Analysis on the frequency-domain numerical method to compute the noise radiated from rotating sources

A frequency-domain solution of the Ffowcs Williams-Hawkings equation with a penetrable data surface is presented for the thickness, loading and quadrupole noise to avoid the singularities that exist in the time-domain methods. Since this method is based on the numerical integration over source time, there is no need to solve the retarded-time equation or to perform the interpolation on time-domain data, and the time-domain source information obtained by modern CFD codes can be utilized directly. The acoustic pressure spectra of monopole, dipole and quadrupole point sources in subsonic and supersonic rotation are calculated with the presented method, and the results agree well with those obtained by the retarded-time method and frequency-domain analytical method.     

Frequency-domain wave equation and its time-domain solutions in attenuating media

Our purpose in this paper is to describe the wave propagation in media whose attenuation obeys a frequency power law. To achieve this, a frequency-domain wave equation was developed using previously derived causal dispersion relations. An inverse space and time Fourier transform of the solution to this algebraic equation results in a time-domain solution. It is shown that this solution satisfies the convolutional time-domain wave equation proposed by Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)]. The form of the convolutional loss operator contained in this wave equation is obtained. Solutions representing the propagation of both plane sinusoidal and transient waves propagating in media with specific power law attenuation coefficients are investigated as special cases of our solution. Using our solution, comparisons are made for transient one-dimensional propagation in a medium whose attenuation is proportional to frequency with recently obtained numerical solutions of Szabo's equation. These show good agreement.     

On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs

The theory of differential equations and differential operators on geometric graphs is actively developing in recent decades. One of the directions is devoted to the study of the socalled Gaussian packets, i.e., localized asymptotic solutions of the nonstationary Schrödinger equation. An interesting feature of such solutions is in their close connection with problems of analytic number theory and, in particular, with estimates for the number of integer points in polyhedra and the number of integer solutions of linear inequalities. At the same time, from the point of view of applications to quantum mechanics, it is natural to raise the question of the energy distribution of such solutions along the graph (in other words, the probabilities of finding a quantum particle in some area). Seemingly, this question is very complicated for general graphs, because the energy distribution is much more sensitive to the type of boundary conditions and to the initial state than the asymptotics of the number of localized functions.A similar problem is to describe the energy distribution of a solution of the wave equation on a geometric graph. For infinite regular trees, this question was studied in the paper [10, 11]; at the same time, the general case is practically unstudied. The main observation of the present paper is that the situation is considerably simplified if we consider strongly localized asymptotic solutions; in this case, a general unitary operator describing the scattering at a vertex is replaced by the operator of reflection from the subspace. In the simplest situations, this circumstance makes it possible to obtain comparatively simple formulas for the energy distribution along the edges.     

Repeated application of the recursion operator for a new hierarchy of negative-order integrable KdV equations

ABSTRACT

In this work we use the repeated application of the recursion operator to establish a new hierarchy of negative-order integrable KdV equations of higher orders. The concept of the inverse recursion operator allows us to develop this new hierarchy. The complete integrability of each equation is guaranteed via the use of the recursion operator. We show that the dispersion relations of this hierarchy follow an infinite geometric series. Multiple soliton solutions for each equation of the hierarchy are obtained.     

Crack detection in structures using deviation from normal distribution of measured vibration responses

Cracks are one of the common defects in structural components that may ultimately lead to failure of structures if not detected. Generally, most of the vibration based crack detection methods transform measured vibration responses from time-domain into frequency-domain using Fourier or wavelet transform for damage detection. However, it would be more convenient if the vibration responses could be analysed in their original time-domain. Therefore, a practical method based on probability distribution function is proposed which performs all the data processing in time-domain for the purpose of crack detection in beam-like structures. The application of the proposed method to both numerical and experimental examples and their results are presented.     

Lattice gas activity series from secular equations

The secular equations for finite tori of lattice sites are obtained by computer expansion of determinants for a hard-particle lattice gas. The secular equations yield all of the thermodynamic functions for finite systems and the beginning terms of activity expansions for all of the eigenvalues of the infinite system. The same secular equation that yields the low-density series for the equation of state of the infinite-circumference system also yields the beginning terms in the highdensity expansion. As examples we treat two hard-particle lattice gases in two dimensions, the lattice gas with nearest-neighbor exclusion (which has a secondorder transition), and the case of dimers (which is analytic all the way to close packing).     

Reflectance of acoustic horns and solution of the inverse problem

A method is described for solving the inverse problem of determining the profile of an acoustic horn when time-domain reflectance (TDR) is known only at the entrance. The method involves recasting Webster's horn equation in terms of forward and backward propagating wave variables. An essential feature of this method is a requirement that the backward propagating wave be continuous at the wave-front at all locations beyond the entrance. Derivation of the inverse solution raises questions about the meaning of causality in the context of wave propagation in non-uniform tubes. Exact reflectance expressions are presented for infinite exponential, conical and parabolic horns based on exact solutions of the horn equation. Diameter functions obtained with the inverse solution are a good match to all three horn profiles.     

超短激光脉冲作用下生物组织体光学响应的时域和频域分析──Dirichlet边界条件和无向点激励源

生物组织体在超短激光脉冲激励下的表面光学响应特性,如光子平均飞行路径、光通量、相移和调制深度等,在光学时域及频域无损测量、组织体光谱学和光学三维成象研究中具有重要的意义,而生物组织体对近红外和可见光呈现的高散射特性使得激励光子在组织体内的传输行为复杂化,精确地测定和计算上述光学响应量一直是人们感兴趣的问题.本文基于描述组织体内光子传输的扩散方程模型,阐述了时域、频域测量的等效性,从无限空间几何结构出发,逐次导出了常见几何形状均匀组织体光学响应的解析表示,在此基础上给出了典型参数下的计算结果并讨论了计算中可能出现的问题及其解决方法.     

Symmetries and symmetry reductions of the combined KP3 and KP4 equation

To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34) equation is found by means of a direct method.The related point symmetries can be obtained simply by taking the infinitesimal form of the finite point symmetry group.The point symmetries of the CKP34 equation constitute an infinite dimensional KacMoody-Virasoro algebra.The point symmetry invariant so...     

基于BLT方程的微带线电磁耦合终端响应

为定量研究电磁波与微带线的耦合终端响应问题,提出一种基于BLT方程的电磁波与微带线耦合分析方法,相比传统方法计算效率高、占用内存少。将PCB板上微带线等效为有耗传输线模型,对辐照平面波进行矢量分析并求解等效激励源,运用BLT方程研究不同入射方式、脉冲波形对微带线终端的影响,并对入射波与终端响应进行了时域、频域分析。研究表明:当入射波频率与微带线长度满足一定关系式时对微带线的耦合最强,耦合电压峰值达2.4 mV;电场平行微带线入射比垂直PCB入射时的终端电压峰值大一倍;且同幅同脉宽的矩形脉冲较高斯脉冲和三角脉冲对微带线的耦合峰值电压大;不同波形的脉冲通过调节脉宽都可对微带线耦合终端电压达到mV量级。     

扩展的混合指数方法及其应用

改进了Hereman提出的构造非线性发展方程孤波解的混合指数方法,通过将非线性发展方程孤波解的表示形式推广到实指数解或复指数解的无穷级数,得到了扩展的混合指数方法.以正则长波方程为例,说明通过扩展的混合指数方法可获得包括正则孤波解、奇异孤波解及周期解在内的诸多精确解 关键词： 孤波解 混合指数法 正则长波方程     

Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method

This paper presents the exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an equivalent system with cyclic periodicity in two directions is established, the difference governing equation for such an equivalent system can be uncoupled by applying the double U-transformation. Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived. These results cannot be obtained if other methods are used instead.     

Fractional diffusion with two time scales

Moving particles that rest along their trajectory lead to time-fractional diffusion equations for the scaling limit distributions. For power law waiting times with infinite mean, the equation contains a fractional time derivative of order between 0 and 1. For finite mean waiting times, the most revealing approach is to employ two time scales, one for the mean and another for deviations from the mean. For finite mean power law waiting times, the resulting equation contains a first derivative as well as a derivative of order between 1 and 2. Finite variance waiting times lead to a second-order partial differential equation in time. In this article we investigate the various solutions with regard to moment growth and scaling properties, and show that even infinite mean waiting times do not necessarily induce subdiffusion, but can lead to super-diffusion if the jump distribution has non-zero mean.     

Classification of an infinite series of static solutions to the vacuum Einstein equations

We propose a classification of an infinite series of the static solutions to the vacuum Einstein equation by means of their soliton number and the real and/or complex pole trajectories. We also show that in the 4-soliton solution there appears an intriguing ring solution of which the curvature invariant has a finite limit at the rings.     

一种求解锂离子电池单粒子模型液相扩散方程的新方法

电解液中的锂离子浓度表达是锂离子电池电化学模型求解的基本任务之一.为了平衡单粒子模型的液相动态性能和计算效率,假设反应仅发生在集电极和电解质界面上,为此,提出一种基于液相扩散方程无穷级数解析解的界面浓度求解新方法.在恒流工况下,利用数列单调收敛准则将解析解转化为一个收敛和函数.在动态工况下,将该解析解简化为输入与和函数的无限离散卷积.利用和函数随时间单调衰减并收敛至零的特性对其进行截断,从而得到有限离散卷积求解算法.对比专业有限元分析软件,该方法在恒流工况和动态工况下均能以较少的计算时间获得相当好的精度.而且,该方法仅有一个配置参数.因此,所提方法将有效减小应用于实时电池管理系统上的电化学模型计算负担.     

一种求解锂离子电池单粒子模型液相扩散方程的新方法

电解液中的锂离子浓度表达是锂离子电池电化学模型求解的基本任务之一.为了平衡单粒子模型的液相动态性能和计算效率,假设反应仅发生在集电极和电解质界面上,为此,提出一种基于液相扩散方程无穷级数解析解的界面浓度求解新方法.在恒流工况下,利用数列单调收敛准则将解析解转化为一个收敛和函数.在动态工况下,将该解析解简化为输入与和函数的无限离散卷积.利用和函数随时间单调衰减并收敛至零的特性对其进行截断,从而得到有限离散卷积求解算法.对比专业有限元分析软件,该方法在恒流工况和动态工况下均能以较少的计算时间获得相当好的精度.而且,该方法仅有一个配置参数.因此,所提方法将有效减小应用于实时电池管理系统上的电化学模型计算负担.     

两半无限长圆柱形导体管内电位的计算与分析

分别运用分离变量法和有限差分法计算和分析两半无限长圆柱形导体管内电位的解析解和数值解,并通过MAT LAB编程算出其场域中一些点的电位结果,由相对误差的比较说明数值解的有效性,以此对保角变换的解析解结果进行了验证,找到缺陷并作了修正,从而说明把数值计算与求解析解综合起来分析场域内的电位分布会使结果更加可靠和准确.     

构造非线性发展方程无穷序列类孤子精确解的一种方法

辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bäcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解.     

KAM Tori for 1D Nonlinear Wave Equations¶with Periodic Boundary Conditions

In this paper, one-dimensional (1D) nonlinear wave equations