一个渐近非线性二阶两点边值问题的存在性

利用拓扑度理论获得了一个渐近非线性二阶两点边值问题的存在定理。     

Ultrafast photo-induced turning of magnetization and its relaxation dynamics in GaMnAs

We report that,by linearly polarized pumping of different wavelengths,Kerr transients appear at zero magnetic field only in the case when GaMnAs samples are initialized at 3 K by first applying a 0.8 Tesla field and then returning to zero field.We find that,instead of magnetization precession,the near-band gap excitation induces a coherent out-of-plane turning of magnetization,which shows very long relaxation dynamics with no precession.When photon energy increases,the peak value of the Kerr transient incre...     

Lower bounds for blow-up time in a nonlinear parabolic problem

For a parabolic problem with a gradient nonlinearity which was introduced by Chipot and Weissler [M. Chipot, F.B. Weissler, Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal. 20 (1989) 886-907] (see also [B. Kawohl, L.A. Peletier, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989) 207-217]), the question of blow-up is investigated. Specifically, if the solution blows up, a lower bound for the time of blow-up is derived     

Nonlinear inversion of strong scatterer of elastic wave for two parameters in half-space

The inversion of strong scatterer embedded in the half-space is an important problem in engineering and a very difficult nonlinear problem in mathematics, for which the Born iterative method is of no effect. In this paper the moment method is used in the discretization procedure. A numerical approach is presented by employing the regularization technique and DBI (distorted Born iterative) method. The simulation results show that the approach presented is efficient. Project supported by the Research Fund for the Doctoral Program of Higher Education (RFDP: 98048705).     

Comparing Metrics at Large: Harmonic vs Quo-Harmonic Coordinates

To compare two space-times on large domains, and in particular the global structure of their manifolds, requires using identical frames of reference and associated coordinate conditions. In this paper we use and compare two classes of time-like congruences and corresponding adapted coordinates: the harmonic and quo-harmonic classes. Besides the intrinsic definition and some of their intrinsic properties and differences we consider with some detail their differences at the level of the linearized approximation of the field equations. The hard part of this paper is an explicit and general determination of the harmonic and quo-harmonic coordinates adapted to the stationary character of three well-know metrics, Schwarzschild's, Curzon's and Kerr's, to order five of their asymptotic expansions. It also contains some relevant remarks on such problems as defining the multipoles of vacuum solutions or matching interior and exterior solutions.     

Electro-optic response of cubic liquid crystal compounds in Kerr cell geometry

We present the results of our investigations on the electro-optic response of the cubic phase liquid crystal compounds 1,2-bis-[4-n-octyloxy-benzoyl]-hydrazine (BABH8) and 4'-n-hexadecyloxy-3'-nitrobiphenyl-4-carboxylic acid (ANBC16) in Kerr cell geometry. The AC electric field response in the BABH8 cubic phase was found to be as small as that of the isotropic phase, even though there was a response in the adjacent smectic C (SmC) phase. The response in the SmC phase means that the BABH8 molecule itself has an electric field coupling ability, but this ability is strongly inactivated in the cubic phase. This inactivity to the AC fields was also found in the cubic phase of ANBC16. This behaviour could be explained by the small structural unit size of the cubic phase.     

Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Bifurcations and chaos in parametrically excited single-degree-of-freedom systems

The behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated. Both fundamental and principal parametric resonances are considered. A global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady-state solutions (attractors). Fractal basin maps for fundamental and principal parametric resonances when three attractors coexist are presented in color. An enlargement of one region of the map for principal parametric resonance reveals a Cantor-like set of fractal boundaries. For some cases, both periodic and chaotic attractors coexist.