Some new results on the weaving of K-g-frames in Hilbert spaces

In this paper, we provide some conditions for a K-woven pair of K-g-frames to be preserved under an operator and particularly, we report that applying two different operators to a K-woven pair of K-g-frames can leave them K-woven. Several new methods on the construction of K-woven pair of K-g-frames are also given. We end the paper with a new perturbation result on the weaving of K-g-frames, which shows that, under the perturbation condition involved in one known result on this topic, two K-g-frames can be K-woven in the whole space, not merely in the subspace Range(K).

On quasinormal frequencies of black hole perturbations with an external source

In the study of perturbations around black hole configurations, whether an external source can influence the perturbation behavior is an interesting topic to investigate. When the source acts as an initial pulse, it is intuitively acceptable that the existing quasinormal frequencies will remain unchanged. However, the confirmation of such an intuition is not trivial for the rotating black hole, since the eigenvalues in the radial and angular parts of the master equations are coupled. We show that for the rotating black holes, a moderate source term in the master equation in the Laplace s-domain does not modify the quasinormal modes. Furthermore, we generalize our discussions to the case where the external source serves as a driving force. Different from an initial pulse, an external source may further drive the system to experience new perturbation modes. To be specific, novel dissipative singularities might be brought into existence and enrich the pole structure. This is a physically relevant scenario, due to its possible implication in modified gravity. Our arguments are based on exploring the pole structure of the solution in the Laplace s-domain with the presence of the external source. The analytical analyses are verified numerically by solving the inhomogeneous differential equation and extracting the dominant complex frequencies by employing the Prony method.

Chiral perturbation theory for GR

We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.

First characterization of a new perturbation system for gust generation: the chopper

We present a new system for the generation of rapid, strong flow perturbations in the aerodynamic wind tunnel at École Centrale de Nantes. The system is called the chopper, and it consists of a rotating bar cutting through the inlet of a wind tunnel test section, thus generating an inverse gust that travels downstream. The flow generated by the chopper is investigated with respect to the rotational frequency using an array equipped with hot-wires that is traversed downstream in the flow field. It is found that the gust can be described as a superposition of the mean gust velocity, an underlying gust shape, and additional turbulence. Following this approach, the evolution of the mean gust velocity and turbulence intensity are presented, and the evolution of the underlying inverse gust shape is explained. The turbulence is shown to be characterized by an integral length scale of approximately half the chopper blade width and a turbulence decay according to E(f)∝f-5/3.

Characterization of a new perturbation system for gust generation: The Chopper

We present a new system for the generation of rapid, strong flow disturbances in a wind tunnel that was recently installed at Ecole Centrale Nantes. The system is called the chopper, and it consists of a rotating bar cutting through the inlet of a wind tunnel test section, thus generating a gust that travels downstream. The flow generated by the chopper is investigated with respect to the rotational frequency using an array equipped with hot-wires that is traversed downstream the flow field. It is found that the gust can be described as a superposition of the mean gust velocity, an underlying gust shape and additional turbulence. Following this approach, the evolution of the mean gust velocity and turbulence intensity are presented, and the evolution of the underlying gust shape is explained. The turbulence is shown to be characterized by an integral length scale of approximately half the chopper blade width and a turbulence decay according to E(f) ∝ f−5/3.

An Efficient Laguerre-Based FDTD Iterative Algorithm in 3D Cylindrical Coordinate System

Here an efficient Laguerre-based finite-difference time-domain iterative algorithm is proposed. Different from the previously developed iterative procedure used in the efficient FDTD algorithm, a new perturbation term combined with the Gauss–Seidel iterative procedure is introduced to form the new Laguerre-based FDTD algorithm in the 3D cylindrical coordinate system. Such a treatment scheme can reduce the splitting error to a low level and obtain a good convergence; in other words, it can improve the efficiency and accuracy than other algorithms. To verify the performance of the proposed algorithm, two scattering numerical examples are given. The computation results show that the proposed algorithm can be better than the ADI-FDTD algorithm in terms of efficiency and accuracy. Meanwhile, the proposed algorithm is extremely useful for the problems with fine structures in the 3D cylindrical coordinate system.