Orthogonal Sets

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Jan Luca Van Den Busch - One of the best experts on this subject based on the ideXlab platform.

  • kids 1000 cosmology cosmic shear constraints and comparison between two point statistics
    Astronomy and Astrophysics, 2021
    Co-Authors: Marika Asgari, Chiehan Lin, Benjamin Joachimi, Benjamin Giblin, Catherine Heymans, Hendrik Hildebrandt, Arun Kannawadi, Benjamin Stolzner, Tilman Troster, Jan Luca Van Den Busch
    Abstract:

    We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), doubling the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat $\Lambda$CDM model, we find $S_8 = \sigma_8 (\Omega_{\rm m}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021}$ for our fiducial analysis, which is in $3\sigma$ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our $S_8$ constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data pass the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample.

  • KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics
    'EDP Sciences', 2021
    Co-Authors: Marika Asgari, Chiehan Lin, Benjamin Joachimi, Benjamin Giblin, Catherine Heymans, Hendrik Hildebrandt, Arun Kannawadi, Benjamin Stolzner, Tilman Troster, Jan Luca Van Den Busch
    Abstract:

    We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), which doubles the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat standard cosmological model, we find $ S_8 = \sigma_8 (\Omega_{\mathrm{m}}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021} $ for our fiducial analysis, which is in 3σ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding the results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our S8 constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data passes the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low-redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample

V.s. Deshpande - One of the best experts on this subject based on the ideXlab platform.

  • Compressive response of a 3D non-woven carbon-fibre composite
    International Journal of Solids and Structures, 2017
    Co-Authors: K. Kandan, Haydn N. G. Wadley, Sohrab Kazemahvazi, V.s. Deshpande
    Abstract:

    The compressive response of a three-dimensional (3D) non-interlaced composite comprising three Orthogonal Sets of carbon fibre tows within an epoxy matrix is analysed. First, the compressive response is measured in three Orthogonal directions and the deformation/failure modes analysed by a combination of X-ray tomography and optical microscopy. In contrast to traditional unidirectional and two-dimensional (2D) composites, stable and multiple kinks (some of which zig-zag) form in the tows that are aligned with the compression direction. This results in an overall composite compressive ductility of about 10% for compression in the low fibre volume fraction direction. While the stress for the formation of the first kink is well predicted by a usual micro-buckling analysis, the composite displays a subsequent hardening response associated with formation of multiple kinks. Finite element (FE) calculations are also reported to analyse the compressive response with the individual tows modelled as anisotropic continua via a Hill plasticity model. The FE calculations are in good agreement with the measurements including prediction of multiple kinks that reflect from the surfaces of the tows. The FE calculations demonstrate that the three-dimensionality of the microstructure constrains the kinks and this results in the stable compressive response. In fact, the hardening and peak strength of these composites is not set by the tows in direction of compression, but rather set by the out-of-plane compressive response of the tows perpendicular to the compression direction.

Maryam Ramezani - One of the best experts on this subject based on the ideXlab platform.

  • Orthogonal Sets the axiom of choice and proof of a fixed point theorem
    Journal of Fixed Point Theory and Applications, 2016
    Co-Authors: Hamid Baghani, Madjid Eshaghi Gordji, Maryam Ramezani
    Abstract:

    In this paper, we prove some fixed point theorem on Orthogonal spaces. Our result improve the main result of the paper by Eshaghi Gordji et al. [On Orthogonal Sets and Banach fixed point theorem, to appear in Fixed Point Theory]. Also we prove a statement which is equivalent to the axiom of choice. In the last section, as an application, we consider the existence and uniqueness of a solution for a Volterra-type integral equation in L p space.

Marika Asgari - One of the best experts on this subject based on the ideXlab platform.

  • kids 1000 cosmology cosmic shear constraints and comparison between two point statistics
    Astronomy and Astrophysics, 2021
    Co-Authors: Marika Asgari, Chiehan Lin, Benjamin Joachimi, Benjamin Giblin, Catherine Heymans, Hendrik Hildebrandt, Arun Kannawadi, Benjamin Stolzner, Tilman Troster, Jan Luca Van Den Busch
    Abstract:

    We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), doubling the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat $\Lambda$CDM model, we find $S_8 = \sigma_8 (\Omega_{\rm m}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021}$ for our fiducial analysis, which is in $3\sigma$ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our $S_8$ constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data pass the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample.

  • KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics
    'EDP Sciences', 2021
    Co-Authors: Marika Asgari, Chiehan Lin, Benjamin Joachimi, Benjamin Giblin, Catherine Heymans, Hendrik Hildebrandt, Arun Kannawadi, Benjamin Stolzner, Tilman Troster, Jan Luca Van Den Busch
    Abstract:

    We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), which doubles the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat standard cosmological model, we find $ S_8 = \sigma_8 (\Omega_{\mathrm{m}}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021} $ for our fiducial analysis, which is in 3σ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding the results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our S8 constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data passes the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low-redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample

K. Kandan - One of the best experts on this subject based on the ideXlab platform.

  • Compressive response of a 3D non-woven carbon-fibre composite
    International Journal of Solids and Structures, 2017
    Co-Authors: K. Kandan, Haydn N. G. Wadley, Sohrab Kazemahvazi, V.s. Deshpande
    Abstract:

    The compressive response of a three-dimensional (3D) non-interlaced composite comprising three Orthogonal Sets of carbon fibre tows within an epoxy matrix is analysed. First, the compressive response is measured in three Orthogonal directions and the deformation/failure modes analysed by a combination of X-ray tomography and optical microscopy. In contrast to traditional unidirectional and two-dimensional (2D) composites, stable and multiple kinks (some of which zig-zag) form in the tows that are aligned with the compression direction. This results in an overall composite compressive ductility of about 10% for compression in the low fibre volume fraction direction. While the stress for the formation of the first kink is well predicted by a usual micro-buckling analysis, the composite displays a subsequent hardening response associated with formation of multiple kinks. Finite element (FE) calculations are also reported to analyse the compressive response with the individual tows modelled as anisotropic continua via a Hill plasticity model. The FE calculations are in good agreement with the measurements including prediction of multiple kinks that reflect from the surfaces of the tows. The FE calculations demonstrate that the three-dimensionality of the microstructure constrains the kinks and this results in the stable compressive response. In fact, the hardening and peak strength of these composites is not set by the tows in direction of compression, but rather set by the out-of-plane compressive response of the tows perpendicular to the compression direction.