927 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
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
Moduli and periods of simply connected Enriques surfaces
We describe a period map for those simply connected Enriques surfaces in
characteristic 2 whose canonical double cover is K3. The moduli stack for these
surfaces has a Deligne-Mumford quotient that is an open substack of a -bundle over the period space. We also give some general results relating
local and global moduli for algebraic varieties and describe the difference in
their dimensions in terms of the failure of the automorphism group scheme to be
reduced
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
Penetration And Scattering Of Lower Hybrid Waves By Density Fluctuations
Lower Hybrid [LH] ray propagation in toroidal plasma is controlled by a combination of the azimuthal spectrum launched from the antenna, the poloidal variation of the magnetic field, and the scattering of the waves by the density fluctuations. The width of the poloidal and radial RF wave spectrum increases rapidly as the rays penetrate into higher density and scatter from the turbulence. The electron temperature gradient [ETG] spectrum is particularly effective in scattering the LH waves due to its comparable wavelengths and parallel phase velocities. ETG turbulence is also driven by the radial gradient of the electron current density giving rise to an anomalous viscosity spreading the LH-driven plasma currents. The scattered LH spectrum is derived from a Fokker-Planck equation for the distribution of the ray trajectories with a diffusivity proportional to the fluctuations. The LH ray diffusivity is large giving transport in the poloidal and radial wavenumber spectrum in one -or a few passes - of the rays through the core plasma.Institute for Fusion Studie
On double Hurwitz numbers in genus 0
We study double Hurwitz numbers in genus zero counting the number of covers
\CP^1\to\CP^1 with two branching points with a given branching behavior. By
the recent result due to Goulden, Jackson and Vakil, these numbers are
piecewise polynomials in the multiplicities of the preimages of the branching
points. We describe the partition of the parameter space into polynomiality
domains, called chambers, and provide an expression for the difference of two
such polynomials for two neighboring chambers. Besides, we provide an explicit
formula for the polynomial in a certain chamber called totally negative, which
enables us to calculate double Hurwitz numbers in any given chamber as the
polynomial for the totally negative chamber plus the sum of the differences
between the neighboring polynomials along a path connecting the totally
negative chamber with the given one.Comment: 17 pages, 3 figure
A new B-dot probe-based diagnostic for amplitude, polarization, and wavenumber measurements of ion cyclotron range-of frequency fields on ASDEX Upgrade
A new B-dot probe-based diagnostic has been installed on an ASDEX Upgrade tokamak to characterize ion cyclotron range-of frequency (ICRF) wave generation and interaction with magnetized plasma. The diagnostic consists of a field-aligned array of B-dot probes, oriented to measure fast and slow ICRF wave fields and their field-aligned wavenumber (k(//)) spectrum on the low field side of ASDEX Upgrade. A thorough description of the diagnostic and the supporting electronics is provided. In order to compare the measured dominant wavenumber of the local ICRF fields with the expected spectrum of the launched ICRF waves, in-air near-field measurements were performed on the newly installed 3-strap ICRF antenna to reconstruct the dominant launched toroidal wavenumbers (k(tor)). Measurements during a strap current phasing scan in tokamak discharges reveal an upshift in k(//) as strap phasing is moved away from the dipole configuration. This result is the opposite of the k(tor) trend expected from in-air near-field measurements; however, the near-field based reconstruction routine does not account for the effect of induced radiofrequency (RF) currents in the passive antenna structures. The measured exponential increase in the local ICRF wave field amplitude is in agreement with the upshifted k(//), as strap phasing moves away from the dipole configuration. An examination of discharges heated with two ICRF antennas simultaneously reveals the existence of beat waves at 1 kHz, as expected from the difference of the two antennas' operating frequencies. Beats are observed on both the fast and the slow wave probes suggesting that the two waves are coupled outside the active antennas. Although the new diagnostic shows consistent trends between the amplitude and the phase measurements in response to changes applied by the ICRF antennas, the disagreement with the in-air near-field measurements remains. An electromagnetic model is currently under development to address this issue. (C) 2015 AIP Publishing LLC
Ultrafast control of inelastic tunneling in a double semiconductor quantum
In a semiconductor-based double quantum well (QW) coupled to a degree of
freedom with an internal dynamics, we demonstrate that the electronic motion is
controllable within femtoseconds by applying appropriately shaped
electromagnetic pulses. In particular, we consider a pulse-driven AlxGa1-xAs
based symmetric double QW coupled to uniformly distributed or localized
vibrational modes and present analytical results for the lowest two levels.
These predictions are assessed and generalized by full-fledged numerical
simulations showing that localization and time-stabilization of the driven
electron dynamics is indeed possible under the conditions identified here, even
with a simultaneous excitations of vibrational modes.Comment: to be published in Appl.Phys.Let
Lower hybrid counter-current drive experiment in JET
12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France)Lower hybrid current drive has been demonstrated to be an efficient tool to modify the current profile in order to access to high energy confinement regimes. Counter-current drive could be an alternative scenario provided the current drive efficiency is not too small when fast electrons flow in the opposite way to the DC electric field. By reversing the toroidal field (Bt=-3.1T) and the plasma current (Ip=-1.45MA), counter current drive with lower hybrid waves has been investigated for the first time in JET. The experiments were carried out at low plasma density ( =1.0 x1019m-3 , ne(0)=1.6 x 1019m-3) with 2.9MW of lower hybrid power. The CRONOS code[1], which couples the diffusion equations to a 2-D equilibrium code, has been used to estimate the RF driven current. Runs indicate that loop voltage and internal inductance are best simulated with a current drive efficiency of –1.0 x 1019 A.W-1.m-2 with a peaked central LH power deposition deduced from DELPHINE[2]. This efficiency is indeed very close to the one found for co-LHCD at similar plasma current and density. Current profile evolves from a hollow profile (with a minimum at r/a ~0) and a maximum at r/a~0.4-0.5) to a rather flat profile (up to r/a=0.3)
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