Electric field generation in hollow dielectric waveguide lasers II: First-order perturbation theory in the presence of waveguide imperfections due to rough boundaries

1988 ◽  
Vol 5 (7) ◽  
pp. 1438 ◽  
Author(s):  
M. Arnz ◽  
H.-E. Ponath
Keyword(s):  
Perturbation Theory ◽  
Electric Field ◽  
Dielectric Waveguide ◽  
Order Perturbation ◽  
First Order ◽  
Waveguide Lasers ◽  
Hollow Dielectric Waveguide ◽  
Rough Boundaries ◽  
Electric Field Generation ◽  
First Order Perturbation

Note on Interference Effects in Two-Step Reaction Processes

1975 ◽  
Vol 53 (23) ◽  
pp. 2590-2592
Author(s):  
J. Cejpek ◽  
J. Dobeš
Keyword(s):  
Perturbation Theory ◽  
Point Of View ◽  
Order Perturbation ◽  
Interference Effects ◽  
Qualitative Explanation ◽  
First Order ◽  
One Step ◽  
Step Transition ◽  
Reaction Processes ◽  
First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

First-Order Perturbation Theory

2011 ◽  
pp. 121-147
Author(s):  
Jean-Pierre Fouque ◽  
George Papanicolaou ◽  
Ronnie Sircar ◽  
Knut Solna
Keyword(s):  
Perturbation Theory ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
First Order ◽  
First Order Perturbation

scholarly journals Low-degree mixed modes in red giant stars with moderate core magnetic fields

2019 ◽  
Author(s):  
Shyeh Tjing Loi ◽  
John C B Papaloizou
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Magnetic Fields ◽  
Differential Equations ◽  
Order Perturbation ◽  
First Order ◽  
Low Degree ◽  
Mixed Modes ◽  
The Magnetic Field ◽  
First Order Perturbation

Abstract Observations of pressure-gravity mixed modes, combined with a theoretical framework for understanding mode formation, can yield a wealth of information about deep stellar interiors. In this paper, we seek to develop a formalism for treating the effects of deeply buried core magnetic fields on mixed modes in evolved stars, where the fields are moderate, i.e. not strong enough to disrupt wave propagation, but where they may be too strong for non-degenerate first-order perturbation theory to be applied. The magnetic field is incorporated in a way that avoids having to use this. Inclusion of the Lorentz force term is shown to yield a system of differential equations that allows for the magnetically-affected eigenfunctions to be computed from scratch, rather than following the approach of first-order perturbation theory. For sufficiently weak fields, coupling between different spherical harmonics can be neglected, allowing for reduction to a second-order system of ordinary differential equations akin to the usual oscillation equations that can be solved analogously. We derive expressions for (i) the mixed-mode quantisation condition in the presence of a field and (ii) the frequency shift associated with the magnetic field. In addition, for modes of low degree we uncover an extra offset term in the quantisation condition that is sensitive to properties of the evanescent zone. These expressions may be inverted to extract information about the stellar structure and magnetic field from observational data.

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