海洋浮体水弹性力学研究历史与现状

全面系统地介绍了海洋浮体水弹性力学的国内外研究历史与现状。将水弹性力学分为二维线性、二维非线性、三维线性、三维非线性等几类，并依次进行了论述。重点介绍了水弹性分析理论在超大型浮体的动力特性研究中的应用现状。     

海洋内波遥感探测中的数学问题

海洋内波是重要的海洋动力过程,在海洋中普遍存在,对海洋内波的遥感探测具有重要的研究意义和应用需求。内波的遥感探测涉及内波传播模型的建立与求解、内波遥感图像处理与特征提取、基于遥感图像的内波参数提取与反演,最终建立内波传播的预测与预警模型,上述都需要数学方法的支持。基于内波遥感研究的迫切需求,论述其在各环节上亟待解决的数学问题,以期为数学与应用搭建桥梁,促进内波遥感技术的进步。     

轴向流中平行简支弹性薄板的大挠度流固耦合的数值模拟

分析研究了轴向流中简支弹性薄板大挠度流固耦合系统的振动响应和流场特性.板结构动力学方程采用基于位移的有限元法离散;流场采用二维不可压缩粘性流体N-S方程,并用有限体积法离散;在此基础上结合动网格控制技术,建立模拟双向流固耦合作用下轴向流中简支弹性薄板的二维数值模型.利用该数值模型得到了单块简支板随流速变化流致振动特性,研究了结构大挠度的振动稳定性,分别得到了Pitchfork分岔曲线和非线性系统结构的Hopf分叉曲线.通过轴向流恒定流速下不同间距的平行两块简支弹性薄板流固耦合的数值模拟得到了的流致振动特性.     

一类新4维Hindmarsh-Rose碰撞模型的动力学分析

研究了一类4维H-R神经元碰撞模型平衡点的数目及稳定性,通过数值仿真清楚地刻画出参数变化对系统动力学特性的影响,结合理论与数值模拟方法,更加充分地说明了系统丰富的动力学特性.     

NMOS阱内外碰撞SEU特性的仿真分析

通过二维器件模拟软件MEDICI对小尺寸硅SRAM单元SEU特性进行了分析。在阱内外碰撞时,当耦合电阻,NMOS阱深等因素变化时,SRAM单元的SEU特性将发生变化,器件阱外碰撞一直比阱内碰撞时对SEU敏感。参数变化过程中对阱内外碰撞时器件SEU敏感性的影响情况不同,器件阱外碰撞时参数变化对SEU特性影响较小,但器件阱内碰撞时参数变化对SEU特性影响较大。     

多组分复杂等离子体中(3+1)维非线性离子声孤波的研究

研究了在多组分复杂等离子体中(3+1)维非线性离子声孤波的基本传播特性.利用约化摄动方法,推导得到用来描述多组分复杂等离子体中(3+1)维非线性离子声孤波的ZK方程.此外,借助数值模拟的方法分析了原有等离子体系统中的不同参数对非线性离子声孤波的非线性强度、振幅、宽度等传播特性的重要影响.     

内充预压流体的弹性圆管中的孤立波

研究了内充预压流体的弹性管中孤立波的传播.在长波近似条件下,流体流速和压力变化沿半径方向进行平均,流体运动是沿管轴方向的一维流动.管壁处于二维应力状态,在现时构形上建立了其非线性运动方程,管壁材料为不可压超弹性材料,其本构描述采用二维情况下Fung型的应变能函数.借助约化摄动法由管壁与流体耦合作用的非线性方程组导出了KdV方程,表征着系统有孤立波解.最后讨论了系统的参数对孤立波传播特征的影响.     

基于Benjamin-Feir不稳定性的异常波模拟

通过引入四阶非线性薛定谔方程,基于随机波列演化的Benjamin-Feir不稳定性,采用伪谱方法建立了二维深水波浪数值水槽来模拟海洋中的异常波现象。为了验证该数值模型的有效性,计算了二维水槽中边带扰动随机波列的传播变形,从数值和试验结果的比较上看,该模型可以很好地再现异常波现象。     

基于Benjamin-Feir不稳定性的畸形波模拟

通过引入四阶非线性薛定谔方程,基于随机波列演化的Benjamin-Feir不稳定性,采用伪谱方法建立了二维深水波浪数值水槽来模拟海洋中的畸形波现象.为了验证该数值模型的有效性,计算了二维水槽中边带扰动随机波列的传播变形,通过比较数值和试验结果发现该模型可以很好地再现畸形波现象.     

基于二维元胞自动机的交通流模拟分析

BML模型是专门用于模拟分析交通现象的二维元胞自动机模型,采用JAVA语言实现此模型并利用此模型模拟交通流,分析平均密度和平均速度等参数关系,研究交通流的相变和自组织特性,同时对BML模型改进,模拟红绿灯周期变化下的交通流,探求更有价值的研究和应用.     

River plumes as a source of large-amplitude internal waves in the coastal ocean

Satellite images have long revealed the surface expression of large amplitude internal waves that propagate along density interfaces beneath the sea surface. Internal waves are typically the most energetic high-frequency events in the coastal ocean, displacing water parcels by up to 100 m and generating strong currents and turbulence that mix nutrients into near-surface waters for biological utilization. While internal waves are known to be generated by tidal currents over ocean-bottom topography, they have also been observed frequently in the absence of any apparent tide-topography interactions. Here we present repeated measurements of velocity, density and acoustic backscatter across the Columbia River plume front. These show how internal waves can be generated from a river plume that flows as a gravity current into the coastal ocean. We find that the convergence of horizontal velocities at the plume front causes frontal growth and subsequent displacement downward of near-surface waters. Individual freely propagating waves are released from the river plume front when the front's propagation speed decreases below the wave speed in the water ahead of it. This mechanism generates internal waves of similar amplitude and steepness as internal waves from tide-topography interactions observed elsewhere, and is therefore important to the understanding of coastal ocean mixing.     

原子尺度上的波

提出全同粒子以及虚粒子假设,并推导了二维速度控制条件,再结合原子势函数,在原子尺度上描述了线性波的传播。考虑晶格非谐性以及位错的影响,进一步探究了二阶非线性波的产生机理。理论分析表明,晶格非谐性和位错引起的晶格畸变会诱发产生高阶虚粒子,高阶虚粒子是高阶非线性波产生的关键因素,位错等材料早期非线性或细微损伤导致高阶虚粒子增多而引发明显的高次谐波,因此,可以通过探测高次谐波诊断材料早期损伤。     

Nonlinear interactions between gravity waves and background winds

Using the nonlinear propagating gravity waves (GW) model in the two-dimensional compressible atmosphere and the linear GW theory, the process of GW propagation in different background winds, e.g. the direction of the background wind is opposite to (dead wind) or the same as (tail wind) the direction of the horizontal phase velocity of GW, is studied. The results show that the dead wind prolongs the vertical wavelength and accelerates GW propagation. Therefore, GW propagates up to a higher height becomes instable in a short time and eventually induces an inverse jet flow. Then, the vertical wavelength is becoming short due to the nonlinear interactions between GW and the inverse jet flow. The vertical wavelength and group velocity decrease after GW propagates into the tail wind. The initial instable time is delayed. Although most of GW is trapped in the instable region, some of GW propagates above the instable region. Compared with GW propagation in the tail wind, the nonlinear interactions between GW and the dead wind are also strong. In contrast, the linear GW theory predicts that GW can propagate freely in the dead wind. The vertical wavelength simulated by the nonlinear numerical model is different from that predicted by the linear theory greatly after GW propagates into the dead wind.     

Nonlinear interactions between gravity waves and background winds

Using the nonlinear propagating gravity waves (GW) model in the two-dimensional compressible atmosphere and the linear GW theory, the process of GW propagation in different background winds, e.g. the direction of the background wind is opposite to (dead wind) or the same as (tail wind) the direction of the horizontal phase velocity of GW, is studied. The results show that the dead wind prolongs the vertical wavelength and accelerates GW propagation. Therefore, GW propagates up to a higher height becomes instable in a short time and eventually induces an inverse jet flow. Then, the vertical wavelength is becoming short due to the nonlinear interactions between GW and the inverse jet flow. The vertical wavelength and group velocity decrease after GW propagates into the tail wind. The initial instable time is delayed. Although most of GW is trapped in the instable region, some of GW propagates above the instable region. Compared with GW propagation in the tail wind, the nonlinear interactions between GW and the dead wind are also strong. In contrast, the linear GW theory predicts that GW can propagate freely in the dead wind. The vertical wavelength simulated by the nonlinear numerical model is different from that predicted by the linear theory greatly after GW propagates into the dead wind.     

地下结构瞬态响应分析的积分方程法(I)——P波和SV波的传播

本文用积分方程法进行了两维地下结构对爆炸应力波的瞬态响应分析。用两维全空间Green函数建立积分方程,用离散化方法化为一组线性代数方程求解,转换过程中对积分的奇性进行了分析,用双波联合计算等方法解决了奇性积分的计算,根据波传播的特性建立了“过渡元素”。最后给出了求解具有任意形状孔洞的无限、半无限空间中P波和SV波传播问题的离散化积分方程。文章还对计算结果和动力光弹性试验作了比较,以验证计算的正确性。     

水波传播的无网格数值模拟

在水波传播的数值模拟中采用了一种基于配点和径向基函数的无网格方法.采用Laplace方程的基本解作为径向基函数,将源点布置在模拟波浪场之外,沿边界布置配点而不是划分网格,从而自动满足控制方程,且不存在奇点,不需要求解积分方程.数值造波采用给定入射波面和速度势的方法,数值消波综合采用阻尼层消波和Sommerfeld辐射条件,非线性自由面的演化追踪采用二阶Taylor级数展开式.对线性规则波和非线性三阶Stokes波的模拟显示,数值结果与理论解吻合良好.表明无网格方法不但形式简单、计算速度快,而且稳定性和准确性令人满意,有望成为水波模拟问题的一种有效的数值方法.     

Numerical study of the propagation of small-amplitude atmospheric gravity wave

By using a two-dimensional fully nonlinear compressible atmospheric dynamic numerical model, the propagation of a small amplitude gravity wave packet is simulated. A corresponding linear model is also developed for comparison. In an isothermal atmosphere, the simulations show that the nonlinear effects impacting on the propagation of a small amplitude gravity wave are negligible. In the nonisothermal atmosphere, however, the nonlinear effects are remarkable. They act to slow markedly down the propagation velocity of wave energy and therefore reduce the growth ratio of the wave amplitude with time. But the energy is still conserved. A proof of this is provided by the observations in the middle atmosphere.     

内波垂向结构的分段求解方法

为了掌握海洋内坡的特性，针对内波垂向结构的数值解法进行了严谨的分析推导，提出了分段求解方法．将数理方程中的Strm-Liouville本征值问题应用到内波方程，可获得标准化的两种方法，进而探讨了这两种方法的统一性及实用性．计算结果表明，对半日潮的低频情况内波可存在于整个水深，而对周期为20分钟的较高频情况则内波只存在于垂向的有限范围内，在上下两层，其垂向速度的衰减很快．该方法应用于实际海洋中，可以获得一般情况下内波函数的广义Fourier级数，从理论上可以证明解函数的完备性。     

海洋内波破碎及其能量耗散的研究进展

海洋内波是海洋中普遍存在的波动形式。它的不稳定和破碎会对海洋能量的再分配产生本质的影响,直接将能量从大尺度向小尺度过程传递,产生湍流混合。内波破碎产生的湍流混合又会显著地影响海洋环境。该文就近十五年来对内波的破碎机制以及内波破碎导致的能量耗散研究作一简要综述。     

声波衰减的格子-Boltzmann方法模拟

采用格子-Boltzmann方法分别模拟了一维及二维通道内平面声波的衰减过程.模拟中,声源给定速度及密度,出口采用出口边界条件.一维模型下,y方向采用周期性边界条件;二维模型下,y方向采用无滑移边界条件.模拟结果表明:在介质黏性以及壁面摩擦(仅二维)的作用下,声波沿着传播方向逐渐衰减,速度振幅及密度振幅越来越小,压力梯度呈负指数形式减小;随着波长的增大或介质黏度的减小,声波的衰减减缓,压力梯度越小.模拟获得的速度分布、压力梯度分布以及衰减系数与理论值吻合良好.最后,给出了声源的激发声压级.