The Experts below are selected from a list of 125985 Experts worldwide ranked by ideXlab platform
Chyouchi Chien - One of the best experts on this subject based on the ideXlab platform.
-
a Particular Integral bem time discontinuous fem methodology for solving 2 d elastodynamic problems
International Journal of Solids and Structures, 2001Co-Authors: Chyouchi ChienAbstract:Abstract This study proposes a time-discontinuous Galerkin finite element method (FEM) for solving second-order ordinary differential equations in the time domain. The equations are formulated using a Particular Integral boundary element method (BEM) in the space domain for elastodynamic problems. The Particular Integral BEM technique depends only on elastostatic displacement and traction fundamental solutions, without resorting to commonly used complex fundamental solutions for elastodynamic problems. Based on the time-discontinuous Galerkin FEM, the unknown displacements and velocities are approximated as piecewise linear functions in the time domain, and are permitted to be discontinuous at the discrete time levels. This leads to stable and third-order accurate solution algorithms for ordinary differential equations. Numerical results using the time-discontinuous Galerkin FEM are compared with results using a conventional finite difference method (the Houbolt method). Both methods are employed for a Particular Integral BEM analysis in elastodynamics. This comparison reveals that the time-discontinuous Galerkin FEM is more stable and more accurate than the traditional finite difference methods.
Chris Peterson - One of the best experts on this subject based on the ideXlab platform.
-
manifold curvature learning from hypersurface Integral invariants
Linear Algebra and its Applications, 2020Co-Authors: Javier Alvarezvizoso, Michael Kirby, Chris PetersonAbstract:Abstract Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any dimension major results known for surfaces in space, which in turn yield a method to estimate the extrinsic and intrinsic curvature tensor of an embedded Riemannian submanifold of general codimension. In Particular, Integral invariants are defined by the volume, barycenter, and the EVD of the covariance matrix of the domain. We obtain the asymptotic expansion of such invariants for a spherical volume component delimited by a hypersurface and for the hypersurface patch created by ball intersections, showing that the eigenvalues and eigenvectors can be used as multi-scale estimators of the principal curvatures and principal directions. This approach may be interpreted as performing statistical analysis on the underlying point-set of a submanifold in order to obtain geometric descriptors at scale with potential applications to Manifold Learning and Geometry Processing of point clouds.
-
manifold curvature descriptors from hypersurface Integral invariants
arXiv: Differential Geometry, 2018Co-Authors: Javier Alvarezvizoso, Michael Kirby, Chris PetersonAbstract:Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any dimension major results known for surfaces in space, which in turn yield a method to estimate the extrinsic and intrinsic curvature of an embedded Riemannian submanifold of general codimension. In Particular, Integral invariants are defined by the volume, barycenter, and the EVD of the covariance matrix of the domain. We obtain the asymptotic expansion of such invariants for a spherical volume component delimited by a hypersurface and for the hypersurface patch created by ball intersetions, showing that the eigenvalues and eigenvectors can be used as multi-scale estimators of the principal curvatures and principal directions. This approach may be interpreted as performing statistical analysis on the underlying point-set of a submanifold in order to obtain geometric descriptors at scale with potential applications to Manifold Learning and Geometry Processing of point clouds.
M A Escobarruiz - One of the best experts on this subject based on the ideXlab platform.
-
two charges on a plane in a magnetic field hidden algebra Particular integrability polynomial eigenfunctions
Journal of Physics A, 2013Co-Authors: A V Turbiner, M A EscobarruizAbstract:The quantum mechanics of two Coulomb charges on a plane (e1, m1) and (e2, m2) subject to a constant magnetic field B perpendicular to the plane is considered. Four Integrals of motion are explicitly indicated. It is shown that for two physically important Particular cases, namely that of two particles of equal Larmor frequencies, (e.g. two electrons) and one of a neutral system (e.g. the electron–positron pair, hydrogen atom) at rest (the center-of-mass momentum is zero) some outstanding properties occur. They are the most visible in double polar coordinates in CMS (R, ϕ) and relative (ρ, φ) coordinate systems: (i) eigenfunctions are factorizable, all factors except one with the explicit ρ-dependence are found analytically, they have definite relative angular momentum, (ii) dynamics in the ρ-direction is the same for both systems, it corresponds to a funnel-type potential and it has hidden sl(2) algebra, at some discrete values of dimensionless magnetic fields b ⩽ 1, (iii) Particular Integral(s) occur, (iv) the hidden sl(2) algebra emerges in finite-dimensional representation, thus, the system becomes quasi-exactly-solvable and (v) a finite number of polynomial eigenfunctions in ρ appear. Nine families of eigenfunctions are presented explicitly.
-
two charges on a plane in a magnetic field hidden algebra Particular integrability polynomial eigenfunctions
arXiv: Mathematical Physics, 2013Co-Authors: A V Turbiner, M A EscobarruizAbstract:The quantum mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field $B$ perpendicular to the plane is considered. Four Integrals of motion are explicitly indicated. It is shown that for two physically-important Particular cases, namely that of two particles of equal Larmor frequencies, ${e_c} \propto \frac{e_1}{m_1}-\frac{e_2}{m_2}=0$ (e.g. two electrons) and one of a neutral system (e.g. the electron - positron pair, Hydrogen atom) at rest (the center-of-mass momentum is zero) some outstanding properties occur. They are the most visible in double polar coordinates in CMS $(R, \phi)$ and relative $(\rho, \varphi)$ coordinate systems: (i) eigenfunctions are factorizable, all factors except one with the explicit $\rho$-dependence are found analytically, they have definite relative angular momentum, (ii) dynamics in $\rho$-direction is the same for both systems, it corresponds to a funnel-type potential and it has hidden $sl(2)$ algebra; at some discrete values of dimensionless magnetic fields $b \leq 1$, (iii) Particular Integral(s) occur, (iv) the hidden $sl(2)$ algebra emerges in finite-dimensional representation, thus, the system becomes {\it quasi-exactly-solvable} and (v) a finite number of polynomial eigenfunctions in $\rho$ appear. Nine families of eigenfunctions are presented explicitly.
Antoine Lavie - One of the best experts on this subject based on the ideXlab platform.
-
numerical analysis of eigenproblem for cavities by a Particular Integral method with a low frequency approximation of surface admittance
Journal of the Acoustical Society of America, 2012Co-Authors: Alexandre Leblanc, Antoine LavieAbstract:In this paper, a three-dimensional boundary element method for the eigenanalysis of complex-shaped cavity is presented. A Particular Integral method is proposed with general absorbing boundary conditions, well suited for determination of the lower modes. In this approach, a polynomial approximation of surface admittance is used with a recent class of compactly supported radial basis function. Two common absorbent models are employed in order to demonstrate the relevance of high-order approximation of the admittance. Resulting eigenproblems of several orders (linear to cubic) are thus performed on basic geometries and a car interior. Results show significant improvements for the computed damped eigenfrequencies and the associated modal reverberation time while using an approximation polynomial matching the surface admittance variation order.
-
compactly supported radial basis functions for the acoustic 3d eigenanalysis using the Particular Integral method
Engineering Analysis With Boundary Elements, 2012Co-Authors: Alexandre Leblanc, Alain Malesys, Antoine LavieAbstract:This paper discusses the efficiency of several Compactly Supported Radial Basis Functions (CSRBFs) for the eigenanalysis of 3D acoustic cavities using the Particular Integral Method. Starting with the two most popular CSRBF families due to Wendland and Wu, a third family proposed by Buhmann is suggested. Results on rectangular parallelepiped highlight the benefit of CSRBFs compared to the classical conical function, especially when dealing with cavities discretized by few elements. On the other hand, when the mesh is refined, numerical difficulties arise and Particular attention should be paid to the order of the employed CSRBF. Indeed, and while the conical function is likely to be the most robust function, high-order CSRBFs should be avoided. However, the proposed Buhmann's functions appear to bring significant improvements on eigenanalysis when compared to their Wendland and Wu counterparts.
-
an acoustic resonance study of complex three dimensional cavities by a Particular Integral method
Acta Acustica United With Acustica, 2005Co-Authors: Alexandre Leblanc, Antoine Lavie, Christian VanhilleAbstract:In this paper, a three-dimensional boundary element method developed to evaluate the acoustic resonance of complex cavity is presented. The formulation is based on a Particular Integral method. Neumann or mixed boundary conditions are considered. Some numerical tests are carried out and results compared to classic models. General agreement is observed. A practical eigenfrequency analysis is realized by applying the model to a complex car cabin. The Arnoldi method is used to achieve the eigenfrequencies. A good numerical behaviour is observed and its implementation and use are quite easy.
Javier Alvarezvizoso - One of the best experts on this subject based on the ideXlab platform.
-
manifold curvature learning from hypersurface Integral invariants
Linear Algebra and its Applications, 2020Co-Authors: Javier Alvarezvizoso, Michael Kirby, Chris PetersonAbstract:Abstract Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any dimension major results known for surfaces in space, which in turn yield a method to estimate the extrinsic and intrinsic curvature tensor of an embedded Riemannian submanifold of general codimension. In Particular, Integral invariants are defined by the volume, barycenter, and the EVD of the covariance matrix of the domain. We obtain the asymptotic expansion of such invariants for a spherical volume component delimited by a hypersurface and for the hypersurface patch created by ball intersections, showing that the eigenvalues and eigenvectors can be used as multi-scale estimators of the principal curvatures and principal directions. This approach may be interpreted as performing statistical analysis on the underlying point-set of a submanifold in order to obtain geometric descriptors at scale with potential applications to Manifold Learning and Geometry Processing of point clouds.
-
manifold curvature descriptors from hypersurface Integral invariants
arXiv: Differential Geometry, 2018Co-Authors: Javier Alvarezvizoso, Michael Kirby, Chris PetersonAbstract:Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any dimension major results known for surfaces in space, which in turn yield a method to estimate the extrinsic and intrinsic curvature of an embedded Riemannian submanifold of general codimension. In Particular, Integral invariants are defined by the volume, barycenter, and the EVD of the covariance matrix of the domain. We obtain the asymptotic expansion of such invariants for a spherical volume component delimited by a hypersurface and for the hypersurface patch created by ball intersetions, showing that the eigenvalues and eigenvectors can be used as multi-scale estimators of the principal curvatures and principal directions. This approach may be interpreted as performing statistical analysis on the underlying point-set of a submanifold in order to obtain geometric descriptors at scale with potential applications to Manifold Learning and Geometry Processing of point clouds.
