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Garioud, Renaud. "When perturbation theory goes non-perturbative : applications to strongly-correlated systems." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAX052.
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Cette thèse concerne le développement et l’utilisation de nouveaux algorithmes pour l’étude théorique de systèmes quantiques fortement corrélés. Il s’agit de systèmes dans lesquels les interactions, par exemple l’interaction de Coulomb répulsive entre les électrons d’un matériau, induisent des phénomènes physiques remarquables (comme la supraconductivité à haute température critique) qui ne peuvent être décrits dans le cadre d’une théorie standard à un corps. Pour comprendre l’origine de ces phénomènes, il est indispensable de traiter l’ensemble des particules et leurs interactions: on parle du problème à N -corps.Le projet de thèse consiste à continuer le développement, l’analyse et l’application des méthodes numériques dites diagrammatiques à ces systèmes. Si des progrès ont été faits, il reste beaucoup de questions fondamentales ouvertes quant à l’utilisation de méthodes perturbatives pour décrire un système qui est,par nature, dans un régime non-perturbatif. Quelles sont les limites de ces approches? Comment se manifestent les effets des corrélations dans la structure des séries perturbatives?Les développements algorithmiques seront utilisés pour l’étude de modèles de systèmes fortement corrélés, comme le modèle de Hubbard, ce qui permettra d’aborder des questions physiques d’intérêt actuel, en particulier en relation avec la physique des corrélations magnétiques et du pseudo-gap dans les cuprates supraconducteurs ou avec l’existence d’une transition de Mott sans phase ordonnée préemptive telle qu’elle est observée dans des expériences récentes sur des composés organiquesThis thesis focuses on developing new algorithms for the study of strongly correlated materials. They are quantum systems in which interactions between electrons, such as the Coulomb repulsion, play a major role and give rise to remarkable physical properties (like high temperature superconductivity) which can't be described using a one-body formalism. To fully understand these phenomenon one has to treat the full system of many particles and their interactions : this is the many body problem.The project of this thesis is developing, analyzing and applying numerical methods called diagrammatic to these systems. A lots of fundamental questions remain unanswered about the using of perturbative methods to describe a system which is, by definition, in a non-perturbative regime. What are the limits of these approaches? How do correlations effects control the structure of the perturbative series ?Algorithmic developments will be applied to the study of strongly correlated systems, such as the Hubbard model, which will allow to cope with current topics of interest in condensed matter physics, in particular with the physics of correlated magnetism and of the pseudo gap in cuprate superconductors, or with the existence of a Mott phase transition with no preexisting ordered phase as it has been recently observed in experiments on organic materials
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Brechet, Sylvain David. "Cosmological perturbation theory." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611602.
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Ali, Saad Ahmad. "A unitary perturbation theory /." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33373.
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The use of ordinary perturbation theory is ubiquitous in modern physics. However, it violates probability conservation, one of the fundamental laws of physics. In this thesis a unitarized perturbation theory is briefly described and its predictions for the behaviour of a number of simple systems are compared with those of ordinary perturbation theory. It is found that the new technique performs just as well as the usual perturbative approach in the regime where the latter is valid and provides improved results where perturbation theory fails. In particular, in the cases studied, the new method is found to reproduce the exact result at resonance.
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Lovett-Turner, Charles. "Resumming QCD perturbation series." Thesis, Durham University, 1995. http://etheses.dur.ac.uk/5375/.
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Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most developed and successful means of extracting phenomenologically useful information from a QFT. In the ever- increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have often taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. The benefits of resumming perturbative series are highlighted by the explicit calculation of the three-jet rate in e+e- annihilation, resummed to all orders in leading and next-to-leading large logarithms. It is found that the result can be expressed simply in terms of exponentials and error functions. In general it is found that perturbative expansions in QED and QCD diverge at large orders. The nature of these divergences has been explored and found to come from two sources. The first are instanton singularities, which correspond to the combinatoric factors involved in counting Feynman diagrams at large orders. The second are renormalon singularities, which are closely linked to non-perturbative effects through the operator product expansion (OPE).By using Borel transform techniques, the singularity structure in the Borel plane for the QCD vacuum polarization is studied in detail. The renormalon singularity structure is as expected from OPE considerations. These results and existing exact large-A^/ results for the QCD Adler D-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of the QCD perturbative coefficients which is leading in b, the first coefficient of the QCD beta-function. This part is expected asymptotically to dominate the coefficients in a large-Nj expansion. Resummed results are also obtained for the e+e- R-ratio and the r-lepton decay ratio. The renormalization scheme dependence of these resummed results is discussed in some detail.
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Barclay, David Thomas. "Topics in perturbation theory." Thesis, Durham University, 1992. http://etheses.dur.ac.uk/6006/.
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In providing a means of progressively improving an initial estimate, perturbation series have become a ubiquitous tool in modern physics. However, and mainly because this stepwise process of improvement rapidly becomes increasingly involved, surprisingly little is known about the formal properties of the series obtained. This thesis therefore investigates some aspects of these properties and how they effect the application of these techniques, with an emphasis on quantum field theory and the phenomenology of e+e(^-) colliders. One of the better understood examples of a perturbative series is the WKB one which is widely used to approximate the energy levels of quantum mechanical systems. Recently much interest has centred on a modification of this, the SWKB series. Apart from (possibly) offering an improvement on the original, this is intrinsically interesting in being related to the supersymmetry of field theory. Furthermore, as Chapter 1 explains, there is a close connection between the cases where the initial estimate requires no correction and an important set of quantum mechanical problems (the "shape invariant" ones) which can be solved elegantly and completely. The situation in field theory is more complicated, not least because the series for any particular problem is no longer unique. While this presents few theoretical difficulties, it has serious consequences when attempts are made to compare predictions with experiment. This obstacle is particularly severe in Quantum Chromodynamics and its fundamental constant (A(_QCD)) is therefore only roughly known at present. It will be argued that current responses to this are all imperfect, but that tests of the theory can be envisaged that circumvent the problem. This leads into questions concerning the origin of the divergences in the perturbation series - for although it may initially provide usefully improved estimates, the series probably breaks down eventually. Existing arguments about this topic are critically reviewed - and in one case substantially simplified - before an alternative one is proposed in some detail. By concentrating on a particularly restricted situation, the Common Effective Charge Approach simplifies matters to the extent that issues such as non-analyticity of functions and the potential accuracy of perturbative techniques in realistic applications can be conveniently investigated.
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Amery, Gareth. "Causal cosmological perturbation theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619761.
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Akin, Osman Caglar. "Perturbation of renewal processes." Thesis, University of North Texas, 2008. https://digital.library.unt.edu/ark:/67531/metadc6140/.
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Renewal theory began development in the early 1940s, as the need for it in the industrial engineering sub-discipline operations research had risen. In time, the theory found applications in many stochastic processes. In this thesis I investigated the effect of seasonal effects on Poisson and non-Poisson renewal processes in the form of perturbations. It was determined that the statistical analysis methods developed at UNT Center for Nonlinear Science can be used to detect the effects of seasonality on the data obtained from Poisson/non-Poisson renewal systems. It is proved that a perturbed Poisson process can serve as a paradigmatic model for a case where seasonality is correlated to the noise and that diffusion entropy method can be utilized in revealing this relation. A renewal model making a connection with the stochastic resonance phenomena is used to analyze a previous neurological experiment, and it was shown that under the effect of a nonlinear perturbation, a non-Poisson system statistics may make a transition and end up in the of Poisson basin of statistics. I determine that nonlinear perturbation of the power index for a complex system will lead to a change in the complexity characteristics of the system, i.e., the system will reach a new form of complexity.
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Akin, Osman Caglar Grigolini Paolo. "Perturbation of renewal processes." [Denton, Tex.] : University of North Texas, 2008. http://digital.library.unt.edu/permalink/meta-dc-6140.
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Borinsky, Michael. "Graphs in perturbation theory." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19201.
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Inhalt dieser Arbeit ist eine Erweiterung der Hopfalgebrastruktur der Feynmangraphen und Renormierung von Connes und Kreimer. Zusätzlich wird eine Struktur auf faktoriell wachsenden Potenzreihen eingeführt, die deren asymptotisches Wachstum beschreibt und die kompatibel mit der Hopfalgebrastruktur ist.
Die Hopfalgebrastruktur auf Graphen erlaubt die explizite Enumeration von Graphen mit Einschränkungen in Bezug auf die erlaubten Untergraphen. Im Fall der Feynmangraphen wird zusätzlich eine algebraische Verbandstruktur eingeführt, die weitere eindeutige Eigenschaften von physikalischen Quantenfeldtheorien aufdeckt. Der Differenzialring der faktoriell divergenten Potenzreihen erlaubt es asymptotische Resultate von implizit definierten Potenzreihen mit verschwindendem Konvergenzradius zu extrahieren. In Kombination ergeben beide Strukturen eine algebraische Formulierung großer Graphen mit Einschränkungen für die erlaubten Untergraphen. Diese Strukturen sind motiviert von null-dimensionaler Quantenfeldtheorie and werden zur Analyse ebendieser benutzt.
Als reine Anwendung der Hopfalgebrastruktur wird eine hopfalgebraische Formulierung der Legendretransformation in Quantenfeldtheorien formuliert. Der Differenzialring der faktoriell divergenten Potenzreihen wird dazu benutzt zwei asymptotische Enumerationsprobleme zu lösen: Die asymptotische Anzahl der verbundenen Chorddiagramme und die asymptotische Anzahl der simplen Permutationen. Für beide asymptotischen Lösungen werden vollständige asymptotische Entwicklungen in Form von geschlossenen Erzeugendenfunktionen berechnet. Kombiniert werden beide Strukturen zur Anwendung an null-dimensionaler Quantenfeldtheorie. Zahlreiche Größen werden in den null-dimensionalen Varianten von phi^3, phi^4, QED, quenched QED and Yukawatheorie mit ihren kompletten asymptotischen Entwicklungen berechnet.This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic structure of the asymptotics of formal power series with factorial growth, which is compatible with the Hopf algebraic structure, will be introduced. The Hopf algebraic structure on graphs permits the explicit enumeration of graphs with constraints for the allowed subgraphs. In the case of Feynman diagrams a lattice structure, which will be introduced, exposes additional unique properties for physical quantum field theories. The differential ring of factorially divergent power series allows the extraction of asymptotic results of implicitly defined power series with vanishing radius of convergence. Together both structures provide an algebraic formulation of large graphs with constraints on the allowed subgraphs. These structures are motivated by and used to analyze renormalized zero-dimensional quantum field theory at high orders in perturbation theory. As a pure application of the Hopf algebra structure, an Hopf algebraic interpretation of the Legendre transformation in quantum field theory is given. The differential ring of factorially divergent power series will be used to solve two asymptotic counting problems in combinatorics: The asymptotic number of connected chord diagrams and the number of simple permutations. For both asymptotic solutions, all order asymptotic expansions are provided as generating functions in closed form. Both structures are combined in an application to zero-dimensional quantum field theory. Various quantities are explicitly given asymptotically in the zero-dimensional version of phi^3, phi^4, QED, quenched QED and Yukawa theory with their all order asymptotic expansions.
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Elago, David. "Robust computational methods for two-parameter singular perturbation problems." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1693_1308039217.
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This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.
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Naruko, Atsushi. "Non-linear Cosmological Perturbation Theory." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157769.
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Feng, Yongjian 1969. "Gauge invariance in perturbation theory." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55493.
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Gauge theories and their BRST invariance are reviewed. Gauge-invariant (color) subamplitudes for non-Abelian gauge theories are discussed. BRST transformations of non-Abelian vertices are derived, and are used to obtain the gauge transformation of any Feynman diagram. From this minimal set of gauge-invariant subamplitudes in perturbation theory can be found. This knowledge is useful in the application of the spinor helicity technique, and is indispensible for future developments of non-Abelian perturbation theories.
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North, Clare Geraldine. "Topics in superfield perturbation theory." Thesis, University of Liverpool, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243105.
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Hurst, G. J. B. "Intermolecular interactions by perturbation theory." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356653.
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Nalson, Eleanor Catherine. "Cosmological perturbation theory and magnetogenesis." Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8775.
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Cosmological perturbation theory (CPT) is an important tool with which inhomogeneities that seed the observed structure of our universe can be studied. This thesis introduces the subject of CPT and discusses applications of this at both linear and second order. At linear order the evolution of the curvature perturbation around horizon crossing is examined. We study single field inflation models numerically, and compare the curvature perturbation at horizon crossing to that at the end of inflation. In addition, linear-order CPT is extended to the case of a multi-fluid system and an approximation for the velocities of the baryons and photons in the early universe as well as the strength of the electric field is found. We use second order CPT to study magnetogenesis. By using fully relativistic, non-linear CPT we show how magnetic fields are generated. This is done by presenting the first fully analytical calculation of the magnetic field at second order. Our results suggest that magnetic fields with strengths of the order of 10²⁷G and with scale dependence M ∝ k⁴ may be generated - findings which are largely in agreement with previous numerical results. We end by outlining possible extensions to this work, in particular related to the study of primordial magnetogenesis.
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Christopherson, Adam J. "Applications of cosmological perturbation theory." Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/1308.
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Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, speci cally, to the early universe. Starting with some background material introducing the well-tested `standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative di erence to linear order. Thus, while at linear order vorticity decays with the expansion of the universe, the same is not true at higher orders. This will have important implications on future measurements of the polarisation of the Cosmic Microwave Background, and could give rise to the generation of a primordial seed magnetic eld. Having derived this qualitative result, we then estimate the scale dependence and magnitude of the vorticity power spectrum, nding, for simple power law inputs a small, blue spectrum. The nal part of this thesis concerns higher order perturbation theory, deriving, for the rst time, the metric tensor, gauge transformation rules and governing equations for fully general third order perturbations. We close with a discussion of natural extensions to this work and other possible ideas for o -shooting projects in this continually growing eld.
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Santos, Renato da Costa. "Topics on cosmological perturbation theory /." São Paulo, 2015. http://hdl.handle.net/11449/135870.
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Orientador: Horatiu Stefan NastaseBanca: Robert Brandenberger
Banca: Rogério Rosenfeld
Banca: Nathan Jacob Berkovits
Banca: Luis Raul Weber Abramo
Resumo: Nesta tese a Teoria das Perturbações Cosmológicas é revisada e três tópicos originais, incluídos neste grande ramo da cosmologia teórica, são apresentados. Começamos introduzindo e deduzindo as fórmulas necessárias partindo de primeiros princípios no capítulo 2. Em seguida, no capítulo 3, estudamos em detalhe Teorias Quânticas de Campos em de Sitter que contêm correntes de spin alto. Mostramos que a existência de correntes de spin alto - mesmo em teorias com interação - pode colocar mais vínculos na função de n-pontos, tornando a teoria assintoticamente gaussiana no futuro longínquo. Este resultado pode ser interpretado como o análogo do teorema de ColemanMandula para o espaço-tempo de de Sitter. O capítulo 4 é dedicado a modelos inflacionários conformes com o campo de Higgs fazendo o papel de Inflaton. Modelos com simetria de Weyl e com simetria SO(1, 1) para valores altos da energia são construídos. Verificamos quais as condições necessárias para que se obtenha um valor arbitrário para a razão escalar tensorial, parâmetro que mede a intensidade de ondas gravitacionais primordiais em um dado modelo. Introduzimos também um acoplamento diferente do valor conforme para a interação do campo escalar com o tensor de curvatura. Isto quebra a simetria de Weyl, mas verificamos que existe um forte atrator na direção da linha de Starobinsky. No último capítulo, aplicamos o efeito do 'back reaction' dos modos com comprimentos de onda longo (maiores que o raio de Hubble) em alguns modelos inflacionários e no cenário Ekpyrótico. Checamos se este efeito pode prevenir a inflação eterna nas regiões onde efeitos estocásticos são importantes nestes modelos. Alguns apêndices, com cálculos detalhados, são incluídos no final
Abstract: In this thesis the Theory of Cosmological Perturbations is reviewed and three original topics, that are part of this huge branch of theoretical cosmology, are presented. We start by reviewing and deducing the needed formulas from first principles in chapter 2. After it, in chapter 3, we study in detail Quantum Field Theories in de Sitter spacetime that contain Higher Spin currents. We show that the existence of Higher Spin currents - even in the interacting case - can put further constraints on the n-point function, making it asymptotically gaussian in the far future. This result can be interpreted as the analog of Coleman-Mandula theorem for de Sitter spacetime. Chapter 4 is devoted to conformal inflationary models with the Higgs field playing the role of the Inflaton field. We construct models with a Weyl symmetry and a SO(1, 1) symmetry at high energies. It is verified what are the conditions to get an arbitrary value for the tensor to scalar ratio, which measures the amplitude of primordial gravitational waves in a given model. Also, we introduce a coupling, different from the conformal one, for the scalar field and the curvature tensor. This breaks the Weyl symmetry but we verify that there is a strong attractor towards the Starobinsky line. In the last chapter, we apply the back-reaction effect of long wavelength modes (modes with wavelength bigger than the Hubble radius) in some inflationary models and in the Ekpyrotic scenario. We check if this effect could prevent eternal inflation in the region where stochastic effects are important for these models. Some appendices, with detailed calculations, are also included in the end
Doutor
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Andrawis, Madeleine Y. "Dielectric loss determination using perturbation." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39715.
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A dielectric filled cavity structure is currently being used to estimate the dielectric constant and loss factor over a wide range of frequencies of a dielectric material which fills the cavity structure [Saed, 1987]. A full field analysis is used to compute the effective complex permittivity of the sample material based on reflection coefficient measurements of the cavity structure and associated geometrical dimensions. The method has previously been used successfully to determine the dielectric constant of materials, but limitations in the Inethod have created difficulties in accurate determination of the dielectric loss factor. The effective loss in this method yields an estimate of the total cavity loss, including both the dielectric loss and that of the cavity conductor walls.
In this dissertation a perturbation approach is used to separate the conductor loss from the total loss. The loss-free full-field analysis is used to determine the electric current at the conductor boundaries. This current is used to evaluate the perturbed power dissipated in the cavity walls based on known conductor properties. By subtracting the loss due to the conductor walls from the total loss measured in the structure, the dielectric loss and the resultant dielectric loss factor may be estimated.
Measurements are presented for sample dielectric materials. The dielectric loss tangents computed by this new technique improve the unperturbed estimates in the microwave frequency range.Ph. D.
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Zakirova, Ksenia V. "Perturbation Dynamics on Moving Chains." Scholarship @ Claremont, 2015. http://scholarship.claremont.edu/hmc_theses/90.
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Chain dynamics have gained renewed interest recently, following the release of a viral YouTube video showcasing a phenomenon called the chain fountain. Recent work in the field shows that there exists unexplained behavior in newly proposed chain systems. We consider a general system of a chain traveling at constant velocity in an external force field and derive steady state solutions for the time invariant shape of the chain. Perturbing the solution introduces moving waves along the steady state shape with components that propagate along and against the direction of travel of the chain. Furthermore, we develop a numerical model using a discrete approximation of the chain in order to empirically test our results. The behavior of the chain fountain and related chain systems is discussed in the context of these findings.
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Shoresh, Noam. "Applications of chiral perturbation theory /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/9676.
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Sa, Ngiamsunthorn Parinya. "Domain perturbation for parabolic equations." Thesis, The University of Sydney, 2011. http://hdl.handle.net/2123/7775.
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We study the effect of domain perturbation on the behaviour of parabolic equations. The first aspect considered in this thesis is the behaviour of solutions under changes of the domain. We show how solutions of linear and semilinear parabolic equations behave as a sequence of domains $\Omega_n$ converges to an open set $\Omega$ in a certain sense. In particular, we are interested in singular domain perturbations so that a change of variables is not possible on these domains. For autonomous linear equations, it is known that convergence of solutions under domain perturbation is closely related to the corresponding elliptic equations via a standard semigroup theory. We show that there is also a relation between domain perturbation for non-autonomous linear parabolic equations and domain perturbation for elliptic equations. The key result for this is the equivalence of Mosco convergences between various closed and convex subsets of Banach spaces. An important consequence is that the same conditions for a sequence of domains imply convergence of solutions under domain perturbation for both parabolic and elliptic equations. By applying variational methods, we obtain the convergence of solutions of initial value problems under Dirichlet or Neumann boundary conditions. A similar technique can be applied to obtain the convergence of weak solutions of parabolic variational inequalities when the underlying convex set is perturbed. Using the linear theory, we then study domain perturbation for initial boundary value problems of semilinear type. We are also interested in the behaviour of bounded entire solutions of parabolic equations defined on the whole real line. We establish a convergence result for bounded entire solutions of linear parabolic equations under $L^2$ and $L^p$-norms. For the $L^p$-theory, we also prove H\"{o}lder regularity of bounded entire solutions with respect to time. In addition, the persistence of some classes of bounded entire solutions is given for semilinear equations using the Leray-Schauder degree theory. The second aspect is to study the dynamics of parabolic equations under domain perturbation. In this part, we consider parabolic equation as a dynamical system in an $L^2$ space and study the stability of invariant manifolds near a stationary solution. In particular, we prove the continuity (upper and lower semicontinuity) of both, the local stable invariant manifolds and the local unstable invariant manifolds under domain perturbation.
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Lu, Nan. "Normally elliptic singular perturbation problems: local invariant manifolds and applications." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41090.
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In this thesis, we study the normally elliptic singular perturbation problems including both finite and infinite dimensional cases, which could also be non-autonomous. In particular, we establish the existence and smoothness of O(1) local invariant manifolds and provide various estimates which are independent of small
singular parameters. We also use our results on local invariant manifolds to study
the persistence of homoclinic solutions under weakly dissipative and conservative per-
turbations. We apply Semi-group Theory and Lyapunov-Perron Integral Equations with some
careful estimates to handle the O(1) driving force in the system so that we can approximate the full system through some simpler limiting system. In the investigation of homoclinics, a diagonalization procedure and some normal form transformation should be first carried out. Such diagonalization procedure is not trivial at all. We discuss this issue in the appendix. We use Melnikov type analysis to study the weakly
dissipative case, while the conservative case is based on some energy methods. As a concrete example, we have shown rigrously the persistence of homoclinic solutions of an elastic pendulum model which may be affected by damping, external
forcing and other potential fields.
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Leithes, Alexander. "Perturbations in Lemaître-Tolman-Bondi and Assisted Coupled Quintessence cosmologies." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/24649.
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In this thesis we present research into linear perturbations in Lemaître-Tolman-Bondi (LTB) and Assisted Coupled Quintessence (ACQ) Cosmologies. First we give a brief overview of the standard model of cosmology. We then introduce Cosmological Perturbation Theory (CPT) at linear order for a at Friedmann-Robertson-Walker (FRW) cosmology. Next we study linear perturbations to a Lemaître-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities in LTB. We show, using the perturbed energy conservation equation, that there is a conserved quantitiy in LTB which is conserved on all scales. We then briefly extend our discussion to the Lemaître spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime. We also study the behaviour of linear perturbations in assisted coupled quintessence models in a FRW background. We provide the full set of governing equations for this class of models, and solve the system numerically. The code written for this purpose is then used to evolve growth functions for various models and parameter values, and we compare these both to the standard CDM model and to current and future observational bounds. We also examine the applicability of the "small scale approximation", often used to calculate growth functions in quintessence models, in light of upcoming experiments such as SKA and Euclid. We nd the results of the full equations deviates from the approximation by more than the experimental uncertainty for these future surveys. The construction of the numerical code, Pyessence, written in Python to solve the system of background and perturbed evolution equations for assisted coupled quintessence, is also discussed.
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Huettinger, Rachel. "Perturbation Based Decomposition of sEMG Signals." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/1974.
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Surface electromyography records the motor unit action potential signals in the vicinity of the electrode to reveal information on muscle activation. Decomposition of sEMG signals for characterization of constituent motor unit action potentials in terms of amplitude and firing times is useful for clinical research as well as diagnosis of neurological disorders. Successful decomposition of sEMG signals would allow for pertinent motor unit action potential information to be acquired without discomfort to the subject or the need for a well-trained operator (compared with intramuscular EMG). To determine amplitudes and firing times for motor unit action potentials in an sEMG recording, Szlavik's perturbation based decomposition may be applied. The decomposition was initially applied to synthetic sEMG signals and then to experimental data collected from the biceps brachii. Szlavik's decomposition estimator yields satisfactory results for synthetic and experimental sEMG signals with reasonable complexity.
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Basu, Sayandeb. "Perturbation theory in covariant canonical quantization /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.
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Karamalis, Constantinos. "Data perturbation analyses for linear programming." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/6709.
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This thesis focuses on several aspects of data perturbation for Linear Programming. Classical questions of degeneracy and post-optimal analysis are given a unified presentation, in a view of new interior point methods of linear programming. The performance of these methods is compared to the simplex algorithm; interior point methods are shown to alleviate some difficulties of representation and solution of linear programs. An affine scaling algorithm is implemented in conjunction with a simple rounding heuristic to asses the benefit of interior point trajectories to provide approximate solutions of linear integer programming.
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Chang, Xiao-Wen. "Perturbation analysis of some matrix factorizations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0023/NQ29906.pdf.
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Jakus-Pol, Joanna Ewa. "Pressure perturbation calorimetry of protein unfolding." Thesis, University of Glasgow, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.412944.
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Gonzalez, Rodriguez David. "Development of multi reference perturbation theory." Thesis, King's College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272191.
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Ramakrishnan, Ramya. "Perturbation training for human-robot teams." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99845.
Full textAbstract:
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 63-67).
Today, robots are often deployed to work separately from people. Combining the strengths of humans and robots, however, can potentially lead to a stronger joint team. To have fluid human-robot collaboration, these teams must train to achieve high team performance and flexibility on new tasks. This requires a computational model that supports the human in learning and adapting to new situations. In this work, we design and evaluate a computational learning model that enables a human-robot team to co-develop joint strategies for performing novel tasks requiring coordination. The joint strategies are learned through "perturbation training," a human team-training strategy that requires practicing variations of a given task to help the team generalize to new variants of that task. Our Adaptive Perturbation Training (AdaPT) algorithm is a hybrid of transfer learning and reinforcement learning techniques and extends the Policy Reuse in Q-Learning (PRQL) algorithm to learn more quickly in new task variants. We empirically validate this advantage of AdaPT over PRQL through computational simulations. We then augment our algorithm AdaPT with a co-learning framework and a computational bi-directional communication protocol so that the robot can work with a person in live interactions. These three features constitute our human-robot perturbation training model. We conducted human subject experiments to show proof-of-concept that our model enables a robot to draw from its library of prior experiences in a way that leads to high team performance. We compare our algorithm with a standard reinforcement learning algorithm Q-learning and find that AdaPT-trained teams achieved significantly higher reward on novel test tasks than Q-learning teams. This indicates that the robot's algorithm, rather than just the human's experience of perturbations, is key to achieving high team performance. We also show that our algorithm does not sacrifice performance on the base task after training on perturbations. Finally, we demonstrate that human-robot training in a simulation environment using AdaPT produced effective team performance with an embodied robot partner.
by Ramya Ramakrishnan.
S.M.
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Poole, Travis L. "Geoacoustic inversion by mode amplitude perturbation." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/38932.
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Thesis (Ph. D.)--Joint Program in Applied Ocean Physics and Engineering (Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and the Woods Hole Oceanographic Institution), 2007.Includes bibliographical references (p. 124-126).
This thesis introduces an algorithm for inverting for the geoacoustic properties of the seafloor in shallow water. The input data required by the algorithm are estimates of the amplitudes of the normal modes excited by a low-frequency pure-tone sound source, and estimates of the water column sound speed profiles at the source and receiver positions. The algorithm makes use of perturbation results, and computes the small correction to an estimated background profile that is necessary to reproduce the measured mode amplitudes. Range-dependent waveguide properties can be inverted for so long as they vary slowly enough in range that the adiabatic approximation is valid. The thesis also presents an estimator which can be used to obtain the input data for the inversion algorithm from pressure measurements made on a vertical line array (VLA). The estimator is an Extended Kalman Filter (EKF), which treats the mode amplitudes and eigenvalues as state variables. Numerous synthetic and real-data examples of both the inversion algorithm and the EKF estimator are provided. The inversion algorithm is similar to eigenvalue perturbation methods, and the thesis also presents a combination mode amplitude/eigenvalue inversion algorithm, which combines the advantages of the two techniques.
by Travis L. Poole.
Ph.D.
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Dianzinga, Mamy Rivo. "N-representable density matrix perturbation theory." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0285/document.
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Alors que les approches standards de résolution de la structure électronique présentent un coût de calcul à la puissance 3 par rapport à la complexité du problème, des solutions permettant d’atteindre un régime asymptotique linéaire,O(N), sont maintenant bien connues pour le calcul de l'état fondamental. Ces solutions sont basées sur la "myopie" de la matrice densité et le développement d'un cadre théorique permettant de contourner le problème aux valeurs propres. La théorie des purifications de la matrice densité constitue une branche de ce cadre théorique. Comme pour les approches de type O(N) appliquées à l'état fondamental,la théorie des perturbations nécessaire aux calculs des fonctions de réponse électronique doit être révisée pour contourner l'utilisation des routines coûteuses.L'objectif est de développer une méthode robuste basée uniquement sur la recherche de la matrice densité perturbée, pour laquelle seulement des multiplications de matrices creuses sont nécessaires. Dans une première partie,nous dérivons une méthode de purification canonique qui respecte les conditions de N-representabilité de la matrice densité à une particule. Nous montrons que le polynôme de purification obtenu est auto-cohérent et converge systématiquement vers la bonne solution. Dans une seconde partie, en utilisant une approche de type Hartree-Fock, nous appliquons cette méthode aux calculs des tenseurs de réponses statiques non-linéaires pouvant être déterminés par spectroscopie optique. Au delà des calculs à croissance linéaire réalisés, nous démontrons que les conditions N-representabilité constituent un prérequis pour garantir la fiabilité des résultatsWhereas standard approaches for solving the electronic structures present acomputer effort scaling with the cube of the number of atoms, solutions to overcomethis cubic wall are now well established for the ground state properties, and allow toreach the asymptotic linear-scaling, O(N). These solutions are based on thenearsightedness of the density matrix and the development of a theoreticalframework allowing bypassing the standard eigenvalue problem to directly solve thedensity matrix. The density matrix purification theory constitutes a branch of such atheoretical framework. Similarly to earlier developments of O(N) methodology appliedto the ground state, the perturbation theory necessary for the calculation of responsefunctions must be revised to circumvent the use of expensive routines, such asmatrix diagonalization and sum-over-states. The key point is to develop a robustmethod based only on the search of the perturbed density matrix, for which, ideally,only sparse matrix multiplications are required. In the first part of this work, we derivea canonical purification, which respects the N-representability conditions of the oneparticledensity matrix for both unperturbed and perturbed electronic structurecalculations. We show that this purification polynomial is self-consistent andconverges systematically to the right solution. As a second part of this work, we applythe method to the computation of static non-linear response tensors as measured inoptical spectroscopy. Beyond the possibility of achieving linear-scaling calculations,we demonstrate that the N-representability conditions are a prerequisite to ensurereliability of the results
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DIDELOT, SOPHIE. "Etude d'une perturbation singuliere elliptique degeneree." Reims, 1999. http://www.theses.fr/1999REIMS030.
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Cette these etudie un probleme de perturbation singuliere en dimension un pour un probleme aux limites concernant un operateur de type schrodinger. Ce dernier depend d'un petit parametre strictement positif, et le potentiel, egalement positif, degenere au bord. Cette particularite conduit a introduire des espaces a poids bien adaptes au probleme. On peut alors montrer que le probleme admet une solution bien definie dans ces espaces, pour des donnees convenables. On indique ensuite comment on peut construire des solutions approchees grace a des operateurs integraux bases sur les fonctions d'airy. On peut enfin en deduire des formules asymptotiques pour la vraie solution lorsque le petit parametre tend vers 0. Les termes d'erreur sont controles uniformement par rapport au petit parametre. La seconde partie est consacree a l'etude du probleme spectral. Apres avoir determine la nature du spectre, on utilise les techniques de la premiere partie pour obtenir des developpements asymptotiques des premieres valeurs propres et des fonctions propres associees. Dans le cas de double puits, ce developpement asymptotique des fonctions propres ne suffit pas pour analyser l'effet tunnel. On les approche alors par une methode bkw basee sur les points tournants. On en deduit le premier terme de l'asymptotique de l'effet tunnel.
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El, Mokhtari Rachid. "Solveurs multigrilles et méthode de perturbation." Metz, 2002. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/2002/El_Mokhtari.Rachid.SMZ0229.pdf.
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Dans ce travail de thèse, nous avons proposé deux nouvelles classes d'algorithmes à deux grilles pour résoudre les problèmes d'élasticité de grande taille. Ces méthodes sont basées sur l'association des techniques d'homotopie, de perturbation et sur les approximants de Padé. Un premier algorithme s'appuie sur une décomposition des variables en variables globales (maillage grossier) et variables locales (maillage fin). Cette méthode ne se couple facilement qu'avec un lisseur diagonal. Des résultats numériques ont montré que cet algorithme est beaucoup plus rapide que les méthodes multigrilles classiques et également plus rapide que la méthode du gradient conjugué. Dans une seconde partie, on propose une nouvelle méthode à deux grilles. On introduit un multiplicateur de Lagrange, ce qui permet d'utiliser toutes sortes de lisseurs. On s'est intéressé en particulier au lisseur issu d'une décomposition incomplète de Cholesky, qui conduit à des algorithmes rapides et fiables. Nous avons testé diverses méthodes pour les cas des maillages curvilignes et établi une méthode "optimale". Une autre application de ces solveurs a été réalisée sur des problèmes avec seconds membres répétés. Cette première application laisse entrevoir de réelles possiblités et un bon intérêt d'utiliser ces solveurs pour résoudre des problèmes linéaires issus de la méthode asymptotique-numérique (MAN)In this work, we propose a new class of bi-grid algorithms to solve large scale linear algebraic equations. These methods are based on association on homotopy, perturbation technique and Padé approximants. A first algorithm is based on a decomposition of the variables in global (coarse meshes) and local (fine meshes) one. This methods is easily coupled with a diagonal smoother. The numerical results showed that this algorithms is most faster than classical multigird methods and also faster than a conjugate gradient method. In the second section, we purpose a new bi-gird method. We introduced a Lagrange multipliers, that means used of several type of smoothers. In particular, we are interested in the preconditioners resulting from incomplete decomposition of Cholesky, which leads to fast and efficient algorithms. We have tested various methods for the case of the unstructured meshes and established an "optimal" method. Another first application of these solvers was realized in the case of problems with repeated right hand side. This first application showed real possibilities and a real interest to use these solvers to solve linear problems resulting from the asymptotic numerical-methods (ANM)
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El, Mokhtari Rachid Potier-Ferry Michel. "Solveurs multigrilles et méthode de perturbation." Metz : Université Metz, 2008. ftp://ftp.scd.univ-metz.fr/pub/Theses/2002/El_Mokhtari.Rachid.SMZ0229.pdf.
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Urech, Andreas. "Virtual photons in chiral perturbation theory /." [S.l : s.n.], 1994. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.
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Wong, Chin Pin. "Kato's Perturbation Theorem and honesty theory." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:c72c308b-d96d-4e31-a854-f2a10e99eeb6.
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We study an additive perturbation theorem for substochastic semigroups which is known as Kato's Theorem. There are two previously-known generalisations of Kato's Theorem, namely for abstract state spaces and for KB-spaces. We prove a version of Kato's Theorem for a class of spaces which encompasses both, namely ordered Banach spaces with generating cone and monotone norm. We also study a property of the perturbed semigroup in Kato's Theorem known as honesty of the semigroup. We add a few results to the fairly extensive existing theory of honesty for Kato's Theorem for abstract state spaces. In light of our new generalisation of Kato's Theorem to ordered Banach spaces with monotone norm, we investigate generalising the theory of honesty to these spaces as well. The results for the general case are less complete as many of the results for the case of abstract state spaces depend on the additive norm structure of the space. We also consider some new applications of honesty theory in abstract state spaces. We begin by applying honesty theory to the study of the heat equation on graphs. We prove that honesty of the heat semigroup coincides with a concept known as stochastic completeness of the graph which has been studied independently of honesty. We then look at the application of honesty theory to quantum dynamical semigroups. We show that honesty is the natural generalisation of the concept of conservativity of quantum dynamical semigroups. Conservative quantum dynamical semigroups are known to have certain "nice" properties. We show that similar properties hold for honest semigroups using honesty theory results. Finally, we consider a form of boundary perturbations in the context of transport semigroups. There exists an analogous theory of honesty for this set-up. We formulate a general result from which honesty results of both Kato's Theorem and transport semigroups can be derived.
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Garofalo, Marco. "Dynamics of numerical stochastic perturbation theory." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31086.
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Numerical Stochastic Perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice quantum field theory. The standard algorithm based on the Langevin equation, however, suffers from several limitations which in practice restrict the potential of this technique: first of all it is not exact, a sequence of simulations with finer and finer discretization of the relevant equations have to be performed in order to extrapolate away the systematic errors in the results; and, secondly, the numerical simulations suffer from critical slowing down as the continuum limit of the theory is approached. In this thesis I investigate some alternative methods which improve upon the standard approach. In particular, I present a formulation of Numerical Stochastic Perturbation theory based on the Generalised Hybrid Molecular Dynamics algorithm and a study of the recently proposed Instantaneous Stochastic Perturbation Theory. The viability of these methods is investigated in φ4 theory.
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Bär, Oliver. "Chiral perturbation theory for lattice QCD." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/13976.
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Eine zusammenfassende Übersicht über die Formulierung der chiralen Störungstheorie (ChPT) für die Gitter Quantenchromodynamik (QCD) ist gegeben. Wir beginnen mit kurzen Zusammenfassungen der chiralen Störungstheorie für die Kontinuum-QCD sowie Symanziks effektiver Theorie für die Gitter-QCD. Anschließend wird die Formulierung der ChPT für die Gitter-QCD behandelt. Nach einem weiteren Kapitel über partial quenching und Theorien mit gemischten Wirkungen werden konkrete Anwendungen diskutiert: Wilson ChPT, staggered ChPT sowie Wilson ChPT mit einem chiral verdrehten Massenterm. Die folgenden Kapitel behandeln das Epsilonregime mit Wilsonfermionen sowie ausgewählte Resultate für ChPT mit gemischten Wirkungen. Den Abschluß bildet die Formulierung der chiralen Störungstheorie für schwere Vektormesonen mit Wilsonfermionen.The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed.
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Bianchi, Lorenzo. "Perturbation theory for string sigma models." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17439.
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In dieser Arbeit untersuchen wir Quanten-Aspekte des Green-Schwarz Superstrings in verschiedenen AdS-Hintergründen, die für die AdS/CFT Korrespondenz von Bedeutung sind, und geben einige Beispiele für perturbative Rechnungen in den entsprechenden integrablen Sigma-Modellen. Wir beginnen mit einer detaillierten Darstellung der Konstruktion der Wirkung des Typ-IIB-Superstrings auf dem AdS5 x S5-Hintergrund, die durch eine Supercoset-Sigma-Modell definiert wird, und zeigen die Grenzen dieser Herangehensweise für Hintergründe auf, die in niedrig-dimensionalen Beispielen der Eich/Gravitations-Dualität von Interesse sind. Daraufhin betrachten wir die Entwicklung um das BMN-Vakuum und die S-Matrix für die Streuung von Weltflächen-Anregungen. Um ihre Elemente effizient auszuwerten, entwickeln wir eine auf Unitarität basierende Methode für allgemeine massive, zweidimensionale Feldtheorien. Weiterhin betrachten wir den AdS-Lichtkegel eichfixierten String in AdS4 x CP3 in einer Entwicklung um das "null-cusp"-Vakuum. Die freie Energie dieses Modells hängt zusammen mit der anomalen Cusp-Dimension der Eichtheorie. Wir berechnen Korrekturen zur Zustandssumme des Superstring-Modells und leiten somit die anomale Cusp-Dimension der ABJM-Theorie bei starker Kopplung bis zur Zweischleifen-Ordnung her. Schlie\sslich berechnen wir auf Einschleifen-Ebene die Dispersionsrelation von Anregungen um das GKP-Vakuum. Unsere erfolgreiche Anwendung von auf Unitarität basierenden Cut-Techniken auf verschiedene Beispiele stützt die Vermutung, dass die S-Matrizen zweidimensionaler, integrabler Feldtheorien cut-konstruierbar sind. Weiterhin liefern unsere Ergebnisse wertvolle Daten, die die Konsistenz der String-Wirkung auf Quanten-Niveau belegen und stellen nicht-triviale stringente Tests der Quanten-Integrabilität der untersuchten Modelle dar.In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable sigma-models. We start by reviewing in details the construction of the type IIB superstring action in AdS5 x S5 background defined as a supercoset sigma model, pointing out the limits of this procedure for backgrounds interesting in lower-dimensional examples of the gauge/gravity duality. We then consider the expansion about the BMN vacuum and the S-matrix for the scattering of worldsheet excitations. To evaluate its elements efficiently we develop a unitarity-based method for general massive two-dimensional field theories. We also analyze the AdS light-cone gauge fixed string in AdS4 x CP3 expanded around a “null cusp” vacuum. The free energy of this model is related to the cusp anomalous dimension of the gauge theory and, indirectly, to a non-trivial effective coupling entering all integrability-based calculations in AdS4/CFT3. We calculate corrections to the superstring partition function of the model, thus deriving the cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order and giving support to a recent conjecture. Finally, we calculate at one-loop the dispersion relation of excitations about the GKP vacuum. Our successful application of unitarity-cut techniques on several examples supports the conjecture that S-matrices of two-dimensional integrable field theories are cut-constructible. Furthermore, our results provide valuable data in support of the quantum consistency of the string actions and furnish non-trivial stringent tests for the quantum integrability of the analyzed models.
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Lang, Hunter(Hunter J. ). "Perturbation stability for approximate MAP inference." Thesis, Massachusetts Institute of Technology, 2018. https://hdl.handle.net/1721.1/121627.
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This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 85-88).
The MAP inference problem in discrete graphical models has found widespread applications in machine learning and statistical physics over the past few decades. However, for many useful model classes, this combinatorial optimization problem is NP-hard to solve efficiently. Approximation algorithms, which typically come with theoretical worst-case guarantees on their approximation ratios, are commonplace. On real-world data, however, these algorithms far outperform their worst-case guarantees, often returning solutions that are extremely close to optimal. This thesis asks, and partially answers, the question: "What structure is present in real-world data that makes MAP inference easy?" We propose stability conditions under which we prove that popular approximation algorithms work provably well, and we evaluate these conditions on real-world instances.
by Hunter Lang.
M. Eng.
M.Eng. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science
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Ravenni, Andrea. "Glimpsing at the primordial perturbation field." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3426246.
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In this thesis I will focus on ``non-minimal'' properties of the primordial perturbation field;
both analysing data, and assessing the constraining power of novel probes.
In particular, I will address the problem of finding deviations from a power-law primordial power spectrum, the possibility of better constraining compensated isocurvature perturbations, and detect primordial non-Gaussianity in an ample range of scales.
I present a minimally parametric, model independent reconstruction of the shape of the primordial power spectrum.
We use a comprehensive set of the state-of the art cosmological data:
\Planck observations of the temperature and polarisation anisotropies of the cosmic microwave background (CMB),
WiggleZ and Sloan Digital Sky Survey Data Release 7 galaxy power spectra,
and the Canada-France-Hawaii Lensing Survey correlation function.
This reconstruction strongly supports the evidence for a power law primordial power spectrum with a red tilt and disfavours deviations from a power law power spectrum including small-scale power suppression such as that induced by significantly massive neutrinos.
This offers a powerful confirmation of the inflationary paradigm, justifying the adoption of the inflationary prior in cosmological analyses.
We develop a linear perturbation theory for the spectral $y$-distortions of the CMB.
The $y$-distortions generated during the recombination epoch are usually negligible because the energy transfer due to the Compton scattering is strongly suppressed at that time, but they can be significant if there is are compensated isocurvature perturbations with large amplitude.
Since $y$-distortions explicitly depend on the baryon density fluctuations, they can be used to detect and constrain compensated isocurvature perturbations (CIPs) models.
We compute the cross correlation functions of the $y$-distortions with the CMB temperature and the $E$-mode polarization anisotropies ($T$, $E$ respectively).
We investigate how well measurements of $y$-anisotropies provided by a
PIXIE-like and a PRISM-like survey,
LiteBIRD, and a cosmic variance limited (CVL) survey, will constrain $f'=\Delta^2_{\zeta \text{CIP}}/\Delta^2_{\zeta \zeta}$,
and find that the degradation in constraining power due to the presence of Sunyaev Zel’dovich effect from galaxy clusters
will prevent detections unless the amplitude of CIP is unnaturally high, with forecasted upper limits of, \eg
$f'<2 \times 10^5$ (68\% C.L.) with LiteBIRD, and $f'<2 \times 10^4$ (68\% C.L.) with CVL observations.
Cross-correlations between CMB temperature and $y$-distortions anisotropies have been previously proposed as a way to measure the local bispectrum parameter $\fnl^\text{loc}$ in a range of scales much smaller than those accessible to CMB primary anisotropies.
Unfortunately, the primordial $y$-$T$ signal is strongly contaminated by the late-time correlation between the Integrated Sachs Wolfe and \SZ (SZ) effects.
Moreover, SZ itself generates a large noise contribution in the $y$-parameter map.
We consider two original ways to address these issues:
To remove the bias due to the SZ-CMB temperature coupling, while also adding new signal, we include in the analysis the $y$-$E$ cross-correlation.
In order to reduce the noise, we propose to clean the $y$-map by subtracting a SZ template, reconstructed via cross-correlation with external tracers.
We combine this SZ template subtraction with the previously adopted solution of directly masking detected clusters.
Our forecasts show that, using $y$-distortions, a PRISM-like survey can achieve $\fnl^\text{loc} < 300$ (68\% C.L.), while an ideal experiment will achieve $\fnl^\text{loc} < 130$, with improvements of a factor $\sim 3$ from adding the $y$-$E$ signal, and a further $20 \sim 30 \%$ from template cleaning.
These forecasts are much worse than current $\fnl^\text{loc}$ boundaries from Planck, but we stress again that they refer to completely different scales.Nella presente tesi studierò proprietà non minimali del campo di perturbazioni primordiali; sia analizzando dati che valutando la capacità di futuri esperimenti di vincolare modelli cosmologici.
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Maiocchi, A. "PERTURBATION THEORY AT THE THERMODYNAMIC LIMIT." Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/217563.
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La presente tesi propone un'estensione della teoria delle perturbazioni Hamiltoniana al limite termodinamico (ossia, per sistemi con un numero infinito di gradi di libertà e una temperatura, o energia specifica, finita), nello spirito della teoria ergodica (cioè, in presenza di una misura invariante). Per un sistema concreto, il modello Φ4 discreto, si ottiene una versione debole del teorema di Nehoroscev. Il risultato è che, nel limite termodinamico, esiste almeno un'osservabile, indipendente dall'energia, la cui funzione di
autocorrelazione temporale rimanga significativamente discosta da zero
fino a tempi esponenzialmente lunghi nei parametri perturbativi. La tesi è completata dalla discussione di argomenti correlati, ossia le proprietà analitiche generali delle funzioni di autocorrelazione temporale e un'applicazione euristica della teoria perturbativa al problema del limite di densità nei plasmi magnetizzati.The present thesis provides an extension of Hamiltonian perturbation theory to the thermodynamic limit (i.e., for systems with an infinite number of degrees of freedom and a finite temperature or specific energy), in the spirit of ergodic theory (i.e., in the presence of an invariant measure). For a concrete model, which is the discrete Φ4 model, a weaker version of classical Nekhoroshev theorem is obtained. The result is that, at the thermodynamic limit, there exists at least one observable, independent of energy, such that its time–autocorrelation function does not relax to zero up to times exponentially long in the perturbation parameters. In the thesis, further related subjects are discussed, namely, analytical properties of generic time-autocorrelation functions and a heuristic application of perturbation theory to the problem of the density limit in magnetized plasmas.
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Maurer, Simon. "Efficient distance-including integral screening for Moller-Plesset perturbation theory of second order and symmetry-adapted perturbation theory." Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-183280.
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Derde, Mélanie. "Lysozyme natif et chauffé à sec perturbation de l’intégrité membranaire d’Escherichia coli : perturbation de l’intégrité membranaire d’Escherichia coli." Rennes, Agrocampus Ouest, 2014. http://www.theses.fr/2014NSARB249.
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La recherche de nouveaux composés antimicrobiens naturels est un enjeu important pour répondre d’une part à la problématique des bactéries multirésistantes et d’autre part à la demande croissante de conservateurs naturels. Les protéines et peptides antimicrobiens agissant sur les membranes bactériennes semblent de bons candidats. Une des premières protéines antimicrobiennes découvertes est le lysozyme, connu depuis longtemps pour son activité muramidase contre les bactéries à coloration de Gram positive. Récemment, le lysozyme s’est avéré également actif contre les bactéries à coloration de Gram négative. L’activité membranaire du lysozyme est considérée comme un des mécanismes possibles responsables de cette activité. Dans ce travail, l’activité du lysozyme vis-à-vis des membranes d’E. Coli a été évaluée. Le lysozyme affecte l’intégrité des deux membranes : des pores et des canaux ioniques sont formés respectivement dans les membranes externe et cytoplasmique. Des monocouches de LPS et de phospholipides ont été utilisées pour mimer respectivement les membranes externe et cytoplasmique. Le lysozyme peut s’adsorber à, s’insérer dans et réorganiser les deux monocouches de manière dose-dépendante. Ces résultats obtenus sur membranes modèles sont cohérents avec les observations de perturbations membranaires in vivo. Le lysozyme chauffé à sec, plus flexible, hydrophobe et basique que la protéine native, a une activité antimicrobienne accrue par rapport au lysozyme natif. Cette activité peut être reliée à sa plus grande capacité de perturbation des membranes in vivo. De même, le lysozyme chauffé à sec induit une réorganisation des monocouches plus drastique que le lysozyme natif. En fait, le lysozyme chauffé à sec se révèle être un mélange efficace d’isoformes agissant différemment et de manière complémentaire sur les membranes d’E. Coli. Leur distribution, et un vecteur spécifique des moyennes des variables. A partir du nouveau générateur de porcs virtuels et de ce patron de variance-covariance, une population virtuelle de 2000 porcs a été générée pour simuler l’effet de la stratégie alimentaire et du contexte de prix des matières premières sur les performances moyennes et leur variabilité, et sur les rejets azotés. Notre étude montre notamment qu’en alimentation biphase, une restriction alimentaire maîtrisée permet d’améliorer l'hétérogénéité du poids, la marge par porc et les rejets. Un essai zootechnique a permis de confirmer la pertinence de certains résultats de simulation. L’ensemble de ce travail permet d’envisager à terme l’intégration d’une dimension populationnelle dans les modèles et outils d'aide à la décision qui en sont issusResearch for novel natural antimicrobial compounds is highly stimulated because of the growing number of multi-resistant bacteria on the one hand and the growing consumer demand for natural conservatives on the other hand. Antimicrobial peptides or protein acting on the bacterial membranes could answer this demand. One of the first discovered antimicrobial proteins is lysozyme, is widely known for its muramidase activity against several Gram positive bacteria. Recently, lysozyme was also shown active against Gram negative bacteria. Membrane activity of lysozyme is suggested as one of the possible mechanisms involved. In this work, lysozyme activity on both the outer and cytoplasmic membranes of Escherichia coli is evaluated in vivo and in vitro. Lysozyme has been shown to affect the integrity of both membranes ; pores and ion channels are formed in the outer and cytoplasmic membranes, respectively. LPS and phospholipid monolayers have been used to mimic the E. Coli outer and cytoplasmic membranes, respectively. Lysozyme is able to adsorb onto, to insert into and to reorganize LPS and phospholipid monolayers in a dose-dependent manner. These findings on lipid membrane models are consistent with the membrane disruption observed in vivo. Dry-heated lysozyme, more flexible, hydrophobic and basic than the native protein, has here been shown to exhibit an increased antimicrobial activity compared to native lysozyme. This activity could be related to its increased membrane disruption capacity in vivo. As well dry-heated lysozyme is able to reorganize LPS and phospholipid monolayers in a larger extent than native lysozyme. Actually, dry-heated lysozyme appears to be a efficient, mixture of complementary lysozyme isoforms acting differently on the E. Coli membranes
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Kambor, Joachim. "Nonleptonic weak interactions in chiral perturbation theory /." [S.l.] : [s.n.], 1990. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=9068.
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Knudson, Wade E. "Orbital perturbation analysis of earth-crossing asteroids." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA306616.
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Thesis (Degree of Aeronautical and Astronautical Engineer) Naval Postgraduate School, December 1995.Thesis advisor(s): I.M. Ross. "December 1995." Includes bibliographical references. Also available online.
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Adams, Richelle Vive-Anne. "Infinitesimal Perturbation Analysis for Active Queue Management." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19844.
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Active queue management (AQM) techniques for congestion control in Internet Protocol (IP) networks have been designed using both heuristic and analytical methods. But so far, there has been found no AQM scheme designed in the realm of stochastic optimization. Of the many options available in this arena, the gradient-based stochastic approximation method using Infintesimal Perturbation Analysis (IPA) gradient estimators within the Stochastic Fluid Model (SFM) framework is very promising. The research outlined in this thesis provides the theoretical basis and foundational layer for the development of IPA-based AQM schemes. Algorithms for computing the IPA gradient estimators for loss volume and queue workload were derived for the following cases: a single-stage queue with instantaneous, additive loss-feedback, a single-stage queue with instantaneous, additive loss-feedback and an unresponsive competing flow, a single-stage queue with delayed, additive loss-feedback, and a multi-stage tandem network of $m$ queues with instantaneous, additive loss-feedback. For all cases, the IPA gradient estimators were derived with the control parameter, $ heta$, being the buffer-limits of the queue(s). For the single-stage case and the multi-stage case with instantaneous, additive loss-feedback, the IPA gradient estimators for when the control parameter, $ heta$, is the loss-feedback constant, were also derived. Sensitivity analyses and optimizations were performed with control parameter, $ heta$, being the buffer-limits of the queue(s), as well as the loss-feedback constant.
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Zaballa, Ignacio. "Cosmological effects of the primordial curvature perturbation." Thesis, Lancaster University, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485250.
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In this thesis we study the cosmological effects of the primordial curvature perturbation in two different research areas, which provide useful information about the origin and nature of the curvature perturbation on completely different range of scales. The first one investigates the' generation ofNon-Gaussianity on cosmological models in specific models for the origin of the curvature perturbation. In this case, we are interested in estimating the relative contribution of the NonGaussianity of the field perturbations arising during the inflationary epoch to the Non-Gaussianity of the primordial curvature perturbation. The second one concerns the formation of Primordial Black Holes inside the horizon at the end of inflation, and therefore explores a much smaller range of scales corresponding to horizon scales at the end of inflation.
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Bird, Christopher Shane. "Infrared regularization in relativistic chiral perturbation theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://hdl.handle.net/1828/1062.
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Chiral perturbation theory is a useful tool in the study of low energy reactions involving light particles. However the inclusion of heavy particles in chiral perturbation theory results in large contributions from loop diagrams which violate the standard power counting scheme. We review two methods, referred to as heavy baryon chiral perturbation theory and infrared regularization, which remove the high energy effects of the heavy particles and which therefore do not violate the power counting scheme. We then use these two methods to calculate the amplitude for pion photoproduction to fourth order and prove that the two amplitudes are equivalent.