CALCULATION OF NORMAL MODES OF OCEANS USING A LANCZOS METHOD

1976 ◽  
pp. 409-426 ◽  
Author(s):  
Alan K. Cline ◽  
Gene H. Golub ◽  
George W. Platzman
Keyword(s):  
Normal Modes ◽  
Lanczos Method

TWO-WAY COUPLED-MODE SOLUTIONS IN THE COMPLEX HORIZONTAL WAVENUMBER PLANE

2008 ◽  
Vol 16 (02) ◽  
pp. 225-256 ◽  
Author(s):  
STEVEN A. STOTTS
Keyword(s):  
Normal Modes ◽  
Lanczos Method ◽  
Numerical Implementation ◽  
Coupling Coefficients ◽  
Equation Solution ◽  
The Real ◽  
Coupled Equations ◽  
Coupled Mode ◽  
Layer Mode ◽  
Mode Solution

A coupled-mode formalism based on complex Airy layer mode solutions is presented. It is an extension into the complex horizontal wavenumber plane of the companion article [Stotts, J. Acoust. Soc. Am.111 (2002) 1623–1643], referred to here as the real horizontal wavenumber version, which accounted for general ocean environments but was restricted to normal modes on the real horizontal wavenumber axis. A formulation of the expressions for both trapped and continuum complex coupling coefficients is developed to dramatically reduce computer storage requirements and to make the calculation more practical. The motivation of this work is to demonstrate the numerical implementation of the derivations and to apply the method to an example benchmark. Differences from the real horizontal wavenumber formalism are highlighted. The coupled equations are solved using the Lanczos method [Knobles, J. Acoust. Soc. Am.96 (1994) 1741–1747]. Comparisons of the coupled-mode solution to a parabolic equation solution for the ONR shelf break benchmark validate the results.

Lanczos method in synchro calculation of eigenpairs and their derivatives

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 874-875
Author(s):  
X. R. Yuan ◽  
E. L. Chen ◽  
S. P. Yang
Keyword(s):  
Lanczos Method

Filtering methods for finite-time normal modes and atmospheric error growth

2000 ◽  
Vol 42 ◽  
pp. 1482
Author(s):  
Mozheng Wei ◽  
Jorgen S. Frederiksen ◽  
Steve Kepert
Keyword(s):  
Finite Time ◽  
Normal Modes ◽  
Error Growth

Gravitational Waves

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Black Hole ◽  
Perturbation Theory ◽  
Gravitational Waves ◽  
Transfer Functions ◽  
Normal Modes ◽  
Cosmological Perturbation ◽  
Tests Of General Relativity ◽  
Pulsar Timing ◽  
Tensor Perturbations ◽  
Stochastic Backgrounds

A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).

Triatomic molecules

2018 ◽  
Author(s):  
John H. D. Eland ◽  
Raimund Feifel
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Electronic States ◽  
Triatomic Molecules ◽  
Doubly Charged Ions ◽  
Spectral Bands ◽  
Valence Electrons ◽  
Doubly Charged ◽  
Charged Ions ◽  
Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

Wave chaos in terms of normal modes

1999 ◽  
Vol 59 (2) ◽  
pp. 1656-1668 ◽  
Author(s):  
A. L. Virovlyansky ◽  
G. M. Zaslavsky
Keyword(s):  
Normal Modes ◽  
Wave Chaos

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

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