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.

N = 2 SU quiver with USP ends or SU ends with antisymmetric matter

Abstract: We consider the four dimensional scale invariant N = 2SU quiver gauge theories with USp(2N) ends or SU(2N) ends with antisymmetric matter representations. We argue that these theories are realized as six dimensional A2N−1 (0,2) theories compactified on spheres with punctures. With this realization, we can study various strongly coupled cusps in moduli space and find the S-dual theories. We find a class of isolated superconformal field theories with only odd dimensional operators D() ≥ 3 and superconformal field theories with only even dimensional operators D() ≥ 4.

Antisymmetric stresses in suspensions: vortex viscosity and energy dissipation

Abstract: When the individual particles in an otherwise quiescent suspension of freely suspended spherical particles are acted upon by external couples, the resulting suspension-scale fluid motion is characterized by a non-symmetric state of stress. Viewed at the interstitial scale (i.e. microscopic scale), this coupling between translational and rotational particle motions is a manifestation of particle-particle hydrodynamic interactions and vanishes with the volume fraction Φ of suspended spheres. The antisymmetric portion of the stress is quantified by the suspension-scale vortex viscosity μ v , different from the suspension's shear viscosity μ. Numerical boundary element method (BEM) simulations of such force-free suspensions of spheres uniformly dispersed in incompressible Newtonian liquids of viscosity μ 0 are performed for circumstances in which external couples (of any specified suspension-scale position-dependence) are applied individually to each of the suspended particles in order to cause them to rotate in otherwise quiescent fluids. In the absence of external forces acting on either the spheres or boundaries, such rotations indirectly, through interparticle coupling, cause translational motions of the individual spheres which, owing to the no-slip boundary condition, drag neighbouring fluid along with them. In turn, this combined particle-interstitial fluid movement is manifested as a suspension-scale velocity field, generated exclusively by the action of external couples. Use of this scheme to create suspension-scale particle-phase spin fields Ω and concomitant velocity fields v enables both the vortex and shear viscosities of suspensions to be determined as functions of 0 in disordered systems. This scheme is shown, inter alia, to confirm the constitutive equation, T a = 2μ v e · [(1/2)∇ x v - Ω], proposed in the continuum mechanics literature for the linear relation between the antisymmetric stress T a and the disparity existing between the particle-phase spin rate Ω and half the suspension's vorticity, V x v (with the third-rank pseudotensor e the permutation triadic). Our dynamically based BEM simulations confirm the previous computations of the Prosperetti et al. group for the dependence of the vortex viscosity upon the solids volume fraction in concentrated disordered suspensions, obtained by a rather different simulation scheme. Moreover, our dynamically based rheological calculations are confirmed by our semi-independent, energetically based, calculations that equate the rates of working (equivalently, the energy dissipation rates) at the respective interstitial and suspension scales. As an incidental by-product, the same BEM simulation results also verify the suspension-scale Newtonian constitutive equation, T s = μ[∇v + (∇v) † ], as well as the functional dependence of the shear viscosity μ upon Φ found in the literature.

Simulation of excited states and the sign problem in the path integral Monte Carlo method

Abstract: An approach is presented to compute properties of excited states in path integral Monte Carlo simulations of quantum systems. The approach is based on the introduction of several images of the studied system which have the total wavefunction antisymmetric over permutations of these images, and a simulation of the whole system at low enough temperature. The success of the approach relies, however, on the solution of the sign problem for the corresponding system. In the cases when the sign problem may be resolved (as for fermions in one dimension), properties of excited states can be computed with high precision. This was demonstrated by a simulation of excited states of a single particle in one- and two-dimensional harmonic oscillators. An example of the simulation of excited states of several interacting electrons in one dimension is also given.