The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Method to measure off-axis displacements based on the analysis of the intensity distribution of a vortex beam

We study the properties of the Fraunhofer diffraction patterns produced by Gaussian beams crossing spiral phase plates. We show, both analytically and numerically, that off-axis displacements of the input beam produce asymmetric diffraction patterns. The intensity profile along the direction of maximum asymmetry shows two different peaks. We find that the intensity ratio between these two peaks decreases exponentially with the off-axis displacement of the incident beam, the decay being steeper for higher strengths of the optical singularity of the spiral phase plate. We analyze how this intensity ratio can be used to measure small misalignments of the input beam with a very high precision.Comment: 8 pages, 4 figures. Accepted for publication in PR

SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension

We prove that if $t \mapsto u(t) \in \mathrm {BV}(\R)$ is the entropy solution to a $N \times N$ strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields $$u_t + f(u)_x = 0,$$ then up to a countable set of times $\{t_n\}_{n \in \mathbb N}$ the function $u(t)$ is in $\mathrm {SBV}$, i.e. its distributional derivative $u_x$ is a measure with no Cantorian part. The proof is based on the decomposition of $u_x(t)$ into waves belonging to the characteristic families $$u(t) = \sum_{i=1}^N v_i(t) \tilde r_i(t), \quad v_i(t) \in \mathcal M(\R), \ \tilde r_i(t) \in \mathrm R^N,$$ and the balance of the continuous/jump part of the measures $v_i$ in regions bounded by characteristics. To this aim, a new interaction measure \mu_{i,\jump} is introduced, controlling the creation of atoms in the measure $v_i(t)$. The main argument of the proof is that for all $t$ where the Cantorian part of $v_i$ is not 0, either the Glimm functional has a downward jump, or there is a cancellation of waves or the measure $\mu_{i,\mathrm{jump}}$ is positive

Ocular hypertension in myopia: analysis of contrast sensitivity

Purpose: we evaluated the evolution of contrast sensitivity reduction in patients affected by ocular hypertension and glaucoma, with low to moderate myopia. We also evaluated the relationship between contrast sensitivity and mean deviation of visual field. Material and methods: 158 patients (316 eyes), aged between 38 and 57 years old, were enrolled and divided into 4 groups: emmetropes, myopes, myopes with ocular hypertension (IOP≥21 ±2 mmHg), myopes with glaucoma. All patients underwent anamnestic and complete eye evaluation, tonometric curves with Goldmann’s applanation tonometer, cup/disc ratio evaluation, gonioscopy by Goldmann’s three-mirrors lens, automated perimetry (Humphrey 30-2 full-threshold test) and contrast sensitivity evaluation by Pelli-Robson charts. A contrast sensitivity under 1,8 Logarithm of the Minimum Angle of Resolution (LogMAR) was considered abnormal. Results: contrast sensitivity was reduced in the group of myopes with ocular hypertension (1,788 LogMAR) and in the group of myopes with glaucoma (1,743 LogMAR), while it was preserved in the group of myopes (2,069 LogMAR) and in the group of emmetropes (1,990 LogMAR). We also found a strong correlation between contrast sensitivity reduction and mean deviation of visual fields in myopes with glaucoma (coefficient relation = 0.86) and in myopes with ocular hypertension (coefficient relation = 0.78). Conclusions: the contrast sensitivity assessment performed by the Pelli-Robson test should be performed in all patients with middle-grade myopia, ocular hypertension and optic disc suspected for glaucoma, as it may be useful in the early diagnosis of the disease. Introduction Contrast can be defined as the ability of the eye to discriminate differences in luminance between the stimulus and the background. The sensitivity to contrast is represented by the inverse of the minimal contrast necessary to make an object visible; the lower the contrast the greater the sensitivity, and the other way around. Contrast sensitivity is a fundamental aspect of vision together with visual acuity: the latter defines the smallest spatial detail that the subject manages to discriminate under optimal conditions, but it only provides information about the size of the stimulus that the eye is capable to perceive; instead, the evaluation of contrast sensitivity provides information not obtainable with only the measurement of visual acuity, as it establishes the minimum difference in luminance that must be present between the stimulus and its background so that the retina is adequately stimulated to perceive the stimulus itself. The clinical methods of examining contrast sensitivity (lattices, luminance gradients, variable-contrast optotypic tables and lowcontrast optotypic tables) relate the two parameters on which the ability to distinctly perceive an object depends, namely the different luminance degree of the two adjacent areas and the spatial frequency, which is linked to the size of the object. The measurement of contrast sensitivity becomes valuable in the diagnosis and follow up of some important eye conditions such as glaucoma. Studies show that contrast sensitivity can be related to data obtained with the visual perimetry, especially with the perimetric damage of the central area and of the optic nerve head

Constraints on Cosmological Parameters from the 500 deg² SPTPOL Lensing Power Spectrum

We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg² SPTPOL survey, the most precise CMB lensing measurement from the ground to date. We fit a flat ΛCDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO), as well as primary CMB spectra from Planck and SPTPOL. The cosmological constraints based on SPTPOL and Planck lensing band powers are in good agreement when analyzed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the SPTPOL CMB lensing data alone provide a 4% constraint on σ₈Ω^(0.25)_m = 0.593 ± 0.025. Jointly fitting with BAO data, we find σ₈ = 0.779±0.023, Ω_m = 0.368^(+0.032)_(−0.037), and H₀ = 72.0^(+2.1)_(−2.5)kms⁻¹ Mpc⁻¹, up to 2σ away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTPOL and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat ΛCDM model. The SPTPOL lensing spectrum constrains the spatial curvature to be Ω_K = −0.0007±0.0025 and the sum of the neutrino masses to be ∑m_ν < 0.23 eV at 95% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the signal-to-noise ratio of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement

Understanding the central kinematics of globular clusters with simulated integrated-light IFU observations

The detection of intermediate mass black holes in the centres of globular clusters is highly controversial, as complementary observational methods often deliver significantly different results. In order to understand these discrepancies, we develop a procedure to simulate integral field unit (IFU) observations of globular clusters: Simulating IFU Star Cluster Observations (SISCO). The input of our software are realistic dynamical models of globular clusters that are then converted in a spectral data cube. We apply SISCO to Monte Carlo cluster simulations from Downing et al. (2010), with a realistic number of stars and concentrations. Using independent realisations of a given simulation we are able to quantify the stochasticity intrinsic to the problem of observing a partially resolved stellar population with integrated-light spectroscopy. We show that the luminosity-weighted IFU observations can be strongly biased by the presence of a few bright stars that introduce a scatter in the velocity dispersion measurements up to $\simeq$40% around the expected value, preventing any sound assessment of the central kinematic and a sensible interpretation of the presence/absence of an intermediate mass black hole. Moreover, we illustrate that, in our mock IFU observations, the average kinematic tracer has a mass of $\simeq$0.75 solar masses, only slightly lower than the mass of the typical stars examined in studies of resolved line-of-sight velocities of giant stars. Finally, in order to recover unbiased kinematic measurements we test different masking techniques that allow us to remove the spaxels dominated by bright stars, bringing the scatter down to a level of only a few percent. The application of SISCO will allow to investigate state-of-the-art simulations as realistic observations.Comment: 13 pages, 9 figures, 1 table. Accepted for publication in MNRA