Relevant bibliographies by topics / Lanczos potentials

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Lanczos potentials'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Lanczos potentials"

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Mena, Filipe C., and Paul Tod. "Lanczos potentials for linearly perturbed FLRW spacetimes." Journal of Physics: Conference Series 66 (May 1, 2007): 012019. http://dx.doi.org/10.1088/1742-6596/66/1/012019.

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Pommaret, J. F. "Airy, Beltrami, Maxwell, Einstein and Lanczos Potentials Revisited." Journal of Modern Physics 07, no. 07 (2016): 699–728. http://dx.doi.org/10.4236/jmp.2016.77068.

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CHEN, MIN, and HUA ZHU. "POTENTIAL ENERGY SURFACE, MICROWAVE AND INFRARED SPECTRA OF THE Xe–CO2 COMPLEX FROM AB INITIO CALCULATIONS." Journal of Theoretical and Computational Chemistry 11, no. 03 (June 2012): 537–46. http://dx.doi.org/10.1142/s0219633612500332.

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We present a new three-dimensional potential energy surface for Xe–CO2 including the Q3 normal mode for the υ3 antisymmetric stretching vibration of the CO2 molecule. Two vibrationally adiabatic potentials with CO2 in both the ground (υ3 = 0) and the first excited (υ3 = 1) states are generated by the integration of this potential over the Q3 coordinate. Each potential is found to have a T-shaped global minimum. The radial DVR/angular FBR method and the Lanczos algorithm are employed to calculate the rovibrational energy levels. The calculated band origin shifts, microwave and infrared spectra based on the two averaged potentials are in good agreement with the available experimental data.
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Andersson, Fredrik, and S. Brian Edgar. "Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor." Classical and Quantum Gravity 18, no. 12 (June 6, 2001): 2297–304. http://dx.doi.org/10.1088/0264-9381/18/12/304.

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DOLAN, P., and B. MURATORI. "GRAVITATIONAL POTENTIALS AND THE EXISTENCE OF GRAVITATIONAL GREEN'S TENSORS." Modern Physics Letters A 13, no. 29 (September 21, 1998): 2347–53. http://dx.doi.org/10.1142/s0217732398002497.

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The non-local part of the gravitational field Cabcd can be generated by the 16-component Lanczos tensor potential Labc. When six gauge conditions are imposed, Labe;e=0, its ten degrees of freedom match those of the Weyl tensor. The Penrose wave equation for Cabcd can be independently derived from that for Labc. The consistency between Labc and Cabcd is also shown by the compatibility of their algebraic classifications. An unexpected insight into the relationship of Labc and Cabcd is found in "Euclidean gravity" which in turn leads to the introduction of a gravitational Green's tensor [Formula: see text] corresponding to the potential Labc.
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Andersson, F., and S. Brian Edgar. "Curvature-free asymmetric metric connections and Lanczos potentials in Kerr–Schild spacetimes." Journal of Mathematical Physics 39, no. 5 (May 1998): 2859–61. http://dx.doi.org/10.1063/1.532425.

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Chen, Rong, and Xiao Ling Luo. "Vibrationally Averaged Potential Energy Surfaces and Microwave Spectra for Isotopic Ne-CO2 Complexes." Applied Mechanics and Materials 670-671 (October 2014): 235–39. http://dx.doi.org/10.4028/www.scientific.net/amm.670-671.235.

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Averaged potential energy surfaces for isotopic Ne–CO2complexes (20Ne–18O13C16O,20Ne–17O12C16O and22Ne–17O12C16O) are presented. According to the latestab initiopotential of20Ne–12C16O2(R. Chen, H. Zhu, D. Q. Xie, J. Chem. Phys, 133, 2010, 104302,) which incorporates its dependence on theQ3normal mode for the antisymmetric stretching vibration of the CO2molecule, we obtain the averaged potentials for20Ne–18O13C16O,20Ne–17O12C16O and22Ne–17O12C16O complexes by integrating the potential energy surface overQ3normal mode. Each averaged potential surfaces are found to have a T-shaped global minimum and two equivalent linear local minima. The radial DVR/angular FBR method and the Lanczos algorithm are applied to calculate the rovibrational energy levels. Comparison with the available experimental values showed an overall excellent agreement for all spectroscopic parameters and the microwave spectra.
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Wang, Xiao-Gang, and Tucker Carrington,. "Theoretical study of the rovibrational spectrum of He2–OCS." Canadian Journal of Chemistry 88, no. 8 (August 2010): 779–86. http://dx.doi.org/10.1139/v10-030.

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We report calculated microwave and infrared rovibrational transitions of the van der Waals complex He2–OCS. The calculations were done using a product basis, a Lanczos eigensolver, and potentials built from He–OCS, and He–He potential functions taken from the literature. All five of the large amplitude coordinates are treated exactly and calculations are done for J values up to five. All rovibrational levels are converged to 0.001 cm–1 by using basis sets with as many as 87 million funcions. Good agreement is found with previously reported experimental results. Although we assume that the dipole moment is along the OCS axis, we find transitions with appreciable intensity between different torsion states.
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CHANG, S. L., and C. S. CHIEN. "NUMERICAL CONTINUATION FOR NONLINEAR SCHRÖDINGER EQUATIONS." International Journal of Bifurcation and Chaos 17, no. 02 (February 2007): 641–56. http://dx.doi.org/10.1142/s0218127407017501.

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We discuss numerical methods for studying numerical solutions of N-coupled nonlinear Schrödin-ger equations (NCNLS), N = 2, 3. First, we discretize the equations by centered difference approximations. The chemical potentials and the coupling coefficient are treated as continuation parameters. We show how the predictor–corrector continuation method can be exploited to trace solution curves and surfaces of the NCNLS, where the preconditioned Lanczos method with iterative refinement is used as the linear solver. When the chemical potential is large enough, we obtain peak solutions of the NCNLS for certain values of the coupling coefficient. The contours of the peak solutions resemble those of the experimental results of Anglin and Ketterle [2002], and Anderson et al. [1995].
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Mena, Filipe C., and Paul Tod. "Lanczos potentials and a definition of gravitational entropy for perturbed Friedman–Lemaitre–Robertson–Walker spacetimes." Classical and Quantum Gravity 24, no. 7 (March 13, 2007): 1733–45. http://dx.doi.org/10.1088/0264-9381/24/7/004.

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Dissertations / Theses on the topic "Lanczos potentials"

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Holgersson, David. "Lanczos potentialer i kosmologiska rumtider." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2582.

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We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.

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Singh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.

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The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods that are highly efficient in the semiclassical regime. Our analysis takes place in the Lie algebra generated by multiplicative operators and polynomials of the differential operator. This Lie algebra is completely characterised by Jordan polynomials in the differential operator, which constitute naturally symmetrised differential operators. Combined with the $\mathbb{Z}_2$-graded structure of this Lie algebra, the symmetry results in skew-Hermiticity of the exponents for Zassenhaus-style splittings, resulting in unitary evolution and numerical stability. The properties of commutator simplification and height reduction in these Lie algebras result in a highly effective form of $\textit{asymptotic splitting:} $exponential splittings where consecutive terms are scaled by increasing powers of the small semiclassical parameter. This leads to high accuracy methods whose costs grow quadratically with higher orders of accuracy. Time-dependent potentials are tackled by developing commutator-free Magnus expansions in our Lie algebra, which are subsequently split using the Zassenhaus algorithm. We present two approaches for developing arbitrarily high-order Magnus--Zassenhaus schemes${-}$one where the integrals are discretised using Gauss--Legendre quadrature at the outset and another where integrals are preserved throughout. These schemes feature high accuracy, allow large time steps, and the quadratic growth of their costs is found to be superior to traditional approaches such as Magnus--Lanczos methods and Yoshida splittings based on traditional Magnus expansions that feature nested commutators of matrices. An analysis of these operatorial splittings and expansions is carried out by characterising the highly oscillatory behaviour of the solution.
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Muratori, Bruno Donato. "The Lanczos tensor potential : its wave equation and methods of solution with a new approach to algebraically special spacetimes." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266117.

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Bouakline, Foudhil. "Application des méthodes L2 à la photodissociation des molécules d' intérêt astrophysique." Paris 6, 2005. http://www.theses.fr/2005PA066482.

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Book chapters on the topic "Lanczos potentials"

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Ahsan, Zafar. "Lanczos Potential and Tetrad Formalism." In The Potential of Fields in Einstein's Theory of Gravitation, 41–50. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8976-4_4.

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Ahsan, Zafar. "Lanczos Potential for Algebraically Special Spacetimes." In The Potential of Fields in Einstein's Theory of Gravitation, 51–65. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8976-4_5.

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Ahsan, Zafar. "Lanczos Potential and Perfect Fluid Spacetimes." In The Potential of Fields in Einstein's Theory of Gravitation, 67–80. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8976-4_6.

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Ahsan, Zafar. "Lanczos Potential For the Spacetime Solutions." In The Potential of Fields in Einstein's Theory of Gravitation, 81–101. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8976-4_7.

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LÓPEZ-BONILLA, J. L., J. MORALES, G. OVANDO, and J. M. RIVERA-REBOLLEDO. "LANCZOS POTENTIAL." In The Ninth Marcel Grossmann Meeting, 1090–91. World Scientific Publishing Company, 2002. http://dx.doi.org/10.1142/9789812777386_0172.

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Conference papers on the topic "Lanczos potentials"

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DEL CASTILLO, G. F. TORRES. "LANCZOS POTENTIALS VIA THE $\mathcal{HH}$ FORMALISM." In Proceedings of 2002 International Conference. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772732_0040.

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Ramzanpour, Mohammadreza, Mohammad Hosseini-Farid, Jayse McLean, Mariusz Ziejewski, and Ghodrat Karami. "A Logistic Regression Analysis for Tissue Stiffness Categorization Through Magnetic Resonance Elastography." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23929.

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Abstract Magnetic resonance elastography (MRE) is commonly used as an image-based alternative for palpation of the internal organs of human body. The presence of tumor or other kind of pathologies in biological tissues can increase its stiffness. Therefore, while MRE technique is capable to provide a quantitative measurement, the qualitative description of the tissue stiffness could be potentially informative as well for physicians. MRE can be divided into several steps including the generation of waves in the tissue, measuring the field displacement of the tissue by magnetic resonance imaging devices, and then applying the constitutive based inversion algorithms to measure the material properties of the tissue. The inversion algorithms are dependent to the constitutive model in use, and moreover, it could be computationally expensive. To overcome this hindrance, in this paper, we propose a machine learning framework for categorizing the tissue stiffness based on the magnetic resonance elastography finite element simulation data. In our finite element simulation, the shear waves are generated in an axisymmetrical model by applying harmonic displacement at the center of the model with the known excitation frequency. To obtain the field displacement of the model, in the first step, the natural frequencies of the system will be calculated through numerical Block-Lanczos eigensolver algorithm. Thereafter, a transient dynamic modal analysis is carried out to find the corresponding displacement response of the tissue in different time steps of the simulation. To obtain the training dataset, ten simulations with the pre-assigned linear elastic modulus in the range of 2 to 6 kPa is conducted and the displacement of the tissue in three points at the end of the first and second cycle will be recorded as the features of the dataset. Each instance of the dataset is labelled as “Low“ or “High”, corresponding to its stiffness quantitative value lying in ranges of 2–4 kPa or 4–6 kPa. A machine learning classifying algorithm, a logistic regression hypothesis will be trained on this dataset. The trained hypothesis will be then tested on six new unseen simulation data with known elastic modulus values. The trained logistic regression was able to classify the tissue stiffness with the perfect accuracy score of 1.0. The findings of this study can be used for qualitative description of the tissue stiffness that can be beneficial for pathology diagnosis and moreover, it eliminates the need on the usage of inversion algorithms which leads to reduction in the computational complexity of tissue characterization.
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