Adjoining Almost Disjoint Permutations

We show that it is consistent with ZFC + ¬CH that there is a maxima a most disjoint permutation family A ⊆ Sym(ℕ)such that A is a proper subset of an eventually different family E ⊆ ^ℕℕ and |A| < |E|. We also ask severa questions in this area.     

Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata

We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation, then the cardinal was originally supercompact. We then apply this theorem to show that the hypothesis of supercompactness is necessary for certain proof schemata.     

Revisiting the inhomogeneously driven sine–Gordon equation

The sine–Gordonequation is a semilinear wave equation used to model many physical phenomenon like seismic events that includes earthquakes, slow slip and after-slip processes, dislocation in solids etc. Solution of homogeneous sine–Gordon equation exhibit soliton like structure that propagates without change in its shape and structure. The question whether solution of sine–Gordon equation still exhibit soliton like behavior under an external forcing has been challenging as it is extremely difficult to obtain an exact solution even under simple forcing like constant. In this study solution to an inhomogeneous sine–Gordon equation with Heaviside forcing function is analyzed. Various one-dimensional test cases like kink and breather with no flux and non-reflecting boundary conditions are studied.     

飞机舱音记录器背景声的联合时频分析研究

飞机舱音记录器记录的舱音主要是由话语音、噪声和具有不同物理意义的背景声组成的复杂混合体,用传统的辨听和分析方法难以获取较多的舱音特征参数。本文以一个舱音记录器记录的主告警声为例,针对传统短时傅立叶变换在舱音辨听、分析的不足,将联合时频分析引入到飞机舱音分析中,扩展了舱音分析方法。对比分析结果表明:时频分布及其重排,在时频分辨率、时频凝聚性、交叉项干扰的抑制上各有所长,都适合分析非平稳舱音背景声,从而为飞行事故调查提供一种值得采用的方法。     

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.     

带强迫项的高阶中立型时滞差分方程的振动定理

本文研究带有强迫项的高阶中立型时滞差分方程的振动性.我们建立了方程(E)的新的振动准则且给出了说明定理应用的例子.     

Motion of spiral tip driven by local forcing in excitable media

We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed： the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.     

Numerical prediction of locally forced turbulent separated and reattaching flow

An unsteady numerical simulation was performed for locally forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the k––f_μ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at Re_H=33 000, and the forcing frequency was varied in the range 0St_H2. The predicted results were compared and validated with the experimental data of Chun and Chun. It was shown that the unsteady locally forced separated and reattaching flows are predicted reasonably well with the k––f_μ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.     

Simulation of two‐phase flow–body interaction problems using direct forcing/fictitious domain–level set method

In the present paper, a direct forcing/fictitious domain (DF/FD)–level set method is proposed to simulate the twophase flow–body interaction. The DF/FD does not sacrifice accuracy and robustness by employing a discrete δ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, the easy implementation and the utilization of original governing equation without modification. The main idea is to combine DF/FD method with the level set method in the Cartesian coordinates. We present the results of a number of test cases to illustrate the effectiveness of the proposed method for single‐phase flow–body interaction problem and the two‐phase flows with a stationary body. Eventually, the simulations of various water entry problems have been conducted to validate the capability and the accuracy of the present method on solving the twophase flow–body interaction. Consequently, the present results are found to be in good agreement with those of previous studies. Copyright © 2013 John Wiley & Sons, Ltd.