814 research outputs found
On the birational section conjecture with local conditions
A birationally liftable Galois section s of a hyperbolic curve X/k over a
number field k yields an adelic point x(s) in the smooth completion of X. We
show that x(s) is X-integral outside a set of places of Dirichlet density 0, or
s is cuspidal. The proof relies on -quotients of for
some open U of X.
If k is totally real or imaginary quadratic, we prove that all birationally
adelic, non-cuspidal Galois sections come from rational points as predicted by
the section conjecture of anabelian geometry. As an aside we also obtain a
strong approximation result for rational points on hyperbolic curves over Q or
imaginary quadratic fields.Comment: Theorem C (and Section 7) of the original version have been deleted
due to a gap in the proof. This is the journal versio
Kinetic instability of drift-Alfven waves in solar corona and stochastic heating
The solar atmosphere is structured and inhomogeneous both horizontally and
vertically. The omnipresence of coronal magnetic loops implies gradients of the
equilibrium plasma quantities like the density, magnetic field and temperature.
These gradients are responsible for the excitation of drift waves that grow
both within the two-component fluid description (in the presence of collisions
and without it) and within the two-component kinetic descriptions (due to
purely kinetic effects). In the present work the effects of the density
gradient in the direction perpendicular to the magnetic field vector are
investigated within the kinetic theory, in both electrostatic and
electromagnetic regimes. The electromagnetic regime implies the coupling of the
gradient-driven drift wave with the Alfven wave. The growth rates for the two
cases are calculated and compared. It is found that, in general, the
electrostatic regime is characterized by stronger growth rates, as compared
with the electromagnetic perturbations. Also discussed is the stochastic
heating associated with the drift wave. The released amount of energy density
due to this heating should be more dependent on the magnitude of the background
magnetic field than on the coupling of the drift and Alfven waves. The
stochastic heating is expected to be much higher in regions with a stronger
magnetic field. On the whole, the energy release rate caused by the stochastic
heating can be several orders of magnitude above the value presently accepted
as necessary for a sustainable coronal heating.Comment: To appear in ApJ (2010
Relativistic Landau damping of longitudinal waves in isotropic pair plasmas
Landau damping is described in relativistic electron-positron
plasmas. Relativistic electron-positron plasma theory contains
important new effects when compared with classical plasmas. For
example, there are undamped superluminal wave modes arising from
both a continuous and discrete mode structure, the former even in
the classical limit. We present here a comprehensive analytical
treatment of the general case resulting in a compact and useful
form for the dispersion relation. The classical pair-plasma case
is addressed, for completeness, in an appendix
The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes
Observations show that solar activity is distributed non-axisymmetrically,
concentrating at "preferred longitudes". This indicates the important role of
non-axisymmetric magnetic fields in the origin of solar activity. We
investigate the generation of the non-axisymmetric fields and their coupling
with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model
operating in a sphere includes solar differential rotation, which approximates
the differential rotation obtained by inversion of helioseismic data, modelled
distributions of the turbulent resistivity, non-axisymmetric mean helicity, and
meridional circulation in the convection zone. We find that (1) the
non-axisymmetric modes are localised near the base of the convection zone,
where the formation of active regions starts, and at latitudes around
; (2) the coupling of non-axisymmetric and axisymmetric modes
causes the non-axisymmetric mode to follow the solar cycle; the phase relations
between the modes are found. (3) The rate of rotation of the first
non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical
Journa
High Resolution Ionization of Ultracold Neutral Plasmas
Collective effects, such as waves and instabilities, are integral to our
understanding of most plasma phenomena. We have been able to study these in
ultracold neutral plasmas by shaping the initial density distribution through
spatial modulation of the ionizing laser intensity. We describe a relay imaging
system for the photoionization beam that allows us to create higher resolution
features and its application to extend the observation of ion acoustic waves to
shorter wavelengths. We also describe the formation of sculpted density
profiles to create fast expansion of plasma into vacuum and streaming plasmas
Mechanisms of degassing at Nevado del Ruiz volcano, Colombia
Author Posting. © Geological Society, 2003. This article is posted here by permission of Geological Society for personal use, not for redistribution. The definitive version was published in Journal of the Geological Society 160 (2003): 507-521, doi:10.1144/0016-764902-028.Nevado del Ruiz volcano is an andesite stratovolcano located in the northern Andes of Colombia. The volcano erupted on 11 September 1985, 13 November 1985, and 1 September 1989. The last two eruptions emitted juvenile solid material. This paper examines the volatile and light lithophile trace element contents of melt inclusions and matrix glasses from this juvenile material, and proposes a model for degassing within the volcano. Major element distributions in the glasses show two evolutionary trends, with subsidiary points that lie between the two trends. The data suggest the existence of two separate magmas, which have interacted, mingled, and mixed during their ascent and eruption. Water contents in melt inclusions, as determined by secondary ionization mass spectrometric analysis, are generally low, averaging between 1.6 and 3.3 wt.%. Halogen concentrations in the glasses range from 400 to 1200 ppm for fluorine and from 1100 to 1500 ppm for chlorine. Sulphur contents are low, not exceeding 500 ppm, with most glasses containing <200 ppm. Lithium concentrations range from 20 to 40 ppm, beryllium from 1.5 to 2 ppm, and boron exhibits high variability from 30 to 100 ppm. The only significant difference between melt inclusions and matrix glasses is for water, with matrix glasses having significantly lower concentrations (<0.5 wt.%) than the melt inclusions. The generally elevated concentrations of boron in the magma may be a consequence of enrichment in the source region of the magma, i.e. by subduction of altered oceanic crust and/or sediments. Yet the large degree of boron heterogeneity in both melt inclusions and matrix glasses necessitates subsequent addition of boron at shallower depths as well, by the assimilation of crustal sedimentary rocks or by interaction with hydrothermal fluids. Evidence for pre-eruptive magma emplacement at shallow levels is provided by (1) anhydrous mineral assemblages of plagioclase and pyroxene, (2) high silica contents of glasses, and (3) low water contents in melt inclusions. When combined, these observations suggest a period of magma residence at shallow depths, probably <3 km beneath the summit of the volcano. A multistage model of magma transport and degassing involves alternating periods of magma ascent and magma ponding. Initially, volatile-bearing magma ascends from depths of 9–15 km, driven by buoyancy. During decompression, the magma loses gas, particularly CO2 and sulphur. The magma eventually ponds at its neutral buoyancy level. At this point, the gas-saturated magma cools and crystallizes, thereby liberating gas under isobaric conditions. As a result, CO2 is depleted from the magma whereas H2O and SiO2 are enriched. The H2O enrichment is caused by its increased solubility in the magma as CO2 is degassed, whereas SiO2 is enriched by fractional crystallization. The density of the magma decreases as the level of dissolved H2O increases, eventually causing the magma to become buoyant once more and to continue its ascent, either to erupt or to freeze at shallow depths.This work was funded with grants to J.S. by the Natural Sciences
and Engineering Research Council of Canada and by the Fonds pour la
formation de chercheurs et l’aide a` la recherche (Que´bec)
Quantum key distribution with higher-order alphabets using spatially-encoded qudits
We propose and demonstrate a quantum key distribution scheme in higher-order
-dimensional alphabets using spatial degrees of freedom of photons. Our
implementation allows for the transmission of 4.56 bits per sifted photon,
while providing improved security: an intercept-resend attack on all photons
would induce an error rate of 0.47. Using our system, it should be possible to
send more than a byte of information per sifted photon.Comment: 4 pages, 5 figures. Replaced with published versio
Vlasov equation and collisionless hydrodynamics adapted to curved spacetime
The modification of the Vlasov equation, in its standard form describing a
charged particle distribution in the six-dimensional phase space, is derived
explicitly within a formal Hamiltonian approach for arbitrarily curved
spacetime. The equation accounts simultaneously for the Lorentz force and the
effects of general relativity, with the latter appearing as the gravity force
and an additional force due to the extrinsic curvature of spatial
hypersurfaces. For an arbitrary spatial metric, the equations of collisionless
hydrodynamics are also obtained in the usual three-vector form
Theoretical and numerical studies of wave-packet propagation in tokamak plasmas
Theoretical and numerical studies of wave-packet propagation are presented to
analyze the time varying 2D mode structures of electrostatic fluctuations in
tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave
equations directly, the solution of the initial value problem is used to obtain
the 2D mode structure, following the propagation of wave-packets generated by a
source and reconstructing the time varying field. As application, the 2D WKB
method is applied to investigate the shaping effects (elongation and
triangularity) of tokamak geometry on the lower hybrid wave propagation and
absorbtion. Meanwhile, the Mode Structure Decomposition (MSD) method is used to
handle the boundary conditions and simplify the 2D problem to two nested 1D
problems. The MSD method is related to that discussed earlier by Zonca and Chen
[Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning
formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40,
396 (1978)], when spatial scale separation applies. This method is used to
investigate the time varying 2D electrostatic ITG mode structure with a mixed
WKB-full-wave technique. The time varying field pattern is reconstructed and
the time asymptotic structure of the wave-packet propagation gives the 2D
eigenmode and the corresponding eigenvalue. As a general approach to
investigate 2D mode structures in tokamak plasmas, our method also applies for
electromagnetic waves with general source/sink terms, either by an
internal/external antenna or nonlinear wave interaction with zonal structures.Comment: 24 pages, 14 figure
A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU
(Abridged) Turbulence in the solar wind is believed to generate an energy
cascade that is supported primarily by Alfv\'en waves or Alfv\'enic
fluctuations at MHD scales and by kinetic Alfv\'en waves (KAWs) at kinetic
scales . Linear Landau damping of KAWs increases with
increasing wavenumber and at some point the damping becomes so strong that the
energy cascade is completely dissipated. A model of the energy cascade process
that includes the effects of linear collisionless damping of KAWs and the
associated compounding of this damping throughout the cascade process is used
to determine the wavenumber where the energy cascade terminates. It is found
that this wavenumber occurs approximately when ,
where and are, respectively, the real frequency and
damping rate of KAWs and the ratio is evaluated in the limit as
the propagation angle approaches 90 degrees relative to the direction of the
mean magnetic field.Comment: Submitted to Ap
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