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

Resolving on 100 pc scales the UV-continuum in Lyman-α\alpha emitters between redshift 2 to 3 with gravitational lensing

We present a study of seventeen LAEs at redshift 2$<z<$3 gravitationally lensed by massive early-type galaxies (ETGs) at a mean redshift of approximately 0.5. Using a fully Bayesian grid-based technique, we model the gravitational lens mass distributions with elliptical power-law profiles and reconstruct the UV-continuum surface brightness distributions of the background sources using pixellated source models. We find that the deflectors are close to, but not consistent with isothermal models in almost all cases, at the $2\sigma$-level. We take advantage of the lensing magnification (typically $\mu\simeq$ 20) to characterise the physical and morphological properties of these LAE galaxies. From reconstructing the ultra-violet continuum emission, we find that the star-formation rates range from 0.3 to 8.5 M$_{\odot}$ yr$^{-1}$ and that the galaxies are typically composed of several compact and diffuse components, separated by 0.4 to 4 kpc. Moreover, they have peak star-formation rate intensities that range from 2.1 to 54.1 M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$. These galaxies tend to be extended with major axis ranging from 0.2 to 1.8 kpc (median 561 pc), and with a median ellipticity of 0.49. This morphology is consistent with disk-like structures of star-formation for more than half of the sample. However, for at least two sources, we also find off-axis components that may be associated with mergers. Resolved kinematical information will be needed to confirm the disk-like nature and possible merger scenario for the LAEs in the sample.Comment: 19 pages, 7 figures, accepted for publication on MNRA

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

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

Time-Series Intervention Analysis Using ITSACORR: Fatal Flaws

The ITSACORR method (Crosbie, 1993, 1995) is evaluated for the analysis of two-phase interrupted time-series designs. It is shown that each component of the ITSACORR framework (including the structural model, the design matrix, the autocorrelation estimator, the ultimate parameter estimation scheme, and the inferential method) contains fatal flaws

The fundamental plane of evolving red nuggets

We present an exploration of the mass structure of a sample of 12 strongly lensed massive, compact early-type galaxies at redshifts $z\sim0.6$ to provide further possible evidence for their inside-out growth. We obtain new ESI/Keck spectroscopy and infer the kinematics of both lens and source galaxies, and combine these with existing photometry to construct (a) the fundamental plane (FP) of the source galaxies and (b) physical models for their dark and luminous mass structure. We find their FP to be tilted towards the virial plane relative to the local FP, and attribute this to their unusual compactness, which causes their kinematics to be totally dominated by the stellar mass as opposed to their dark matter; that their FP is nevertheless still inconsistent with the virial plane implies that both the stellar and dark structure of early-type galaxies is non-homologous. We also find the intrinsic scatter of their FP to be comparable to the local value, indicating that variations in the stellar mass structure outweight variations in the dark halo in the central regions of early-type galaxies. Finally, we show that inference on the dark halo structure -- and, in turn, the underlying physics -- is sensitive to assumptions about the stellar initial mass function (IMF), but that physically-motivated assumptions about the IMF imply haloes with sub-NFW inner density slopes, and may present further evidence for the inside-out growth of compact early-type galaxies via minor mergers and accretion.Comment: 10 pages, 3 figures, 3 tables; submitted to MNRA

SHARP -- VII. New constraints on the dark matter free-streaming properties and substructure abundance from gravitationally lensed quasars

We present an analysis of seven strongly gravitationally lensed quasars and the corresponding constraints on the properties of dark matter. Our results are derived by modelling the lensed image positions and flux-ratios using a combination of smooth macro models and a population of low-mass haloes within the mass range 10^6 to 10^9 Msun. Our lens models explicitly include higher-order complexity in the form of stellar discs and luminous satellites, as well as low-mass haloes located along the observed lines of sight for the first time. Assuming a Cold Dark Matter (CDM) cosmology, we infer an average total mass fraction in substructure of f_sub = 0.012^{+0.007}_{-0.004} (68 per cent confidence limits), which is in agreement with the predictions from CDM hydrodynamical simulations to within 1 sigma. This result is closer to the predictions than those from previous studies that did not include line-of-sight haloes. Under the assumption of a thermal relic dark matter model, we derive a lower limit on the particle relic mass of m th > 5.58 keV (95 per cent confidence limits), which is consistent with a value of m_th > 5.3 keV from the recent analysis of the Ly-alpha forest. We also identify two main sources of possible systematic errors and conclude that deeper investigations in the complex structure of lens galaxies as well as the size of the background sources should be a priority for this field.Comment: 14 pages, 7 figures, accepted for publication in MNRA

2-D constrained Navier-Stokes equation and intermediate asymptotics

We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics. The analysis we present here is purely formal. A rigorous study of this equation will be done in a forthcoming paper

Shearing Box Simulations of the MRI in a Collisionless Plasma

We describe local shearing box simulations of turbulence driven by the magnetorotational instability (MRI) in a collisionless plasma. Collisionless effects may be important in radiatively inefficient accretion flows, such as near the black hole in the Galactic Center. The MHD version of ZEUS is modified to evolve an anisotropic pressure tensor. A fluid closure approximation is used to calculate heat conduction along magnetic field lines. The anisotropic pressure tensor provides a qualitatively new mechanism for transporting angular momentum in accretion flows (in addition to the Maxwell and Reynolds stresses). We estimate limits on the pressure anisotropy due to pitch angle scattering by kinetic instabilities. Such instabilities provide an effective ``collision'' rate in a collisionless plasma and lead to more MHD-like dynamics. We find that the MRI leads to efficient growth of the magnetic field in a collisionless plasma, with saturation amplitudes comparable to those in MHD. In the saturated state, the anisotropic stress is comparable to the Maxwell stress, implying that the rate of angular momentum transport may be moderately enhanced in a collisionless plasma.Comment: 20 pages, 9 figures, submitted to Ap