Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

Forced oscillations with continuum models of atomic force microscopy

The dynamics of the AFM-atomic force microscope follows a model based in a Timoshenko cantilever beam with a tip attached at the free end and acting with the surface of a sample. General boundary conditions arise when the tip is either in contact or non-contact with the surface. The governing equations are given in matrix conservative form subject to localized loads. The eigenanalysis is done with a fundamental matrix response of a damped second-order matrix differential equation. Forced responses are found by using a Galerkin approximation of the matrix impulse response. Simulations results with harmonic and pulse forcing show the filtering character and the effects of the tip-sample interaction at the end of the beam. © 2012 American Institute of Physics.

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.

Multiple period resonances in long period gratings in photonic crystal fibres

In order to characterise long period gratings fabricated in endlessly single mode photonic crystal fibres with bulk cladding we perform eigenanalysis of guided modes supported by these fibres. Resonant coupling occurs only when the beating length equals the multiple grating periods. Experimentally obtained grating spectra and sensitivity are fully explained using modified phase matching condition.

Multiple period resonances in long period gratings in photonic crystal fibres

In order to characterise long period gratings fabricated in endlessly single mode photonic crystal fibres with bulk cladding we perform eigenanalysis of guided modes supported by these fibres. Resonant coupling occurs only when the beating length equals the multiple grating periods. Experimentally obtained grating spectra and sensitivity are fully explained using modified phase matching condition. © Springer 2006.

Investigations on birefringence effects in polymer optical fiber Bragg gratings

Step-index polymer optical fiber Bragg gratings (POFBGs) and microstructured polymer optical fiber Bragg gratings (mPOFBGs) present several attractive features, especially for sensing purposes. In comparison to FBGs written in silica fibers, they are more sensitive to temperature and pressure because of the larger thermo-optic coefficient and smaller Young's modulus of polymer materials. (M)POFBGs are most often photowritten in poly(methylmethacrylate) (PMMA) materials using a continuous-wave 325 nm HeCd laser. For the first time to the best of our knowledge, we study photoinduced birefringence effects in (m)POFBGs. To achieve this, highly reflective gratings were inscribed with the phase mask technique. They were then monitored in transmission with polarized light. For this, (m)POF sections a few cm in length containing the gratings were glued to angled silica fibers. Polarization dependent loss (PDL) and differential group delay (DGD) were computed from the Jones matrix eigenanalysis using an optical vector analyser. Maximum values exceeding several dB and a few picoseconds were obtained for the PDL and DGD, respectively. The response to lateral force was finally investigated. As it induces birefringence in addition to the photo-induced one, an increase of the PDL and DGD values were noticed. © 2014 Copyright SPIE.

Polarization effects in polymer FBGs:study and use for transverse force sensing

Bragg gratings photo-inscribed in polymer optical fibers (POFs) are more sensitive to temperature and pressure than their silica counterparts, because of their larger thermo-optic coefficient and smaller Young's modulus. Polymer optical fiber Bragg gratings (POFBGs) are most often photo-written in poly(methylmethacrylate) (PMMA) based materials using a continuous-wave 325 nm HeCd laser. In this work, we present the first study about birefringence effects in POFBGs manufactured in different types of fiber. To achieve this, highly reflective (> 90%) gratings were produced with the phase mask technique. Their spectral response was then monitored in transmission with polarized light. Polarization dependent loss (PDL) and differential group delay (DGD) were computed from the Jones matrix eigenanalysis using an optical vector analyzer. Maximum values exceeding several dB and a few picoseconds were obtained for the PDL and DGD, respectively. An inverse scattering technique applied to the experimental data provided an estimate of the photo-induced birefringence value arising from the side fabrication process. The response to lateral force was finally investigated for various incident directions using the PDL response of FBGs manufactured in step-index POFs. As the force induced birefringence adds to the photo-induced one, a force dependent evolution of the PDL maximum value was noticed, with a good temperature-insensitivity.