803 research outputs found
Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve
For a projective variety X defined over a field K, there is a special class
of self-morphisms of X called algebraic dynamical systems. In this paper we
take K to be the function field of a smooth curve and prove that at each place
of K, subvarieties of X of dynamically small height are equidistributed on the
associated Berkovich analytic space. We carefully develop all of the arithmetic
intersection theory needed to state and prove this theorem, and we present
several applications on the non-Zariski density of preperiodic points and of
points of small height in field extensions of bounded degree.Comment: v2: Various typos fixed; statement and proof of auxiliary Prop. 6.1
corrected. During the process of preparing this manuscript for submission, it
came to the author's attention that Walter Gubler has recently proved many of
the same results. See arXiv:0801.4508v3. v3: References updated and a few
more typos corrected. To appear in Acta Arithmetic
A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems
Fix a rational basepoint b and a rational number c. For the quadratic
dynamical system f_c(x) = x^2+c, it has been shown that the number of rational
points in the backward orbit of b is bounded independent of the choice of
rational parameter c. In this short note we investigate the dependence of the
bound on the basepoint b, assuming a strong form of the Mordell Conjecture.Comment: 5 pages; Final version to appear in Comptes Rendus Mathematiqu
The Finite Field Kakeya Problem
A Besicovitch set in AG(n,q) is a set of points containing a line in every
direction. The Kakeya problem is to determine the minimal size of such a set.
We solve the Kakeya problem in the plane, and substantially improve the known
bounds for n greater than 4.Comment: 13 page
Conformally Flat Smoothed Particle Hydrodynamics: Application to Neutron Star Mergers
We present a new 3D SPH code which solves the general relativistic field +
hydrodynamics equations in the conformally flat approximation. Several test
cases are considered to test different aspects of the code. We finally apply
then the code to the coalescence of a neutron star binary system. The neutron
stars are modeled by a polytropic equation of state (EoS) with adiabatic
indices , and . We calculate the
gravitational wave signals, luminosities and frequency spectra by employing the
quadrupole approximation for emission and back reaction in the slow motion
limit. In addition, we consider the amount of ejected mass.Comment: 23 pages, 12 figures. Accepted for publication in Phys. Rev. D. v3:
Final Versio
Superconducting properties and c-axis superstructure of Mg1-xAlxB2
The superconducting and structural properties of a series of Mg1-xAlxB2
samples have been investigated. X-ray diffraction results confirmed the
existence of a structural transition associated with the significant change in
inter-boron layer distance as reported previously by Slusky et al.
Moreover,transmission-electron-microscopy observations revealed the existence
of a superstructure with doubled lattice constant along the c-axis direction.
We propose that this superstructure is essentially related to the structural
transition. The modifications of superconducting transition temperature Tc, the
normal state resistivity, and the upper critical field Bc2 by Al doping are
discussed in terms of Al-substitution induced changes in the electronic
structure at the Fermi energy.Comment: 15 pages, 7 figure
Ab Initio Molecular Dynamics Simulation of Liquid Ga_xAs_{1-x} Alloys
We report the results of ab initio molecular dynamics simulations of liquid
Ga_xAs_{1-x} alloys at five different concentrations, at a temperature of 1600
K, just above the melting point of GaAs. The liquid is predicted to be metallic
at all concentrations between x = 0.2 and x = 0.8, with a weak resistivity
maximum near x = 0.5, consistent with the Faber-Ziman expression. The
electronic density of states is finite at the Fermi energy for all
concentrations; there is, however, a significant pseudogap especially in the
As-rich samples. The Ga-rich density of states more closely resembles that of a
free-electron metal. The partial structure factors show only a weak indication
of chemical short-range order. There is also some residue of the covalent
bonding found in the solid, which shows up in the bond-angle distribution
functions of the liquid state. Finally, the atomic diffusion coefficients at
1600K are calculated to be 2.1 \times 10^{-4} cm^2/sec for Ga ions in
Ga_{0.8}As_{0.2} and 1.7 \times 10^{-4} cm^2/sec for As ions in
Ga_{0.2}As_{0.8}.Comment: 29 pages, 10 eps figures, accepted for publication in Phys. Rev.
Comparison of advanced gravitational-wave detectors
We compare two advanced designs for gravitational-wave antennas in terms of
their ability to detect two possible gravitational wave sources. Spherical,
resonant mass antennas and interferometers incorporating resonant sideband
extraction (RSE) were modeled using experimentally measurable parameters. The
signal-to-noise ratio of each detector for a binary neutron star system and a
rapidly rotating stellar core were calculated. For a range of plausible
parameters we found that the advanced LIGO interferometer incorporating RSE
gave higher signal-to-noise ratios than a spherical detector resonant at the
same frequency for both sources. Spheres were found to be sensitive to these
sources at distances beyond our galaxy. Interferometers were sensitive to these
sources at far enough distances that several events per year would be expected
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