Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems [PDF]
Journal of Computational and Nonlinear Dynamics, 2021 Abstract This article presents methods to efficiently compute the Coriolis matrix and underlying Christoffel symbols (of the first kind) for tree-structure rigid-body systems. The algorithms can be executed purely numerically, without requiring partial derivatives as in unscalable symbolic techniques.
Patrick M Wensing
exaly +3 more sources
Ultrasonic Phased Array Imaging Approach Using Omni-Directional Velocity Correction for Quantitative Evaluation of Delamination in Composite Structure [PDF]
Sensors, 2023 The ultrasonic detectability of buried defects within composite materials is dependent on the anisotropy of the composite material by which the propagation property of acoustic wave in each direction is variably affected.
Xiangting Xu +4 more
doaj +2 more sources
Generalized Christoffel–Darboux formula for skew-orthogonal polynomials and random matrix theory [PDF]
Journal of Physics A, 2006 We obtain generalized Christoffel-Darboux (GCD) formula for skew-orthogonal polynomials (SOP). Using this, we present an alternative derivation of the level density and two-point function for Gaussian orthogonal ensembles (GOE) and Gaussian symplectic ensembles (GSE) of random matrices.
Saugata Ghosh
exaly +3 more sources
On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials
Journal of Mathematical Analysis and Applications, 2014 We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal ...
Manuel Manas
exaly +4 more sources
Photon-Sphere Modes in Curved Optical Microcavities: A Black-Hole Analogue Laser. [PDF]
Adv Sci (Weinh)An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Xu C +9 more
europepmc +2 more sources
Enhancement Efficiency of Calculation of the Phonon Images for GaP Piezoelectric Crystal [PDF]
مجلة التربية والعلم, 2022 In this paper an improved phonon imaging for GaP has been calculated, this crystal is one of III-V group. In the presence of piezoelectric properties, the computation treatment is based on increasing the number of points in the reduced Brillouin zone and
Mumtaz Hussien, abeer bader
doaj +1 more source
Matrix biorthogonal polynomials on the real line: Geronimus transformations [PDF]
Bulletin of Mathematical Sciences, 2019 In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegenerate continuous sesquilinear form, which in turn is determined ...
Gerardo Ariznabarreta +3 more
doaj +1 more source
Computation of velocities and polarization vectors in weakly anisotropic media
Геофизический журнал, 2021 To compute the phase velocities in the weakly anisotropic media, we propose to transform the Christoffel matrix K into an adapted coordinate system, and, then, apply the perturbation theory to the resulting matrix X. For a weakly anisotropic medium, the
Yu. V. Roganov +2 more
doaj +1 more source
Properties of singular points in a special case of orthorhombic media
Геофизический журнал, 2023 The position of singular lines for orthorhombic (ORT) media with fixed diagonal elements of the elasticity matrix cij, i=1…6 is studied under the condition that c11, c22, c33>c66>c44>c55.
Yu.V. Roganov, A. Stovas, V.Yu. Roganov
doaj +1 more source
Location of singular points in orthorhombic media
Геофизический журнал, 2022 The dependence of the location of singular points of orthorhombic (ORT) media on the stiffness coefficients , and phase velocity at the singularity point is studied under the assumption that are larger than and .
Yu.V. Roganov +2 more
doaj +1 more source