Doctor of Philosophy / A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.

Cette thèse aborde le problème de la modélisation et de la détection des filaments dans des images 3D. Nous avons développé des méthodes variationnelles pour quatre applications spécifiques : l'extraction de routes où nous avons introduit la notion de courbure totale pour conserver les réseaux réguliers en tolérant les discontinuités de direction ; la détection et la complétion de filaments fortement bruités et présentant des occultations. Nous avons utilisé la magnétostatique et la théorie de Ginzburg-Landau pour représenter les filaments comme ensemble de singularités d'un champ vectoriel ; la détection de filaments dans des images biologiques acquises en microscopie confocale. On modélise les filaments en tenant compte des spécificités de cette dernière. Les filaments sont alors obtenus par une méthode de maximum à posteriori ; la détection de cibles dans des séquences d'images infrarouges. Dans cette application, on cherche des trajectoires optimisant la différence de luminosité moyenne entre la trajectoire et son voisinage en tenant compte des capteurs utilisés. Par ailleurs, nous avons démontré des résultats théoriques portant sur la courbure totale et la convergence de la méthode d'Alouges associée aux systèmes de Ginzburg-Landau. Ce travail réunit à la fois modélisation, résultats théoriques et recherche d'algorithmes numériques performants permettant de traiter de réelles applications.

In dieser Arbeit werden Knickinstabilitäten von Filamenten in biologischen Systemen untersucht. Das Zytoskelett von Zellen ist aus solchen Filamenten aufgebaut. Sie sind für die mechanische Stabilität der Zelle verantwortlich und spielen eine große Rolle bei intrazellulären Transportprozessen durch molekulare Motoren, die verschiedene Lasten wie beispielsweise Organellen entlang der Filamente des Zytoskeletts transportieren. Filamente sind semiflexible Polymere, deren Biegeenergie ähnlich groß ist wie die thermische Energie, so dass sie auch als elastische Balken auf der Nanoskala gesehen werden können, die signifikante thermische Fluktuationen zeigen. Wie ein makroskopischer elastischer Balken können auch Filamente eine mechanische Knickinstabilität unter Kompression zeigen. Im ersten Teil dieser Arbeit wird untersucht, wie diese Instabilität durch thermische Fluktuationen der Filamente beeinflusst wird. In Zellen können Kompressionskräfte durch molekulare Motoren erzeugt werden. Das geschieht zum Beispiel während der Zellteilung in der mitotischen Spindel. Im zweiten Teil der Arbeit untersuchen wir, wie die stochastische Natur einer von Motoren generierten Kraft die Knickinstabilität von Filamenten beeinflusst. Zunächst stellen wir kurz das Problem von Knickinstabilitäten auf der makroskopischen Skala dar und führen ein Modell für das Knicken von Filamenten oder elastischen Stäben in zwei Raumdimensionen und in Anwesenheit thermischer Fluktuationen ein. Wir präsentieren eine analytische Lösung für Knickinstabilitäten in Anwesenheit thermischer Fluktuationen, die auf einer Renormierungsgruppenrechnung im Rahmen des nichtlinearen Sigma-Models basiert. Wir integrieren die kurzwelligen Fluktuationen aus, um eine effektive Theorie für die langwelligen Moden zu erhalten, die die Knickinstabilität bestimmen. Wir berechnen die Änderung der kritischen Kraft für die Knickinstabilität und zeigen, dass die thermischen Fluktuationen in zwei Raumdimensionen zu einer Zunahme der kritischen Kraft führen. Außerdem zeigen wir, dass thermische Fluktuationen im geknickten Zustand zu einer Zunahme der mittleren projizierten Länge des Filaments in Richtung der wirkenden Kraft führen. Als Funktion der Konturlänge des Filaments besitzt die mittlere projizierte Länge eine Spitze an der Knickinstabilität, die durch thermische Fluktuationen abgerundet wird. Unser Hauptresultat ist die Beobachtung, dass ein geknicktes Filament unter dem Einfluss thermischer Fluktuationen gestreckt wird, d.h. dass seine mittlere projizierte Länge in Richtung der Kompressionskraft auf Grund der thermischen Fluktuationen zunimmt. Unsere analytischen Resultate werden durch Monte-Carlo Simulationen der Knickinstabilität semiflexibler Filamente in zwei Raumdimensionen bestätigt. Wir führen auch Monte-Carlo Simulationen in höheren Raumdimensionen durch und zeigen, dass die Zunahme der projizierten Länge unter dem Einfluss thermischer Fluktuationen weniger ausgeprägt ist und stark von der Wahl der Randbedingungen abhängt. Im zweiten Teil der Arbeit formulieren wir ein Modell für die Knickinstabilität semiflexibler Filamente unter dem Einfluss molekularer Motoren. Wir untersuchen ein System, in dem sich eine Gruppe von Motoren entlang eines fixierten Filaments bewegt, und dabei ein zweites Filament als Last trägt. Das Last-Filament wird gegen eine Wand gedrückt und knickt. Während des Knickvorgangs können die Motoren, die die Kraft auf das Filament generieren, stochastisch von dem Filament ab- und an das Filament anbinden. Wir formulieren ein stochastisches Model für dieses System und berechnen die “mean first passage time“, d.h. die mittlere Zeit für den Übergang von einem Zustand, in dem alle Motoren gebundenen sind zu einem Zustand, in dem alle Motoren abgebunden sind. Dieser Übergang entspricht auch einem Übergang aus dem gebogenen zurück in einen ungebogenen Zustand des Last-Filaments. Unser Resultat zeigt, dass für genügend kurze Mikrotubuli die Bewegung der Motoren von der durch das Last-Filament generierten Kraft beeinflusst wird. Diese Ergebnisse können in zukünftigen Experimenten überprüft werden. / We study buckling instabilities of filaments in biological systems. Filaments in a cell are the building blocks of the cytoskeleton. They are responsible for the mechanical stability of cells and play an important role in intracellular transport by molecular motors, which transport cargo such as organelles along cytoskeletal filaments. Filaments of the cytoskeleton are semiflexible polymers, i.e., their bending energy is comparable to the thermal energy such that they can be viewed as elastic rods on the nanometer scale, which exhibit pronounced thermal fluctuations. Like macroscopic elastic rods, filaments can undergo a mechanical buckling instability under a compressive load. In the first part of the thesis, we study how this buckling instability is affected by the pronounced thermal fluctuations of the filaments. In cells, compressive loads on filaments can be generated by molecular motors. This happens, for example, during cell division in the mitotic spindle. In the second part of the thesis, we investigate how the stochastic nature of such motor-generated forces influences the buckling behavior of filaments. In chapter 2 we review briefly the buckling instability problem of rods on the macroscopic scale and introduce an analytical model for buckling of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical treatment of the buckling instability in the presence of thermal fluctuations based on a renormalization-like procedure in terms of the non-linear sigma model where we integrate out short-wavelength fluctuations in order to obtain an effective theory for the mode of the longest wavelength governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and find that, in two spatial dimensions, thermal fluctuations increase this force. Furthermore, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our main result is the observation that a buckled filament is stretched by thermal fluctuations, i.e., its mean projected length in the direction of the applied force increases by thermal fluctuations. Our analytical results are confirmed by Monte Carlo simulations for buckling of semiflexible filaments in two spatial dimensions. We also perform Monte Carlo simulations in higher spatial dimensions and show that the increase in projected length by thermal fluctuations is less pronounced than in two dimensions and strongly depends on the choice of the boundary conditions. In the second part of this work, we present a model for buckling of semiflexible filaments under the action of molecular motors. We investigate a system in which a group of motors moves along a clamped filament carrying a second filament as a cargo. The cargo-filament is pushed against the wall and eventually buckles. The force-generating motors can stochastically unbind and rebind to the filament during the buckling process. We formulate a stochastic model of this system and calculate the mean first passage time for the unbinding of all linking motors which corresponds to the transition back to the unbuckled state of the cargo filament in a mean-field model. Our results show that for sufficiently short microtubules the movement of kinesin-I-motors is affected by the load force generated by the cargo filament. Our predictions could be tested in future experiments.

The aim of this study was to investigate the effects of resin and fiber on the abrasion, impact and internal pressure resistances of fiber reinforced plastic composite pipes produced by continuous filament winding method. For this study, pipe samples were produced with different combinations of resin type, fiber type, fiber amount and fiber length. All the samples were tested in accordance with the related ISO (International Organization for Standardization), DIN (German Standardization Institution) and BSI (British Standards Institution) standards. Three types of resins were used as ortophthalic, isophthalic and vinylester / two types of fibers were used as E-glass and ECR-glass and one type of GLASSFLAKES was used as C-glass. It was observed that the type of resin did not have any significant effect on burst pressure. However, the vinylester resin had a considerable positive effect on the abrasion and impact resistances. Moreover, it was observed that the type of fiber did not have any significant effect on impact and internal pressure resistances, but the use of C-glass GLASSFLAKES resulted in a positive effect on the abrasion resistance. Additionally, it was found that the increase in the amount of glass fiber resulted in increase of burst pressure, impact and abrasion resistances. Finally, it was observed that the length of glass fiber did not have any significant effect on abrasion resistance, but the decrease in fiber length resulted in a higher internal pressure and impact resistances.

Having an in vivo model of development that develops quickly and efficiently is important for investigators to elucidate the critical steps, components and signaling pathways involved in building a myofibril; hence a compliant in vivo model would provide a pivotal foundation for deciphering muscle disease mechanisms as well as the development of myopathy-related therapeutics. Here, we take advantage of a relatively quick, cost effective, and molecularly pliable developmental model system in the Xenopus laevis (frog) embryo and establish it as an in vivo model to study the roles of sarcomeric proteins during de novo myofibrillogenesis.Using the Xenopus model, we elucidated the functional roles of Leiomodin3 (Lmod3) and Tropomodulin 4 (Tmod4) during de novo skeletal myofibrillogenesis. Tmods have been demonstrated to contribute to thin filament length uniformity by regulating both elongation and depolymerization of actin-thin filaments' pointed-ends. Lmods, which are structurally related to Tmod proteins also localize to actin filament pointed-ends. In situ hybridization studies demonstrated that of their respective families, only tmod4 and lmod3 transcripts were expressed at high levels in skeletal muscle from the earliest stages of development. When reducing their protein levels via morpholino (MO) treatment, thin filament regulation and sarcomere assembly were compromised. Surprisingly, alternate rescues (i.e., lmod3 mRNA co-injected with Tmod4 MO and vice versa) partially restored myofibril structure and actin-thin filament organization. Thus, our results not only indicate that both Tmod4 and Lmod3 are critical for myofibrillogenesis during Xenopus skeletal muscle development, but also revealed that they may share redundant functions during skeletal muscle thin filament assembly.

The purpose of this research was to investigate the factors that enhance conductive anodic filament (CAF) formation in printed wiring boards. The variables studied were (1) flux formulation, (2) conductor spacing, (3) operating voltage, and (4) temperature. A Weibull distribution of failure times due to CAF was observed. A novel test circuit was designed and implemented that allowed the mean time to failure to be determined for boards processed with three different fluxes, at 0.5 mm and 0.75 mm conductor spacings and at 150V and 200V. The boards were aged at 85%RH and a temperature of 75°C, 85°C or 95°C. It was found that the flux formulation affected the rate of CAF formation. A modified linear aliphatic polyether flux with a chloride activator had a significantly different activation energy than control printed wiring boards or those boards processed with a poly(ethylene/propylene) glycol flux or a poly(ethylene/propylene) glycol flux with a bromide activator. The addition of bromine to a poly(ethylene/propylene) glycol flux decreased the rate of CAF formation as compared to poly(ethylene/propylene) glycol without a halide activator. The inter-relation between voltage and conductor spacing was quantified as a L4/V2 relationship for the plated through hole test pattern used in this study. 325V/mm was found to be a critical voltage gradient for the formation of CAF. The maximum temperature of the reflow profile also greatly enhances CAF formation and decreases the mean time to failure. Microscopic analysis showed distinct differences in CAF morphology between the various processed boards. Control boards had small halo-like CAF formations around a separated fiber / epoxy interface. CAF that formed on boards processed with poly(ethylene/propylene) glycol or poly(ethylene/propylene) glycol with a bromine activator had a stratified appearance that penetrated well into the epoxy. Boards that were processed with the modified linear aliphatic polyether with chlorine activator had a striated morphology that also penetrated into the epoxy. All CAFs were consistently copper and chlorine containing despite the use of a bromine containing flux. Electron diffraction revealed that a CAF observed in this study was synthetic atacamite. Stainless steel (i.e., iron, nickel, and chromium) residues were also observed as a result of drill bit breakage during PTH formation.

This thesis is for the investigation of the design and analysis processes of filament wound composite tubes under combined loading. The problem is studied by using a computational tool based on the Finite Element Method (FEM). Filament wound tubes are modeled as multi layered orthotropic tubes. Several analyses are performed on layered orthotropic tubes by using FEM. Results of the FEM are examined in order to investigate characteristics of filament wound tubes under different combined loading conditions. Winding angle, level of orthotropy and various ratios of the loading conditions were the main concerns of the study. The results of the FEM analysis are discussed for each loading condition. Both pure loading and combined loading analysis results were consistent with the ones mentioned in literature, such as optimum winding angles, optimum loading ratios and optimum level of orthotropy. Modeling parameters, assumptions and source of errors are also discussed. Finally, the required data is obtained for the design of filament wound composite tubes under combined loading.

The aim of this study is to determine the mechanical characteristics of the filament wound composite tubes working under internal pressure loads, generating data for further investigation with a view of estimating the remaining life cycle of the tubes during service. Data is generated experimentally by measuring the mechanical behavior like strains in hoop direction, maximum hoop stresses that are formed during internal pressure loading. Results have been used to identify and generate the necessary data to be adopted in the design applications. In order to determine these parameters, internal pressure tests are done on the filament wound composite tube specimens according to ASTM D 1599-99 standard. The test tubes are manufactured by wet filament winding method, employing two different fiber types, two different fiber tension settings and five different winding angle configurations. The internal pressure test results of these specimens are studied in order to determine the mechanical characteristics, and the effects of the production variables on the behavior of the tubes. Pressure tests revealed that the carbon fiber reinforced composite tubes exhibited a better burst performance compared to the glass fiber reinforced tubes, and the maximum burst performance is achieved at a winding angle configuration of [&plusmn / 54&deg / ]3[90&deg / ]1. In addition, the tension setting is found not to have a significant effect on the burst performance. The burst pressure data and the final failure modes are compared with the results of the ASME Boiler and Pressure Vessel Code laminate analysis, and it was observed that there is a good agreement between the laminate analysis results and the experimental data. The stress &ndash / strain behavior in hoop direction are also studied and hoop elastic constants are determined for the tubes.

This experimental study focuses on the links that exist between the mechanical pull-out behaviour of multi-filament yarns embedded in concrete and the impregnation of the yarn by the concrete. To this aim, 5 glass yarns have been embedded in concrete (AR and E glass yarns from assembled or direct roving). A pre-treatment was applied to the yarn before the casting, and was chosen in the following three: wetting, drying or pre-impregnation with a cement slurry. By this way, 15 yarn / pre-treatment combinations were obtained that generate 15 conditions of impregnation of the yarn by the cementitious matrix. In each case, the mechanical properties were determined from a classical pull-out test and the yarns impregnation properties were characterized by two dedicated tests: yarns porosity measurements and along yarn water flow measurements. By studying the relationship between the mechanical behaviour and the physical properties of the impregnated yarns, it is shown that the pre- and post-peak behaviour are mainly connected to the flow rate measured during the water flow measurements, which suggest a specific influence of the connected pores parallel to the filaments and of the penetration depth of the matrix into the yarn. The postpeak and the residual behaviour are moreover linked to the yarn pore volume associated to the disorder induced in the filaments assembly by the penetration of the matrix. The overall result of this work is a contribution to the understanding of the relationship between the impregnation of the yarns and the pull-out behaviour.

Doctor of Philosophy / A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.