Stability of a liquid-dielectric jet in a longitudinal electrostatic field

Conclusions A longitudinal electrostatic field tends to stabilize a jet of liquid dielectric.     

Asymptotic analysis of nonlinear nonaxisymmetric waves on the surface of a neutral dielectric jet in a longitudinal electrostatic field

The problem of calculation of finite-amplitude waves on the cylindrical surface of an ideal incompressible dielectric liquid jet in a uniform electrostatic field collinear to the unperturbed jet axis is solved using a second-order asymptotic analytic procedure in ratio of the wave amplitude to the jet radius. Nonlinear corrections to the jet profile, velocity field potential, and electrostatic potentials inside and outside the jet are of resonant nature. The degenerate resonant interaction between the wave determining the initial strain and the waves excited due to nonlinearity of the hydrodynamic equations can take place for waves with different symmetries (different azimuth numbers).     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.     

On the capillary stability of a cylindrical dielectric liquid jet in a longitudinal electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a cylindrical jet of an ideal incompressible dielectric liquid subjected to an electrostatic field aligned with the symmetry axis of the jet. It is shown that only long axisymmetric waves can experience capillary instability in such a system. The wavenumber range into which unstable waves fall begins with a zero value, and its width depends on the permittivities of the liquid and ambient and on the electrostatic field strength squared. As the field strength grows, the wavenumber range for unstable waves rapidly narrows and the capillary instability growth rate, as well as the wavenumber of the wave with the greatest growth rate, decreases.     

Effect of electric field on the longitudinal ultrasonic waves in Rochelle salt

The temperature dependence of velocity and attenuation for the longitudinal ultrasonic waves propagating along the (100) direction has been measured in the vicinity of the upper transition temperature under the various electric conditions in Rochelle salt.     

On the stability of capillary waves on the surface of a charged jet moving relative to the environment

A dispersion relation is derived for capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid moving relative to an ideal incompressible dielectric medium. It is shown that a tangential discontinuity in the velocity field on the surface of the jet leads to periodic instability of waves (similar to the Kelvin-Helmholtz instability) at the interface and destabilizes both axisymmetric and flexural waves. The wavenumber range for unstable waves and the instability growth rate increase with the field strength and relative speed of motion, varying as the square of these parameters. In the case of the neutral jet, the flexural instability is of the threshold character and sets in starting from a certain finite value of the speed rather than at an arbitrary small speed.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

电介质表面纵向射频电场对次级电子倍增效应的影响

基于次级电子倍增动力学模型和次级电子发射曲线,运用蒙特卡罗方法模拟电介质表面具有纵向射频电场作用下的单边次级电子倍增现象,研究次级电子倍增的表面电场敏感曲线和时间演化图像. 以一个S波段射频介质窗为例,计算次级电子在其介质表面的沉积功率. 结果表明,纵向射频电场可能加剧电介质表面的次级电子倍增效应,易于导致介质片破裂,不利于高频能量传输. 关键词： 纵向射频场 次级电子倍增效应 蒙特卡罗方法 功率沉积     

Nonlinear development of capillary waves in a viscous liquid jet

The one-dimensional approximate equations describing the dynamics of a Newtonian viscous fluid are used to analyze the nonlinear development of capillary waves in a jet. It is shown that the size of satellite droplets resulting from a nonuniform jet breakup decreases with the Reynolds number at a constant wavenumber. The satellite-droplet formation ceases at a certain value of the Reynolds number, which depends on the wavenumber and initial perturbation amplitude.     

Interaction of strongly nonlinear waves on the free surface of a dielectric liquid in a horizontal electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid with a large relative permittivity in a strong horizontal electric field has been considered. It has been demonstrated that the interaction between oppositely propagating solitary waves in arbitrary geometry is elastic: they conserve their energy and momentum. The interaction between waves has been numerically simulated with the use of conformal variables. It has been shown that the interaction deforms the waves; this effect is weak for waves with a relatively small amplitude: deformation for oppositely propagating waves with the identical shape is determined by the fourth power of their amplitude. At multiple collisions of strongly nonlinear waves, a tendency to the formation of singularities, i.e., points with a high energy density of the field, is observed.     

Band gap characteristics of plasma with periodically varying external magnetic field

The reflectance characteristics of a one-dimensional periodically magnetized plasma structure is studied by using the transfer matrix method. It is found that this system has the band gap characteristics of photonic crystals, so we also name it a plasma photonic crystal. The results show that the gap location and gap width can be controlled by the incident angle. If the external magnetic field is small, the gap location and gap width change significantly with incident angle, while they change only slightly when the external magnetic field is sufficiently large. The collision frequency has little effect on the gap location and gap width while it makes the amplitude of reflectance and transmission decrease. This new type of plasma photonic crystal could have potential applications in designing tunable photonic crystal devices.     

Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals

We study the propagation of thickness-twist (TT) waves in a crystal plate of AT-cut quartz with periodically varying, piecewise constant thickness. The scalar differential equation by Tiersten and Smythe is employed. The problem is found to be mathematically equivalent to the motion of an electron in a periodic potential field governed by Schrodinger’s equation. An analytical solution is obtained. Numerical results show that the eigenvalue (frequency) spectrum of the waves has a band structure with allowed and forbidden bands. Therefore, for TT waves, plates with periodically varying thickness can be considered as phononic crystals. The effects of various parameters on the frequency spectrum are examined.     

Stability of cylindrical conducting fluids with heat and mass transfer in longitudinal periodic electric field

A novel system to study the effect of an axial periodic electric field on the stability of a system of cylinders of conducting fluids in the presence of heat and mass transfer is investigated. The stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is found to be of damped Mathieu-type equation with real coefficients. The method of multiple time scales is used to obtain approximate solution and analyze the stability criteria for both the nonresonant and resonant cases. The stability of the system is also discussed analytically and numerically for such cases. It is found that both the heat and mass transfer coefficient and the dimensions of the system have destabilizing influences on the considered system, while azimuthal wavenumber is found to have a stabilizing effect. The dual role of the electric field frequency is also observed on the stability of the system depending on the electrical conductivities values. Finally the behaviour of the resonance points corresponding to the effects of each of the above physical parameters are determined, and a comparison between the obtained results with the corresponding results in the case of a constant applied electric field is achieved.     

Production of materials with periodically arranged microparticles by photopolymerization of patterns formed at parametric excitation of capillary surface waves

It is experimentally demonstrated that parametric excitation of capillary waves in a liquid polymer can result in a spatially periodic distribution of microparticles. The distribution of the particles follows the pattern of the waves excited on the surface of the liquid. It is shown that photopolymerization allows positions of microparticles to be fixed and materials with controlled spatially periodic inhomogeneity to be produced.     

Calculation of the number density of particles produced by a variable electric field during an arbitrary time

A calculation is made of the number density n of quasiparticles determined by the condition of diagonality of the Hamiltonian of a quantized field in a nonstationary external electric field. It is shown that for finite t the number n contains terms that describe real produced particles, vacuum polarization, and interference between the polarization and production effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 52–56, January, 1981.I thank A. A. Grib and V. M. Mostepanenko for helpful discussions.     

Stability of transverse vibration of a circular plate subjected to a periodically varying torque

The paper is concerned with transverse vibration of a circular plate subjected to periodically varying torsion. The instability regions are found and plotted for the plate under a tangent uniform load and a tangent concentrated force.