Relevant bibliographies by topics / Linear perturbation theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Linear perturbation theory'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Linear perturbation theory"

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Hwang, Jai-Chan. "COSMOLOGICAL LINEAR PERTURBATION THEORY." Publications of The Korean Astronomical Society 26, no. 2 (July 6, 2011): 55–70. http://dx.doi.org/10.5303/pkas.2011.26.2.055.

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Dudkin, M. E., and O. Yu Dyuzhenkova. "Singularly perturbed rank one linear operators." Matematychni Studii 56, no. 2 (December 26, 2021): 162–75. http://dx.doi.org/10.30970/ms.56.2.162-175.

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The basic principles of the theory of singularly perturbed self-adjoint operatorsare generalized to the case of closed linear operators with non-symmetric perturbation of rank one.Namely, firstly linear closed operators are considered that coincide with each other on a dense set in a Hilbert space.The theory of singularly perturbed self-adjoint operators arose from the need to consider differential expressions in such terms as the Dirac $\delta$-function.Since it is important to consider expressions given not only by symmetric operators, the generalization (transfer) of the basic principles of the theory of singularly perturbed self-adjoint operators in the case of non-symmetric ones is important problem. The main facts of the theory include the definition of a singularly perturbed linear operator and the resolvent formula in the cases of ${\mathcal H}_{-1}$-class and ${\mathcal H}_{-2}$-class.The paper additionally describes the possibility of the appearance a point of the point spectrum and the construction of a perturbation with a predetermined point.In comparison with self-adjoint perturbations, the description of perturbations by non-symmetric terms is unexpected.Namely, in some cases, when the perturbed by a vectors from ${\mathcal H}_{-2}$ operator can be conveniently described by methods of class ${\mathcal H}_{-1}$, that is impossible in the case of symmetric perturbations of a self-adjoint operator. The perturbation of self-adjoint operators in a non-symmetric manner fully fits into the proposed studies.Such operators, for example, generalize models with nonlocal interactions, perturbations of the harmonic oscillator by the $\delta$-potentials, and can be used to study perturbations generated by a delay or an anticipation.
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NYE, V. A. "Perturbation Theory for Degenerate Linear Systems." IMA Journal of Mathematical Control and Information 2, no. 4 (1985): 261–73. http://dx.doi.org/10.1093/imamci/2.4.261.

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Renegar, James. "Some perturbation theory for linear programming." Mathematical Programming 65, no. 1-3 (February 1994): 73–91. http://dx.doi.org/10.1007/bf01581690.

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Fedorov, A. K., and A. I. Ovseevich. "Perturbation theory of observable linear systems." Mathematical Notes 98, no. 1-2 (July 2015): 216–21. http://dx.doi.org/10.1134/s0001434615070226.

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Pixius, C., S. Celik, and M. Bartelmann. "Kinetic field theory: perturbation theory beyond first order." Journal of Cosmology and Astroparticle Physics 2022, no. 12 (December 1, 2022): 030. http://dx.doi.org/10.1088/1475-7516/2022/12/030.

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Abstract We present recent improvements in the perturbative treatment of particle interactions in Kinetic Field Theory (KFT) for inertial Zel'dovich trajectories. KFT has been developed for the systematic analytical calculation of non-linear cosmic structure formation on the basis of microscopic phase-space dynamics. We improve upon the existing treatment of the interaction operator by deriving a more rigorous treatment of phase-space trajectories of particles in an expanding universe. We then show how these results can be applied to KFT perturbation theory by calculating corrections to the late-time dark matter power spectrum at second order in the interaction operator. We find that the modified treatment of interactions w.r.t. inertial Zel'dovich trajectories improves the agreement of KFT with simulation results on intermediate scales compared to earlier results. Additionally, we illustrate that including particle interactions up to second order leads to a systematic improvement of the non-linear power spectrum compared to the first-order result.
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Nájera, Antonio, and Amanda Fajardo. "Cosmological perturbation theory in f(Q,T) gravity." Journal of Cosmology and Astroparticle Physics 2022, no. 03 (March 1, 2022): 020. http://dx.doi.org/10.1088/1475-7516/2022/03/020.

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Abstract We developed the cosmological linear theory of perturbations for f(Q,T) gravity, which is an extension of symmetric teleparallel gravity, with Q the non-metricity and T the trace of the stress-energy tensor. By considering an ansatz of f(Q,T) = f 1(Q)+f 2(T), which has been broadly studied in the literature and the coincident gauge where the connection vanishes, we got equations consistent with f(Q) gravity when fT = 0. In the case of the tensor perturbations, the propagation of gravitational waves was found to be identical to f(Q), as expected. For scalar perturbations, outside the limit fT = 0, we got that the coupling between Q and T in the Lagrangian produces a coupling between the perturbation of the density and the pressure. This coupling is preserved when considering the weak coupling limit between Q and T. On the other hand, in the strong coupling limit with a generic function of the form f 2(T) = αT + β T 2, the perturbative equations are heavily driven by the f 2(T) derivatives when β ≠ 0. However, when β = 0, the perturbative equations are identical to the weak coupling limit even though this case is a non-minimally coupling one. The presence of T in the Lagrangian breaks the equation of the conservation of energy, which in turn breaks the standard ρ' + 3𝓗 (ρ+p) = 0 relation. We also derived a coupled system of differential equations between δ, the density contrast and v in the 𝓗 ≪ k limit and with negligible time derivative of the scalar perturbation potentials, which will be useful in future studies to see whether this class of theories constitute a good alternative to dark matter. These results might also enable to test f(Q,T) gravity with CMB and standard siren data that will help to determine if these models can reduce the Hubble constant tension and if they can constitute an alternative to the ΛCDM model.
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Zhang, J., L. Hui, and Z. Haiman. "A linear perturbation theory of inhomogeneous reionization." Monthly Notices of the Royal Astronomical Society 375, no. 1 (February 11, 2007): 324–36. http://dx.doi.org/10.1111/j.1365-2966.2006.11311.x.

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KOLB, EDWARD W., SABINO MATARRESE, ALESSIO NOTARI, and ANTONIO RIOTTO. "COSMOLOGICAL INFLUENCE OF SUPER-HUBBLE PERTURBATIONS." Modern Physics Letters A 20, no. 35 (November 20, 2005): 2705–10. http://dx.doi.org/10.1142/s0217732305018682.

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The existence of cosmological perturbations of wavelength larger than the Hubble radius is a generic prediction of the inflationary paradigm. We provide the derivation beyond perturbation theory of a conserved quantity which generalizes the linear comoving curvature perturbation. As a by-product, we show that super-Hubble-radius (super-Hubble) perturbations have no physical influence on local observables (e.g. the local expansion rate) if cosmological perturbations are of the adiabatic type.
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Ángyán, János G. "Rayleigh-Schrödinger perturbation theory for nonlinear Schrödinger equations with linear perturbation." International Journal of Quantum Chemistry 47, no. 6 (September 15, 1993): 469–83. http://dx.doi.org/10.1002/qua.560470606.

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Dissertations / Theses on the topic "Linear perturbation theory"

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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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Heck, Bonnie S. "On singular perturbation theory for piecewise-linear systems." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/15054.

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Hidalgo-Cuellar, Juan Carlos. "Primordial black holes in non-linear perturbation theory." Thesis, Queen Mary, University of London, 2009. http://qmro.qmul.ac.uk/xmlui/handle/123456789/495.

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The thesis begins with a study of the origin of non-linear cosmological fluctuations. In particular, a class of models of multiple field inflation are considered, with specific reference to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter fNL. Next, the effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored. For this purpose, a non-Gaussian probability distribution function (PDF) for the curvature perturbationR is required. Such a PDF is derived from first principles in the context of quantum field theory, with n-point correlation functions as the only input. Under reasonable power-spectrum conditions, an explicit expression for the PDF is presented, with corrections to the Gaussian distribution from the three-point correlation function hRRRi. The method developed for the derivation of the non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs). First, the non-Gaussian probability is used to compute corrections to the number of PBHs generated from the primordial curvature fluctuations. Particular characteristics of such corrections are explored for a variety of inflationary models. The non-Gaussian corrections explored consist exclusively of non-vanishing three-point correlation functions. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. The latter has so far been ignored in the estimation of the probability of PBH formation. We account for this by using two parameters to describe the profile: The amplitude of the inhomogeneity and its second radial derivative, both evaluated at the centre of the configuration. The method developed to derive the non-Gaussian PDF is modified to find the joint probability of these two parameters. We discuss the implications of the derived probability for the fraction of mass in the universe in the form of PBHs.
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Reid, Richard D. "Feynman-Dyson perturbation theory applied to model linear polyenes." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/76488.

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In the work described in this thesis, the Feynman-Dyson perturbation theory, developed from quantum field theory, was employed in semiempirical calculations on trans - polyacetylene. A variety of soliton-like excited states of the molecule were studied by the PPP-UHF-RPA method. The results of this study provide useful information on the nature of these states, which are thought to account for the unique electrical conduction properties of trans - polyacetylene and similar conducting polymers. Feynman-Dyson perturbation theory was also used to extend Hartree-Fock theory by the inclusion of time-independent second-order self-energy insertions. The results of calculations on polyenes show that consideration of this approach is warranted, as the contribution of the second- order terms is significant. The computer program, written during the course of the research reported here, is discussed as well.
Ph. D.
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Goldberg, Sophia Rachel. "Two-parameter perturbation theory for cosmologies with non-linear structure." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/43168.

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We propose and construct a two-parameter expansion around a Friedmann-Lemaitre- Robertson-Walker geometry which uses both large-scale and small-scale perturbations analogous to cosmological perturbation theory and post-Newtonian gravity. We justify this observationally, derive a set of field equations valid on a fraction of the horizon size and perform a detailed investigation of the associated gauge problem. We find only the Newtonian gauge, out of the standard gauges used in cosmological perturbation theory, is applicable to post-Newtonian perturbations; we can identify a consistent set of perturbed quantities in the matter and gravity sectors and construct corresponding gauge-invariant quantities. The field equations, written in terms of these quantities, takes on a simpler form, and allows the effects of small-scale structure on the large-scale properties of the Universe to be clearly identified and discussed for different physical scenarios. With a definition of statistical homogeneity, we find that the cosmological constant and the average energy density, of radiation and dust, source the Friedmann equation, whereas only the inhomogeneous part of the Newtonian energy density sources the Newton-Poisson equation { even though both originate from the same equation. There exists field equations at new orders in our formalism, such as a frame-dragging field equation a hundred times larger than expected from using cosmological perturbation theory alone. Moreover, we find non-linear gravity, mode-mixing and a mixing-of-scales at orders one would not expect from intuition based on cosmological perturbation theory. By recasting the field equations as an effective fluid we observe that these non-linearities lead to, for example, a large-scale effective pressure and anisotropic stress. We expect our formalism to be useful for accurately modelling our Universe, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.
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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 résultats
Whereas 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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Eltzner, Benjamin. "Local Thermal Equilibrium on Curved Spacetimes and Linear Cosmological Perturbation Theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-117472.

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In this work the extension of the criterion for local thermal equilibrium by Buchholz, Ojima and Roos to curved spacetime as introduced by Schlemmer is investigated. Several problems are identified and especially the instability under time evolution which was already observed by Schlemmer is inspected. An alternative approach to local thermal equilibrium in quantum field theories on curved spacetimes is presented and discussed. In the following the dynamic system of the linear field and matter perturbations in the generic model of inflation is studied in the view of ambiguity of quantisation. In the last part the compatibility of the temperature fluctuations of the cosmic microwave background radiation with local thermal equilibrium is investigated
In dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft
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Coine, Clément. "Continuous linear and bilinear Schur multipliers and applications to perturbation theory." Thesis, Bourgogne Franche-Comté, 2017. http://www.theses.fr/2017UBFCD074/document.

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Dans le premier chapitre, nous commençons par définir certains produits tensoriels et identifions leur dual. Nous donnons ensuite quelques propriétés des classes de Schatten. La fin du chapitre est dédiée à l’étude des espaces de Bochner à valeurs dans l'espace des opérateurs factorisables par un espace de Hilbert. Le deuxième chapitre est consacré aux multiplicateurs de Schur linéaires. Nous caractérisons les multiplicateurs bornés sur B(Lp, Lq) lorsque p est inférieur à q puis appliquons ce résultat pour obtenir de nouvelles relations d'inclusion entre espaces de multiplicateurs. Dans le troisième chapitre, nous caractérisons, au moyen de multiplicateurs de Schur linéaires, les multiplicateurs de Schur bilinéaires continus à valeurs dans l'espace des opérateurs à trace. Dans le quatrième chapitre, nous donnons divers résultats concernant les opérateurs intégraux multiples. En particulier, nous caractérisons les opérateurs intégraux triples à valeurs dans l'espace des opérateurs à trace puis nous donnons une condition nécessaire et suffisante pour qu'un opérateur intégral triple définisse une application complètement bornée sur le produit de Haagerup de l'espace des opérateurs compacts. Enfin, le cinquième chapitre est dédié à la résolution des problèmes de Peller. Nous commençons par étudier le lien entre opérateurs intégraux multiples et théorie de la perturbation pour le calcul fonctionnel des opérateurs autoadjoints pour finir par la construction de contre-exemples à ces problèmes
In the first chapter, we define some tensor products and we identify their dual space. Then, we give some properties of Schatten classes. The end of the chapter is dedicated to the study of Bochner spaces valued in the space of operators that can be factorized by a Hilbert space.The second chapter is dedicated to linear Schur multipliers. We characterize bounded multipliers on B(Lp, Lq) when p is less than q and then apply this result to obtain new inclusion relationships among spaces of multipliers.In the third chapter, we characterize, by means of linear Schur multipliers, continuous bilinear Schur multipliers valued in the space of trace class operators. In the fourth chapter, we give several results concerning multiple operator integrals. In particular, we characterize triple operator integrals mapping valued in trace class operators and then we give a necessary and sufficient condition for a triple operator integral to define a completely bounded map on the Haagerup tensor product of compact operators. Finally, the fifth chapter is dedicated to the resolution of Peller's problems. We first study the connection between multiple operator integrals and perturbation theory for functional calculus of selfadjoint operators and we finish with the construction of counter-examples for those problems
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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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Bandy, Rebecca Anne. "Location-Aware Adaptive Vehicle Dynamics System: Linear Chassis Predictions." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48171.

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One seminal question that faces a vehicle's driver (either human or computer) is predicting the capability of the vehicle as it encounters upcoming terrain. A Location-Aware Adaptive Vehicle Dynamics (LAAVD) System is being developed to assist the driver in maintaining vehicle handling capabilities through various driving maneuvers. In contrast to current active safety systems, this system is predictive, not reactive. The LAAVD System employs a predictor-corrector method in which the driver's input commands (throttle, brake, steering) and upcoming driving environment (terrain, traffic, weather) are predicted. An Intervention Strategy uses a novel measure of handling capability, the Performance Margin (PM), to assess the need to intervene. The driver's throttle and brake control are modulated to affect desired changes to the PM in a manner that is minimally intrusive to the driver's control authority. This system depends heavily on an understanding of the interplay between the vehicle's longitudinal, lateral, and vertical forces, as well as their resulting moments. These vehicle dynamics impact the PM metric and ultimately the point at which the Intervention Strategy will modulate the throttle and brake controls. Real-time implementation requires the development of computationally efficient predictive models of the vehicle dynamics. In this work, a method for predicting future vehicle states, based on current states and upcoming terrain, is developed using perturbation theory. An analytical relationship between the change in the spindle forces and the resulting change in the PM is derived, and the inverse relationship, between change in PM and resulting changes in longitudinal forces, is modeled. This model is implemented in the predictor-corrector algorithm of the Intervention Strategy. Corrections to the predicted states are made at each time step using a detailed, full, non-linear vehicle model. This model is run in real-time and is intended to be replaced with a drive-by-wire vehicle. Finally, the impact of this work on the automotive industry is discussed and recommendations for future work are given.
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Books on the topic "Linear perturbation theory"

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Jeribi, Aref. Perturbation Theory for Linear Operators. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-2528-2.

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Kato, Tosio. Perturbation Theory for Linear Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9.

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Katō, Tosio. Perturbation theory for linear operators. Berlin: Springer, 1995.

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

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Limaye, Balmohan Vishnu. Spectral perturbation and approximation with numerical experiments. [Canberra]: Centre for Mathematical Analysis, Australian National University, 1987.

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Craig, Ian J. D. Linear theory of fast reconnection at an X-type neutral point. Hamilton, N.Z: University of Waikato, 1992.

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Exponentially dichotomous operators and applications. Basel: Birkhäuser, 2008.

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Operator functions and localization of spectra. Berlin: Springer, 2003.

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Myo-Taeg, Lim, ed. Optimal control of singularly perturbed linear systems and applications: High-accuracy techniques. New York: Marcel Dekker, 2001.

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United States. National Aeronautics and Space Administration., ed. Comparison of dynamical approximation schemes for non-linear gravitational clustering. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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Book chapters on the topic "Linear perturbation theory"

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Gaeta, Giuseppe. "Symmetry and Perturbation Theory in Non-linear Dynamics." In Perturbation Theory, 185–209. New York, NY: Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_361.

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van Neerven, Jan. "Perturbation theory." In The Adjoint of a Semigroup of Linear Operators, 69–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0085012.

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Kato, Tosio. "Analytic perturbation theory." In Perturbation Theory for Linear Operators, 364–426. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9_7.

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Kato, Tosio. "Asymptotic perturbation theory." In Perturbation Theory for Linear Operators, 426–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9_8.

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SchlÜchtermann, G. "Perturbation of linear semigroups." In Recent Progress in Operator Theory, 263–77. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8793-9_14.

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Beilina, Larisa, Evgenii Karchevskii, and Mikhail Karchevskii. "Elements of Perturbation Theory." In Numerical Linear Algebra: Theory and Applications, 231–48. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57304-5_7.

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Kato, Tosio. "Perturbation theory for semigroups of operators." In Perturbation Theory for Linear Operators, 479–515. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9_9.

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Kato, Tosio. "Operator theory in finite-dimensional vector spaces." In Perturbation Theory for Linear Operators, 1–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9_1.

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Kato, Tosio. "Perturbation theory in a finite-dimensional space." In Perturbation Theory for Linear Operators, 62–126. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9_2.

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Kato, Tosio. "Perturbation of continuous spectra and unitary equivalence." In Perturbation Theory for Linear Operators, 516–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9_10.

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Conference papers on the topic "Linear perturbation theory"

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Alman, Gregory M., Hongen Shen, Lynne A. Molter, and Mitra B. Dutta. "Refractive index approximations from linear perturbation theory for planar MQW waveguides." In Semiconductors '92, edited by David Yevick. SPIE, 1992. http://dx.doi.org/10.1117/12.60471.

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Boyer, Mark, and Anne McCoy. "A SPARSE LINEAR ALGEBRAIC APPROACH TO ARBITRARY-ORDER VIBRATIONAL PERTURBATION THEORY." In 2021 International Symposium on Molecular Spectroscopy. Urbana, Illinois: University of Illinois at Urbana-Champaign, 2021. http://dx.doi.org/10.15278/isms.2021.wk05.

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Jiménez-Mejía, Raúl E., Rodrigo Acuna Herrera, and Pedro Torres. "Stationary Perturbation Theory applied to Linear and Non-Linear Analysis in Multi-mode Optical-Fiber." In Latin America Optics and Photonics Conference. Washington, D.C.: OSA, 2016. http://dx.doi.org/10.1364/laop.2016.lth3b.4.

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Bazzani, A., M. Giovannozzi, and G. Turchetti. "Stochastic perturbation of the linear tune and diffusion for simple lattice models." In Nonlinear dynamics in particle accelerators: Theory and experiments. AIP, 1995. http://dx.doi.org/10.1063/1.48971.

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Malomed, B. A., I. M. Uzunov, and F. Lederer. "An Improved Perturbation Theory for Optical Solitons Near the Zero-Dispersion Point." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/nlgw.1996.sad.8.

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In communication lines operated near the zero-dispersion point, the third-order dispersion (TOD) can strongly affect the pulse dynamics. Hence, it is necessary to develop proper theoretical tools for this case. Besides the numerical methods, a perturbation theory that can take into account the bandwidth-limited amplification (BLA) and nonlinear gain (NLG) or losses is required. The latter perturbations can considerably reduce soliton interactions. With regard to a combined effect of TOD and BLA, it was shown [1] that, e.g., a decay of a two-soliton bound state caused by TOD can be prevented by BLA. A new idea put forward in [2, 3] was that BLA which compensates for the linear and nonlinear losses can, simultaneously, absorb the resonance radiation emitted under the action of TOD, thus lending the soliton a much better stability. This effect has been experimentally observed in [4]. For large values of TOD, however, the soliton was obtained numerically [3] in a state with a conspicuous velocity, which differed from that predicted by the usual perturbation approach [5] by a factor of 2.
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Agarwal, Vijyant, and Harish Parthasarathy. "Optimal trajectory tracking based on perturbation theory of linear systems with feedback error." In 2015 International Conference on Computer, Communication and Control (IC4). IEEE, 2015. http://dx.doi.org/10.1109/ic4.2015.7375512.

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Zupan, Dominik. "Application of Perturbation Theory of Non-Linear Systems to an Amplifier Circuit for EMI Analysis." In 2019 12th International Workshop on the Electromagnetic Compatibility of Integrated Circuits (EMC Compo). IEEE, 2019. http://dx.doi.org/10.1109/emccompo.2019.8919872.

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Hashemi, A., K. Busch, D. N. Christodoulides, S. K. Ozdemir, and R. El-Ganainy. "Linear Response of Optical Systems With Exceptional Points." In CLEO: QELS_Fundamental Science. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.fm4b.2.

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We develop a linear theory for non-Hermitian optical systems having exceptional points. In contrast to previous studies, our analysis results in an exact expression for the resolvent operator without the need to use perturbation expansions.
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Wang, Fengxia, and Anil K. Bajaj. "On the Equivalence of Normal Form Theory and Multiple Time Scale Method." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35603.

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Multiple time scales technique has long been an important method for the analysis of weakly nonlinear systems. In this technique, a set of multiple time scales are introduced that serve as the independent variables. The evolution of state variables at slower time scales is then determined so as to make the expansions for solutions in a perturbation scheme uniform in natural and slower times. Normal form theory has also recently been used to approximate the dynamics of weakly nonlinear systems. This theory provides a way of finding a coordinate system in which the dynamical system takes the “simplest” form. This is achieved by constructing a series of near-identity nonlinear transformations that make the nonlinear systems as simple as possible. The “simplest” differential equations obtained by the normal form theory are topologically equivalent to the original systems. Both methods can be interpreted as nonlinear perturbations of linear differential equations. In this work, the equivalence of these two methods for constructing periodic solutions is proven, and it is explained why some studies have found the results obtained by the two techniques to be inconsistent.
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Chatterjee, Pranesh, and Biswajit Basu. "Non-Stationary Response of Non-Linear SDOF Systems by Perturbation of Wavelet Coefficients." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21007.

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Abstract A wavelet based random vibration theory has been developed for the non-stationary seismic response of single degree of freedom (SDOF) systems with cubic type non-linearity in the spring force. The ground motion process has been characterized by statistical functionals of wavelet coefficients. The wavelet transformed coefficient of the displacement response of the oscillator has been perturbed to obtain a series of wavelet domain algebraic equations. The stochastic response of the system has been obtained by using these sets of wavelet domain equations. The root mean square (r.m.s.) displacement response has been obtained in terms of the functionals of the input wavelet coefficients. Parametric variations are carried out to observe the effects of variation of the magnitudes of non-linear spring stiffness on the temporal variation of instantaneous r.m.s. values of oscillator displacements.
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Reports on the topic "Linear perturbation theory"

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Chandrasekaran, Shivkumar, and Ilse Ipsen. Perturbation Theory for the Solution of Systems of Linear Equations. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada254994.

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Gu, Ming F., Tomer Holczer, Ehud Behar, and Steven M. Kahn. Inner-Shell Absorption Lines of Fe 6-Fe 16: a Many-Body Perturbation Theory Approach. Office of Scientific and Technical Information (OSTI), January 2006. http://dx.doi.org/10.2172/878002.

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Taucher, Jan, and Markus Schartau. Report on parameterizing seasonal response patterns in primary- and net community production to ocean alkalinization. OceanNETs, November 2021. http://dx.doi.org/10.3289/oceannets_d5.2.

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We applied a 1-D plankton ecosystem-biogeochemical model to assess the impacts of ocean alkalinity enhancement (OAE) on seasonal changes in biogeochemistry and plankton dynamics. Depending on deployment scenarios, OAE should theoretically have variable effects on pH and seawater pCO2, which might in turn affect (a) plankton growth conditions and (b) the efficiency of carbon dioxide removal (CDR) via OAE. Thus, a major focus of our work is how different magnitudes and temporal frequencies of OAE might affect seasonal response patterns of net primary productivity (NPP), ecosystem functioning and biogeochemical cycling. With our study we aimed at identifying a parameterization of how magnitude and frequency of OAE affect net growth rates, so that these effects could be employed for Earth System Modell applications. So far we learned that a meaningful response parameterization has to resolve positive and negative anomalies that covary with temporal shifts. As to the intricacy of the response patterns, the derivation of such parameterization is work in progress. However, our study readily provides valuable insights to how OAE can alter plankton dynamics and biogeochemistry. Our modelling study first focuses at a local site where time series data are available (European Station for Time series in the Ocean Canary Islands ESTOC), including measurements of pH, concentrations of total alkalinity, dissolved inorganic carbon (DIC), chlorophyll-a and dissolved inorganic nitrogen (DIN). These observational data were made available by Andres Cianca (personal communication, PLOCAN, Spain), Melchor Gonzalez and Magdalena Santana Casiano (personal communication, Universidad de Las Palmas de Gran Canaria). The choice of this location was underpinned by the fact that the first OAE mesocosm experiment was conducted on the Canary Island Gran Canaria, which will facilitate synthesizing our modelling approach with experimental findings. For our simulations at the ESTOC site in the Subtropical North Atlantic we found distinct, non-linear responses of NPP to different temporal modes of alkalinity deployment. In particular, phytoplankton bloom patterns displayed pronounced temporal phase shifts and changes in their amplitude. Notably, our simulations suggest that OAE can have a slightly stimulating effect on NPP, which is however variable, depending on the magnitude of OAE and the temporal mode of alkalinity addition. Furthermore, we find that increasing alkalinity perturbations can lead to a shift in phytoplankton community composition (towards coccolithophores), which even persists after OAE has stopped. In terms of CDR, we found that a decrease in efficiency with increasing magnitude of alkalinity addition, as well as substantial differences related to the timing of addition. Altogether, our results suggest that annual OAE during the right season (i.e. physical and biological conditions), could be a reasonable compromise in terms of logistical feasibility, efficiency of CDR and side-effects on marine biota. With respect to transferability to global models, the complex, non-linear responses of biological processes to OAE identified in our simulations do not allow for simple parameterizations that can easily adapted. Dedicated future work is required to transfer the observed responses at small spatiotemporal scales to the coarser resolution of global models.
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Jander, Georg, Gad Galili, and Yair Shachar-Hill. Genetic, Genomic and Biochemical Analysis of Arabidopsis Threonine Aldolase and Associated Molecular and Metabolic Networks. United States Department of Agriculture, January 2010. http://dx.doi.org/10.32747/2010.7696546.bard.

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Since the amino acids threonine and isoleucine can be limiting in mammalian diet and there is interest in increasing their abundance in certain crop plants. To meet this need, a BARD proposal was written with two main research objectives: (i) investigate new avenues for manipulating threonine and isoleucine content in plants and (ii) study the role of threonine aldolase in plant metabolism. Research conducted to meet these goals included analysis of the sub-cellular localization of threonine aldolase in the plant, analysis of metabolic flux in developing embryos, over- and under-expression of Arabidopsis threonine aldolases, and transcriptional and metabolic analysis of perturbations resulting from altered threonine aldolase expression. Additionally, the broader metabolic effects of increasing lysine biosynthesis were investigated. An interesting observation that came up in the course of the project is that threonine aldolase activity affects methionine gamma-lyase in Arabidopsis. Further research showed that threonine deaminase and methionine gamma-lyase both contribute to isoleucine biosynthesis in plants. Therefore, isoleucine content can be altered by manipulating the expression of either or both of these enzymes. Additionally, both enzymes contribute to the up to 100-fold increase in isoleucine that is observed in drought-stressed Arabidopsis. Toward the end of the project it was discovered that through different projects, both groups had been able to independently up-regulate phenylalanine accumulation by different mechanisms. The Galili lab transformed Arabidopsis with a feedbackinsensitive bacterial enzyme and the Jander lab found a feedback insensitive mutation in Arabidopsis arogenate dehydratase. Exchange of the respective plant lines has allowed a comparative analysis of the different methods for increasing phenylalanine content and the creation of double mutants. The research that was conducted as part of this BARD project has led to new insights into plant amino acid metabolism. Additionally, new approaches that were found to increase the accumulation of threonine, isoleucine, and phenylalanine in plants have potential practical applications. Increased threonine and isoleucine levels can increase the nutritional value of crop plants. Elevated isoleucine accumulation may increase the osmotic stress tolerance of plants. Up-regulation of phenylalanine biosynthesis can be used to increase the production of downstream higher-value plant metabolites of biofuel feed stocks.
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