Slow Rotation Limit Research Articles

Normal modes of relativistic stars in slow rotation limit

view Abstract Citations (45) References (26) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Normal Modes of Relativistic Stars in Slow Rotation Limit Kojima, Yasufumi Abstract Rotational shifts of normal frequencies in polytropic stellar models are calculated within the framework of general relativity. The stellar rotation is assumed to be slow and the first-order rotational effects are included to the eigenfrequencies of the nonrotating stars. Unlike in Newtonian theory, the normal frequencies of nonradial oscillations of slowly rotating configurations are complex numbers. The real and imaginary parts correspond to the oscillatory and damping rates of the mode. The frequency and decay rate of the corotating f-mode increase with the increase of the stellar angular velocity. On the other hand, those of the counterrotating mode decrease. The counterrotating mode eventually becomes unstable beyond a critical angular velocity. The critical angular velocity cannot be determined exactly but can be estimated by extrapolating the behavior of the normal mode of a slowly rotating star. The critical value is smaller for larger azimuthal wavenumber and harder equation of state. The relativistic effects also tend to diminish the critical value. Publication: The Astrophysical Journal Pub Date: September 1993 DOI: 10.1086/173073 Bibcode: 1993ApJ...414..247K Keywords: Neutron Stars; Relativistic Theory; Stellar Models; Stellar Oscillations; Stellar Rotation; Angular Velocity; Boundary Conditions; Variational Principles; Astrophysics; RELATIVITY; STARS: NEUTRON; STARS: OSCILLATIONS; STARS: ROTATION full text sources ADS |

Nonlinear spiral waves in rotating pipe flow

A numerical investigation of finite-amplitude, non-axisymmetric disturbances, in the form of travelling spiral waves, is made in pipe flow with superimposed solid-body rotation. Rotating pipe flow is found to be supercritically unstable both in the rapid and slow-rotation regimes. Earlier weakly nonlinear calculations, suggesting subcritical instability in the slow-rotation limit, are shown to be in error. Bifurcating neutral waves are calculated for various axial and azimuthal Reynolds numbers and wavenumbers. For fixed axial mean pressure gradient, the axial mean flow induced by these waves gives rise to a significant flux defect, in certain cases as large as 40-50% of the undisturbed mass flux; the possible relevance of this finding to the phenomenon of vortex breakdown is pointed out. In non-rotating pipe flow, no neutral disturbances in the assumed form of spiral waves are found for moderate Reynolds numbers; this indicates that previous conjectures, regarding a possible connection between nonlinear spiral waves in slowly rotating pipe flow and the asymptotic neutral states of Smith & Bodonyi (1982) in non-rotating pipe flow, are not valid.

Aggregation of anisotropic particles

The diffusion limited aggregation of particles with anisotropic sticking probabilities has been investigated using computer models. All of our simulations have been carried out using 2d square lattices with square ‘‘particles’’ having two more sticky and two less sticky sides with sides of different kinds adjacent to each other. In both the limits of fast and slow particle rotation the anisotropy of the particles enhances the anisotropy of the square lattice and cross-shaped clusters (with side branches) are formed which resemble those generated by very much larger scale simulations of the regular DLA process. In the slow rotation limit a bias in the number of particles launched with sticky sides facing in the X or Y directions on the lattice leads to the formation of needle-shaped clusters whose radius of gyration (Rg) increases with cluster mass (M) according to Rg ∼M2/3.

Differential rotation set up by latitude-dependent heat transport

Abstract Models of differentially rotating compressible deep spherical shells are computed according to the method of Belvedere and Paterno (1977): the heat transport is entirely convective, small-scale motions are parametrized by a thermal diffusivity and a kinematic viscosity, and the limit of slow rotation and large viscosity is considered. In order to adapt the resulting differential rotation to the observed equatorial acceleration of the Sun, the heat transport must be more effective in the vicinity of the equator. In all models the latitude dependence of the transport coefficient induces meridional circulation in the form of a large cell, with rising material at high latitudes and sinking material near the equator. On top of this cell, one or two thin countercells develop in a minority of cases. Large pole-equator temperature differences and meridonal velocities at the surface are obtained when the Prandtl number is 1. But values of, say, 1/10 are sufficiently small to allow the models to be applied...

Proton NMR Investigation of Hindered Methyl Rotation in Paramagnetic Cr(II) Complexes

It is shown that in a paramagnetic complex, methyl rotation can act as an effective correlation time for spin relaxation through the Fermi contact interaction. For unhindered methyl groups, this mechanism can lead to methyl line narrowing. In the limit of slow methyl rotation resulting from steric hinderance, methyl rotation is capable of modulating the average hyperfine interaction (contact shift), which leads to methyl line broadening similar to that observed from chemical exchange effects. The proton linewidths of a series of tris-Cr(II) chelates with methyl-substituted ortho-phenanthrolines have been investigated. The linewidths of the aromatic protons in all complexes are determined by primarily the dipolar interaction. The linewidths of methyl groups which are expected to be sterically hindered are considerably broader than accountable by either dipolar or hyperfine exchange relaxation. We conclude that the anomalous methyl linewidths arise from modulation of the average hyperfine interaction by methyl rotation. The temperature dependence of the observed linewidths yields the barrier to methyl rotation.

EPR Studies of the Rotation of Phenyl Rings in Benzophenone Ketyls

Temperature dependence of the EPR spectra of various benzophenone ketyls and related compounds was studied in detail. Complete ranges of spectra from the spectra in the limit of rapid rotation of phenyl ring to the spectra in the limit of slow rotation of phenyl ring were obtained for benzophenone free ions and ion-pair ketyls and explained in terms of Freed–Fraenkel relaxation matrix theory, using a four-jump model. Unequivalent ortho and meta hyperfine splittings, rates, and activation energies for the rotation of phenyl rings were determined. Effects of ion-pair formation and higher aggregation on the rates of rotations of rings have been studied in several systems.