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 $\alpha$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $\alpha=\frac{2}{1+p}$. 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 $\alpha$. (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 $\log^\alpha N$, where $N$ is the size of the population, in contrast with neutral models for which they scale like $N$. An argument relating this time scale to the diffusion constant of the noisy traveling wave leads to a prediction for $\alpha$ 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