一种模拟波动过程的方法

计算机模拟复杂波动现象需要使用波动方程。仅少数专业学生必修波动方程的知识,大部分学生无法自行编写模拟程序,进行模拟实验。介绍一种使用牛顿力学定律和差分法的模拟方法(简称实物模拟法)。在模拟程序中,一维横波的传播介质被定义为存在张力的弦,张力与弦长度成正比。通过理论证明,弦的运动满足波动方程。那么模拟波动过程只需要模拟弦的运动即可,从而简化了模拟要求。因只需牛顿力学知识,实物模拟法具有简单直观的特点,有助于学生理论联系实际,充分理解波动现象。     

重力对弦振动特征频率的影响

本文从非均匀弦波动方程出发探讨重力对弦振 动特征频率的影响．讨论了两种不同边界条件下竖直 均质弦驻波特征频率与其重量之间的关系，给出了在 弦重量远小于其张力时两端固定的竖直均质弦驻波特 征频率修正项的解析表达式．     

相对转动运动学方程的级数解

为解决相对转动体非线性运动微分方程的计算难题，构造了一种级数解耦方法，把微分方程转化为代数方程求解，得到了相对转动体运动方程的级数解.据此可以计算工程应用中稳态相对转动体的真实转速波动.同时该法可实现测控标定仪器的转动体匀速旋转时的不均匀性测量误差分离，也为大型复杂重型旋转轴系在线实时扭振监测提供了高效算法. 关键词： 相对转动 运动学方程 速度波动 级数解     

敲击乐器弦振动的Matlab可视化模拟

敲击乐器能够演奏出优美动听的音调旋律,其敲击工具与弦振动之间存在着规律性数理关系,不同形状的锤击工具,产生的音调具有明显差异.利用数理方法推导出敲击乐器采用不同锤击工具(平面锤、余弦凸面锤、细棒锤)产生的弦振动波动方程,通过计算软件Matlad)实现对弦振动复杂的波动方程数值求解,以直观的图像形式对弦振动进行了可视化仿真模拟.     

弦振动方程的一种推导方法

一些有关声学基础和数学物理方法的著作,[1][2][3]在讨论弦横振动方程时,总是从考虑张力的角度出发。这种讨论方法固然简单,但对弦振动的物理实质却没能清晰地揭示出来,而且张力究竟是怎样一个力,叙述得不够准确。本文根据弹性力学理论,用另一种方法导出弦的横振动方程,旨在阐明这一现象的物理实质。 一、弦做微小横振动的物理过程 一根绷紧的长弦,当其受到突然作用而后立即撤消的外力作用时,就要发生振动。当只考虑弦元的横向位移(垂直于弦长方向的位移)而不考虑其纵向位移(平行于弦长方向的位移)时,或说弦的横向位移和弦长之比很小时,称之…     

欧拉-拉格朗日方程在一维波动方程中的应用

本文以一维弦上微元的动能和势能为基础,推导出了一维波动方程。文章首先介绍了通过力学分析得到一维波动方程的方法。然后分析了一维自由运动粒子的动能和势能,引入系统的哈密顿量和拉格朗日函数,由最小作用原理得到了欧拉-拉格朗日方程,也就是粒子的运动方程。将这一方法用于分析一维弦上波动,给出微元的拉格朗日密度函数,得到可以描写无穷多自由度系统的欧拉-拉格朗日方程,从而导出了一维波动方程。最后分析了一维弦上波动的拉格朗日密度与弦理论中Polyakov作用量中的拉格朗日密度的关系。     

弦线上驻波的研究

讨论了弦振动横波波动方程,研究了固定线密度时弦振动的张力与波长、张力与频率之间的关系,利用origin软件得出实验曲线,并找出研究张力和波长曲线关系时的最佳频率及研究张力和频率曲线关系时的最佳波长.     

理想流体一维绝热稳定流动能量方程推导

对理想流体一维绝热稳定流动作了讨论．对一般理想流体(可压缩或不可压缩)，用两种方法推出了能量方程．在此基础上，讨论了流动可逆性及不同流体性质对流动参数的影响．     

叶片的周向弯曲与弦向弯曲及其数值分析

六十年代提出的静叶片的倾斜或弯曲方法是以透平轴的平行线为转动轴将叶片转动（构成倾斜叶片）或沿叶高弯曲（构成弯曲叶片）。本文提出将转动轴在Ｓ１平面旋转到弦向，然后倾斜或弯曲叶片，称这种叶片为弦向倾斜或弯曲叶片。应用欧拉方程和高精度ＴＶＤ格式对不同弯曲方法的叶片的数值分析表明弦向弯曲叶片控制径向二次流的能力大于周向弯曲叶片。     

弦振动定解问题级数解的截断误差分析

基于弦振动方程在定解条件下的三种不同形式的级数解,讨论了是否忽略自变量两种条件下级数解的截断误差.其中,在考虑自变量的情况下通过对普遍截断误差进行估计,定义出类吉布斯现象,从而得到最大截断误差的估计.     

Black holes in brane worlds

A Kerr metric describing a rotating black hole is obtained on the three brane in a five-dimensional Randall-Sundrum brane world by considering a rotating five-dimensional black string in the bulk. We examine the causal structure of this space-time through the geodesic equations.     

Cosmic Strings Coupled with a Massless Scalar Field

A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum-Einstein equations is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis, asymptotically flat, and free from the curvature singularities. The solution describes a stable, rotating cosmic string of infinite length interacting with gravitational and scalar waves.     

Exciting the GKP string at any coupling

We analyze the spectrum of excitations around the Gubser-Klebanov-Polyakov (GKP) rotating string in the long string limit and construct a parametric representation for their dispersion relations at any value of the string tension. On the gauge theory side of the AdS/CFT correspondence, i.e., in the planar N=4 super Yang-Mills theory, the problem is equivalent to finding the spectrum of scaling dimensions of large spin, single-trace operators. Their scaling dimensions are obtained from the analysis of the Beisert-Staudacher asymptotic Bethe ansatz equations, which are believed to solve the spectral problem of the planar gauge theory. We examine the resulting dispersion relations in various kinematical regimes, both at weak and strong coupling, and detail the matching with the Frolov-Tseytlin spectrum of transverse fluctuations of the long GKP string. At a more dynamical level, we identify the mechanism for the restoration of the SO(6) symmetry, initially broken by the choice of the Berenstein-Maldacena-Nastase vacuum in the Bethe ansatz solution to the mixing problem.     

Two mass relations for mesons from string-quark duality

We generalize a self-consistency equation derived previously by us for the Nambu string to strings carrying SU(6) quantum numbers.The self-consistency equations are derived by considering the propagation of a string with the quantum numbers of the physical vacuum. Since we can map the world sheet that the string sweeps out onto rectangles, and the wave function of the physical vacuum is a constant, the boundary conditions are the same on all four sides of the rectangles. We can then calculate the propagator in two ways and this leads to the self-consistency equations. For the strings carrying SU(6) quantum numbers we consider the propagator o strings with the quantum numbers of the physical vacuum all along the string except for having quark quantum numbers either attached or removed from the ends. We can solve these self-consistency equations in a certain approximation and for this case they lead to mass formulae for mesons that are well satisfied in nature.     

The vibration of a rotating circular string subject to a fixed elastic restraint

The natural frequencies of a rotating circular string, subject to a fixed elastic restraint, are calculated. This simple system is important because its dynamic behavior has most of the characteristics of more complex rotating systems. The variation of the natural frequencies with change in rotation speed and spring constant is examined. The results show “avoided crossing”, a characteristics of eigenvalue problems where there is coupling between modes. When the string is rotating, the vibration is harmonic, but it does not have a uniform phase at all points in space. At particular rotation speeds, standing waves are formed which have stationary nodal points. The phase within these standing waves is also non-uniform, except when the string is stationary. The critical rotation speed, at which all the natural frequencies degenerate to zero, is independent of spring stiffness.     

Effective dynamics of an electrically charged string with a current

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparameterization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are derived. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function ofbosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant λ introduced ingeneralized uncertainty principle takes a proper value, we derive Bekenstein-Hawking entropy and the correction value corresponding cosmological horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small massapproximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropyof the black string cosmological horizon in non-spherical coordinate spacetime.     

Entropy of the rotating and charged black string to all orders in the Planck length

<正>By using the entanglement entropy method,this paper calculates the statistical entropy of the Bose and Fermi fields in thin films,and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string.Here,the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string.Taking into account the effect of the generalized uncertainty principle on quantum state density,it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model.These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect.The ultraviolet cut-off in the brick-wall model is not reasonable.The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon.From the viewpoint of quantum statistical mechanics,the correction value of Bekenstein-Hawking entropy is obtained.This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.     

Inheriting Conformal and Special Conformal Killing Vectors in String Cosmology

In this paper we study the consequences of the existence of conformal and special conformal Killing vectors (CKV, SCKV) for string cloud and string fluid in the context of general relativity. The inheritance symmetries of the string cloud and string fluid are discussed. Einstein's field equations have been solved for static spherically symmetric space-time with cloud and fluid of strings source via CKV.     

Stationary properties of Nambu strings

It is shown that the string equations and boundary conditions for the open massless string do not follow consistently from the Nambu action. Nevertheless, all solutions are stationary under those variations which result in time-like or null surfaces. For strings with masses attached to the ends no consistency problems arise.