Cracks often exist in structural members that are exposed to repeated loading, which will certainly lower the structural integrity. A crack on a structural member introduces a local flexibility which is a function of the crack depth and location. This may cause nonlinear dynamic response of the structure. In this thesis, a new method is suggested to detect and locate a crack in a structural component. The method is based on the fact that nonlinear response of a structure with a crack will be a function of the crack location and crack magnitude. The method suggested is the extension of a recently developed technique for identification of non-linearity in vibrating multi degree of freedom system. In this method, experimentally measured receptances at different forcing levels are used as input, and the existence and location of a nonlinearity are sought. In order to validate the method, simulated experimental data is used. Characteristics of a cracked beam are simulated by using experimentally obtained analytical expressions, given in the literature. The structure itself is modelled by using finite element method. Several case studies are performed to test and demonstrate the applicability, efficiency and sensitivity of the method suggested. The effect of crack depth on nonlinear system response is also studied in numerical examples.

No description available.

Esse trabalho consiste na determinação das velocidades críticas do vento e das amplitudes das vibrações numa estrutura composta por uma viga engastada suspensa por um estai (cabo), submetida aos efeitos de vento e chuva. Foi considerada a deformação no cabo devido ao carregamento do peso próprio e o acoplamento não-linear das vibrações do cabo e da viga. Três modos de vibração são de especial interesse, chamados de primeiro modo global (flexão da viga e vibração no cabo), primeiro modo local (vibração no cabo, com flexão na viga desprezável) e primeiro modo à torção. O modelo foi reduzido a três graus de liberdade. A modelagem dos carregamentos aerodinâmicos aplicados na viga foi feita segundo procedimentos tradicionais. O carregamento aerodinâmico aplicado ao cabo sob efeito de chuva e vento também foi levado em consideração. Para a redução do modelo matemático, os coeficientes de rigidez e de amortecimento equivalente são definidos e dependem parametricamente da velocidade do vento. Os termos não-lineares são devidos ao acoplamento das vibrações do cabo e da viga à flexão (no plano do cabo) e também aos efeitos aeroelásticos no cabo. Os seguintes regimes instáveis são avaliados: o efeito de galope (galloping) no cabo, o drapejamento (flutter) unimodal na torção e o drapejamento (flutter) do modo de flexão da viga em conjunto com vibrações transversais do cabo. / This paper is concerned with determining wind critical velocities and post-critical vibration amplitudes in a cable-stayed beam, under wind-rain condition. It is considered the cable sag due to the dead load plus the non-linear coupling between the vibration of both the cable and the beam. Three modes are of special interest, namely the first global mode (beam bending & cable vibration), the first local mode (cable vibration & negligible beam bending) and the first torsion mode. A reduced mathematical model, with three degrees of freedom, is also developed. With regard to the modelling of the aerodynamic loads applied to the beam, it can be performed after extension of classical guidelines. The aerodynamic loads applied to the cable under rain are also taken into account. For the reduced mathematical model, equivalent damping and stiffness coefficients will be defined, which depend parametrically on the wind velocity. Non-linear terms appear due to the coupling between the cable and the beam bending vibrations, and also to the aero-elastic non-linear effects on the cable. Different unstable regimes are surveyed such as the cable galloping, the unimodal flutter in torsion and the unimodal flutter with beam bending and cable vibrations coupled.

Power grids constitute an essential infrastructure providing and distributing electrical energy. The grid structure is currently subject to rapid changes due to the integration of renewable energy sources. In this development one is confronted with several challenges and opportunities as, for instance, the reduction of inertial masses in the system, the strongly increasing decentralisation of generators, and the fluctuating power feed-in by generators relying on renewable energy sources. In this thesis, models are studied that describe the non-linear power-grid dynamics in the presence of fluctuating power feed-in from renewable energy sources, primarily wind turbines. Realistic features of wind-power feed-in are captured by using real data measured at a research platform located in the North Sea. This approach is applied to test systems provided by the Institute of Electrical and Electronics Engineers (IEEE), in which one conventional generator is replaced by a wind turbine. It is found that so-called dead ends and other weakly coupled network parts are particularly prone to power fluctuations and perturbations. In contrast to previous studies, the often pronounced heterogeneities of the power grid elements are taken into account when solving the non-linear power-flow and swing equations. Also reactances between locations of power generation and power feed-in are considered, which causes the link topology in the power grid to correspond to a full graph, where all nodes are effectively connected. Both the grid heterogeneities and the additional generator reactances have a decisive impact on power grid stability. Some structures considered as particularly stable in simplified models are prone to perturbations when utilising the more realistic model and vice versa. By the analysis of various quantities characterising functional grid operation, it is shown that a reliable assessment of power grid stability requires the consideration of heterogeneities and generator reactances.

Quasi two-dimensional turbulent flows, like mesoscale oceanic and large-scale atmospheric flows, create finite-time coherent structures, compact fluid masses that resist mixing for finite-time despite the turbulent nature of the ambient flow. These coherent structures significantly affect the mixing and transport of fluid elements. In return, the transport of passive scalars like heat, humidity, salinity, chemical concentration, nutrients and even algae has a substantial impact on countless geophysical phenomena. Thus, in order to understand these effects reliable methods for coherent structure detection and the identification of their boundaries are necessary. Here, in this thesis, we present two contributions in this regard. First, we present improvements of the transfer operator approach, an established stochastic approach for the detection of almost-invariant and coherent sets. The approach approximates the transport properties of a complicated flow by a linear transfer operator and aims to partition a given domain in multiple sets such that the inter-set mass transport is minimized. The improvements include the introduction of mixing boundary conditions in stationary and time-dependent flows. By modifying the transfer operator we couple the filaments that surround the coherent and jointly rotating fluid volume such that effectively only two non-communicating sets remain: the coherent eddy core and the ambient flow. This significantly stabilizes the inference of coherent eddy cores and makes the use of popular but error-prone clustering techniques unnecessary. In addition, we discuss the identification of temporally consistent areas of increased coherence. Instead of coherent structures that are defined by advected non-filamenting masses, the concept describes consistent and moving patches of reduced mixing whose mass can change over time. This permits the decoupling of the coherence time scale from the time window under consideration. Both modifications are used to study the transport properties of eight selected Baltic Sea eddies. Secondly, we introduce the MSCS-search, a new algorithm for the inference of finite-time coherent volumes that is solely based upon the concept of convexity. Persistent convexity is a sufficient condition for coherence in two-dimensional flows if coherent structures are understood as non-filamenting volumes. However, convexity has never been considered as condition of coherence, even though some methods use it, for practical reasons, as an explicit constraint. The approach identifies the largest structure inside a given volume that remains star-convex with respect to a given reference trajectory within a given time window. We test the approach thoroughly and our results show that the approach yields good and reliable estimations of coherent structures in all test cases. Moreover, since the results depend explicitly on the considered time window, the results are intuitive and enable the identification and study of filaments. The novel approach is then used to re-evaluate transport processes in the data set of Baltic eddies.:1 Introduction 2 Theoretical Background 2.1 Methods 2.1.1 Okubo-Weiss criterion 2.1.2 Finite-Time Lyapunov Exponents 2.1.3 Lagrangian Descriptors and Lagrangian averaged vorticity deviation 2.2 Models 2.2.1 Euler equation 2.2.2 Stationary Gaussian Blob Model 2.2.3 Periodically Perturbed Gaussian Blob Model 2.2.4 Bickley-Jet 3 Transfer Operator Approach I: State of the Art 3.1 Frobenius-Perron Operator 3.2 Markov-Chains 3.3 Laplacian matrices 3.4 Finding Almost-Invariant Sets 3.5 Finding Coherent Sets 3.5.1 Coherent pairs as tuples 3.5.2 Coherent pairs as triples 3.6 Spectral Clustering 3.7 Critique and Discussion 4 Transfer Operator Approach II: Mixing Boundary Conditions in Stationary Flows 4.1 Overview 4.2 Estimation of Transfer Probability Matrices P 4.3 Mixing Boundary Conditions 4.4 Thresholding 4.5 Results 4.5.1 Robustness with respect to parameters 4.5.2 Comparison and alternatives 4.5.3 Handling of false positives 4.5.4 Periodically perturbed flow 4.6 Closing Remark 5 Transfer operator approach III: Analysis of Oceanic Transport 5.1 Mixing Boundary Conditions: Time-Dependent Flows 5.1.1 Method 5.1.2 Results 5.2 Temporal consistency 5.2.1 Method 5.2.2 Results 5.3 Treatment of Coastal Effects 5.4 Application to Baltic velocity fields 5.4.1 Method 5.4.2 Results 5.5 Closing Remark 6 Prototypes of Coherent Sets: Star-Convex Structures 6.1 Mathematical Considerations 6.2 MSCS-Algorithm 6.3 Extracting star-convex sub-volumes 6.4 Results 6.4.1 Stationary Gaussian blob model 6.4.2 Bickley-Jet 6.4.3 Two dimensional inviscid flow 6.4.4 Real data sets 6.5 Closing Remark 7 Conclusion and Outlook / Es ist bekannt, dass quasi-zweidimensionale turbulente Strömungen, wie etwa Strömungen an der Meeresoberfläche oder großskalige Atmosphärenbewegungen, kohärente Strukturen ausbilden, kompakte Volumina, welche einer Mischung mit dem umgebenden Material für endliche Zeit widerstehen, obwohl die Strömung als solche turbulent ist. Diese Strukturen haben einen signifikanten Einfluss auf den Transport von Fluidelementen. Der Transport von passiven skalaren Größen, wie etwa Wärme, Feuchtigkeit, Salzgehalt, Nährstoffgehalt, jegliche Konzentration che- mischer Stoffe und sogar Algendichte hat wiederum einen Effekt auf unzählige geophysikalische Phänomene. Um diese Phänomene im Detail zu verstehen, sind zuverlässige Methoden für die Detektion von kohärenten Strukturen und die Identifikation ihrer Grenzen notwendig. In der vorliegenden Arbeit präsentieren wir zwei Beiträge zur Lösung dieses Problems. Als erstes präsentieren wir Verbesserungen der Transferoperatormethode. Diese etablierte Methode zur Identifikation von fast-invarianten und kohärenten Mengen approximiert die Transporteigenschaften eines Flusses mithilfe eines linearen Transferoperators, mit dem Ziel, das betrachtete Gebiet in Bereiche zu unterteilen, welche den Materialaustausch zwischen den Bereichen minimieren. Die Verbesserungen beinhalten die Einführung von mischenden Randbedingungen in stationären und nicht-stationären Flüssen. Dabei wird der Transferoperator so modifiziert, dass Filamente, welche die kohärente Struktur umgeben, gekoppelt werden, was zur Folge hat, dass effektiv nur zwei nicht kommunizierende Strukturen übrig bleiben: die kohärente Struktur und das sie umgebende Volumen. Dies führt zu einer signifikant erhöhten Stabilität der Methode ohne auf die sonst üblichen aber fehleranfälligen clustering-Techniken zurückgreifen zu müssen. Des Weiteren diskutieren wir die Identifikation von zeitlich konsistenten Regionen erhöhter Kohärenz. Anstatt von kohärenten Strukturen als bewegliche nicht filamentierende Massen zu sprechen, beschreibt dieses Konzept kohärente Strukturen als konsistente sich bewegende Regionen reduzierten Mischverhaltens deren beteiligte Masse zeitlich veränderlich ist. Dies erlaubt die Entkopplung der Kohärenzzeitskala vom betrachteten Zeitfenster. Im Anschluss verwenden wir beide Modifikationen, um die Transporteigenschaften von acht ausgewählten Ostseewirbeln zu untersuchen. Als zweiten Beitrag stellen wir den MSCS-Algorithmus vor, eine neue Methode zur Identifikation von kohärenten Strukturen, welche einzig und allein auf dem Prinzip von Konvexität basiert. Versteht man kohärente Strukturen als nicht filamentierende Massen, ist persistente Konvexität eine hinreichende Bedingung für Kohärenz. Konvexität wurde bisher noch nie als Grundlage für Kohärenz untersucht, obwohl sie aus praktischen Gründen in einigen Methoden bereits als einschränkende Bedingung verwendet wird. Die Methode identifiziert die größte Struktur innerhalb eines gegebenen Volumens, welches während eines gegebenen Zeitraums stern-konvex bezüglich einer gegebenen Referenztrajektor bleibt. Alle studierten Testszenarien zeigen, dass der Ansatz gute und zuverlässige Ergebnisse liefert. Diese Ergebnisse hängen darüber hinaus direkt von den Eingangsparametern ab, was die Interpretation der Ergebnisse stark erleichtert und zusätzlich die Untersuchung von Filamentbildung erlaubt. Die neue Methode wird verwendet um den kohärenten Transport in den bereits untersuchten Ostseewirbeln zu reevaluieren.:1 Introduction 2 Theoretical Background 2.1 Methods 2.1.1 Okubo-Weiss criterion 2.1.2 Finite-Time Lyapunov Exponents 2.1.3 Lagrangian Descriptors and Lagrangian averaged vorticity deviation 2.2 Models 2.2.1 Euler equation 2.2.2 Stationary Gaussian Blob Model 2.2.3 Periodically Perturbed Gaussian Blob Model 2.2.4 Bickley-Jet 3 Transfer Operator Approach I: State of the Art 3.1 Frobenius-Perron Operator 3.2 Markov-Chains 3.3 Laplacian matrices 3.4 Finding Almost-Invariant Sets 3.5 Finding Coherent Sets 3.5.1 Coherent pairs as tuples 3.5.2 Coherent pairs as triples 3.6 Spectral Clustering 3.7 Critique and Discussion 4 Transfer Operator Approach II: Mixing Boundary Conditions in Stationary Flows 4.1 Overview 4.2 Estimation of Transfer Probability Matrices P 4.3 Mixing Boundary Conditions 4.4 Thresholding 4.5 Results 4.5.1 Robustness with respect to parameters 4.5.2 Comparison and alternatives 4.5.3 Handling of false positives 4.5.4 Periodically perturbed flow 4.6 Closing Remark 5 Transfer operator approach III: Analysis of Oceanic Transport 5.1 Mixing Boundary Conditions: Time-Dependent Flows 5.1.1 Method 5.1.2 Results 5.2 Temporal consistency 5.2.1 Method 5.2.2 Results 5.3 Treatment of Coastal Effects 5.4 Application to Baltic velocity fields 5.4.1 Method 5.4.2 Results 5.5 Closing Remark 6 Prototypes of Coherent Sets: Star-Convex Structures 6.1 Mathematical Considerations 6.2 MSCS-Algorithm 6.3 Extracting star-convex sub-volumes 6.4 Results 6.4.1 Stationary Gaussian blob model 6.4.2 Bickley-Jet 6.4.3 Two dimensional inviscid flow 6.4.4 Real data sets 6.5 Closing Remark 7 Conclusion and Outlook

Solutions of self-assembled wormlike micelles are used with ever increasing frequency in a multitude of consumer products ranging from cosmetic to industrial applications. Owing to the wide range of applications, flows of interest are often complex in nature; exhibiting both extensional and shear regions that can make modeling and prediction both challenging and valuable. Adding to the complexity, the micellar dynamics are continually changing, resulting in a number of interesting phenomena, such as shear banding and extensional flow instabilities. Presented in this thesis are the results of an investigation into the flow fields generated by both a controllable and idealized porous media, effected as a periodic array of cylinders as well as a single circular cylinder. In order to fully characterize the kinematics, two rheologically documented test fluids were used. The first test channel geometry consists of six equally spaced cylinders, arranged perpendicular to the flow, while the second consists of a single circular cylinder. By systematically varying the Deborah number, the flow kinematics, stability and pressure drop were measured. A combination of particle image velocimetry in conjunction with flush mount pressure transducers were used to characterize the flow, while flow induced birefringence measurements were used to determine micelle deformation and alignment. In the periodic geometry, the pressure drop was found to decrease initially due to the shear thinning of the test fluid, and then exhibit a dramatic upturn as other elastic effects begin to dominate in one of the test fluids. In the case of the single cylinder, no such upturn was observed. Presented is evidence of the onset of an elastic instability in one of the test fluids above a critical Deborah number, manifest in fluctuating transient pressure drop measurements and asymmetric streamlines. This instability was observed in both test geometries. It is argued that this instability can be attributed to the measurable differences in the extensional rheology of the two fluids.

Komplexe Netzwerke sind mächtige Werkzeuge, die die Untersuchung komplexer Systeme unterstützen. In vielen Bereichen werden komplexe Netzwerke eingesetzt, um die Dynamik interagierender Entitäten wie Neuronen, Menschen oder sogar Wettersysteme zu verstehen. Darüber hinaus erweitern sich die Anwendungsbereiche mit der stetigen Entwicklung neuer theoretischer Ansätze. In dieser Arbeit wollen wir sowohl den theoretischen Rahmen der Netzwerkwissenschaften weiterentwickeln als auch komplexe Netzwerke in der Klimatologie und der computergestützten Sozialwissenschaft anwenden. / Complex networks are powerful tools enabling the study of complex systems. In many fields, complex networks are used as a tool to gain an understanding of the dynamics of interacting entities such as neurons in a brain, humans on social media, or global weather systems. At the same time, new theoretical frameworks that extend the toolbox of Network Science promote the application of network tools in new research fields. In this thesis, we aim for both, advancing the theoretical framework of Network Science as well as applying complex networks in Climatology and Computational Social Science.

No description available.

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method. For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process. First, we create a model of hematopoiesis, the processes of creating new blood cells. We analyze stem cell collection regimens and statistically sample parameter space in order to create a model accounts for the dynamics of multiple patients. Next, we modify an existing model of the wound healing response by introducing a variable for two inflammatory cell types. We analyze the timing of the inflammatory response and introduce the presence of systemic estrogen in the model, as there is evidence that the presence of estrogen leads to a more efficient wound healing response. Last, we mathematically model the gas exchange process in the lungs and body in order to lay the foundation for a model of the inflammatory response in the lung under conditions of mechanical ventilation. We introduce normal and ventilation breathing waveforms and a third state of hemoglobin in a closed loop partial differential equations model. We account for gas exchange in the lung and body compartments in addition to introducing a third discretized well-mixing compartment between the two. We use ordinary and partial differential equations to model these systems over one or more independent variables, as well as classical analysis techniques and computational methods to analyze systems. Statistical sampling is also used to investigate parameter values in order for the mathematical models developed to account for patient-to-patient variability. This alters the traditional mathematical model, which yields a single set of parameter values that represent one instance of the physiology, into a mathematical model that accounts for many different instances of physiology.}