In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between layers, while close packing leads to geometrically induced curvature singularities. When creation of voids is penalized by external pressure, the system trades off these competing effects, leading to various accommodating formations. Three two dimensional energy based nonlinear models are presented to describe the formation of voids at areas of intense geological folding. For each model the layers are assumed to be flexible elastic beams under hard unilateral contact constraint; which are solved as quasi-static obstacle problems with a free boundary. In each case an application of Kuhn-Tucker theory leads to representation as a nonlinear fourth order differential equation. Firstly a single layered model for voiding is presented. An elastic layer is forced into a V-shaped singularity by a uniform overburden pressure, where the fourth order free boundary problem is shown to have a unique, convex, symmetric solution. Drawing parallels with the Kuhn-Tucker theory, virtual work and ideas of duality, the physical significance of this differential equation is emphasised. Finally, appropriate scaling of either the potential energy or the differential equation shows the solutions scale to a single parametric group, for which the size of the void scales inversely with the ratio of overburden pressure to bending stiffness of the layer. Common to structural geology, one or several especially thick layers can dominate the deformation process. As a result, the remaining weak layers must accommodate into the geometry imposed by these competent layers. The second model, extends the first by introducing a plastic hinge to replicate the geometry imposed by the competent layer, and also axial springs to resist the slip over the limbs. The equilibrium equations for the system are investigated using the mathematical techniques developed for the first model. Under rigid loading the system may snap from an initially flat state to a convex voiding solution, as seen in the first model. However, if resistance to slip is high, the slightest imperfection causes the system to jump to a convoluted up-buckled solution, following a de-stiffened path to a point of self contact. These solutions have similarities with the delamination of carbon fibre composites. Finally, we extend the two single layered models to a simple multilayered model, which describes the periodic formation of voids in a chevron fold. The model shows that in the limit of high overburden pressures solutions form voids every layer, producing straight limbs punctured by sharp corners. This analysis shows good agreement when compared with recent experiments. This work provides the basis for future work on the buckling of thin multilayer assemblies in which voids may develop, and emphasizes the importance of the intricate nonlinear constraints of layers fitting together in multilayered folds.

L’objectif de cette recherche est de contribuer à la connaissance des pratiques d’achat et de consommation d’un groupe d’individus formant une famille. Cette recherche doctorale explore les notions de crise, d’événements et d’accidents de vie à l’échelle familiale et leurs influences sur les pratiques d’achat et consommation. L’approche choisie est longitudinale, le travail de collecte de données s’étend sur plus de 3 ans et combine plusieurs techniques de collectes de données. Le protocole utilisé est celui de l’ethnomarketing, méthode de recherche inspirée de l’anthropologie et de l’ethnographie appliquée en marketing. Ce travail s’est centré sur l’étude de l’influence des grands changements de la vie de famille (les naissances, départ de enfants de la maison, départ à la retraite, décès par exemple) ainsi que les crises (crise financière de 2008 par exemple) sur la consommation, l’analyse a été menée à l’aide de technique d’analyse thématique et sémiotique. Ce mémoire doctoral présente la méthodologie de recherche, la narration des portraits de six des familles suivies, l’analyse intra-famille et inter-famille, la discussion théorique et les apports managériaux. Le travail réalisé fait émerger l’importance de la perception de l’individu sur l’événement. Par ailleurs, la notion d’identité apparaît centrale dans la compréhension de l’influence des changements. Cette recherche ouvre également sur une réflexion autour des notions suivantes : l’autre, l’objet, les lieux et les temps dans la consommation. / The goal of this thesis is to expand our understanding of purchasing and consumption practices for a group of individuals that make up a family. We explore the notions of crisis, events, life accidents, turning points at the family level, and their influences on buying and consumption practices. We adopt a longitudinal approach with data collection extending over more than 3 years and combine several data collection techniques. The protocol used is ethnomarketing, a research method adapted from anthropology and ethnography to marketing research. The research focuses on the influence of major life changes (e.g., births, children leaving home, retirement, death) and crises (the 2008 economic crisis for example) on consumption practices with analysis carried out using thematic analysis and semiotics. This doctoral thesis starts with a look at the research methodology, followed by a description of six of the families studied, intra-familial and inter-family analysis, theoretical discussion and finally managerial contributions. The thesis highlights the importance of the individual’s perception of the event. Furthermore, the idea of identity is a key factor in understanding the influence of changes and crises. This research also considers the following notions- others, objects, places and times - in consumption practices.

Inner hair cells (IHCs) are the actual sensory receptors in hearing. Immature IHCs generate spontaneous calcium-dependent action potentials. Changing the characteristic of the Ca2Å signals modulates the amplitude and duration of the action potentials in these cells. These spontaneous action potential firing patterns are thought to be important for the development of the auditory system. The aim of this thesis is to gain a deeper understanding of the electrical activity and calcium signalling during development of IHCs from a mathematical point of view. A numerical bifurcation analysis is performed to delineate the relative contributions of the model parameters to the asymptotic behaviour of the model. In particular, we investigate the pattern of periodic solutions including single (normal) spiking, pseudoplateau burstings and complex solutions using two-parameter sections of the parameter space. We also demonstrate that a simplified (three-dimensional) model can generate similar dynamics as the original (four-dimensional) IHC model. This reduced model could be characterised by two fast and one slow or one fast and two slow variables depending on the parameters’ choice. Hence, the mechanisms underlying the bursting dynamics and mixed mode oscillations in the model are studied applying 1-slow/2-fast and 2-slow/1-fast analysis, respectively.

We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion. The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence results can be applied. We then show that as the bifurcation parameter r decreases and passes through a critical value rc, the stationary solution loses stability and a stable periodic solution appears. Several figures have been included, which illustrate this transistion. The pascal source program used in the numerical simulation is included in an appendix.

No description available.

Thesis (M.S.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaf 28).

Shankar Sastry, Omar Hijab. / Bibliography: leaf 20. / "May 1981." / Department of Energy contract DOE-ET-A01-2295T050

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Rotor-dynamic stability is a very important subject impacting the design, control, maintenance, and operating safety and reliability of rotary mechanical systems. As rotor-dynamic nonlinearities are significantly more prominent at higher rotary speeds, the demand for better and improved performance achievable through higher speeds has rendered the use of a linear approach for rotor-dynamic analysis both inadequate and ineffective. To establish the fundamental knowledge base necessary for addressing the need, it is essential that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instability, be fully characterized. The objectives of the research are to study the various rotor-dynamic instabilities induced by crack breathing and bearing fluid film forces using a model rotor-bearing system and to investigate the applicability of the fundamental concept of instantaneous frequency for characterizing rotor-dynamic nonlinear responses. A comprehensive finite element model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The intrinsic modes extracted using the Empirical Mode Decomposition along with their instantaneous frequencies resolved using the Hilbert transform are applied to characterize the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. The dissertation presents and demonstrates an effective approach that integrates nonlinear rotor-dynamics, instantaneous time-frequency analysis, advanced notions of dynamic system diagnostics and numerical modeling applied to the detection and identification of sensitive variations indicative of a bifurcated dynamic state. All presented studies on rotor response subjected to various system configurations and ranges of parameters show good agreements with published results. Under the influence of crack opening, the rotor-bearing model system displays transitional behaviors typical of a nonlinear dynamic system, going from periodic to period-doubling, chaotic to eventual failure. When film forces are also considered, the model system demonstrates very different behaviors and failures from different settings and ranges of control parameters. As a result, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart. Observations and results such as these have important practical implications on the design and safe operation of high performance rotary machinery.

Rotor-dynamic stability is a very important subject impacting the design, control, maintenance, and operating safety and reliability of rotary mechanical systems. As rotor-dynamic nonlinearities are significantly more prominent at higher rotary speeds, the demand for better and improved performance achievable through higher speeds has rendered the use of a linear approach for rotor-dynamic analysis both inadequate and ineffective. To establish the fundamental knowledge base necessary for addressing the need, it is essential that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instability, be fully characterized. The objectives of the research are to study the various rotor-dynamic instabilities induced by crack breathing and bearing fluid film forces using a model rotor-bearing system and to investigate the applicability of the fundamental concept of instantaneous frequency for characterizing rotor-dynamic nonlinear responses. A comprehensive finite element model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The intrinsic modes extracted using the Empirical Mode Decomposition along with their instantaneous frequencies resolved using the Hilbert transform are applied to characterize the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. The dissertation presents and demonstrates an effective approach that integrates nonlinear rotor-dynamics, instantaneous time-frequency analysis, advanced notions of dynamic system diagnostics and numerical modeling applied to the detection and identification of sensitive variations indicative of a bifurcated dynamic state. All presented studies on rotor response subjected to various system configurations and ranges of parameters show good agreements with published results. Under the influence of crack opening, the rotor-bearing model system displays transitional behaviors typical of a nonlinear dynamic system, going from periodic to period-doubling, chaotic to eventual failure. When film forces are also considered, the model system demonstrates very different behaviors and failures from different settings and ranges of control parameters. As a result, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart. Observations and results such as these have important practical implications on the design and safe operation of high performance rotary machinery.