Experimental study of core MHD behavior and a novel algorithm for rational surface detection based on profile reflectometry in EAST

Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasma perturbations on the reflect signal is important.The characteristics of the reflect signal from profile reflectometry,the time-of-flight(TOF)signal associated with the MHD instabilities,are investigated in EAST.Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain(FDTD)method,it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude.Experimental TOF signals under different types of MHD instabilities(sawtooth,sawtooth precursors and tearing mode)are studied in detail and show agreement with the simulation.Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface,the cross-correlation and gradient threshold(CGT)method and the 2D convolutional neural network approach(CNN)are presented for the first time.It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control,which will be beneficial for the advanced tokamak operation.

Spinodal surface instability of soft elastic thin films

When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.

Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.

Step instability of the surface during Ino.2Gao.sAs （001） annealing

Anisotropic evolution of the step edges on the compressive-strained In0.2Ga0.8As/GaAs（001） surface has been investigated by scanning tunneling microscopy （STM）. The experiments suggest that step edges are indeed sinuous and protrude somewhere a little way along the [110] direction, which is different from the classical waviness predicted by the theoretical model. We consider that the monatomic step edges undergo a morphological instability induced by the anisotropic diffusion of adatoms on the terrace during annealing, and we improve a kinetic model of step edge based on the classical Burton Cabrer-Frank （BCF） model in order to determine the normal velocity of step enlargement. The results show that the normal velocity is proportional to the arc length of the peninsula, which is consistent with the first result of our kinetic model. Additionally, a significant phenomenon is an excess elongation along the [110] direction at the top of the peninsula with a higher aspect ratio, which is attributed to the restriction of diffusion lengths.

Stress distribution and surface instability of an inclined granular layer

Static granular materials may avalanche suddenly under continuous quasi-static drives. This phenomenon, which is important in many engineering applications, can be explained by analyzing the stability of the elastic solutions. We show this for a granular layer driven by its inclination angle in gravity, where the elastic problem can be solved generally and analytically. It is found that a loss of stability may occur only at the free surface of the layer. This result is considered to be relevant for understanding surface avalanches and the flows observed experimentally.

Surface Tension Effect on Harmonics of Rayleigh-Taylor Instability

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability （RTI） for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third har- monics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.

复合坐标系跨临界液滴表面Kelvin-Helmholtz不稳定增长高效预测方法

针对混合动力专用内燃机实际运行的跨临界条件,传统方法对于主导可燃混合气形成质量的液滴表面Kelvin-Helmholtz不稳定性分析方法难以实现跨临界宽范围的有效预测。采用复合坐标系方法,建立跨临界强对流环境的等效液滴不稳定性高效预测模型,分别采用全局扩散动力学模型、热力学控制模型及局部液滴表面切向不稳定模型。在全局坐标系模型可以通过模态坐标变换求得解析解,局部坐标系引入势函数等,提高求解速度。而对于可实用性流体计算仿真模型,可通过无量纲物理参数描述不同跨临界条件下空气动力、惯性力、黏性力、表面张力、加速度等控制因素的变化规律,以及其对液滴表面切向和法向不稳定波增长的影响规律。结果表明:液滴表面的空气动力仍然支配着跨临界条件液滴表面切向不稳定波的发展;压力增大时,液相雷诺数控制的流动特性减小与欧尼索控制的液滴黏性力减弱基本抵消;环境温度增加时,雷诺数表征的流动特性对Kelvin-Helmholtz波增长的贡献越来越小,液滴的惯性力影响也越来越弱。

Surface Expressions of Rayleigh-Taylor Instability in Continental Interiors

Two-dimensional thermal-mechanical numerical models show that Rayleigh-Taylor-type （RT） gravitational removal of high-density lithosphere may produce significant surface deformation （vertical deflection 〉1000 m） in the interior of a continental plate.A reasonable range of crustal strengths and thicknesses,representing a variation from a stable continental interior to a hot orogen with a thick crust,is examined to study crustal deformation and the surface deflection in response to an RT instability.In general,three types of surface deflection are observed during the RT drip event：（1） subsidence and negative topography; （2） uplift and positive topography; （3） subsidence followed by uplift and inverted topography.One key factor that determines the surface expression is the crustal thickness.Models with a thin crust mainly show subsidence and develop a basin.In the thick crust models,surface expressions are more variable,depending on the crustal strength and depth of highdensity anomaly.With weak crust and a deep high-density anomaly,the RT drip is decoupled from the overlying crust,and the surface exhibits uplift or little deflection,as the RT drip induces contraction and thickening of the overlying crust.In contrast,with a strong crust and shallow anomaly,the surface is more strongly coupled with the drip and undergoes subsidence,followed by uplift.

ANALYSIS OF DYNAMIC INSTABILITY OF INTERFACIAL SLIP WAVES BASED ON THE SURFACE IMPEDANCE TENSOR

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves.The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value,and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor.Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle.As an example,the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details.A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed.An explicit expression for the instability condition of the interfacial slip waves was presented.

Effect of surface tension and viscosity on bubble growth of single mode Rayleigh-Taylor instability

Based on the Zufiria theoretical model, a new model regarding the asymptotic bubble velocity for the Rayleigh-Taylor （RT） instability is presented by use of the complex velocity potential proposed by Sohn. The proposed model is an extension of the ordinary Zufiria model and can deal with non-ideal fluids. With the control variable method, the effect of the viscosity and surface tension on the bubble growth rate of the RT instability is studied. The result is consistent with Cao＇s result if we only consider the viscous effect and with Xia＇s result if we only consider the surface tension effect. The asymptotic bubble velocity predicted by the Zufiria model is smaller than that predicted by the Layzer model, and the result from the Zufiria model is much closer to White＇s experimental data.

INSTABILITY AND (2×1) RECONSWUCTON OF Ge (001) SURFACE FROM SOLID-STAIE POTENTIALS

An empirical potential energy function comprising two-and three-body terms, whose parameters have been determiaed from the properties of solid germanium, is used to study the (2Xl) reconstruction of the Ge(001) surface. It is found that the formation of a dimer bond lowers the total energy by 0. 73eV/atom, as compared to the surface atoms on the ideal Ge(001) surface.

Nonlinear beam formulation incorporating surface energy and size effect:application in nano-bridges

A nonlinear beam formulation is presented based on the Gurtin-Murdoch surface elasticity and the modified couple stress theory. The developed model theoretically takes into account coupled effects of the energy of surface layer and microstructures size- dependency. The mid-plane stretching of a beam is incorporated using von-Karman nonlinear strains. Hamilton＇s principle is used to determine the nonlinear governing equation of motion and the corresponding boundary conditions. As a case study, pull-in instability of an electromechanical nano-bridge structure is studied using the proposed formulation. The nonlinear governing equation is solved by the analytical reduced order method （ROM） as well as the numerical solution. Effects of various parameters including surface layer, size dependency, dispersion forces, and structural damping on the pull- in parameters of the nano-bridges are discussed. Comparison of the results with the literature reveals capability of the present model in demonstrating the impact of nano- scale phenomena on the pull-in threshold of the nano-bridges.

Mode coupling in nonlinear Kelvin-Helmholtz instability

This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.

NONLINEAR MHD KELVIN-HELMHOLTZ INSTABILITY IN A PIPE

Nonlinear MHD Kelvin-Helmholtz(K-H)instability in a pipe is treated with the deriva- tive expansion method in the present paper The linear stability problem was discussed in the past by Chandrasekhar(1961)and Xu et al.(1981).Nagano(1979)discussed the nonlinear MHD K-H instability with infinite depth.He used the singular perturbation method and extrapolated the ob- tained second order modifier of amplitude vs.frequency to seek the nonlinear effect on the instability growth rate γ.However,in our view,such an extrapolation is inappropriate.Because when the instabili- ty sets in,the growth rates of higher,order terms on the right hand side of equations will exceed the cor- responding secular producing terms,so the expansion will still become meaningless even if the secular producing terms are eliminated.Mathematically speaking,it's impossible to derive formula(39) when γ_0~2 is negative in Nagano's paper.Moreover,even as early as γ_0~2→O^+,the expansion be- comes invalid because the 2nd order modifier γ_2(in his formula(56))tends to infinity.This weak- ness is removed in this paper,and the result is extended to the case of a pipe with finite depth.

Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability(KHI)of two superposed finite-thickness fluid layers with the magnetic field effect into consideration.The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased.When the thickness and the magnetic field act together on the KHI,the effect of thickness is more obvious when the magnetic field intensity is weak.The magnetic field transition layer destabilizes(enforces)the KHI,especially in the case of small thickness of the magnetic field transition layer.When considering the effect of magnetic field,the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness.The stronger the magnetic field intensity is,the more obvious the growth rate decreases with the total thickness.Thus,it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored,such as in double-cone ignition scheme for inertial confinement fusion.

Applications of Non-Classical Equations and Their Approaches to the Solution of Some of Classes Equations Arise in the Kelvin-Helmholtz Mechanism and Instability

In the presented work, we consider applications of non-classical equations and their approaches to the solution of some classes of equations that arise in the Kelvin-Helmholtz Mechanism (KHM) and instability. In all areas where the Kelvin-Helmholtz instability (KHI) problem is investigated with the corresponding data unchanged, the solution can be taken directly in a specific form (for example, to determine the horizontal structure of a perturbation in a barotropic rotational flow, which is a boundary condition taken, as well as other types of Kelvin-Helmholtz instability problems). In another example, the shear flow along the magnetic field in the Z direction, which is the width of the contact layer between fast and slow flows, has a velocity gradient along the X axis with wind shear. The most difficult problems arise when the above unmentioned equation has singularities simultaneously at points and in this case, our results also remain valid. In the case of linear wave analysis of Kelvin-Helmholtz instability (KHI) at a tangential discontinuity (TD) of ideal magneto-hydro-dynamic (MHD) plasma, it can be attributed to the presented class, and in this case, as far as we know, solutions for eigen modes of instability KH in MHD plasma that satisfy suitable homogeneous boundary conditions. Based on the above mentioned area of application for degenerating ordinary differential equations in this work, the method of functional analysis in order to prove the generalized solution is used. The investigated equation covers a class of a number of difficult-to-solve problems, namely, generalized solutions are found for classes of problems that have analytical and mathematical descriptions. With the aid of lemmas and theorems, the existence and uniqueness of generalized solutions in the weight space are proved, and then general and particular exact solutions are found for the considered problems that are expressed analytically explicitly. Obtained our results may be used for all the difficult-to-solve processes of KHM and instabilities and instabilities, which cover widely studied areas like galaxies, Kelvin-Helmholtz instability in the atmospheres of planets, oceans, clouds and moons, for example, during the formation of the Earth or the Red Spot on Jupiter, as well as in the atmospheres of the Sun and other stars. In this paper, also, a fairly common class of equations and examples are indicated that can be used directly to enter data for the use of the studied suitable tasks.

Primary Results of Liquid Metal Free Surface Jet Research

The liquid metal free surface innovation concept have been considered as liquid metal devices of divertor/limiter and tile of first wall in fusion device because it can withstand over 50 MW·m^2 heating load, is easily renewed by circulation and many overcome neutron irradiation damage life time limit. There are three types of free surface in the innovation concept as film, curtain （jets or drops） and capillary. The free surface jet is played a more attention at present. But it is no so clear and only a few available data that their magneto-hydrodynamics （MHD） instabilities, interaction with plasma and exclusion of the particles （ions, Alpha particles and so on） from liquid metal, in despite of many liquid metal free surface facilities built and operated especially in US in last two years. Recently, some primary results are carried out at LMEL facility at Southwestern Institute of Physics.

计及表面残余应力的旋转凸凹型纳米圆板失稳分析

根据纳米材料表面残余应力和弹性板小挠度理论,建立旋转凸凹型纳米圆板横向振动微分方程,采用微分求积法得到不同条件下凸凹型纳米圆板的无量纲复频率随无量纲角速度和无量纲表面残余应力参数变化情况。研究结果显示:在周边固支和简支条件下,旋转凸凹型纳米圆板均发生第1阶发散失稳现象。在其他条件一定的情况下,周边固支凹型纳米圆板的临界失稳角速度小于凸型纳米圆板,周边简支凹型纳米圆板的临界失稳角速度大于凸型纳米圆板。临界失稳角速度随着表面残余应力的增加而增大,临界表面残余应力随着无量纲角速度的增加而增大。

可延展压电薄膜基底结构界面脱粘的预测与调控

调控薄膜基底结构的表面不稳定性已被成功应用于制备可延展的新型电子设备中。然而,该类电子器件在工作中需要承受外部载荷作用,致使薄膜-基底结构界面处残余应力集中,容易诱发薄膜电子器件与基底脱粘与分层。该文将从理论分析和数值仿真角度,研究压电薄膜在柔性基底表面上的失稳特性。由于压电薄膜变形具有大位移小应变的特点,该文基于非线性Euler-Bernoulli梁理论与能量最小化原理,建立压电薄膜基底结构无屈曲、褶皱、局部屈曲及全脱层屈曲模式的理论分析模型;从能量角度定量分析了薄膜-基底结构4种模式相互演变的临界条件;通过数值仿真,验证了该文解析结的有效性,定量、定性的讨论了薄膜基底结构的材料、几何参数对4种模式演变的影响。研究结果表明:改变基底弹性模量、预应变、物理场强度和界面粘附系数能够调控压电薄膜基底结构的屈曲模式;通过调控温度变化量和电压的方式,能够实现对压电薄膜基底结构的失稳特性精细化调控。该文的研究结果将为提升薄膜基底型的电子器件的稳定性及优化设计提供理论支持。

基于海表温度遥感资料重构的热带不稳定波特征分析

[目的]研究赤道东太平洋热带不稳定波(tropical instability waves,TIWs)的时空分布特征及其驱动机制.[方法]利用数据插值经验正交函数方法对MODIS卫星2003-2018年赤道东太平洋海表面温度(sea surface temperature,SST)数据进行重构,进而提取TIWs的波长和速度,并分析其时空分布特征以及与赤道风场和流场的关系.[结果]研究发现:TIWs在纬向上呈正负相位交替分布,在经向上则表现为双峰结构.季节性方面,TIWs在3-5月强度最弱,而在8-10月强度最强.纬向风场通过影响赤道纬向流场,特别是南赤道流(South Equatorial Current,SEC)的北分支(SEC-N)和北赤道逆流(North Equatorial Countercurrent,NECC)的剪切调控TIWs的生成;经向风场则通过调制“冷舌”边缘的SST梯度影响TIWs的生成.在年际尺度上,TIWs在厄尔尼诺(El Nino)年受到抑制,在拉尼娜(La Nina)年得到加强.纬向风场、纬向流场和TIWs三者的异常均超前于厄尔尼诺-南方涛动(El Nino-Southern Oscillation,ENSO)指数所刻画的赤道东太平洋SST异常,这表明纬向风场影响下的纬向流场剪切同样驱动TIWs的年际变化.NECC上空纬向风异常较弱,而SEC-N上空纬向风异常较强,这使得SEC-N年际变化主导流场剪切的强度,对TIWs的年际特征有重要作用.[结论]这一发现强调了大气风场和海洋动力过程共同驱动TIWs的季节性特征和年际变化.