scholarly journals A second order perturbation expansion for small singular values

1984 ◽  
Vol 56 ◽  
pp. 231-235 ◽  
Author(s):  
G.W. Stewart
Keyword(s):  
Perturbation Expansion ◽  
Singular Values ◽  
Second Order ◽  
Order Perturbation

Second-Order Perturbation Analysis of In-Plane Blade-Hub Dynamics of Horizontal-Axis Wind Turbines

2018 ◽  
Author(s):  
Ayse Sapmaz ◽  
Brian F. Feeny
Keyword(s):  
Perturbation Analysis ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Second Order ◽  
Horizontal Axis ◽  
Dynamic Responses ◽  
Order Perturbation ◽  
Resonance Case ◽  
Horizontal Axis Wind Turbine ◽  
Rotor Angle

This paper deals with a second-order perturbation analysis of the in-plane dynamic responses of both tuned and mistuned three-blade-hub horizontal-axis wind-turbine equations. The blades are under effect of gravitational and cyclic aerodynamics forces and centrifugal forces. Although the blades and hub equations are coupled, they can be decoupled by changing the independent variable from time to rotor angle and by using a small parameter approximation. A second-order method of multiple scales is applied in the rotor-angle domain to analyze in-plane blade-hub dynamics. A superharmonic resonance case at one third the natural frequency was revealed. This resonance case was not captured by a first-order perturbation expansion. The relationship between response amplitude and frequency is studied. The effect of blade mistuning on the coupled blade-hub dynamics are taken into account.

STRINGENT VERIFICATION OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTION THEORY: BASED ON SHORT-RANGE SQUARE WELL POTENTIAL

2010 ◽  
Vol 24 (32) ◽  
pp. 6291-6306
Author(s):  
YUANTAO XIANG ◽  
A. JAMNIK
Keyword(s):  
Short Range ◽  
Density Functional ◽  
Perturbation Expansion ◽  
Second Order ◽  
Order Perturbation ◽  
Perturbation Scheme ◽  
Third Order ◽  
Density Profiles ◽  
Ensemble Monte Carlo ◽  
Square Well

A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

Investigation of the Spin Hamiltonian Parameters of Yb3+ in CaWO4 Crystal

2004 ◽  
Vol 59 (12) ◽  
pp. 943-946 ◽  
Author(s):  
Hui-Ning Dong ◽  
Shao-Yi Wu
Keyword(s):  
Hyperfine Structure ◽  
Local Structure ◽  
Reasonable Agreement ◽  
Second Order ◽  
Order Perturbation ◽  
Superposition Model ◽  
Spin Hamiltonian ◽  
Structure Constants ◽  
Hamiltonian Parameters ◽  
G Factors

In this paper, the spin Hamiltonian parameters g factors g∥ and g⊥ of Yb3+ and hyperfine structure constants A∥ and A⊥ of 171Yb3+ and 173Yb3+ in CaWO4 crystal are calculated from the two-order perturbation formulae. In these formulae, the contributions of the covalence effects, the admixture between J =7/2 and J =5/2 states as well as the second-order perturbation are included. The needed crystal parameters are obtained from the superposition model and the local structure of the studied system. The calculated results are in reasonable agreement with the observed values. The results are discussed.

Second-Order Perturbation in Intrinsically BrokenŨ(12)

1965 ◽  
Vol 139 (6B) ◽  
pp. B1587-B1590 ◽  
Author(s):  
R. J. Rivers
Keyword(s):  
Second Order ◽  
Order Perturbation
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