Dissertations / Theses: 'Variational principles'

1

Springborn, Boris Andre Michael. "Variational principles for circle patterns." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969719892.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Figueiredo, Djairo G. de. "On some recent variational principles." Pontificia Universidad Católica del Perú, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/95486.

Full text

Abstract:

In this paper we survey some recent variational principies, which have proved to be very useful in the applications to the theory of differential equations, both ordinary and partial. We start with a basic principle due to Ekeland [4}, which provides new proofs to the well known minimax theorems of Ambrosetti - Rabinowitz [2} and Rabinowitz{7}, {8}. For proofs of these results we refer to{8}. We also mention some applications to semilinear elliptic equations.

APA, Harvard, Vancouver, ISO, and other styles

3

LEVI, FRANCESCA. "Variational principles for evolution problems." Doctoral thesis, Università degli studi di Brescia, 2023. https://hdl.handle.net/11379/571585.

Full text

Abstract:

Lo studio di fenomeni che evolvono nel tempo è spesso condotto attraverso la loro modellazione come sistemi dinamici, la cui formulazione matematica, in genere, richiede la risoluzione di sistemi di equazioni differenziali a condizioni iniziali. Risolvere le equazioni che governano un fenomeno fisico evolutivo significa determinarne l'evoluzione nel tempo a partire da un insieme di condizioni iniziali; ad esempio, considerando i sistemi meccanici, attraverso una legge matematica che ne determina la posizione e la velocità in funzione del tempo. Tuttavia, le equazioni che governano il moto spesso non possono essere risolte analiticamente e quindi vengono utilizzate tecniche di integrazione numerica per ottenere un'approssimazione accurata della soluzione. Trattare il problema dello studio di un sistema fisico da un punto di vista variazionale può essere un approccio diverso, motivato dalla formulazione Lagrangiana della meccanica classica. L'idea di sostituire un dato problema con uno equivalente in forma variazionale non è certo nuova: l'interesse per questa formulazione è infatti giustificato dalla validità dei cosiddetti metodi diretti del calcolo delle variazioni. Questi metodi sono validi sia per uno studio qualitativo del problema (verifica dell'esistenza e unicità della soluzione, la sua regolarità, ecc.), sia per uno studio quantitativo, cioè da un punto di vista numerico (valutazione della convergenza, stima dell'errore della soluzione approssimata). In questa tesi vengono analizzati problemi evolutivi di interesse ingegneristico, formulati per via variazionale. In primo luogo, il problema viscoelastico lineare viene risolto numericamente utilizzando tre diverse formulazioni variazionali: la formulazione di Gurtin, la formulazione di Gurtin splittata e la formulazione di Huet. Il metodo degli elementi finiti viene utilizzato per la discretizzazione spaziale e il metodo Ritz viene utilizzato per la discretizzazione temporale. Successivamente, si prende in considerazione il problema della conduzione del calore. Vengono considerate due formulazioni: la prima basata su una forma bilineare convolutiva, la seconda su una forma bilineare biconvolutiva. Numerosi esperimenti numerici mettono in luce la bontà dei due diversi approcci. Viene poi affrontato il tema della determinazione di upper e lower bounds per le proprietà meccaniche di materiali compositi costituiti da fasi aventi legami costitutivi viscoelastici. Successivamente viene analizzato il problema dell'evoluzione di una frattura sia in un mezzo elastico sia in un mezzo viscoelastico. Nel primo caso viene proposta una formulazione estremale analoga a quella di Capurso e Maier, valida in ambito elastoplastico. Infine, viene considerata la stabilità dinamica di sistemi piani con una sola massa concentrata e soggetti a forze follower.
The study of phenomena that evolve over time is often conducted through their modelling as dynamic systems, whose mathematical formulation generally requires the resolution of systems of differential equations with initial conditions. Solving the governing equations of a physical phenomenon means determining its evolution over time starting from a set of initial conditions; for example, considering mechanical systems, through a mathematical law that determines its position and speed as functions of time. However, the equations governing motion cannot be often solved analytically and therefore, numerical integration techniques are used in order to obtain an accurate approximation of the solution. Treating the problem of studying a physical system from a variational point of view may be a different approach, motivated by the Lagrangian formulation of classical mechanics. The idea of replacing a given problem with an equivalent one in variational form is certainly not new: the interest in this formulation is in fact justified by the validity of the so-called direct methods of the calculation of variations. These methods are valid both for a qualitative study of the problem (verification of existence and uniqueness of the solution, its regularity, etc.), and for a quantitative study, namely from a numerical point of view (evaluation of convergence, estimation of the error of the approximate solution). In this thesis, evolution problems of engineering interest are analyzed, formulated in a variational way. Firstly, the linear viscoelastic problem is numerically solved using three different variational formulation, such as Gurtin's variational formulation, Split Gurtin formulation and the Huet formulation. The Finite Element Method is used for the space discretization and the Ritz method is used for the time discretization. Then, the heat conduction problem is taken into account. Two formulations are considered: the first one based on a convolutive bilinear form, the second one based on a biconvolutive bilinear form. Several numerical examples highlight the goodness of the two different approaches. Next, the problem of the determination of upper and lower bounds for the mechanical properties of composite materials, consisting of phases having viscoelastic constitutive laws, is addressed. Subsequently, the problem of the evolution of a fracture is analyzed both in an elastic medium and in a viscoelastic medium. In the first case, an extremal formulation, similar to that of Capurso and Maier, is proposed, valid in the elastoplastic field. Finally, the dynamical stability of plane systems with just one lumped mass, subjected to follower forces, is considered.

APA, Harvard, Vancouver, ISO, and other styles

4

Brown, Geoffrey James Nicholas. "Variational principles in atomic collisions and electromagnetism." Thesis, Queen's University Belfast, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335344.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Kocillari, Loren. "Variational principles and optimality in biological systems." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3425402.

Full text

Abstract:

The aim of this thesis is to investigate the signatures of evolutionary optimization in biological systems, such as in proteins, human behaviours and transport tissues in vascular plants (xylems), by means of the Pareto optimality analysis and the calculus of variations. In the first part of this thesis, we address multi-objective optimization problems with tradeoffs through the Pareto optimality analysis ( [132],[69]), according which the best tradeoff solutions correspond to the optimal species, enclosed onto low-dimensional geometrical polytopes, defined as Pareto optimal fronts, in the space of physical traits, called morphospace. Chapter 3 is devoted to the Pareto optimality analysis in the Escherichia coli proteome by projecting proteins onto the space of solubility and hydrophobicity. In chapter 4 we analyze the HCP dataset of cognitive and behavioral scores in 1206 humans, in order to identify any signature of Pareto optimization in the space of Delay Discounting Task (DDT), which measures the tendency for people to prefer smaller, immediate monetary rewards over larger, delayed rewards. The second part of this thesis is devoted to solving an optimization problem regarding xylems, which are the internal conduits in angiosperms that deliver water and other nutrients from roots to petioles in plants. Based on the optimization criteria of minimizing the energy dissipated in a fluid flow, we propose in chapter 5 a biophysical model with the goal of explaining the underlying physical mechanism that affects the structure of xylem conduits in vascular plants, which results in tapered xylem profiles [104, 105, 117, 164]. We address this optimization problem by formulating the model in the context of the calculus of variations. The results of these investigations, besides providing quantitative support to previous theories of natural selection, demonstrate how processes of optimization can be identified in different biological systems by applying statistical methods such as the Pareto optimality and the variational one, showing the relevance of employing these statistical approaches to various biological systems.
Lo scopo di questa tesi è quello di identificare le impronte che l’evoluzione ha avuto nei sistemi biologici, come ad esempio nelle proteine, nei comportamenti umani e nei tessuti trasportatori delle piante vascolari (xilemi), attraverso un’analisi di ottimizzazione di Pareto ed il calcolo delle variazioni. Nella prima parte della tesi, affrontiamo l’ottimizzazione di problemi multi-obiettivo con competizione, attraverso l’analisi di ottimizzazione di Pareto, in base alla quale le migliori soluzioni di compromesso corrispondono alle specie ottimali, le quali vengono racchiuse in politopi geometrici, definiti come fronti ottimali di Pareto, nello spazio dei tratti fisici. Il capitolo 3 è dedicato all’analisi dell’ottimizzazione di Pareto nel proteoma dell’Escherichia coli, proiettando le proteine nello spazio della solubilitá ed idrofobicitá. Nel capitolo 4 analizziamo il set di dati HCP cognitivi e comportamentali in 1206 umani, al fine di identificare qualsiasi traccia di ottimizzazione alla Pareto nello spazio del “Delay Discounting Task” (DDT), che misura la tendenza per le persone a preferire ritorni economici piú piccoli e immediati rispetto a ricompense di premi piú grandi e ritardati. La seconda parte di questa tesi è dedicata alla risoluzione di un problema di ottimizzazione riguardante gli xilemi, che sono i condotti interni degli angiospermi e forniscono con acqua ed altri nutrienti le piante, dalle radici ai piccioli. Basandosi sui criteri di ottimizzazione per minimizzare l’energia dissipata in un flusso di fluido, nel capitolo 5 proponiamo un modello biofisico con l’obiettivo di spiegare il meccanismo fisico sottostante che influenza la struttura di condotti dello xilema nelle piante vascolari, che si traducono in profili di xilema affusolati. Affrontiamo questo problema di ottimizzazione formulando il modello nel contesto del calcolo delle variazioni. I risultati di queste indagini, oltre a fornire supporto quantitativo sulle precedenti teorie sulla selezione naturale, dimostra come i processi dell’ottimizzazione possono essere identificati in diversi sistemi biologici applicando metodi statistici come l’ottimalitá di Pareto e il variazionale uno, mostrando la rilevanza di impiegare questi approcci statistici a vari sistemi biologici.

APA, Harvard, Vancouver, ISO, and other styles

6

Kerce, James Clayton. "Geometric problems relating evolution equations and variational principles." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28739.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Gheorghiu, Horia-Nicolae Mihalache. "Generalized variational principles for steady-state neutron balance equations." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/16793.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Thompson, Daniel J. "Irregular sets and conditional variational principles in dynamical systems." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/2046/.

Full text

Abstract:

We derive key results from dimension theory in dynamical systems and thermodynamic formalism at a level of generality suitable for the study of systems which are beyond the scope of the standard uniformly hyperbolic theory. Let (X, d) be a compact metric space, f : X → X be a continuous map and φ : X → R be a continuous function. The subject of chapters 4 and 5 is the multifractal analysis of Birkhoff averages for φ when topological pressure (in the sense of Pesin and Pitskel) is the dimension characteristic and f has the specification property. In chapter 4, we consider the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set for φ) and show that this set is either empty or has full topological pressure. We formulate various equivalent natural conditions on φ that completely describe when the latter situation holds. In chapter 5, we prove a conditional variational principle for topological pressure for non-compact sets of the form {x∈X : lim n→∞ 1/n n−1 Σ i=0 φ(fi(x))= α}, generalising a previously known result for topological entropy. As one application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification. In chapter 6, we assume that f : X 7→ X is a continuous map satisfying a property we call almost specification (which is weaker than specification). We show that the set of points for which the Birkhoff average of φ does not exist is either empty or has full topological entropy. Every β-shift satisfies almost specification and we show that the irregular set for any β-shift or β-transformation is either empty or has full topological entropy and Hausdorff dimension. In chapter 7, we introduce an alternative definition of topological pressure for arbitrary (noncompact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable conditional variational principle, leading to an alternative definition of an equilibrium state. We study the properties of this new quantity and compare it with existing notions of topological pressure. We apply our new definition to some interesting examples, including the level sets of the pointwise Lyapunov exponent for the Manneville-Pomeau family of maps.

APA, Harvard, Vancouver, ISO, and other styles

9

McCulloch, Lee Nolan. "Spinor formulations and variational principles for Einstein's field equations." Thesis, King's College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314105.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Babish, John. "A modal/spectral analysis of mass distribution effects in a fluid-load plate." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/19472.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Engelkemier, Douglas G. "International ampacity model based on IEC 287 standard." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/19493.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Wu, Xiao-Feng. "Variational principles for acoustic radiation and diffraction from underwater structures." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/17377.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Wakelin, Sarah Louise. "Variational principles and the finite element method for channel flows." Thesis, University of Reading, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357172.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

SADE, MARTIN CHARLES. "VARIATIONAL PRINCIPLES FOR FIELD VARIABLES SUBJECT TO GROUP ACTIONS (GAUGE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188075.

Full text

Abstract:

This dissertation is concerned with variational problems whose field variables are functions on a product manifold M x G of two manifolds M and G. These field variables transform as type (0,1) tensor fields on M and are denoted by ψ(h)ᵅ (h = 1, ..., n = dim M, α = 1, ..., r = dim G). The dependence of ψ(h)ᵅ on the coordinates of G is given by a generalized gauge transformation that depends on a local map h:M → G. The requirement that a Lagrangian that is defined in terms of these field variables be independent of the coordinates of G and the choice of the map h endows G with a local Lie group structure. The class of Lagrangians that exhibits this type of invariance may be characterized by three invariance identities. These identities, together with an arbitrary solution of a system of partial differential equations, may be used to define field strengths associated with the ψ(h)ᵅ as well as connection and curvature forms on M. The former may be used to express the Euler-Lagrange equations in a particularly simple form. An energy-momentum tensor may also be defined in the usual manner; however additional conditions must be imposed in order to guarantee the existance of conservation laws resulting from this tensor. The above analysis may be repeated for the case that the field variables behave as type (0,2) tensor fields under coordinate transformations on M. For these field variables, the Euler-Lagrange expressions may be expressed as a product of a covariant divergence with the components λʰ of a type (1,0) vector field on M. An unexpected consequence of this construction is the fact that the Euler-Lagrange equations that result for the vector field λʰ are satisfied whenever the Euler-Lagrange equations associated with the field variables are satisfied.

APA, Harvard, Vancouver, ISO, and other styles

15

Transchel, Fabian Wolfgang Günter [Verfasser]. "On Monte Carlo time-dependent variational principles / Fabian Wolfgang Günter Transchel." Hannover : Technische Informationsbibliothek (TIB), 2016. http://d-nb.info/1122131755/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Schiefeneder, Daniela [Verfasser], and Felix [Akademischer Betreuer] Finster. "On minimizers of causal variational principles / Daniela Schiefeneder. Betreuer: Felix Finster." Regensburg : Universitätsbibliothek Regensburg, 2011. http://d-nb.info/1022819992/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Barbagallo, Mathias. "Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures." Doctoral thesis, KTH, MWL Marcus Wallenberg Laboratoriet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-118427.

Full text

Abstract:

Multilayered structures have many application in industry and society: they have peculiar properties and serve a variety of purposes, like structural support, thermal insulation, vibrational and acoustic isolation. This thesis concerns the prediction of sound transmission in multilayered structures. Two problems are herein investigated: the transmission of energy through structures and the transmission of energy along structures. The focus of the analysis is on the mid to high frequency range. To predict sound transmission in these structures, statistical energy analysis (SEA) is used.SEA models are devised for the prediction of the sound reduction index for two kinds of multilayered structures, double-walls used in buildings and trim-panels in vehicles; the double-walls comprise an air cavity in between flat plasterboard or glass plates, whereas the trim-panels a porous layer in between curved aluminium and rubber layers. The SEA models are based upon the wave-types carrying energy. The novelty in these SEAs is an element describing the waves in the air cavity, or in the porous layer, fully coupled to the mass-impeded external layers. Compared to measurements, the proposed SEA performs well: for double-walls, it performs better than previous models; for trim-panels, it is an original result. The parameters of the new SEA element, such as modal density, are derived from the coupling equations describing the fully coupled waves. For double-walls, these equations are derived via Newton's laws. For trim-panels, a variational approach based upon a modified Hamilton's principle valid for non-conservative systems is preferred, because it is a powerful machinery for deriving equations of motion and coupling conditions of a medium as complex as the porous layer. The modified Hamilton's principle for non-conservative systems is based upon a self-adjoint functional analogous to the Lagrangian, inspired by Morse and Feshbach's construction. A self-adjoint variational principle for Biot's equations in the displacement formulation is devised. An equivalent mixed formulation is obtained changing the coordinates of the displacement formulation via Lagrange multipliers. From this mixed formulation, the Lagrangian for a porous material with a limp frame is derived, which yields the continuity of the total displacement of the porous layer. Lagrange multipliers help to obtain the correct coupling functionals between a porous material and a solid. The Lagrange multipliers introducing the continuity of the frame and the solid displacements equal the traction of the in-vacuo frame, thus disappearing if the latter is limp. Measurements to gather material parameters for a Biot model of the porous layer have been conducted.The effects of spatial energy decay in the transmission along structures predicted by SEA is studied: a major effect is the increased relevance of indirect coupling loss factors between SEA elements. This may jeopardize the usefulness of SEA at higher frequencies.

QC 20130218

APA, Harvard, Vancouver, ISO, and other styles

18

Hammond, Richard C. II. "The development of design metrics for remanufacturing." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/16851.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Driessen, Brian James. "Analytical and numerical studies in nonholonomic dynamical systems." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/17338.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

DiMarco, John Stephen. "Finite element implementation of a new variational principle for acoustic radiation from a circular disk." Thesis, Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/17649.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Davis, Hurley Thomas Jr. "An investigation of passive actuation for trajectory control." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/17843.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Eshleman, Eric D. "Vibration and shock isolation through use of passive, nonlinear mounts." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/20019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Kelly, William B. "Numerical approximation to the solution of multi-phase stefan-type problems." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/31015.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Doole, Stuart Harvey. "Steady gravity waves on flows with vorticity : bifurcation theory and variational principles." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357537.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Richardson, Kyle Dennis. "Blending and Mixed Variational Principles to Overcome Locking Phenomena in Isogeometric Beams." BYU ScholarsArchive, 2017. https://scholarsarchive.byu.edu/etd/6495.

Full text

Abstract:

Two methods for overcoming locking phenomena in isogeometric beams are presented. The first method blends the rotation of a Timoshenko beam with the rotation of a Bernoulli beam to produce realistic displacements in straight beams. The second method uses mixed variational principles, specifically the Hu-Washizu Principle, to produce realistic displacements as well as realistic strains without post-processing.

APA, Harvard, Vancouver, ISO, and other styles

26

Li, Tianyi. "Gradient-damage modeling of dynamic brittle fracture : variational principles and numerical simulations." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX042/document.

Full text

Abstract:

Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration
In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement

APA, Harvard, Vancouver, ISO, and other styles

27

Wong, Chi-wing, and 黃志榮. "Drop theorem, variational principle and their applications in locally convex spaces: a bornological approach." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B45015065.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

McClurkin, Joel E. "A computer aided build style decision support method for stereolithography." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/16684.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Stoll, William Allard III. "Nonlinear constitutive behavior of PZT." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/17117.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Sweezy, Jeremy Ed. "A multisphere neutron spectrometer measurement of the Georgia Tech Research Reactor bio-medical facility." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/17138.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Billington, Scott Alexander. "Sensor and machine condition effects in roller bearing diagnostics." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/17796.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Simpson, Timothy W. "Development of a design process for realizing open engineering systems." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/17901.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Day, Kevin. "Thermal elastohydrodynamic analysis of a radial lip seal." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/17970.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Pilger, Brian Lee. "Performance of steam eductors operating at low suction-discharge differential pressures." Thesis, Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/18381.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Bakman, Aleksandr Israel. "Elastohydrodynamic simulator." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/19492.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Anderson, William Boyd. "Detection of lubricating film breakdown in mechanical seals." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/20148.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Wu, Kuangcheng. "Extension of surface variational principle to nonsymmetric acoustic radiation and scattering problems." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/17386.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Allen, Ross Roundy Jr. "Variational Principles of Fluid Mechanics and Electromagnetism: Imposition and Neglect of the Lin Constraint." DigitalCommons@USU, 1987. https://digitalcommons.usu.edu/etd/7540.

Full text

Abstract:

Variational principles in classical fluid mechanics and electromagnetism have sprinkled the literature since the eighteenth century. Even so, no adequate variational principle in the Eulerian description of matter was had until 1968 when an Eulerian variational principle was introduced which reproduces Euler's equation of fluid dynamics. Although it successfully produces the appropriate equation of motion for a perfect fluid, the variational principle requires imposition of a constraint which was not fully understood at the time the variational principle was introduced. That constraint is the Lin constraint. The Lin constraint has subsequently been utilized by a number of authors who have sought to develop Eulerian variational principles in both fluid mechanics and electromagnetics (or plasmadynamics). How-ever, few have sought to fully understand the constraint. This dissertation first reviews the work of earlier authors concerning the development of variational principles in both the Eulerian and Lagrangian nomenclatures. In the process, it is shown rigorously whether or not the Euler-Lagrange equations which result from the variational principles are equivalent to the generally accepted equations of motion. In particular, it is shown in the case of several Eulerian variational principles that imposition of the Lin constraint results in Euler-Lagrange equations which are equivalent to the generally accepted equations of motion. On the other hand, it is shown that neglect of the Lin constraint results in Euler-Lagrange equations restrictive of the generally accepted equations of motion. In an effort to improve the physical motivation behind introduction of the Lin constraint a new variational constraint is developed based on the concept of surface forces within a fluid. The new constraint has the advantage of producing Euler-Lagrange equations which are globally correct whereas the Lin constraint itself allows only local equivalence to the standard classical equations of fluid motion. Several additional items of interest regarding variational principles are presented. It is shown that a quantity often referred to as "the canonical momentum" of a charged fluid is not always a constant of the motion of the fluid. This corrects an error which has previously appeared in the literature. In addition, it is demonstrated that there does not exist an unconstrained Eulerian variational principle giving rise to the generally accepted equations of motion for both a perfect fluid and a cold, electromagnetic fluid.

APA, Harvard, Vancouver, ISO, and other styles

39

Harker, Shaun Russell. "Classical mechanics with dissipative constraints." Thesis, Montana State University, 2009. http://etd.lib.montana.edu/etd/2009/harker/HarkerS0809.pdf.

Full text

Abstract:

The aim of this thesis is to consider the mathematical treatment of mechanical systems in the presence of constraints which are energetically dissipative. Constraints may be energetically dissipative due to impacts and friction. In the frictionless setting, we generalize Hamilton's principle of stationary action, central to the Lagrangian formulation of classical mechanics, to reflect optimality conditions in constrained spaces. We show that this generalization leads to the standard measure-theoretic equations for shocks in the presence of unilateral constraints. Previously, these equations were simply postulated; we derive them from a fundamental variational principle. We also present results in the frictional setting. We survey the extensive literature on the subject, which focusses on existence results and numerical schemes known as time- stepping algorithms. We consider a novel model of friction (which is more dissipative than standard Coulomb friction) for which we can give better well-posedness results than what is currently available for the Coulomb theory. To this end, we study multi-valued maps, differential inclusions, and optimization theory. We construct a differential inclusion we call the feedback problem, for which the multi-valued map is the solution set of a convex program. We give existence and uniqueness results regarding this feedback problem. We cast the persistent contact evolution problem of our novel model of friction into the form of a feedback problem to derive an existence result.

APA, Harvard, Vancouver, ISO, and other styles

40

Le, Gall Carole A. "Thermomechanical stress analysis of flip chip packages." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/16002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Ilas, Danut. "Coarse mesh transport theory model for heterogeneous systems." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/16089.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Hamel, Timothy Allen. "The role of the side mirror and A-pillar on automobile wind noise." Thesis, Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/17219.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Yano, Daisuke. "Application of a contact potential difference probe to detection of nanometer-scale lubricant on a hard disk." Thesis, Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/17528.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Ehnert, Jesse James. "Acoustic assessment of the Robert Ferst Center for the Arts theater." Thesis, Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/17625.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Chengalur-Smith, Indushobha Narayanan. "Variable sampling in multiparameter Shewhart charts." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54782.

Full text

Abstract:

This dissertation deals with the use of Shewhart control charts, modified to have variable sampling intervals, to simultaneously monitor a set of parameters. Fixed sampling interval control charts are modified to utilize sampling intervals that vary depending on what is being observed from the data. Two problems are emphasized, namely, the simultaneous monitoring of the mean and the variance and the simultaneous monitoring of several means. For each problem, two basic strategies are investigated. One strategy uses separate control charts for each parameter. A second strategy uses a single statistic which combines the information in the entire sample and is sensitive to shifts in any of the parameters. Several variations on these two basic strategies are studied. Numerical studies investigate the optimal number of sampling intervals and the length of the sampling intervals to be used. Each procedure is compared to corresponding fixed interval procedures in terms of time and the number of samples taken to signal. The effect of correlation on multiple means charts is studied through simulation. For both problems, it is seen that the variable sampling interval approach is substantially more efficient than fixed interval procedures, no matter which strategy is used.
Ph. D.

APA, Harvard, Vancouver, ISO, and other styles

46

Pourzand, Mehran. "Application of new variational principles in finite element method solutions of the radiation transport equation." Thesis, Imperial College London, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393263.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Rauch, Marc [Verfasser], Martina [Gutachter] Zähle, Manfred Gutachter] Denker, and De-Jun [Gutachter] [Feng. "Variational principles for topological pressure / Marc Rauch ; Gutachter: Martina Zähle, Manfred Denker, De-Jun Feng." Jena : Friedrich-Schiller-Universität Jena, 2018. http://d-nb.info/1170398235/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Valcárcel, Flores Carlos Enrique [UNESP]. "Estudo clássico completo do formalismo de Hamilton-Jacobi." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102544.

Full text

Abstract:

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-08-17Bitstream added on 2014-06-13T20:27:17Z : No. of bitstreams: 1 valcarcelflores_ce_dr_ift.pdf: 694272 bytes, checksum: e1b097c2bc884f3cf2ae38593c38d4ba (MD5)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Nesta tese, apresentamos a formulação clássica completa da teoria de Hamilton-Jacobi para sistemas vinculados. Usando o método de Lagrangianas Equivalentes de Carathéodory obtemos um conjunto de Equações Diferenciais Parciais de Hamilton-Jacobi, também chamado de Hamiltonianos. A Condição de Integrabilidade nos permite dividir os Hamiltonianos entre involutivos e não-involutivos. Construímos os Parênteses Generalizados a ﬁm de eliminar os Hamiltonianos não-involutivos, enquanto que relacionamos os Hamiltonianos involutivos com o Gerador das transformações canônicas. Por outro lado, a Equação de Lie é resultado da realização das variações totais no funciona lde ação, e que é relacionada às simetrias da teoria. Usamos a Equação de Lie e a estrutura das Equaçõoes Características, que indicam a evolução dinâmica do sistemas, para associar o Gerador de transformações canônicas às simetrias de calibre. Aplicamos o formalismo de Hamilton-Jacobi ao modelo da Mecânica Quântica Topologica, ao modelo BF bi-dimensional equivalente à Teoria de Jackiw-Teitelboim, ao campo de Yang-Mills Topologicamente Massivo e seu equivalente Auto-dual, assim como para o campo da Gravitação linearizada
It is presented the complete classical formulation of the Hamilton-Jacobi theory for constrained systems. From ﬁxed point variations and using the Carathéodory’s method of Equivalent Lagrangian we obtain a set of Hamilton-Jacobi Partial Differential Equations, also called Hamiltonians. The Integrability Condition allow us to divide the Hamiltonians between involutive and non-involutive ones. We build the Generalized Brackets in order to eliminate the non-involutive Hamiltonians, whereas we relate the involutive Hamiltonians to the Generator of Canonical Transformations. On the other hand, we build the Lie Equation, result of perform total variations to the action functional and which is related to the symmetries of the theory. We use the Lie equation along with the structure of the Characteristic Equations, related to the dynamical evolution of the systems, to associate the Generator of Canonical Transformation to Gaugesymmetries. We apply this formalism to the Topologically Quantum Mechanics, the two dimensional BF model equivalent to the Jackiw-Teitelboim theory, the Topologically Massive Yang-Mills ﬁeld as well as its correspondent self-dual and to the Linearized Gravity ﬁeld

APA, Harvard, Vancouver, ISO, and other styles

49

Maia, Natália Tenório [UNESP]. "Estudo sobre a teoria de vínculos de Hamilton-Jacobi." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/132007.

Full text

Abstract:

Made available in DSpace on 2015-12-10T14:23:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-03-07. Added 1 bitstream(s) on 2015-12-10T14:27:52Z : No. of bitstreams: 1 000852795.pdf: 576204 bytes, checksum: 28ede436e9367885bc3b672b1903caad (MD5)
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para ﬁnalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo
The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the ﬁeld theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism
CNPq: 133488/2011-0

APA, Harvard, Vancouver, ISO, and other styles

50

Valcárcel, Flores Carlos Enrique. "Estudo clássico completo do formalismo de Hamilton-Jacobi /." São Paulo, 2012. http://hdl.handle.net/11449/102544.

Full text

Abstract:

Orientador: Bruto Max Pimentel Escobar
Banca: Abraham Zimerman
Banca: Denis Dalmazi
Banca: Ion Vasile Vancea
Banca: Vladislav Kupriyanov
Resumo: Nesta tese, apresentamos a formulação clássica completa da teoria de Hamilton-Jacobi para sistemas vinculados. Usando o método de Lagrangianas Equivalentes de Carathéodory obtemos um conjunto de Equações Diferenciais Parciais de Hamilton-Jacobi, também chamado de Hamiltonianos. A Condição de Integrabilidade nos permite dividir os Hamiltonianos entre involutivos e não-involutivos. Construímos os Parênteses Generalizados a ﬁm de eliminar os Hamiltonianos não-involutivos, enquanto que relacionamos os Hamiltonianos involutivos com o Gerador das transformações canônicas. Por outro lado, a Equação de Lie é resultado da realização das variações totais no funciona lde ação, e que é relacionada às simetrias da teoria. Usamos a Equação de Lie e a estrutura das Equaçõoes Características, que indicam a evolução dinâmica do sistemas, para associar o Gerador de transformações canônicas às simetrias de calibre. Aplicamos o formalismo de Hamilton-Jacobi ao modelo da Mecânica Quântica Topologica, ao modelo BF bi-dimensional equivalente à Teoria de Jackiw-Teitelboim, ao campo de Yang-Mills Topologicamente Massivo e seu equivalente Auto-dual, assim como para o campo da Gravitação linearizada
Abstract: It is presented the complete classical formulation of the Hamilton-Jacobi theory for constrained systems. From ﬁxed point variations and using the Carathéodory's method of Equivalent Lagrangian we obtain a set of Hamilton-Jacobi Partial Differential Equations, also called Hamiltonians. The Integrability Condition allow us to divide the Hamiltonians between involutive and non-involutive ones. We build the Generalized Brackets in order to eliminate the non-involutive Hamiltonians, whereas we relate the involutive Hamiltonians to the Generator of Canonical Transformations. On the other hand, we build the Lie Equation, result of perform total variations to the action functional and which is related to the symmetries of the theory. We use the Lie equation along with the structure of the Characteristic Equations, related to the dynamical evolution of the systems, to associate the Generator of Canonical Transformation to Gaugesymmetries. We apply this formalism to the Topologically Quantum Mechanics, the two dimensional BF model equivalent to the Jackiw-Teitelboim theory, the Topologically Massive Yang-Mills ﬁeld as well as its correspondent self-dual and to the Linearized Gravity ﬁeld
Doutor

APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic 'Variational principles'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles