Gravity-capillary waves modulated by linear shear flow in arbitrary water depth

Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) describing the evolution dynamics of gravity-capillary wavetrains in arbitrary constant depth. The gravity-capillary waves(GCWs) are influenced by a linear shear flow(LSF) which consists of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of GCWs with the LSF is analyzed using the NLSE. The MI is effectively modified by the LSF. In infinite depth, there are four asymptotes which are the boundaries between MI and modulational stability(MS) in the instability diagram. In addition, the dimensionless free surface elevation as a function of time for different dimensionless water depth,surface tension, uniform flow and vorticity is exhibited. It is found that the decay of free surface elevation and the steepness of free surface amplitude change over time, which are greatly affected by the water depth, surface tension, uniform flow and vorticity.

Particle-in-cell simulation of ion-acoustic solitary waves in a bounded plasma

We study some nonlinear waves in a viscous plasma which is confined in a finite cylinder.By averaging the physical quantities on the radial direction in some cases,we reduce this system to a simple one-dimensional model.It seems that the effects of the bounded geometry(the radius of the cylinder in this case)can be included in the damping coefficient.We notice that the amplitudes of both Korteweg–de Vries(KdV)solitary waves and dark envelope solitary waves decrease exponentially as time increases from the particle-in-cell(PIC)simulation.The dependence of damping coefficient on the cylinder radius and the viscosity coefficient is also obtained numerically and analytically.Both are in good agreement.By using a definition,we give a condition whether a solitary wave exists in a bounded plasma.Moreover,some of potential applications in laboratory experiments are suggested.

Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities

Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.

BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r^＊ which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if ｜r｜≥ r^＊; while they appear as damped oscillatory waves if ｜r｜ 〈 r^＊. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u（ξ） in the global phase portraits, and then obtain the approximate solutions （u（ξ）, H（ξ））. Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.

均匀磁场下二维拓扑绝缘体边缘态的多重Andreev反射研究

研究均匀磁场下的二维拓扑绝缘体在超导隧道结中的电压偏置约瑟夫森结的输运性质,电流-电压特性显示了马约拉纳束缚态的存在。在亚谐隙结构中,也可以观察到磁场对超导能隙的影响。研究结果表明,在S波超导体/正常金属/S波超导结的隧道谱中存在亚谐隙结构。透明度只影响超导结的零偏压电导值的大小,而不影响亚谐隙结构的位置。但是在磁场作用下,亚谐隙结构会发生变化,不再固定出现在特定位置。这一结果对应于拓扑螺旋态中超导和铁磁序之间的相互作用。

基于FUNWAVE-TVD模型的岸礁次重力波数值模拟

为了研究不规则波条件下岸礁上次重力波的传播规律,采用完全非线性的Boussinesq数值模型FUNWAVE-TVD对波浪水槽的物理模型试验进行了数值模拟。在对短波、次重力波有效波高与时均水位模拟结果验证的基础上,采用互相关分析与小波二阶谱研究了次重力波的生成、传播过程及相关的非线性能量传递。结果表明:礁前次重力波从谱峰频段获得能量;礁前斜坡上水深变浅时,非线性作用加剧,更多波能从谱峰频段传至高频段与低频段并伴随着约束波的成长;礁坪上次重力波主要由破碎点移动产生,礁坪末端能量传递主要发生在低频段之间。

The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded

Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time solutions,provided that the initial data are compactly supported and sufficiently small in Sobolev norm.In this work,Alinhac obtained an upper bound with polynomial growth in time for the top-order energy of the solutions.A natural question then arises whether the time-growth is a true phenomenon,despite the possible conservation of basic energy.In the present paper,we establish that the top-order energy of the solutions in Alinhac theorem remains globally bounded in time.

基于5G波束成形的变电站作业人员高精度定位技术

针对变电站室内作业人员定位精度差的问题,文章提出了多个智能反射面(intelligent reflecting surface,IRS)辅助的5G毫米波高精度室内定位系统。首先基于最大似然估计和三维室内定位模型,获得关于作业人员位置的初始估计,并推导得出克拉美罗下界(cramer-rao lower bound,CRLB)的闭式表达式;然后以最小化CRLB为目标,建立了IRS反射波束和作业人员侧终端接收波束成形的优化问题;最后基于块坐标下降(block coordinate descent,BCD)和粒子群优化(particle swarm optimization,PSO)的波束成形交替优化算法求解得到最优反射和接收波束,并据此进一步优化作业人员定位精度。仿真结果表明所提方案可以有效提高系统定位精度。

有界波模拟器中线缆倾角对电磁耦合的影响

电力设备中的断路器、隔离开关等一次设备与二次控保设备距离越来越小,由于一次设备操作而引起的电磁场环境突变,降低了二次设备的可靠性。例如变电站中的隔离开关在合闸和分闸时会产生瞬态强电磁脉冲,该脉冲所携带的部分能量与暴露在二次设备外部的线缆耦合,流入设备内部并对其中的电子元器件造成电磁干扰,严重时器件失效并导致设备工作异常。为探明其电磁耦合机理,本文汇总整理了不同电压等级的变电站因开关操作所产生的瞬态电磁场,提取出电磁脉冲的特征波形,利用有界波模拟器在实验室环境下近似再现了特征波形,并对线缆在有界波模拟器中的摆放形态进行了全波仿真分析,揭示了线缆摆放角度对电磁耦合的影响,为电力芯片在复杂电磁场环境下开展可靠性检测提供了理论基础。

地震波斜入射下港珠澳大桥沉管隧道地震响应分析

斜入射地震波引起的非一致性地震动对地下管廊、沉管隧道等细长结构影响明显。在细长结构抗震中,需要考虑地震动的非一致性。针对港珠澳大桥沉管隧道,采用黏弹性人工边界的方法建立三维有限元模型,对比分析P波、SV波和SH波在不同角度斜入射下的隧道动力响应。研究结果表明:不同的入射波、不同的角度在隧道中的响应差别显著。P波、SH波作用下结构加速度随入射角的变化先增大后减小,SV波作用下结构加速度随入射角增大而减小。相较于自下而上的垂直入射,地震波斜入射下结构应力响应被明显放大且不同入射波下结构应力响应的分布特点不同,P波在隧道顶、底板的中部的应力较大,SV波作用下结构纵向非一致性表现得更明显,SH波在隧道侧墙、中隔墙与顶底板相交的角点区以及两个斜向板块应力较大。随着入射角度增大,P波、SV波应力逐渐增大,SH波应力逐渐减小。

Unconventional bound states in the continuum from metamaterial-induced electron acoustic waves

Photonic bound states in the continuum(BICs)are spatially localized modes with infinitely long lifetimes,which exist within a radiation continuum at discrete energy levels.These states have been explored in various systems,including photonic and phononic crystal slabs,metasurfaces,waveguides,and integrated circuits.Robustness and availability of the BICs are important aspects for fully taming the BICs toward practical applications.Here,we propose a generic mechanism to realize BICs that exist by first principles free of fine parameter tuning based on non-Maxwellian double-net metamaterials(DNMs).An ideal warm hydrodynamic double plasma(HDP)fluid model provides a homogenized description of DNMs and explains the robustness of the BICs found herein.In the HDP model,these are standing wave formations made of electron acoustic waves(EAWs),which are pure charge oscillations with vanishing electromagnetic fields.EAW BICs have various advantages,such as(i)frequency-comb-like collection of BICs free from normal resonances;(ii)robustness to symmetry-breaking perturbations and formation of quasi-BICs with an ultrahigh Q-factor even if subject to disorder;and(iii)giving rise to subwavelength microcavity resonators hosting quasi-BIC modes with an ultrahigh Q-factor.

Acoustic Based Crosshole Full Waveform Slowness Inversion in the Time Domain

We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the constrained optimization together which can inverse the slowness effectively. One advantage of slowness inversion is that there is no further approximation in the gradient derivation. Moreover, a new algorithm named the skip method for solving the constrained optimization problem is proposed. The TV regularization has good ability to inverse slowness at its discontinuities while the constrained optimization can keep the inversion converging in the right direction. Numerical computations both for noise free data and noisy data show the robustness and effectiveness of our method and good inversion results are yielded.

A Numerical Model for Nonlinear Wave Propagation on Non-uniform Current

On the basis of the new type Boussinesq equations （Madsen et al., 2002）, a set of equations explicitly including the effects of currents on waves are derived. A numerical implementation of the present equations in one dimension is described. The numerical model is tested for wave propagation in a wave flume of uniform depth with current present. The present numerical results are compared with those of other researchers. It is validated that the present numerical model can reasonably reflect the nonlinear influences of currents on waves. Moreover, the effects of inputting different incident boundary conditions on the calculated results are studied.

Anti-periodic traveling wave solution to a forced two-dimensional generalized KdV-Burgers equation

The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied. Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.

Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to that in the twodimensional case,the flat band could not survive.At the same time,the flat band states are transformed into localized states with a logarithmic singularity near the center position.In addition,the wave function near the origin would collapse for an arbitrarily weak Coulomb potential.Due to the wave function collapses,the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter.For a Coulomb potential of type II,there exist infinite bound states that are generated from the flat band.Furthermore,when the bound state energy is very near the flat band,the energy is inversely proportional to the natural number,e.g.,E_(n)∝1/n,n=1,2,3,...It is expected that the 1/n energy spectrum could be observed experimentally in the near future.

Approximate Bound State Solutions for Certain Molecular Potentials

We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.

Kinematic Relativity of Quantum Mechanics:Free Particle with Different Boundary Conditions

An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schr&oumldinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.

大尺寸Split型垂直极化有界波EMP模拟器场的特性分析

采用并行时域有限差分(finite-difference time-domain, FDTD)方法对大尺寸分裂型垂直极化有界波电磁脉冲模拟器(简称“Split型模拟器”)的电场进行模拟,研究分析了该类型模拟器天线的尺寸参数对模拟器内对称剖面上监测点电场垂直分量时域特性的影响,给出了该剖面上电场的瞬态分布特性,并与常规模拟器进行了比较。模拟结果表明:模拟器架高越高,监测点处的电场垂直分量的半高宽出现异常的起始高度越高,且同一监测点电场垂直分量的峰值随模拟器最大高度的增大而减小;距离源越近且距离下极板越近的监测点,电场垂直分量的峰值随整个上极板投影长度的增加有明显的减小;同一监测点电场垂直分量的上升沿会随着模拟器梯形金属板投影长度的增加而减小,峰值随该投影长度的增加而增加;监测点电场垂直分量的半高宽随上极板最大空隙宽度的增加而减小,峰值随上极板最大空隙宽度的增加而减小;当Split型模拟器选择合适的尺寸参数及工作空间高度时,电场垂直分量的上升沿和半高宽均满足IEC61000-4-25标准,且电场垂直分量的峰值与常规模拟器差别不大。