Instability of a spherical drop in a nonuniform electric field

Analytical calculation in the first order of smallness shows that the equilibrium shape of a drop in the field of a point charge is axisymmetric about the plane passing through the center of mass of the drop normally to the axis connecting the center of mass with the point charge. Whether the equilibrium shape of the drop is stable or not depends on the value of the field parameter, which, in turn, depends on the point charge and the distance to it. There is an asymptotic value of the critical parameter above which all modes become unstable. In the field of the point charge, the mode coupling grows; that is, a mode excited at the zero time generates oscillations of the six nearest modes with amplitudes proportional to that of the initially excited mode. If the initially excited mode loses stability, all the modes coupled with it also become unstable. The surface instability of the drop also develops when the initially excited mode is stable but at least one of the modes coupled with it is unstable.     

Capillary oscillations and stability of a charged drop rotating about the axis of symmetry

The stability of a charged conductive liquid drop rotating about the axis of symmetry against the pressure of the self-charge electric field and inertial force pressure is investigated in an approximation linear in oscillation amplitude and square of the spheroidal drop deformation eccentricity. It is found that the axisymmetric modes of the rotating drop are stable. Only nonaxisymmetric modes with azimuthal numbers maximal for a given mode may be unstable. The Coriolis force plays a stabilizing role.     

Linear (in oscillation dimensionless amplitude) interaction between the modes of a nonspherical charged drop in an external electrostatic field

The stability of a heavily charged drop in a weak uniform electrostatic field (in which the equilibrium shape of the drop can be represented by a prolate spheroid) is calculated in the fourth order of smallness in the eccentricity of the spheroidal drop and in the first order of smallness in the drop oscillation dimensionless amplitude. It is found that as the order of approximation in eccentricity grows, so does the number of modes interacting with the initially excited mode. In the given order of smallness, the preferred (initially excited) mode is shown to interact with the nearest eight modes. The drop becomes unstable if such is the second mode.     

Mechanisms behind spheroidal oscillations and electrostatic instability of a charged drop

Mechanisms behind the oscillations of a charged spheroidal drop deformed at the zero time and the sequence of oscillation modes are investigated. It is shown that two modes adjacent to those governing the initial deformation are also excited on either side due to interaction between the spheroidal deformation and oscillation modes. If the charge of the drop is so close to a value critical for electrostatic instability that the finite-amplitude virtual initial deformation makes the fundamental mode unstable, its amplitude, as well as the amplitude of the nearest neighbor coupled to the fundamental mode through deformation, starts to exponentially grow with time. If the charge is equal to, or slightly exceeds the critical value, the amplitudes of the fundamental mode and all modes deformation-coupled with it lose stability almost simultaneously. This qualitatively changes the conditions under which the charged drop becomes unstable against the self-charge. The superposition of higher oscillation modes at the vertices of the spheroidal drop generates dynamic (i.e., time-oscillating) hillocks emitting an excessive charge.     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

Analytical study of nonlinear vibrations of a charged viscous liquid drop

The generatrix of a nonlinearly vibrating charged drop of a viscous incompressible conducting liquid is found by directly expanding the equilibrium spherical shape of the drop in the amplitude of initial multimode deformation up to second-order terms. A fact previously unknown in the theory of nonlinear interaction is discovered: the energy of an initially excited vibration mode of a low-viscosity liquid drop is gradually (within several vibrations periods) transferred to the mode excited by only nonlinear interaction. Irrespectively of the form of the initial deformation, an unstable viscous drop bearing a charge slightly exceeding the critical Rayleigh value takes the shape of a prolate spheroid because of viscous damping of all the modes (except for the fundamental one) for a characteristic time depending on the damping rates of the initially excited modes and the further evolution of the drop is governed by the fundamental mode. In a high-viscosity drop, the rate of rise of the unstable fundamental mode amplitude does not increase continuously with time, contrary to the predictions of nonlinear analysis in terms of the ideal liquid model: it first decreases to a value slightly differing from zero (which depends on the extent of supercriticality of the charge and viscosity of the liquid), remains small for a while (the unstable mode amplitude remains virtually time-independent), and then starts growing.     

Nonlinear oscillations of a drop moving at a constant velocity in an insulating medium subjected to an electrostatic field

Nonlinear asymptotic calculations of the second order of smallness in the amplitude of the initial deformation of an ideally conducting liquid drop show that the laminar flow of an ideal conducting incompressible dielectric liquid flowing about the drop in an external electrostatic field parallel to the flow causes oscillation mode’s interaction in the first and second orders of smallness. Both linear and nonlinear interactions between the oscillation modes of the drop excite modes that are absent in the spectrum of modes governing the initial deformation of the drop’s equilibrium shape. In the second order of smallness, the mode interaction decreases the electrostatic field strength, as well as the velocity and density of the environment, that are critical for development of instability of the drop against the polarization charge.     

On the possibility of corona initiation near a conducting drop nonlinearly vibrating in an external electrostatic field

An analytical asymptotic expression for the field strength near an ideal incompressible electrically conducting liquid drop nonlinearly vibrating in external electrostatic field E ₀ is found in an order of 5/2 in a small parameter. The small parameter here is the amplitude of deformation of the spherical shape of the drop. It is found that the strength of the electric field resulting at the tops of the drop exceeds the corona-initiating field even if E ₀ is one order of magnitude lower than the value at which the drop becomes unstable against the induced charge (that is, at such values of E ₀ as are observed in storm clouds in full-scale experiments).     

DMD和POD对超燃冲压发动机凹腔流动的稳定性分析

开式凹腔作为超燃冲压发动机中增加掺混和稳焰的装置, 其流动稳定性的研究对深入理解凹腔增加掺混和稳焰机理以及凹腔的设计有着重要的学术意义和工程应用价值.基于大涡模拟方法对超燃冲压发动机开式凹腔流动进行数值模拟, 分别采用动力学模态分解(dynamic mode decomposition, DMD)和本征正交分解方法(proper orthogonal decomposition, POD)对自激振荡流动进行稳定性分析. DMD方法可准确提取凹腔的振荡频率, 与Rossiter模型以及压力脉动FFT分析得到的频率吻合较好, 且DMD中对应Rossiter前3阶频率的模态在流动中的主导作用顺序也与FFT分析结果一致, 自激振荡中RossiterⅢ模态占据主导作用, 同时DMD方法对Rossiter 3阶以上模态频率的预测能力明显强于FFT分析方法.在对低频的提取方面, DMD方法比Rossiter模型更具有优势.与前6阶Rossiter模态对应DMD模态均缓慢收敛, 主要表现为剪切层中的分离涡结构和中部及下游区域中的涡结构.前3阶不稳定模态中的分离涡结构主要集中在中部剪切层以及后缘附近区域. POD方法中较少的模态包含流场绝大部分的能量.但是, 通过POD方法提取的模态频率在分辨率上效果不佳, 提取到最低频率为Rossiter 3阶模态对应的频率, 且模态中均存在次频, 次频与主频之间的耦合导致模态的形态相差较大.另外, 与DMD方法相比POD方法无法判断所提取的模态的稳定性.      

声悬浮条件下黏性液滴的扇谐振荡规律研究

采用单轴式声悬浮方法研究了黏度μ =0.94-75.65 mPa·s的甘油-水溶液液滴的扇谐振荡规律. 发现一定阶数的振荡模式存在一定的临界黏度μ_c, 只有当μ < μ_c时, 该阶扇谐振荡才能被激发. 实验测定了声场调制幅度η = 0.23 时, l =2-9 阶扇谐振荡的临界黏度, 发现ln μ_c与l近似呈线性递减关系. 采用参数共振理论分析了黏性液滴的扇谐振荡过程, 发现激发扇谐振荡的液滴赤道半径扰动阈值h_c正比于液滴黏度μ, 并随l增大而增大, 因此扇谐振荡难以在高黏度和高阶模式下发生. 实验还发现, 各阶扇谐振荡的振幅和共振频率宽度随液滴黏度增大而减小, 黏度对液滴本征频率无明显影响.     

Photon statistics and autocorrelation of a multi-mode laser

The intensity fluctuation properties were experimentally studied for one mode among many oscillating longitudinal modes of an argon ion laser in a region sufficiently above threshold. The individual longitudinal mode fluctuated considerably even well above the threshold, while the laser intensity summed over all the longitudinal modes was observed stable. This fluctuation was found to be much larger than expected from the previous theoretical work by Arecchi and Ricca which did not consider the combination-tone polarization. The slowing-down and the increase of the fluctuation were observed when the excitation was lowered toward to its threshold value. The correlation time of the intensity fluctuation measured ranged from 0.7 μs to 20 μs depending on the oscillation condition.     

Onset of oscillatory binary fluid convection in finite containers

The onset of oscillatory convection in binary fluid mixtures in a two-dimensional domain with realistic boundary conditions on all boundaries is determined as a function of the fluid parameters and the aspect ratio Gamma of the container. The first unstable mode has either odd or even parity under left-right reflection. Depending on Gamma and the separation ratio S, this mode has the form of a standing wave, or a "chevron," consisting of a pair of waves propagating outwards from the cell center (or, in some cases, inwards towards it). Codimension--two points at which odd and even parity modes are simultaneously marginally stable are determined, as are various Takens-Bogdanov points. For fixed Sinfinity, and to the gap (in Rayleigh number and oscillation frequency) between successively unstable modes. The results quantify the parameter regime in which the weakly nonlinear dynamics of the system can be described in terms of the interaction of the first odd and even parity oscillatory modes.     

Effect of transverse static magnetic field on stimulated brillouin scattering of electromagnetic wave

Stimulated Brillouin scattering of a plane polarised electromagnetic wave propagating perpendicular to a static magnetic field has been investigated analytically in ann-type piezoelectric semiconductor-plasma. Using coupled mode theory the dispersion relation is obtained and the threshold value of the amplitude of electromagnetic wave for the onset of instability is studied for both the forward and back-scattered modes. The role of the magnetostatic field on the threshold conditions for the unstable mode has been discussed.     

The shape of a drop in a constant electric field

The variation of the shape of a drop immersed in an immiscible liquid under the action of an electric field is calculated. The charge is transferred both by ohmic current through the interface and by the convective component over the interface. A solution quadratic in the parameter that is the ratio of the electric pressure to the capillary pressure is analyzed. Conditions where the drop transforms into a spheroid that is prolate or oblate along the electric field vector are found. An experimental study of the drop deformation by electric forces is carried out.     

带通道插件管道流磁流体动力学效应的数值模拟

采用二维完全发展流模型对聚变反应堆包层带通道插件和压力平衡槽隙的矩形磁流体管流的MHD效应进行数值模拟,分析速度分布,MHD压降随哈德曼数以及通道插件的电导率的变化规律.与无插件磁流体管流相比,带绝缘通道插件管流MHD压降显著降低,MHD压降随哈德曼数的增加而减小,通道插件材料的电导率增加MHD压降系数减小.压力平衡槽隙处的回流与通道插件的电导率有关.在宏观上计算结果与实验结果和简化理论结果一致.     

过载条件下流动沸腾压降振荡的建模与仿真研究

流动沸腾系统中,压降振荡是系统不稳定性的主要型式之一。过载条件下流动沸腾压降振荡缺乏研究。本文采用数值仿真方法,对过载条件下管内流动沸腾的压降振荡特性进行了研究。建立了不同重力条件下压降振荡计算的数学模型,基于此,对过载条件下R134a在2.168 mm水平管内的压降振荡进行了仿真分析,得出了1.41 g、3.16 g(g=9.8 m/s^2)过载条件下的压降振荡特性及其引起的流量振荡、流体温度振荡和壁温振荡,并与对常重力(1 g)下的压降振荡特性进行了对比。结果表明,随着重力增加,流动特性N曲线的负斜率段缩短;一定条件下,当过载增加时,系统从稳定状态趋于不稳定状态。     

Behavior of prebreakdown emission centers with 200-kv 100-ns pulses applied to a vacuum gap

Using an electron-transparent anode (titanium foil), the behavior of prebreakdown emission centers on a cathode made of 12X18H10T stainless steel is studied for the case of vacuum gap excitation by 100-ns-wide voltage pulses with an amplitude of 200 kV. To raise the working electric field to 1 MV/cm or higher, the electrodes are preprocessed by a low-energy high-current electron beam in the surface melting mode. It is found that prebreakdown emission centers may be stable and unstable. The stable ones arise at an electric field strength of 0.4?C0.6 MV/cm, and their activity grows with voltage up to breakdown. As the electric field increases, new unstable emission centers occur at sites other than those observed at the previous voltage pulse. Reasons for the appearance of unstable emission centers are discussed.     

On the dynamics of pulsating detonations

To understand the circumstances in which a pulsatingdetonation wave may prefer a low-frequency mode ofoscillation, and the implications this has formathematical modelling, the dynamics of a detonation waveare studied when the underlying linear stability spectrumconsists of at most two unstable modes. One mode α₁ has a period much larger than the time-scaleof particle passage through the half-reaction length inthe steady one-dimensional detonation; the second α₂ has a smaller period than α₁. Thequestion addressed in this paper concerns the long-timebehaviour of the pulsating detonation in the presence ofthe unstable modes α₁ and α₂. Westudy two general scenarios related to a crossing of theneutral stability boundaries traced out by α₁ and α₂. In all cases where the mode α₁ is unstable, the pulsating detonation emerges with alow-frequency, large-amplitude oscillation, regardlessof the relative growth rates of α₁ and α₂. Only in one case, where thehigher-frequency mode α₂ is alone unstable, isthe long-time nonlinear pulsation of high frequency. Inthis case, the amplitude of the oscillation issignificantly smaller than that observed in thelow-frequency oscillations. In all cases, the finalperiod of the nonlinear oscillation is closely related tothat of the relevant underlying linear mode.     

石墨烯量子磁输运性质的电场效应

最近研究发现石墨烯在一维周期性电学或磁学调制势下, 其扩散电导率会出现Weiss振荡. 本文进一步探索了面外加垂直磁场和面内加横向电场以及一维周期性弱调制电学势的多场耦合作用下, 石墨烯的量子磁输运性质, 结果表明: Weiss振荡振幅和电导率数值都随着静电场的增加而增加. 有趣的是, 当电场与磁场的比值达到某一临界值, 即时, 输运电导率的Weiss振荡突然消失. 这一奇特现象在传统的二维电子气体中是不存在的, 因此可以归因于石墨烯载流子外加电磁场的反常相对论性能谱. 关键词：石墨烯; 静电场; Weiss振荡; 磁输运性质     

Deformation and nonlinear corrections to critical conditions of charged drop instability in an electrostatic suspension

Nonlinear asymptotic analysis of a charged drop placed in electrostatic and gravitational fields reveals a correction to the oscillation frequency and, accordingly, to the critical Rayleigh parameter. The analysis uses approximations quadratic in oscillation amplitude and linear in dimensionless equilibrium deformation of the drop. The correction is found to be proportional to the product of the oscillation amplitude and deformation. It is natural to name this correction deformational. In computations of the third order of smallness in oscillation dimensionless amplitude, a correction to the frequency and Rayleigh parameter appears, which is due to a nonlinear interaction between oscillation modes. This correction is larger than the deformational one in magnitude. Deformational corrections can be eliminated by experimenting under no-gravity conditions, but corrections due to the nonlinearity of hydrodynamic equations cannot be eliminated in this way. It is these corrections that are responsible for a critical Rayleigh parameter measurement inaccuracy.