Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Constrained Wave Equations and Wave Maps

In this paper we establish that wave maps can be obtained by a penalization method if the initial data is well prepared. When the data is not well prepared, we prove that the solution of the penalized equation converges weakly to the solution of the system of coupled equations obtained in [11] by a multi-scale formal analysis. In particular, the interaction between the rapid normal oscillations and the tangential motions creates a new term in the limit system whose well-posedness is proved by using the Nash-Moser Implicit Function Theorem. The first author is funded in part by NSF DMS 0203485.The second author is funded in part by NSF DMS 0101969.     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Study of Novel Slow Wave Circuit for Miniaturized Millimeter Wave Helical Traveling Wave Tube

Two kinds of novel helical slow wave circuit, supported by Chemical Vapor Deposition (CVD) diamond, are presented. They are applying in miniaturized millimeter wave helical traveling wave tube. Cold test characteristic of these circuits are simulated by MAFIA code. Higher performances are achieved with smaller size, compared with conventional circuit supported by BeO rods. The nonlinear analysis is implemented by Beam and Wave Interaction (BWI) module, which is a part of TWTCAD Integrated Framework. Results have been found to be consistent with the expectation. It should be wider apply in microwave and millimeter wave vacuum electronic devices.     

光纤中声波导布里渊散射声波对斯托克斯波的影响

利用全矢量有限元法模拟了单模光纤中声波导布里渊散射R0,m和TR2,m声波模式对斯托克斯波增益、相位调制和双折射的影响.研究结果表明:当布里渊频移与R0,8和TR2,10声波频率相同时,斯托克斯波的增益最大,且增益随泵浦功率的增大而增大;R0,1、TR2,1、TR2,5、TR2,7和TR2,10声波模式对斯托克斯波相位调制较大,且相位调制随泵浦功率的增大呈线性增大,其中TR2,m模对斯托克斯波相位调制比R0,m模大;TR2,1、TR2,5、TR2,7、TR2,10声波模式对斯托克斯波产生较为明显的附加双折射,且附加双折射程度随着泵浦功率的增加呈线性增大.     

关于热声压缩机原理的讨论

回顾了驻波、行波热声机械的发展历史 ,分析了行波与驻波热声压缩机的优缺点。介绍行波驻波混合型热声压缩机的工作原理及结构 ,指出了今后研究的重点和方向。     

Periodic Wave,Solitary Wave and Compacton Solutions of a Nonlinear Wave Equation with Degenerate Dispersion

In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.     

表面波布拉格声光互作用耦合波方程的研究

定义了压电晶体的增劲声光系数,它反映压电晶体中声光、电光和压电效应共同作用的结果。从参量互作用基本理论出发,同时考虑声光效应、电光效应和压电效应三个因素,用一个压电增劲声光系数来表示三种因素的共同作用,导出表面波声光布拉格互作用的耦合波方程。并求解得出相应衍射效率的计算公式。该式说明在弱声光互作用条件下,衍射导光波强度与超声功率成正比。表面波声光器件具有体积小、工作稳定、能耗小、易于集成等优点。可以用作光偏转器、光调制器、滤光器。在光通信以及各类实时信号处理,如相关、卷积、频谱分析、矩阵光计算等领域具有广泛的应用前景。     

Wave Relations

The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly, there is still something to say about this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian evolution are not problematic from the viewpoint of relations. In the two-dimensional Minkowski case, these relations are shown to be Lagrangian. This result is then extended to a wide class of metrics and is conjectured to be true also in higher dimensions for nice enough metrics. A counterexample where the relation is not Lagrangian is provided by the Misner space.     

Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

Abstract

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in di!erent physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive di!erential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.     

讲机械波慎以水波为例

水波是一种常见的波，讲机械波时以水波为例，说明波的折射、波的衍射和波的干涉现象，取材方便、实验易做，并且演示现象明显，能够取得很好的教学效果．教科书《物理》第二册“机械波”一章也多次提到了水波这个例子．     

Wave Trajectories and Damping of Lower Hybrid Wave in Tokamak Plasmas

Incident lower hybrid waves (LHW) propagate toward the center of the plasma in a spiral form in the poloidal and the toroidal sections, and finally are absorbed by the ion Landau damping (ILD) and/or the electron Landau damping (ELD) in accordance with the refractive index parallel to the magnetic field N?, which is varied considerably along the trajectory because of the toroidicity and the rotational transform. We propose the scaling law of the wave trajectories on plasma parameters, which shows that the control of N? or the applied frequency is necessary during the lower hybrid heating (LHH).     

Solitary Wave and Wave Front as Viewed From Curvature

The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometrically, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s), which varies with arc length s. For solitary wave when s → ±∞, then its curvature c(s) approaches zero, and when s=0, the curvature c(s) reaches its maximum. For wave front, when s → ±∞, then its curvature c(s) approaches zero, and when s=0, the curvature c(s) is still zero, but c'(s) ≠ 0. That is, s=0 is a turning point. When c(s) is given, the variance at some point (x,y) in stream line with arc length s satisfies a 2-order linear variable-coefficient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front.     

The Millimeter Wave Radiation of a Traveling Wave Sinusoidal Wire Antenna

In this paper, investigation of radiation properties of the traveling-wave sinusoidal wire antennas is extended to the millimeter-wave frequencies (Ka-band) for the antennas whose geometrical dimensions vary in a wide range. Far-field patterns and S-parameters of composed three antenna sets were measured. A mathematical model was constructed for the structure and a MATLAB code based on this theoretical approach was written to calculate patterns, phase and attenuation constants of all investigated antennas. Frequency characteristics and the relation of antenna dimensions with wave parameters were investigated. Measured and calculated patterns were also compared with the constructed far-field patterns obtained by MoM (method of moments) and the MoM current distributions were used to explain the loss mechanisms of antennas. A directive, undistorted and smooth radiation can be achieved only choosing small undulated antennas whose peak-to-peak amplitude to period ratio κ is smaller than 0.4 (κ < 0.4). It is shown that wavelength of broadside radiation is not equal to antenna period for all antennas, except for very small undulated antennas (κ < 0.2). This antenna type can be used as a frequency-scan antenna for millimeter wave radars.

A Wave Automaton for Wave Propagation in Inhomogeneous Anisotropic Media

This paper presents an extension built on a hexagonal grid of the wave automaton, which was introduced in past few years for describing wave propagation in inhomogeneous media. This new method is capable of computing wave propagation in 2D anisotropic media without the need for introducing interpolating schemes. After a comparison of isotropic single scattering with analytical results using Mie theory, the method is used to compute the field scattered by one anisotropic particle for various orientations of its principal axes. Scattering by a collection of anisotropic particles is also presented.     

Synchronization of Distributed Electron–Wave Self-Oscillatory Systems with a Backward Wave

We present the results of studying the phenomenon of synchronization in distributed electron–wave self-oscillatory systems with a counterpropagating wave. General laws governing the appearance of the classical synchronization in distributed systems are revealed. We propose methods for increasing the synchronization bandwidth by using the distributed input of a signal to the interaction space by means of coupled waveguide structures. Transient processes in nonautonomous self-oscillation regimes are studied. In particular, the effect of ultrafast synchronization is found. The possibility of chaotic synchronization in a gyro-oscillator with a counterpropagating wave under the action of a deterministic chaotic signal is shown. Mutual oscillation regimes in a system of two distributed oscillators with coupled waveguide systems are studied.     

Dispersive Solitary Wave Solutions of Strain Wave Dynamical Model and Its Stability

In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp\((-\phi(\xi))\)-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and anti-Kink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.     

Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave

We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave,and particularly calculate the atomic inversion of the wave packet.A general method of calculation is presented.The results are interesting.For example,if the wave packet is very narrow or /and the interaction is very strong,no matter the atom is initially in its ground state or excited state,the atomic inversion approaches zero as time approaches infinity.If the atom is initially in its ground state and excited state with the probability 1/2 respectively,and if the momentum density is an even function,then the atomic inversion equals zero at any time.