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.

FE modeling of Lamb mode diffraction by defects in anisotropic viscoelastic plates

Abstract: A Finite Element code is used in a stationary mode to compute, at a single frequency, the stress and displacement fields in plates made of anisotropic, viscoelastic materials. An appropriated spatial load at one boundary of the plate is applied to generate a guided mode. This step is included in a frequency loop for which the number of iterations (≈ usually less than 50) is defined by the frequency spectrum of a temporal excitation. Then the temporal response at any location in the plate can be reconstructed with inverse Fourier transform. The phase velocity, attenuation and nature of one or several propagating modes can be identified in the classical frequency/wave number representation. The first example concerns the interaction of the symmetric Lamb mode S0 with an opening notch in a Perspex plate. The proportion of S0 and converted antisymmetric A0 mode, transmitted past the notch is evaluated by the FE method and validated by a comparison with measurements made on a real system using an air coupled transducer. The second example shows the effect of the viscoelasticity on the propagation of the symmetric Lamb mode S0 in a cross-ply, carbon-epoxy material plate. Focus is made on some difficulties that the attenuation causes on the detection of a delamination between plies.

Symmetry breaking in dipolar matter-wave solitons in dual-core couplers

Abstract: We study the effects of spontaneous symmetry breaking (SSB) in solitons composed of a dipolar Bose-Einstein condensate trapped in a dual-core system with dipole-dipole interactions (DDIs) and hopping between the cores. Two realizations of such a matter-wave coupler are introduced: weakly and strongly coupled. The former is based on two parallel pipe-shaped traps, whereas the latter is represented by a single pipe sliced by an external field into parallel layers. The dipoles are oriented along the axes of the pipes. In these systems, the dual-core solitons feature SSB of the supercritical and subcritical types, respectively. Stability regions are identified for symmetric and asymmetric solitons and nonbifurcating antisymmetric solitons, as well as for symmetric flat states, which may also be stable in the strongly coupled system due to competition between the attractive and repulsive intracore and intercore DDIs. The effects of the contact interactions are considered too. Collisions between moving asymmetric solitons in the weakly symmetric system feature an elastic rebound, a merger into a single breather, and passage accompanied by excitation of intrinsic vibrations of the solitons for small, intermediate, and large collision velocities, respectively. A $\mathcal{PT}$-symmetric version of the weakly coupled system is considered briefly, which may be relevant for matter-wave lasers. Stability boundaries for $\mathcal{PT}$-symmetric and -antisymmetric solitons are identified.

Effect of Antisymmetric Interactions on Critical Phenomena: A System with Helical Ground State

Abstract: A classical Heisenberg Hamiltonian, to which is added single-ion anisotropy and antisymmetric Dzialoshinsky-Moriya interactions is studied with use of Wilson theory. The phase diagram is obtained; it consists of ferromagnetic, spiral, and ferromagnetic-spiral regions, with critical exponents that are Ising-like, $\mathrm{xy}$-like, and Heisenberg-like, respectively. These results lead to the conclusion that breaking of exchange symmetry does not change the nature of the phase transition. Crossover behavior is also discussed.

Few-electron molecular states and their transitions in a single InAs quantum dot molecule.

Abstract: We study electronic configurations in a single pair of vertically coupled self-assembled InAs quantum dots, holding just a few electrons. By comparing the experimental data of nonlinear single-electron transport spectra in a magnetic field with many-body calculations, we identify the spin and orbital configurations to confirm the formation of molecular states by filling both the quantum mechanically coupled symmetric and antisymmetric states. Filling of the antisymmetric states is less favored with increasing magnetic field, and this leads to various magnetic field induced transitions in the molecular states.