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Hadley, Kathryn Z. 1955. "Linear stability analysis of nonaxisymmetric instabilities in self-gravitating polytropic disks." Thesis, University of Oregon, 2011. http://hdl.handle.net/1794/11253.
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xvii, 371 p. : col. ill.An important problem in astrophysics involves understanding the formation of planetary systems. When a star-forming cloud collapses under gravity its rotation causes it to flatten into a disk. Only a small percentage of the matter near the rotation axis falls inward to create the central object, yet our Sun contains over 99% of the matter of our Solar System. We examine how global hydrodynamic instabilities transport angular momentum through the disk causing material to accrete onto the central star. We analyze the stability of polytropic disks in the linear regime. A power law angular velocity of power q is imposed, and the equilibrium disk structure is found through solution of the time-independent hydrodynamic equations via the Hachisu self-consistent field method. The disk is perturbed, and the time-dependent linearized hydrodynamic equations are used to evolve it. If the system is unstable, the characteristic growth rate and frequency of the perturbation are calculated. We consider modes with azimuthal e im[varphi] dependence, where m is an integer and [varphi] is the azimuthal angle. We map trends across a wide parameter space by varying m , q and the ratios of the star-to-disk mass M * /M d and inner-to-outer disk radius r - /r + . We find that low m modes dominate for small r - /r + , increasing to higher r - /r + as M * /M d increases, independent of q . Three main realms of behavior are identified, for M * << M d , M * [approximate] M d and M * >> M d , and analyzed with respect to the I, J and P mode types as discussed in the literature. Analysis shows that for M * << M d , small r - /r + disks are dominated by low m I modes, which give way to high m J modes at high r - /r + . Low m J modes dominate M * [approximate] M d disks for small r - /r + , while higher m I modes dominate for high r - /r + . Behavior diverges with q for M * >> M d systems with high q models approximating M * [approximate] M d characteristics, while low q models exhibit m = 2 I modes dominating where r - /r + < 0.60.
Committee in charge: Raymond Frey, Chairperson; James Imamura, Advisor; Robert Zimmerman, Member; Paul Csonka, Member; Alan Rempel, Outside Member
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Tun, Yarzar. "Nonmodal Analysis of Temporal Transverse Shear Instabilities in Shallow Flows." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36886.
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Shallow flows are those whose width is significantly larger than their depth. In these types of flows, two dimensional coherent structures can be generated and can influence the flow greatly by the lateral transfer of mass and momentum. The development of coherent structures as a result of flow instabilities has been a topic of interest for environmental fluid mechanics for decades. Studies on the use of linear modal stability analysis is commonly found in literature. However, the relatively recent development in the field of hydrodynamic stability suggests that the traditional linear modal stability analysis does not describe the behaviour of the perturbations in finite time. The discrepancy between asymptotic behaviour and finite time behaviour is particularly large in shear driven flows and it is most likely to be the case for shallow flows. This study aims to provide a better understanding of finite time growth of perturbation energy in shallow flows. The three cases of shallow flows evaluated are the mixing layer, jet and wake. The critical cases are obtained through the linear modal analysis and nonmodal analysis was conducted to show the transient behaviour in finite time for what is so-called marginally stable. Finally, the thesis concludes by generalizing the finite time energy growth in the S-k space.
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Bridel-Bertomeu, Thibault. "Investigation of unsteady phenomena in rotor/stator cavities using Large Eddy Simulation." Thesis, Toulouse, INPT, 2016. http://oatao.univ-toulouse.fr/17867/1/BRIDEL_BERTOMEU.pdf.
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This thesis provides a numerical and theoretical investigation of transitional and turbulent enclosed rotating flows, with a focus on the formation of macroscopic coherent flow structures. The underlying processes are strongly threedimensional due to the presence of boundary layers on the discs and on the walls of the outer (resp. inner) cylindrical shroud (resp. shaft). The complexity of these flows poses a great challenge in fundamental research however the present work is also of importance for industrial rotating machinery, from hard-drives to space engines turbopumps - the design issues of the latter being behind the motivation for this thesis. The present work consists of two major investigations. First, industrial cavities are modeled by smooth rotor/stator cavities and therein the dominant flow dynamics is investigated. For the experimental campaigns on industrial machinery revealed dangerous unsteady phenomena within the cavities, the emphasis is put on the reproduction and monitoring of unsteady pressure fluctuations within the smooth cavities. Then, the LES of three configurations of real industrial turbines are conducted to study in situ the pressure fluctuations and apply the diagnostics already vetted on academic problems.
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Bengana, Yacine. "Simulations numériques pour la prédiction de fréquences par champs moyens." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLET032.
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Les écoulements fluides jouent un rôle important dans de nombreux phénomènes naturels ainsi que dans de nombreux secteurs industriels. On s’intéresse dans cette thèse aux écoulements instationnaires oscillants provenant d’une bifurcation de Hopf.L’écoulement affleurant une cavité carrée ouverte présente deux cycles limites séparés par un état quasi-périodique instable. Nous avons décrit en détail ce scénario au moyen de simulations numériques directes, de l’analyse de stabilité linéaire et de l’analyse de Floquet. La bifurcation de Hopf dans la geometry de Taylor-Couette donne naissance à deux solutions, les spirals (ondes progressives) et les rubans (ondes stationnaires dans la direction axiale). Nous avons découvert que la branche des rubans est suivie de deux cycles hétéroclines consécutifs avec deux états axisymétriques comme point d’ancrage.L’analyse de stabilité linéaire autour des solutions stationnaires permet d’obtenir le seuil de bifurcation. Une autre approche, est la linéarisation autour du champ moyen. Cette approche permet d’obtenir des fréquences très proches des fréquences non linéaires et montre dans la plupart des cas un taux de croissance proche de zéro. Nous avons montré que les spirales, les rubans, la cavité entrainée ainsi que l’écoulement autour d’un objet prismatique vérifient cette propriété.Dans la convection thermosolutal, la linéarisation autour du champ moyen des ondes stationnaires ne permet pas d’obtenir les fréquences non linéaires et le taux de croissance est loin d’être zéro, par contre pour les ondes progressives cette propriété est pleinement satisfaite. Nous avons étudié la validité d’un modèle auto-cohérent dans le cas de ces ondes progressives. En effet, si l’écoulement vérifie la propriété du champ moyen, ce modèle est supposé calculer le champ moyen, la fréquence nonlinear ainsi que l’amplitude. Ce modèle est constitué de l’équation gouvernant le champ moyen couplé avec l’équation linéarisé au travers le mode le plus instable et des contraintes de Reynolds. Nous avons montré que dans le cas des ondes progressives ce modèle permet de prédire la fréquence non linéaire seulement très proche du seuil. La prédiction est améliorée significativement en considérant les ordres supérieurs dans le terme des contraintes de ReynoldsFluid flows play an important role in many natural phenomena as well as in many industrial applications. In this thesis, we are interested in oscillating flows origins from a Hopf bifurcation.The open shear-driven square cavity has two limit cycles separated by an unsteady quasi-periodic state. We have described this scenario in detail by using direct numerical simulations, linear stability analysis, and Floquet analysis. The Hopf bifurcation in Taylor-Couette flow gives rise to two solutions, spirals (traveling waves) and ribbons (standing waves in the axial direction). We discovered that the ribbons branch is followed by two consecutive heteroclinic cycles connecting two pairs of axisymmetric vortices. We studied in detail these two heteroclinic cycles.The linear stability analysis about the stationary solution is used to compute the threshold of the bifurcations. Another approach is the linearization about the mean field. This approach gives frequencies very close to that of the nonlinear system and shows in most cases a nearly zero growth rate. We have shown that spirals, ribbons, the lid-driven cavity and the flow around a prismatic object verify this property.In the thermosolutal convection, the frequencies obtained by the linearization about the mean field of the standing waves do not match the nonlinear frequencies and the growth rate is far from zero, on the other hand for the traveling waves this property is fully satisfied. We studied the validity of a self-consistent model in the case of the traveling waves. The self-consistent model consists of the mean field governing equation coupled with the linearized Navier-Stokes equation through the most unstable mode and the Reynolds stress term. This model calculates the mean field, the nonlinear frequency, and the amplitude without time integration. The self-consistent model is assumed to be valid for flows that satisfy the property of the mean field. We have shown that in this case, this model predicts the nonlinear frequency only very close to the threshold. We have improved significantly the predictions by considering higher orders in the Reynolds stress term
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Zhang, Mengqi. "Linear stability Analysis of Viscoelastic Flows." Thesis, KTH, Mekanik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-95137.
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The goal of present work is to investigate the instability of jet ow, mixing layer and Poiseuille ow of viscoelastic uids. According to Boeta et al: [4], small elastic eect in Kolmogorov ow will result in increasing critical Re for hydrodynamic instability, however, at high elasticity a new instability of elastic nature occurs even at vanishing Re. This thesis aims to test this result in jet and mixing layer. In addition, linear stability analysis (modal and non-modal) of viscoelastic Poiseuille ow is carried out to understand the elastic eects on the ows of both Oldroyd-B and FENE-P model uids. Energy analysis is used to reveal the instability mechanism.
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Hu, Bin. "Stability analysis of linear thin shells." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7360/.
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Shell structure is widely used in engineering area. The purpose of this dissertation is to show the behavior of a thin shell under external load, especially for long cylindrical shell under compressive load, I analyzed not only for linear elastic problem and also for buckling problem, and by using finite element analysis it shows that the imperfection of a cylinder could affect the critical load which means the buckling capability of this cylinder.
For linear elastic problem, I compared the theoretical results with the results got from Straus7 and Abaqus, and the results are really close. For the buckling problem I did the same: compared the theoretical and Abaqus results, the error is less than 1%, but in reality, it’s not possible to reach the theoretical buckling capability due to the imperfection of the cylinder, so I put different imperfection for the cylinder in Abaqus, and found out that with the increasing of the percentage of imperfection, the buckling capability decreases, for example 10% imperfection could decrease 40% of the buckling capability, and the outcome meet the buckling behavior in reality.
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VALERIO, JULIANA VIANNA. "LINEAR STABILITY ANALYSIS OF VISCOUS AND VISCOELASTIC FLOWS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10021@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
As informações sobre a sensibilidade da solução de um dado escoamento mediante a perturbações infinitesimais é importante para o seu completo entendimento. A análise de estabilidade de escoamentos pode ser utilizada na otimização de processos industriais. Na indústria de revestimento o controle da estabilidade é fundamental, uma vez que o escoamento na região de aplicação da camada de líquido sobre o substrato, de um modo geral, tem que ser laminar, bidimensional e em regime permanente. O objetive é determinar, dentro do espaço de parâmetros de operação, a região onde o escoamento é estável e conseqüêntemente a camada a ser revestida uniforme. Porém, por ser uma análise complexa, só é usada na indústria em estudos mais apurados. O sistema linear que descreve a estabilidade vai ser discretizado com o método de Galerkin / elementos finitos, dando origem a um problema de autovalor generalizado.Tanto para escoamentos com líquidos newtonianos como para escoamentos com líquidos viscoelásticos, uma das matrizes do problema de autovalor generalizado é singular e alguns autovalores se encontram no infinito. No escoamento com líquidos viscoelásticos parte do espectro é contínuo, aumentando o grau de dificuldade da análise numérica para encontrá-lo. Nesse trabalho, vamos apresentar um método baseado em transformações lineares tirando vantagem das estruturas matriciais e transformando-as em um problema de autovalor clássico com dimens são, pelo menos, três vezes menor que o original. O método elimina os autovalores infinitos do problema com um baixo custo computacional. A estabilidade de um escoamento de Couette unidimensional de líquido newtoniano é analisada como um primeiro exemplo. Depois, o início do estudo da estabilidade em um escoamento de Couette bidimensional e também um escoamento pistonado com o mesmo líquido. Generaliza-se o método para o escoamento de Couette de um líquido viscoelástico, os resultados para o escoamento de um líquido cujo comportamento mecânico é descrito pelo modelo de Maxwell são apresentados e comparados com a solução analítica de Gorodtsov & Leonov, 1967. A relação entre os autovetores do problema transformado e do original é apresentada.
Steady state,two-dimensional flows may become unstable under two and three-dimensional disturbances, if the flow parameters exceed some critical values. In many practical situations, determining the parameters at which the flow becomes unstable is essential. The complete understanding of viscous and viscoelastic flows requires not only the steady state solution of the governing equations, but also its sensitivity to small perturbations. Linear stability analysis leads to a generalized eigenvalue problem, GEVP. Solving the GEVP is challenging, even for Newtonian liquids, because the incompressibility constraint creates singularities that lead to nonphysical eigenvalues at infinity. For viscoelastic flows, the difficulties are even higher because of the continuous spectrum of eigenmodes associated with differential constitutive equations. The complexity and high computational cost of solving the GEVP have probably discouraged the use of linear stability analysis of incompressible flows as a general engineering tool for design and optimization. The Couette flow of UCM liquids has been used as a classical problem to address some of the important issues related to stability analysis of viscoelastic flows. The spectrum consists of two discrete eigenvalues and a continuous segment of eigenvalues with real part equal to -1/We (We is the Weissenberg number). Most of the numerical approximation of the spectrum of viscoelastic Couette flow presented in the literature were obtained using spectral expansions. The eigenvalues close to the continuous part of the spectrum show very slow convergence. In this work, the linear stability of Couette flow of a Newtonian and UCM liquids were studied using finite element method, which makes it easier to extend the analysis to complex flows. A new procedure to eliminate the eigenvalues at infinity from the GEVP that come from differential equations is also proposed. The procedure takes advantage of the structure of the matrices involved and avoids the computational effort of common mapping techniques. With the proposed procedure, the GEVP is transformed into a smaller simple EVP, making the computations more effcient. Reducing the computational memory and time. The relation between the eigenvector from the original problem and the reduced one is also presented.
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Flynn, Terrance J. "Linear stability analysis of a solidifying ternary alloy." Fairfax, VA : George Mason University, 2009. http://hdl.handle.net/1920/4594.
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Thesis (M.S.)--George Mason University, 2009.Vita: p. 164. Thesis director: Daniel Anderson. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics. Title from PDF t.p. (viewed Oct. 12, 2009). Includes bibliographical references (p. 163). Also issued in print.
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Fang, Yuguang. "Stability analysis of linear control systems with uncertain parameters." Case Western Reserve University School of Graduate Studies / OhioLINK, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=case1057598985.
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Beneddine, Samir. "Characterization of unsteady flow behavior by linear stability analysis." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX010/document.
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Au cours des dernières décennies, la théorie de la stabilité a été intensivement utilisée pour caractériser le comportement instationnaire d'écoulements. Cela a donné naissance à un grand nombre d'approches, mais malheureusement chacune d'entre elles semble présenter ses propres limitations. De plus, leurs conditions de validité sont encore très mal connues, ce qui soulève la question de la fiabilité de ce genre de méthodes dans un cas général.Cette problématique est traitée dans cette thèse en s'intéressant dans un premier temps aux approches classiques de stabilité, qui étudient l'évolution de petites perturbations autour d'une solution stationnaire -- un champ de base -- des équations de Navier-Stokes. Pour cela, le phénomène du screech -- un bruit tonal que peuvent causer les jets sous-détendus -- est étudié d'un point de vue de la stabilité linéaire. Les résultats obtenus montrent que la dynamique non-linéaire du phénomène est correctement prédite par une analyse linéaire de stabilité du champ de base. Une confrontation avec d'autres analyses similaires montre qu'un tel résultat n'est pas toujours observé. Cependant, lorsque les oscillations auto-entretenues d'un écoulement sont provoquées par un bouclage acoustique, comme c'est le cas entre autres pour le screech, l'écoulement de cavité ou encore les jets impactants, alors les non-linéarités ont une faible influence sur le phénomène de sélection de fréquence. Cela explique la capacité d'une analyse linéaire à caractériser ces écoulements, même dans le régime non-linéaire.Une autre approche, consistant à étudier la stabilité linéaire du champ moyen, a montré de bons résultats dans certaines configurations qui ne peuvent être correctement étudiées par une analyse linéaire du champ de base. Cela est justifié dans cette thèse en mettant en évidence le rôle que joue la résolvante autour du champ moyen dans la dynamique d'un écoulement. Il est montré que lorsque cet opérateur présente une forte séparation de valeurs singulières, ce qui correspond à l'existence d'un mécanisme d'instabilité fort, alors les modes de Fourier de l'écoulement sont proportionnels aux modes de résolvante dominants. Ce résultat fournit des conditions mathématiques et physiques pour l'utilisation et le sens de diverses méthodes d'analyse du champ moyen, telles qu'une analyse d'équations de stabilité parabolisées (Parabolised Stability Equations). De plus, cela permet de mettre en place un modèle de prédiction du spectre fréquentiel en tout point d'un écoulement, à partir d'une ou de quelques mesures ponctuelles et du champ moyen. L'ensemble de ces résultats est illustré et validé sur un cas de marche descendante turbulente. Enfin, cela est exploité dans un cadre expérimental, afin de reconstruire le comportement instationnaire d'un jet rond transitionnel, à partir de la seule connaissance du champ moyen et d'une mesure ponctuelle. L'étude montre que, sous certaines précautions expérimentales, la reconstruction est très précise et robusteLinear stability theory has been intensively used over the past decades for the characterization of unsteady flow behaviors. While the existing approaches are numerous, none has the ability to address any general flow. Moreover, clear validity conditions for these techniques are often missing, and this raises the question of their general reliability.In this thesis, this question is addressed by first considering the classical stability approach, which focuses on the evolution of small disturbances about a steady solution -- a base flow -- of the Navier-Stokes equations.To this end, the screech phenomenon -- a tonal noise that is sometimes generated by underexpanded jets -- is studied from alinear stability point of view. The results reveal that the nonlinear dynamics of this phenomenon is well-predicted by a linear base flow stability analysis. A confrontation with other similar analyses from the literature shows that such a satisfactory result is not always observed. However, when a self-sustained oscillating flow is driven by an acoustic feedback loop, as it is the case for the screech phenomenon, cavity flows and impinging jets for instance, then the nonlinearities have a weak impact on the frequency selection process, explaining the ability of a linear analysis to characterize the flow, even in the nonlinear regime.Another alternative approach, based on a linearization about the mean flow, is known to be successful in some cases where a base flow analysis fails. This observation from the literature is explained in this thesis by outlining the role of the resolvent operator, arising from a linearization about the mean flow, in the dynamics of a flow. The main finding is that if this operator displays a clear separation of singular values, which relates to the existence of one strong convective instability mechanism, then the Fourier modes areproportional to the first resolvent modes. This result provides mathematical and physical conditions for the use and meaning of several mean flow stability techniques, such as a parabolised stability equations analysis of a mean flow.Moreover, it leads to a predictive model for the frequency spectrum of a flow field at any arbitrary location, from the sole knowledge of the mean flow and the frequency spectrum at one or more points. All these findings are illustrated and validated in the case of a turbulent backward facing step flow. Finally, these results are exploited in an experimental context, for the reconstruction of the unsteady behavior of a transitional round jet, from the sole knowledge of the mean flow and one point-wise measurement. The study shows that, after following a few experimental precautions, detailed in the manuscript, the reconstruction is very accurate and robust
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Zhou, Qing. "Combined linear/nonlinear stability analysis of plane and space frames." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-07112009-040327/.
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Allen, Leanne. "Modelling dolphin hydrodynamics : the numerical analysis and hydrodynamic stability of flow past compliant surfaces." Thesis, University of Surrey, 2001. http://epubs.surrey.ac.uk/844005/.
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Historical numerical methods for solving stiff ordinary differential equations are investigated and a new numerical framework developed and applied to a variety of hydrodynamic stability problems where the effects of passive wall compliance are investigated. The compound matrix method is set in a general coordinate free framework using exterior algebra, and is considered to be the most accurate and easy to implement method for complex systems. The effect of passive wall compliance on the Blasius boundary layer flow is studied. The linear stability of the mean flow state is considered using the new numerical framework and shooting technique. A Newton algorithm is implemented to converge the eigenvalue such that the boundary condition at the surface is satisfied. Curves of neutral stability are produced in the Re-alpha plane for various degrees of compliance, damping and tension parameters. Three dimensionality is incorporated first by a simple introduction of rotation in the flow leading to the investigation of the Ekman boundary layer problem where a Coriolis force instability mechanism (type-2) produces streamwise rolls at modest Reynolds numbers. The linear stability of the Ekman mean flow state is considered using an extension of the new numerical framework for use on the vector space Lambda(3)(C6). Curves of neutral stability are produced in the E-gamma plane for constant values of the Reynolds number and in the Re-gamma plane for a selection of constant angle of orientation, E. This work is extended to consider the effects of wall compliance on the type-2 viscous instability mechanism, with the type-1 mode of instability briefly discussed. Three-dimensionality is then used for a direct application to the dolphin. The stability of the attachment-line boundary layer is investigated on flows past swept wings, relating directly to the dolphins swept-back fins. Wall compliance, modelling the dolphins skin, is included for analysis of its effect on the attachment-line instability.
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Wirth, Walter M. "Linear modeling of rotorcraft for stability analysis and preliminary design." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1993. http://handle.dtic.mil/100.2/ADA274869.
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Douglas, Jamie George Iain. "Linear stability analysis of non ideal tokamak plasma fluid models." Thesis, University of Sheffield, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614645.
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Huang, Shiling. "Linear stability analysis of non-reacting and reacting elliptical jets." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-164706/.
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Xiong, Dapeng. "Stability analysis and controller synthesis of linear parameter varying systems /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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Atalayer, Senem Hayriye. "Analysis Of Stability And Transition In Flat Plate Compressible Boundary Layers Using Linear Stability Theory." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/2/12605366/index.pdf.
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In this study, numerical investigations of stability and transition problems were performed for 2D compressible boundary layers over a flat plate in adiabatic wall condition. Emphasis was placed on linear stability theory. The mathematical formulation for 3D boundary layers with oblique waves including detailed theoretical information was followed by use of the numerical techniques for the solution of resulting differential system of the instability problem, consequently an eigenvalue problem.
First, two-dimensional sinusoidal disturbances were analyzed at various Mach numbers including the subsonic, transonic, supersonic and even hypersonic flow speeds. In this case, the second mode (acoustic mode), namely the Mack mode, and its behavior with the increasing Mach number were visualized. The results were then compared with the available data in literature concluding with good agreements.
Secondly, similar analysis was carried out for oblique waves. Here, not only the effect of flow speed but also the effect of wave orientation was demonstrated. For this purpose, instability problem was solved for several wave angles at each Mach number in the range of M=0 and M=5. In this respect, the angle at which the waves were most unstable was also obtained at each investigated flow speed. The resultant stability diagrams corresponding to M=4 and higher Mach numbers for which both first and the second modes appear revealed that plane waves were more stable than oblique waves for the Tollmien-Schlichting mode, however, this was the opposite for the acoustic mode where oblique waves were observed to be more stable.
As a final step, estimation of the transition location was handled for the most unstable wave condition. Smith-Van Ingen transition method was applied as the prediction device. The results representing the influence of Mach number on transition Reynolds number were then compared with the experimental data as well as the numerical ones in literature ending up with very good agreements.
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Allievi, Alejandro. "Experimental and numerical analysis of a fishing vessel motions and stability in a longitudinal seaway." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26680.
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Motions and stability of a typical B.C. fishing vessel were experimentally and numerically investigated in a longitudinal seaway condition. The experimental model was self-propelled, radio-controlled and equipped with an on-board data acquisition system. Pitch, roll, yaw, surge, and heave responses to regular waves of predetermined frequencies and amplitudes generated along a 220-ft model basin were obtained. Different displacement conditions and GM configurations were tested.
The numerical model for the dynamic analysis of the fishing vessel motions has been implemented using strip theory. A computer program was developed to study the nonlinear motions of the vessel. The velocity dependent coupling terms, responsible for a major part of the nonlinear behavior, were included. A time dependent component analysis of the roll damping has been performed. Regular linear and nonlinear waves were used.
A parametric study of the fishing vessel stability has been carried out by considering its dynamic response in waves of varying characteristics. Unstable behaviour was found to be closely related to waves of length of similar magnitude to the ship length. The effects of wave amplitude and rudder usage were found to be of capital importance in the capsizing process. Experimental and numerical results showed good agreement.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Burckhart, Andreas. "Different ELM regimes at ASDEX Upgrade and their linear stability analysis." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-164858.
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Tang, Ying. "Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT054/document.
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Les dynamiques des systèmes modélisés par des équations aux dérivées partielles (EDPs) en dimension infinie sont largement liées aux réseaux physiques. La synthèse de la commande et l'analyse de la stabilité de ces systèmes sont étudiées dans cette thèse. Les systèmes singulièrement perturbés, contenant des échelles de temps multiples sont naturels dans les systèmes physiques avec des petits paramètres parasitaires, généralement de petites constantes de temps, les masses, les inductances, les moments d'inertie. La théorie des perturbations singulières a été introduite pour le contrôle à la fin des années $1960$, son assimilation dans la théorie du contrôle s'est rapidement développée et est devenue un outil majeur pour l'analyse et la synthèse de la commande des systèmes. Les perturbations singulières sont une façon de négliger la transition rapide, en la considérant dans une échelle de temps rapide séparée. Ce travail de thèse se concentre sur les systèmes hyperboliques linéaires avec des échelles de temps multiples modélisées par un petit paramètre de perturbation. Tout d'abord, nous étudions une classe de systèmes hyperboliques linéaires singulièrement perturbés. Comme le système contient deux échelles de temps, en mettant le paramètre de la perturbation à zéro, deux sous-systèmes, le système réduit et la couche limite, sont formellement calculés. La stabilité du système complet de lois de conservation implique la stabilité des deux sous-systèmes. En revanche un contre-exemple est utilisé pour illustrer que la stabilité des deux sous-systèmes ne suffit pas à garantir la stabilité du système complet. Cela montre une grande différence avec ce qui est bien connu pour les systèmes linéaires en dimension finie modélisés par des équations aux dérivées ordinaires (EDO). De plus, sous certaines conditions, l'approximation de Tikhonov est obtenue pour tels systèmes par la méthode de Lyapunov. Plus précisément, la solution de la dynamique lente du système complet est approchée par la solution du système réduit lorsque le paramètre de la perturbation est suffisamment petit. Deuxièmement, le théorème de Tikhonov est établi pour les systèmes hyperboliques linéaires singulièrement perturbés de lois d'équilibre où les vitesses de transport et les termes sources sont à la fois dépendant du paramètre de la perturbation ainsi que les conditions aux bords. Sous des hypothèses sur la continuité de ces termes et sous la condition de la stabilité, l'estimation de l'erreur entre la dynamique lente du système complet et le système réduit est obtenue en fonction de l'ordre du paramètre de la perturbation. Troisièmement, nous considérons des systèmes EDO-EDP couplés singulièrement perturbés. La stabilité des deux sous-systèmes implique la stabilité du système complet où le paramètre de la perturbation est introduit dans la dynamique de l'EDP. D'autre part, cela n'est pas valable pour le système où le paramètre de la perturbation est présent dans l'EDO. Le théorème Tikhonov pour ces systèmes EDO-EDP couplés est prouvé par la technique de Lyapunov. Enfin, la synthèse de la commande aux bords est abordée en exploitant la méthode des perturbations singulières. Le système réduit converge en temps fini. La synthèse du contrôle aux bords est mise en œuvre pour deux applications différentes afin d'illustrer les résultats principaux de ce travailSystems modeled by partial differential equations (PDEs) with infinite dimensional dynamics are relevant for a wide range of physical networks. The control and stability analysis of such systems become a challenge area. Singularly perturbed systems, containing multiple time scales, often occur naturally in physical systems due to the presence of small parasitic parameters, typically small time constants, masses, inductances, moments of inertia. Singular perturbation was introduced in control engineering in late $1960$s, its assimilation in control theory has rapidly developed and has become a tool for analysis and design of control systems. Singular perturbation is a way of neglecting the fast transition and considering them in a separate fast time scale. The present thesis is concerned with a class of linear hyperbolic systems with multiple time scales modeled by a small perturbation parameter. Firstly we study a class of singularly perturbed linear hyperbolic systems of conservation laws. Since the system contains two time scales, by setting the perturbation parameter to zero, the two subsystems, namely the reduced subsystem and the boundary-layer subsystem, are formally computed. The stability of the full system implies the stability of both subsystems. However a counterexample is used to illustrate that the stability of the two subsystems is not enough to guarantee the full system's stability. This shows a major difference with what is well known for linear finite dimensional systems. Moreover, under certain conditions, the Tikhonov approximation for such system is achieved by Lyapunov method. Precisely, the solution of the slow dynamics of the full system is approximated by the solution of the reduced subsystem for sufficiently small perturbation parameter. Secondly the Tikhonov theorem is established for singularly perturbed linear hyperbolic systems of balance laws where the transport velocities and source terms are both dependent on the perturbation parameter as well as the boundary conditions. Under the assumptions on the continuity for such terms and under the stability condition, the estimate of the error between the slow dynamics of the full system and the reduced subsystem is the order of the perturbation parameter. Thirdly, we consider singularly perturbed coupled ordinary differential equation ODE-PDE systems. The stability of both subsystems implies that of the full system where the perturbation parameter is introduced into the dynamics of the PDE system. On the other hand, this is not true for system where the perturbation parameter is presented to the ODE. The Tikhonov theorem for such coupled ODE-PDE systems is proved by Lyapunov technique. Finally, the boundary control synthesis is achieved based on singular perturbation method. The reduced subsystem is convergent in finite time. Boundary control design to different applications are used to illustrate the main results of this work
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Kalavagunta, Sushma. "Computational algorithms for stability analysis of linear systems with time-delay /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p1418036.
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Li, Rihua. "Analysis for Taylor vortex flow." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/53628.
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Taylor vortex flow is one of the basic problems of nonlinear hydrodynamic stability. In contrast with the wide region of wavenumber predicted by the linear theory, experiments show that Taylor vortex flow only appears in a small region containing the critical wavenumber ßer This phenomenon is called wave selection. In this work, several high-order perturbation methods and a numerical method are established. Both evolution and steady state of the How caused by single or several disturbances are studied. The existence of multiple steady states for disturbances with small wavenumber is discovered and proved. The stable and unstable steady state solutions and some associated phenomena such as jump phenomenon and hysteresis phenomenon are found. and explained. In the small region, the wavenumbers and initial amplitudes of disturbances determine the wavenumber of the flow. But outside this region, only the wavenumbers of the disturbances have effect on the wave selection. These results indicate that unstable solutions play a key role in wave selection. The side-band stability curve produced by the high-order perturbation methods is accurate at low Taylor numbers but incorrect at relatively high Taylor numbers. The relation of the unstable solutions and side-band stability is discussed. Besides, the overshoot and the oscillation phenomena during evolution are studied in detail. Connections between this work and experiments are discussed.Ph. D.
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KOWTA, SRINIVAS. "ROBUST STABILITY ANALYSIS OF SERVO-HYDRAULIC SYSTEM IN PARAMETER SPACE." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060970575.
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Hughes, Jonathan L. "Applications of Stability Analysis to Nonlinear Discrete Dynamical Systems Modeling Interactions." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/3819.
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Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model interactions involving economic agents and biological populations. In particular we will explore the stability properties of equilibria associated with inter-species and intergenerational population dynamics in biology and market price and agent composition dynamics in economics.
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Haber, Ludwig Christian. "Investigation of Dynamics in Turbulent Swirling Flows Aided by Linear Stability Analysis." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11076.
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Turbulent swirling flows are important in many applications including gas turbines, furnaces and cyclone dust separators among others. Although the mean flow fields have been relatively well studied, a complete understanding of the flow field including its dynamics has not been achieved. The work contained in this dissertation attempts to shed further light on the behavior of turbulent swirling flows, especially focused on the dynamic behavior of a turbulent swirling flow encountering a sudden expansion. Experiments were performed in a new isothermal turbulent swirling flow test facility. Two geometrical nozzle configurations were studied. The \cb\ nozzle configuration exhibits a cylindrical \cb\ in the center of the nozzle. The free vortex nozzle configuration is obtained when the cylindrical \cb\ is removed. Detailed laser velocimeter measurements were performed to map out the flow field near the sudden expansion of the 2.9" (ID) nozzle leading to the 7.4" (ID) downstream section.
In addition to presenting detailed flow profiles for both nozzle and downstream flow fields, representative frequency spectra of the flow dynamics are presented. Along with the flow time histories and histograms, the wide variety of dynamic behavior was thus described in great detail. The dynamics observed in the experiment can be classified into three main categories: coherent and large scale motion, intermittent motion and coherent periodic motion. Free vortex geometry flows, in the parameter space of the experiments (Swirl number = 0 - 0.21), exhibited mostly coherent and large scale motion. The spectra in these cases were broadband with very light concentration of spectral energy observed in some specific cases. Center--body geometry flows exhibited all three categories of flows as swirl strength was increased from zero. Flows with little or no swirl exhibited broad--band spectra similar to those for the free vortex geometry. Intermediate swirl levels resulted in a large amount of low frequency energy which, with the aid of the time histories, was identified as a large scale intermittence associated with radial movement of the annular jet as it enters the sudden expansion. Large swirl levels resulted in high magnitude coherent oscillations concentrated largely just downstream of the sudden expansion.
Linear stability analysis was used to help in the interpretation of the observed dynamics. Although, as implemented here (using the parallel flow assumption), the analysis was not successful in quantitatively matching the experimentally observed dynamics, significant insight into the physical mechanisms of the observed dynamics was obtained from the analysis. Specifically, the coherent oscillations observed for larger swirl levels were able to be described in terms of the interaction between the inner and outer shear layers of the flow field.Ph. D.
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Du, Baozhu, and 杜宝珠. "Stability analysis and controller synthesis of continous-time linear time-delay systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44765186.
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Leimkuhler, Matthew Pancoast. "Linear stability analysis of circular jets : integer, fractional, and multiple mode excitation /." Thesis, This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-06082009-170937/.
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Muller, Susan Sanette. "The effect of temperature on the linear dimensional stability of elastomers." University of the Western Cape, 2012. http://hdl.handle.net/11394/4624.
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Masters of ScienceSometimes, dental impressions need to be transported to distant laboratories. It has been reported that the temperature in a vehicle can reach up to 66C when the outdoor temperature is 38C. These temperatures may be reached during South African summers. The objective of this in vitro study was to investigate the effect of temperature and time on the dimensional stability of two elastomeric impression materials. Methodology: Specimens consisted of impressions made of an ISO-specified test-block featuring a pattern of grooves. Materials used were polyether (Impregum Penta) and polyvinylsiloxane (Affinis Precious regular body). Using an SLR camera and standardized technique, the specimens were photographed at 2 different temperatures (21°C and 66°C) and 3 time intervals (30min, 8hrs and 14 days). This resulted in a total of 12 groups (n=10) to be compared. Digital images of the impressions were calibrated and measured using digital analyzing software. These distances were used to evaluate the mean % dimensional change (%DC) for each group. VEPAC module of Statistica 10 was used for the statistical analysis. To analyze exactly where the differences lied, a Fisher LSD correction was applied to correct for multiple pair wise comparisons. Results: Comparing polyether with silicone, there was no difference in the mean %DC for specimens kept at 21°C for 8hrs (polyether=0.364; silicone=0.237). Neither was there a difference between polyether and silicone when heated to 66°C, cooled off, and measured after 8hrs (polyether=0.306; silicone=0.297) or after 14 days (polyether=-0.272; silicone=-0.093). For both polyether and silicone, the mean %DC of the groups exposed to 66°C, cooled off and measured after 8hrs (polyether=0.306; silicone=0.297) differed significantly when compared to the group measured after 14 days (polyether=-0.2723; silicone=-0.092) (P<0.0001 and P=0.0029 resp). For both polyether and silicone, the mean %DC of the groups exposed to 66°C, cooled off and measured after 8hrs (polyether=0.306; silicone=0.297) did not differ when compared to the 21°C (polyether=0.364; silicone=0.237). Conclusions: Within limitations of this study, both materials were heat-sensitive. It is recommended that materials return to 21°C before casting. Despite statistical differences, all results were within ISO specifications of maximum 1.5%DC.
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Weeks, Mark Alexander. "Plane-layer convection and magnetoconvection." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248180.
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Er, Aynur. "Stability of Linear Difference Systems in Discrete and Fractional Calculus." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1946.
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The main purpose of this thesis is to define the stability of a system of linear difference equations of the form,
∇y(t) = Ay(t),
and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem.
This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are discussed by using particular example.
In the second chapter, we focus on solving the linear difference equations by using the undetermined coefficient method and the variation of constants formula. Moreover, we establish the matrix exponential function which is the solution of the initial value problems (IVP) by the Putzer algorithm.
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Marinósson, Sigurour Freyr. "Stability analysis of nonlinear systems with linear programming a Lyapunov functions based approach /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=982323697.
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Zhang, Xiping. "Parameter-Dependent Lyapunov Functions and Stability Analysis of Linear Parameter-Dependent Dynamical Systems." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/5270.
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The purpose of this thesis is to develop new stability conditions for several linear dynamic systems, including linear parameter-varying (LPV), time-delay systems (LPVTD), slow LPV
systems, and parameter-dependent linear time invariant (LTI) systems. These stability conditions are less conservative and/or computationally easier to apply than existing ones.
This dissertation is composed of four parts. In the first part of this thesis, the complete stability domain for LTI parameter-dependent (LTIPD) systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The stability domain is
synthesized for both single- and multi-parameter dependent LTI systems. The single-parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the
bialternate sum of a matrix with itself is also exploited to reduce the computational complexity.
In the second part of the thesis, a class of parameter-dependent Lyapunov functions is proposed, which can be used to assess the stability properties of single-parameter LTIPD systems in a non-conservative manner. It is shown
that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. The bound of polynomial degree of the Lyapunov functions is then reduced by taking advantage of the fact that the Lyapunov matrices are symmetric. If the matrix multiplying the parameter is not full rank, the polynomial order
can be reduced even further. It is also shown that checking the feasibility of these matrix
inequalities over a compact set can be cast as a convex optimization problem. Such Lyapunov functions and stability conditions for affine single-parameter LTIPD systems are then generalized to single-parameter polynomially-dependent LTIPD systems and affine multi-parameter LTIPD systems.
The third part of the thesis provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of LPV time-delayed systems. It presents both
delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as Linear Matrix Inequalities (LMI's). In cases when
the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMI's can be solved efficiently using available software. A numerical example of a
time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results.
In the last part of the thesis, topics for future
investigation are proposed. Among the most interesting avenues for research in this context, it is proposed to extend the existing stability analysis results to controller synthesis, which will be based on the same Lyapunov functions used
to derive the nonconservative stability conditions. While designing the dynamic ontroller for linear and parameter-dependent systems, it is desired to take the advantage of the rank deficiency of the system matrix multiplying the parameter such that the controller is of lower dimension, or rank deficient without sacrificing the performance of closed-loop systems.
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SEREBRENICK, GUSTAVO. "STABILITY ANALYSIS OF SLENDER COLUMNS PARTIALLY BURIED IN A NON-LINEAR ELASTIC FOUNDATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2004. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=6168@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORO presente trabalho tem por objetivo estudar o comportamento de colunas esbeltas parcialmente enterradas, quando submetidas a um carregamento axial de compressão. A fundação é representada, ora por um modelo linear, o qual considera que a reação exercida pelo solo é proporcional às deflexões da coluna, ora por um modelo não-linear no qual esta relação de proporcionalidade não é mais verificada. Para a modelagem da coluna, é usada a teoria inextensional de barras esbeltas. Inicialmente, mostra-se como são deduzidas as equações diferenciais do problema a partir dos funcionais de energia da coluna. No problema linear, buscam-se obter as cargas críticas e modos críticos da coluna. Neste caso, sua solução analítica é encontrada a partir da resolução do problema de valor de contorno usando-se um programa de álgebra simbólica. Também é obtida uma solução aproximada através do método de Ritz. Um estudo paramétrico detalhado analisa a influência das condições de apoio da coluna e altura e rigidez da fundação na carga e modo críticos. Entretanto, no caso nãolinear, as equações diferenciais são mais complexas, não permitindo a obtenção de uma solução analítica. É utilizado, então, o método de Ritz, no qual as soluções analíticas obtidas para o problema linear (autofunções) são usadas como funções de interpolação. Em seguida, chega-se à uma equação não- linear de equilíbrio, da qual se obtém o caminho pós-crítico da coluna. Os resultados do problema nãolinear são comparados com os obtidos através do método dos elementos finitos.
In this thesis the behavior of slender, partially embedded columns under axial compressive forces is studied. The foundation is either represented by a linear model, which considers that the soil reaction is proportional to the column’s deflections or by a non-linear model in which this proportionality relation is not observed. The inextensional slender beam theory is used to model the column. Initially, the governing differential equations are deduced from the energy functional of the column-foundation system. In the linear problem, the critical loads and corresponding critical modes are looked for. In this case, an analytic solution is obtained by the solution of the associated boundary value problem, using a symbolic algebra software. An approximate solution is also found by Ritz’s method. A parametric study is conducted to study the influence of the column boundary conditions and foundation’s height and stiffness on critical loads and modes. However, in the non-linear case, differential equations are much more complex and an analytical solution is not possible. So, the Ritz’s method is used once again, in which the analytic solutions of the linear problem (eigenfunctions) are used as interpolation functions. After that, a non-linear equilibrium equation is obtained together with the column post-buckling path. These results are compared with the ones obtained using the finite element method.
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Keo, Pisey. "Non-linear analysis of steel-concrete hybrid members with application to stability design." Thesis, Rennes, INSA, 2015. http://www.theses.fr/2015ISAR0040/document.
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Le travail de cette thèse a pour but de développer des outils de simulation et une méthode de dimensionnement pour les poteaux hybrides soumis à des chargements combinés. La thèse est composée de 4 parties essentielles et comprend 6 chapitres. Dans la première partie, nous développons un élément fini poutre/poteau hybride élastique et l’interaction partielle avec matrice de raideur exacte. Cet élément fini découle de la solution analytique du système d'équations différentielles couplées obtenues en combinant les équations de champs (équilibre, cinématique et comportement). Les inconnues fondamentales sont les glissements aux interfaces et la déformation de cisaillement de l'élément principal. Ces équations sont résolues pour des conditions de chargement et des conditions aux limites arbitraires en accordant un soin particulier à la détermination des constantes d'intégration. Dans la seconde partie de cette thèse, nous proposons une formulation d'élément fini originale pour l'analyse en grand déplacement des poutres hybrides avec prise en compte des glissements qui se produisent à chaque interface acier-béton. La méthode de co-rotationnelle est retenue. Dans cette approche, le mouvement de l'élément se décompose en un mouvement de corps rigide ct en une partie déformable définie dans un repère co-rotationnel local qui se déplace de manière continue avec l'élément mais qui ne se déforme pas avec ce dernier. Un choix judicieux des variables cinématiques locales accompagné des matrices de transformation correspondantes permet de transposer l'élément linéaire développé en partie 1 en un élément géométriquement non-linéaire performant. La partie 3 est consacrée à l'analyse non linéaire matérielle par élément finis de poutres hybrides en interaction partielle et soumise aux forces combinées de flexion et de cisaillement. Dans la formulation élément fini proposée, nous adoptons la discrétisation par libres et une modèle 3D de comportement du béton avec prise en compte des états plans ce qui permet de reproduire rigoureusement l'effet du confinement et l'action des étriers. En partie 4, nous évaluons la pertinence de la méthode d'amplification des moments proposées dans I'Eurocode 2 et 4 à évaluer la charge ultime de poteaux hybrides soumis à une combinaison de charge axiale et de moment de flexion uni-axial. Dans un premier temps, nous conduisons une étude paramétrique sur 1140 cas différents de poteaux hybrides; étude destinés à couvrir les différentes typologies possibles, afin de disposer d'une base de résultats permettant d'évaluer la pertinence des méthodes simplifiées de I'Eurocode 2 ct de I'Eurocode 4 pour de tels éléments. Cette étude a été réalisée à l'aide d'un élément fini non-linéaire (géométrique et matériel), avec une hypothèse de Bemouilli pour tous les composants du poteau hybride. Il ressort de cette étude que ces méthodes simplifiées ne peuvent être appliquées aux poteaux hybrides. Sur base de l'analyse d'un nombre de cas plus important (2960 configurations), la méthode d'amplification des moments est calibrée pour les poteaux hybridesThis thesis aims at developing simulation tools and a design method for hybrid beam-columns subjected to combined axial force, bending and shear. The thesis is divided in four main parts and comprises 6 chapters. In the first part, we develop a new finite element formulation based on the exact stiffness matrix for the linear elastic analysis of hybrid beam-columns in partial interaction taking into account the shear deformability of the encasing component. This element relies on the analytical solution of a set of coupled system of differential equations in which the primary variables are the slips and the shear deformation of the encasing beam. The latter is derived by combining the governing equations (equilibrium, kinematics, constitutive laws) and solved for a specific element with arbitrary boundary conditions and loading. Special care has been taken while dealing with the constants of integration. The second part of the thesis addresses a new finite element formulation for a large displacement analysis of elastic hybrid beam-columns taking into account the slips that occur at each steel-concrete interface. The co-rotational method is adopted in which the movement of the clement is divided into a rigid body motion and a deformable portion in the local co-rotational frame which moves and rotates continuously with the element but does not deform with it. Appropriate selection of local kinematic variables along with corresponding transformation matrices allows transforming the linear finite element developed in Part I into a nonlinear one resulting in an efficient locking-free formulation. In Part 3, we derive a finite element formulation for materially nonlinear analysis of hybrid beam-columns with shear deformable encasing component, in partial interaction and subjected to the combined shear and bending. The fiber model is adopted with condensation of the 3D stress-strain relations which allow to account for confinement in a rigorous manner as well as the effect of the stirrups. Part 4 examines the adequacy of the moment magnification method given in Eurocode 2 and 4 to provide an accura te estimation of the ultimate load of hybrid columns subjected to a combination of axial load and uniaxial bending moment. The developed finite element model with a shear rigid encasing component is used to conduct a parametric study comprising 1140 cases to cover the various possible situations. The predictions of the model are compared against the values given by the simplified methods of Eurocode 2 and Eurocode 4. lt is shown that these simplified methods does not give satisfactorily results. Based on the analysis of larger number of cases (2960 configurations), the moment magnification method has been calibrated for hybrid columns
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Fannin, Christopher A. "Linear Modeling and Analysis of Thermoacoustic Instabilities in a Gas Turbine Combustor." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/28400.
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A dynamic model is developed for the purpose of predicting stability characteristics of an industrial-scale, swirl-stabilized premixed combustor located at the National Energy Technology Laboratory (NETL) in Morgantown, WV. The model consists of modular blocks that assemble into an open-loop transfer function depicting the frequency response of the thermoacoustic system. These blocks include the system acoustic response to unsteady heat release forcing, the air-side coupling of acoustic particle velocity to inlet fuel mass fraction, transport delays present in the mixing nozzle and combustion chamber, and dynamic heat release excitation from unsteady inlet fuel mass fraction. By examing the frequency response with linear stability techniques, the existence of limit cycles due to linear instabilities is predicted. Further, the frequency response analysis is used to predict limit cycle frequencies in the case of predicted instability. The analysis predictions are compared with the results of tests performed at NETL, demonstrating a capability of replicating many of the observed stability characteristics.Ph. D.
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Clinger, Richard A. "Stability Analysis of Systems of Difference Equations." VCU Scholars Compass, 2007. http://hdl.handle.net/10156/1318.
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Civin, Damon. "Stability of charged rotating black holes for linear scalar perturbations." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247397.
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In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.
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Tilton, Nils G. "A linear stability analysis of the destabilizing effects of wall permeability in channel flows /." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=99546.
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We perform a three-dimensional linear stability analysis of a laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous blocks. We consider porous materials in which the permeability is small and the inertial effects can be neglected. We solve the coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We consider symmetric flows in channels with two identical porous walls and skewed flows in channels with only one porous wall. In both cases, permeability significantly affects the Orr-Sommerfeld spectrum; however, the homogeneous Squire modes remain damped. In channels with two porous walls, permeability destabilizes up to two Orr-Sommerfeld wall modes and introduces two new damped wall modes on the left branch of the spectrum. In channels with only one porous wall, permeability destabilizes up to one wall mode and introduces one new damped wall mode on the left branch of the spectrum. In both channels, permeability also introduces a new class of damped modes associated with the porous regions. We find that very small amounts of wall permeability can dramatically decrease the stability of the channel flow. The neutral curve becomes significantly larger and the critical Reynolds number can decrease to only 10% its Poiseuille value.
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Haapanen, Siina Ilona. "Linear stability analysis and direct numerical simulation of a miscible two-fluid channel flow /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Liljenberg, Scott Alan. "Modeling and Stability Analysis of Thermoacoustic Instabilities in Gas Turbine Combustor Sections." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/35469.
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In order to predict the linear stability of combustion systems in industrial-scale gas turbines, a stability analysis was completed using models generated for each of the major dynamic components. Changes in the combustion process of gas turbines to reduce emissions has resulted in large amplitude pressure oscillations associated with a coupling between the natural acoustic modes of the combustor and the unsteady heat release from the flame. Detailed models of the acoustics and the heat release processes were created and assembled, with a time delay element and the appropriate scaling, into a system block diagram to investigate the stability of the system using linear system theory. Wherever possible the analytical models were validated with experimental data. The main goal of this work was to create a design methodology which could be used by industry to predict where instabilities were likely to occur during the design phase. Results show that the system based stability analysis can predict some of the instability frequencies seen in the experimental data, but more refined models are needed to predict every instability. Future work will involve designing experiments to validate and refine the dynamic models already developed.Master of Science
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Marinosson, Sigurdur Freyr. "Stability Analysis of Nonlinear Systems with Linear Programming - Stabilitätsanalyse nicht-linearer Systeme mit linearer Optimierung." Gerhard-Mercator-Universitaet Duisburg, 2002. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-02152002-111745/.
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In this thesis the stability and the region of attraction of nonlinear dynamical systems' equilibrium points are considered. Methods from linear programming are combined with theorems from the Lyapunov theory of dynamical systems to develop numerical algorithms. These algorithms deliver non-trivial information about the stability-behaviour of an equilibrium of a continuous, autonomous, nonlinear system. Two linear programs, LP1 and LP2, are developed. LP1 depends on a simply connected open neighborhood N of the equilibrium at the origin and two constants, a and m. The construction of LP1 implies that if it does not possess a feasible solution, then the corresponding system is not a,m-exponentially stable on N. LP2 has the property that every feasible solution of the linear program defines a piecewise-affine (piecewise-linear) Lyapunov function or a Lyapunov-like function V for the system.
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Qu, Yuhui. "Periodic Motions and Stability Analysis of a Non-linear Rotating Beam Subjected to Torsional Excitation." Thesis, Southern Illinois University at Edwardsville, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1565859.
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The periodic motions and stability of a nonlinear rotating beam subjected to a torsional excitation is investigated in this thesis. Both quadratic and cubic geometric stiffening nonlinearities are retained in the equation of motion, and the reduced model is obtained via the Galerkin method. Saddle-node bifurcations and Hopf bifurcations of the Period-1 motions of the model were obtained via the high order harmonic balance method. The period-2 and period-4 solutions, which are emanated from the period-1 and period-2 motions, respectively, are obtained by the combined implementation of the harmonic balance method, Floquet theory, and Discrete Fourier Transform (DFT). Stabilities are detected by Floquet theory. Stable and unstable periodic motions are illustrated from numerical and analytical solutions. The analytical periodic solutions and their stabilities are verified through numerical simulation.
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Stirner, Tobias [Verfasser], and Georg [Akademischer Betreuer] Raffelt. "Fast neutrino flavour conversions : Stability analysis in the linear regime / Tobias Stirner ; Betreuer: Georg Raffelt." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2020. http://d-nb.info/1218465859/34.
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Suliman, Ridhwaan. "A quadratic non-linear elasticity formulation for the dynamic behaviour of fluid-loaded structures." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277824.
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This work details the development and implementation of a numerical model capable of solving strongly-coupled fluid-structure interaction problems involving long thin structures, which are common multi-physics problems encountered in many applications. In most fluid-structure interaction problems the deformation of the slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal decomposition technique for linear structural analysis, the governing equations and boundary conditions are updated to account for the leading-order non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. Two computational fluid-structure interaction approaches are then implemented in a partitioned manner: a finite volume method for discretisation of both the fluid and solid domains and the quadratic modal formulation for the structure coupled with a finite volume fluid solver. Strong-coupling is achieved by means of a fixed-point solver with dynamic relaxation. The fluid-structure interaction approaches are validated and compared on benchmark problems of increasing complexity and strength of coupling between the fluid and solid domains. Fluid-structure interaction systems may become unstable due to the interaction between the fluid-induced pressure and structural rigidity. A thorough stability analysis of finite elastic plates in uniform flow is conducted by varying the structural length and flow velocity showing that these are critical parameters. Validation of the results with those from analytical methods is done. An analysis of the dynamic interactions between multiple finite plates in various configurations is also conducted.
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Simmons, Skyler C. "Analysis of Multiple Collision-Based Periodic Orbits in Dimension Higher than One." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5584.
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We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.
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Klein, Gary D. "Linear modeling of tiltrotor aircraft (in helicopter and airplane modes) for stability analysis and preliminary design." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1996. http://handle.dtic.mil/100.2/ADA316795.
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Thesis (M.S. in Electrical Engineering and M.S. in Aeronautical Engineering) Naval Postgraduate School, June 1996.Thesis advisor(s): Robert G. Hutchins, E.R. Wood. "June 1996." Bibliography: p. 201. Also available online.
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Burckhart, Andreas [Verfasser], and Hartmut [Akademischer Betreuer] Zohm. "Different ELM regimes at ASDEX Upgrade and their linear stability analysis / Andreas Burckhart. Betreuer: Hartmut Zohm." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://d-nb.info/1047062321/34.
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Pan, Zhenguo. "Simulation and analysis of coupled surface and grain boundary motion." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2733.
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At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis.
Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth.
The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems.
We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable.
A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.
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Fisher, Charles Edward. "The Effects of a Navier-Slip Boundary Condition on the Flow of Two Immiscible Fluids in a Microchannel." Digital WPI, 2013. https://digitalcommons.wpi.edu/etd-theses/294.
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We consider the flow of two immiscible fluids in a thin inclined channel subject to gravity and a change in pressure. In particular, we focus on the effects of Navier slip along the channel walls on the long-wave linear stability. Of interest are two different physical scenarios. The first corresponds to two incompressible fluid layers separated by a sharp interface, while the second focuses on a more dense fluid below a compressible gas. From a lubrication analysis, we find in the first scenario that the system is stable in the zero-Reynolds number limit with the slip effects modifying the decay rate of the stable perturbation. In the case of the Rayeligh-Taylor problem, slip along the less dense fluid wall has a destabilizing effect. In the second scenario, fluid inertia is pertinent, and we find neutral stability criteria are not significantly affected with the presence of slip.
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Morris, Craig C. "Flight Dynamic Constraints in Conceptual Aircraft Multidisciplinary Analysis and Design Optimization." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/25787.
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This work details the development of a stability and control module for implementation into a Multidisciplinary Design Optimization (MDO) framework for the conceptual design of conventional and advanced aircraft. A novel approach, called the Variance Constrained Flying Qualities (VCFQ) approach, is developed to include closed-loop dynamic performance metrics in the design optimization process. The VCFQ approach overcomes the limitations of previous methods in the literature, which only functioned for fully decoupled systems with single inputs to the system. Translation of the modal parameter based flying qualities requirements into state variance upper bounds allows for multiple-input control laws which can guarantee upper bounds on closed-loop performance metrics of the aircraft states and actuators to be rapidly synthesized. A linear matrix inequality (LMI) problem formulation provides a general and scalable numerical technique for computing the feedback control laws using convex optimization tools. The VCFQ approach is exercised in a design optimization study of a relaxed static stability transonic transport aircraft, wherein the empennage assembly is optimized subject to both static constraints and closed-loop dynamic constraints. Under the relaxed static stability assumption, application of the VCFQ approach resulted in a 36% reduction in horizontal tail area and a 32% reduction in vertical tail area as compared to the baseline configuration, which netted a weight savings of approximately 5,200 lbs., a 12% reduction in cruise trimmed drag, and a static margin which was marginally stable or unstable throughout the flight envelope. State variance based dynamic performance constraints offer the ability to analyze large, highly coupled systems, and the linear matrix inequality problem formulation can be extended to include higher-order closed-loop design objectives within the MDO. Recommendations for further development and extensions of this approach are presented at the end.This material is based on research sponsored by Air Force Research Laboratory under agreement number FA8650-09-2-3938. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Air Force Research Laboratory or the U.S. Government.
Ph. D.