Готові списки джерел за темами / Coulomb operator

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Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "Coulomb operator"

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Frei, B. J., S. Ernst, and P. Ricci. "Numerical implementation of the improved Sugama collision operator using a moment approach." Physics of Plasmas 29, no. 9 (September 2022): 093902. http://dx.doi.org/10.1063/5.0091244.

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The numerical implementation of the linearized gyrokinetic and drift-kinetic improved Sugama (IS) collision operators, recently introduced by Sugama et al. [Phys. Plasmas 26, 102108 (2019)], is reported. The IS collision operator extends the validity of the widely used original Sugama (OS) operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)] to the Pfirsch–Schlüter collisionality regime. Using a Hermite–Laguerre velocity–space decomposition of the perturbed gyrocenter distribution function that we refer to as the gyro-moment approach, the IS collision operator is written in a form of algebraic coefficients that depend on the mass and temperature ratios of the colliding species and perpendicular wavenumber. A comparison between the IS, OS, and Coulomb collision operators is performed, showing that the IS collision operator is able to approximate the Coulomb collision operator in the case of trapped electron mode in H-mode pedestal conditions better than the OS operator. In addition, the IS operator leads to a level of zonal flow residual which has an intermediate value between the Coulomb and the OS collision operators. The IS operator is also shown to predict a parallel electrical conductivity that approaches the one of the Coulomb operator within less than 1%, while the OS operator can underestimate the parallel electron current by at least 10%. Finally, closed analytical formulas of the lowest order gyro-moments of the IS, OS, and Coulomb operators are given, which are ready to use to describe the collisional effects in reduced gyro-moment fluid models.
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2

ESPOSITO, GIAMPIERO. "A SPECTRAL APPROACH TO YANG-MILLS THEORY." International Journal of Modern Physics A 17, no. 06n07 (March 20, 2002): 926–35. http://dx.doi.org/10.1142/s0217751x02010327.

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Yang–Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator [Formula: see text] built from the Laplacian and from a first-order differential operator. The operator [Formula: see text] is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of [Formula: see text] are evaluated as a first step towards the more difficult problems of quantized Yang–Mills theory.
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3

KHACHIDZE, TAMARI T., and ANZOR A. KHELASHVILI. "AN "ACCIDENTAL" SYMMETRY OPERATOR FOR THE DIRAC EQUATION IN THE COULOMB POTENTIAL." Modern Physics Letters A 20, no. 30 (September 28, 2005): 2277–81. http://dx.doi.org/10.1142/s0217732305018505.

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On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is closely connected to the familiar Laplace–Runge–Lenz vector. Our approach guarantees not only derivation of Johnson–Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian.
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4

Hogreve, H. "The overcritical Dirac–Coulomb operator." Journal of Physics A: Mathematical and Theoretical 46, no. 2 (December 10, 2012): 025301. http://dx.doi.org/10.1088/1751-8113/46/2/025301.

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5

Varganov, Sergey A., Andrew T. B. Gilbert, Evelyne Deplazes, and Peter M. W. Gill. "Resolutions of the Coulomb operator." Journal of Chemical Physics 128, no. 20 (May 28, 2008): 201104. http://dx.doi.org/10.1063/1.2939239.

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6

Schmidt, Karl Michael. "Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 5 (1996): 1087–96. http://dx.doi.org/10.1017/s0308210500023271.

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Анотація:
For the one-dimensional Dirac operator, examples of electrostatic potentials with decay behaviour arbitrarily close to Coulomb decay are constructed for which the operator has a prescribed set of eigenvalues dense in the whole or part of its essential spectrum. A simple proof that the essential spectrum of one-dimensional Dirac operators with electrostatic potentials is never empty is given in the appendix.
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7

KHABIBRAKHMANOV, I. K., and D. SUMMERS. "Spectral representation of the isotropic Coulomb collisional operator." Journal of Plasma Physics 58, no. 3 (October 1997): 475–84. http://dx.doi.org/10.1017/s0022377897005904.

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A spectral representation for the isotropic part of the Coulomb collisional operator is given. The particle distribution function is expanded in a series of generalized Laguerre polynomials, and the Coulomb collisional operator is expressed in terms of the spectral amplitudes. When the spectral representation is applied to the Fokker–Planck equation, a system of coupled ordinary differential equations for the spectral amplitudes is obtained. The spectral coefficients related to the Coulomb operator are defined through recurrence relations, which we reduce to simplified form. This makes possible accurate and efficient analytical and numerical evaluations of the interaction matrices. The results presented can be used in analytical investigations of the properties of the Coulomb collisional operator as well as in numerical calculations for plasmas far from thermal equilibrium. The method can also be generalized to include angular dependencies for non-isotropic particle distributions.
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8

Seri, Marcello, Andreas Knauf, Mirko Degli Esposti, and Thierry Jecko. "Resonances in the two-center Coulomb systems." Reviews in Mathematical Physics 28, no. 07 (August 2016): 1650016. http://dx.doi.org/10.1142/s0129055x16500161.

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We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrödinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.
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9

Lee, Aaron M., Stephen W. Taylor, Jeremy P. Dombroski, and Peter M. W. Gill. "Optimal partition of the Coulomb operator." Physical Review A 55, no. 4 (April 1, 1997): 3233–35. http://dx.doi.org/10.1103/physreva.55.3233.

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10

Kyniene, A., and R. Karazija. "Standard Atomic Operators and Coulomb Interaction Operator in the Quasispin Space." Physica Scripta 60, no. 5 (November 1, 1999): 407–13. http://dx.doi.org/10.1238/physica.regular.060a00407.

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Більше джерел

Дисертації з теми "Coulomb operator"

1

Hyder, Asif M. "Green's operator for Hamiltonians with Coulomb plus polynomial potentials." California State University, Long Beach, 2013.

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2

Verri, Alessandra Aparecida. "O átomo de hidrogênio em 1, 2 e 3 dimensões." Universidade Federal de São Carlos, 2007. https://repositorio.ufscar.br/handle/ufscar/5848.

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Анотація:
Made available in DSpace on 2016-06-02T20:28:22Z (GMT). No. of bitstreams: 1 1452.pdf: 916103 bytes, checksum: 40179df116306bc34414ecc8e0c08457 (MD5) Previous issue date: 2007-08-10
Financiadora de Estudos e Projetos
In this work we study the Hamiltonian of the hydrogen atom in 1, 2 and 3 dimensions. Especifically, it is defined as a self-adjoint operator in the Hilbert space L2(Rn), n = 1, 2, 3. Nevertheless, the main goal is to study the hydrogen atom 1-D. Particularly, for this is model we address some problens related to the singularity of the Coulomb potential.
Neste trabalho vamos estudar o Hamiltoniano do átomo de hidrogênio em 1, 2 e 3 dimensões. Especificamente, queremos defini-lo como um operador auto-adjunto no espaço de Hilbert L2(Rn), n = 1, 2, 3. No entanto, o principal objetivo é estudar o átomo de hidrogênio 1-D. Em particular, para este modelo, abordaremos algumas questões relacionadas à singularidade do potencial de Coulomb −1/|x|.
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3

Müller, David [Verfasser], and Heinz [Akademischer Betreuer] Siedentop. "Projizierte gestörte Coulomb-Dirac-Operatoren und ihre Eigenwerte / David Müller ; Betreuer: Heinz Siedentop." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2018. http://d-nb.info/1164376950/34.

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4

Hartig, Michael. "Loi de van der Waals-London pour les systèmes d'atomes et de molécules relativistes." Thesis, Toulon, 2019. http://www.theses.fr/2019TOUL0009.

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On considère un système constitué de plusieurs atomes où les noyaux sont supposés fixes et ponctuels. Les particules interagissent via le potentiel de Coulomb et les électrons ont une énergie cinétique pseudo-relativiste donnée par (p2+m2)1/2-m. On démontre la loi de van der Waals-London qui dit que l'énergie d'interaction entre atomes neutres décroit comme |D|-6 où |D| est la distance entre atomes. Nous calculons rigoureusement tous les termes de l'énergie de liaison jusqu'à l'ordre |D|-9 avec un terme d'erreur en O(|D|-10). Comme étape intermédiaire, nous établissons la décroissance exponentielle des fonctions propres de l'opérateur de Schrödinger à plusieurs particules avec les symétries imposées par le principe de Pauli, et des estimations sur le terme d'erreur de localisation. Nous montrons de plus la loi de van der Waals-London pour l'opérateur de Dirac projeté connu sous le nom d'opérateur de Brown et Ravenhall. Dans ce dernier cas on obtient un terme d'erreur en O(|D|-7)
We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions.Particles interact via Coulomb potential and electrons have relativistic kinetic energy given by (p2+m2)1/2-m.We prove the van der Waals-London law, which states that the interaction energy between neutral atoms decays as the sixth power of the distance |D| between the atoms. We rigorously compute all terms in the binding energy up to order |D|-9 with error term of order O(|D|-10). As intermediate steps we prove exponential decay of eigenfunctions of multiparticle Schrödinger operators with permutation symmetry imposed by the Pauli principle and new estimates of the localization error. In addition we prove the van der Waals-London law for the projected Dirac operator, known as the Brown-Ravenhall operator. In this case we do not calculate the coefficients explicitly and we obtain an error term of order O(|D|-7)
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5

Mukhtar, Qaisar. "On Monte Carlo Operators for Studying Collisional Relaxation in Toroidal Plasmas." Doctoral thesis, KTH, Fusionsplasmafysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-120590.

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This thesis concerns modelling of Coulomb collisions in toroidal plasma with Monte Carlo operators, which is important for many applications such as heating, current drive and collisional transport in fusion plasmas. Collisions relax the distribution functions towards local isotropic ones and transfer power to the background species when they are perturbed e.g. by wave-particle interactions or injected beams. The evolution of the distribution function in phase space, due to the Coulomb scattering on background ions and electrons and the interaction with RF waves, can be obtained by solving a Fokker-Planck equation.The coupling between spatial and velocity coordinates in toroidal plasmas correlates the spatial diffusion with the pitch angle scattering by Coulomb collisions. In many applications the diffusion coefficients go to zero at the boundaries or in a part of the domain, which makes the SDE singular. To solve such SDEs or equivalent diffusion equations with Monte Carlo methods, we have proposed a new method, the hybrid method, as well as an adaptive method, which selects locally the faster method from the drift and diffusion coefficients. The proposed methods significantly reduce the computational efforts and improves the convergence. The radial diffusion changes rapidly when crossing the trapped-passing boundary creating a boundary layer. To solve this problem two methods are proposed. The first one is to use a non-standard drift term in the Monte Carlo equation. The second is to symmetrize the flux across the trapped passing boundary. Because of the coupling between the spatial and velocity coordinates drift terms associated with radial gradients in density, temperature and fraction of the trapped particles appear. In addition an extra drift term has been included to relax the density profile to a prescribed one. A simplified RF-operator in combination with the collision operator has been used to study the relaxation of a heated distribution function. Due to RF-heating the density of thermal ions is reduced by the formation of a high-energy tail in the distribution function. The Coulomb collisions tries to restore the density profile and thus generates an inward diffusion of thermal ions that results in a peaking of the total density profile of resonant ions.

QC 20130415

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6

Limpanuparb, Taweetham. "Applications of Resolutions of the Coulomb Operator in Quantum Chemistry." Phd thesis, 2011. http://hdl.handle.net/1885/8879.

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This dissertation shows that the Coulomb operator and the long-range Coulomb operators can be resolved as a sum of products of one-particle functions. These resolutions provide a potent new route to tackle quantum chemical problems. Replacing electron repulsion terms in Schrodinger equations by the truncated resolutions yields the reduced-rank Schrodinger equations (RRSE). RRSEs are simpler than the original equations but yield energies with chemical accuracy even for low-rank approximations. Resolutions of the Coulomb operator factorize Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. This factorization is the key to the reduction of computational cost of quantum chemical methods.
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7

Lapointe, Andréanne. "Le problème de Coulomb-Dunkl dans le plan." Thèse, 2014. http://hdl.handle.net/1866/11158.

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Анотація:
Ce mémoire, composé d'un article en collaboration avec Monsieur Luc Vinet et Vincent X. Genest, est la suite du travail effectué sur les systèmes quantiques super-intégrables définis par des Hamiltoniens de type Dunkl. Plus particulièrement, ce mémoire vise l'analyse du problème de Coulomb-Dunkl dans le plan qui est une généralisation du système quantique de l'atome d'hydrogène impliquant des opérateurs de réflexion sur les variables x et y. Le modèle est défini par un potentiel en 1/r. Nous avons tout d'abord remarqué que l'Hamiltonien est séparable en coordonnées polaires et que les fonctions d'onde s'écrivent en termes de produits de polynômes de Laguerre généralisés et des harmoniques de Dunkl sur le cercle. L'algèbre générée par les opérateurs de symétrie nous a également permis de confirmer le caractère maximalement super-intégrable du problème de Coulomb-Dunkl. Nous avons aussi pu écrire explicitement les représentations de cette même algèbre. Nous avons finalement trouvé le spectre de l'énergie de manière algébrique.
This master's thesis, composed of an article in collaboration with Luc Vinet and Vincent X. Genest, is the result of a work done on superintegrable quantum systems defined by Hamiltonians of the Dunkl kind. More specifically, the aim of this paper is to analyse the Coulomb-Dunkl problem in the plane which is a generalization of the quantum system of hydrogen involving operators of reflection on the variables x and y. The model is defined by a potential in 1/r. First, we notice that the Hamiltonian is separable in polar coordinates and the wave functions are written in terms of products of generalized Laguerre polynomials and Dunkl harmonics on the circle. The algebra generated by the symmetry operators has also allowed us to confirm the maximally superintegrable character of the Coulomb-Dunkl problem. We also write explicitly the representations of the same algebra. We finally found the energy spectrum algebraically.
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8

Kirchberg, Andreas [Verfasser]. "Dirac operators and supersymmetry : from the coulomb problem to field theories / von Andreas Kirchberg." 2004. http://d-nb.info/972135685/34.

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9

Hsu, Chung-Jye, and 許仲傑. "A PWM-based DC-DC Buck Converter with High-efficiency Light Load Mode Operation and SOC Estimation Circuit Using Coulomb Counting Method with Dynamic Voltage Calibration." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/rhu4gh.

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碩士
國立中山大學
電機工程學系研究所
106
The research topics of this thesis are related to two sub-circuits in a Battery Management System of the AUV research project, which are a PWM-based DC-DC buck converter with high-efficiency light load mode operation and SOC estimated circuit using Coulomb counting method with dynamic voltage calibration. They are realized using TSMC 0.50 um CMOS High Voltage and TSMC 0.18 um CMOS processes, respectively. The first topic is meant to resolve the poor efficiency in the light load operation of PWM-based DC/DC converters. By turning off an optimal number of power MOSFETs, the switching loss is reduced such that the efficiency is enhanced effectively. Most importantly, the optimal light load efficiency is found by the derivation of analytic equations, and then justified by post-layout simulations to prove the best efficiency theoretically. The light load mode efficiency is proved to be improved by 36%, while the peak efficiency is 91.68%. Since AUV (autonomous underwater vehicle) is only operated by battery power, the correct information of SOC (state of charge) is a must for safety. Although coulomb counting method has been widely used for SOC estimation, it is suffered from the accumulative error. The consequence is that the actual battery’s capacity is far from the estimated capacity. To reduce the error therein between, the function between the battery voltage and the capacity is used to calibrate the estimated capacity. Namely, by taking the battery voltage variation into the estimation, the reliability of the SOC estimation circuit can be effectively enhanced.
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Книги з теми "Coulomb operator"

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Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

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Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is necessary to introduce non-correlation decoupling procedures involving the Hartree and Hartree-Fock approximations for G2 in the G1 equation; and a similar factorization “ansatz” for G3 in the G2 equation, resulting in the Sum of Ladder Diagrams integral equation for G2, with multiple Born iterates and finite collisional lifetimes. Similar treatment of the G11-equation for the joint propagation of one-electron and one-hole subject to mutual Coulomb attraction leads to bound electron-hole exciton states having a discrete hydrogen like spectrum of energy eigenstates. Its role in single-particle propagation is also discussed in terms of one-electron self-energy Σ‎ and the T-matrix
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2

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
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Частини книг з теми "Coulomb operator"

1

Gitman, D. M., I. V. Tyutin, and B. L. Voronov. "Dirac Operator with Coulomb Field." In Self-adjoint Extensions in Quantum Mechanics, 411–48. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-4662-2_9.

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2

Gallone, Matteo. "Self-Adjoint Extensions of Dirac Operator with Coulomb Potential." In Advances in Quantum Mechanics, 169–85. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58904-6_10.

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3

Kröger, Helmut. "Time-Dependent Scattering in Coulombic Few-Body Systems and the Strong Operator Approximation Method." In Coulomb Interactions in Nuclear and Atomic Few-Body Collisions, 169–219. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-9880-7_3.

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4

Keller, Ole. "The Route to the Maxwell–Lorentz Operator Equations in the Coulomb Gauge." In Quantum Theory of Near-Field Electrodynamics, 435–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17410-0_23.

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5

Koutschan, Christoph, Peter Paule, and Sergei K. Suslov. "Relativistic Coulomb Integrals and Zeilberger’s Holonomic Systems Approach II." In Algebraic and Algorithmic Aspects of Differential and Integral Operators, 135–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54479-8_6.

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6

Dolbeault, Jean, Maria Esteban, and Michael Loss. "Critical magnetic field for 2D magnetic Dirac–Coulomb operators and Hardy inequalities." In Partial Differential Equations, Spectral Theory, and Mathematical Physics, 41–63. Zuerich, Switzerland: European Mathematical Society Publishing House, 2021. http://dx.doi.org/10.4171/ecr/18-1/4.

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7

Mussardo, Giuseppe. "Minimal Conformal Models." In Statistical Field Theory, 399–442. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0011.

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Chapter 11 discusses the so-called minimal conformal models, all of which are characterized by a finite number of representations. It goes on to demonstrate how all correlation functions of these models satisfy linear differential equations. It shows how their explicit solutions are given by using the Coulomb gas method. It also explains how their exact partition functions can be obtained by enforcing the modular invariance of the theory. The chapter also covers null vectors, the Kac determinant, unitary representations, operator product expansion, fusion rules, Verlinde algebra, screening operators, structure constants, the Landau–Ginzburg formulation, modular invariance, and Torus geometry. The appendix covers hypergeometric functions.
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8

Steel, Duncan G. "Bound States in Three Dimensions: The Atom." In Introduction to Quantum Nanotechnology, 82–92. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895073.003.0006.

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In this chapter, we go to three dimensions in space and look at the solution of the time independent Schrödinger equation for the hydrogen atom. The Hamiltonian is then the kinetic energy plus the potential energy due to the Coulomb coupling between the positively charged nucleus and the electron. We construct the angular momentum operator and find that the partial differential equation for the angular momentum eigenfunctions of the spherical coordinates θ,ϕ is the same as the angular part of the ∇2 operator in spherical coordinates. The angular momentum eigenfunctions are the spherical harmonics, with two quantum numbers, l and m, and the solution to the radial part of the Hamiltonian including the Coulomb potential are Laguerre polynomials with one quantum number, called the principle quantum number, n. The hydrogen wave function is the product of a Laguerre polynomial and a spherical harmonic with three quantum numbers. Since these are two- and three-dimensional functions for angular momentum and hydrogen respectively, they are best understood in a series of plots. The chapter concludes by giving the historical letter names to specific orbitals, since they continue to be used today.
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9

"Coulomb Propagator and Scattering Operators." In Fundamentals in Hadronic Atom Theory, 41–51. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812775481_0004.

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10

Iliopoulos, J., and T. N. Tomaras. "Quantisation of the Electromagnetic Field and Spontaneous Photon Emission." In Elementary Particle Physics, 4–23. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844200.003.0002.

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We develop the method of canonical quantisation for the case of the free electromagnetic field. We choose the Coulomb gauge, which has a simpler physical interpretation. We introduce the creation and annihilation operators in this framework. The formalism is applied to the problem of spontaneous emission of radiation from an excited atomic state at first order in the perturbation expansion. This allows us to obtain a concrete physical result, namely the computation of an excited state decay rate, and, at the same time, have a first look at abstract concepts, such as gauge invariance and renormalisation.
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Тези доповідей конференцій з теми "Coulomb operator"

1

Dimits, A. M., J. Banks, R. L. Berger, S. Brunner, T. Chapman, D. Gosh, and I. Joseph. "Linearized Coulomb Collision Operator for Simulation of Interpenetrating Plasma Streams." In 2018 IEEE International Conference on Plasma Science (ICOPS). IEEE, 2018. http://dx.doi.org/10.1109/icops35962.2018.9575890.

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2

Haack, J. R., A. Szczekutowicz, and I. Gamba. "Spectral Formulation Of The Fokker-Planck-Landau Operator With Velocity Dependent Coulomb Logarithm." In 2022 IEEE International Conference on Plasma Science (ICOPS). IEEE, 2022. http://dx.doi.org/10.1109/icops45751.2022.9812991.

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3

Canfield, Stephen L., Joseph S. Owens, and Stephen G. Zuccaro. "Zero Moment Control for Lead-Through Teach Programming on a Collaborative Robot." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22510.

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Abstract Robots are commonly used for automated welding in many industries such as automotive manufacturing. The complexity and time of programming presents an obstacle in using robotic automation in welding or other tasks for small to medium enterprises that lack resources for training or expertise in traditional robot programming strategies. It also dictates a high level of repeated parts to offset the cost of weld programming. Collaborative Robots or Cobots are robots designed for more collaborative operations with humans. Cobots permit new methods of task instruction (programming) through direct interaction between the operator and robot. This paper presents a model and calibration strategy for a collaborative robot to aid intuitive teaching methods for tasks such as welding. The method makes use of a torque estimation model based on robot momentum to create an observer to evaluate external forces. The torque observer is first used to characterize the friction that exists within the robot joints. This data is used to define the parameters of a friction model that combines static, Coulomb and viscous friction properties with a sigmoid function to represent transition between motion states and a second level Fourier series to represent position dependency of the Coulomb friction terms. The friction model is then integrated into the robot control and used to provide a mode in which the robot can be easily dragged around the workspace to provide weld path training.
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4

Bouazara, M., M. J. Richard, and S. Rakheja. "Safety and Comfort Analysis of Optimal Seats With Active and Semi-Active Suspension." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33196.

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A generalized nonlinear model is formulated for dynamic analysis of suspension seats with passive, semi-active and active dampers. The model incorporates coulomb friction due to suspension linkages and bushings, forces arising from interactions with the elastic limit stops, a linear suspension spring and nonlinear damping force on the basis of passive, semi-active and active dampers, while the contribution due to biodynamics of the human operator is considered to be negligible. The semi-active and active dampers are charcterized by force generators in accordance with the control laws based upon suspension mass velocity. Two different suspension seats are experimentally assessed in the laboratory under sinusoidal and random excitations arising from an urban bus, and the measured data is used to demonstrate the validity of the proposed generalized model. The results showed reasonably good agreement between the model results and the measured data. Optimal model parameters are selected using the sequential unconstrained minimization technique with an objective to minimize the acceleration due to vibration transmitted to the occupant mass. The comfort and safety performance characteristics of the optimal suspension seat with semi-active and active dampers are evaluated under both the sinusoidal and random excitations on the basis of the guidelines provided in ISO-2631. From the results it is concluded that the comfort performance of a suspension seat with semi-active and active dampers can be considerably enhanced, in the 20% to 30% range.
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5

Frederick, Jeffrey R., and Mark S. Darlow. "Operation of a Torsionally-Loaded, Composite Shaft Above Two Flexural Critical Speeds." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0300.

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Abstract A graphite/epoxy composite shaft has been successfully balanced to operate above two flexural critical speeds while subjected to a steady torsional load. This experimental investigation has been conducted as part of a research program concerning the optimal design of supercritical composite power transmission shafts for rotorcraft applications. Of particular interest is the use of composite materials in the design of tail rotor and synchronization shafts. Rotating tests were conducted with a composite shaft that models the half length of the tail rotor drive shaft of the AH-64 helicopter. Tests were performed with magnetic and coulomb damping. It was shown in past research that an unloaded composite shaft could be balanced through and operated above two flexural critical speeds [1,2]. In this series of tests, a steady torsional load has been applied which models that of a tail rotor driveshaft. Adequate magnetic damping performance was observed up to 1000 rpm, although its effectiveness diminished at higher speeds. The remaining tests were conducted with an external coulomb damper. Results show controllable operation above two critical speeds, and smooth operation was observed at the scaled operating speed of 3500 rpm. All synchronous and nonsynchronous vibrations were easily controlled with 6% external damping applied through the entire speed range up to 5000 rpm.
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6

Vance, John M., and Luis A. San Andrés. "Analysis of Actively Controlled Coulomb Damping for Rotating Machinery." In ASME 1999 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/99-gt-175.

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Attempts have been made in the past to use Coulomb damping for vibration suppression in rotating machinery. Typically, a dry friction damper is designed to operate on a flexible bearing support. These designs have usually been unsuccessful in practice, partly because the Coulomb coefficient changes with temperature, with ingress of dirt or lubricant, and with the surface wear conditions. It is known that purely Coulomb damping forces cannot restrain the peak rotor whirl amplitudes at a critical speed. The invention of a disk type of electroviscous damper, utilizing a fluid with electrorheological (ER) properties, has recently revived the interest in Coulomb type dampers. Several investigations have suggested that a Coulomb friction model was the best representation for an ER damper with voltage applied. This model was used to study the feasibility of developing actively controlled bearing dampers for aircraft engines. This paper analyzes the imbalance response of two different rotordynamic models with Coulomb friction damping and shows the benefit of adding active control. Control laws are derived to achieve minimum rotor vibration amplitudes while avoiding large bearing forces over a speed range that includes a critical speed. The control laws are derived for purely Coulomb type of damping and assuming a combination of Coulomb and viscous damping effects. It is shown that the most important feature of Coulomb damping for minimal rotordynamic amplitude response is the control of rotor support stiffness, i.e. leading to the relocation of critical speeds, rather than control of a damping coefficient.
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7

Oka, Hiroshi, Takumi Inaba, Shota Iizuka, Hidehiro Asai, Kimihiko Kato, and Takahiro Mori. "Effect of Conduction Band Edge States on Coulomb-Limiting Electron Mobility in Cryogenic MOSFET Operation." In 2022 IEEE Symposium on VLSI Technology and Circuits (VLSI Technology and Circuits). IEEE, 2022. http://dx.doi.org/10.1109/vlsitechnologyandcir46769.2022.9830505.

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8

Noguchi, Yutaka, Takaaki Manaka, and Mitsumasa Iwamoto. "Photoinduced Gate Operation and Temperature Dependence in the Coulomb Staircase of Organic Single Electron Tunneling Junctions." In 2003 International Conference on Solid State Devices and Materials. The Japan Society of Applied Physics, 2003. http://dx.doi.org/10.7567/ssdm.2003.c-9-3.

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9

Zhu, Farong, and Robert G. Parker. "Influence of Tensioner Dry Friction on the Vibration of Belt Drives With Belt Bending Stiffness." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35817.

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A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which reduces the dimension of the iteration matrices when employing the harmonic balance method. The Coulomb damping at the tensioner arm pivot mitigates the tensioner arm vibration but not necessarily the vibrations of other system components. The extent of the mitigation varies for different excitation frequency ranges. The critical amplitude of the dry friction torque beyond which the system operates with a locked arm is determined analytically. Superharmonic resonances are observed in the responses of the generalized span coordinates but their amplitudes are small. The energy dissipation at the tensioner arm hub is discussed, and the stick-slip phenomena of the arm are reflected in the velocity reversals near the arm extreme location. Dependence of the span tension fluctuations on Coulomb torque is explored.
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10

Fournais, S., M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. o̸stergaard So̸rensen, Jacob S. Møller, and Dmitri Fedorov. "Local and global properties of eigenfunctions and one-electron densities of Coulombic Schrödinger operators." In QUANTUM FEW-BODY SYSTEMS: Proceedings of the Joint Physics∕Mathematics Workshop on Quantum Few-Body Systems. AIP, 2008. http://dx.doi.org/10.1063/1.2915642.

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