1,749 research outputs found
Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by
F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of
functions that satisfy the Dirichlet boundary conditions and whose derivatives
are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into
manifolds of codimension 1 in X. If f''0, the set C_j is shown to be
non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the
range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure
Heating and acceleration of coronal and chromospheric ions during solar flares
One-dimensional, electrostatic, particle-in-cell simulations are used to explore two mechanisms proposed to explain turbulent broadening of soft x ray emission lines of heavy ions observed during solar flares and the presence of blue-shifted components. Results from the simulations are in qualitative agreement with the observations
Chromospheric-coronal coupling during solar flares: Current systems and particle acceleration
Two-dimensional (three velocity) electrostatic particle simulations are used to investigate the particle heating and acceleration associated with the impulsive phase of a solar flare. A crossfield current in the high corona (which is presumably driven by reconnection processes) is used to initiate the flare. Due to the differential motion of the electrons and ions, currents, and associated quasi-static electric fields are generated with the primary current and balancing return current being on adjacent field lines. These currents extend from the corona down into the chromosphere. Electrons can be accelerated to energies exceeding 100 keV on short time scales via the quasi-static fields and wave-particle interactions. The spectra of these electrons has a broken power-law distribution which hardens in time. The spatially separate primary and return currents are closed by the cross-field acceleration of the ambient ions into the primary current regions. These ions are then accelerated upwards into the corona by the same quasi-static electric field accelerating the electrons downwards. This acceleration can account for the broadened stationary and weak blue shifted component seen in soft x ray line emissions and enhancements in heavy ion abundances seen in the solar wind in associations with solar flares
Keck spectroscopy of CLASS gravitational lenses
We present the optical spectra of four newly discovered gravitational lenses
from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried
out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope
as part of a program to study galaxy-scale gravitational lenses. From our
spectra we found the redshift of the background source in CLASS B0128+437
(z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123
(z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we
also discovered that CLASS B0631+519 may have two lensing galaxies
(z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single
unidentified emission line from the lensing galaxy in CLASS B0128+437 and the
lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS
B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein
Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type
galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA
Complete characterization of convergence to equilibrium for an inelastic Kac model
Pulvirenti and Toscani introduced an equation which extends the Kac
caricature of a Maxwellian gas to inelastic particles. We show that the
probability distribution, solution of the relative Cauchy problem, converges
weakly to a probability distribution if and only if the symmetrized initial
distribution belongs to the standard domain of attraction of a symmetric stable
law, whose index is determined by the so-called degree of
inelasticity, , of the particles: . This result is
then used: (1) To state that the class of all stationary solutions coincides
with that of all symmetric stable laws with index . (2) To determine
the solution of a well-known stochastic functional equation in the absence of
extra-conditions usually adopted
Gauge fixing and equivariant cohomology
The supersymmetric model developed by Witten to study the equivariant
cohomology of a manifold with an isometric circle action is derived from the
BRST quantization of a simple classical model. The gauge-fixing process is
carefully analysed, and demonstrates that different choices of gauge-fixing
fermion can lead to different quantum theories.Comment: 18 pages LaTe
Water vapour at high redshift: Arecibo monitoring of the megamaser in MG J0414+0534
The study of water masers at cosmological distances would allow us to
investigate the parsec-scale environment around powerful radio sources, to
probe the physical conditions of the molecular gas in the inner parsecs of
quasars, and to estimate their nuclear engine masses in the early universe. To
derive this information, the nature of the maser source, jet or disk-maser,
needs to be assessed through a detailed investigation of the observational
characteristics of the line emission. We monitored the maser line in the lensed
quasar MGJ0414+0534 at z = 2.64 with the 300-m Arecibo telescope for ~15 months
to detect possible additional maser components and to measure a potential
velocity drift of the lines. In addition, we follow the maser and continuum
emissions to reveal significant variations in their flux density and to
determine correlation or time-lag, if any, between them. The main maser line
profile is complex and can be resolved into a number of broad features with
line widths of 30-160 km/s. A new maser component was tentatively detected in
October 2008 that is redshifted by 470 km/s w.r.t the systemic velocity of the
quasar. The line width of the main maser feature increased by a factor of two
between the Effelsberg and EVLA observations reported by Impellizzeri et al.
(2008) and the first epoch of the Arecibo monitoring campaign. After correcting
for the lens magnification, we find that the total H2O isotropic luminosity of
the maser in MGJ0414+0534 is now ~30,000 Lsun, making this source the most
luminous ever discovered.[Abridged]Comment: 8 pages, 6 figures, accepted for publication in A&
Noisy traveling waves: effect of selection on genealogies
For a family of models of evolving population under selection, which can be
described by noisy traveling wave equations, the coalescence times along the
genealogical tree scale like , where is the size of the
population, in contrast with neutral models for which they scale like . An
argument relating this time scale to the diffusion constant of the noisy
traveling wave leads to a prediction for which agrees with our
simulations. An exactly soluble case gives trees with statistics identical to
those predicted for mean-field spin glasses in Parisi's theory.Comment: 4 pages, 2 figures New version includes more numerical simulations
and some rewriting of the text presenting our result
Gauge Fixing and BFV Quantization
Nonsingularity conditions are established for the BFV gauge-fixing fermion
which are sufficient for it to lead to the correct path integral for a theory
with constraints canonically quantized in the BFV approach. The conditions
ensure that anticommutator of this fermion with the BRST charge regularises the
path integral by regularising the trace over non-physical states in each ghost
sector. The results are applied to the quantization of a system which has a
Gribov problem, using a non-standard form of the gauge-fixing fermion.Comment: 14 page
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