Arc Root Motions In An Argon-Hydrogen Direct-Current Plasma Torch At Reduced Pressure

Arc root motions in generating dc argon-hydrogen plasma at reduced pressure are optically observed using a high-speed video camera. The time resolved angular position of the arc root attachment point is measured and analysed. The arc root movement is characterized as a chaotic and jumping motion along the circular direction on the anode surface.

Plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant materials

The plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant material are investigated in this paper. Applying the stress-strain relation for the pressure-sensitive dilatant material, we have obtained an exact asymptotic solution for the plane strain tip fields for two types of cracks, one of which lies in the pressure-sensitive dilatant material and the other in the elastic material and their tips touch both the bimaterial interface. In cases, numerical results show that the singularity and the angular variations of the fields obtained depend on the material hardening exponent n, the pressure sensitivity parameter mu and geometrical parameter lambda.

MILU-CG method and the numerical study on the flow around a rotating circular cylinder

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Numerical estimate of the stability curve for the flow past a rotating cylinder

It is demonstrated that the primary instability of the wake of a two-dimensional circular cylinder rotating with constant angular velocity can be qualitatively well described by the Landau equation. The coefficients of the Landau equation are determined by means of numerical simulations for the Navier-Stokes equations. The critical Reynolds numbers, which depend on the angular velocity of the cylinder, are evaluated correctly by linear regression. (C) 2004 American Institute of Physics.

Attractor crisis and bursting in a fluid flow with two no-slip directions

Characteristic burtsing behavior is observed in a driven, two-dimensional viscous flow, confined to a square domain and subject to no-slip boundaries. Passing a critical parameter value, an existing chaotic attractor undergoes a crisis, after which the flow initially enters a transient bursting regime. Bursting is caused by ejections from and return to a limited subdomain of the phase space, whereas the precrisis chaotic set forms the asymptotic attractor of the flow. For increasing values of the control parameter the length of the bursting regime increases progressively. Passing another critical parameter value, a second crisis leads to the appearance of a secondary type of bursting, of very large dynamical range. Within the bursting regime the flow then switches in irregular intervals from the primary to the secondary type of bursting. Peak enstrophy levels for both types of bursting are associated to the collapse of a primary vortex into a quadrupolar state.

Singular behaviour near the tip of a sharp V-notch in a power law hardening material

This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

Simplified Navier-Stokes equations (SNSE)

Ten kinds of the simplified Navier-Stokes equations (SNSE) are reviewed and also used to calculate the Jeffery-Hamel flow as well as to analyze briefly the seven kinds of flows to which the exact solutions of the complete Navier-Stokes equations (CNSE) have been found. Analysis shows that the actual differences among the solutions of the different SNSE can go beyond the range of the order of magnitude of Re-1/2 and result even in different flow patterns, therefore, how to choose the viscous terms included in the SNSE is worthy of notice where Re=S∞u∞ L/μ∞ is the Reynolds numbers. For the aforesaid eight kinds of flows, the solutions to the inner-outer-layer-matched SNSE and to the thin-layer-2-order SNSE agree completely with the exact solutions to CNSE. But the solutions to all the other SNSE are not completely consistent with the exact solutions to CNSE and not a few of them are actually the solutions of the classical boundary layer theory. The innerouter-layer-matched SNSE contains the shear stress causing angular displacement of the inormal axis with respect to the streamwise axis and the normal stress causing expansion-contraction in the direction of the normal axis and the viscous terms being of the order of magnitude of the normal stress; and it can also reasonably treat the inertial terms as well as the relation between the viscous and inertial terms. Therefore, it seems promising in respects of both mechanics and mathematics.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

Characteristics of Wake Flow in Long Bluff Bodies

Vortex shedding is the main characteristics of bluff bodies, which will cause the bluff bodies to vibrate and sometimes result in the structures failure. In this paper the wake flow characteristics of 21 bluff bodies with rectangular, rounded and angular profiles and the length-to-width ratio in the range of 4~12 were deeply studied by Micro ADV. Two parameters, namely the relative intensity of the load due to Karman vortices and the large scale vortex intensity, were introduced to measure the wake flow intensity. Generally, the values of these parameters for different bluff bodies are consistent with each other. The experiment results showed that the key factor affecting the wake flow characteristics is the bluff edge, especially the leading edge geometry. The wake flow in bluff bodies with rounded edge profiles has more regular vortices and becomes more periodic than that in bluff bodies with rectangular ones. A bluff body with angular edged profile was witnessed to have not only small wake loading but small hydraulic resistance also.

AUTOROTATION OF TWO TANDEM TRIANGULAR CYLINDERS

The autorotation of two tandem triangular cylinders at different gap distances is investigated by numerical simulations. At the Reynolds number of 200， three distinct regimes are observed with the increase of gap distance: namely, angular oscillation, quasi-periodic autorotation and ‘chaotic’ autorotation. For various gap distances, the characteristic of vortex shedding and vortex interaction are discussed. The phase graphs (angular acceleration vs. angular velocity) and the power spectra of moment are analyzed to characterize the motion of the cylinder. The Lyapunov exponent is also calculated to identify the existence of chaos.

Electron dynamics and harmonics emission spectra due to electron oscillation driven by intense laser pulses

The dynamics and harmonics emission spectra due to electron oscillation driven by intense laser pulses have been investigated considering a single electron model. The spectral and angular distributions of the harmonics radiation are numerically analyzed and demonstrate significantly different characteristics from those of the low-intensity field case. Higher-order harmonic radiation is possible for a sufficiently intense driving laser pulse. A complex shifting and broadening structure of the spectrum is observed and analyzed for different polarization. For a realistic pulsed photon beam, the spectrum of the radiation is redshifted for backward radiation and blueshifted for forward radiation, and spectral broadening is noticed. This is due to the changes in the longitudinal velocity of the electron during the laser pulse. These effects are much more pronounced at higher laser intensities giving rise to even higher-order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that broadening of the high harmonic radiation can be limited by increasing the laser pulse width. The complex shifting and broadening of the spectra can be employed to characterize the ultrashort and ultraintense laser pulses and to study the ultrafast dynamics of the electrons. (c) 2006 American Institute of Physics.

The intensity distributions of collected signals in coherent anti-Stokes Raman scattering microscopy

Coherent anti-Stokes Raman scattering (CARS) microscopy with the combining of confocal and CARS techniques is a remarkable alternative for imaging chemical or biological specimens that neither fluoresce nor tolerate labeling. The CARS is a nonlinear optical process, the imaging properties of CARS microscopy will be very different from the conventional confocal microscopy. In this paper, we calculated the propagation of CARS signals by using the wave equation in medium and the slowly varying envelope approximation (SVEA), and find that the intensity angular distributions vary considerably with the different experimental configurations and the different specimen shapes. So the conventional description of microscopy (e.g.. the point spread function) will fail to descript the imaging properties of CARS microscopy. (c) 2004 Elsevier B.V. All rights reserved.