2,540 research outputs found
Coincidence of length spectra does not imply isospectrality
Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs
with the same geodesic length spectrum. Recently S. Zelditch raised the
question whether such billiards also have the same eigenvalue spectrum for the
Dirichlet Laplacian (conjecturing ``no''). Here we show that generically (in
the class of smooth domains) the two members of a mushroom pair have different
spectra.Comment: 8 pages, 5 figure
Two-Dimensional Hydrodynamic Simulations of Convection in Radiation-Dominated Accretion Disks
The standard equilibrium for radiation-dominated accretion disks has long
been known to be viscously, thermally, and convectively unstable, but the
nonlinear development of these instabilities---hence the actual state of such
disks---has not yet been identified. By performing local two-dimensional
hydrodynamic simulations of disks, we demonstrate that convective motions can
release heat sufficiently rapidly as to substantially alter the vertical
structure of the disk. If the dissipation rate within a vertical column is
proportional to its mass, the disk settles into a new configuration thinner by
a factor of two than the standard radiation-supported equilibrium. If, on the
other hand, the vertically-integrated dissipation rate is proportional to the
vertically-integrated total pressure, the disk is subject to the well-known
thermal instability. Convection, however, biases the development of this
instability toward collapse. The end result of such a collapse is a gas
pressure-dominated equilibrium at the original column density.Comment: 10 pages, 7 figures, accepted for publication in ApJ. Please send
comments to [email protected]
Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential
The Schwarz function has played an elegant role in understanding and in
generating new examples of exact solutions to the Laplacian growth (or "Hele-
Shaw") problem in the plane. The guiding principle in this connection is the
fact that "non-physical" singularities in the "oil domain" of the Schwarz
function are stationary, and the "physical" singularities obey simple dynamics.
We give an elementary proof that the same holds in any number of dimensions for
the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17]
(1989). A generalization is also given for the so-called "elliptic growth"
problem by defining a generalized Schwarz potential. New exact solutions are
constructed, and we solve inverse problems of describing the driving
singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n -
techniques can be used to locate the singularity set of the Schwarz potential.
One of our methods is to prolong available local extension theorems by
constructing "globalizing families". We make three conjectures in potential
theory relating to our investigation
Steep sharp-crested gravity waves on deep water
A new type of steady steep two-dimensional irrotational symmetric periodic
gravity waves on inviscid incompressible fluid of infinite depth is revealed.
We demonstrate that these waves have sharper crests in comparison with the
Stokes waves of the same wavelength and steepness. The speed of a fluid
particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Initial Data for General Relativity with Toroidal Conformal Symmetry
A new class of time-symmetric solutions to the initial value constraints of
vacuum General Relativity is introduced. These data are globally regular,
asymptotically flat (with possibly several asymptotic ends) and in general have
no isometries, but a group of conformal isometries. After
decomposing the Lichnerowicz conformal factor in a double Fourier series on the
group orbits, the solutions are given in terms of a countable family of
uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12
Uniqueness properties of the Kerr metric
We obtain a geometrical condition on vacuum, stationary, asymptotically flat
spacetimes which is necessary and sufficient for the spacetime to be locally
isometric to Kerr. Namely, we prove a theorem stating that an asymptotically
flat, stationary, vacuum spacetime such that the so-called Killing form is an
eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr.
Asymptotic flatness is a fundamental hypothesis of the theorem, as we
demonstrate by writing down the family of metrics obtained when this
requirement is dropped. This result indicates why the Kerr metric plays such an
important role in general relativity. It may also be of interest in order to
extend the uniqueness theorems of black holes to the non-connected and to the
non-analytic case.Comment: 30 pages, LaTeX, submitted to Classical and Quantum Gravit
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
Determination of some trace elements in nails from population nearby oil fields in Southern Iraq
Level of some trace elements Cadmium ( Cd), Cobalt (Co), Cupper (Cu),Nickel(Ni), Lead (Pb), and Zinc (Zn) in nails from 10 human being samples taken randomly from population nearby oil fields were examined from different subjects with respect to gender, age, smoking habit, the period of time living or working nearby the oil fields area and the health case were carried out using flame atomic absorption spectrophotometer (Sens AA GBC Scientific Equipment DUAL). Co showed the highest concentration (56.5
Gravitational Constraint Combinations Generate a Lie Algebra
We find a first--order partial differential equation whose solutions are all
ultralocal scalar combinations of gravitational constraints with Abelian
Poisson brackets between themselves. This is a generalisation of the Kucha\v{r}
idea of finding alternative constraints for canonical gravity. The new scalars
may be used in place of the hamiltonian constraint of general relativity and,
together with the usual momentum constraints, replace the Dirac algebra for
pure gravity with a true Lie algebra: the semidirect product of the Abelian
algebra of the new constraint combinations with the algebra of spatial
diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section
3 is expanded and an additional solution provided, minor errors correcte
Determination of some trace elements in nails from population nearby oil fields in Southern Iraq
Level of some trace elements Cadmium ( Cd), Cobalt (Co), Cupper (Cu),Nickel(Ni), Lead (Pb), and Zinc (Zn) in nails from 10 human being samples taken randomly from population nearby oil fields were examined from different subjects with respect to gender, age, smoking habit, the period of time living or working nearby the oil fields area and the health case were carried out using flame atomic absorption spectrophotometer (Sens AA GBC Scientific Equipment DUAL). Co showed the highest concentration (56.58µg/g) while no level were reported for Cu (ND) . The levels of the Co, Zn, and Ni elements were statistically higher in male subjects (56.58, 42.03, and 8.99) µg/g compared to 26.72, 36.20, and 0.73 µg/g for female subjects while Pb showed the highest level in female subjects 48.48 µg/g compared to 17.03 µg/g in male subjects. high levels of trace elements were observed in non-smokers, compared to smokers. The highest level of trace elements were appeared to those who are between (20-40) years old and also who are living period of time limited between (8-21) years nearby the oil field areas . Occupationally exposure showed no effect for trace elements accumulation in human finger nails compared to the time living nearby the oil field area that was limited between (9-10) years. One of the voluntaries who have a health problem hypertension as his case showed a highest level for the Pb element compared with the other  hypertension case and the diabetes case, and the other voluntaries who have no health problems
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