Thermoacoustic instability is of fundamental and applied interest in both scientific research and practical applications. This study aims to explore several very important sub-aspects in this field and contribute to a better understanding of thermoacoustic instability as encountered in typical gas turbines and rocket engines. Atomization has been recognized as a key mechanism in driving applied thermoacoustic instability. In this regard, this study mainly focuses on the atomization process relevant for delineation of thermoacoustic instability, contributing to a comprehensive understanding of the effect of acoustics on primary and secondary atomization. Firstly, a tree-based adaptive solver and VOF method are employed to simulate the jet primary atomization. The code is validated by theoretical, numerical and experimental results to demonstrate its capability and accuracy in terms of atomization in both low-speed and high-speed regime. Perturbation frequency and amplitude have shown to affect the atomization significantly. Besides, the effect of acoustic forcing on liquid ligament has also been numerically investigated. A volume source term is introduced to extend the solver to model the compressible effects in the presence of acoustic forcing. The influence of acoustic wave number, amplitude and frequency has been examined in detail. In terms of modelling the thermoacoustic instability, bifurcation analysis is carried out for a time-delayed thermoacoustic system using the Method of Line approach. Good predictions have been obtained to capture the nonlinear behaviors inherent in the system. Moreover, model-based simulation and control of thermoacoustic instability have been conducted. A low-order wave-based network model for acoustics is coupled with nonlinear flame describing function to predict the nonlinear instability characteristics in both frequency and time domain. Furthermore, active feedback control is implemented. Two different controllers have been designed to eliminate the thermoacoustic instability to an acceptably low level and may be employed in a practical manner.

abstract: Neglected tropical diseases (NTDs) comprise of diverse communicable diseases that affect mostly the developing economies of the world, the “neglected” populations. The NTDs Visceral Leishmaniasis (VL) and Soil-transmitted Helminthiasis (STH) are among the top contributors of global mortality and/or morbidity. They affect resource-limited regions (poor health-care literacy, infrastructure, etc.) and patients’ treatment behavior is irregular due to the social constraints. Through two case studies, VL in India and STH in Ghana, this work aims to: (i) identify the additional and potential hidden high-risk population and its behaviors critical for improving interventions and surveillance; (ii) develop models with those behaviors to study the role of improved control programs on diseases’ dynamics; (iii) optimize resources for treatment-related interventions. Treatment non-adherence is a less focused (so far) but crucial factor for the hindrance in WHO’s past VL elimination goals. Moreover, treatment non-adherers, hidden from surveillance, lead to high case-underreporting. Dynamical models are developed capturing the role of treatment-related human behaviors (patients’ infectivity, treatment access and non-adherence) on VL dynamics. The results suggest that the average duration of treatment adherence must be increased from currently 10 days to 17 days for a 28-day Miltefosine treatment to eliminate VL. For STH, children are considered as a high-risk group due to their hygiene behaviors leading to higher exposure to contamination. Hence, Ghana, a resource-limited country, currently implements a school-based Mass Drug Administration (sMDA) program only among children. School staff (adults), equally exposed to this high environmental contamination of STH, are largely ignored under the current MDA program. Cost-effective MDA policies were modeled and compared using alternative definitions of “high-risk population”. This work optimized and evaluated how MDA along with the treatment for high-risk adults makes a significant improvement in STH control under the same budget. The criticality of risk-structured modeling depends on the infectivity coefficient being substantially different for the two adult risk groups. This dissertation pioneers in highlighting the cruciality of treatment-related risk groups for NTD-control. It provides novel approaches to quantify relevant metrics and impact of population factors. Compliance with the principles and strategies from this study would require a change in political thinking in the neglected regions in order to achieve persistent NTD-control. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2020

Turbulent collapse and recovery are both observed to occur abruptly in the atmospheric stable boundary layer (SBL). The understanding and predictability of turbulent recovery remains limited, reducing numerical weather prediction accuracy. Previous studies have shown that regime occupation is the result of the net effect of highly variable processes, from turbulent to synoptic scales, making stochastic methods a compelling approach. Idealized stable boundary layer models have shown that under some circumstances, regimes can be related to the stable branches of model equilibria, and an additional unstable equilibrium is predicted. This work seeks to determine the extent to which the SBL regime occupation can be explained using a one-dimensional stochastic differential equation (SDE). The drift and diffusion coefficients of the SDE of an input time series are approximated from the statistics of its averaged time tendencies. These approximated coefficients are fit using Gaussian Process Regression. Probabilistic estimates of the system's equilibrium points are then found and used to create an empirical bifurcation diagram without making any prior assumptions on the dynamical form of the system. This data driven bifurcation diagram is compared to modelled predictions. The analysis is repeated on several meteorological towers around the world to assess the influence of local meteorological settings. This work provides empirical insights into the nature of regime dynamics and the extent to which the SBL displays hysteresis. / Graduate

A coupled fluid-structure interaction solver capability is developed and validated. A high fidelity fluids solver, Loci-Chem, is coupled with a finite-element structural dynamics toolkit, MAST. The coupled solver is validated for the prediction of several panel instability cases in uniform flows and in the presence of an impinging shock for a range of subsonic and supersonic Mach numbers, dynamic pressures, and pressure ratios. The panel deflections and limit-cycle oscillation amplitudes, frequencies, and bifurcation point predictions compare very well with benchmark results for 2D simulations. The same procedures outlined in the validation study have been applied to simulations of varying dynamic pressures at M = 2 for an impinging oblique shockwave. The influence of inviscid, laminar and turbulent boundary layer profiles on the development of flow field characteristics has been analyzed, and laminar predictions characterized by a large flow separation results in vastly different behavior than that of traditional flutter.

No description available.

We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models, and of the SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.

The focus of this thesis is the dynamical behaviour of linear arrays of laser oscillators with nearest-neighbour coupling. In particular, we study how laser dynamics are influenced by laser-coupling strength, $\kappa$, the natural frequencies of the uncoupled lasers, $\tilde{\Omega}_j$, and the coupling between the magnitude and phase of each lasers electric field, $\alpha$. Equivariant bifurcation analysis, combined with Lyapunov exponent calculations, is used to study different aspects of the laser dynamics. Firstly, codimension-one and -two bifurcations of relative equilibria determine the laser coupling conditions required to achieve stable phase locking. Furthermore, we find that global bifurcations and their associated infinite cascades of local bifurcations are responsible for interesting locking-unlocking transitions. Secondly, for large $\alpha$, vast regions of the parameter space are found to support chaotic dynamics. We explain this phenomenon through simulations of $\alpha$-induced stretching-and-folding of the phase space that is responsible for the creation of horseshoes. A comparison between the results of a simple {\it coupled-laser model} and a more accurate {\it composite-cavity mode model} reveals a good agreement, which further supports the use of the simpler model to study coupling-induced instabilities in laser arrays. Finally, synchronisation properties of the laser array are studied. Laser coupling conditions are derived that guarantee the existence of synchronised solutions where all the lasers emit light with the same frequency and intensity. Analytical stability conditions are obtained for two special cases of such laser synchronisation: (i) where all the lasers oscillate in-phase with each other and (ii) where each laser oscillates in anti-phase with its direct neighbours. Transitions from complete synchronisation (where all the lasers synchronise) to optical turbulence (where no lasers synchronise and each laser is chaotic in time) are studied and explained through symmetry breaking bifurcations. Lastly, the effect of increasing the number of lasers in the array is discussed in relation to persistent optical turbulence.

A bactéria Zymomonas mobilis atraiu considerável interesse nas últimas décadas devido ao seu metabolismo único e eficientes características fermentativas na produção de etanol a partir de açúcares simples. No entanto, apesar das aparentes vantagens na conversão e taxas específicas quando comparada com as leveduras, estas ainda dominam o mercado produtivo de etanol. Dentre os diversos modelos encontrados na literatura para representar o processo fermentativo de glicose através de Z. mobilis, o modelo proposto por Jöbses et al. (1986) aparenta ser bem estruturado e ideal para a criação de estratégias de controle e otimização de processos fermentativos com este microrganismo, viabilizando sua utilização em escala industrial. Fermentações de Z. mobilis em regime contínuo apresentam comportamento oscilatório para baixas taxas de diluição, fenômeno este comprovado experimentalmente. Experimentos laboratoriais foram utilizados para a estimação de parâmetros do modelo de Jöbses, através da técnica de minimização da derivada do erro da função objetivo. O novo modelo ajustado apresenta dinâmica equivalente ao modelo original de Jöbses, fato este comprovado através da construção dos diagramas de bifurcação. Os diagramas de fase dos modelos apresentam algumas diferenças estruturais entre si, entretanto, a ocorrência de multiplicidade de estados estacionários em baixos valores de taxa de diluição está presente em todos. Em bioprocessos, a obtenção de informações sobre o sistema é um tanto complexa, devido a estes meios serem muito suscetíveis a distúrbios, contaminações, além de que medidas de concentrações são relativamente dispendiosas, associadas com um alto tempo morto, o que impossibilita, muitas vezes, a implementação de sistemas de controle eficientes. Para contribuir com a resolução deste problema foi desenvolvida uma nova inferência das variáveis de estado através da informação de consumo de hidróxido de sódio, utilizado no controle de pH do meio. Inferidores de variáveis de estado que utilizam a variação no consumo de hidróxido de sódio foram ajustados e apresentaram resultados promissores, mostrando a viabilidade do desenvolvimento de metodologias para este tipo de análise, tornando a caracterização de sistemas fermentativos mais rápida e acessível, não apenas em nível acadêmico, que a desenvolvida atualmente, principalmente devido ao baixo custo associado, e a dinâmica rápida deste tipo de sensor. / The bacterium Zymomonas mobilis has attracted considerable interest in recent decades due to their unique metabolism and efficient characteristics in the production of ethanol by simple sugars. However, despite the apparent advantages in the conversion and specific rates, when compared with yeast, there is no industrial-scale fermentations with these bacteria. Among the various models found in literature to represent glucose fermentation with Z. mobilis, the model proposed by Jöbses et al. (1986) appears to be well structured and ideal for the creation of control strategies and optimization methods for increase productions. Fermentation in continuous mode with this organism exhibit oscillatory behavior at low dilution rates, phenomenon showed or demonstrated by experiments performed on laboratory scale. A laboratorial experiment also was used for estimation of new parameters group of Jöbses models, using the technique of minimization of error derivative for objective function. The new adjusted model set presents dynamics similar to the original model, fact confirmed by bifurcation analyses of both models. The diagram for these models show structural differences, but both presents steady states multiplicity and Hopf bifurcations. The obtained of fermentation characteristics is very complex, due to these reactive means being very susceptible to disturbances, contamination, among others, and concentrations measures are relatively expensive and whit a high dead time associated, which often prevents the implementation of control tools. The proposed inference of state variables by consumption rate of hydroxide sodium, used for maintenance pH medium, was tested and confirmed. Virtual sensors using the information of consumption rate of hydroxide were adjusted and have shown promising results, demonstrating the feasibility of developing methods of analysis based on this methodology, making the characterization of fermentative systems faster and cheaper them currently developed, mainly due to low cost associated, and the dynamics of this fast type of sensor.

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequency occurrence in engineering applications. Therefore, the present thesis focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on optimization and sensitivity analysis procedures, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this thesis sets the emphasis on a tuning procedure of nonlinear vibration absorbers that can be computationally tractable and treat strongly nonlinear regimes of motion. The proposed methodology is a two-step procedure relying on a frequency-energy based approach followed by a bifurcation analysis. The first step, carried out in the free vibration case, imposes the absorber to possess a qualitatively similar dependence on energy as the primary system. This gives rise to an optimal nonlinear functional form and an initial set of absorber parameters. Based upon these initial results, the second step, carried out in the forced vibration case, exploits the relevant information contained within the nonlinear frequency response functions, namely, the bifurcation points. Their tracking in parameter space enables the adjustment of the design parameter values to reach a suitable tuning of the absorber. The use of the resulting integrated tuning methodology on nonlinear vibration absorbers coupled to systems with nonlinear damping is then investigated. The objective lies in determining an appropriate functional form for the absorber so that the limit cycle oscillation suppression is maximized. Finally, the proposed tuning methodology of nonlinear vibration absorbers may impose the use of complicated nonlinear functional forms whose practical realization, using mechanical elements, may be difficult. In this context, an electro-mechanical nonlinear vibration absorber relying on piezoelectric shunting possesses attractive features as various functional forms for the absorber nonlinearity can be achieved through proper circuit design. The foundation of this new approach are laid down and the perspectives are discussed.

An increasing number of contemporary studies in aquatic ecology emphasize the im- portance of highly unsaturated fatty acids (HUFAs) at the plant-animal interface. Studies have demonstrated a wide range of fatty acid profiles in primary producers, forcing her- bivorous zooplankton to differentially retain fatty acids to meet somatic requirements. Herbivores also vary in their somatic fatty acid profiles; cladocerans collect Eicosapen- taenoic Acid (EPA), copepods prefer Docosahexaenoic Acid (DHA). Fatty acid internal reserves can be broken down to meet structural needs (i.e. phospholipid synthesis), fuel reproduction and may play a role in cold weather adaptation. Several authors have noted increases in HUFA concentration with lowering ambient temperatures. Cladoceran membranes form a gel at lower temperatures, while copepod membranes remain fluid and allow active overwintering. Both fish and crustaceans accumulate high concentrations of HUFAs during periods of rapid growth, but colimitation with elemental resources may exist. Recent modeling results suggest food webs with high quality (nutritional and biochemical) primary producers can attain inverted biomass distributions with efficient energy transfer between trophic levels. The adoption rate for this material into man- agement studies remains low, and while other sectors of the scientific community thrive on the potential of HUFAs, planktonic food-web studies are choosing traditional view points over forward thinking. Bearing in mind the emerging hypotheses on the critical factors that drive the energy flow in the plant-animal interface, my dissertation will at- tempt to address the following general questions: What are the distinct signatures of food quality and food quantity on planktonic food web dynamics? How do nutritional and biochemical factors affect the flow of energy at the plant-animal interface? What is our current understanding of the role of highly unsaturated fatty acids (HUFAs) in aquatic food webs? To what extent can the current generation of plankton models reproduce the lower food web patterns when explicitly accounting for HUFAs? Is the integration of the HUFA role into water quality management models feasible? Explicitly accounting for HUFAs requires integrating factors of animal physiology with macro-ecology: what are the ramifications? Finally, what are the evolutionary aspects of animals coping with food quality?