In this work we rst study the non-Newtonian effects on the inertial instabilities in shear flows and second the inertial suspensions of finite size rigid particles by means of numerical simulations. In the first part, both inelastic (Carreau) and elastic models (Oldroyd-B and FENE-P) have been employed to examine the main features of the non-Newtonian fluids in several congurations; flow past a circular cylinder, in a lid-driven cavity and in a channel. In the framework of the linear stability analysis, modal, non-modal, energy and sensitivity analysis are used to determine the instability mechanisms of the non-Newtonian flows. Signicant modifications/alterations in the instability of the different flows have been observed under the action of the non-Newtonian effects. In general, shear-thinning/shear-thickening effects destabilize/stabilize the flow around the cylinder and in a lid driven cavity. Viscoelastic effects both stabilize and destabilize the channel flow depending on the ratio between the viscoelastic and flow time scales. The instability mechanism is just slightly modied in the cylinder flow whereas new instability mechanisms arise in the lid-driven cavity flow. In the second part, we employ Direct Numerical Simulation together with an Immersed Boundary Method to simulate the inertial suspensions of rigid spherical neutrally buoyant particles in a channel. A wide range of the bulk Reynolds numbers, 500&lt;Re&lt;5000, and particle volume fractions, 0&lt;\Phi&lt;3, is studied while fixing the ratio between the channel height to particle diameter, 2h/d = 10. Three different inertial regimes are identied by studying the stress budget of two-phase flow. These regimes are laminar, turbulent and inertial shear-thickening where the contribution of the viscous, Reynolds and particle stress to transfer the momentum across the channel is the strongest respectively. In the inertial shear-thickening regime we observe a signicant enhancement in the wall shear stress attributed to an increment in particle stress and not the Reynolds stress. Examining the particle dynamics, particle distribution, dispersion, relative velocities and collision kernel, confirms the existence of the three regimes. We further study the transition and turbulence in the dilute regime of finite size particulate channel flow. We show that the turbulence can sustain in the domain at Reynolds numbers lower than the one of the unladen flow due to the disturbances induced by particles. / <p>QC 20151127</p>

We investigate the dynamics and stability of nonlinear time-delayed one-degree-of-freedom systems possessing quadratic and cubic nonlinearities and subjected to external and parametric disturbances. Due to the time-delay terms, the trivial solution of the unforced system undergoes Hopf bifurcations. We use the method of multiple scales to determine the normal forms of the Hopf bifurcations and hence determine whether they are locally supercritical or subcritical. Then, we use a combination of a path following scheme, the normal forms, and the method of harmonic balance to calculate and trace small- and large-amplitude limit cycles and use Floquet theory to ascertain their stability and hence generate global bifurcation diagrams. We validate these diagrams using numerical simulations. We apply the results to two important physical problems: machine-tool chatter in lathes and control of the sway of container cranes using time-delayed position feedback. We find that the Hopf bifurcations in machine tools are globally subcritical even when they are locally supercritical. We find multiple large-amplitude solutions coexisting with the linearly stable trivial solution. Consequently, there are three operating regions for machine tools: an unconditionally stable region, an unconditionally unstable region, and a conditionally stable region. In the latter region, the multiple responses lead to hysteresis. Then, we investigate the use of bifurcation control to transform the subcritical bifurcations into supercritical ones. We find that cubic-velocity feedback with appropriate gains can shrink or even eliminate the conditionally stable region. Then, we find that time-delayed acceleration feedback with an appropriate gain can completely eliminate the linear instability region. In contrast, we find that the Hopf bifurcations in controlled cranes are locally and globally supercritical. Finally, we investigate the effectiveness of time-delayed position feedback in rejecting external and parametric disturbances in ship-mounted cranes. / Ph. D.

O principal objetivo desta tese é estudar os difeomorfismos planares que satisfazem as hipóteses da Versão Modificada da Conjectura Discreta de Markus-Yamabe. Para estes difeomorfismos, definimos um conceito construtivo de número de rotação. Além disto, exibimos um contra-exemplo para a Versão Modificada da Conjectura Discreta de Markus-Yamabe que apresenta uma intersecção homoclínica transversal e implica a existência de infinitos pontos periódicos hiperbólicos / The main goal of this thesis is to study the plane diffeomorphisms satisfying the hypothesis of the Modified Version of the Discrete Conjecture of Markus-Yamabe. For these diffeomorphisms, we define a constructive concept of rotation number. Moreover, we present a counter-example to the Modified Version of the Discrete Markus-Yamabe Conjecture which exhibits a transversal homoclinic intersection, implying the existence of infinitely many hyperbolic periodic points

For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoffs Matrix-Tree Theorem in graph theory plays an essential role in the approachs development. The approach is successfully applied to several coupled systems well-known in the literature to demonstrate its applicability and effectiveness. / Applied Mathematics

In this thesis the stability of generic boundary layer flows is studied from a global viewpoint using optimization methods. Global eigenmodes of the incompressible linearized Navier-Stokes equations are computed using the Krylov subspace Arnoldi method. These modes serve as a tool both to study asymptotic stability and as a reduced basis to study transient growth. Transient growth is also studied using adjoint iterations. The knowledge obtained from the stability analysis is used to device systematic feedback control in the Linear Quadratic Gaussian framework. The dynamics is assumed to be described by the linearized Navier-Stokes equations. Actuators and sensors are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier-Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier-Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. A standard method to construct a reduced order model is to perform a Galerkin projection of the full equations onto the subspace spanned by a suitable set of vectors, such as global eigenmodes and balanced truncation modes. / QC 20100924

In this dissertation, we will investigate the global stability for some uncertain neural networks with multiple time-varying delays. These well-known neural networks include delayed cellular neural networks (DCNNs), delayed bidirectional associative memory neural networks (DBAMNNs), and delayed Cohen-Grossberg neural networks (DCGNNs). Delay-dependent and delay-independent criteria will be proposed to guarantee the robust stability of these uncertain delayed neural networks via linear matrix inequality (LMI) approach. Three types of uncertainties on feedback and delayed feedback matrices in these uncertain delayed neural networks will be considered in this study, namely uncertainties with structured perturbation, norm-bounded unstructured perturbation, and interval perturbation. Some numerical examples will be given to illustrate the effectiveness of our results. Some comparisions are made to show that our results are better than some results in recent literature.

This dissertation can be essentially divided into two parts. The first, consisting of Chapters I, II, and III, studies the graph theoretic nature of complex systems. This includes the spectral properties of such systems and in particular their influence on the systems dynamics. In the second part of this dissertation, or Chapter IV, we consider a new class of one-dimensional dynamical systems or functions with an eventual negative Schwarzian derivative motivated by some maps arising in neuroscience. To aid in understanding the interplay between the graph structure of a network and its dynamics we first introduce the concept of an isospectral graph reduction in Chapter I. Mathematically, an isospectral graph transformation is a graph operation (equivalently matrix operation) that modifies the structure of a graph while preserving the eigenvalues of the graphs weighted adjacency matrix. Because of their properties such reductions can be used to study graphs (networks) modulo any specific graph structure e.g. cycles of length n, cliques of size k, nodes of minimal/maximal degree, centrality, betweenness, etc. The theory of isospectral graph reductions has also lead to improvements in the general theory of eigenvalue approximation. Specifically, such reductions can be used to improved the classical eigenvalue estimates of Gershgorin, Brauer, Brualdi, and Varga for a complex valued matrix. The details of these specific results are found in Chapter II. The theory of isospectral graph transformations is then used in Chapter III to study time-delayed dynamical systems and develop the notion of a dynamical network expansion and reduction which can be used to determine whether a network of interacting dynamical systems has a unique global attractor. In Chapter IV we consider one-dimensional dynamical systems of an interval. In the study of such systems it is often assumed that the functions involved have a negative Schwarzian derivative. Here we consider a generalization of this condition. Specifically, we consider the functions which have some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. This includes both systems with regular as well as chaotic dynamic properties.

No description available.

Les amplifications optimales d'énergie de structures quasiment alignées dans le sens de l'écoulement sont calculées dans le cas d'un sillage parallèle, d'un sillage synthétique faiblement non-parallèle et du sillage d'un cylindre. Il a été observé que de très grandes amplifications d'énergie peuvent être supportés par ces sillages. L'amplification d' énergie s'accroît avec la longueur d'onde des perturbations en envergure à l'exception du sillage du cylindre pour lequel l'accroissement d'énergie est maximal pour λz ≈ 5 − 7 D. Les structures amplifiées de manière optimale sont les streaks fluctuant dans le sens de l’écoulement. Il est montré que ces streaks sont capables de supprimer complètement l'instabilité absolue d'un sillage parallèle lorsqu'ils sont déclenchés avec une amplitude finie. L'instabilité globale d'un sillage faiblement non-parallèle et celle du sillage d'un cylindre peuvent être complètement supprimées par des streaks d'amplitude modeste. L'énergie de contrôle requise pour stabiliser le sillage est très faible lorsque les perturbations optimales sont utilisées, et il est montré qu'elle est toujours plus faible que celle qui devrait être utilisée pour un contrôle uniforme en envergure (2D). Il est aussi montré que la dépendance du taux de croissance est quadratique et que, par conséquent, les classiques analyses de sensibilité au premier ordre ne permettent pas de prédire la grande efficacité de la technique de contrôle par streaks. La dernière partie de ce travail livre des résultats préliminaires sur l'étude expérimentale du contrôle par streaks dans le cas du sillage turbulent d'un corps 3D. Il est montré que les streaks forcés artificiellement dans la zone d'instabilité absolue de l'écoulement sont capables de modifier la dynamique du sillage. / We compute optimal energy growths leading to streamwise streaks in parallel, weakly non-parallel and the circular cylinder wakes. We find that very large energy amplifications can be sustained by these wakes. The energy amplifications increase with the spanwise wavelength of the perturbations except in the circular cylinder wake where maximum energy growths are reached for λz ≈ 5 − 7 D. The optimally amplified structures are streamwise streaks. When forced with finite amplitudes these streaks are shown, in parallel wakes, to be able to completely suppress the absolute instability. The global instability of the weakly non-parallel and the circular cylinder wakes can be completely suppressed with moderate streaks amplitudes. The energy required to stabilize the wake is much reduced when optimal perturbations are used, and it is shown to be always smaller than the one that would be required if a 2D control was used. It is also shown that the sensitivity of the global mode growth rate is quadratic and that therefore usual first order sensitivity analyses are unable to predict the high efficiency of the control-by-streaks strategy.

Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2016-09-21T13:53:20Z No. of bitstreams: 1 DissLFS.pdf: 15776549 bytes, checksum: d345f39604b7efb99df0f362ce8001a2 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-21T18:26:06Z (GMT) No. of bitstreams: 1 DissLFS.pdf: 15776549 bytes, checksum: d345f39604b7efb99df0f362ce8001a2 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-21T18:26:13Z (GMT) No. of bitstreams: 1 DissLFS.pdf: 15776549 bytes, checksum: d345f39604b7efb99df0f362ce8001a2 (MD5) / Made available in DSpace on 2016-09-21T18:26:19Z (GMT). No. of bitstreams: 1 DissLFS.pdf: 15776549 bytes, checksum: d345f39604b7efb99df0f362ce8001a2 (MD5) Previous issue date: 2015-08-25 / Não recebi financiamento / The use of precast concrete system in multi-storey buildings demand for structural solutions that enable its horizontal stability without implicating the architectural and economic aspects, its challenge is borne by the structural engineer, who often need to assign additional structures (substructures of bracing) that provide the rigidity necessary to ensure the overall stability of the assembly. This study aims to analyze and evaluate the technical and economic performance of bracing systems applied to buildings with multiple floors with precast concrete structure and can be justified by the current need to develop appropriate technically ways of choice in the constructive system. The development of this study is the analysis of global stability in multi-storey buildings with the application of bracing systems, evaluating the influence of the stiffness and the arrangement of these elements in the performance of the structure, and comparing the concrete consumption values of the structures formed by beams and columns (disregarding the slabs and the foundation), and also values of the efforts in the foundation. To develop this study we used the commercial software STRAP® as a support tool for calculations, where the results gotten by it, showed that the bracing substructures improved the behavior of the structures analyzed in the issue of global stability. Finally, they were provided the necessary subsidies for the proper choice of the wind bracing system to be employed on the structures analyzed in this work. / O emprego do sistema pré-moldado de concreto em edifícios de múltiplos pavimentos demanda por soluções estruturais que viabilizem a sua estabilidade horizontal, sem o comprometimento dos aspectos arquitetônicos e econômicos, tal desafio fica a cargo do engenheiro de estruturas, que muitas vezes necessita atribuir estruturas complementares (subestruturas de contraventamento) que ofereçam a rigidez necessária para garantir a estabilidade global do conjunto. Este estudo tem como objetivo analisar e avaliar o desempenho técnico e econômico dos sistemas de contraventamento aplicados em edifícios de múltiplos pavimentos com estrutura prémoldada de concreto e pode ser justificado pela necessidade atual de desenvolver maneiras tecnicamente adequadas de escolha do sistema construtivo. O desenvolvimento deste estudo consiste na análise da estabilidade global em edifícios de múltiplos pavimentos com a aplicação dos sistemas de contraventamento, avaliando a influência da rigidez e da disposição desses elementos no desempenho da estrutura, e comparando os valores dos consumos de concreto das estruturas formadas por vigas e pilares (desconsiderando as lajes e a fundação), e também os valores dos esforços na fundação. Para o desenvolvimento deste estudo foi utilizado o software comercial STRAP® como ferramenta de auxílio para os cálculos, onde os resultados obtidos através do mesmo, demonstraram que as subestruturas de contraventamento melhoraram o comportamento das estruturas analisadas na questão da estabilidade global. Por fim, foram fornecidos os subsídios necessários para a escolha adequada do sistema de contraventamento a ser empregados sobre as estruturas analisadas neste trabalho.