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Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the sag-to-span ratio of the cable considered is such that the natural frequency of the first symmetric in-plane mode is at first crossover, which may result in two to one and one-toone internal resonances.
Abstract: We investigate the nonlinear nonplanar responses of suspended cables to external excitations. The equations of motion governing such systems contain quadratic and cubic nonlinearities, which may result in two-to-one and one-to-one internal resonances. The sag-to-span ratio of the cable considered is such that the natural frequency of the first symmetric in-plane mode is at first crossover. Hence, the first symmetric in-plane mode is involved in a one-to-one internal resonance with the first antisymmetric in-plane and out-of-plane modes and, simultaneously, in a two-to-one internal resonance with the first symmetric out-of-plane mode. Under these resonance conditions, we analyze the response when the first symmetric in-plane mode is harmonically excited at primary resonance. First, we express the two governing equations of motion as four first-order (i.e., state-space formulation) partial-differential equations. Then, we directly apply the methods of multiple scales and reconstitution to determine a second...

101 citations

Journal ArticleDOI
TL;DR: In this paper, a lower bound of the size of the support for a given regularity exponent to achieve symmetry and antisymmetry is derived for compactly supported o.n. wavelets with scale factor a = 3.

101 citations

Journal ArticleDOI
TL;DR: In this paper, a combined finite element and Lamb wave modal expansion method is presented for analysing scattering of time harmonic Lamb waves by material and geometric irregularities in an isotropic linearly elastic infinite plate.

101 citations

Journal ArticleDOI
R.J. Noll1, S.H. Macomber1
TL;DR: In this paper, an approach to the analysis of grating-coupled semiconductor lasers is presented, where it is shown that there are only two resonant solutions when the grating has infinite extent and the solutions are either symmetric or antisymmetric about the center of the longitudinal coordinate system.
Abstract: An approach to the analysis of grating-coupled semiconductor lasers is presented. It is shown that there are only two resonant solutions when the grating has infinite extent. The solutions are either symmetric or antisymmetric about the center of the longitudinal coordinate system where the antisymmetric solution is nonradiating. The field in the grating layer is expressed in terms of grating eigenfunctions and rigorously matched to the boundary conditions at the waveguide interface. Solutions to the finite-length grating problem are expressed as linear combinations of the infinite-length solutions. It is shown that the two diffraction parameters in the coupled-wave equations are composed of sums and differences of the eigenvalues from the infinite-length problem. >

101 citations

Journal ArticleDOI
TL;DR: It is shown that the collision term in the Boltzmann equation vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity.
Abstract: We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-$1/2$ particles. To next-to-lowest order in $\ensuremath{\hbar}$, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

100 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023145
2022286
2021109
2020112
2019118
2018122