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.

Second Order Boltzmann–Gibbs Principle for Polynomial Functions and Applications

Abstract: In this paper we give a new proof of the second order Boltzmann–Gibbs principle introduced in Goncalves and Jara (Arch Ration Mech Anal 212(2):597–644, 2014). The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards (1) a trivial process in case of super-diffusive systems, (2) an Ornstein–Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, as defined in Gubinelli and Jara (SPDEs Anal Comput (1):325–350, 2013) and Gubinelli and Perkowski ( Arxiv:1508.07764 , 2015), in case of weakly asymmetric diffusive systems. Examples and applications are presented for weakly and partial asymmetric exclusion processes, weakly asymmetric speed change exclusion processes and hamiltonian systems with exponential interactions.

Low-energy Limits on the Antisymmetric Tensor Field Background on the Brane and on the Non-commutative Scale

Abstract: A non-vanishing vacuum expectation value for an antisymmetric tensor field leads to the violation of Lorentz invariance on the brane. This violation is controlled by the $\theta_{\mu u}$ parameter, which has a dimension of inverse mass squared. We assume that the zeroth order term in theta-expansion represents the Standard Model and study the effects induced by linear terms in theta_{\mu u}. Low-energy precision experiments place the limit on the possible size of this background at the level of $1/\sqrt{\theta} > 5 \times 10^{14}$ GeV. This poses certain difficulty for the TeV-range string scale models, in which the antisymmetric field has to acquire a relatively large mass to ensure that $\theta_{\mu u}=0$ and avoid cosmological moduli problem.

Multidimensional cosmology for intersecting p-branes with static internal spaces.

Abstract: Multidimensional cosmological model with static internal spaces describing the evolution of an Einstein space of non-zero curvature and n internal spaces is considered. The action contains several dilatonic scalar fields φ and antisymmetric forms A and Λ -term. When forms are chosen to be proportional to volume forms of p -brane submanifolds of internal space manifold, the Toda-like Lagrange representation arises. Exact solutions for the model are obtained, when scale factors of internal spaces are constant. It is shown that they are de Sitter or anti-de Sitter. Behaviour of cosmological constant and its generation by p-branes is demonstrated.

On the degeneracy problem in SU(3)

Abstract: The recent suggestion of Macfarlane, O'Raifeartaigh, and Rao that mixed Casimir operators be used to resolve the external degeneracy problem is applied to the group SU(3). The significant operator is the part of the cubic mixed Casimir operator which is antisymmetric with respect to the two factor spaces and also with respect to starred and unstarred variables. The matrix of this operator is derived with respect to a convenient set of functions and is found to have a simple form. The eigenfunctions are simply related to the usual symmetric and antisymmetric functions in the case of degeneracy 2 with equal factor representations.

A novel L-shaped linear ultrasonic motor operating in a single resonance mode.

Abstract: In this study, a large thrust linear ultrasonic motor using an L-shaped stator is described. The stator is constructed by two mutually perpendicular rectangular plate vibrators, one of which is mounted in parallel with the slider to make the motor structure to be more compact. The symmetric and antisymmetric modes of the stator based on the first order bending vibration of two vibrators are adopted, in which each resonance mode is assigned to drive the slider in one direction. The placement of piezoelectric ceramics in a stator could be determined by finite element analysis, and the influence of slots in the head block on the vibration amplitudes of driving foot was studied as well. Three types of prototypes (non-slotted, dual-slot, and single-slot) were fabricated and experimentally investigated. Experimental results demonstrated that the prototype with one slot exhibited the best mechanical output performance. The maximum loads under the excitation of symmetric mode and antisymmetric mode were 65 and 90 N, respectively.