Topic
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.
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TL;DR: In this paper, the complete N = 8 d = 5 supergravity action and supersymmetry transformation laws (without four and three-fermion terms) were obtained from the ungauged model by reinterpreting part of the field strenghts of the abelian vector fields as real self-dual second-rank antisymmetric tensors.
199 citations
TL;DR: A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented in this article, which is a generalization of Mindlin's theory for isotropic plates to laminated aisotropic plates and includes shear deformation and rotary inertia effects.
196 citations
TL;DR: In this paper, three local criteria for the identification of vortices are analyzed and discussed; they are based on the analysis of invariants of the velocity gradient tensor ▿u or invariant of the tensor S 2 + Ω 2, where S and Ω are the symmetric and antisymmetric parts of ▾u.
Abstract: Three proposed local criteria for the identification of vortices are analyzed and discussed; they are based on the analysis of invariants of the velocity gradient tensor ▿u or invariants of the tensor S 2 +Ω 2 , where S and Ω are the symmetric and antisymmetric parts of ▿u. Moreover, a tentative non-local procedure is proposed, which takes advantage of the observation that vortices tend to be made up of the same fluid particles; this leads to the definition of a Galilean invariant quantity, which can be computed and used to identify vortical structures. Three analytical flow fields are used for a comparative evaluation of both local and non-local criteria, which allows a deeper understanding of the physical meaning of the considered techniques.
195 citations
TL;DR: In this article, the dominant axisymmetric (AAS) modes in a cylinder containing liquid with a free surface are subjected to a vertical oscillation of amplitude eg/ω2 and frequency 2ω, where ω is within O(eω) of the natural frequency of a particular (primary) mode in the surface wave spectrum and 0 δ, where δ is the damping ratio (actual/critical) of a primary mode, is a necessary condition for subharmonic response of that mode.
Abstract: A cylinder containing liquid with a free surface is subjected to a vertical oscillation of amplitude eg/ω2 and frequency 2ω, where ω is within O(eω) of the natural frequency of a particular (primary) mode in the surface-wave spectrum and 0 δ, where δ is the damping ratio (actual/critical) of the primary mode, is a necessary condition for subharmonic response of that mode. Explicit results are given for the dominant axisymmetric and antisymmetric modes in a circular cylinder. Internal resonance, in which a pair of modes have frequencies that approximate ω and 2ω, is discussed separately, and the fixed points and their stability for the special case ω2 = 2ω1 are determined. Internal resonance for ω2 = ω1 is discussed in an appendix.
188 citations
TL;DR: The derivation of a model for the simulation of phase transformations in multicomponent real alloys starting from a grand-potential functional is described and a modification to the model is proposed in order to decouple the bulk and interface contributions.
Abstract: In this paper, we describe the derivation of a model for the simulation of phase transformations in multicomponent real alloys starting from a grand-potential functional. We first point out the limitations of a phase-field model when evolution equations for the concentration and the phase-field variables are derived from a free energy functional. These limitations are mainly attributed to the contribution of the grand-chemical-potential excess to the interface energy. For a range of applications, the magnitude of this excess becomes large and its influence on interface profiles and dynamics is not negligible. The related constraint regarding the choice of the interface thickness limits the size of the domain that can be simulated and, hence, the effect of larger scales on microstructure evolution can not be observed. We propose a modification to the model in order to decouple the bulk and interface contributions. Following this, we perform the thin-interface asymptotic analysis of the phase-field model. Through this, we determine the thin-interface kinetic coefficient and the antitrapping current to remove the chemical potential jump at the interface. We limit our analysis to the Stefan condition at lowest order in $\ensuremath{\epsilon}$ (parameter related to the interface width) and apply results from previous literature that the corrections to the Stefan condition (surface diffusion and interface stretching) at higher orders are removed when antisymmetric interpolation functions are used for interpolating the grand-potential densities and the diffusion mobilities.
184 citations