The Pulsational Instability of Non-Isothermal Magnetized Accretion Disk with Self-Gravity in the Transition Zone

By analyzing the fifth-order dispersion relation, the influence of coupled magnetic field and self-gravity on the pulsational instability of gas pressure dominated accretion disk is investigated. Our main results are that the viscous modes become more stable with the increase of self-gravity, magnetized field and viscosity, while they enhance the instabilities of acoustic modes. The effect of self-gravity to the instability is much greater than that of magnetic field in transition zone of the accretion disk. Especially, the self-gravity affects the thermal-modes and acoustic modes strongly. Finally, we discuss our results.     

The Radial-Azimut ha1 Inst ability of an Isothermal Magnetized Accretion Disk

The radial-azimuthal instability of an isothermal magnetized accretion disk is examined in this paper. We find that the azimuthal perturbation enhances the instability of the magneto-acoustic and non-axisymmetric modes. The magnetic field induces and enhances the instability of magneto-acoustic modes, but stabilizes the non-axisymmetric modes in the outer disk. The viscous modes are always stable. The instability of magneto-acoustic modes are dominant in this disk.     

The Radial-Azimuthal Instability of a Radiation-Pressure-Dominated Accretion Disk with Advection

A radial-azimuthal instability analysis of a radiation-pressure-dominated accretion disk with advection is presented. We find that the including of a very little advection has significant effect on two acoustic modes, which are no longer complex conjugates of each other. With the increase of azimuthal perturbations, the thermal mode becomes more unstable and the viscous mode more stable, but there has no effect on acoustic mode. For geometrically slim and advection-dominated disks, the azimuthal perturbation and increasing of advection do not affect the stability of all the modes.     

Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis

The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We contrast mode coupling in radial flow with rectangular flow geometry.     

Rotating flexible disk under shaft temperature increment

A rotating flexible annular thin disk subjected to the temperature increment of the shaft clamping the disk was modeled in this paper. At disk top and bottom surfaces and free outer edge, the heat convection boundaries were assumed. Disk transverse deflection was considered as a function of both disk radial and circumferential coordinates, and temperature distribution was solved along disk thickness and radial directions simultaneously. As a result, the shaft temperature increment causes thermo-elastic instability of some disk modes. Effects of the shaft temperature increment, ratio of disk convective heat transfer coefficient to thermal conductivity, disk thickness, nodal circle and diameter numbers of disk mode on the natural frequencies, thermo-elastic instability and critical angular speed of the disk were discussed.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Entropy analysis on unsteady MHD biviscosity nanofluid flow with convective heat transfer in a permeable radiative stretchable rotating disk

We examine the entropy analysis in three-dimensional hydromagnetic flow and convective heat transport of a biviscosity nanofluid over a rotating porous disk with a time-dependent stretching rate in the direction of the radius of the circular disk. We also examine the influence of thermal radiation and viscous dissipation due to nanoparticles and applied magnetic field. We invoked suitable self-similar transformations to covert the modeled coupled nonlinear PDEs into a set of nonlinear ODEs. The transformed system of equations is then worked out numerically by a well-known shooting technique and the fourth-order Runge–Kutta–Fehlberge method. The rotating phenomenon yields an additional parameter known as a rotation parameter, which controls the disk’s rotation. The study shows that the fluid motion is accelerated along the radial and cross-radial directions with an increase in the rotation of the disk. The skin-friction and the heat transfer rate at the disk strongly depend on the rotation of the disk, permeability of the porous medium, thermal radiation, and nanoparticle size. The Bejan number quantifies the entropy production of the system. It has a considerable impact on the magnetic field, rotation of the disk, thermal radiation, and Biot number. The efficient performance of the system is possible by a suitable choice of the physical parameters discussed in this article.     

A steadily rotating plasma disk

A homogeneously rotating plasma disk can be formed in a radially directed Ar-arc discharge at reduced pressure with an externally applied axial magnetic field. The radial pressure distribution is measured, as well as the emitted continuum radiation and the arc voltage. With these experimental values profiles of temperature, radial and azimuthal current density, and flow velocity in the disk are evaluated. Viscosity determines the flow pattern essentially. The effects of magnetic field and rotational motion on the discharge are investigated. The disk exhibits at nonrigid rotation a strong centrifugal force and a minor Coriolis force. A weak double vortex is found to develop in the meridional plane. The electric field in the discharge is altered by the azimuthal plasma flow.     

Stability analysis using multiple scales homotopy approach of coupled cylindrical interfaces under the influence of periodic electrostatic fields

The influence of axial periodic electric fields on streaming flows through three coaxial infinitely vertical cylinders is considered. The three fluid layers are assumed to be incompressible, dielectric, viscous and saturated through porous media. To relax the mathematical manipulation of the problem, the viscous potential theory is considered. Through the current work, the stability analysis of the coupled Mathieu equations is developed in the analogy of the multiple scales homotopy technique. Away from the symmetric and anti-symmetric modes, the present study investigates a general case of the surface waves deflections. To overcome the lengthy of the algebraic calculations, the matrices concept is utilized. The stability analysis reveals the resonance as well as non-resonance cases. A set of graphs are depicted to indicate some resonance cases for a chosen sample through a dimensionless system. Therefore, the influence of some physical parameters on the stability picture is indicated. In addition, the perturbed solutions of the governed Mathieu equations are graphed.     

An approximated 3-d model of the Langevin transducer and its experimental validation

In this work, an approximated 3-D analytical model of the Langevin transducer is proposed. The model, improving the classical 1-D approach describing the thickness extensional mode, allows us to predict also the radial modes of both the piezoelectric ceramic disk and the loading masses; furthermore, it is able to describe the coupling between radial and thickness extensional modes. In order to validate the model, the computed frequency spectrum is compared with that obtained by measurements carried out on 13 manufactured samples of different thicknesses to diameter ratios. The comparison shows that the model predicts with quite good accuracy the resonance frequencies of the two lowest frequency modes, i.e., those of practical interest, all over the explored range. Finally, the coupling effect between thickness and radial modes on the frontal displacement is measured and discussed.     

高密度光盘径向倾斜对DPD循轨误差信号影响分析

根据高密度光盘参数 ,计算了聚焦光斑在光盘表面扫描过程中每个位置的光瞳光强分布 ,得到DPD(Differ entialPhaseDetection)循轨误差信号。考虑盘片的径向倾斜 ,在光瞳光强分布方程中引入盘片的径向倾斜角度参数 ,计算了高密度盘片产生径向倾斜时DPD循轨误差信号的变化 ,进而分析了盘片的径向倾斜引入的循轨伺服误差及其对循轨伺服的负面影响。结果表明 ,高密度盘片产生 0 .5°的径向倾斜相当于引入了 0 .0 12 μm的循轨误差     

Investigation on arc characteristics in cup-shaped contacts with different structure for transverse magnetic field vacuum circuit breaker

The cup-shaped transverse magnetic field (TMF) contacts contain radial components and tangential components in the TMF generated when the current is interrupted. The tangential force generated by the radial magnetic field component drives the vacuum arc to rotate, and the tangential magnetic field component generates a radial force that causes the vacuum arc to move radially outward. In this paper, in order to study the influence of the arc force direction on the arc characteristics, the influence of the contact structure parameters such as the inclination of the inner wall on the arc force direction is simulated, and the breaking tests of different levels of current are carried out on the contact with different structure parameters. It is found that the direction of the Lorentz force has a significant effect on the breaking characteristics of the current, and the tangential and radial force components have varying degrees of influence on the motion characteristics of the arc during the start process and the metal droplet splashing.     

Crossover between 2D and 3D fluid dynamics in the diffusion of islands in ultrathin freely suspended smectic films

The Stokes paradox, that moving a disk at finite velocity through an infinite two-dimensional (2D) viscous fluid requires no force, leads, via the Einstein relation, to an infinite diffusion coefficient D for the disk. Saffman and Delbrück proposed that if the 2D fluid is a thin film immersed in a 3D viscous medium, then the film should behave as if it were of finite size, and D～ -ln(aη'), where a is the inclusion radius and η' is the viscosity of the 3D medium. By studying the Brownian motion of islands in freely suspended smectic liquid crystal films a few molecular layers thick, we verify this dependence using no free parameters, and confirm the subsequent prediction by Hughes, Pailthorpe, and White of a crossover to 3D Stokes-like behavior when the diffusing island is sufficiently large.     

The Magnetic Model of Accretion Disk and the Overstability of .Radial Oscillation

We put forward, in the essay, the assumption of the magnetic model of accretion disk with magnetic viscosity. Optically thick, is the disk whose radiation is thermal in the outer region, while in the inner region it is optically thin and the radiation mechanism is synchrotron. From this we derive the general dispersion relation of the accretion dik for the radial oscillation and discuss the stability and overstability in each region of the disk. The conclusion, therefore, is reached that the accretion disk is globally stable and locally overstable. The global stability may avoid the break of the disk, and the local overstability can cause the optical variation on a short-time scale. Calculating the time scale and the magnitude of the variation caused by the overstability, we get the result which fits well the observed result of BL Lac. objects.     

Moment and forces exerted on the inner cylinder in eccentric annular flow

This paper presents results of numerical modeling for analysis of the moment and forces exerted on an eccentrically positioned rotating inner cylinder due to the annular flow between two cylinders with parallel axes. Laminar stationary fully developed flows of Newtonian and power law fluid flows are considered. An impact of annulus geometry, flow regime, and fluid characteristics are studied. The study indicates that the moment exerted on the inner cylinder increases monotonically with the eccentricity. Forces acting on the inner cylinder include pressure and viscous friction. The pressure forces provide a predominant contribution. When eccentricity does not exceed a certain critical value, the radial force pushes the inner cylinder to the channel wall. When eccentricity is large enough, the radial force reverses its sign, and the inner cylinder is pushed away from the outer wall. Circumferential component of the force has always the same direction and induces precession of the inner cylinder.     

高密度光盘循轨伺服中盘片径向倾斜的影响分析

基于标量衍射理论,根据实际光盘的参数,对数字多用途光盘(DVD光盘)的循轨行为进行了分析。在此基础上,针对盘片产生径向倾斜的情况引入了倾斜参数,对盘片模型进行了补充。对光盘的径向倾斜误差和系统循轨伺服的交叉影响进行了分析和讨论。     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

Three-dimensional analysis of blade force and sound generation for an annular cascade in distorted flows

An unsteady lifting-surface theory for a rotating subsonic annular cascade has been developed to predict the unsteady blade forces and the acoustic power generation caused by interaction of blades with inlet distortions or wakes. Disturbance pressure and velocity fields induced by the rotor blades with fluctuating blade force are expressed in terms of the blade force distribution and kernel functions. The spanwise distribution of the blade force is given as a sum of blade force modes, and the kernel functions are resolved into the corresponding modal components. The sound pressure and intensity are expressed as a sum of acoustic modes, the modal components of which are given in terms of the blade force mode components.Numerical computations have been conducted .for interaction with the external disturbance flows that are sinusoidal in the circumferential direction, but possess a phase skewing in the radial direction. Correlations among the acoustic modes, the blade force modes and the flow patterns of the external disturbance have been investigated. When the predominant acoustic mode is subresonant, the blade force amplitude is reduced by the three-dimensional effect, which is lessened as the frequency increases. At deeply superresonant states, however, the three-dimensional effect upon the spanwise average of the blade force amplitude is small. The generated sound power is effectively reduced by increasing the radial non-uniformity of the external disturbance.     

A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.     

Effect of trapped energetic ions on MHD activity in spherical tori

It is shown that the increase of β (the ratio of plasma pressure to the magnetic field pressure) may change the character of the influence of trapped energetic ions on MHD stability in spherical tori. Namely, the energetic ions, which stabilize MHD modes (such as the ideal kink mode, collisionless tearing mode and semi-collisional tearing mode) at low β, have a destabilizing influence at high β unless the radial distribution of the energetic ions is very peaked.