Normal Forms in Perturbation Theory

2011 ◽  
Keyword(s):  
Perturbation Theory ◽  
Normal Forms

Analysis of the Interaction between Modes by Normal Forms and Singular Perturbation Theory

2012 ◽  
Vol 157-158 ◽  
pp. 381-385
Author(s):  
Jing Zhang ◽  
Ting Ting Jiang
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Power System ◽  
Voltage Stability ◽  
Vector Fields ◽  
Normal Forms ◽  
Interaction Analysis ◽  
System Structure ◽  
System Stability ◽  
Singular Perturbation Theory

Due to the nonlinear characteristics of modern power systems, strong interaction between system angle stability and voltage stability will present. However, because of extreme complexity, these two kinds of stability are often investigated separately and the interactions between them are normally neglected in traditional studies. In this paper, a new method based on the theory of normal forms of vector fields and singular perturbation theory is introduced to deal with the power system structure preserving model for system stability modes interaction analysis. The relationship between angle and voltage stability is discovered. The method is validated with a sample power system.

Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

2017 ◽  
Vol 14 (06) ◽  
pp. 1750086 ◽  
Author(s):  
Misael Avendaño-Camacho ◽  
Yury Vorobiev
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Deformation Theory ◽  
Normal Forms ◽  
Geometric Approach ◽  
Fiber Bundles ◽  
Poisson Structures ◽  
Averaging Theorem ◽  
Fibered Manifolds ◽  
Adiabatic Perturbation Theory

In the context of normal forms, we study a class of slow–fast Hamiltonian systems on general Poisson fiber bundles with symmetry. Our geometric approach is motivated by a link between the deformation theory for Poisson structures on fibered manifolds and the adiabatic perturbation theory. We present some normalization results which are based on the averaging theorem for horizontal 2-cocycles on Poisson fiber bundles.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Normal Forms and Bifurcation of Planar Vector Fields

1994 ◽  
Author(s):  
Shui-Nee Chow ◽  
Chengzhi Li ◽  
Duo Wang
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Planar Vector Fields ◽  
Planar Vector

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

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