Cz结构浅池内硅熔体热对流的分岔特性

为了了解水平温度梯度作用时Czochralski结构浅池内硅熔体热对流的分岔特性,利用有限差分法进行了非稳态三维数值模拟,坩埚外壁被加热,液池深度为3 mm.模拟结果表明,当逐渐增加温差时,会发生两次流型转变,第一次由二维轴对称流动转变为三维稳态流动,第二次由三维稳态流动转变为热流体波,其可能沿顺时针方向旋转、也可能沿逆时针方向旋转,同时,第二次转变存在分岔现象.     

薛定谔扰动耦合系统孤波的行波近似解法

研究了一类薛定谔非线性耦合系统.利用精确解与近似解相关联的特殊技巧,首先讨论了对应的无扰动耦合系统,利用投射法得到了精确的孤波解.再利用泛函映射方法得到了薛定谔非线性扰动耦合系统的行波近似解.     

强阻尼广义sine-Gordon方程特征问题的变分迭代法

研究了在数学、力学中广泛出现的一类非线性强阻尼广义sine-Gordon扰动微分方程问题. 首先, 引入行波变换, 求出退化方程的精确解. 再构造一个泛函, 创建了一个变分迭代算法, 最后, 求出原非线性强阻尼广义sine-Gordon扰动微分方程问题的近似行波解析解. 用变分迭代法可得到的各次近似解, 具有便于求解、精度高等特点. 求得的近似解析解弥补了单纯用数值方法的模拟解的不足.     

Turbulence regeneration in pipe flow at moderate Reynolds numbers

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.     

Analytical studies on the Benney–Luke equation in mathematical physics

The enhanced (G′/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney–Luke equation by using the enhanced (G′/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.     

行波和驻波模式下热声振荡的临界温度梯度

热声机械作为一种能量转化装置。其效率于传统发动机还有较大差距。本文讨论了热声发动机在驻波和行波两种不同工作状态下,其声功率产生的临界温度梯度与流道尺寸和工作介质的关系,得出了两种模式下最佳的工作条件。结果表明;采用行波形式的热声发动机结构,可以有效降低临界温度梯度,提高热致声的效率,同时可以利用一些低品位来做为热声发动机的高温端。     

一类扰动发展方程近似解

采用了一个简单而有效的技巧, 研究了一类扰动发展方程. 首先引入求解一个相应典型方程的行波孤波解. 然后利用渐近方法得到了原扰动发展方程的近似解. 利用泛函分析的不动点定理, 指出了近似解级数的收敛性, 并讨论了近似解的精度.     

水平温差对环形浅液池内Marangoni-热毛细对流的影响

双向温差驱动下的Marangoni-热毛细对流在许多工程技术领域具有重要作用, 但是, 已有的大部分研究集中于单向温差作用下的流动. 因此, 采用数值模拟的方法研究了水平温差对双向温差驱动下的环形浅液池内Marangoni-热毛细对流的影响. 在一个给定的顶部换热条件下, 确定了不同水平温差作用下流动由轴对称稳态流动向三维非稳态流动转变的临界底部热流密度. 结果表明, 水平温差使得Marangoni-热毛细对流不稳定; 随着水平温差的持续增强, 稳态流动转变为一种规律的振荡流动, 最终变得混乱; 发现两种新的状态演化过程; 确定了水平温差和垂直温差在共同驱动流体运动时各自发挥的作用; 随着水平温差的增强, 最初出现在中间区域的最高表面温度不断向热壁移动, 在此过程中, 内壁附近的流动增强, 而外壁附近的流动减弱.     

Acoustical power amplification and damping by temperature gradients

Ceperley proposed a concept of a traveling wave heat engine ["A pistonless Stirling engine-The traveling wave heat engine," J. Acoust. Soc. Am. 66, 1508-1513 (1979).] that provided a starting point of thermoacoustics today. This paper verifies experimentally his idea through observation of amplification and strong damping of a plane acoustic traveling wave as it passes through axial temperature gradients. The acoustic power gain is shown to obey a universal curve specified by a dimensionless parameter ωτα; ω is the angular frequency and τα is the relaxation time for the gas to thermally equilibrate with channel walls. As an application of his idea, a three-stage acoustic power amplifier is developed, which attains the gain up to 10 with a moderate temperature ratio of 2.3.     

扰动Vakhnenko方程物理模型的行波解

研究了一类扰动Vakhnemko方程.给出了改进的渐近方法.首先, 对原模型系统对应的典型方程得到对应的行波解.其次, 引入一个泛函, 建立迭代关系式,将求解非线性问题转化为求解一系列的迭代序列.然后, 逐次地求出对应的解的近似式, 最后,得到了原扰动Vakhnemko模型行波解的任意次精度的近似展开式,并讨论了它的精度. 关键词： 泛函 行波解 Vakhnemko方程     

Exact traveling wave solutions of an autonomous system via the enhanced (G′/G)-expansion method

Mathematical modeling of many autonomous physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear evolution equations plays a significant role in the study of nonlinear physical phenomena. In this article, the enhanced (G′/G)-expansion method has been applied for finding the exact traveling wave solutions of longitudinal wave motion equation in a nonlinear magneto-electro-elastic circular rod. Each of the obtained solutions contains an explicit function of the variables in the considered equations. It has been shown that the applied method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering fields.     

激波内部的导热问题

本文从实际气体有粘流的激波厚度解,用分子运动论讨论了激波内部导热问题,并且通过重组范诺流和瑞利流的选加提出了激波中导热问题的物理模型和相应的定态激波非平衡态不可逆过程的模型。证明了激波是一种负熵流波,是依靠激波波速输运热流的热波。     

The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. Several abrupt phenomena observed in tokamaks, such as intermittent excitation of geodesic acoustic mode (GAM) shown in this paper, could be attributed to the sudden and fast radial motion of Instanton. The composite drift wave—zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale. The eigenmode equation of the model defines the zero-order (micro-scale) variation; it is solved by making use of the two-dimensional (2D) weakly asymmetric ballooning theory (WABT), a theory suitable for modes localized to rational surface like drift waves, and then refined by shifted inverse power method, an iterative finite difference method. The next order is the equation of electron drift wave (EDW) envelope (containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW. This equation is coupled to the zonal flow equation, and numerically solved in spatiotemporal representation; the results are displayed in self-explanatory graphs. One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW. The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition. Then, it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz. The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM. The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.     

Analysis of peristaltic flow of Jeffrey six constant nano fluid in a vertical non-uniform tube

Peristaltic flow of non-Newtonian nano fluid through a non-uniform surface has been investigated in this paper. The fluid motion along the wall of the surface is caused by the sinusoidal wave traveling with constant speed. The governing equations are converted into cylindrical coordinate system and assuming low Reynolds number and long wave length partial differential equations are simplified. Analytically solutions of the problem are obtained by utilizing the homotopy perturbation method (HPM). In order to insight the impact of embedded parameters on temperature, concentration and velocity some graphs are plotted for different peristaltic waves. At the end, some observations were made from the graphical presentation that velocity, pressure rise and nano particle concentration are increasing function of thermophoresis parameter N_t while temperature and frictional forces show opposite trend.     

Drag reduction in turbulent channel flow using bidirectional wavy Lorentz force

Turbulent control and drag reduction in a channel flow via a bidirectional traveling wave induced by spanwise oscillating Lorentz force have been investigated in the paper. The results based on the direct numerical simulation (DNS) indicate that the bidirectional wavy Lorentz force with appropriate control parameters can result in a regular decline of near-wall streaks and vortex structures with respect to the flow direction, leading to the effective suppression of turbulence generation and significant reduction in skin-friction drag. In addition, experiments are carried out in a water tunnel via electro-magnetic (EM) actuators designed to produce the bidirectional traveling wave excitation as described in calculations. As a result, the actual substantial drag reduction is realized successfully in these experiments.     

非线性LC电路方程的显式精确行波解

理论上考察了具有耗散的非线性LC电路中的行波. 借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程. 一致地获得了丰富的显式精确解析行波解, 包括精确冲击波解和奇异的行波解, 和三角函数有理形式的周期波解. 关键词： LC电路')" href="#">非线性LC电路 非线性耗散波动方程 冲击波 周期波     

气相爆轰波在分叉管中传播现象的数值研究

数值研究气相爆轰波在分叉管中的传播现象.用二阶附加半隐龙格-库塔法和5阶WENO格式求解二维欧拉方程,用基元反应描述爆轰化学反应过程,得到了密度、压力、温度、典型组元质量分数场及数值胞格结构和爆轰波平均速度.结果表明:气相爆轰波在分叉管中传播,分叉口左尖点的稀疏波导致诱导激波后压力、温度急剧下降,诱导激波和化学反应区分离,爆轰波衰减为爆燃波(即爆轰熄灭).分离后的诱导激波在垂直支管右壁面反射,并导致二次起爆.畸变的诱导激波在水平和垂直支管中均发生马赫反射.分叉口上游均匀胞格区和分叉口附近大胞格区的边界不是直线,其起点通常位于分叉口左尖点上游或恰在左尖点.水平支管中马赫反射三波点迹线始于右尖点下游.分叉口左尖点附近的流场中出现了复杂的旋涡结构、未反应区及激波与旋涡作用.旋涡加速了未反应区的化学反应速率.反射激波与旋涡作用并使旋涡破碎.反射激波与未反应区作用,加速其反应消耗,并形成一个内嵌的射流.数值计算得到的波系演变和胞格结构与实验定性一致.     

气液两相流压力波色散特性实验研究

设计了可调频式压力扰动源的气液两相流压力波实验装置,实验研究了垂直上升管内气液两相流泡状流、弹状流压力波的色散规律。实验结果表明,对泡状流,在实验范围内,压力波的传播速度及其衰减跟扰动频率有关,随着扰动频率的增加,波速及其衰减都增加;工质的流速对压力波的色散特性没有影响。结合数值模拟结果,验证了泡状流压力波色散特性的临界频率现象,即高于临界频率,压力波色散特性消失,本文分析了相应的物理机制。对弹状流,压力波同样具有典型的色散特性,已有研究结果还不能预测其色散规律。     

Global Well-Posedness for the KP-I Equation on the Background of a Non-Localized Solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).     

Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion

The asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics. 1) The solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet ^– (for some>0) ast, provided that the initial disturbance is small and of integral zero, and in addition decays at an algebraic rate for |x|. 2) The traveling wave solution with Nishida and Smoller's condition of the system of a viscous heat-conductive ideal gas is asymptotically stable, provided the initial disturbance is small and of integral zero. 3) The traveling wave solution with weak shock profile of the Broadwell model system of the Boltzmann equation is asymptotically stable, provided the initial disturbance is small and its hydrodynamical moments are of integral zero. Each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one. The property of integral zero of the initial disturbance plays a crucial role in this procedure.