Stationary, axisymmetric, vacuum, solutions of Einstein’s equations are obtained as critical points of the total mass among all axisymmetric and (t, φ) symmetric initial data with fixed angular momentum. In this variational principle, the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if an absolute minimum exists then it is equal to the ab...

An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also obse...

[1] In the paper ‘‘Single-layer axisymmetric model for a Hadley circulation with parameterized eddy momentum forcing’’ by Adam H. Sobel and Tapio Schneider (Journal of Advances in Modeling Earth Systems, 1, 10, doi:10.3894/ JAMES.2009.1.10., 2009) [hereinafter referred to as SS09], we presented an axisymmetric single-layer model for Hadley circulations with parameterized eddy momentum fluxes. R...

In this paper, the general governing equations of three-dimensional vibrations of an Euler-Bernoulli Beam under influences of system dynamics are derived by the Hamiltonian method. Then two fundamental cases of a cantilever beam and a rotating beam are considered. The conventional methods for vibration suppression debit to expenses and make new problems such as control spillover because they ar...

We report a new critical solution found at the threshold of axisymmetric gravitational collapse of a complex scalar field with angular momentum. To carry angular momentum the scalar field cannot be axisymmetric; however, its azimuthal dependence is defined so that the resulting stress-energy tensor and spacetime metric are axisymmetric. The critical solution found is nonspherical, discretely se...

In this article we investigate the LBB condition for axisymmetric flow problems. Specifically, the sufficiency condition for approximating pairs to satisfy the LBB condition established by Stenberg in the Cartesian coordinate setting is presented for the cylindrical coordinate setting. For the cylindrical coordinate setting, the Taylor-Hood (k = 2) and conforming Crouzeix-Raviart elements are s...

This short paper describes a numerical model study of an axisymmetric atmospheric circulation (somewhat akin to the Earth’s tropical Hadley circulation) subject to a periodic forcing that cyclically modifies the static stability. The configuration is not particularly realistic as a representation of the true circulation in the Earth’s tropics, but its motivation is justified as an idealized tes...

1.0 Introduction 2.0 The 2.1 2.2 2.3 2.4 2.4 Experiment Position Control Velocity Sensors Recording and Analysis Flux Control Rotation Control 3.0 Vibrations of An Annular~Vortex 3.1 An Old Problem 3.2 An Axisymmetric Annular Vortex 3.3 Equations of Motion 3.3.1 Perturbations and Scaling 3.3.2 Complete Equation for the Perturbation Pressure 3.3.3 The Rayliezh Discriminant -3.3.4 Boundary Condit...

In the framework of the complex cubic-quintic Ginzburg-Landau equation, we perform a systematic analysis of two-dimensional axisymmetric doughnut-shaped localized pulses with the inner phase field in the form of a rotating spiral. We put forward a qualitative argument which suggests that, on the contrary to the known fundamental azimuthal instability of spinning doughnut-shaped solitons in the ...

For high amplitudes of vibrations, loudspeakers are subject to nonlinear phenomena that are responsible for audible distortions. In order to describe the complex dynamics of the system, the displacement field as well as the radiated sound pressure must be expressed in the time-domain. Thus the present study proposes a transient model of the acoustic radiation of axisymmetric structures. The pre...