The successive perturbation method in the various orders of perturbation

1990 ◽  
Vol 68 (12) ◽  
pp. 1476-1478
Author(s):  
V. A. Popescu ◽  
I. M. Popescu ◽  
M. Jitaru
Keyword(s):  
Perturbation Method ◽  
Interaction Parameter ◽  
Complex Plane ◽  
Energy Levels ◽  
Perturbation Expansion ◽  
Radius Of Convergence ◽  
Variational Functional ◽  
Functional Methods

We consider the case where the radius of convergence of the perturbation expansion can be related to a "crossing" of two energy levels in the complex plane of the interaction parameter. This case is suitable for the comparison of the performance of the successive perturbation method with those of the Padé, Borel–Padé, and the variational functional methods.

Accurate power series for eigenvalues of spheroidal angle functions and their convergence radii

2011 ◽  
Vol 89 (11) ◽  
pp. 1083-1099
Author(s):  
Tam Do-Nhat
Keyword(s):  
Power Series ◽  
Least Squares ◽  
Complex Plane ◽  
Branch Point ◽  
Upper Bound ◽  
Least Squares Method ◽  
Radius Of Convergence ◽  
New Method ◽  
Recursion Relations

In this paper, the radius of convergence of the spheroidal power series associated with the eigenvalue is calculated without using the branch point approach. Studying the properties of the power series using the recursion relations among its coefficients in the new method offers some insights into the spheroidal power series and its associated eigenfunction. This study also used the least squares method to accurately compute the convergence radii to five or six significant digits. Within the circle of convergence in the complex plane of the parameter c = kF, where k is the wavenumber and F is the semifocal length of the spheroidal system, the extremely fast convergent spheroidal power series are computed with full precision. In addition, a formula for the magnitude of the upper bound of the error is obtained.

Combination of the successive perturbation method with other common methods

1987 ◽  
Vol 65 (5) ◽  
pp. 462-463 ◽  
Author(s):  
V. A. Popescu ◽  
I. M. Popescu
Keyword(s):  
Hydrogen Atom ◽  
Perturbation Method ◽  
Perturbation Series ◽  
Radius Of Convergence ◽  
Fundamental State

For the hydrogen atom in the fundamental state perturbed by βr−1, it is shown how the successive perturbation method can be combined with the method in which some fraction of a nonperturbed term (in the Hamiltonian) is included in the perturbation. Thus, the radius of convergence of the perturbation series is increased.

Hypervirial perturbation calculations for double-well potentials of perturbed oscillator type

1993 ◽  
Vol 71 (9-10) ◽  
pp. 475-483 ◽  
Author(s):  
M. R. M. Witwit ◽  
J. P. Killingbeck
Keyword(s):  
Perturbation Method ◽  
Energy Levels ◽  
Wide Range ◽  
Oscillator Type ◽  
Double Well Potential

The renormalized hypervirial perturbation method is used to compute the energy levels for a double-well potential V(x) = −Z2x2 + x2J. Results are produced for a wide range of parameters [Formula: see text] and of state numbers [Formula: see text]. Comparison is made with results obtained by other means.

scholarly journals Asymptotic Power Series of Field Correlators

10.14311/1199 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
I. Caprini ◽  
J. Fischer ◽  
I. Vrkoč
Keyword(s):  
Power Series ◽  
Large Class ◽  
Complex Plane ◽  
Perturbation Expansion ◽  
Asymptotic Power ◽  
General Contour ◽  
Asymptotic Perturbation ◽  
Class Of Functions ◽  
Borel Type

We address the problem of ambiguity of a function determined by an asymptotic perturbation expansion. Using a modified form of theWatson lemma recently proved elsewhere, we discuss a large class of functions determined by the same asymptotic power expansion and represented by various forms of integrals of the Laplace-Borel type along a general contour in the Borel complex plane. Some remarks on possible applications in QCD are made.

Two Particle – One Hole Contributions to Magnetic Moments and M1 Transitions

1971 ◽  
Vol 49 (12) ◽  
pp. 1641-1643 ◽  
Author(s):  
B. Castel ◽  
I. P. Johnstone
Keyword(s):  
Perturbation Method ◽  
Marked Improvement ◽  
Magnetic Moments ◽  
Energy Levels ◽  
Nuclear Model ◽  
Core Particle ◽  
Green Is ◽  
Spectroscopic Parameters ◽  
The Core

The success of the core-particle nuclear model in predicting energy levels and E2 transitions is partially offset by strong disagreements on M1 rates. A perturbation method suggested recently by Green is used to determine the contributions to magnetic moments and M1 transitions from 2p-1h components. A marked improvement on previous M1 results is obtained with realistic values of spectroscopic parameters.

STOCHASTIC POST-BUCKLING OF FRAMES USING KOITER'S METHOD

2006 ◽  
Vol 06 (03) ◽  
pp. 333-358 ◽  
Author(s):  
B. W. SCHAFER ◽  
L. GRAHAM-BRADY
Keyword(s):  
Monte Carlo ◽  
Perturbation Method ◽  
Perturbation Expansion ◽  
Random Variable ◽  
Order Perturbation ◽  
Initial Slope ◽  
First Order ◽  
Post Buckling ◽  
The Impact ◽  
First Order Perturbation

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

A NEW EFFICIENT APPROACH FOR MODELING AND SIMULATION OF NANO-SWITCHES UNDER THE COMBINED EFFECTS OF INTERMOLECULAR SURFACE FORCES AND ELECTROSTATIC ACTUATION

2009 ◽  
Vol 01 (02) ◽  
pp. 349-365 ◽  
Author(s):  
MAHDI MOJAHEDI ◽  
HAMID MOEENFARD ◽  
MOHAMMAD TAGHI AHMADIAN
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Electrostatic Force ◽  
Perturbation Expansion ◽  
Electrostatic Actuation ◽  
Surface Forces ◽  
Design Tool ◽  
Galerkin Projection ◽  
Homotopy Perturbation ◽  
Fringing Field Effect

This paper applies the homotopy perturbation method to the simulation of the static response of nano-switches to electrostatic actuation and intermolecular surface forces. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Using a mode approximation in the Galerkin projection method, the nonlinear boundary value differential equation describing the statical behavior of nano-switch is reduced to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The number of included terms in the perturbation expansion for achieving a reasonable response has been investigated. Three cases have been specifically studied. These cases correspond to when the effective external force is the electrostatic force, the combined electrostatic and Casimir force and the combined electrostatic and van der Waals force. In all three cases the pull-in characteristics has been investigated thoroughly. Results have been compared with numerical results and also analytical results available in the literature. It was found that HPM modifies the overestimation of N/MEMS instability limits reported in the literature and can be used as an effective and accurate design tool in the analysis of N/MEMS.

A quantum theory of Wheeler–Feynman electrodynamics

1970 ◽  
Vol 68 (3) ◽  
pp. 751-764 ◽  
Author(s):  
P. C. W. Davies
Keyword(s):  
Energy Levels ◽  
Perturbation Expansion ◽  
Formal Structure ◽  
Spontaneous Transition ◽  
Self Energy ◽  
Quantum Mechanical Theory ◽  
Action At A Distance ◽  
Quantized Field ◽  
Atomic Energy Levels ◽  
The Universe

AbstractA quantum mechanical theory of the action-at-a-distance electrodynamics of Wheeler and Feynman is given using an S-matrix approach. The response of the universe is introduced, and a perturbation expansion leads to the usual expression for the spontaneous transition rate between atomic energy levels, an effect normally attributed to quantized field oscillators. The Feynman propagator is then recovered, leading to the familiar self-energy formulae. Finally, a comparison of the formal structure of the new theory with the conventional is shown to establish a complete mathematical equivalence to all orders in the expansion.

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