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.

Higher-order shear deformation theory for thin-walled composite beams

Abstract: A higher-order shear deformation theory for the static and dynamic analysis of thin-walled composite beams of arbitrary lay-ups and cross sections is presented. The method is applicable to beams of open as well as closed cross sections. The formulation includes Euler-Bernoulli and Timoshenko theories as subsets. The bendingand torsion-related warping functions are derived in closed form. The method is validated by comparison with experimental and analytical results for static deflections of composite beams with symmetric and antisymmetric lay-ups. Comparison with experimental results for the vibration of beams exhibiting bending torsion coupling shows that the present method gives better correlations. The significance of the higher-order theory is brought out by validating the results of the analyses against results from other theoretical methods. The results show the importance of the lay-up sequence on the shear lag in thin-walled composite beams.

Dynamical Lorentz symmetry breaking in a tensor bumblebee model

Abstract: In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor; calculate the one-loop effective potential of the (pseudo)tensor field; and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrary to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.

Examples of embedded eigenvalues for problems in acoustic waveguides

Abstract: This short article discusses the spectrum of the Neumann Laplacian in the infinite domain Ω ⊂ R n , n ≥ 2 created by inserting a compact obstacle P into the uniform cylinder Ω 0 = (- ∞, ∞) × Ω'. The main result is the existence of at least one embedded eigenvalue when P is an (n - 2)-dimensional surface whose unit normal is parallel to Ω' at each point of P. The special case when P is symmetric about {0} × Ω' is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector.

Free vibration of thick laminated circular and annular plates using three-dimensional finite element analysis

Abstract: This paper presents a numerical analysis of free vibration of thick laminated circular plates, having free, clamped as well as simply-supported boundary conditions at outer edges. The finite element method that works on the basis of three-dimensional theory of elasticity is employed to evaluate the first ten natural frequencies of uniform circular plate. The effect of thickness ratios, fiber orientation angle (angle-ply and cross-ply), stacking sequences (symmetric and antisymmetric), radius ratios and boundary conditions on frequency parameter are discussed in detail. The first five natural modes of flexural vibrations for different boundary conditions are presented in pictorial forms. Verification of the accuracy of these results is verified by appropriate convergence study and checked with the results available in the literature.

Snakes and ghosts in a parity-time-symmetric chain of dimers.

Abstract: We consider linearly coupled discrete nonlinear Schrodinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time (PT)-symmetric coupler composed by a chain of dimers. We study uniform states and site-centered and bond-centered spatially localized solutions and present that each solution has a symmetric and antisymmetric configuration between the arms. The symmetric solutions can become unstable due to bifurcations of asymmetric ones, that are called ghost states, because they exist only when an otherwise real propagation constant is taken to be complex valued. When a parameter is varied, the resulting bifurcation diagrams for the existence of standing localized solutions have a snaking behavior. The critical gain and loss coefficient above which the PT symmetry is broken corresponds to the condition when bifurcation diagrams of symmetric and antisymmetric states merge. Past the symmetry breaking, the system no longer has time-independent states. Nevertheless, equilibrium solutions can be analytically continued by defining a dual equation that leads to ghost states associated with growth or decay, that are also identified and examined here. We show that ghost localized states also exhibit snaking bifurcation diagrams. We analyze the width of the snaking region and provide asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained.