Diffraction of a Plane Discontinuos Wave in Layered Anisotropic Elastic Media

The problem of transformation of the front of a plane longitudinal shock wave by curvilinear interfaces of layered anisotropic elastic media with different mechanical properties is considered. To solve the nonlinear Snell equations, the approach based on a synthesis of the Newton method and the algorithm of parametric continuation of a solution is used. The cases of focusing and scattering of rays by convex and concave interfaces of layered composite media and by convex lenses are investigated. Numerical examples are given for various ratios between the parameters of the elastic media.     

REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

The authors consider the Cauchy problem for the following nonlinear wave equationswhere x ∈ R3, t ≥ 0, ε > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ε, then the lifespan T(ε) satisfies the folowing inequalities     

Travelling waves for reaction-diffusion equations with time depending nonlinearities

The existence of travelling wave with given end points for parabolic system of nonlinear equations is proven. The nonlinear term depends also on a·x−ct where x is the multidimensional space variable, t—time, c—the speed of the wave and a—the direction of travel.     

Analytic continuation and identities involving heat,Poisson, wave and Bessel kernels

In this article we use classical formulas involving the K–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromorphic continuation of the associated Poisson kernel to all values of complex time with identifiable singularities. This result reproves in a different setting by different means a well–known theorem due to Duistermaat and Guillemin [DG 75]. Also, we develop analytic expressions for the heat kernel beyond asymptotic expansions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum Euler-Poisson System: Local Existence of Solutions

The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects. The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity, where the pressure-density is general (can be non-convex or non-monotone).     

Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions

Summary A tool for analyzing spatio-temporal complex physical phenomena was recently proposed by the authors, Aubry et al. [5]. This tool consists in decomposing a spatially and temporally evolving signal into orthogonal temporal modes (temporal “structures”) and orthogonal spatial modes (spatial “structures”) which are coupled. This allows the introduction of a temporal configuration space and a spatial one which are related to each other by an isomorphism. In this paper, we show how such a tool can be used to analyze space-time bifurcations, that is, qualitative changes in both space and time as a parameter varies. The Hopf bifurcation and various spatio-temporal symmetry related bifurcations, such as bifurcations to traveling waves, are studied in detail. In particular, it is shown that symmetry-breaking bifurcations can be detected by analyzing the temporal and spatial eigenspaces of the decomposition which then lose their degeneracy, namely their invariance under the symmetry. Furthermore, we show how an extension of the theory to “quasi-symmetries” permits the treatment of nondegenerate signals and leads to an exponentially decreasing law of the energy spectrum. Examples extracted from numerically obtained solutions of the Kuramoto-Sivashinsky equation, a coupled map lattice, and fully developed turbulence are given to illustrate the theory.     

相关技术在滚动轴承故障诊断中的应用

众所周知自相关技术能够有效地从随机嘈声中提取周期性信号.在滚动轴承元件的故障诊断中,由于信号图象不同,我们无法从原信号直接得到故障的情况,这种信号的显示就像宽频带随机嘈声在自相关函数的显示一样.本文中,信号经过了预处理,其结果证明是行之有效的.应用自相关技术我们还可以得到已测定的可比采样,这对于建立轴承运行条件的数据基础和进行故障诊断是十分重要的.     

关于非线性波动方程的爆破现象

通过引入一类“爆破因子K(u,ut）”,讨论了非线性波动方程分别具Newmann边界条件和Dirichlet边界条件时,混合问题对于常见的各种非线性情形及初值条件,解在有限时间内的爆破行为。     

Transport phenomena in a plane shock wave

With the use of the nonpolynomial closure 1/ _z in the Mott-Smith approximation of the solution of the Boltzmann equation, we obtain a value of the density gradient in the limit of a very weak shock wave that is close to the correct value. For the determination of the transverse temperature gradient we calculated the _x ² / _z moment of the Mott-Smith collision integral. The effective values of viscosity and thermal conductivity in the limit of a very weak shock wave were calculated for inverse-power potentials and found to agree almost exactly with the Chapman-Enskog values. Such a comparison can serve as a criterion for the evaluation of different bimodal theories. Various bimodal theories give different values of viscosity and thermal conductivity, but all of them give 33 % too high a value of the Eucken ratio.