A first-order perturbation expansion for solutions of molecules interacting through the triangle-well convex-core potential

1978 ◽  
Vol 43 (11) ◽  
pp. 2821-2827 ◽  
Author(s):  
Tomáš Boublík ◽  
Joachim Winkelmann
Keyword(s):  
Perturbation Expansion ◽  
Order Perturbation ◽  
Core Potential ◽  
First Order ◽  
First Order Perturbation ◽  
Convex Core

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.

scholarly journals Strongly coupled overdamped pendulums

2008 ◽  
Vol 30 (4) ◽  
pp. 4304.1-4304.4
Author(s):  
R. De Luca
Keyword(s):  
Dynamical Equation ◽  
Second Harmonic ◽  
Perturbation Expansion ◽  
Order Perturbation ◽  
Dynamical Equations ◽  
Strongly Coupled ◽  
First Order ◽  
The One ◽  
First Order Perturbation

It is shown, by a first-order perturbation expansion, that the dimensionality of the dynamical equations for the angular variables of two strongly coupled identical overdamped pendulums can be reduced from two to one. The resulting dynamical equation is seen to be similar to the one of a single pendulum with an additional fictitious torque characterized by a second harmonic contribution.

scholarly journals Perturbation Analysis with Approximate Integration for Propagation Mode in Two-Dimensional Two-Slab Waveguides

ISRN Optics ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Naofumi Kitsunezaki
Keyword(s):  
Taylor Expansion ◽  
Propagation Constant ◽  
Perturbation Expansion ◽  
Order Perturbation ◽  
Propagation Mode ◽  
Two Dimensional ◽  
Slab Waveguides ◽  
First Order ◽  
Core Width ◽  
First Order Perturbation

On the basis of perturbation expansion from a gapless system, we calculate the propagation constant and propagation mode wave function in two-dimensional two-slab waveguides with a core gap small enough that there is only one propagation mode. We also perform calculations without the approximation for comparison. Our result shows that first-order perturbation contains the first-order Taylor expansion of (core gap)/(core width), and when the integration of the perturbation is suitably approximated, the result of the first-order perturbation is the same as that of the first-order Taylor expansion of (core gap)/(core width).

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