Submitted by Jordan (jordanbiblio@gmail.com) on 2017-01-10T15:19:57Z No. of bitstreams: 1 DISS_2014_Hilda Regina Pereira Menezes Olea.pdf: 563490 bytes, checksum: 9fc5e4a7449e9326e86d149878f50f9b (MD5) / Approved for entry into archive by Jordan (jordanbiblio@gmail.com) on 2017-01-11T12:41:12Z (GMT) No. of bitstreams: 1 DISS_2014_Hilda Regina Pereira Menezes Olea.pdf: 563490 bytes, checksum: 9fc5e4a7449e9326e86d149878f50f9b (MD5) / Made available in DSpace on 2017-01-11T12:41:12Z (GMT). No. of bitstreams: 1 DISS_2014_Hilda Regina Pereira Menezes Olea.pdf: 563490 bytes, checksum: 9fc5e4a7449e9326e86d149878f50f9b (MD5) Previous issue date: 2014-03-10 / CAPES / A interdisciplinaridade, mais que uma moda pedagógica ou um procedimento didático, denota uma transformação epistemológica em curso, o que faz com que compareça nesta pesquisa sob a condição de um dos paradigmas epistemológicos vigentes na contemporaneidade. Tributária de um pensamento que confere às composições entre as áreas do saber a possibilidade heurística e a possibilidade de negociação com a violência inerente às relações de aprendizagem e de produção de saber deixa-se pensar através de uma teoria das bifurcações, a qual parte da concepção de que o conhecimento não é sólido, mas disperso, frágil, capaz de desaparecer a qualquer instante; o próprio objeto do conhecimento é fugaz. Este trabalho opera no sentido de apreender e experimentar tais postulados. / Interdisciplinarity, more than a fad or a didactic pedagogical procedure, denotes an epistemological ongoing transformation, which makes an appearance in this research on the condition of the current epistemological paradigms in contemporary times. Tax a thought that gives the compositions of the areas of knowledge the heuristic possibility and the possibility of negotiating with the violence inherent relations of learning and knowledge production is allowed to think through a bifurcation theory, which starts from the conception that knowledge is not solid, but scattered, fragile, able to disappear at any moment, the object of knowledge itself is fleeting. This work operates to learn and experience such postulates.

In this work we studing a generalized predator-prey system in a spatial domain, in terms of formation. We show parameter, regions where transcritical, Hopf and Turing bifurcations appear are presented, and also some spatial patterns that arise for specific parameters in the Turing region are also shown. / Neste trabalho estudamos um sistema presa-predador generalizado, num domínio espacial, sob o aspecto de formação de bifurcações. Regiões de parâmetros onde bifurcações transcrítica, de Hopf e de Turing aparecem são apresentadas, assim como alguns padrões espaciais que surgem para parâmetros específicos na região de Turing também são mostrados.

We propose in this thesis a way to study deformations of plane curves that take into consideration the geometry of the curves as well as their singularities. We deal in details with local phenomena that occur generically in two-parameter families of curves. We obtain information on the inflections and vertices appearing on the deformed curves. We also obtain the configurations of the evolutes of the curves and of their deformations, and apply our results to orthogonal projections of space curves. Finally, we consider the profile (outline, apparent contour) of a smooth surface in the Euclidian 3-space. This is the image of the singular set of an orthogonal projection of the surface. The profile is a plane curve and may have singularities. We study the changes in the geometry of the profile as the direction of projection changes locally in the unit sphere. / Propomos nesta tese um método para estudar deformações de curvas planas que leva em consideração a geometria delas, bem como as suas singularidades. Consideramos em detalhes os fenômenos locais que ocorrem genericamente em famílias de curvas com dois parâmetros. Obtemos informações sobre as inflexões e vértices que aparecem nas curvas deformadas. Obtemos também as configurações das evolutas das curvas e das suas deformações e aplicamos os nossos resultados nas projeções ortogonais de curvas espaciais. Finalmente, consideramos o perfil de uma superfície regular no espaço Euclidiano R3. O perfil é a imagem do conjunto singular de uma projeção ortogonal da superfície, esta é uma curva plana e pode ter singularidades. Estudamos as alterações na geometria do perfil quando a direção de projeção muda localmente na esfera unitária.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-28T17:43:40Z No. of bitstreams: 2 Dissertação - Marcos Tsujii - 2015.pdf: 919903 bytes, checksum: e6e6bb36b7e9700b446e1807f1854651 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T19:52:00Z (GMT) No. of bitstreams: 2 Dissertação - Marcos Tsujii - 2015.pdf: 919903 bytes, checksum: e6e6bb36b7e9700b446e1807f1854651 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-07T19:52:00Z (GMT). No. of bitstreams: 2 Dissertação - Marcos Tsujii - 2015.pdf: 919903 bytes, checksum: e6e6bb36b7e9700b446e1807f1854651 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2015-03-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we will study the dynamics in smooth vector elds, in vector elds near the boundary and in piecewise-smooth vector elds and each of their most popular types of bifurcations up to now. / Neste trabalho, estudaremos a dinâmica em campos de vetores suaves, em campos de vetores em variedades com bordo e em campos de vetores suaves por partes e cada um dos seus respectivos tipos de bifurcações mais conhecidos.

Aplica-se a Teoria Qualitativa de Equações Diferenciais aos problemas de sincronismo de fase, associando às diversas regiões do espaço de parâmetros os tipos de atratores esperados. <p style=\"margin: 11px 0px;\">Três casos básicos são estudados: <ol type=\"i\" style=\"padding: 0px 40px\"> Malha de Sincronismo de fase Autônoma de 2ª Ordem Modulação em Frequência Acidental em Malha de Sincronismo de Fase de 2ª Ordem Malha de Sincronismo de Fase Autônoma de 3ª Ordem <p style=\"margin: 11px 0px;\">No caso (i), usando resultados clássicos da teoria de sistemas dinâmicos, discute-se os pontos de equilíbrio e os ciclos limite. <p style=\"margin: 11px 0px;\">No caso (ii), usando o método de Melnikov propõem-se critérios para previsão de aparecimento de atratores caóticos.<p style=\"margin: 11px 0px;\">No caso (iii), usando o teorema de bifurcações de Hopf, a estabilidade dos pontos de equilíbrio e a formação dos ciclos limite são analisadas / The Qualitative Theory of Differential Equations is applied to the phaselock problems, and the several parameters space regions are associated to the expected attractors. <p style=\"margin: 11px 0px;\">Three basic cases are studied: <ol type=\"i\" style=\"padding: 0px 40px\"> Autonomous Second Order Phaselock Loop Accidental Frequency Modulation on Second Orer Phaselock Loop Autonomous Third Order Phaselock Loop <p style=\"margin: 11px 0px;\">In case i), using classical results of dynamical systems theory, the equilibrium points and limit cycles are analyses. <p style=\"margin: 11px 0px;\">In case ii), the Melnikov technique gives some criteria for chaotic attractors.<p style=\"margin: 11px 0px;\">In case iii), Hopf bifurcation theorem provides propositions about equilibrium points and limit cycles.

<p> Nonlinear flexural vibrations of simply supported rectangular plates with thermal coupling  are studied for the case when the plate is harmonically excited by the force acting normal to the  midplane of the plate. The coupled thermo-mechanical equations are derived by applying the  Galerkin procedure on the von-Karman equation and the energy equation for an element of the  plate. The thermo-mechanical equations are second order in transverse displacement and first order  in thermal dynamics. In our first study, we represent the transverse displacement, bending moment  and membrane force due to temperature by one mode approximation, and study the response of  thermoelastic plate in time and frequency domain. The analysis of forced vibration to a transverse  harmonic excitation is carried out using harmonic balance as well as direct time integration coupled  to a Fourier analysis for a range of excitation frequencies. The effects of thermal coupling, material  nonlinearity and different amplitudes of excitation on the thermoelastic plate’s transverse  displacement and thermoelastic variables are investigated. The method of averaging is applied to the one mode case to transform the nonlinear modal  equations into sets of two-dimensional dynamical systems which govern the amplitudes and phases  of the two modes. The averaged system is studied in detail by using pseudo arc-length continuation  schemes implemented in MATCONT. The physical phenomena of interest in this study arise when a plate exhibits two distinct  linear modes of vibration with nearly the same natural frequency. To analyze the dynamics of the  thermoelastic plate in this scenario, we utilize a two-mode approximation. The response of the  plate, as a function of excitation frequency, is determined for the two-mode model using  MATCONT, and several bifurcation points are identified. Our analysis reveals two types of  solutions: single-mode and coupled-mode solutions. We find that stable single-mode and coupled mode solutions can coexist over a wide range of amplitudes and excitation frequencies. Under the influence of thermal coupling, our analysis using MATCONT reveals the  identification of Neimark-Sacker bifurcation points. After a detailed study of the Neimark-Sacker  region using Fourier spectrum and Poincare section, we conclude that a pitchfork bifurcation  occurs, resulting in stable asymmetric solutions. We further investigate the effect of in-plane forces  or mechanical precompression on the thermoelastic plate, using MATCONT for a fixed value of  force, damping, and excitation frequency. We find that the in-plane forces lead to buckling, which  12 is identified as a branch point cycle (pitchfork bifurcation) in MATCONT. Consequently, the  bifurcation diagram of transverse displacement as a function of in-plane forces can be divided into  prebuckling and post buckling regions, with multistable solutions in each region. To validate our one mode model, we use ANSYS software to verify the transverse  displacement and temperature results. We validate the frequency and time domain results for both  the linear and nonlinear cases, and plot contours using ANSYS to observe the variation of  displacement and temperature over the surface of the plate. Our one mode model results closely  match with the ANSYS results, leading us to conclude that our one mode approximation is accurate  and that the coupled thermo-mechanical equations we derived are correct.  </p>

Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic--quintic Ginzburg--Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non--integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse--type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this dissertation, we develop a theoretical framework for these novel classes of solutions. In the first part, we use a traveling wave reduction or a so--called spatial approximation to comprehensively investigate the bifurcations of plane wave and periodic solutions of the CGLE. The primary tools used here are Singularity Theory and Hopf bifurcation theory respectively. Generalized and degenerate Hopf bifurcations have also been considered to track the emergence of global structure such as homoclinic orbits. However, these results appear difficult to correlate to the numerical bifurcation sequences of the dissipative solitons. In the second part of this dissertation, we shift gears to focus on the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. For this part, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the two alternative starting formulations for the Lagrangian are recent and not well explored. Also, after extensive discussions with David Kaup, the trial functions have been generalized considerably over conventional ones to keep the shape relatively simple (and the trial function integrable!) while allowing arbitrary temporal variation of the amplitude, width, position, speed and phase of the pulses. In addition, the resulting Euler--Lagrange equations are treated in a completely novel way. Rather than consider the stable fixed points which correspond to the well--known stationary solitons or plain pulses, we use dynamical systems theory to focus on more complex attractors viz. periodic, quasiperiodic, and chaotic ones. Periodic evolution of the trial function parameters on stable periodic attractors constructed via the method of multiple scales yield solitons whose amplitudes are non--stationary or time dependent. In particular, pulsating, snake (and, less easily, creeping) dissipative solitons may be treated in this manner. Detailed results are presented here for the pulsating solitary waves --- their regimes of occurrence, bifurcations, and the parameter dependences of the amplitudes, widths, and periods agree with simulation results. Finally, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Results will be presented for the pulsating and snake soliton cases. Chaotic evolution of the trial function parameters in chaotic regimes identified using dynamical systems analysis would yield chaotic solitary waves. The method also holds promise for detailed modeling of chaotic solitons as well. This overall approach fails only to address the fifth class of dissipative solitons, viz. the exploding or erupting solitons.

<p>Ferrofluids are remarkable materials composed of magnetic nanoparticles dispersed in a carrier liquid. These suspensions exhibit fluid-like behavior in the absence of a magnetic field, but when exposed to a magnetic field, they can respond and deform into a variety of patterns. This responsive behavior of ferrofluids makes them an excellent material for applications such as drug delivery for targeted therapies and soft robots. In this thesis, we will focus on the interfacial dynamics of ferrofluids in Hele-Shaw cells. The three major objectives of this thesis are: understanding the pattern evolution, unraveling the underlying nonlinear dynamics, and ultimately achieving passive control of ferrofluid interfaces. First, we introduce a novel static magnetic field setup, under which a confined circular ferrofluid droplet will deform and spin steadily like a `gear’, driven by interfacial traveling waves. This study combines sharp-interface numerical simulations with weakly nonlinear theory to explain the wave propagation. Then, to better understand these interfacial traveling waves, we derive a long-wave equation for a ferrofluid thin film subject to an angled magnetic field. Interestingly, the long-wave equation derived, which is a new type of generalized Kuramoto--Sivashinsky equation (KSE), exhibits nonlinear periodic waves as dissipative solitons and reveals fascinating issues about linearly unstable but nonlinearly stable structures, such as transitions between different nonlinear periodic wave states. Next, inspired by the low-dimensional property of the KSE, we simplify the original 2D nonlocal droplet problem using the center manifold method, reducing the shape evolution to an amplitude equation (a single local ODE). We show that the formation of the rotating `gear’ arises from a Hopf bifurcation, which further inspires our work on time-dependent control. By introducing a slowly time-varying magnetic field, we propose strategies to effectively control a ferrofluid droplet's evolution into a targeted shape at a targeted time. The final chapter of this thesis concerns our ongoing research into the interfacial dynamics under the influence of a fast time-varying and rotating magnetic field, which induces a nonsymmetric viscous stress tensor in the ferrofluid, requiring the balance of the angular momentum equation. As a consequence, wave propagation on a ferrofluid interface can be now triggered by magnetic torque. A new thin-film long-wave equation is consistently derived taking magnetic torque into account.</p>

L'étude théorique de la transition vers la turbulence d'écoulements en tuyau de fluides non newtoniens rhéofluidifiants (fluides de Carreau) est menée, avec l'approche consistant à calculer des «~structures très cohérentes~» sous la forme d'«~ondes non linéaires~». Pour cela un code pseudo-spectral de type Petrov-Galerkin, permettant de suivre des solutions ondes non linéaires tridimensionnelles dans l'espace des paramètres par continuation, est développé. Ce code est validé par comparaison à des résultats existants en fluide newtonien, et grâce à un test de consistance en fluide non newtonien. Une convergence spectrale exponentielle est obtenue dans tous les cas. Ce code est utilisé pour chercher (guidé par des résultats expérimentaux récents) de nouvelles solutions de nombre d'onde azimutal fondamental égal à 1, sans succès pour l'instant. Par contre des solutions de nombre d'onde azimutal fondamental égal à 2 ou 3 sont obtenues par continuation à partir du cas newtonien. La rhéofluidification induit, en termes de nombres de Reynolds critiques, un retard à l'apparition de ces ondes par rapport au cas newtonien. Ce retard est caractérisé, et le parallèle est fait avec divers résultats expérimentaux qui montrent un retard à l'apparition de bouffées turbulentes en fluides non newtoniens / The transition to turbulence in pipe flows of shear-thinning fluids is studied theoretically. The method used is the computation of `exact coherent structures' that are tridimensional nonlinear waves. For this purpose a pseudo-spectral Petrov-Galerkin code is developped, which also allows to follow solution branches in the parameter space with continuation methods. This code is validated by recovering already published results in the Newtonian case, and by a consistency test in the non-Newtonian case. A spectral exponential convergence is obtained in all cases. This code is used to seek (guided by recent experimental results) new solutions of fundamental azimuthal wavenumber equal to 1,without success at the time being. On the contrary solutions with a fundamental azimuthal wavenumber equal to 2 and 3 are obtained by continuation from the Newtonian case. The shear-thinning effects induce, in terms of critical Reynolds numbers, a delay for the onset of these waves, as compared with the Newtonian case. This delay is characterized. An analogy is made with various experimental results that show a delay in the transition to turbulence, more precisely, in the onset of `puffs', in non-Newtonian fluids

Dans cette thèse nous étudions les propriétés d'ondes stationnaires dans des structures composées d'une couche diélectrique nonlinéaire de type Kerr et des couches métalliques et diélectriques linéaires. Nous élaborons différents modèles pour étudier les propriétées de plasmons-solitons dans deux types de structures : (i) une région diélectrique nonlinéaire semi-infinie, des couches de métal et de diélectrique linéaires et (ii) une couche de diélectrique nonlinéaire d'épaisseur finie entre deux régions métalliques (guide d'onde métallique à coeur nonlinéaire). Pour le premier type de structures, nous montrons qu'en utilisant une structure à quatre couches, il est possible d'obtenir des plasmons-solitons de basses puissance. Pour des guides d'onde métalliques à coeur nonlinéaire, nous trouvons de modes d'ordres supérieurs. Pour certains des modes symétriques, nous observons une bifurcation par brisure de symétrie donnant naissance à des modes asymétriques dans une structure symétrique. / In this PhD thesis, we study the properties of stationary transverse magnetic polarized waves in structures composed of a Kerr-type nonlinear dielectric layer, metal and linear dielectric layers. We develop several models to study the properties of plasmon-soliton waves in two types of structures: a semi-infinite nonlinear dielectric in contact with metal and linear dielectric layers and a finite-size nonlinear dielectric layer sandwiched between two metal regions (nonlinear slot waveguide). Our models allow us to compute the nonlinear dispersion relations and the corresponding field profiles. For the first type of structure, we prove that using the four-layer structures that we propose, it is possible to obtain plasmon-soliton waves at the power levels. For nonlinear slot waveguide structures, we discover the existence of new, higher order modes. For some of the symmetric modes, we observe a symmetry breaking bifurcation giving birth to asymmetric modes in symmetric structure.