92 research outputs found
Stationary motion of a self gravitating toroidal incompressible liquid layer
We consider an incompressible fluid contained in a toroidal stratum which is
only subjected to Newtonian self-attraction. Under the assumption of
infinitesimal tickness of the stratum we show the existence of stationary
motions during which the stratum is approximatly a round torus (with radii r, R
and R>>r) that rotates around its axis and at the same time rolls on itself.
Therefore each particle of the stratum describes an helix-like trajectory
around the circumference of radius R that connects the centers of the cross
sections of the torus
Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars
We prove general nonlinear stability and existence theorems for rotating star
solutions which are axi-symmetric steady-state solutions of the compressible
isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our
results to rotating and non-rotating white dwarf, and rotating high density
supermassive (extreme relativistic) stars, stars which are in convective
equilibrium and have uniform chemical composition. This paper is a continuation
of our earlier work ([28])
Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations
We prove existence of rotating star solutions which are steady-state
solutions of the compressible isentropic Euler-Poisson (EP) equations in 3
spatial dimensions, with prescribed angular momentum and total mass. This
problem can be formulated as a variational problem of finding a minimizer of an
energy functional in a broader class of functions having less symmetry than
those functions considered in the classical Auchmuty-Beals paper. We prove the
nonlinear dynamical stability of these solutions with perturbations having the
same total mass and symmetry as the rotating star solution. We also prove local
in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations
are entropy-weak solutions of the EP equations. Finally, we give a uniform (in
time) a-priori estimate for entropy-weak solutions of the EP equations
Turing Instability in a Boundary-fed System
The formation of localized structures in the chlorine dioxide-idodine-malonic
acid (CDIMA) reaction-diffusion system is investigated numerically using a
realistic model of this system. We analyze the one-dimensional patterns formed
along the gradients imposed by boundary feeds, and study their linear stability
to symmetry-breaking perturbations (Turing instability) in the plane transverse
to these gradients. We establish that an often-invoked simple local linear
analysis which neglects longitudinal diffusion is inappropriate for predicting
the linear stability of these patterns. Using a fully nonuniform analysis, we
investigate the structure of the patterns formed along the gradients and their
stability to transverse Turing pattern formation as a function of the values of
two control parameters: the malonic acid feed concentration and the size of the
reactor in the dimension along the gradients. The results from this
investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review
(In)finite extent of stationary perfect fluids in Newtonian theory
For stationary, barotropic fluids in Newtonian gravity we give simple
criteria on the equation of state and the "law of motion" which guarantee
finite or infinite extent of the fluid region (providing a priori estimates for
the corresponding stationary Newton-Euler system). Under more restrictive
conditions, we can also exclude the presence of "hollow" configurations. Our
main result, which does not assume axial symmetry, uses the virial theorem as
the key ingredient and generalises a known result in the static case. In the
axially symmetric case stronger results are obtained and examples are
discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar
The uses and abuses of power: teaching school leadership through children's literature
There are relatively few studies of how representations of teachers, schools and educational administrators in popular films and television might be, and are, used in leadership preparation. This paper seeks to add to this small body of work; it reports on an exploratory study of the representation of headteachers in contemporary children's fiction. Thirty-one texts are analysed to ascertain key themes and the major characterisations. The paper draws on children's literature scholars to argue that both the historical school story and its contemporary counterpart focus heavily on the power of the head to control the micro-world of the school. Because these fictional accounts deal with issues of power and justice more openly than many mainstream educational administration texts, this makes them particularly useful in the preparation of potential school leaders
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