An Iterative Ab Initio Non-Hermitian Floquet Method for Photoionization Resonances

10.26434/chemrxiv.13054556.v1 ◽

2020 ◽

Author(s):

sajeev Y

Keyword(s):

Ab Initio ◽

Eigenvalue Problems ◽

Electronic System ◽

Bound State ◽

New Method ◽

Computational Techniques ◽

Floquet Method ◽

Linearly Polarized ◽

Diagonalization Method ◽

Matrix Eigenvalue Problems

We present an efficient ab initio non-Hermitian Floquet method for computing the photoionization resonances of an electronic system interacting with linearly polarized monochromatic laser light. Unlike the direct "brute force" diagonalization method, which has been used for huge Floquet matrix eigenvalue problems, the new method follows a simple iterative process. The computational advantages of the iterative method are very remarkable as it avoids computation, storage, and diagonalization of the huge Floquet matrix. The new method can also be used in conjunction with the ab initio computational techniques that were originally developed for the field-free bound state calculations. The method is best illustrated with the photoionization resonance of the hydrogen atom.

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ANALYSIS OF OPTICAL WAVEGUIDES WITH ARBITRARY INDEX PROFILE USING AN IMMERSED INTERFACE METHOD

International Journal of Modern Physics C ◽

10.1142/s0129183111016543 ◽

2011 ◽

Vol 22 (07) ◽

pp. 687-710 ◽

Cited By ~ 4

Author(s):

THEODOROS P. HORIKIS

Keyword(s):

Optical Waveguides ◽

Eigenvalue Problems ◽

Numerical Technique ◽

Interface Problems ◽

Index Profile ◽

Immersed Interface Method ◽

Immersed Interface ◽

Light Confinement ◽

Bragg Fibers ◽

Matrix Eigenvalue Problems

A numerical technique is described that can efficiently compute solutions of interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces. A prime example of these problems are optical waveguides, and as such the scheme is applied to Maxwell's equations as they are formulated to describe light confinement in Bragg fibers. It is based on standard finite differences appropriately modified to take into account all possible discontinuities across the waveguide's interfaces due to the change of the refractive index. Second- and fourth-order schemes are described with additional adaptations to handle matrix eigenvalue problems, demanding geometries and defects.

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Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems.

Journal of Mathematical Analysis and Applications ◽

10.1016/s0022-247x(02)00356-6 ◽

2002 ◽

Vol 276 (1) ◽

pp. 64-79

Author(s):

E. Adams ◽

M. Plum

Keyword(s):

Eigenvalue Problems ◽

Forced Vibrations ◽

Homotopy Methods ◽

Fourier Decomposition ◽

Matrix Eigenvalue ◽

Free And Forced Vibrations ◽

Nonlinear Matrix ◽

Matrix Eigenvalue Problems

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Two-Parameter Matrix Eigenvalue Problems

Bounds for Determinants of Linear Operators and Their Applications ◽

10.1201/9781315156231-13 ◽

2017 ◽

pp. 209-214

Author(s):

Michael Gil’

Keyword(s):

Eigenvalue Problems ◽

Matrix Eigenvalue ◽

Parameter Matrix ◽

Matrix Eigenvalue Problems ◽

Two Parameter

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Protein Structure Prediction

Biotechnology ◽

10.4018/978-1-5225-8903-7.ch007 ◽

2019 ◽

pp. 156-184

Author(s):

Hirak Jyoti Chakraborty ◽

Aditi Gangopadhyay ◽

Sayak Ganguli ◽

Abhijit Datta

Keyword(s):

Protein Structure ◽

Ab Initio ◽

Protein Structure Prediction ◽

Structure Prediction ◽

Future Research ◽

Computational Techniques ◽

Target Sequence ◽

Knowledge Based ◽

Research Areas ◽

Three Phases

The great disagreement between the number of known protein sequences and the number of experimentally determined protein structures indicate an enormous necessity of rapid and accurate protein structure prediction methods. Computational techniques such as comparative modeling, threading and ab initio modelling allow swift protein structure prediction with sufficient accuracy. The three phases of computational protein structure prediction comprise: the pre-modelling analysis phase, model construction and post-modelling refinement. Protein modelling is primarily comparative or ab initio. Comparative or template-based methods such as homology and threading-based modelling require structural templates for constructing the structure of a target sequence. The ab initio is a template-free modelling approach which proceeds by satisfying various physics-based and knowledge-based parameters. The chapter will elaborate on the three phases of modelling, the programs available for performing each, issues, possible solutions and future research areas.

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Protein Structure Prediction

Advances in Bioinformatics and Biomedical Engineering - Applying Big Data Analytics in Bioinformatics and Medicine ◽

10.4018/978-1-5225-2607-0.ch003 ◽

2018 ◽

pp. 48-79 ◽

Cited By ~ 1

Author(s):

Hirak Jyoti Chakraborty ◽

Aditi Gangopadhyay ◽

Sayak Ganguli ◽

Abhijit Datta

Keyword(s):

Protein Structure ◽

Ab Initio ◽

Protein Structure Prediction ◽

Structure Prediction ◽

Future Research ◽

Computational Techniques ◽

Target Sequence ◽

Knowledge Based ◽

Research Areas ◽

Three Phases

The great disagreement between the number of known protein sequences and the number of experimentally determined protein structures indicate an enormous necessity of rapid and accurate protein structure prediction methods. Computational techniques such as comparative modeling, threading and ab initio modelling allow swift protein structure prediction with sufficient accuracy. The three phases of computational protein structure prediction comprise: the pre-modelling analysis phase, model construction and post-modelling refinement. Protein modelling is primarily comparative or ab initio. Comparative or template-based methods such as homology and threading-based modelling require structural templates for constructing the structure of a target sequence. The ab initio is a template-free modelling approach which proceeds by satisfying various physics-based and knowledge-based parameters. The chapter will elaborate on the three phases of modelling, the programs available for performing each, issues, possible solutions and future research areas.

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A note on the Ritz method with an application to overtone stellar pulsation theory

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700005334 ◽

1968 ◽

Vol 8 (2) ◽

pp. 275-286 ◽

Cited By ~ 2

Author(s):

A. L. Andrew

Keyword(s):

Numerical Solution ◽

Eigenvalue Problems ◽

Ritz Method ◽

Linear Operators ◽

Matrix Equations ◽

Infinite Dimensional ◽

Stellar Pulsation ◽

Finite Matrix ◽

The Matrix ◽

Matrix Eigenvalue Problems

The Ritz method reduces eigenvalue problems involving linear operators on infinite dimensional spaces to finite matrix eigenvalue problems. This paper shows that for a certain class of linear operators it is possible to choose the coordinate functions so that numerical solution of the matrix equations is considerably simplified, especially when the matrices are large. The method is applied to the problem of overtone pulsations of stars.

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