1,497 research outputs found
Axial instability of rotating relativistic stars
Perturbations of rotating relativistic stars can be classified by their
behavior under parity. For axial perturbations (r-modes), initial data with
negative canonical energy is found with angular dependence for all
values of and for arbitrarily slow rotation. This implies instability
(or marginal stability) of such perturbations for rotating perfect fluids. This
low -instability is strikingly different from the instability to polar
perturbations, which sets in first for large values of . The timescale for
the axial instability appears, for small angular velocity , to be
proportional to a high power of . As in the case of polar modes,
viscosity will again presumably enforce stability except for hot, rapidly
rotating neutron stars. This work complements Andersson's numerical
investigation of axial modes in slowly rotating stars.Comment: Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of
timescales is corrected and update
Constraining phases of quark matter with studies of r-mode damping in neutron stars
The r-mode instability in rotating compact stars is used to constrain the
phase of matter at high density. The color-flavor-locked phase with kaon
condensation (CFL-K0) and without (CFL) is considered in the temperature range
10^8K < T <10^{11} K. While the bulk viscosity in either phase is only
effective at damping the r-mode at temperatures T > 10^{11} K, the shear
viscosity in the CFL-K0 phase is the only effective damping agent all the way
down to temperatures T > 10^8 K characteristic of cooling neutron stars.
However, it cannot keep the star from becoming unstable to gravitational wave
emission for rotation frequencies f ~ 56-11 Hz at T ~ 10^8-10^9 K. Stars
composed almost entirely of CFL or CFL-K0 matter are ruled out by observation
of rapidly rotating neutron stars, indicating that dissipation at the
quark-hadron interface or nuclear crust interface must play a key role in
damping the instability.Comment: 8 pages, 2 figure
A simple derivation of Kepler's laws without solving differential equations
Proceeding like Newton with a discrete time approach of motion and a
geometrical representation of velocity and acceleration, we obtain Kepler's
laws without solving differential equations. The difficult part of Newton's
work, when it calls for non trivial properties of ellipses, is avoided by the
introduction of polar coordinates. Then a simple reconsideration of Newton's
figure naturally leads to en explicit expression of the velocity and to the
equation of the trajectory. This derivation, which can be fully apprehended by
beginners at university (or even before) can be considered as a first
application of mechanical concepts to a physical problem of great historical
and pedagogical interest
Generalized r-Modes of the Maclaurin Spheroids
Analytical solutions are presented for a class of generalized r-modes of
rigidly rotating uniform density stars---the Maclaurin spheroids---with
arbitrary values of the angular velocity. Our analysis is based on the work of
Bryan; however, we derive the solutions using slightly different coordinates
that give purely real representations of the r-modes. The class of generalized
r-modes is much larger than the previously studied `classical' r-modes. In
particular, for each l and m we find l-m (or l-1 for the m=0 case) distinct
r-modes. Many of these previously unstudied r-modes (about 30% of those
examined) are subject to a secular instability driven by gravitational
radiation. The eigenfunctions of the `classical' r-modes, the l=m+1 case here,
are found to have particularly simple analytical representations. These r-modes
provide an interesting mathematical example of solutions to a hyperbolic
eigenvalue problem.Comment: 12 pages, 3 figures; minor changes and additions as will appear in
the version to be published in Physical Review D, January 199
Had the planet mars not existed: Kepler's equant model and its physical consequences
We examine the equant model for the motion of planets, which has been the
starting point of Kepler's investigations before he modified it because of Mars
observations. We show that, up to first order in eccentricity, this model
implies for each orbit a velocity which satisfies Kepler's second law and
Hamilton's hodograph, and a centripetal acceleration with an inverse square
dependence on the distance to the sun. If this dependence is assumed to be
universal, Kepler's third law follows immediately. This elementary execice in
kinematics for undergraduates emphasizes the proximity of the equant model
coming from Ancient Greece with our present knowledge. It adds to its
historical interest a didactical relevance concerning, in particular, the
discussion of the Aristotelian or Newtonian conception of motion
The R-Mode Oscillations in Relativistic Rotating Stars
The axial mode oscillations are examined for relativistic rotating stars with
uniform angular velocity. Using the slow rotation formalism and the Cowling
approximation, we have derived the equations governing the r-mode oscillations
up to the second order with respect to the rotation. In the lowest order, the
allowed range of the frequencies is determined, but corresponding spatial
function is arbitrary. The spatial function can be decomposed in non-barotropic
region by a set of functions associated with the differential equation of the
second-order corrections. The equation however becomes singular in barotropic
region, and a single function can be selected to describe the spatial
perturbation of the lowest order. The frame dragging effect among the
relativistic effects may be significant, as it results in rather broad spectrum
of the r-mode frequency unlike in the Newtonian first-order calculation.Comment: 19 pages, 4 figures, AAS LaTeX, Accepted for publication in The
Astrophysical Journa
The meaning of variation to healthcare managers, clinical and health-services researchers, and individual patients
Healthcare managers, clinical researchers and individual patients (and their physicians) manage variation differently to achieve different ends. First, managers are primarily concerned with the performance of care processes over time. Their time horizon is relatively short, and the improvements they are concerned with are pragmatic and 'holistic.' Their goal is to create processes that are stable and effective. The analytical techniques of statistical process control effectively reflect these concerns. Second, clinical and health-services researchers are interested in the effectiveness of care and the generalisability of findings. They seek to control variation by their study design methods. Their primary question is: 'Does A cause B, everything else being equal?' Consequently, randomised controlled trials and regression models are the research methods of choice. The focus of this reductionist approach is on the 'average patient' in the group being observed rather than the individual patient working with the individual care provider. Third, individual patients are primarily concerned with the nature and quality of their own care and clinical outcomes. They and their care providers are not primarily seeking to generalise beyond the unique individual. We propose that the gold standard for helping individual patients with chronic conditions should be longitudinal factorial design of trials with individual patients. Understanding how these three groups deal differently with variation can help appreciate these three approaches
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