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.

Dynamics of higher-order solitons in regular and PT-symmetric nonlinear couplers

Abstract: Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi-solitons are found. In the PT-symmetric system, with the balanced gain and loss acting in the two cores, borders of the stability against the blowup are identified. Notably, in all the cases the stability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts, on the contrary to previously known results for fundamental solitons (N=1). Dynamical regimes (switching) are also studied for the 2-soliton injected into a single core of the coupler. In particular, a region of splitting of the input into a pair of symmetric solitons is found, which is explained as a manifestation of the resonance between the vibrations of the 2-soliton and oscillations of energy between the two cores in the coupler.

Preservation of properties of fuzzy relations during aggregation processes

Abstract: Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy relations R 1 ,.. R n and n-argument operation F on the interval [0,1], a new fuzzy relation R F = F(R 1 ,..,R n ) is created. Characterization theorems concerning the problem of preservation of fuzzy relations properties are given. Some conditions on aggregation functions are weakened in comparison to those previously given by other authors.

Chirality-induced antisymmetry in magnetic domain wall speed

Abstract: In chiral magnetic materials, numerous intriguing phenomena such as built-in chiral magnetic domain walls (DWs) and skyrmions are generated by the Dzyaloshinskii–Moriya interaction (DMI). The DMI also results in asymmetric DW speeds under an in-plane magnetic field, which provides a useful scheme to measure the strength of the DMI. However, recent findings of additional asymmetries such as chiral damping have inhibited the unambiguous determination of the DMI strength, and the underlying mechanism of overall asymmetries comes under debate. Here, we experimentally investigate the nature of the additional asymmetry by extracting the DMI-induced symmetric contribution from the DW speed. Our results reveal that the additional asymmetry has a truly antisymmetric nature with the typical behavior governed by the DW chirality. In addition, the antisymmetric contribution alters the DW speed by a factor of 100, dominating the overall variation in DW speed. Thus, experimental inaccuracies can be largely removed by calibration with such antisymmetric contributions, enabling the standard DMI measurement scheme. Fast-moving domain walls separating regions with spin-up or spin-down states are desirable for high-performance spintronic memory and logic devices. The Dzyaloshinskii–Moriya interaction gives rise to an asymmetric distribution of domain wall speeds in chiral magnetic materials, providing a convenient way to determine the strength of the interaction. However, the recent discovery of additional asymmetries has complicated the analysis of measurements. Now, Sug-Bong Choe from Seoul National University and co-workers have experimentally determined the chiral nature of the additional symmetry for the first time. This contribution, which could arise from either a form of energy dissipation called chiral damping or from natural variations in domain wall widths, can alter domain wall speeds by a factor of 100. Chiral magnetic domain-wall (DW) speed variation is investigated. We demonstrate that the symmetric contribution in the DW speed attributes to the chiral DW energy density. Next, by deducing this symmetric contribution, the additional asymmetry was extracted. The extracted additional asymmetry exhibits truly antisymmetric nature and is governed by DW chirality. Moreover, this antisymmetry (additional asymmetry) changes overall DW speed more than a factor of 100 to the extent of dominating the symmetric contribution. These findings not only provide the artifact-free Dyzaloshinskii–Moriya interaction measurement scheme, but also contribute to the investigation of the origin of the additional asymmetry.

Coframe Energy–Momentum Current. Algebraic Properties

Abstract: The coframe (teleparallel) description of gravity is known as a viable alternative to GR. One of advantages of this model is the existence of a conserved energy–momentum current witch is covariant under all symmetries of the three-parameter Lagrangian. In this paper we study the relation between the covector valued current and the energy–momentum tensor. Algebraic properties of the conserved current for different values of parameters are derived. It is shown that the tensor corresponding to the coframe current is traceless and, in contrast to the electromagnetic field, has in general a non vanishing antisymmetric part. The symmetric part is also non zero for all values of the parameters. Consequently, the conserved current involves the energy–momentum as well as the rotational (spin) properties of the field.