Relevant bibliographies by topics / Analytic perturbations

Academic literature on the topic 'Analytic perturbations'

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Published: 25 May 2023

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Journal articles on the topic "Analytic perturbations"

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Lewowicz, Jorge, and Eduardo Lima De Sá. "Analytic models of pseudo-Anosov maps." Ergodic Theory and Dynamical Systems 6, no. 3 (September 1986): 385–92. http://dx.doi.org/10.1017/s0143385700003564.

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AbstractWe give a new proof of the existence of analytic models of pseudo-Anosov maps. The persistence properties of Thurston's maps ensure that any Co-perturbation of them presents all their dynamical features. Using Lyapunov functions of two variables we are able to choose certain analytic perturbations which do not add any new dynamical behaviour to the original pseudo-Anosov map.
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Inomata, Keisuke. "Analytic solutions of scalar perturbations induced by scalar perturbations." Journal of Cosmology and Astroparticle Physics 2021, no. 03 (March 9, 2021): 013. http://dx.doi.org/10.1088/1475-7516/2021/03/013.

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Oharu, Shinnosuke. "Nonlinear perturbations of analytic semigroups." Semigroup Forum 42, no. 1 (December 1991): 127–46. http://dx.doi.org/10.1007/bf02573415.

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Veloz, Tomas, Pedro Maldonado, Evo Bussseniers, Alejandro Bassi, Shima Beigi, Marta Lenartowicz, and Francis Heylighen. "Towards an Analytic Framework for System Resilience Based on Reaction Networks." Complexity 2022 (January 31, 2022): 1–29. http://dx.doi.org/10.1155/2022/9944562.

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Reaction network is a promising framework for representing complex systems of diverse and even interdisciplinary types. In this approach, complex systems appear as self-maintaining structures emerging from a multitude of interactions, similar to proposed scenarios for the origin of life out of autocatalytic networks. The formalism of chemical organization theory (COT) mathematically specifies under which conditions a reaction network is stable enough to be observed as a whole complex system. Such conditions specify the notion of organization, crucial in COT. In this paper, we show that the structure and operation of organizations can be advanced towards a formal framework of resilience in complex systems. That is, we show that there exist three fundamental types of change (state, process, and structural) defined for reaction networks, and that these perturbations not only provide a general representation of perturbations in the context of resilience but also pave the ground to formalize different forms of resilient responses. In particular, we show that decomposing the network’s operational structure into dynamically decoupled modules allows to formalize what is the impact of a perturbation and to what extent any potential compensation to that perturbation will be successful. We illustrate our approach with a toy model of a farm that operates in a sustainable way producing milk, eggs, and/or grains from other resources. With the help of simulations, we analyze the different types of perturbations and responses that the farm can undergo and how that affects its sustainable operation.
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KODAMA, HIDEO, and MISAO SASAKI. "EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE." International Journal of Modern Physics A 01, no. 01 (April 1986): 265–301. http://dx.doi.org/10.1142/s0217751x86000137.

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The isocurvature perturbation in the photon-baryon universe is comprehensively studied by analytic methods in the framework of the gauge-invariant perturbation theory. In particular the evolutionary behavior of the isocurvature perturbation and its influence on the anisotropy in the cosmic microwave background are examined in detail. The results are compared with those for the adiabatic perturbation and some peculiar features of the isocurvature perturbation are pointed out and their origin is clarified. Besides these studies the ambiguities associated with the definition of non-adiabatic perturbations, especially the so-called isothermal perturbation are critically discussed and a clear definition of isocurvature perturbation is given.
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DE SIMONE, EMILIANO. "A RENORMALIZATION PROOF OF THE KAM THEOREM FOR NON-ANALYTIC PERTURBATIONS." Reviews in Mathematical Physics 19, no. 06 (July 2007): 639–75. http://dx.doi.org/10.1142/s0129055x07003085.

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We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which the perturbations are analytic approximations of the original one. We shall finally show that the sequence of the approximate solutions will converge to a differentiable solution of the original problem.
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Nusser, A. "Analytic solutions for coupled linear perturbations." Monthly Notices of the Royal Astronomical Society 317, no. 4 (October 1, 2000): 902–6. http://dx.doi.org/10.1046/j.1365-8711.2000.03708.x.

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Bonnans, Joseph Frédéric, Eduardo Casas, and Miguel Lobo. "Analytic singular perturbations of elliptic systems." Journal of Mathematical Analysis and Applications 122, no. 2 (March 1987): 422–26. http://dx.doi.org/10.1016/0022-247x(87)90271-x.

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DE COSTER, C., and K. HEYDE. "F-SPIN SYMMETRY BREAKING: APPLICATION TO THE U(5) AND SU(3) LIMIT." International Journal of Modern Physics A 04, no. 15 (September 1989): 3907–38. http://dx.doi.org/10.1142/s0217751x8900159x.

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Starting from the U(5) and SU(3) dynamic symmetries, perturbations on an F-spin scalar IBM-2 Hamiltonian are studied. The parameters describing the perturbations are chosen such as to introduce only the F-spin vector and the F-spin tensor terms of rank two. Effects on the F-spin structure of the wave functions, excitation energies and electromagnetic transition probabilities are studied for the lowest symmetric and mixed-symmetry states. If possible, numerical results are compared to analytic expressions derived via the first-order perturbation calculations.
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Park, Chan. "Observation of Gravitational Waves by Invariants for Electromagnetic Waves." Astrophysical Journal 940, no. 1 (November 1, 2022): 58. http://dx.doi.org/10.3847/1538-4357/ac9bff.

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Abstract We lay a theoretical foundation in the observation of gravitational waves (GWs) by electromagnetic waves (EMWs) performing a full electromagnetic analysis without any optical approximation. For that, the perturbation of plane EMWs is obtained by solving the perturbed Maxwell equation with GWs in the Minkowski background spacetime. In a GW detector using the EMWs, we propose to measure the electromagnetic invariants that are independent of the motion of the EMW receiver and whose perturbations are gauge-invariant. Imposing a physical boundary condition at EMW emitters, we have analytic results for the perturbations of invariants that can be measured in the EMW receiver. Finally, we show antenna patterns of the detector with monochromatic plane GWs and EMWs.
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Dissertations / Theses on the topic "Analytic perturbations"

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Coiculescu, Ion. "Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4783/.

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In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.
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Gatse, Franchel. "Spectre ordonné et branches analytiques d'une surface qui dégénère sur un graphe." Electronic Thesis or Diss., Orléans, 2020. http://www.theses.fr/2020ORLE3205.

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Dans ce travail, nous donnons un cadre général de surfaces riemanniennes qui dégénèrent sur des graphes métriques que nous appelons surfaces décomposables en cylindres et en jonctions. Les surfaces décomposables en cylindres et en jonctions dépendent d’un paramètre t qui traduit le mécanisme d’écrasement sur le graphe. Quand le paramètre t tend vers 0, les circonférences des cylindres tendent vers 0 et leurs longueurs restent fixes. On obtient ainsi les arêtes du graphe limite. Les jonctions, elles, sont écrasées dans toutes les directions et donc dégénèrent sur les sommets du graphe limite. Nous étudions alors le comportement asymptotique du spectre de ces variétés lors de cette déformation. Nous adoptons les points de vue de la convergence des valeurs propres ordonnées et de celle des branches analytiques. Ces deux approches sont fondamentalement différentes. Le cas des valeurs propres ordonnées est assez classique et nous retrouvons la convergence vers le spectre du graphe limite. L’étude des branches analytiques est plus original. Nous montrons la convergence et donnons une caractérisation des limites possibles. Ces résultats s’appliquent dans le cas des surfaces de translations qui possèdent une direction complètement périodique
In this work, we give a general framework of Riemannian surfaces that can degenerate on metric graphs and that we call surfaces made from cylinders and connecting pieces. The latter depend on a parameter t that describes the degeneration. When t goes to 0, the waists of the cylinders go to 0 but their lengths stay fixed. We thus obtain the edges of the limiting graph. The connecting pieces are squeezed in all directions and degenerate on the vertices of the limiting graph. We then study the asymptotic behaviour of the spectrum of these surfaces when t varies from two different points of view, considering the spectrum either as a sequence of ordered eigenvalues or as a collection of analytic eigenbranches. In the case of ordered eigenvalues, we recover a rather classical statement, and prove that the spectrum converges to the spectrum of the limiting object. The study of the analytic eigenbranches is more original. We prove that any such eigenbranch converges and we give a characterisation of the possible limits. These results apply to translation surfaces on which there is a completely periodic direction
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Neuner, Christoph. "On Supersingular Perturbations." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-147396.

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This thesis consists of four papers and deals with supersingular rank one perturbations of self-adjoint operators and their models in Hilbert or Pontryagin spaces. Here, the term supersingular describes perturbation elements that are outside the underlying space but still obey a certain regularity conditions. The first two papers study certain Sturm-Liouville differential expressions that can be realised as Schrödinger operators. In Paper I we show that for the potential consisting of the inverse square plus a comparatively well-behaved term we can employ an existing model due to Kurasov to describe these operators in a Hilbert space. In particular, this approach is in good agreement with ODE techniques. In Paper II we study the inverse fourth power potential.While it is known that the ODE techniques still work, we show that the above model fails and thus that there are limits to the above operator theoretic approach. In Paper III we concentrate on generalising Kurasov's model. The original formulation assumes that the self-adjoint operator is semi-bounded, whereas we drop this requirement. We give two models with a Hilbert and Pontryagin space structure, respectively, and study the connections between the resulting constructions. Finally, in Paper IV, we consider the concrete case of the operator of multiplication by the independent variable, a self-adjoint operator whose spectrum covers the real line, and study its perturbations. This illustrates some of the formalism that was developed in the previous paper, and a number of more explicit results are obtained, especially regarding the spectra of the appearing perturbed operators.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.

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Pond, Jarrad W. T. "Perturbation analysis of fluctuations in the universe on large scales, including decaying solutions and rotational velocities." Honors in the Major Thesis, University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1309.

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This item is only available in print in the UCF Libraries. If this is your Honors Thesis, you can help us make it available online for use by researchers around the world by following the instructions on the distribution consent form at http://library.ucf.edu/Systems/DigitalInitiatives/DigitalCollections/InternetDistributionConsentAgreementForm.pdf You may also contact the project coordinator, Kerri Bottorff, at kerri.bottorff@ucf.edu for more information.
Bachelors
Sciences
Physics
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Hiller, Steven Mark. "Automatic acoustic analysis of waveform perturbations." Thesis, University of Edinburgh, 1985. http://hdl.handle.net/1842/18962.

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ROCCHI, Marta. "Ecosystem response to perturbations: insight from qualitative analysis." Doctoral thesis, Università degli studi di Ferrara, 2017. http://hdl.handle.net/11392/2488077.

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Present changing environment calls for improvements of our knowledge of natural systems structure and function through a holistic view. Such a whole system perspective might help to better understand responses of ecosystems to perturbations. Models of ecological networks have proven to be very useful tools for understanding structure, and dynamics of ecosystems. I am presenting two modelling techniques to deal with the whole system approach: topological food web analysis (chapter 2) and loop analysis (chapter 3 and 4). Both these studies privilege the qualitative analysis over the quantitative one, to overcome the lack of data. In chapter 2 the topology of the food web is considered to study the functioning of the Baja California Sur ecosystem. I identified through centrality indices key node species and analyzed system resilience to the removal of the most vulnerable fish species based on a previous classification of high, medium and low risk species. Effects are evaluated by using global indices. Results highlight the structural resilience of the web to removals, but also that removals of highly vulnerable species result in significant changes in system attributes compared to random removal. In chapter 3 the evolution of the Black Sea ecosystem during the period 1960-1990 is evaluated through qualitative models (i.e. loop analysis). These models reconstruct the linkage structure of the whole community. I validated the outcomes of loop analysis with statistical investigation of biomass time series. This helped to understand how the structure of the interactions can explain variations in the biomass level of the variables and what hypotheses about drivers and mechanisms responsible for the changes could be shaped accordingly. In chapter 4 a database of real and random food webs was taken into account. I studied these food webs through loop analysis to unveil how positive input on basal and top species affects top and basal species, respectively. The aim was to identify possible differences in the propagation of indirect impacts in response to positive perturbations that occur at the extreme of the food webs (i.e. either targeting basal or top species). I compared real systems (i.e. marine, terrestrial and freshwater food webs) with random networks. I found an overrepresentation of positive predictions (i.e. the species are predicted to increase their abundance) and an underrepresentation of negative predictions for the top species when basal species are perturbed. This occurs in both real and random systems. Considering the latter the same trend (i.e. overrepresentation of positives signs and underrepresentation of negative ones) was found when predicting the responses of basal species following perturbations on top species. I showed that these findings are due to the topological structure of the food webs (e.g. number and length of trophic paths) rather than depending on the patterning of interactions strengths. Thus, the responses of top species following perturbations on basal species are predictable, while the same trend does not hold when studying the responses of basal species after perturbations targeted on top species. These results are particularly relevant and interesting considering the importance of basal and top species as target for many anthropogenic impacts. This thesis contributes to unfold a path toward: 1) the understanding of the effect of disturbance on ecological communities and ecosystems; 2) an improved comprehension of the interplay between top-down and bottom-up control; 3) the capability to deal with uncertainty in assessing the response of communities and ecosystems in the face of disturbance. I used relatively simple methodologies that focus on the qualitative arrangement of trophic interactions. This may seem a limitation. However, I show there are cases for which even the study of qualitative data can be of crucial importance in terms of management (i.e. ecosystem-based management).
I cambiamenti ambientali in atto richiedono un miglioramento delle conoscenze su struttura e funzionamento dei sistemi naturali attraverso un approccio olistico. Una visione d’insieme potrebbe aiutare a comprendere meglio la risposta degli ecosistemi alle perturbazioni. E’ stato provato che lo studio dei network ecologici è utile per comprendere la struttura e le dinamiche degli ecosistemi. In questa tesi presento due tecniche modellistiche: l’analisi topologica di food web (capitolo 2) e la loop analysis (capitolo 3 e 4). Entrambi gli studi privilegiano l’analisi qualitativa a quella quantitativa per superare la mancanza di dati. Nel capitolo 2 ho considerato alcune caratteristiche topologiche per lo studio del funzionamento dell’ecosistema di Baja California Sur. Ho identificato, attraverso gli indici di centralità, le specie chiave e analizzato la resilienza del sistema alla rimozione delle specie definite più vulnerabili (es. precedente classificazione di alto, medio e basso rischio). Gli effetti sono stati valutati attraverso indici globali. I risultati evidenziano la resilienza strutturale della food web alle rimozioni, ma anche che la rimozione delle specie più vulnerabili cambia significatamente alcuni attributi del sistema rispetto alle rimozioni random. Nel capitolo 3 ho valutato l’evoluzione dell’ecosistema del Mar Nero nel periodo 1960-1990 attraverso la loop analysis. I modelli qualitativi indagati ricostruiscono la struttura dei legami dell’intera comunità. Ho validato i risultati emersi con indagini statistiche sulle serie temporali di biomasse per capire come la struttura delle interazioni può spiegare le variazioni nei livelli di biomassa delle variabili e quali ipotesi possono essere fatte sui drivers e i meccanismi responsabili dei cambiamenti. Nel capitolo 4 ho costruito un database di food web reali e random, che ho studiato attraverso la loop analysis, per capire come un input positivo sulle specie basali e apicali si ripercuote rispettivamente sulle specie apicali e basali. Lo scopo era quello di identificare possibili differenze nella propagazione degli effetti indiretti in risposta a input positivi che si verificano agli estremi delle food web. Ho confrontato sistemi reali (marini, terrestri e di acqua dolce) con networks random. Ho trovato una sovrarappresentazione di predizioni positive (aumento dell’abbondanza delle specie) e una sottorappresentazione di predizione negative per le specie apicali a seguito di un input positivo sulle specie basali, sia nei sistemi reali che in quelli random. Considerando questi ultimi lo stesso trend (sovrarappresentazione di segni positivi e sottorappresentazione di segni negativi) è stato trovato nelle predizioni riguardanti la risposta delle specie basali a seguito di un input sulle specie apicali. Ho mostrato che questi risultati sono dovuti alla struttura topologica delle food web (es. il numero e la lunghezza dei percorsi trofici) piuttosto che alla forza delle interazioni. Sembra che le risposte delle specie apicali a seguito di perturbazioni delle specie basali siano prevedibili, al contrario delle risposte delle specie basali a seguito di un input sulle apicali. Questi risultati sono particolarmente rilevanti e interessanti considerando l’importanza delle specie basali e apicali come target degli impatti antropici. Questa tesi contribuisce allo sviluppo di un percorso verso: 1)la comprensione degli effetti di disturbo sulle comunità ecologiche e sugli ecosistemi; 2)una migliore comprensione delle interazioni di controllo top-down e bottom-up; 3)la capacità di affrontare l'incertezza per valutare la risposta delle comunità e degli ecosistemi di fronte al disturbo. Nonostante l’uso di metodologie relativamente semplici che si concentrano sulla disposizione qualitativa delle interazioni trofiche, ho dimostrato che vi sono casi in cui anche lo studio di dati qualitativi può essere di cruciale importanza in termini di gestione.
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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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Dendievel, Sarah. "Skip-free markov processes: analysis of regular perturbations." Doctoral thesis, Universite Libre de Bruxelles, 2015. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209050.

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A Markov process is defined by its transition matrix. A skip-free Markov process is a stochastic system defined by a level that can only change by one unit either upwards or downwards. A regular perturbation is defined as a modification of one or more parameters that is small enough not to change qualitatively the model.

This thesis focuses on a category of methods, called matrix analytic methods, that has gained much interest because of good computational properties for the analysis of a large family of stochastic processes. Those methods are used in this work in order i) to analyze the effect of regular perturbations of the transition matrix on the stationary distribution of skip-free Markov processes; ii) to determine transient distributions of skip-free Markov processes by performing regular perturbations.

In the class of skip-free Markov processes, we focus in particular on quasi-birth-and-death (QBD) processes and Markov modulated fluid models.

We first determine the first order derivative of the stationary distribution - a key vector in Markov models - of a QBD for which we slightly perturb the transition matrix. This leads us to the study of Poisson equations that we analyze for finite and infinite QBDs. The infinite case has to be treated with more caution therefore, we first analyze it using probabilistic arguments based on a decomposition through first passage times to lower levels. Then, we use general algebraic arguments and use the repetitive block structure of the transition matrix to obtain all the solutions of the equation. The solutions of the Poisson equation need a generalized inverse called the deviation matrix. We develop a recursive formula for the computation of this matrix for the finite case and we derive an explicit expression for the elements of this matrix for the infinite case.

Then, we analyze the first order derivative of the stationary distribution of a Markov modulated fluid model. This leads to the analysis of the matrix of first return times to the initial level, a charactersitic matrix of Markov modulated fluid models.

Finally, we study the cumulative distribution function of the level in finite time and joint distribution functions (such as the level at a given finite time and the maximum level reached over a finite time interval). We show that our technique gives good approximations and allow to compute efficiently those distribution functions.

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Un processus markovien est défini par sa matrice de transition. Un processus markovien sans sauts est un processus stochastique de Markov défini par un niveau qui ne peut changer que d'une unité à la fois, soit vers le haut, soit vers le bas. Une perturbation régulière est une modification suffisamment petite d'un ou plusieurs paramètres qui ne modifie pas qualitativement le modèle.

Dans ce travail, nous utilisons des méthodes matricielles pour i) analyser l'effet de perturbations régulières de la matrice de transition sur le processus markoviens sans sauts; ii) déterminer des lois de probabilités en temps fini de processus markoviens sans sauts en réalisant des perturbations régulières.

Dans la famille des processus markoviens sans sauts, nous nous concentrons en particulier sur les processus quasi-birth-and-death (QBD) et sur les files fluides markoviennes.

Nous nous intéressons d'abord à la dérivée de premier ordre de la distribution stationnaire – vecteur clé des modèles markoviens – d'un QBD dont on modifie légèrement la matrice de transition. Celle-ci nous amène à devoir résoudre les équations de Poisson, que nous étudions pour les processus QBD finis et infinis. Le cas infini étant plus délicat, nous l'analysons en premier lieu par des arguments probabilistes en nous basant sur une décomposition par des temps de premier passage. En second lieu, nous faisons appel à un théorème général d'algèbre linéaire et utilisons la structure répétitive de la matrice de transition pour obtenir toutes les solutions à l’équation. Les solutions de l'équation de Poisson font appel à un inverse généralisé, appelé la matrice de déviation. Nous développons ensuite une formule récursive pour le calcul de cette matrice dans le cas fini et nous dérivons une expression explicite des éléments de cette dernière dans le cas infini.

Ensuite, nous analysons la dérivée de premier ordre de la distribution stationnaire d'une file fluide markovienne perturbée. Celle-ci nous amène à développer l'analyse de la matrice des temps de premier retour au niveau initial – matrice caractéristique des files fluides markoviennes.

Enfin, dans les files fluides markoviennes, nous étudions la fonction de répartition en temps fini du niveau et des fonctions de répartitions jointes (telles que le niveau à un instant donné et le niveau maximum atteint pendant un intervalle de temps donné). Nous montrerons que cette technique permet de trouver des bonnes approximations et de calculer efficacement ces fonctions de répartitions.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Preciso, Luca. "Perturbation Analysis of the Conformal Sewing Problem and Related Problems." Doctoral thesis, Università degli studi di Padova, 1998. http://hdl.handle.net/11577/3425905.

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In this dissertation, we develop two related problems in the nonlinear functional analysis. The first is the analyticity of the Cauchy singular integral in Schauder spaces which is motivated by the second problem, namely the perturbation analysis of the conformal sewing problem in Schauder and Roumieu spaces. In Chapter II, we consider the Cauchy singular integral f (t)φ0 (t) f ◦ φ(−1) (ξ) 1 1 C[φ, f ]( · ) ≡ p. v. dt = p. v. dξ 2πi ∂D φ(t) − φ(·) 2πi φ ξ − φ(·) where the oriented simple closed curve φ and the density function f are both defined on the counterclockwise oriented boundary ∂D of the plane unit disk D. Although the linear operator C[φ, ·], for a fixed φ, and the numerical computation of C[φ, f ] have been extensively studied for the last century, in view to several applications to integral equations and boundary value problems (cf. e.g. Muskhelishvili (1953) and Gakhov (1966)), the analysis of the nonlinear functional dependence of C[φ, f ] upon both its arguments seems to be a subject analyzed only more recently (see Introduction Ch. II). This new subject of research finds application in the nonlinear problems of perturbation nature which involve the Cauchy singular integral. In Chapter II we extend the analyticity result for the operator C[·, ·] of Coifman & Meyer (1983b) to a Schauder spaces setting. We assume that both φ and f belong to a Schauder space, say C∗m,α (∂D, C), of complex-valued function of class C m,α on ∂D, with m a positive natural number and α ∈ ]0, 1[. As it is well-known, under such conditions on φ and f , the function C[φ, f ](·) is also of class C m,α . By proving the unique solvability of a boundary value problem of elliptic nature in D and by applying Implicit Function Theorem to a suitable functional equation, we show the real analyticity of C[·, ·]. Then we show the complex analyticity of C[·, ·] and we compute all its differentials. This result of Lanza & Preciso (1998) will be applied in the second part of this dissertation and in another perturbation problem associated to a nonlinear integral equation (cf. Lanza & Rogosin (1997)). In Chapter III, we introduce the conformal sewing problem associated to a shift φ of ∂D, i.e. a homeomorphism of ∂D to itself. It consists in finding a pair of conformal functions (F, G) defined in D and C \ cl D, respectively, such that their continuous extensions to cl D e C \ D, Fe and G e respectively, satisfy Fe(φ(t)) = G(t) for all t ∈ ∂D. A simple normalization condition and well-known results ensure that the sewing problem associated to φ has a unique solution (F, G) and we denote by (F [·], G[·]) the pair of operators which maps φ to the trace on ∂D of such solution. The regularity properties of the operators F [φ] and G[φ] in spaces of regular functions can be used in the study of Teichmüller spaces, which constitute an important subject in geometric function theory (see Nag (1996)). Our aim is to find natural Banach spaces of regular functions where to obtain the analyticity of F [·] and G[·]. First we study the regularity of such operators in Schauder spaces C∗m,α (∂D, C), with m ≥ 1, α ∈ ]0, 1[. By using the classical integral equation approach to the sewing problem, we show that G[φ] and F [φ] = G[φ] ◦ φ(−1) belong to C∗m,α (∂D, C) when φ belongs to C∗m,α (∂D, C). In this setting, by using the analyticity of the Cauchy singular integral (cf. Ch. II) and by applying Implicit Function Theorem to a suitable integral equation, we show that G[·] extends to a complex analytic operator. Then we prove that this Schauder spaces setting is not sufficient in order to obtain an analytic extension of the operator F [·]. Indeed a natural assumption in order to have F [·] analytic, is that φ belongs to a space of real analytic functions of ∂D to C. In Chapter IV we introduce Banach spaces of real analytic functions, namely the Roumieu spaces associated to the differentiation operator. In this setting we show that G[·] and F [·] can be extended to complex analytic operators by employing the regularity results on the composition and on the inversion operator of Lanza (1994 and 1996b).
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Onen, Onursal. "Analytical Modeling, Perturbation Analysis and Experimental Characterization of Guided Surface Acoustic Wave Sensors." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4555.

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In this dissertation, guided surface acoustic wave sensors were investigated theoretically and experimentally in detail for immunosensing applications. Shear horizontal polarized guided surface acoustic wave propagation for mass loading sensing applications was modeled using analytical modeling and characterized by perturbation analysis. The model verification was performed experimentally and a surface acoustic wave immunosensor case study was presented. The results of the immunosensing were also investigated using the perturbation analysis. Guided surface acoustic wave propagation problem was investigated in detail for gravimetric (or mass loading) guided wave sensors, more specifically for immunosensors. The analytical model was developed for multilayer systems taking viscoelasticity into account. The closed form algebraic solutions were obtained by applying appropriate boundary conditions. A numerical approach was used to solve dispersion equation. Detailed parametric investigation of dispersion curves was conducted using typical substrate materials and guiding layers. Substrate types of ST-cut quartz, 41° YX lithium Niobate and 36° YX lithium tantalate with guiding layers of silicon dioxide, metals (chromium and gold), and polymers (Parylene-C and SU-8) were investigated. The effects of frequency and degree of viscoelasticity were also studied. The results showed that frequency only has effect on thickness with same shaped dispersion curves. Dispersion curves were found to be unaffected by the degree of viscoelasticity. It was also observed that when there was a large shear velocity difference between substrate and guiding layer, a transition region with a gradual decrease in phase velocity was obtained. However, when shear velocities were close, a smooth transition was observed. Furthermore, it was observed that, large density differences between substrate and guiding layer resulted in sharp and with nearly constant slope transition. Smooth transition was observed for the cases of minimal density differences. Experimental verification of the model was done using multi-layer photoresists. It was shown that with modifications, the model was able to represent the cases studied. Perturbation equations were developed with first order approximations by relating the slope of the dispersion curves with sensitivity. The equations were used to investigate the sensitivity for material selection (substrate, guiding layer, and mass perturbing layer) and degree of viscoelasticity. The investigations showed that the sensitivity was increased by using guiding layers with lower shear velocities and densities. Among the guiding layers investigated, Parylene C showed the highest sensitivity followed by gold and chrome. The perturbation investigations were also extended to viscoelasticity and to protein layers for immunosensing applications. It was observed that, viscous behavior resulted in slightly higher sensitivity; and sensitivity to protein layers was very close to sensitivity for polymers. The optimum case is found to be ST-cut quartz with Parylene-C guiding layer for protein layer sensing. Finally, an immunosensing case study was presented for selective capture of protein B-cell lymphoma 2 (Bcl-2), which is elevated in many cancer types including ovarian cancer. The immunosensor was designed, fabricated, and experimentally characterized. An application-specific surface functionalization scheme with monoclonal antibodies, ODMS, Protein A/G and Pluronic F127 was developed and applied. Characterization was done using the oscillation frequency shift of with sensor used as the feedback element of an oscillator circuit. Detection of Bcl-2 with target sensitivity of 0.5 ng/ml from buffer solutions was presented. A linear relation between frequency shift and Bcl-2 concentration was observed. The selectivity was shown with experiments by introducing another protein, in addition to Bcl-2, to the buffer. It was seen that similar detection performance of Bcl-2 was obtained even with presence of control protein in very high concentrations. The results were also analyzed with perturbation equations.
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Books on the topic "Analytic perturbations"

1

H, Miller John J., ed. Singular perturbation problems in chemical physics: Analytic and computational methods. New York: J. Wiley, 1997.

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Singular perturbations I. Spaces and singular perturbations on manifolds without boundary. Amsterdam: North-Holland, 1990.

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Bonnans, J. Frédéric, and Alexander Shapiro. Perturbation Analysis of Optimization Problems. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1394-9.

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Glasserman, Paul. Gradient estimation via perturbation analysis. Boston: Kluwer Academic, 1991.

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Gradient estimation via perturbation analysis. Boston: Kluwer Academic Publishers, 1991.

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Algebraic analysis of singular perturbation. Providence, R.I: American Mathematical Society, 2005.

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Analytic perturbation theory for matrices and operators. Basel: Birkhäuser Verlag, 1985.

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Holmes, Mark H. Introduction to Perturbation Methods. 2nd ed. New York, NY: Springer New York, 2013.

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Saint-Yves, Aurèle. Perturbations familiales et analyse transactionnelle thérapeutique. Saint-Foy, Québec: Presses de l'Université du Québec, 1992.

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I, Minchenko L., and Satsura Tatyana, eds. Multivalued analysis and nonlinear programming problems with perturbations. Dordrecht: Kluwer Academic Publishers, 2003.

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Book chapters on the topic "Analytic perturbations"

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Devaney, Robert L. "Singular Perturbations of Complex Analytic Dynamical Systems." In Understanding Complex Systems, 13–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04629-2_2.

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Martin, Robert H., Toshitaka Matsumoto, Shinnosuke Oharu, and Naoki Tanaka. "Time-dependent Nonlinear Perturbations of Analytic Semigroups." In Functional Analysis and Evolution Equations, 457–502. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7794-6_29.

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Martinez, André, Shu Nakamura, and Vania Sordoni. "Propagation of Analytic Singularities for Short and Long Range Perturbations of the Free Schrödinger Equation." In Algebraic and Analytic Microlocal Analysis, 575–87. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01588-6_12.

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Da Prato, Giuseppe. "Perturbations of Ornstein—Uhlenbeck Operators: an Analytic Approach." In Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics, 127–39. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8085-5_9.

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Kachalov, Vasiliy I. "Analytic Theory of Singular Perturbations and Lomov’s Regularization Method." In Finite Difference Methods. Theory and Applications, 305–12. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_34.

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Filar, Jerzy A., Irene Hudson, Thomas Mathew, and Bimal Sinha. "Analytic perturbations and systematic bias in statistical modeling and inference." In Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 17–34. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008. http://dx.doi.org/10.1214/193940307000000022.

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Peng, J. H., and J. S. Tang. "An Analytic Proof for the Sensitivity of Chaos to Initial Condition and Perturbations." In Dynamical Systems, 13–21. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-5754-2_2.

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Spallicci, A. D. A. M. "Analytic Solution of Regge-Wheeler Differential Equation for Black Hole Perturbations in Radial Coordinate and Time Domains." In Recent Developments in General Relativity, 373–78. Milano: Springer Milan, 2000. http://dx.doi.org/10.1007/978-88-470-2113-6_29.

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Verhulst, Ferdinand. "Perturbation Analysis of Parametric Resonance." In Perturbation Theory, 167–83. New York, NY: Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_393.

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Lurie, A. I. "Perturbation theory." In Analytical Mechanics, 585–668. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-45677-3_11.

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Conference papers on the topic "Analytic perturbations"

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Peng, Jie-Hua, and Jia-Shi Tang. "An Analytic Study on Controlling Duffing Chaos in Amplitude Domain and in Frequency Domain." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84970.

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An analytical study on the chaos control of Duffing oscillator both in amplitude domain and in frequency domain is made in this paper. By means of the combined action of harmonically parametrical perturbation and forcing perturbation and suitably adjusting the parameters of perturbations, the chaotic motion of Duffing oscillator can be effectively controlled in a small region in the parametric space. We find that, in the amplitude domain, the chaotic motion exists only in the region where the ratio of the amplitudes of the perturbations is large than critical ratio, and, in the frequency domain, the chaotic motion exists only in a limited region where the frequency of perturbation is lower than superior frequency limit and larger than inferior frequency limit. The inferior frequency limit and superior frequency limit of chaotic region are discovered and determined firstly. An analytical expression of the critical ration of the amplitudes of forcing and parametrical perturbations is established.
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"On analytic perturbations of non-self-adjoint anharmonic oscillator." In Уфимская осенняя математическая школа - 2022. Т.1. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh1t-2022-09-28.13.

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DUFFY, E. M., and B. C. NOLAN. "ANALYTIC STUDY OF ODD PARITY PERTURBATIONS OF THE SELF-SIMILAR LTB SPACETIME." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0327.

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RIVA, M. DALLA. "THE LAYER POTENTIALS OF SOME PARTIAL DIFFERENTIAL OPERATORS: REAL ANALYTIC DEPENDENCE UPON PERTURBATIONS." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_0014.

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Kim, Kyu Tae, Hyung Ju Lee, Jong Guen Lee, Bryan D. Quay, and Domenic Santavicca. "Flame Transfer Function Measurement and Instability Frequency Prediction Using a Thermoacoustic Model." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-60026.

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The dynamic response of a turbulent premixed flame to an acoustic velocity perturbation was experimentally determined in a lean-premixed, swirl-stabilized, lab-scale gas turbine combustor. Fuel was injected far upstream of a choked inlet to eliminate equivalence ratio oscillations. A siren-type modulation device was used to provide acoustic perturbations at the forcing frequency of 100 ∼ 400 Hz. To measure global heat release rate, OH*, CH*, and CO2* chemiluminescence emissions were used. The two-microphone method was utilized to estimate inlet velocity fluctuations, and it was calibrated by direct measurements using a hot wire anemometer under cold-flow conditions. Gain of the flame transfer function (FTF) shows a low pass filter behavior, and it is well-fitted by a second-order model. Phase difference increases quasi-linearly with the forcing frequency. Using the n-τ formulation, gain and phase of FTF were incorporated into an analytic thermoacoustic model in order to predict instability frequencies and corresponding modal structures. Self-excited flame response measurements were also performed to verify eigenfrequencies predicted by the thermoacoustic model. Instability frequency predicted by the thermoacoustic model is supported by experimental results. Two instability frequency bands were measured in the investigated gas turbine combustor at all operating conditions: f ∼ 220 Hz and f ∼ 350 Hz. Results show that the self-excited instability frequency of f ∼ 220 Hz results from the fact that the flames amplify flow perturbations with f = 150 ∼ 250 Hz. This frequency range was observed in the flame transfer function measurements. The other instability frequency of f ∼ 350 Hz occurs because the whole combustion system has an eigenfrequency corresponding to the 1/4-wave eigenmode of the mixing section. This was analytically and experimentally demonstrated. Results also show that the flame length, LCH*max, plays a critical role in determining self-induced instability frequency.
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Kaiser, Thomas Ludwig, and Kilian Oberleithner. "Modeling the Transport of Fuel Mixture Perturbations and Entropy Waves in the Linearized Framework." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14715.

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Abstract In this paper a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier-Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields, which serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These in this study are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then the method is applied to predict the convection, mean flow dispersion and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with Direct Numerical Simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs, when the DNS mean flow and Reynolds stresses are provided. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.
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Porfyri, K. N., I. K. Nikolos, A. I. Delis, and M. Papageorgiou. "Stability Analysis of a Macroscopic Traffic Flow Model for Adaptive Cruise Control Systems." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50977.

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Since the early days of traffic engineering, traffic flow stability has attracted a lot of attention, as the frequent occurrence of traffic jams, caused by small perturbations in traffic flow such as a sudden deceleration of a vehicle, deteriorate the performance of traffic flow and the utilization of the available infrastructure. Such traffic jams are usually related to instabilities in traffic flow, resulting in the formation of stop-and-go waves, propagating upstream the traffic flow. Emerging technologies in the field of Vehicle Automation and Communication Systems (VACS), such as Adaptive Cruise Control (ACC) systems, appear to be a remedy to reduce the amplitude or to eliminate the formation of such traffic instabilities. To this end, this work aims to derive a stability threshold of a novel macroscopic model, developed to simulate the flow of ACC-equipped vehicles, and study the impact of such vehicles on the stabilization of the traffic flow, with respect to small perturbations. The adopted macroscopic approach reflecting ACC traffic dynamics is based on the gas-kinetic (GKT) traffic flow model. The analytic results show that ACC vehicles enhance the stabilization of the traffic flow; the instability region is very narrow and by reducing the ACC time-gap setting it moves to higher values of density.
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Renshaw, Anthony A. "Solution of the One Dimensional Foil Bearing Problem Using Matched Asymptotic Expansions." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0206.

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Abstract The foil bearing problem describes a longitudinally translating, flexible, tensioned, magnetic tape that rides on a thin film of air as it partially wraps around a stationary recording head. Equilibrium and linear, harmonic vibration analyses of the one dimensional formulation of this problem are performed using matched asymptotic expansions including the effects of tape bending stiffness, compressibility, and molecular slip as regular perturbations. Simple analytic expressions are derived for the nominal film thickness and the vibration frequencies of the free spans. These expressions give designers sharper insight into the usefulness of potential design changes that normally would be evaluated using extensive numerical computations.
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Thode. "A normal-mode expression for the sensitivity of acoustic fields to three-dimensional refractive index perturbations in a constant-depth waveguide, using an analytic adjoint approach." In Oceans 2003. Celebrating the Past ... Teaming Toward the Future. IEEE, 2003. http://dx.doi.org/10.1109/oceans.2003.178565.

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Parker, R. G., and C. D. Mote. "Exact Perturbation for the Vibration of Almost Annular or Circular Plates." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0647.

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Abstract Using perturbation analysis, the eigensolutions for plate vibration problems on nearly annular or circular domains are determined. The irregular domain eigensolutions are calculated as perturbations of the corresponding annular or circular domain eigensolutions. These perturbations are determined exactly. The simplicity of these exact solutions allows the perturbation to be carried through third order for distinct unperturbed eigenvalues and through second order for degenerate unperturbed eigenvalues. Furthermore, this simplicity allows the resulting orthonormalized eigenfunctions to be readily incorporated into response, system identification, and control analyses. The clamped, nearly circular plate is studied in detail, and the exact eigensolution perturbations are derived for an arbitrary boundary shape deviation. Rules governing the splitting of degenerate unperturbed eigenvalues at both first and second orders of perturbation are presented. These rules, which apply for arbitrary shape deviation, generalize those obtained in previous works where specific, discrete asymmetries and first order splitting are examined. The eigensolution perturbations and splitting rules reduce to simple, algebraic formulae in the Fourier coefficients of the boundary shape asymmetry. Elliptical plate eigensolutions are calculated and compared to finite element analysis and, for the fundamental eigenvalue, to the exact solution given by Shibaoka (1956).
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Reports on the topic "Analytic perturbations"

1

Tang, Ping Tak Peter. Strong uniqueness of best complex Chebyshev approximation to analytic perturbations of analytic function. Office of Scientific and Technical Information (OSTI), March 1988. http://dx.doi.org/10.2172/6357493.

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Lane, M. T. On Analytic Modeling of Lunar Perturbations of Artificial Satellites of the Earth. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada210440.

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Liu, Zhenyue, and Norman Bleistein. Velocity Analysis by Perturbation. Fort Belvoir, VA: Defense Technical Information Center, May 1993. http://dx.doi.org/10.21236/ada272537.

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Stepin, Stanislav A. Fredholm Analytic Operator Families and Perturbation of Resonances. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-6-2006-109-117.

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Adams, C., and Micheal A. Smith. VARI3D & PERSENT: Perturbation and Sensitivity Analysis. Office of Scientific and Technical Information (OSTI), August 2018. http://dx.doi.org/10.2172/1480522.

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Smith, M. A., C. Adams, W. S. Yang, and E. E. Lewis. VARI3D & PERSENT: Perturbation and Sensitivity Analysis. Office of Scientific and Technical Information (OSTI), August 2013. http://dx.doi.org/10.2172/1091498.

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Petkov, Petko, and Mihail Konstantinov. Perturbation Analysis of the Feedback Control Problem. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2018. http://dx.doi.org/10.7546/crabs.2018.02.12.

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Petkov, Petko. Perturbation Analysis of the Feedback Control Problem. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2018. http://dx.doi.org/10.7546/grabs2018.2.12.

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van Raalte, Alyson A., and Hal Caswell. Perturbation analysis of indices of lifespan variability. Rostock: Max Planck Institute for Demographic Research, January 2012. http://dx.doi.org/10.4054/mpidr-wp-2012-004.

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Smith, M., C. Adams, W. Yang, and E. Lewis. VARI3D & PERSENT: Perturbation and Sensitivity Analysis. Office of Scientific and Technical Information (OSTI), April 2020. http://dx.doi.org/10.2172/1869777.

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