Discussion on the geometric structure of strange attractor

We discuss the transversal heteroclinic cycle formed by hyperbolic periodic pointes of diffeomorphism on the differential manifold. We point out that every possible kind of transversal heteroclinic cycle has the Smalehorse property and the unstable manifolds of hyperbolic periodic points have the closure relation mutually. Therefore the strange attractor may be the closure of unstable manifolds of a countable number of hyperbolic periodic points. The Henon mapping is used as an example to show that the conclusion is reasonable.

The geometric structure and dynamic properties of lauwerier attractor

 Introduction The strange chaotic attractor (ACS) is an important subject in the nonlinear field. On the basis of the theory of transversal heteroclinic cycles, it is suggested that the strange attractor is the closure of the unstable manifolds of countable infinite hyperbolic periodic points. From this point of view some nonlinear phenomena are explained reasonably. 更多还原

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.

激光二极管端面抽运Nd∶YVO_4板条激光器及其热效应

激光器中激光介质采用板条状几何结构可以极大地降低它的热效应,但仍然需要进一步分析其影响,进而优化激光器效率。利用有限元分析方法分析了部分端面抽运的混合腔板条激光器中激光介质的热效应,计算的热透镜焦距与实测结果基本相符。分析了热效应对模式匹配的影响,分析结果对于优化激光器效率、改进谐振腔设计具有一定的参考价值。并在分析的基础上进行了混合腔实验,抽运功率为110 W时,获得连续输出激光功率41.5 W,光-光转换效率约38%,斜效率达58.8%,M2因子为非稳腔方向M2x=1.59,稳定腔方向M2y=1.55。

地震反射界面形态与介质各向异性属性联立成像：地震反射波旅行时与偏振信息综合反演

It has been a difficult problem faced by seismologists for long time that how exactly to reconstruct the earth's geometric structure and distribution of physical attributes according to seismic wave's kinematical and dynamic characteristics, obtained in seismological observation. The jointing imaging of seismic reflector and anisotropy attributes in the earth interior is becoming the research hot spot. The limitation of shoot and observation system makes that the obtained seismic data are too scarce to exactly reconstruct the geological objects. It is popular that utilizing only seismic reflection traveltimes or polarizations information make inversion of the earth's velocity distribution by fixing seismic reflector configuration (vice versa), these will lead to the serious non-uniqueness reconstruction due to short of effective data, the non-uniqueness problem of reconstructing anisotropy attributes will be more serious than in isotropy media. Obviously it is not enough to restrict the media structure only by information of seismic reflection traveltimes or polarizations, which even sometimes will lead to distorted images and misinterpretation of subsurface structure. So we try to rebuild seismic reflection structure (geometry) and media anisotropic structure (physics) in the earth interior by jointing data of seismic wave kinematics and dynamics characteristics, we carry out the new experiment step by step, and the research mainly comprises of two parts: one is the reconstruction of P-wave vertical velocity and anisotropic structure(Thomsen parameter s and 8) in the transversely isotropic media with vertical symmetrical axis(VTI) by fixing geometrical structure, and the other is the simultaneous inversion of the reflector surface conformation and seismic anisotropic structure by jointing seismic reflection traveltimes and polarizations data. Simulated annealing method is used to the first research part, linear inversion based on BG theory and Simulated annealing are applied to the second one. All the research methods are checked by model experiments, then applied to the real data of the wide-angle seismic profile from Tunxi, Anhui Province, to Wenzhou, Zhejiang Province. The results are as following The inversion results based on jointing seismic PP-wave or PSV-wavereflection traveltimes and polarizations data are more close to real model than themodels based simply on one of the two data respectively. It is shown that the methodwe present here can effectively reconstruct the anisotropy attributes in the earth'sinterior when seismic reflector structure is fixed.The layer thickness, P-wave vertical velocity and Thomsen anisotropicparameters {s and 8) could be resolved simultaneously by jointing inversion ofseismic reflection traveltimes and polarizations with the linear inversion methodbased on BG theory.The image of the reflector structure, P-wave vertical velocity and theanisotropy parameters in the crust could be obtained from the wide-angle seismicprofile from Tunxi (in Anhui Province), to Wenzhou (in Zhejiang Province). Theresults reveal the difference of the reflector geometrical structure and physicalattributes in the crust between Yangtze block and Cathaysia block, and attempt tounderstand the characteristics of the crustal stress field in the areas.

Preparation of supported PtRu/C electrocatalyst for direct methanol fuel cells

In this work, high-surface supported PtRu/C were prepared with Ru(NO)(NO3)(3) and [Pt(H2NCH2CH2NH2)(2)]Cl-2 as the precursors and hydrogen as a reducing agent. XRD and TEM analyses showed that the PtRu/C catalysts with different loadings possessed small and homogeneous metal particles. Even at high metal loading (40 wt.% Pt, 20 wt.% Ru) the mean metal particle size is less than 4 nm. Meanwhile, the calculated Pt crystalline lattice parameter and Pt (220) peak position indicated that the geometric structure of Pt was modified by Ru atoms. Among the prepared catalysts, the lattice parameter of 40-20 wt.% PtRu/C contract most. Cyclic voltammetry (CV), chronoamperometry (CA), CO stripping and single direct methanol fuel cell tests jointly suggested that the 40-20 wt.% PtRu/C catalyst has the highest electrochemical activity for methanol oxidation. (c) 2004 Elsevier Ltd. All rights reserved.

Structure approximate based on double weighted neural network

Double weighted neural network; is a kind of new general used neural network, which, compared with BP and RBF network, may approximate the training samples with a move complicated geometric figure and possesses a even greater approximation. capability. we study structure approximate based on double weighted neural network and prove its rationality.

Spatial structure of internal tidal waves generated on weak topographies

The generation of internal gravity waves by barotropic tidal flow passing over a two-dimensional topography is investigated. Rather than calculating the conversion of tidal energy, this study focuses on delineating the geometric characteristics of the spatial structure of the resulting internal wave fields (i.e., the configurations of the internal beams and their horizontal projections) which have usually been ignored. it is found that the various possible wave types can be demarcated by three characteristic frequencies: the tidal frequency, wo; the buoyancy frequency, N; and the vertical component of the Coriolis vector or earth's rotation.f. When different possibilities arising from the sequence of these frequencies are considered, there occur 12 kinds of wave structures in the full 3D space in contrast to the 5 kinds identified by the 2D theory. The constant wave phase lines may form as ellipses or hyperbolic lines on the horizontal plane, provided the buoyancy frequency is greater or less than the tidal frequency. The effect that stems from the consideration of the basic flow is also found, which not only serves as the reason for the occurrence of higtter harmonics but also increases the wave strength in the direction of basic flow. (C) 2009 Elsevier B.V. All rights reserved.

Studies on the structure and properties of thermotropic liquid crystalline poly(aryl ether ketone)s

Series of thermotropic liquid crystalline poly (aryl ether ketone) s were synthesized by mucleophilic substitution reactions of 4,4'-biphenol and substituted hydroquinone with different difluoromonomers, The relationship between structure and properties of the novel copolymers was investigated. For the copolymers with liquid crystalline properties, their melting transition temperatures show no great change with increase the content of the crystal-disrupting unit. The reason is that the crystal phase is directly transformed from the ordered liquid crystal phase. Side-groups have important effect on mesophase stability, The temperature range of mesophase stability for the chloro-polymers is smaller than those of other series of copolymers (P-phenyl, t-butyl, methoxy, 3-trifluoromethylbenzene). This behavior indicates that the effect of geometric repulsive factor on the thermodynamic stability of the mesophase is much larger than that of the polarizability attractive factor. Different ordered liquid crystal phases are observed in the polymers with different molecular weights. At low molecular weight, highly ordered smectic liquid crystal phases form. With increasing the molecular weight, the ordered degree of the liquid crystals decreases, and only the nematic liquid crystal phase is observed in the polymer with higher molecular weight.