour of an adhering cell is strongly influenced by the chemical, topographical and mechanical properties of the surface it attaches to. During recent years, it has been found experimentally that adhering cells actively sense the elastic properties of their environment by pulling on it through numerous sites of adhesion. The resulting build-up of force at sites of adhesion depends on the elastic properties of the environment and is converted into corresponding biochemical signals, which can trigger cellular programmes like growth, differentiation, apoptosis, and migration. In general, force is an important regulator of biological systems, for example in hearing and touch, in wound healing, and in rolling adhesion of leukocytes on vessel walls. In the habilitation thesis by Ulrich Schwarz, several theoretical projects are presented which address the role of forces and elasticity in cell adhesion. (1) A new method has been developed for calculating cellular forces exerted at sites of focal adhesion on micro-patterned elastic substrates. The main result is that cell-matrix contacts function as mechanosensors, converting internal force into protein aggregation. (2) A one-step master equation for the stochastic dynamics of adhesion clusters as a function of cluster size, rebinding rate and force has been solved both analytically and numerically. Moreover this model has been applied to the regulation of cell-matrix contacts, to dynamic force spectroscopy, and to rolling adhesion. (3) Using linear elasticity theory and the concept of force dipoles, a model has been introduced and solved which predicts the positioning and orientation of mechanically active cells in soft material, in good agreement with experimental observations for fibroblasts on elastic substrates and in collagen gels.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
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.
It has been known for several years that under certain conditions electrons can be confined within thin layers even if these layers consist of metal and are supported by a metal substrate. In photoelectron spectra, these layers show characteristic discrete energy levels and it has turned out that these lead to large effects like the oscillatory magnetic coupling technically exploited in modern hard disk reading heads. The current work asks in how far the concepts underlying quantization in two-dimensional films can be transferred to lower dimensionality. This problem is approached by a stepwise transition from two-dimensional layers to one-dimensional nanostructures. On the one hand, these nanostructures are represented by terraces on atomically stepped surfaces, on the other hand by atom chains which are deposited onto these terraces up to complete coverage by atomically thin nanostripes. Furthermore, self organization effects are used in order to arrive at perfectly one-dimensional atomic arrangements at surfaces. Angle-resolved photoemission is particularly suited as method of investigation because is reveals the behavior of the electrons in these nanostructures in dependence of the spacial direction which distinguishes it from, e. g., scanning tunneling microscopy. With this method intense and at times surprisingly large effects of one-dimensional quantization are observed for various exemplary systems, partly for the first time. The essential role of bandgaps in the substrate known from two-dimensional systems is confirmed for nanostructures. In addition, we reveal an ambiguity without precedent in two-dimensional layers between spacial confinement of electrons on the one side and superlattice effects on the other side as well as between effects caused by the sample and by the measurement process. The latter effects are huge and can dominate the photoelectron spectra. Finally, the effects of reduced dimensionality are studied in particular for the d electrons of manganese which are additionally affected by strong correlation effects. Surprising results are also obtained here. ---------------------------- Die Links zur jeweiligen Source der im Appendix beigefügten Veröffentlichungen befinden sich auf Seite 83 des Volltextes.