Relevant bibliographies by topics / Perturbative computations

Academic literature on the topic 'Perturbative computations'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Perturbative computations"

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Shindler, Andrea. "Gradient Flow: Perturbative and Non-Perturbative Renormalization." EPJ Web of Conferences 274 (2022): 01005. http://dx.doi.org/10.1051/epjconf/202227401005.

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We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of renormalization with the gradient flow.
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Debbio, Luigi Del, Francesco Di Renzo, and Gianluca Filaci. "High-order perturbative expansions in massless gauge theories with NSPT." EPJ Web of Conferences 175 (2018): 11023. http://dx.doi.org/10.1051/epjconf/201817511023.

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We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently in finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.
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Lüscher, M., and P. Weisz. "Efficient numerical techniques for perturbative lattice gauge theory computations." Nuclear Physics B 266, no. 2 (March 1986): 309–56. http://dx.doi.org/10.1016/0550-3213(86)90094-5.

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Bern, Z. "Perturbative gravity from gauge theory." Modern Physics Letters A 29, no. 32 (October 20, 2014): 1430036. http://dx.doi.org/10.1142/s0217732314300365.

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Here, we describe a recently conjectured duality between color and kinematics for gauge-theory amplitudes. Whenever this duality is manifest, the integrands of loop-level gravity scattering amplitudes can be obtained from corresponding gauge-theory amplitudes via a double-copy relation. This duality has been used to enormously simplify a number of explicit multiloop supergravity calculations. The results of these computations is that supergravity theories have a surprisingly tame ultraviolet behavior, and in some cases may even be finite. As an example, we summarize a recent calculation showing that half-maximal [Formula: see text] supergravity in four spacetime dimensions is ultraviolet finite at three loops, contrary to previous expectations.
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DEMETERFI, KRESIMIR, ANTAL JEVICKI, and JOĀO P. RODRIGUES. "PERTURBATIVE RESULTS OF COLLECTIVE STRING FIELD THEORY." Modern Physics Letters A 06, no. 35 (November 20, 1991): 3199–212. http://dx.doi.org/10.1142/s0217732391003699.

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We present a summary of perturbative results obtained in the framework of collective string field theory. We discuss computations of tree-level scattering amplitudes, loop corrections to tachyon self-energy, ground state energy and finite temperature free energy. A comparison with results obtained in different approaches is given. We also discuss the physical implications of our results.
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Reyes, Edilson, and Raffaele Fazio. "High-Precision Calculations of the Higgs Boson Mass." Particles 5, no. 1 (February 17, 2022): 53–73. http://dx.doi.org/10.3390/particles5010006.

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In this paper, we review the status of the computations of the perturbative quantum corrections to the Higgs boson mass in the Standard Model and in its supersymmetric extensions. In particular, supersymmetric theories require a very accurate computation of the Higgs boson mass, which includes corrections even up to the three-loop level, since their predictions are limited by theoretical uncertainties. A discussion about these uncertainties in the context of the Minimal and Next To Minimal Supersymmetric Standard Model is included.
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MANIN, YURI I. "Renormalisation and computation II: time cut-off and the Halting Problem." Mathematical Structures in Computer Science 22, no. 5 (September 6, 2012): 729–51. http://dx.doi.org/10.1017/s0960129511000508.

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This is the second instalment in the project initiated in Manin (2012). In the first Part, we argued that both the philosophy and technique of perturbative renormalisation in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view.In this second part, we address some of the issues raised in Manin (2012) and develop them further in three contexts: a categorification of the algorithmic computations; time cut-off and anytime algorithms; and, finally, a Hopf algebra renormalisation of the Halting Problem.
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SURGULADZE, LEVAN R. "COMPUTER PROGRAMS FOR ANALYTICAL PERTURBATIVE CALCULATIONS IN HIGH ENERGY PHYSICS." International Journal of Modern Physics C 05, no. 06 (December 1994): 1089–101. http://dx.doi.org/10.1142/s0129183194001161.

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A short review of the present status of computer packages for the high order analytical perturbative calculations is presented. The mathematical algorithm and the quantum field theory methods used are briefly discussed. The most recent computer package HEPLoops for analytical computations in high energy physics up to four-loops is also discussed.
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Karanikas, A. I., and C. N. Ktorides. "Polyakov's spin factor and new algorithms for efficient perturbative computations in QCD." Physics Letters B 500, no. 1-2 (February 2001): 75–86. http://dx.doi.org/10.1016/s0370-2693(01)00062-4.

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Creedon, Ryan, Bernard Deconinck, and Olga Trichtchenko. "High-Frequency Instabilities of a Boussinesq–Whitham System: A Perturbative Approach." Fluids 6, no. 4 (April 1, 2021): 136. http://dx.doi.org/10.3390/fluids6040136.

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We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estimate the asymptotic behavior of these instabilities in the small-amplitude regime. We compare these asymptotic results with direct numerical computations.
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Dissertations / Theses on the topic "Perturbative computations"

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Heymes, David Verfasser], Michal [Akademischer Betreuer] [Czakon, and Werner [Akademischer Betreuer] Bernreuther. "A general subtraction scheme for next to next to leading order computations in perturbative quantum chromodynamics / David Heymes ; Michal Czakon, Werner Bernreuther." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/1128157233/34.

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Heymes, David [Verfasser], Michal [Akademischer Betreuer] Czakon, and Werner [Akademischer Betreuer] Bernreuther. "A general subtraction scheme for next to next to leading order computations in perturbative quantum chromodynamics / David Heymes ; Michal Czakon, Werner Bernreuther." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/1128157233/34.

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RATTI, CARLOALBERTO. "Topics in sym theories: * Ads/CFT & Mesonic Spectra ** Superspace & Scattering Amplitudes." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/11607.

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In this thesis two different topics in SYM theories are investigated. In the first part we use the AdS/CFT correspondence to study the problem of flavor symmetry for theories that are marginal deformations of the maximal SYM theory. In particular, we compute exactly the masses of the mesons of these theories. The results show that the mass spectrum is discrete, with a mass gap and a Zeeman-like splitting of the mass levels occurs. In the second part of the thesis, we develop a direct computational technique for scattering amplitudes in SYM theories. A combined use of background field method, superspace technologies and new pc programs makes a Feynman diagrammatic approach available. We apply this technique to compute the full two-loop MHV effective action of the maximal SYM theory. From there we move towards the extraction of the four point MHV scattering amplitude.
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Elago, David. "Robust computational methods for two-parameter singular perturbation problems." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1693_1308039217.

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This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.

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Ettenhuber, Christian. "Computational approaches for metabolic flux analysis in 13C perturbation experiments." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=974209961.

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Lindquist, Dana Rae. "Computation of unsteady transonic flowfields using shock capturing and the linear perturbation Euler equations." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/13090.

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Gilbert, Michael Stephen. "A Small-Perturbation Automatic-Differentiation (SPAD) Method for Evaluating Uncertainty in Computational Electromagnetics." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354742230.

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Higgins, Erik Tracy. "Multi-Scale Localized Perturbation Method for Geophysical Fluid Flows." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/99889.

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An alternative formulation of the governing equations of a dynamical system, called the multi-scale localized perturbation method, is introduced and derived for the purpose of solving complex geophysical flow problems. Simulation variables are decomposed into background and perturbation components, then assumptions are made about the evolution of these components within the context of an environmental flow in order to close the system. Once closed, the original governing equations become a set of one-way coupled governing equations called the "delta form" of the governing equations for short, with one equation describing the evolution of the background component and the other describing the evolution of the perturbation component. One-way interaction which arises due to non-linearity in the original differential equations appears in this second equation, allowing the background fields to influence the evolution of a perturbation. Several solution methods for this system of equations are then proposed. Advantages of the delta form include the ability to specify a complex, temporally- and spatially-varying background field separate from a perturbation introduced into the system, including those created by natural or man-made sources, which enhances visualization of the perturbation as it evolves in time and space. The delta form is also shown to be a tool which can be used to simplify simulation setup. Implementation of the delta form of the incompressible URANS equations with turbulence model and scalar transport within OpenFOAM is then documented, followed by verification cases. A stratified wake collapse case in a domain containing a background shear layer is then presented, showing how complex internal gravity wave-shear layer interactions are retained and easily observed in spite of the variable decomposition. The multi-scale localized perturbation method shows promise for geophysical flow problems, particularly multi-scale simulation involving the interaction of large-scale natural flows with small-scale flows generated by man-made structures.
Master of Science
Natural flows, such as those in our oceans and atmosphere, are seen everywhere and affect human life and structures to an amazing degree. Study of these complex flows requires special care be taken to ensure that mathematical equations correctly approximate them and that computers are programmed to correctly solve these equations. This is no different for researchers and engineers interested in studying how man-made flows, such as one generated by the wake of a plane, wind turbine, cruise ship, or sewage outflow pipe, interact with natural flows found around the world. These interactions may yield complex phenomena that may not otherwise be observed in the natural flows alone. The natural and artificial flows may also mix together, rendering it difficult to study just one of them. The multi-scale localized perturbation method is devised to aid in the simulation and study of the interactions between these natural and man-made flows. Well-known equations of fluid dynamics are modified so that the natural and man-made flows are separated and tracked independently, which gives researchers a clear view of the current state of a region of air or water all while retaining most, if not all, of the complex physics which may be of interest. Once the multi-scale localized perturbation method is derived, its mathematical equations are then translated into code for OpenFOAM, an open-source software toolkit designed to simulate fluid flows. This code is then tested by running simulations to provide a sanity check and verify that the new form of the equations of fluid dynamics have been programmed correctly, then another, more complicated simulation is run to showcase the benefits of the multi-scale localized perturbation method. This simulation shows some of the complex fluid phenomena that may be seen in nature, yet through the multi-scale localized perturbation method, it is easy to view where the man-made flows end and where the natural flows begin. The complex interactions between the natural flow and the artificial flow are retained in spite of separating the flow into two parts, and setting up the simulation is simplified by this separation. Potential uses of the multi-scale localized perturbation method include multi-scale simulations, where researchers simulate natural flow over a large area of land or ocean, then use this simulation data for a second, small-scale simulation which covers an area within the large-scale simulation. An example of this would be simulating wind currents across a continent to find a potential location for a wind turbine farm, then zooming in on that location and finding the optimal spacing for wind turbines at this location while using the large-scale simulation data to provide realistic wind conditions at many different heights above the ground. Overall, the multi-scale localized perturbation method has the potential to be a powerful tool for researchers whose interest is flows in the ocean and atmosphere, and how these natural flows interact with flows created by artificial means.
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Khabir, Mohmed Hassan Mohmed. "Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_7416_1320395978.

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Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.
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PASTORE, Mariachiara. "Multireference Perturbation Theories for the accurate calculation of energy and molecular properties." Doctoral thesis, Università degli studi di Ferrara, 2009. http://hdl.handle.net/11392/2388724.

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This Ph.D. thesis deals with the development and the applications of N-Electron Valence State Perturbation Theory (NEVPT), a novel form of Multireference Perturbation Theory (MRPT) put forward in collaboration between the theoretical chemistry groups of the uni- versities of Ferrara and Toulouse. A review of the NEVPT approach is presented, starting from the original second order state–specific formulation, going through the quasidegenerate multi–state extension and arriving at the implementations of the third order in the energy and of the internally contracted configuration interaction, accomplished during the Ph.D. The chief properties of NEVPT are analyzed and the test case of the C2 molecule is discussed. An important field of applications of MRPTs is the calculation of the electronically excited states of molecules, where the strong differential correlation effects and the possible multiref- erence nature of the wavefunctions can be, in principle, successfully handled by a “variational plus perturbation” scheme. Concerning the applications, the thesis is divided in two parts. Part I concerns the calculation of electronically excited states. Different issues are addressed: on the one hand the treatment of small aromatic molecules, Pyrrole, Furan and Thiophene, whose description is complicated by the possible interaction with low-lying Rydberg states and by the ionic nature of some valence states, extremely sensitive to the so-called dynamical − polarization; on the other hand the case of a large-sized aromatic molecule, Free-Base Por- phin, for which the crucial problem is the choice of a balanced variational space to accurately describe the wavefunctions of the ground and of the excited states. The second part is devoted to the description, by means of MRPT, of the Electron Transfer (ET) process in Mixed-Valence systems. The investigation is carried out on a model spiro − − compound, for which the ET reaction is simulated using a simplified one-mode two-state model. The inadequacy of a standard second order MRPT approach is shown and the application of an alternative and effective computational strategy is discussed.
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Books on the topic "Perturbative computations"

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Kamiński, Marcin. The Stochastic Perturbation Method for Computational Mechanics. Chichester, UK: John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781118481844.

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

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Freidman, M. J. Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1993.

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Friedman, M. J. Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems. Huntsvilla, Ala: George C. Marshall Space Flight Center, 1993.

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Celestial mechanics: A computational guide for the practitioner. New York: Wiley, 1985.

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Lindquist, Dana R. Computation of unsteady transonic flowfields using shock capturing and the linear perturbation Euler equations. Cambridge, Mass: Gas Turbine Laboratory, Massachusetts Institute of Technology, 1991.

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C, Monteiro A., and United States. National Aeronautics and Space Administration., eds. Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems: Preliminary technical report for the period February 22, 1990, through October 21, 1992. [Huntsville, Ala.]: Research Institute, University of Alabama in Huntsville, 1992.

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Stanley, Turner Michael, Fermi National Accelerator Laboratory, and United States. National Aeronautics and Space Administration., eds. Second-order reconstruction of the inflationary potential. Batavia, IL: Fermi National Accelerator Laboratory, 1994.

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Stanley, Turner Michael, Fermi National Accelerator Laboratory, and United States. National Aeronautics and Space Administration., eds. Second-order reconstruction of the inflationary potential. Batavia, IL: Fermi National Accelerator Laboratory, 1994.

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Stanley, Turner Michael, Fermi National Accelerator Laboratory, and United States. National Aeronautics and Space Administration., eds. Second-order reconstruction of the inflationary potential. Batavia, IL: Fermi National Accelerator Laboratory, 1994.

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Book chapters on the topic "Perturbative computations"

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Jorba, Àngel. "Computational Methods in Perturbation Theory." In Perturbation Theory, 153–65. New York, NY: Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-2621-4_758.

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Kvale, Mark, and Christoph E. Schreiner. "Perturbative M-Sequences for Auditory Systems Identification." In Computational Neuroscience, 615–17. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-4831-7_102.

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Jorba, Àngel. "Computational Methods in Perturbation Theory." In Encyclopedia of Complexity and Systems Science, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-642-27737-5_758-1.

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Heijungs, Reinout, and Sangwon Suh. "Perturbation theory." In The Computational Structure of Life Cycle Assessment, 131–50. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-015-9900-9_6.

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Che, Maolin, and Yimin Wei. "Perturbation Theory." In Theory and Computation of Complex Tensors and its Applications, 51–96. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2059-4_3.

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Sverdlov, Viktor. "Perturbative Methods for Band Structure Calculations in Silicon." In Computational Microelectronics, 63–81. Vienna: Springer Vienna, 2010. http://dx.doi.org/10.1007/978-3-7091-0382-1_6.

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O’Malley, Robert. "Singular Perturbation Problems." In Encyclopedia of Applied and Computational Mathematics, 1330–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_145.

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Quiney, Harry M. "Relativistic Many-Body Perturbation Theory." In Methods in Computational Chemistry, 227–78. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-0711-2_5.

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Dinkler, D., and B. Kroplin. "Perturbation Sensitivity of Dynamically Loaded Structures." In Computational Mechanics ’88, 677–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61381-4_176.

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Surján, Péter R., and Ágnes Szabados. "Perturbative Approximations to Avoid Matrix Diagonalization." In Challenges and Advances in Computational Chemistry and Physics, 83–95. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-90-481-2853-2_4.

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Conference papers on the topic "Perturbative computations"

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TAYLOR, WASHINGTON. "PERTURBATIVE COMPUTATIONS IN STRING FIELD THEORY." In TASI 2003 Lecture Notes. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812775108_0006.

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Semenoff, Gordon W. "Perturbative computations in SUSYM: Testing AdS/CFT." In STRING THEORY; 10th Tohwa University International Symposium on String Theory. AIP, 2002. http://dx.doi.org/10.1063/1.1454377.

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Safronov, Anton, Carlo Flore, Daniel Kikola, Aleksander Kusina, Jean-Philippe Lansberg, Olivier Mattelaer, and Hua-Sheng Shao. "A tool for automated perturbative cross section computations of asymmetric hadronic collisions at next-to-leading order using the $\texttt{MadGraph5_aMC@NLO}$ framework." In 41st International Conference on High Energy physics. Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.414.0494.

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Berman, Gennady, D. I. Kamenev, and V. I. Tsifrinovich. "Perturbation Approach for Quantum Computation." In International Conference on Quantum Information. Washington, D.C.: OSA, 2001. http://dx.doi.org/10.1364/icqi.2001.pb20.

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Sumino, Yukinari. "Computation of Heavy Quarkonium Spectrum in Perturbative QCD." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.260.0011.

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Perlt, Holger. "Perturbative subtraction of lattice artefacts in the computation of renormalization constants." In The 30th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.164.0239.

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Kim, Namhyo, and David L. Rhode. "A New CFD-Perturbation Model for the Rotordynamics of Incompressible Flow Seals." In ASME Turbo Expo 2000: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/2000-gt-0402.

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A new, quasi-three-dimensional perturbation model is developed for the computation of rotordynamic forces for all incompressible flow seals with an axisymmetric geometry. The model assumes a small circular whirl motion of the rotor around the stator center. By avoiding the complicated perturbation coordinate transformation, the perturbation solution directly accounts for the disturbance of the wall shear stresses that are caused by the whirl motion of the rotor. The primary advantage of the present model is that it can immediately be applied to any radial-clearance seal of axisymmetric geometry without ad hoc adjustments. It was found from computations that include the upstream chamber that the magnitude of the first-order variables at the seal inlet are much larger and abruptly changing than was previously assumed.
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Blouin, Vincent Y., and Michael M. Bernitsas. "Cognate Space Identification for Forced Response Structural Redesign." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28135.

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LargE Admissibility Perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the Incremental Method (IM) and the Direct Method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate space, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.
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Valorani, Mauro, Francesco Creta, Antonino Li Brizzi, Habib Najm, and Dimitris Goussis. "Surrogate Fuel Analysis and Reduction using Computational Singular Perturbation." In 46th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-1009.

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Lan, Hu, and Jiang Renpei. "Perturbation Theory and Simulation Computation For Dual-mode Ferrite Devices." In 2006 CIE International Conference on Radar. IEEE, 2006. http://dx.doi.org/10.1109/icr.2006.343321.

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