Relevant bibliographies by topics / Spin-wave separation of variables

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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 'Spin-wave separation of variables'

Author: Grafiati
Published: 7 September 2024

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Journal articles on the topic "Spin-wave separation of variables"

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Kalnins, E. G., and G. C. Williams. "Symmetry operators and separation of variables for spin‐wave equations in oblate spheroidal coordinates." Journal of Mathematical Physics 31, no. 7 (July 1990): 1739–44. http://dx.doi.org/10.1063/1.528670.

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Amico, Luigi, Holger Frahm, Andreas Osterloh, and Tobias Wirth. "Separation of variables for integrable spin–boson models." Nuclear Physics B 839, no. 3 (November 2010): 604–26. http://dx.doi.org/10.1016/j.nuclphysb.2010.07.005.

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Zhdanov, R. Z. "Separation of variables in the nonlinear wave equation." Journal of Physics A: Mathematical and General 27, no. 9 (May 7, 1994): L291—L297. http://dx.doi.org/10.1088/0305-4470/27/9/009.

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BEREST, YURI, and PAVEL WINTERNITZ. "HUYGENS' PRINCIPLE AND SEPARATION OF VARIABLES." Reviews in Mathematical Physics 12, no. 02 (February 2000): 159–80. http://dx.doi.org/10.1142/s0129055x00000071.

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We demonstrate a close relation between the algebraic structure of the (local) group of conformal transformations on a smooth Lorentzian manifold [Formula: see text] and the existence of nontrivial hierarchies of wave-type hyperbolic operators satisfying Huygens' principle on [Formula: see text]. The mechanism of such a relation is provided through a local separation of variables for linear second order partial differential operators with a metric principal symbol. The case of flat (Minkowski) spaces is studied in detail. As a result, some new nontrivial classes of Huygens operators are constructed. Their relation to the classical Hadamard conjecture and its modifications is discussed.
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Zhdanov, R. Z., I. V. Revenko, and V. I. Fushchich. "Separation of variables in two-dimensional wave equations with potential." Ukrainian Mathematical Journal 46, no. 10 (October 1994): 1480–503. http://dx.doi.org/10.1007/bf01066092.

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Smirnov, Yu G., V. Yu Martynova, M. A. Moskaleva, and A. V. Tikhonravov. "MODIFIED METHOD OF SEPARATION OF VARIABLES FOR SOLVING DIFFRACTION PROBLEMS ON MULTILAYER DIELECTRIC GRATINGS." Eurasian Journal of Mathematical and Computer Applications 9, no. 4 (December 2021): 76–88. http://dx.doi.org/10.32523/2306-6172-2021-9-4-76-88.

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A modified method of separation of variables is proposed for solving the direct problem of diffraction of electromagnetic wave by multilayer dielectric gratings (MDG). To apply this method, it is necessary to solve a one-dimensional eigenvalue problem for a 2nd- order differential equation on a segment with piecewise constant coefficients. The accuracy of the method is verified by comparison with the results obtained by the commercially available RCWA method. It is demonstrated that the method can be applied not only to commonly used MDG elements with one line in a grating period but also to potentially promising MDG elements with several different lines in a grating period.
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Sergeev, S. M. "Functional Equations and Quantum Separation of Variables for 3d Spin Models." Theoretical and Mathematical Physics 138, no. 2 (February 2004): 226–37. http://dx.doi.org/10.1023/b:tamp.0000015070.88403.f9.

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Osetrin, Konstantin, and Evgeny Osetrin. "Shapovalov Wave-Like Spacetimes." Symmetry 12, no. 8 (August 18, 2020): 1372. http://dx.doi.org/10.3390/sym12081372.

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A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.
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Casals, Marc, Adrian C. Ottewill, and Niels Warburton. "High-order asymptotics for the spin-weighted spheroidal equation at large real frequency." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2222 (February 2019): 20180701. http://dx.doi.org/10.1098/rspa.2018.0701.

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The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal eigenvalues and eigenfunctions to high order. This expansion corrects and extends existing results in the literature and we validate it via a high-precision numerical calculation.
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Osetrin, Konstantin, Ilya Kirnos, Evgeny Osetrin, and Altair Filippov. "Wave-Like Exact Models with Symmetry of Spatial Homogeneity in the Quadratic Theory of Gravity with a Scalar Field." Symmetry 13, no. 7 (June 29, 2021): 1173. http://dx.doi.org/10.3390/sym13071173.

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Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves).
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Dissertations / Theses on the topic "Spin-wave separation of variables"

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Trifa, Youssef. "Dynamiques de corrélations et d'intrication dans des gaz d'atomes froids." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0018.

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Le problème quantique à N corps, notamment l’étude des propriétés dynamiques d’un système quantique composite est l’un des problèmes les plus durs de la physique moderne, car il y a peu de résultats analytiques et les méthodes numériques exactes requièrent des ressources numériques exponentielles en la taille du système. Dans cette thèse, nous avons étudié la mise en évidence de propriétés de corrélations et d’intrication pour des systèmes d’atomes magnétiques sur réseau, par exemple via la compression de spin. Pour cela nous avons mis au point de nouvelles méthodes numériques approchées, qui permettent de simuler des systèmes de grande taille. Cela nous a permis de proposer des protocoles qui permettent de générer de la compression de spin qui croit d’autant plus que le système est grand, ce qui a un double intérêt. D’une part, il s’agit d’un témoin d’intrication, qui permettrait donc de détecter de l’intrication dans un système d’atomes magnétiques, ce qui n’a pas encore été réalisée expérimentalement à ce jour. D’autre part la compression de spin présente un important intérêt métrologique, puisque les états comprimés permettent des mesures extrêmement précises de champs magnétiques par exemple, bien au-delà de ce qui est possible avec des atomes indépendants. Enfin, nous avons étudié la génération d’autres formes d'intrication, à savoir la compression à deux modes (de spin, ou d'impulsion), cette fois pour des systèmes d’atomes condensés. Connue dans le cas de condensats d’atomes de spin-1, nous avons proposé comment généraliser ce processus au cas de compression en impulsion, en utilisant un Hamiltonien modulé dans le temps. Les états intriqués ainsi produits sont potentiellement très intéressants dans la mesure à haute précision de forces inertielles
The quantum many-body problem, and especially the study of dynamical properties of a multipartite quantum system, is one of the hardest problems of modern physics. There exist only a few analytical results and exact numerical simulations require an amount of resources that grow exponentially with the system size.In this thesis, we studied correlations and entanglement properties for systems composed of magnetic atoms on a lattice, for instance via the generation of spin squeezing. For this purpose we have developed new approximate numerical methods that allow us to study large system sizes. This enabled us to propose protocols to generate an amount of spin squeezing that scales with the system size. The advantage is twofold. Since spin squeezing is an entanglement witness, this would allow for entanglement detection in a system of magnetic atoms - which has yet to be realized experimentally. Moreover, spin squeezing offers an important metrological advantage, asspin-squeezed states can be used for extremely precise measurements of external magnetic fields, far beyond what one can achieve within dependent atoms.Finally, we studied the generation of other forms of entanglement, namely Dicke squeezing (of spin or momentum), in systems of Bose condensed atoms. This form of entanglement is well-known in spin-1 atomic condensates. Here, we propose a protocol to generalize it to the case of momentum modes, using a time-dependent Hamiltonian. The entangled states generated during the dynamics are potentially useful for the precision measurements of inertial forces
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Faldella, Simone. "Solutions de chaînes de spin XXZ et XYZ avec bords par la séparation des variables." Thesis, Dijon, 2014. http://www.theses.fr/2014DIJOS075/document.

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Dans cette thèse nous donnons une solution des chaînes quantiques de spin-1/2 XXZ et XYZ ouvertes avec les termes de bord intégrables les plus généraux. En utilisant la méthode de la Séparation des Variable (SoV), à la Sklyanin, on est capable, dans le cas inhomogène, de construire l’ensemble complet des états propres et des valeurs propres associés. La caractérisation de ces quantités est faite par un système maximal de N équations quadratiques, où N est la taille du système. Des méthodes différentes, comme l’ansatz de Bethe algébrique (ABA) ou autres généralisations de l’ansatz de Bethe, ont été utilisés dans le passé pour résoudre ces problèmes. Aucune méthode a pu effectivement reproduire l’ensemble complet des états propres et valeur propres dans le cas de conditions au bord les plus génériques. Une expression, sous forme d’un déterminant à la Vandermonde, pour les produits scalaires entre les états en représentation de SoV est aussi obtenue. La formule pour les produits scalaires représente la première étape pour approcher le problème relié au calcul des facteurs de forme et fonctions de corrélations
In this thesis we give accounts on the solution of the open XXZ and XYZ quantum spin-1/2 chains with the most generic integrable boundary terms. By using the the Separation of Variables method (SoV), due to Sklyanin, we are able, in the inhomogeneous case, to build the complete set of eigenstates and the associated eigenvalues. The characterization of these quantities is made through a maximal system of N quadratic equations, where N is the size of the chain. Different methods, like the Algebraic Bethe ansatz (ABA) or other generalized Bethe ansatz techniques, have been used, in the past, in order to tackle these problems. None of them resulted effective in the reproduction of the full set of eigenstates and eigenvalues in the case of most general boundary conditions. A Vandermonde determinant formula for the scalar products of SoV states is obtained as well. The scalar product formula represents a first step towards the calculation of form factors and correlation functions
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Slizovskiy, Sergey. "Yang-Mills Theory in Gauge-Invariant Variables and Geometric Formulation of Quantum Field Theories." Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-129670.

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In Part I we are dealing with effective description of Yang-Mills theories based on gauge-invarint variables. For pure Yang-Mills we study the spin-charge separation varibles. The dynamics in these variables resembles the Skyrme-Faddeev model. Thus the spin-charge separation is an important intermediate step between the fundamental Yang-Mills theory and the low-energy effective models, used to model the low-energy dynamics of gluons. Similar methods may be useful for describing the Electroweak sector of the Standard Model in terms of gauge-invariant field variables called supercurrents. We study the geometric structure of spin-charge separation in 4D Euclidean space (paper III) and elaborate onconnection with gravity toy model. Such reinterpretation gives a way to see how effective flat background metric is created in toy gravity model by studying the appearance of dimension-2 condensate in the Yang-Mills (paper IV). For Electroweak theory we derive the effective gauge-invariant Lagrangian by doing the Kaluza-Klein reduction of higher-dimensional gravity with 3-brane, thus making explicit the geometric interpretation for gauge-invariant supercurrents. The analogy is then made more precise in the framework of exact supergravity solutions. Thus, we interpret the Higgs effect as spontaneous breaking of Kaluza-Klein gauge symmetry and this leads to interpretation of Higgs field as a dilaton (papers I and II). In Part II of the thesis we study rather simple field theories, called “geometric” or “instantonic”. Their defining property is exact localization on finite-dimensional spaces – the moduli spaces of instantons. These theories allow to account exactly for non-linearity of space of fields, in this respect they go beyond the standard Gaussian perturbation theory. In paper V we show how to construct a geometric theory of chiral boson by embedding it into the geometric field theory. In Paper VI we elaborate on the simplest geometric field theory – the supersymmetric Quantum Mechanics and construct new non-perturbative topological observables that have a transparent meaning both in geometric and in the Hamiltonian formalisms. In Paper VII we are motivated by making perturbations away from the simple instantonic limit. For that we need to carefully define the observables that are quadratic in momenta and develop the way to compute them in geometric framework. These correspond geometrically to bivector fields (or, in general, the polyvector fields). We investigate the local limit of polyvector fields and compare the geometric calculation with free-field approach.
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Hasnain, Shahid. "Steady Periodic Water Waves Solutions Using Asymptotic Approach." Thesis, Linköpings universitet, Tillämpad matematik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-69421.

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The aim of this work is to study the relation between two invariants of water flow in a channel of finite depth. The first invariant is the height of the water wave and the second one is the flow force. We restrict ourselves to water waves of small amplitude. Using asymptotic technique together with the method of separation of variables, we construct all water waves of small amplitude which are parameterized by a small parameter. Then we demonstrate numerically that the flow force depends monotonically on the height.
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Books on the topic "Spin-wave separation of variables"

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service), SpringerLink (Online, ed. Electromagnetic wave scattering on nonspherical particles: Basic methodology and simulations. Berlin: Springer, 2009.

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Mann, Peter. Wave Mechanics & Elements of Mathematical Physics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0005.

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This chapter presents an in-depth look at classical wave mechanics and mathematical physics, containing key examples directly relevant to molecular physics. The separation of variables is used to construct the Helmholtz equation from the one-dimensional wave equation before considering the three-dimensional wave equation. From this, equations for the temporal, radial, azimuth and angular components are developed and solutions using the Bessel equations and Legendre polynomials are found. Boundary conditions are explained and the Rayleigh plane wave expansion as the general solution to the Helmholtz equation is reconstructed. Both the Hermite equation and the Legendre equation are derived using the series solution method, and the Laplace equation is discussed.
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Rother, Tom, and Michael Kahnert. Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Simulations. Springer, 2016.

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Rother, Tom, and Michael Kahnert. Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Simulations. Springer, 2013.

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Rother, Tom, and Michael Kahnert. Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Simulations. Springer, 2013.

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Rother, Tom. Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Simulations. Springer, 2010.

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Book chapters on the topic "Spin-wave separation of variables"

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Garrett, Steven L. "Three-Dimensional Enclosures." In Understanding Acoustics, 621–72. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44787-8_13.

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Abstract In this chapter, solutions to the wave equation that satisfies the boundary conditions within three-dimensional enclosures of different shapes are derived. This treatment is very similar to the two-dimensional solutions for waves on a membrane of Chap. 10.1007/978-3-030-44787-8_6. Many of the concepts introduced in Sect. 10.1007/978-3-030-44787-8_6#Sec1 for rectangular membranes and Sect. 10.1007/978-3-030-44787-8_6#Sec5 for circular membranes are repeated here with only slight modifications. These concepts include separation of variables, normal modes, modal degeneracy, and density of modes, as well as adiabatic invariance and the splitting of degenerate modes by perturbations. Throughout this chapter, familiarity with the results of Chap. 10.1007/978-3-030-44787-8_6 will be assumed. The similarities between the standing-wave solutions within enclosures of different shapes are stressed. At high enough frequencies, where the individual modes overlap, statistical energy analysis will be introduced to describe the diffuse (reverberant) sound field.
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Deville, Yannick, and Alain Deville. "New Classes of Blind Quantum Source Separation and Process Tomography Methods Based on Spin Component Measurements Along Two Directions." In Latent Variable Analysis and Signal Separation, 204–14. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93764-9_20.

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"One-Dimensional Wave Equation." In Separation of Variables for Partial Differential Equations, 177–210. Chapman and Hall/CRC, 2005. http://dx.doi.org/10.4324/9780203498781-10.

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"Potential, Heat, and Wave Equation." In Separation of Variables for Partial Differential Equations, 17–40. Chapman and Hall/CRC, 2005. http://dx.doi.org/10.4324/9780203498781-4.

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Green, N. J. B. "Separations." In Quantum Mechanics 1. Oxford University Press, 1997. http://dx.doi.org/10.1093/hesc/9780198557616.003.0003.

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This chapter examines the separation of variables in quantum mechanics. Although many mathematical methods are available for one-dimensional eigenvalue problems, multi-dimensional partial differential equations are much more difficult to solve, often requiring computational methods. The first step is therefore to search for some means of reducing the problem to a collection of one-dimensional equations, which can be solved separately. The procedure involved is called the separation of variables. The chapter first outlines the method of separation of variables before considering how it is applied to problems in chemistry. It looks at spherical symmetry; the Born–Oppenheimer separation; spin; orbital approximation; the diatomic molecule; and the vibrations of a polyatomic molecule.
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Steward, David R. "Analytic Elements from Separation of Variables." In Analytic Element Method, 165–226. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198856788.003.0004.

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Separation of variables provides influence functions for analytic elements, which extend the solutions available with complex functions to problems involving the Helmholtz and modified Helmholtz equations. Methods are introduced for one-dimensional problems that provide the background vector field for many problems, and these solutions are extended to finite domains with interconnected rectangle elements in Section 4.3. Circular elements are developed in Section 4.4 using series of Bessel and Fourier functions to model wave propagation around and through collections of elements, and vadose zone solutions are extended to solve the nonlinear interface conditions occurring along circles. Methods are extended to three-dimensional problems for spheres (Section 4.5), and prolate and oblate spheroids in Section 4.6.
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Steiner, Erich. "Partial differential equations." In The Chemistry Maths Book. Oxford University Press, 2008. http://dx.doi.org/10.1093/hesc/9780199205356.003.0014.

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This chapter focuses on partial differential equations, which are equations that contains partial derivatives. It shows different examples that demonstrate a number of important principles in the solution of partial differential equations. The chapter describes the general solutions as well as the method of separation of variables. It particularly looks at the time-independent Schrödinger equation for the particle in a rectangular box, and in a circular box, and for the hydrogen atom. Furthermore, it discusses how the one-dimensional wave equation is applied to the vibrations of an elastic string, such as a guitar string. The chapter also introduces the phenomenon of degeneracy.
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Collins, Peter J. "The Diffusion and Wave Equations and the Equation of Laplace." In Differential and Integral Equations, 115–47. Oxford University PressOxford, 2006. http://dx.doi.org/10.1093/oso/9780198533825.003.0008.

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Abstract The material in this chapter is in many ways of considerable significance. The equations under consideration arise from classical, and classic, problems in mathematical physics. They have provoked some of the finest work in classical analysis. The range of theory and techniques that have been invented to tackle the various instances that arise is extraordinary and has occupied some of the most celebrated figures in the history of mathematics. We have necessarily had to have rather limited objectives here. The aim is to find some important, if elementary, solutions to the equations which in turn will expose some of their main properties. Our main tool is indeed an elementary one which may already be familiar to the reader: the method of separation of variables. However, even with this tool, we find ourselves working with such well-known analytical objects as Bessel functions and Legendre polynomials. Later chapters discuss other aspects of the subject in the context of the calculus of variations, of the Sturm–Liouville equation, of complex analysis and of transform theory. The final section of this chapter fulfils a promise made in the last: we shall discuss existence and uniqueness of solutions and, what is so important these days when numerical analysis and the computer provide approximate solutions to otherwise intractable equations, whether a problem is ‘well-posed’, that is, whether its possible solutions are ‘continuously dependent on the boundary conditions’, and so, approximations are likely to be accurate.
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Alwin, Duane F. "Developing Reliable Measures." In Measurement Error in Longitudinal Data, 113–54. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198859987.003.0006.

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This chapter presents a general approach to assessing the reliability of measurement of survey questions—those in common use in many surveys. The approach, which relies on a robust set of longitudinal design requirements, applies the quasi-Markov simplex model to multi-wave data in the evaluation of measurement errors for survey questions. Under particular assumptions, this model produces a set of estimates that conform to the psychometric definition of measurement reliability, defined as the ratio of true variance to observed variance. These models attribute some of the over-time inconsistency in measurements to unreliability and some to true change. This strategy rejects traditional notions of reliability that rely on internal consistency estimates for composite variables, as well as the simple test–retest approach to estimating reliability. Rather, the emphasis is on the separation of unreliability from true change in observations made over time. The importance of meeting several design requirements for using these over-time statistical models is also emphasized. These include the use of large-scale panel studies representative of known populations, with a minimum of three waves of measurement, separated by lengthy re-interview intervals, and limited to exactly replicated questions over the multiple waves. Results are presented from several three-wave panel studies that have employed this design, which provide evidence for the utility of the approach in the evaluation of the quality of survey measurement with respect to question content, context, and form.
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Dyall, Kenneth G., and Knut Faegri. "Spin Separation and the Modified Dirac Equation." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0022.

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In the preceding chapters, the theory for calculations based on the Dirac equation has been laid out in some detail. The discussion of the methods included a comparison with equivalent nonrelativistic methods, from which it is apparent that four-component calculations will be considerably more expensive than the corresponding nonrelativistic calculations—perhaps two orders of magnitude more expensive. For this reason, there have been many methods developed that make approximations to the Dirac equation, and it is to these that we turn in this part of the book. There are two elements of the Dirac equation that contribute to the large amount of work: the presence of the small component of the wave function and the spin dependence of the Hamiltonian. The small component is primarily responsible for the large number of two-electron integrals which, as will be seen later, contain all the lowest-order relativistic corrections to the electron–electron interaction. The spin dependence is incorporated through the kinetic energy operator and the correction to the electronic Coulomb interaction, and also through the coupling of the spin and orbital angular momenta in the atomic 2-spinors, which form a natural basis set for the solution of the Dirac equation. Spin separation has obvious advantages from a computational perspective. As we will show for several spin-free approaches below, a spin-free Hamiltonian is generally real, and therefore real spin–orbitals may be employed for the large and small components. The spin can then be factorized out and spin-restricted Hartree–Fock methods used to generate the one-electron functions. In the post-SCF stage, where the no-pair approximation is invoked, the transformation of the integrals from the atomic to the molecular basis produces a set of real molecular integrals that are indistinguishable from a set of nonrelativistic MO integrals, and therefore all the nonrelativistic correlation methods may be employed without modification to obtain relativistic spin-free correlated wave functions. In most cases, spin–free relativistic effects dominate the relativistic corrections to electronic structure. We will show later that in a perturbation expansion based on the nonrelativistic wave function, the spin-free effects for a closed-shell system enter in first order, whereas the spin-dependent effects make their first contribution in second order.
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Conference papers on the topic "Spin-wave separation of variables"

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Biletskyy, Vasyl, and Sergiy Yaroshko. "A Method of Generalized Separation of Variables for Solving Three-Dimensional Integral Equations." In XIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic Acoustic Wave Theory. IEEE, 2006. http://dx.doi.org/10.1109/diped.2006.314315.

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Velytiak, T. I., and S. A. Yaroskho. "A method of generalized separation of variables for solving two-dimensional integral equations." In Proceedings of III International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. DIPED-98. IEEE, 1998. http://dx.doi.org/10.1109/diped.1998.730949.

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Schmidt, Karsten, Jochen Wauer, and Tom Rother. "Application of the separation of variables method to plane wave scattering on non-axisymmetric particles." In Lidar Multiple Scattering Experiments, edited by Christian Werner, Ulrich G. Oppel, and Tom Rother. SPIE, 2003. http://dx.doi.org/10.1117/12.512338.

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Biletskyy, Vasyl, and Sergiy Yaroshko. "A Method of Generalized Separation of Variables for Solving Many-Dimensional Linear Fredholm Integral Equations." In 2007 XIIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. IEEE, 2007. http://dx.doi.org/10.1109/diped.2007.4373583.

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Abramov, Aleksander A., Nadezhda B. Konyukhova, and Tatyana V. Levitina. "Numerical Investigation of the Problem of a Plane Acoustic Wave Scattering by a Triaxial Ellipsoid." 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/detc1995-0433.

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Abstract The problem of scalar scattering by a triaxial ellipsoid is considered. A triaxial ellipsoid is the unique essentially three-dimensional object for which the scattering problem may be solved ‘exactly’ via separation of variables. The solution is expressed in terms of ellipsoidal coordinates associated with a given ellipsoid. The expansions in ellipsoidal wave functions are given for a point source field, a plane wave, and diffraction characteristics of a scattering ellipsoid. These expansions were first obtained by Fedoryuk. The resultant formulas have permitted, in particular, numerical investigation of plane acoustic wave scattering by both ideally soft and ideally rigid triaxial ellipsoids. Far field amplitudes have been calculated and plotted for various parameter values. Separation of the variables allows effective parallel implementation.
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Wang, Zerun, and Aichun Feng. "Investigation on Semi-Analytical Solution of Diffracted Wave Field Caused by a Bottom-Mounted Block." In ASME 2024 43rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/omae2024-127500.

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Abstract A number of marine structures can be represented by bottom-mounted blocks when analyzing the diffracted wave field. In this paper, the method of domain decomposition and separation of variables are used to derive the velocity potential of diffracted wave field by a bottom-mounted block in a semi-infinite tank. The semi-analytical solutions are compared with the free surface elevation RAO of a block in open waters obtained by commercial software WAMIT, and good agreement is reached. The present solution can be applied as benchmark to verify the results obtained by other numerical methods.
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7

Wang, Yuhan, and Sheng Dong. "Wave Attenuation Performance of Arranging a Rectangular Buoy in a Perforated Caisson Using Quadratic Pressure Drop Condition." In ASME 2022 41st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/omae2022-79289.

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Abstract Integrating a rectangular buoy type wave energy converter (WEC) inside the perforated caisson can be advantageous to the wave attenuation performance as well as the stability of the WEC. As a preliminary study on such integration system, a theoretical model was established to investigate the wave attenuation performance of the integration system with a fixed buoy inside a perforated caisson. The methods of separation of variables and eigenfunction function expansion were used to determine the velocity potentials in different fluid domains. Instead of the traditional linear pressure drop condition for perforated walls, a quadratic condition, which is more consistent with the practical truth, was used in this study. The proposed model was validated by results in a former research. The wave attenuation performance was then investigated and discussed through a parametric study.
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Zhen, Yanpei. "ROGUE WAVES ARISING ON THE STANDING PERIODIC WAVE IN THE HIGH-ORDER ABLOWITZ-LADIK EQUATION." In Pure & Applied Sciences International Conference, 14-15 March 2024, Singapore. Global Research & Development Services, 2024. http://dx.doi.org/10.20319/icstr.2024.2034.

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The nonlinear Schr¨odinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves generated on the periodic background.
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9

Leblond, Ce´dric, Serguei Iakovlev, and Jean-Francois Sigrist. "A Fully Elastic Model for Studying Submerged Circular Cylindrical Shells Subjected to a Weak Shock Wave." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-77382.

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The transient dynamics of evacuated and fluid-filled circular elastic shells, submerged in an infinite fluid medium and subjected to an external weak shock wave, is considered in this paper. This circular shell/acoustic medium interaction problem has already been tackled with simplified thin shell models, based on the Love-Kirchhoff hypotheses for the structural dynamics. In this case, the resulting radiated pressure field displays some discrepancies related to the A0/S0 waves when compared to the experimental data available in the literature for the evacuated case. These drawbacks are overcome here by the use of an isotropic elastic model for the structural dynamics and an inviscid acoustic flow for the fluid dynamics, in a two-dimensional framework. It is assumed that the shell displacements are small compared to both its radius and thickness. The approach is based on the methods of Laplace transform in time, Fourier series expansions and separation of variables in space. For the fluid-filled case, the transient thick shell-weak shock wave interaction problem is explored and the radiated acoustic field described.
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Quan, Haiyong, and Zhixiong Guo. "Analytical Solution of Whispering-Gallery Modes." In ASME 2007 InterPACK Conference collocated with the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ipack2007-33124.

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Advances in MEMS/NEMS techniques have enabled high-Q whispering-gallery modes in integrated microcavities. Potential applications of optical microcavities include quantum informatics, novel micro/nano sources, dynamic filters, and micro/nanosensors. It is important to understand the intrinsic resonant modes of a cavity. In this report, we will analyze whispering-gallery modes in resonators of planar structure which is common in MEMS devices. The wave equation is solved by using the method of separation of variables with appropriate boundary conditions. Analytical formulations are established. The resonance frequencies as well as the electric field distributions in exemplary resonators are presented for a variety of whispering-gallery modes.
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Reports on the topic "Spin-wave separation of variables"

1

Mickens, Ronald, and Kale Oyedeji. Exponential and Separation of Variables Exact Solutions to the Linear, Delayed, Unidirectional Wave Equation. Atlanta University Center Robert W. Woodruff Library, 2019. http://dx.doi.org/10.22595/cau.ir:2020_mickens_oyedeji_exponential.

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