25,463 research outputs found
First steps towards total reality of meromorphic functions
It was earlier conjectured by the second and the third authors that any
rational curve such that the inverse
images of all its flattening points lie on the real line is real algebraic up to a linear fractional transformation of
the image . (By a flattening point on we mean a point
at which the Frenet -frame is degenerate.) Below we
extend this conjecture to the case of meromorphic functions on real algebraic
curves of higher genera and settle it for meromorphic functions of degrees
and several other cases.Comment: 10 pages, 1 figur
On total reality of meromorphic functions
We show that if a meromorphic function of degree at most four on a real
algebraic curve of an arbitrary genus has only real critical points then it is
conjugate to a real meromorphic function after a suitable projective
automorphism of the image.Comment: 13 page
Hurwitz numbers and intersections on moduli spaces of curves
This article is an extended version of preprint math.AG/9902104. We find an
explicit formula for the number of topologically different ramified coverings
of a sphere by a genus g surface with only one complicated branching point in
terms of Hodge integrals over the moduli space of genus g curves with marked
points.Comment: 30 pages (AMSTeX). Minor typos are correcte
Implementing Quantum Gates by Optimal Control with Doubly Exponential Convergence
We introduce a novel algorithm for the task of coherently controlling a
quantum mechanical system to implement any chosen unitary dynamics. It performs
faster than existing state of the art methods by one to three orders of
magnitude (depending on which one we compare to), particularly for quantum
information processing purposes. This substantially enhances the ability to
both study the control capabilities of physical systems within their coherence
times, and constrain solutions for control tasks to lie within experimentally
feasible regions. Natural extensions of the algorithm are also discussed.Comment: 4+2 figures; to appear in PR
The Role of Functional, Social, and Mobility Dynamics in Facilitating Older African Americans Participation in Clinical Research
Purpose: Older African Americans experience disproportionately higher incidence of morbidity and mortality related to chronic and infectious diseases, yet are significantly underrepresented in clinical research compared to other racial and ethnic groups. This study aimed to understand the extent to which social support, transportation access, and physical impediments function as barriers or facilitators to clinical trial recruitment of older African Americans. Methods: Participants (N=221) were recruited from six African American churches in Atlanta and surveyed on various influences on clinical trial participation
Dependence of inner-shell vacancy production upon distance in hard Li-Al collisions
We match the predictions of molecular-dynamics simulations of 1.2 keV and 2.0 keV 7Li+ scattered from Al(100) to observed total Li atom spectra measured by time-of-flight spectroscopy. In doing so we determine the relevant parameters in a simple distance of closest approach model for the probability of production of single and double vacancies in the Li 1s shell during hard Li-Al collisions. In the standard Fano-Lichten model of vacancy production, vacancies are produced with unit probability if the collision is hard enough to force the collision partners past some critical distance of closest approach. We find that such an assumption is insufficient to fit our simulations to experimental observations, and that we must allow for a gradual turning on of the vacancy production probability as the distance of closest approach decreases. The resulting model may be useful in modeling atomic excitation effects in simulations of other ion-impact processes
Magnetic Braking and Viscous Damping of Differential Rotation in Cylindrical Stars
Differential rotation in stars generates toroidal magnetic fields whenever an
initial seed poloidal field is present. The resulting magnetic stresses, along
with viscosity, drive the star toward uniform rotation. This magnetic braking
has important dynamical consequences in many astrophysical contexts. For
example, merging binary neutron stars can form "hypermassive" remnants
supported against collapse by differential rotation. The removal of this
support by magnetic braking induces radial fluid motion, which can lead to
delayed collapse of the remnant to a black hole. We explore the effects of
magnetic braking and viscosity on the structure of a differentially rotating,
compressible star, generalizing our earlier calculations for incompressible
configurations. The star is idealized as a differentially rotating, infinite
cylinder supported initially by a polytropic equation of state. The gas is
assumed to be infinitely conducting and our calculations are performed in
Newtonian gravitation. Though highly idealized, our model allows for the
incorporation of magnetic fields, viscosity, compressibility, and shocks with
minimal computational resources in a 1+1 dimensional Lagrangian MHD code. Our
evolution calculations show that magnetic braking can lead to significant
structural changes in a star, including quasistatic contraction of the core and
ejection of matter in the outermost regions to form a wind or an ambient disk.
These calculations serve as a prelude and a guide to more realistic MHD
simulations in full 3+1 general relativity.Comment: 20 pages, 19 figures, 3 tables, AASTeX, accepted by Ap
Importance of cooling in triggering the collapse of hypermassive neutron stars
The inspiral and merger of a binary neutron star (NSNS) can lead to the
formation of a hypermassive neutron star (HMNS). As the HMNS loses thermal
pressure due to neutrino cooling and/or centrifugal support due to
gravitational wave (GW) emission, and/or magnetic breaking of differential
rotation it will collapse to a black hole. To assess the importance of
shock-induced thermal pressure and cooling, we adopt an idealized equation of
state and perform NSNS simulations in full GR through late inspiral, merger,
and HMNS formation, accounting for cooling. We show that thermal pressure
contributes significantly to the support of the HMNS against collapse and that
thermal cooling accelerates its "delayed" collapse. Our simulations demonstrate
explicitly that cooling can induce the catastrophic collapse of a hot
hypermassive neutron star formed following the merger of binary neutron stars.
Thus, cooling physics is important to include in NSNS merger calculations to
accurately determine the lifetime of the HMNS remnant and to extract
information about the NS equation of state, cooling mechanisms, bar
instabilities and B-fields from the GWs emitted during the transient phase
prior to BH formation.Comment: 13 pages, 7 figures, matches published versio
Implementing fully relativistic hydrodynamics in three dimensions
We report on our numerical implementation of fully relativistic hydrodynamics
coupled to Einstein's field equations in three spatial dimensions. We briefly
review several steps in our code development, including our recasting of
Einstein's equations and several tests which demonstrate its advantages for
numerical integrations. We outline our implementation of relativistic
hydrodynamics, and present numerical results for the evolution of both stable
and unstable Oppenheimer-Volkov equilibrium stars, which represent a very
promising first test of our code.Comment: 5 Pages, 4 Figures, submitted to Proceedings of the 8th Canadian
Conference on General Relativity and Relativistic Astrophysic
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