Combustion systems utilizing bluff bodies to stabilize the combustion processes can experience oscillatory heat release due to the alternate shedding of coherent, von Kármán vortices under certain operating conditions. This phenomenon needs to be understood in greater detail, since unsteady burning due to vortex shedding can lead to combustion instabilities and flame extinction in practical combustion systems. The primary objective of this study was to elucidate the influence of combustion process heat release upon the Bénard-von Kármán (BVK) instability in reacting bluff body wakes. For this purpose, spatial and temporal heat release distributions in bluff body-stabilized combustion of liquid Jet-A fuel with high-temperature, vitiated air were characterized over a wide range of operating conditions. Upon comparing the spatial and temporal heat release distributions, the fuel entrainment and subsequent heat release in the near-wake were found to strongly influence the onset and amplitude of the BVK instability. As the amount of heat release in the near-wake decreased, the BVK instability increased in amplitude. This was attributed to the corresponding decrease in the local density gradient across the reacting shear layers, which resulted in less damping of vorticity due to gas expansion. The experimental results were compared to the results of a parallel, linear stability analysis in order to further understand the influence of the combustion processes in the near-wake upon the wake instability characteristics. The results of this analysis support the postulate that oscillatory heat release due to BVK vortex shedding is the result of local absolute instability in the near-wake, which is eliminated only if the temperature rise across the reacting shear layers is sufficiently high. Furthermore, the results of this thesis demonstrate that non-uniform fuelling of the near-wake reaction zone increases the likelihood of absolutely unstable, BVK flame dynamics due to the possibility of near-unity products-to-reactants density ratios locally, especially when the reactants temperature is high.

No description available.

A general multidisciplinary design problem features coupling and feedback between contributing analyses. This feedback may lead to convergence issues requiring significant iteration in order to obtain a feasible design. This work casts the multidisciplinary design problem as a dynamical system in order to leverage the benefits of dynamical systems theory in a new domain. Three areas from dynamical system theory are chosen for investigation: stability analysis, optimal control, and estimation theory. Stability analysis is used to investigate the existence of a solution to the design problem and how that solution can be found. Optimal control techniques allow consideration of contributing analysis output and design variables constraints at the same level of the optimization hierarchy. Finally, estimation methods are employed to rapidly evaluate the robustness of the multidisciplinary design. These three dynamical system techniques are then combined in a methodology for the rapid robust design of linear multidisciplinary systems. While inherently linear, the developed robust design methodology is shown to be extensible to nonlinear systems. The applicability and performance of the developed technique is demonstrated through linear and nonlinear test problems including the design of a hypersonic aerodynamic surface for a system in which an increase in range or improvement in landed accuracy is sought. In addition, it is shown that the developed robust design methodology scales well compared to other methods.

<p>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 &lt / 1. This is the case of a disease-free&nbsp / state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic&nbsp / and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We&nbsp / use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on&nbsp / vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious&nbsp / disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.&nbsp / These are the most useful references: [G. Zaman, Y.H Kang, II. H. Jung. BioSystems 93,&nbsp / (2008), 240 &minus / 249], [K. Hattaf, N. Yousfi. The Journal of Advanced Studies in Biology, Vol. 1(8), (2008), 383 &minus / 390.], [Lenhart, J.T. Workman. Optimal Control and Applied to Biological Models.&nbsp / Chapman and Hall/CRC, (2007).], [P. Van den Driessche, J. Watmough. Math. Biosci., 7,&nbsp / (2005)], and [J. Wu, G. R&uml / ost. Mathematical Biosciences and Engineering, Vol 5(2), (2008), 389 &minus / 391].</p>

The materials that exhibit martensite transformation have very important applications in engineering, and the microstructures of the materials play a key role foraffecting their mechanical behavior in macroscope. Therefore many attentions havebeen drawn for studying the related problems. This work focuses on the motion oftwin boundaries. Three questions are being asked: how is a twin boundary is nucleated in a homogenous (untwinned) material? After the twin boundary is nucleated,how is its motion initiated? How fast does it move? This study provides an atomisticunderstanding for these three questions. Linear stability analysis is firstly applied to capture the initiation of motion of atwin boundary. When a twin boundary is about to move, the lowest eigenvalue of thesystem Hessian drops to zero. And the corresponding eigenvector predicts accuratelythe way in which the twin boundary is going to move. The same idea is applied toinvestigate how motion of an irrational twin boundary is initiated. Atomic modelsof irrational twin boundaries are constructed by employment of continuum models,provided that the point group of rotations which relate two variants is extended toany rotations in plane. The zero eigenvectors reveal the complicated behavior ofmotion of irrational twin boundaries. The problem of nonuniqueness of kinetic relations proposed by Schwetlick andZimmer is solved in a thermoelasticity framework. By calculating the net heat fluxcrossing the phase boundary which is carried by the phonons, a unique kinetic relationcan be determined. Finally, a nonlocal criterion for nucleation of twin boundariesis proposed. By checking the stiffness of each unit cell evaluated with respect to asingle variable that represents the displacement along the unit cell diagonal direction,locations and the orientations of nucleated twin boundaries can be predicted.

No description available.

En bergslänts stabilitet styrs av berggrundens egenskaper, så som sprickegenskaper och bergkvalité. För att uppnå önskad stabilitet i en bergslänt behöver de bergmekaniska parametrarna kartläggas och analyseras för att fastställa risker och stabilitetsåtgärder. Syftet med studien är att utvärdera kvalitén på bergteknisk data från digitalfotogrammetriska 3D-modeller genom att jämföra resultatet med manuella mätningar från konventionell kartläggning. Målet är även att utforska potentialen för användning av fotogrammetrisk 3D-modellering vid stabilitetsanalyser i bergslänter genom att utvärdera den bergtekniska analys som kan göras utifrån fotogrammetrisk data. Sprickmätningar framtagna från 3D-modellen visade sig ha samma kvalité som manuella mätningar tagna enligt konventionell metod. Den UAS-baserade fotogrammetrin kan dock inte ersätta den konventionella analysen helt vid stabilitetsanalyser men kan användas som ett kompletterande verktyg i bergtekniska undersökningar. Fotogrammetrin möjliggör datainsamling från ett säkrare avstånd vilket minskar riskmomenten som den konventionella metoden medför vid arbete i fält. Den digitala metoden visade sig även ha fler fördelar såsom möjligheten av kartläggning och analysering framför datorn för mindre tids- och kostnadskrävande moment, digital datalagring samt att slänter med begränsad åtkomst kan karteras. / The stability of a rock slope is controlled by the rock’s mechanical properties, such as rock quality and facets. To achieve the desired stability in a rock slope, the mechanical parameters need to be mapped and analysed to determine possible failures and decide necessary stability measures. The purpose of this study is to evaluate the quality of rock technical data from digital photogrammetry 3D models by comparing the result with manual measurements from conventional mapping. The goal is also to explore the potential uses of photogrammetric 3D models for rock slope stability analyses by evaluate the photogrammetric data. Facets extracted from 3D models were found to have the same quality as manual measurements. However, the UAS-based method cannot completely replace the conventional method but can be useful as a complementary tool. Photogrammetry enables the collection of data from a safer distance, which reduces workplace hazards that the conventional method entails. The digital method also proved to have more advantages, such as the possibility of digital mapping and analysing which is less costly and time-consuming, digital data storage and the possibility to access outcrops that can’t be mapped with manually measurements due to inaccessibility.

Networked predictive control is a new research method for Networked Control Systems (NCS), which is able to handle network-induced problems such as time-delay, data dropouts, packets disorders, etc. while stabilizing the closed-loop system. This work is an extension and complement of networked predictive control methodology. There is always present model uncertainties or physical nonlinearity in the process of NCS. Therefore, it makes the study of the robust control of NCS and that of networked nonlinear control system (NNCS) considerably important. This work studied the following three problems: the robust control of networked predictive linear control systems, the control scheme for networked nonlinear control systems (NNCS) and the robust control of NNCS. The emphasis is on stability analysis and the design of robust control. This work adapted the two control schemes, namely, the time-driven and the event driven predictive controller for the implementation of NCS. It studied networked linear control systems and networked nonlinear control systems. Firstly, time-driven predictive controller is used to compensate for the networked-induced problems of a class of networked linear control systems while robustly stabilizing the closed-loop system. Secondly, event-driven predictive controller is applied to networked linear control system and NNCS and the work goes on to solve the robust control problem. The event-driven predictive controller brings great benefits to NCS implementation: it makes the synchronization of the clocks of the process and the controller unnecessary and it avoids measuring the exact values of the individual components of the network induced time-delay. This work developed the theory of stability analysis and robust synthesis of NCS and NNCS. The robust stability analysis and robust synthesis of a range of different system configurations have been thoroughly studied. A series of methods have been developed to handle the stability analysis and controller design for NCS and NNCS. The stability of the closed-loop of NCS has been studied by transforming it into that of a corresponding augmented system. It has been proved that if some equality conditions are satisfied then the closed-loop of NCS is stable for an upper-bounded random time delay and data dropouts. The equality conditions can be incorporated into a sub-optimal problem. Solving the sub-optimal problem gives the controller parameters and thus enables the synthesis of NCS. To simplify the calculation of solving the controller parameters, this thesis developed the relationship between networked nonlinear control system and a class of uncertain linear feedback control system. It proves that the controller parameters of some types of networked control system can be equivalently derived from the robust control of a class of uncertain linear feedback control system. The methods developed in this thesis for control design and robustness analysis have been validated by simulations or experiments.

>Magister Scientiae - MSc / We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 < 1. This is the case of a disease-free state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.

La thèse est relative à la compréhension de la physique et au contrôle des émissions acoustiques dans les jets turbulents simples et double-flux. La génération du bruit est associé à des structures turbulentes de grandes tailles caractéristiques et à la turbulence de petites échelles. i Il est maintenant admis que les structures de grandes échelles sont des instabilités se propageant dans un champ moyen turbulent. Ici elle sont analysées sur la base de la théorie linéaire non locale appelées PSE pour Parabolized Stability Equations. Ces instabilités inflexionnelles associées à la présence de couche de cisaillement sont des modes de Kelvin-Helmhotz. Dans le cas du jet sous détentu des cellules de choc apparaissent et influencent très fortement les taux d'amplification et fréquences des modes propres. Divers écoulements sont investigués, de faible nombre de Mach au jet double-flux supersonique dont le champ moyen provient de simulation LES (Cerfacs). Le champ acoustique lointain est déterminé par l'analogie de Ffowcs-Williams-Hawkings. Ensuite une étude de sensibilité originales des instabilités et du bruits par rapport à divers forage locaux est produite sur la base deséquations de stabilité PSE adjointes. Les fortes sensibilités apparaissent dans les couches de cisaillements et aussi dans une moindre mesure autour des cellules de chocs. Les sensibilités sont plus complexes pour le jet double flux et dépendent du mode instable étudié lié soit au jet primaire soit au jet secondaire. Les sensibilités maximales se trouvent auvoisinage de la sortie de la tuyère et à la limite ou à l’extérieur du cne potentiel. En complément une étudesur le jet simple flux permet de mettre en rapport les approches de quantification d'incertitude et la sensibilité calculée par des équations adjointes. Les résultats de sensibilité vont permettre de contribuer à proposer des stratégies de contrôle aero-acoustique dans les jets de turboréacteurs. / This thesis leads to a better knowledge of the physic and of the control of acoustic radiation in turbulent single and dual-stream jets.It is known that jet noise is produced by the turbulence present in the jet that can be separated in large coherent structures and fine structures. It is also concluded that these large-scale coherent structures are the instability waves of the jet and can be modelled as the flow field generated by the evolution of instability waves in a given turbulent jet. The growth rate and the streamwise wavenumber of a disturbance with a fixed frequency and azimuthal wavenumber are obtained by solving the non-local approach called Parabolized Stability Equations (PSE). Typically the Kelvin-Helmholtz instability owes its origin into the shear layer of the flow and, moreover, the inflection points of the mean velocity profile has a crucial importance in the instability of such a flow. The problem is more complex in case of imperfectly expanded jet where shock-cells manifest inside the jet and strongly interaction with the instability waves has been observed. Several configurations are tested in this thesis, from a subsonic incompressible case to the dual-stream underexpanded supersonic jet obtained by solving Large Eddy Simulations LES (CERFACS). The acoustic far-field is determined by the Ffowcs-Williams-Hawkings acoustic analogy. Then a sensitivity analysis of the jet with respect to external forcing acting in a localized region of the flow are investigated by solving the adjoint PSE equations. High sensitivity appeared in the shear-layer of the flow showing, also, a high dependency in the streamwise and radial direction. In the case of dual-stream jet the propagation of the instability in the inner and outer shear layer should be taken into account. This configuration leads to two different distinct Klevin-Helmholtz modes that are computed separately. The highest sensitivity is determined in the exit of the nozzle outside of the potential core of the jet. In addition, comparison between sensitivity computed by adjoint equations and Uncertainty Quantification (UQ) methods has been done, in the case of a single-stream jet, showing a link between these two methods for small variations of the input parameters. This result leads to the application of a lower cost tool for mathematical analysis of complex problem of industrial interest. This work and in particular the sensitivity theory investigated in this thesis contribute to a development of a new noise control strategy for aircraft jet.