Uncertainty Propagation in the Band Gap Structure of a 1D Array of Magnetically Coupled Oscillators

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Brian P. Bernard ◽  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Eigenvalue Problem ◽  
Band Gap ◽  
Propagation Constant ◽  
Uncertainty Propagation ◽  
Nonlinear Effects ◽  
Excitation Amplitude ◽  
Standard Uncertainty ◽  
Wave Number ◽  
Design Parameters ◽  
Band Gap Structure

The propagation constant technique has previously been used to predict band gap regions in linear oscillator chains by solving an eigenvalue problem for frequency in terms of a wave number. This paper describes a method by which selected design parameters can be separated from the eigenvalue problem, allowing standard uncertainty propagation techniques to provide closed form solutions for the uncertainty in frequency. Examples are provided for different types of measurement or environmental uncertainty showing the varying robustness of a band gap region to changes in parameters of the same or different order. The system studied in this paper is comprised of repelling magnetic oscillators using a dipole model. Numerical simulation has been performed to confirm the accuracy of analytical solutions up to a certain level of base excitation amplitude after which nonlinear effects change the predicted band gap regions to low energy chaos.

scholarly journals Sensitivity analysis of waveguide eigenvalue problems

2011 ◽  
Vol 9 ◽  
pp. 85-89 ◽  
Author(s):  
N. Burschäpers ◽  
S. Fiege ◽  
R. Schuhmann ◽  
A. Walther
Keyword(s):  
Sensitivity Analysis ◽  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Wave Number ◽  
Design Parameters ◽  
Dielectric Waveguides ◽  
Integration Technique ◽  
Numerical Examples ◽  
Numerical Effort ◽  
Complex Solutions

Abstract. We analyze the sensitivity of dielectric waveguides with respect to design parameters such as permittivity values or simple geometric dependencies. Based on a discretization using the Finite Integration Technique the eigenvalue problem for the wave number is shown to be non-Hermitian with possibly complex solutions even in the lossless case. Nevertheless, the sensitivity can be obtained with negligible numerical effort. Numerical examples demonstrate the validity of the approach.

Gap solitons supported by an optical lattice in biased photorefractive crystals having both the linear and quadratic electro-optic effect

2020 ◽  
Vol 75 (8) ◽  
pp. 749-756
Author(s):  
Aavishkar Katti ◽  
Chittaranjan P. Katti
Keyword(s):  
Band Gap ◽  
Optical Lattice ◽  
Propagation Constant ◽  
Gap Soliton ◽  
Electro Optic ◽  
Quadratic Nonlinearities ◽  
Existence And Stability ◽  
Gap Solitons ◽  
Finite Band ◽  
First Time

AbstractWe investigate the existence and stability of gap solitons supported by an optical lattice in biased photorefractive (PR) crystals having both the linear and quadratic electro-optic effect. Such PR crystals have an interesting interplay between the linear and quadratic nonlinearities. Gap solitons are predicted for the first time in such novel PR media. Taking a relevant example (PMN-0.33PT), we find that the gap solitons in the first finite bandgap are single humped, positive and symmetric solitons while those in the second finite band gap are antisymmetric and double humped. The power of the gap soliton depends upon the value of the axial propagation constant. We delineate three power regimes and study the gap soliton profiles in each region. The gap solitons in the first finite band gap are not linearly stable while those in the second finite band gap are found to be stable against small perturbations. We study their stability properties in detail throughout the finite band gaps. The interplay between the linear and quadratic electro-optic effect is studied by investigating the spatial profiles and stability of the gap solitons for different ratios of the linear and quadratic nonlinear coefficients.

RCS Reduction of Patch Array Antenna by Electromagnetic Band-Gap Structure

2012 ◽  
Vol 11 ◽  
pp. 1048-1051 ◽  
Author(s):  
Jiejun Zhang ◽  
Junhong Wang ◽  
Meie Chen ◽  
Zhan Zhang
Keyword(s):  
Band Gap ◽  
Array Antenna ◽  
Electromagnetic Band Gap ◽  
Band Gap Structure ◽  
Gap Structure

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

scholarly journals Surface transport and band gap structure of exfoliated 2H-MoTe 2 crystals

2D Materials ◽  
2014 ◽  
Vol 1 (2) ◽  
pp. 021002 ◽  
Author(s):  
Ignacio Gutiérrez Lezama ◽  
Alberto Ubaldini ◽  
Maria Longobardi ◽  
Enrico Giannini ◽  
Christoph Renner ◽  
...  
Keyword(s):  
Band Gap ◽  
Surface Transport ◽  
Band Gap Structure ◽  
Gap Structure
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