Long distance wave computation using nonlinear solitary waves

A recently developed method is described to propagate short wave equation pulses over indefinite distances and through regions of varying indices of refraction, including multiple reflections. The method, “Wave Confinement”, utilizes a newly developed nonlinear partial differential equation (pde) that propagates basis functions according to the wave equation. These basis functions are generated as stable solitary waves where the discretized equation can be solved without any numerical dissipation. The method can also be used to solve for harmonic waves in the high frequency (Eikonal) limit, including multiple arrivals. The solution involves discretizing the wave equation on a uniform Eulerian grid and adding a simple nonlinear “Confinement” term. This term does not change the amplitude (integrated through each point on the pulse surface) or the propagation velocity, or arrival time, and yet results in capturing the waves as thin surfaces that propagate as thin nonlinear solitary waves and remain ∼2-3 grid cells in thickness indefinitely with no numerical spreading. A new feature described in this paper involves computing scattering of short pulses from complex objects such as complete aircraft. A simple “immersed surface” approach is used, that utilizes the same uniform grid as the propagation and avoids complex, body fitted or adaptive grid schemes.The new method should be useful in areas of wave propagation, from radar scattering and long distance communications to cell phone transmission.     

A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers

In this work, exact and approximate non-reflecting boundary conditions (NRBCs) are implemented with the Partition of Unity Finite Element Method (PUFEM) to solve short wave scattering problems governed by the Helmholtz equation in two dimensions. By short wave problems, we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer. Various NRBCs are implemented and a comparison of their performance is carried out based on the accuracy of the results, ease of implementation and computational cost. The aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number.     

Periodic solutions to one-dimensional wave equation with x-dependent coefficients

In this paper, we study the nonlinear one-dimensional periodic wave equation with x-dependent coefficients u(x)ytt−(ux(x)yx)+g(x,t,y)=f(x,t) on (0,π)×R under the boundary conditions a₁y(0,t)+b₁yx(0,t)=0, a₂y(π,t)+b₂yx(π,t)=0 ( for i=1,2) and the periodic conditions y(x,t+T)=y(x,t), yt(x,t+T)=yt(x,t). Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. A main concept is the notion “weak solution” to be given in Section 2. For T is the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.     

Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coefficients with Dissipation

Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.     

ON BLOCK MATRICES ASSOCIATED WITH DISCRETE TRIGONOMETRIC TRANSFORMS AND THEIR USE IN THE THEORY OF WAVE PROPAGATION

Block matrices associated with discrete Trigonometric transforms （DTT＇s） arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT＇s are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks （U a fixed unitary matrix） by utilizing the U- diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method＇s computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications.     

On a boundary controller of fractional type

In this paper we consider the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. The boundary controller involves a derivative of non-integer order. It is proved that solutions blow up in finite time in the presence of a nonlinear source.     

电磁波检测

当今无线通讯技术迅猛发展,如何对变电所及输电线与移动电话基地台所产生的电磁场强度进行评估,便成为一个重要的工作.通过分析电磁波特征,论述了对这些电磁波辐射设施所产生的电磁场强度检测的方法.     

波纹管对超导电缆出口液氮温度的影响

建立了30米长高温超导电缆的二维模型,利用Fluent软件对该模型进行仿真分析。在该模型中,采用波纹管恒温器,分析了波纹管的波距、波高等因素对出口液氮温度的影响。结果表明:在相同的热负荷及流量下,波纹管的波距越小,波高越大,出口液氮温度越高。超导电缆波纹管内液氮温度模拟,为低温冷却系统的优化设计提供理论依据。     

Microscopic Studies of 2H-NbSe2 Probed by Positive Muon

Abstract

The microscopic state of the positively charged light particle in the transition metal dichalcogenide 2H-NbSe₂ was studied using the muon spin relaxation method (μ⁺SR) and muon level crossing resonance method (μ-LCR). Muons are expected to stay at interlayer position and behaves as a hydrogen like intercalant. We discuss the relation between conduction electron properties and the muon's behavior.     

A Wave Approach to Signal and Noise Modeling of Dual-Gate MESFET

A new procedure for signal and noise modeling of dual-gate MESFET is described in this paper. The small-signal model is based on two cascoded single-gate MESFET intrinsic equivalent circuits embedded in a network representing device parasitics. The wave interpretation of noise is used for defining the noise parameters of each single gate MESFET. Applying this approach, a CAD oriented procedure for extracting the dual-gate MESFETmodel parameters as well as the noise wave temperatures is developed. Modeled scattering and noise parameter characteristics are comparedto the measured ones and quite a good agreement is observed.