Gamma Matrix

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Hu Zhuangqi - One of the best experts on this subject based on the ideXlab platform.

  • Aspects of primary creep of a single crystal nickel-base superalloy
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1999
    Co-Authors: Tian Sugui, Zhang Jinghua, Zhou Huihua, Yang Hongcai, Xu Yongbo, Hu Zhuangqi
    Abstract:

    Primary tensile creep curve has been measured for a single crystal nickel-base superalloy and microstructure for specimens parallel to (100) crystal plane at different creep times have been observed by means of transmission electron microscopy (TEM). The results show that the 1/2[110] dislocation is activated on the octahedral and cube slip systems in the Gamma Matrix channels and multiplied by dislocation reactions. The dislocation motion must overcome greater resistance on the (100) and (010) crystal planes in the Gamma Matrix channels which are subjected to compression stress. Therefore, the bulk dislocations move in a form of cross-slip and shorter distance. The dislocation loop in one Matrix channel moves into the other Matrix channels subjected to compression stress by means of cross-slip that is similar to Frank-Read (F-R) dislocation configuration due to the pinning on both sides. After the Gamma' is rafted, the climbing of dislocations is the principal mechanism of the creep deformation. (C) 1999 Elsevier Science S.A. All rights reserved.

Richard J. Reynolds - One of the best experts on this subject based on the ideXlab platform.

  • THE DISTRIBUTION AND HYPOTHESIS TESTING OF EIGENVALUES FROM THE CANONICAL ANALYSIS OF THE Gamma Matrix OF QUADRATIC AND CORRELATIONAL SELECTION GRADIENTS
    Evolution; international journal of organic evolution, 2009
    Co-Authors: Richard J. Reynolds, Douglas K. Childers, Nicholas M. Pajewski
    Abstract:

    Canonical analysis measures nonlinear selection on latent axes from a rotation of the Gamma Matrix (Gamma) of quadratic and correlation selection gradients. Here, we document that the conventional method of testing eigenvalues (double regression) under the null hypothesis of no nonlinear selection is incorrect. Through simulation we demonstrate that under the null the expectation of some eigenvalues from canonical analysis will be nonzero, which leads to unacceptably high type 1 error rates. Using a two-trait example, we prove that the expectations for both eigenvalues depend on the sampling variability of the estimates in Gamma. An appropriate test is to slightly modify the double regression method by calculating permutation P-values for the ordered eigenvalues, which maintains correct type 1 error rates. Using simulated data of nonlinear selection on male guppy ornamentation, we show that the statistical power to detect curvature with canonical analysis is higher compared to relying on the estimates from Gamma alone. We provide a simple R script for permutation testing of the eigenvalues to distinguish curvature in the selection surface induced by nonlinear selection from curvature induced by random processes.

  • Multiyear study of multivariate linear and nonlinear phenotypic selection on floral traits of hummingbird-pollinated Silene virginica.
    Evolution; international journal of organic evolution, 2009
    Co-Authors: Richard J. Reynolds, Michele R. Dudash, Charles B. Fenster
    Abstract:

    Pollination syndromes suggest that convergent evolution of floral traits and trait combinations reflects similar selection pressures. Accordingly, a pattern of selection on floral traits is expected to be consistent with increasing the attraction and pollen transfer of the important pollinator. We measured individual variation in six floral traits and yearly and lifetime total plant seed and fruit production of 758 plants across nine years of study in natural populations of Ruby-Throated Hummingbird-pollinated Silene virginica. The type, strength, and direction of selection gradients were observed by year, and for two cohorts selection was estimated through lifetime maternal fitness. Positive directional selection was detected on floral display height in all years of study and stigma exsertion in all years but one. Significant quadratic and correlational selection gradients were rare. However, a canonical analysis of the Gamma Matrix indicated nonlinear selection was common; if significant curvature was detected it was convex with one exception. Our analyses demonstrated selection favored trait combinations and the integration of floral features of attraction and pollen transfer efficiency that were consistent with the hummingbird pollination syndrome.

Nicholas M. Pajewski - One of the best experts on this subject based on the ideXlab platform.

  • THE DISTRIBUTION AND HYPOTHESIS TESTING OF EIGENVALUES FROM THE CANONICAL ANALYSIS OF THE Gamma Matrix OF QUADRATIC AND CORRELATIONAL SELECTION GRADIENTS
    Evolution; international journal of organic evolution, 2009
    Co-Authors: Richard J. Reynolds, Douglas K. Childers, Nicholas M. Pajewski
    Abstract:

    Canonical analysis measures nonlinear selection on latent axes from a rotation of the Gamma Matrix (Gamma) of quadratic and correlation selection gradients. Here, we document that the conventional method of testing eigenvalues (double regression) under the null hypothesis of no nonlinear selection is incorrect. Through simulation we demonstrate that under the null the expectation of some eigenvalues from canonical analysis will be nonzero, which leads to unacceptably high type 1 error rates. Using a two-trait example, we prove that the expectations for both eigenvalues depend on the sampling variability of the estimates in Gamma. An appropriate test is to slightly modify the double regression method by calculating permutation P-values for the ordered eigenvalues, which maintains correct type 1 error rates. Using simulated data of nonlinear selection on male guppy ornamentation, we show that the statistical power to detect curvature with canonical analysis is higher compared to relying on the estimates from Gamma alone. We provide a simple R script for permutation testing of the eigenvalues to distinguish curvature in the selection surface induced by nonlinear selection from curvature induced by random processes.

George Davey Smith - One of the best experts on this subject based on the ideXlab platform.

  • An atom probe study of the distribution of rhenium in a nickel-based superalloy
    Materials Science and Engineering: A, 1998
    Co-Authors: Paul J. Warren, A. Cerezo, George Davey Smith
    Abstract:

    The beneficial effect of Re on the high temperature properties of single-crystal nickel-based superalloys has resulted in a steady increase in the levels of Re used in these alloys. This paper reports an energy compensated 3D atom probe investigation of superalloy RR3000 after high temperature testing. Clear experimental evidence of pileup of Re solute atoms in the Gamma Matrix ahead of the growing Gamma' particles was observed for both large primary Gamma' rafts and also small secondary Gamma' precipitates. The effect of the observed bow wave of Re on the rate of microstructural coarsening during precipitate growth is discussed. (C) 1998 Elsevier Science S.A. All rights reserved

Gregory A. Fiete - One of the best experts on this subject based on the ideXlab platform.

  • Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
    New Journal of Physics, 2012
    Co-Authors: Seth Whitsitt, Victor Chua, Gregory A. Fiete
    Abstract:

    We theoretically study an exactly solvable Gamma Matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.

  • exact chiral spin liquids and mean field perturbations of Gamma Matrix models on the ruby lattice
    New Journal of Physics, 2012
    Co-Authors: Seth Whitsitt, Victor Chua, Gregory A. Fiete
    Abstract:

    We theoretically studied an exactly solvable Gamma Matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with ?expanded? vertices and links. We find that this model displays an exceptionally rich phase diagram that includes (i) gapless phases with stable spin Fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points and (iii) gapped phases with finite Chern numbers possessing the values ?4,?3,?2 and ?1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit where these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results show the richness of possible ground states in closely related magnetic systems.