Valveless pumping assists in fluid transport in various biomedical and engineering systems. Here we focus on one factor that has often been overlooked in previous studies of valveless pumping, namely the impact that a compression actuator exerts upon the pliant part of the system when they collide. In particular, a fluid-filled closed-loop system is considered, which consists of two distensible reservoirs connected by two rigid tubes, with one of the reservoirs compressed by an actuator at a prescribed frequency. A lumped-parameter model with constant coefficients accounting for mass and momentum balance in the system is constructed. Based upon such a model, a mean flow in the fluid loop can only be produced by system asymmetry and the nonlinear effects associated with actuator impact. Through asymptotic and numerical solutions of the model, a systematic parameter study is carried out, thereby revealing the rich and complex system dynamics that strongly depends upon the driving frequency of the actuator and other geometrical and material properties of the system. In particular, a number of critical frequencies that characterize the interactions between the actuator and the system are calculated asymptotically. Guided by such critical frequencies, the numerical results are categorized into different types of dynamical responses, and the parameter regions for their existence are systematically determined. Moreover, the transition of different system responses are observed through critical phase (which corresponding to the moment when different system responses occur) tracking.

It is well known that some driven systems undergo transitions when a system parameter is changed adiabatically around a critical value. This transition can be the result of a fundamental change in the structure of the phase space, called a bifurcation. Most of these transitions are well classified in the theory of bifurcations. Among the driven systems, spatiotemporally periodic (STP) potentials are noteworthy due to the intimate coupling between their time and spatial components. A paradigmatic example of such a system is the Kapitza pendulum, which is a pendulum with an oscillating suspension point. The Kapitza pendulum has the strange property that it will stand stably in the inverted position for certain driving frequencies and amplitudes. A particularly interesting and useful STP system is an array of parallel electrodes driven with an AC electrical potential such that adjacent electrodes are 180 degrees out of phase. Such an electrode array embedded in a surface is called an Electric Curtain (EC). As we will show, by using two ECs and a quadrupole trap it is posible to produce an electric potential simular in form to that of the Kapitza pendulum. Here I will present the results of four related pieces of work, each focused on understanding the behaviors STP systems, long-range interacting particles, and long-range interacting particles in STP systems. I will begin with a discussion on the experimental results of the EC as applied to the cleaning of solar panels in extraterrestrial environments, and as a way to produce a novel one-dimensional multiparticle STP potential. Then I will present a numerical investigation and dynamical systems analysis of the dynamics that may be possible in an EC. Moving to a simpler model in order to explore the rudimentary physics of coulomb interactions in a STP potential, I will show that the tools of statistical mechanics may be important to the study of such systems to understand transitions that fall outside of bifurcation theory. Though the Coulomb and, similarly, gravitational interactions of particles are prevalent in nature, these long-range interactions are not well understood from a statistical mechanics perspective because they are not extensive or additive. Finally, I will present a simple model for understanding long-range interacting pendula, finding interesting non-equilibrium behavior of the pendula angles. Namely, that a quasistationary clustered state can exist when the angles are initially ordered by their index.

L'étude de la dynamique des parois de domaines dans les nano-systèmes ferromagnétiques est cruciale pour le développement des dispositifs de stockage de l'information basés sur le déplacement et le contrôle des parois. Ces dispositifs ont plusieurs avantages : non-volatilité, rapidité d'exécution, haute densité de stockage, et faible consommation de l'énergie. En utilisant des méthodes micro-magnétiques et analytiques, nous avons constaté que l'interaction entre deux parois affectait les processus de dépiégeage sous champ magnétique, dans des nanofils en nickel à géométrie cylindrique et planaire. Nous avons mis en évidence des comportements non linéaires de la dynamique d'une paroi piégée, qui varient selon le matériau et le type de piège utilisé. Les diagrammes de phases représentant l'exposant de Lyapunov ont permis la distinction entre des zones chaotiques et périodiques, en fonction de la fréquence et de l'amplitude d'une excitation harmonique. Nous avons présenté des résultats sur la manipulation précise d'une paroi transverse sous impulsions de courant dans un nanofil planaire en nickel, structuré par une multitude de défauts artificiels. Nous avons montré que le positionnement exact de la paroi à température ambiante est possible uniquement pour des impulsions symétriques de très courte durée. Des effets inertiels pouvant s'opposer au couple de transfert de spin, ou au contraire l'amplifier ont été observés. Ces derniers résultats ouvrent une route vers le déplacement des parois dans les deux directions par des impulsions unipolaires de courant. / The study of the domain wall dynamics in ferromagnetic nano-systems is crucial for the developement of data-storage devices based on control and displacement of the domain walls. These devices have several advantages : non-volatility, fast execution time, high density, and low power consumption. Using micromagnetics and analytical methods, we have shown that the interaction between two domain walls influences the depinning process under magnetic field, in cylindrical and planar shaped nickel nanowires. We highlighted the nonlinear behaviour of the dynamics of a pinned domain wall, which varies with the material properties and the type of the pinning sites. The Lyapunov phase diagrams display chaotic and periodic regions function of the amplitude and frequency of a harmonic excitation. We have also presented results about the precise manipulation of transverse domain walls by current pulses in a nickel planar nanowire with artificial defects. We have shown that exact positioning of the domain walls at room temperature is possible only for very short symmetric current pulses. We observed inertial effects which can oppose or amplify the spin transfert torque effect. These results open a route to domain wall displacement in both directions with unipolar current pulses.

O objetivo deste trabalho foi descrever a dinâmica não linear das vozes de homens adultos sem queixas vocais por meio dos padrões visuais de dinâmica vocal (PVDV). Participaram 77 homens falantes nativos do português brasileiro com idades entre 20 a 40 anos (média 30 anos ± 5,54 anos). Para análise não linear foi adotado o método de reconstrução do espaço de fase e gerado um gráfico bidimensional a partir de uma rotina desenvolvida no MatLab® 10.0. Este gráfico foi analisado qualitativamente pela técnica dos PVDV que considera três aspectos da configuração: número de laços das órbitas, regularidade e espaçamento dos traçados. Cada aspecto foi classificado em uma escala de 4 a 0, da melhor para a pior configuração. Todos os indivíduos apresentaram qualidade de voz adaptada na variabilidade normal de acordo com os resultados da avaliação perceptivo-auditiva pelo protocolo CAPE-V e da análise acústica pelo programa MDVP-Kay Pentax. A avaliação do protocolo CAPE-V apresentou média de 18,07 mm (± 4,14 mm), no grau geral da vogal /a/. Na avaliação acústica as médias foram de 125,44 Hz (± 20,78 Hz) para F0; 0,85% (± 0,64%) para jitter; 3,23% (± 1,75%) para shimmer e 0,13 (± 0,02) para NHR. Os resultados da dinâmica não linear por meio dos PVDV se mostrou com número de laços em grau 4 (85,71% com média de 3,84 ± 0,40), regularidade em grau 3 e 4 (ambos com 40,26% e média de 3,12 ± 0,95) e espaçamento em grau 3 (58,44% e média de 2,95 ± 0,76). Concluiu-se que os PVDV da vogal /a/ de homens adultos brasileiros com vozes adaptadas dentro da variabilidade normal apresentou padrão visual caracterizado em sua maioria por presença de 4 ou mais laços, traçados regulares ou com discretas irregularidades e com espaçamento entre as linhas de médio a pequeno. / This work intended to describe the nonlinear dynamics of voices from adult men without vocal complaints using a qualitative analysis of Vocal Dynamics Visual Pattern (VDVP). 77 men speakers of Brazilian Portuguese, aged between 20-40 years old (mean 30 years ± 5.54 years), participated. For the nonlinear analysis a Phase Space Reconstruction was adopted and a two-dimensional graphic was generated from a routine developed on MatLab® 10.0. This graphic was qualitatively analyzed by a VDVP technique, which considers three aspects of the configuration: orbits loop numbers, regularity and spacing of the traces. Each aspect was classified in a scale ranging from 4 to 0, from the better to the worst configuration. All subjects had voice quality adapted on normal variability according to the results of the perceptual evaluation protocol for CAPE-V and acoustic analysis by the program MDVP Kay-Pentax. The perceptual analysis using CAPE-V protocol showed an average of 18,07 mm (± 4,14 mm), in Overall Severity of vowel /a/. On the acoustic analysis, means of 125,44 Hz (± 20,78 Hz) to F0; 0,85% (± 0,64%) for jitter; 3,23% (± 1,75%) for shimmer and 0,13 (± 0,02) for NHR using MDVP program. The results of nonlinear dynamics through PVDV proved with the number of loops in degree 4 (85.71% with a mean of 3.84 ± 0.40), regularity in degree 3 and 4 (both with 40.26% and mean of 3.12 ± 0.95) and degree 3 in spacing (58.44% and mean 2.95 ± 0.76). It was concluded that PVDV of the vowel /a/ of adult males Brazilians with adapted voices on the normal variability presented visual pattern characterized mostly by the presence of 4 or more loops, regular tracings or with discrete irregularities and spacing between lines of medium to small.

A formação espontânea de padrões espaço-temporais auto-organizados longe do equilíbrio termodinâmico é um comportamento característico de sistemas de reação-transporte. De fato, essa estruturação espacial pode ser entendida como um comportamento coletivo de um grande número de elementos individuais no sistema. Consequentemente o padrão emerge como o resultado da interação entre a dinâmica local dessas subunidades e o mecanismo de acoplamento espacial. Dinâmica não-linear do tipo multi-estável, excitável e oscilatória são exemplos típicos de padrões temporais complexos geralmente associados à estruturação espacial. Nesta tese de doutorado são apresentadas duas frentes de trabalho utilizando-se da dinâmica química não-linear na elucidação de mecanismos reacionais longe do equilíbrio termodinâmico: (a) a investigação da natureza química e efeito do drift nas séries temporais transientes em osciladores eletroquímicos. A análise da evolução temporal do parâmetro de bifurcação foi baseada em um método empírico de estabilização, sendo o acúmulo superficial de espécies oxigenadas o principal responsável pelo drift; (b) o desacoplamento das rotas eletroquímicas paralelas na formação de CO2 pela combinação de experimentos, modelagem e simulações numéricas durante a eletro-oxidação oscilatória de metanol em platina policristalina. O efeito dos ânions perclorato e sulfato nas reações paralelas foi investigado por meio da produção global de CO2 e HCOOCH3. Notavelmente, ânions sulfato inibiram mais fortemente a atividade catalítica proveniente da via direta em contraste com a pequena alteração na via indireta. Em paralelo às duas frentes de trabalho, foi construído um setup experimental com a finalidade de acompanhar a evolução espaço-temporal de uma reação eletroquímica com um sistema de aquisição de dados multicanal. A descrição do processo de confecção da célula e eletrodo de trabalho multicanal, o tratamento de dados e alguns resultados experimentais preliminares são inseridos como um capítulo adicional. A ideia central dessa tese converge na obtenção de informações da cinética química envolvida que não é observada em condições próximas ao equilíbrio termodinâmico. Essa interpretação pode ser utilizada como uma metodologia alternativa no estudo da eletrocatálise em reações químicas complexas. / The spontaneous formation of self-organized spatiotemporal patterns under far from thermodynamic equilibrium conditions is a characteristic behavior in reaction-transport systems. Indeed, this spatial structuration can be understood as a collective behavior of a large number of individual elements in the system. Consequently the pattern emerges as a result of the interaction between the local dynamic of these subunits and the spatial coupling. Multistable, excitable and oscillatory nonlinear dynamics are typical examples of complex temporal patterns usually associated to the spatial structuration. In this doctoral thesis, two work fronts are presented using the nonlinear chemical dynamics in the elucidation of reaction mechanisms under far from thermodynamic equilibrium regime: (a) the investigation of the chemical nature and effect of the drift in the transient time-series in electrochemical oscillators. The analysis of the temporal evolution of the bifurcation parameter was based on an empiric method of stabilization, being the slow accumulation of oxygenated species the main responsible for the drift; (b) the decoupling of the parallel electrochemical routes for CO2 production by a combination of experiments, modeling and numerical simulations during the oscillatory electro-oxidation of methanol on polycrystalline platinum. The effect of perchlorate and sulfate anions in the parallel reactions was investigated by the global production of CO2 and HCOOCH3. Remarkably, sulfate anions inhibited more strongly the catalytic activity from direct pathway in contrast to the small alteration in the indirect pathway. In parallel to the two work fronts, an experimental setup was built in order to obtain a spatiotemporal evolution of a electrochemical reaction with a multichannel data acquisition system. A description of the confection process of the cell and the multichannel working electrode, data treatment and some preliminary experimental results are included as an additional chapter. The main idea of this thesis converges in the obtainment of chemical kinetic information which is not observed in conditions close to the thermodynamic equilibrium. This interpretation might be used as an alternative methodology in the study of electrocatalysis in complex chemical reactions.

[pt] O presente trabalho tem por objetivo desenvolver uma formulação e certas estratégias que permitam a análise da perda de estabilidade de colunas esbeltas submetidas a carregamento axial periódico, fenômeno este conhecido como ressonância paramétrica. Uma excitação é dita paramétrica quando aparece nas equações de movimento do sistema na forma de coeficientes variáveis com o tempo - geralmente periódicos - e não como uma não homogeneidade. A coluna é descrita pela formulação clássica de Navier. O presente trabalho trata a coluna considerando-se um e três graus de liberdade com ou sem não-linearidades. As equações de movimento são obtidas utilizando-se o princípio de Hamilton através do método de Ritz. A equação linear (equação de Mathieu) e a equação de Duffing com pequeno amortecimento, são resolvidas de forma aproximada pelo método das múltiplas escalas, revelando a possibilidade de instabilização da posição de equilíbrio em diversas regiões do espaço definido pelos parâmetros de controle. A mesma conclusão é mostrada utilizando-se procedimentos computacionais para a resolução dos sistemas de equações lineares e nãolineares, com ou sem imperfeição geométrica inicial, podendo-se obter assim, a resposta do sistema, planos fase, seções de Poincaré e diagramas de bifurcação. Mostra-se a partir dos resultados numéricos, que a coluna submetida a cargas axiais harmônicas, pode tanto apresentar soluções com o mesmo período da força excitadora, quanto oscilações subarmônicas e superarmônicas de diversas ordens, além de movimentos caóticos. / [en] The main aim of the present work is to develop a formulation and some strategies for the instability analysis of slender columns under an axial harmonic force this phenomenon is known as parametric ressonance. An excitation is said to be parametric if it appears as timedependent - often periodic - coefficients in the equations governing the motion of the system,and not as an inhomogeneous term.The column is described by Navier classical formulation. The present work consider the column with one or three degrees of freedom with or without nonlinearities. The equations governing the motion are obtained by the Ritz method.The linear equation (Mathieu equation) and the Duffing equation with small damping are solved in an approximate way using multiple scales techniques, revealing the possibility of destabilizing the static equilibrium position in certain regions of the control space. A similar conclusion is obtained by employing numerical methods for the solution of linear and nonlinear equation systems with or without initial geometrical imperfections.This enables one to obtain time response, phase space, projections Poincaré sections and bifurcation diagrams. These numerical results show that the column with nonlinearities and loaded by a periodic longitudinal force can present various solutions with the same period as the forcing and subharmonic e superharmonic oscillations, as well as chaotic motions.

Trente ans après la démonstration de la production d'harmoniques laser par interaction laser-gaz non linéaire, la génération d'harmoniques d’ordre élevées (HHG) est utilisée pour sonder la dynamique moléculaire et réalise son potentiel technologique comme source compacte d'impulsions attosecondes XUV à la gamme de rayons X. Malgré les progrès expérimentaux, le coût de calcul excessif des simulations fondées sur les premiers principes et la difficulté de dériver systématiquement des modèles réduits pour l'interaction non perturbatif et à échelles multiples d'une impulsion laser intense avec un gaz macroscopique d'atomes ont entravé les efforts théoriques. Dans cette thèse, nous étudions des modèles réduits de premier principe pour HHG utilisant la mécanique classique. En utilisant la dynamique non linéaire, nous élucidons le rôle indispensable joué par le potentiel ionique lors des recollisions dans la limite du champ fort. Ensuite, en empruntant une technique de la physique des plasmas, nous dérivons systématiquement une hiérarchie de modèles hamiltoniens réduits pour l’interaction cohérente entre le laser et les atomes lors de la propagation des impulsions. Les modèles réduits permettent une dynamique électronique soit classique, soit quantique. Nous construisons un modèle classique qui concorde quantitativement avec le modèle quantique pour la propagation des composantes dominantes du champ laser. Dans une géométrie simplifiée, nous montrons que le rayonnement à fréquence anormalement élevée observé dans les simulations résulte de l’interaction délicate entre le piégeage d’électrons et les recollisions de plus grande énergie provoqués par les effets de propagation. / Thirty years after the demonstration of the production of high laser harmonics through nonlinear laser-gas interaction, high harmonic generation (HHG) is being used to probe molecular dynamics in real time and is realizing its technological potential as a tabletop source of attosecond pulses in the XUV to soft X-ray range. Despite experimental progress, theoretical efforts have been stymied by the excessive computational cost of first-principles simulations and the difficulty of systematically deriving reduced models for the non-perturbative, multiscale interaction of an intense laser pulse with a macroscopic gas of atoms. In this thesis, we investigate first-principles reduced models for HHG using classical mechanics. Using nonlinear dynamics, we elucidate the indispensable role played by the ionic potential during recollisions in the strong-field limit. Then, borrowing a technique from plasma physics, we systematically derive a hierarchy of reduced Hamiltonian models for the self-consistent interaction between the laser and the atoms during pulse propagation. The reduced models can accommodate either classical or quantum electron dynamics. We build a classical model which agrees quantitatively with the quantum model for the propagation of the dominant components of the laser field. In a simplified geometry, we show that the anomalously high frequency radiation seen in simulations results from the delicate interplay between electron trapping and higher energy recollisions brought on by propagation effects.

[pt] Estruturas offshore têm demandado, em função do aumento da profundidade da lâminha de água e da severidade do ambiente, análises de vibração cada vez mais confiáveis. Em face de oscilações com grandes deslocamentos, torna-se imprescindível uma análise não linear dessas estruturas. Métodos numéricos como os elementos finitos constituem-se numa tarefa computacionalmente custosa, uma vez que os acoplamentos modais tornam necessários modelos com muitos graus de liberdade. Isso dificulta as análises paramétricas e prolonga os ciclos de projeto para estruturas offshore. Uma alternativa a esses problemas é o uso de modelos de ordem reduzida. Os modos normais não lineares têm-se mostrado uma ferramenta eficiente na derivação de modelos de ordem reduzida para análises de vibrações não lineares. Isso ocorre porque um número menor de modos não lineares, em relação aos modelos com modos lineares, é necessário para se obter o mesmo nível de precisão num modelo reduzido. Esse trabalho utiliza modelos de ordem reduzida, obtidos por meio de análise modal não linear, para o estudo de vibração de modelos simplificados de estruturas offshore. Três exemplos de aplicação são utilizados: pêndulo invertido, torre articulada e plataforma spar. Além dos métodos baseado no procedimento de Galerkin e o assintótico, um procedimento numérico alternativo é proposto para obtenção dos modos, podendo ser utilizado para construção dos modos essencialmente não lineares. As vibrações livres e forçadas são estudadas. A estabilidade das soluções é analisada utilizando-se a teoria de Floquet, diagramas de bifurcação e de Mathieu e seções de Poincaré. As seções de Poincaré são também utilizadas para identificar a multiplicidade dos modos não lineares e a existência de multimodos. Os resultados são comparados com a solução obtida da integração numérica do sistema original de equações, mostrando uma boa precisão dos modelos reduzidos. / [en] The increasing water depth and the ocean adverse environment demand more accurate vibration analysis of offshore structures. Due to large amplitude oscillations, a nonlinear vibration analysis becomes necessary. Numerical methods such as finite element constitute a computationally expensive task when applied to these problems, since the occurrence of modal coupling demands a high number of degrees-of-freedom. A feasible possibility to overcome these difficulties is the use of low order models. The nonlinear normal modes have been shown to be an effective tool in the derivation of reduced order models in nonlinear dynamics. In the use of nonlinear modal analysis fewer modes are required to achieve a given level of accuracy in comparison to the use of linear modes. This work uses the nonlinear normal modes to derive low dimensional models to study the vibration of simplified models of offshore structures. Three examples are considered: an inverted pendulum, an articulated tower and a spar platform. Both free and forced vibrations are studied. The asymptotic and Galerkin-based methods are used to derive the normal modes. In addition, an alternative numerical procedure to construct such modes is proposed, which can be used to derive coupled modes. The solution stability is determined by the use of the Floquet theory, bifurcation and Mathieu diagrams, and Poincaré sections. The Poincaré sections are also used to investigate the multiplicity of modes and multimodes. The results obtained from the numerical integration of the original system are favourably compared with those of the reduced order models, showing the accuracy of the reduced models.

A low-order, dynamical systems approach is applied to the modeling of flow induced vibrations of flexible cables. By combining a coupled map lattice wake model with a linear wave equation cable model, both the free response of the cable as well as the resulting wake structures are examined. This represents an extension of earlier coupled map lattice models that only modeled the wake of forced cable vibration. The validity of the model is assessed through comparisons with both Computational Fluid Dynamics models (NEKTAR spectral element code) and wake experiments. The experimental wake data was collected through the use of hot-film anemometry techniques. Eight hot-film probes were placed along the span of a flexible cable mounted in the test section of a water tunnel. Through the use of frequency domain correlation algorithms, the phase of vortex shedding was calculated along the cable span from the hot-film velocity data. Results for an elastically mounted rigid cylinder showed that the freely vibrating CML model predicted behavior characteristic of a self-induced oscillator; the maximum amplitude of vibration was found to occur at a cylinder natural frequency that did not coincide identically with the natural shedding frequency of the cylinder. Furthermore, the variation of the frequency of cylinder vibration with its natural frequency was seen to be linear. For standing wave cable responses, the freely vibrating CML model predicted lace-like wake structures. This result is qualitatively consistent with both the NEKTAR simulations and experimental results. Little difference was found between the wakes of forced and freely vibrating cables at the Reynolds number of the study $Re=100$. Finally, it was found that the freely vibrating CML could match numerical predictions of cross-flow amplitude as the cable mass-damping parameter was varied over an order of magnitude (once the CML was tuned to match results at a specific mass-damping level). In addition to providing wake patterns for comparisons with the freely vibrating CML, experimental data was supplied to a self-learning CML scheme. This self-learning CML was able to estimate the experimental wake data with good accuracy. The self-learning CML is seen as the next extension of the freely-vibrating CML model, capable of estimating unmodeled wake dynamics through the use of experimental data.

As a physical system, a cell interacts with its environment through physical and chemical processes. The cell can change these interactions through modification of its environment or its own composition. This dissertation presents the overarching hypothesis that both biochemical regulation of intercellular adhesion and physical interaction between cells are required to account for the emergence of cluster migration and collective dynamics observed in epithelial cells. Collective migration is defined as the displacement of a group of cells with transient or permanent cell-cell contacts. One mode, cluster migration, plays an important role during embryonic development and in cancer metastasis. Despite its importance, collective migration is a slow process and hard to visualize, and therefore it has not been thoroughly studied in three dimensions (3D). Based on known information about cluster migration from 2D studies of epithelial sheets and 3D single cell migration, this dissertation presents theoretical and experimental techniques to assess the independent contribution of physical and biochemical factors to 3D cluster migration. It first develops two computational models that explore the interaction between cells and the ECM and epithelial discohesion. These discrete mechanistic models reveal the need to account for intracellular regulation of adherens junctions in space and time within a cluster. Consequently, a differential algebraic model is developed that accounts for cross-reactivity of three pathways in a regulatory biochemical network: Wnt/β-catenin signaling, protein N-glycosylation, and E-cadherin adhesion. The model is tested by matching predictions to Wnt/β-catenin inhibition in MDCK cells. The model is then incorporated into a self-propelled particle (SPP) model, creating the first SPP model for study of adhesive mammalian cellular systems. MDCK cell clusters with fluorescent nuclei are grown, seeded, and tracked in 3D collagen gels using confocal microscopy. They provide data on individual cell dynamics within clusters. Borrowed from the field of complex systems, normalized velocity is used to quantify the order of both in vitro and simulated clusters. An analysis of sensitivity of cluster dynamics on factors describing physical and biochemical processes provides new quantitative insights into mechanisms underlying collective cell migration and explains temporal and spatial heterogeneity of cluster behavior.