Interaction of elementary waves for relativistic Euler equations

In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.     

分层流体中弧立波的理论分析和符号运算研究

The study of solitary waves has been a subject highly popular and full of interest sinec Russell[1]first observed the solitary waves in a channel and the research on the internal solitary waves in stratified fluids is one of the branches of this subject.There are extensively internal solitary waves in the atmosphere,oceans.fjords and lakes.To study them is of academic and practical significance[2].Numerous investigators have made contributions since the theoretical work on internal solitary waves was initiated by Keulegan[3].Nevertheless,some problems remain still to be discussed,for example,the higher-order theories for one-dimensional internal solitary waves in stratified fluids of small depth,the two-dimensional internal solitary waves,the explanation of the experimental and the practical phenomena by means of theoretical analysis.In this thesis,we hope to gain an insight into the above three items by combining of theoretical analysis and symbolic computation.The following work has been completed.     

Synthesized Multi-Method to Detect and Classify Epileptic Waves in EEG

In order to sufficiently exploit the advantages of different signal processing methods, such as wavelet transformation (WT), artificial neural networks (ANN) and expert rules (ER), a synthesized multi-method was introduced to detect and classify the epileptic waves in the EEG data. Using this method, at first, the epileptic waves were detected from pre-processed EEG data at different scales by WT, then the characteristic parameters of the chosen candidates of epileptic waves were extracted and sent into the well-trained ANN to identify and classify the true epileptic waves,and at last, the detected epileptic waves were certificated by ER. The statistic results of detection and classification show that, the synthesized multi-method has a good capacity to extract signal features and to shield the signals from the random noise. This method is especially fit for the analysis of the biomedical signals in biomedical engineering which are usually non-placid and nonlinear.     

Screening of plane S waves by an array of rigid piles in poroelastic soil

An array of rigid piles used as a screening barrier for plane shear （S） waves is investigated in a homogeneous unbounded space. The dynamic poroelastic theory of Biot is employed, under the assumption of an incompressible solid grain. Using Fourier-Bessel series, the problem of multiple scattering is solved by imposing continuity conditions and equilibrium conditions at the soil-pile interfaces with the translational addition theorem. A parametric analysis is conducted to investigate the influence of the permeability of poroelastic soil, separation between piles, number of piles and frequency of incident waves on screening effectiveness of the barrier, and the results are compared with those in an elastic soil medium. Computed results show that the intrinsic permeability of the soil medium displays an apparent effect on the screening of plane S waves.     

Influence of structure plane size on seismic response of soil-structure interaction

The influence of the change of structure plane size on seismic response was studied for a soil-structure interaction system. Based on the finite element method, a soil-structure interaction calculation model was established to analyze the seismic response by changing the structure plane size and choosing different earthquake waves for different soil fields. The results show that when the natural periods of vibration for different structure plane sizes are close, under the same earthquake wave, the total displacement on the top layer of the structure and the foundation rotation displacement decrease with the increase of structure plane size, and the proportion of superstructure elastic selfdeformation displacement to the total displacement increases with the increase of structure plane size. While for different types of sites and seismic waves, under the horizontal and vertical seismic waves, the seismic responses of different plane sizes have a similar change rule.     

Numerical analysis of surface plasmons excited on a thin metal grating

INTRODUCTION It is widely known that a metal grating supports plasmon surface waves in the optics region (Raeter, 1982; Nevier, 1980). Excitation of a plasmon surface wave causes resonance absorption, which can be observed as partial or total absorption of incident light accompanied by an abrupt change of diffraction effi- ciency called resonance anomaly. If the grating is thick enough, the surface waves can be excited on the lit surface alone and the surface waves in this case are called…     

Rapid Reading Comprehension

The number of people with loss of hearing in America is about 250,000 people at the present time.Some of these people are fortunate enough to have hearing aids. The ear is a very complex part of the human body.A sound starts with sound waves traveling through the auditory canal towards the eardrum. The sound waves will cause the eardrum to vibrate. This vibration will be conducted by three small     

快速阅读

The number of people with loss of hearing in America is about 250,000 people at the present time. Some of these people are fortunate enough to have hearing aids. The ear is a very complex part of the human body.A sound starts with sound waves traveling through the auditory canal towards the eardrum. The sound waves will cause the eardrum to vibrate. This vibration will be conducted by three small     

Wavy film flow along periodic wall under monochromatic-frequency flowrate perturbation

Surface wave dynamics of falling film on the surface of periodic rectangular wall under monochromatic-frequency flowrate forcing disturbances is studied via numerical simulation. Waveforms formed on the periodic rectangular wall are different from those on the flat plate. At low frequency, the perturbation introduced at the inlet first undergoes a steady flow region and then develops into solitary waves. When the frequency becomes higher, solitary waves disappear. Film deformations in the steady flow region and characteristics of solitary waves are studied as the film travels down. There are circulations at the depression of periodic wall which are dependent on the local film characteristics and geometry of the corrugation. Moreover, the flow rate and geometry of the corrugations can also affect the evolvement of the monochromatic perturbation.     

Propagation of flexural waves in phononic crystal thin plates with linear defects

The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.     

电子椭圆轨道的一种推导方法

运用量子化通则和椭圆参数方程推导电子椭圆轨道的长半轴a和短半轴b与主量子数n、角量子数nφ、径量子数nr的关系．     

Burnside引理的一个推广

用（G，X）表示一个群G作用在集合X上，并用F（g）表示被群G的元素g所稳定的点集．本文得到了关于数■F（g）|n的两个结果，并得到了这个数的几何意义．在某种意义上讲，它们是Burnside引理的推广．     

从比耐公式到类氢原子电子的量子化椭圆轨道

从比耐公式出发，结合玻尔-索末菲量子化条件，对类氢原子电子的量化椭圆轨道，给出了一个简化的推导，并在此基础上，对轨道的稳定性进行进一步的讨论。     

关于人造地球卫星轨道的几点讨论

利用行星运动轨道方程,由初始条件,求出方程中的积分常数,并拓展导出人造地球卫星的运动轨道.     

基于自旋轨道耦合效应的能带分裂机理

从理论上导出了自旋与p轨道耦合效应使能带分裂的具体表达式,阐明了能带分裂的物理机理,讨论了自旋轨道耦合效应使价带顶分裂后能带结构的特征。其结果有助于更深刻的理解自旋轨道耦合引起能带分裂的机理,对研究半导体光学选择定择、输运性质及应变量子阱中能带的分裂也提供了重要的理论基础。     

析4s轨道与3d轨道能

本文从轨道能、能级、屏蔽效应和钻穿效应这四个概念入手 ,运用计算轨道常见能量的两种方法进行分析和比较轨道能与 3d轨道能     

人工与天体引力波源

引力波是广义相对论的重要推论之一。科学家们希望能直接探测到引力波,但是由于产生机制的不同,引力波远弱于电磁波,而人工引力波源产生的引力波目前无探测可能。宇宙中虽然存在大量的天体引力波源,但传到地球上的信号都很弱。目前,科学家们已设计出几种实验装置去探测引力波。     

一类生态模型的研究

本考虑食饵种群具有常数收获率的捕食—食饵模型dx/dt=x(x-t)(k-x)/x n-xy-h,dy/dt=ry(x-1)讨论了该模型的平衡点的类型,极限环的不存在性及分支问题。     

一颗古代彗星破碎的假说

本文通过对中国古代三种特殊的流星现象──进碎炸散、破断和小里随大星等的统计分析,发现这些现象呈周期性的出现,又发现它们的月份分布相对集中在8一门月份。同时,这三种现象不呈互相交错混杂,而是基本上各自分开,有明显的时代界限。由此提出这些现象是由一颗两千多年前的大童星破碎瓦解、随时间流驰而产生的现象的假说。本文还对这颗营星的轨道报数做了分析,并大致确定。