A Nitsche Finite Element Approach for Elliptic Problems with Discontinuous Dirichlet Boundary Conditions

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known singular functions as well as of an $H^2$-regular part. The latter part is expressed in terms of an elliptic problem with regularized Dirichlet boundary conditions, and can be approximated by means of a Nitsche finite element approach. The discrete solution of the original problem is then defined by adding the singular part of the exact solution to the Nitsche approximation. In this way, the discrete solution can be shown to converge of second order with respect to the mesh size

On the predictive power of Local Scale Invariance

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.Comment: 17 pages, 2 eps figure

Challenge of transition in the socio-professional insertion of youngsters with neurodisabilities

Patients with neurodisabilities require early management, continuing into adulthood. Thus, transition services were implemented in hospitals. To have a better support when they enter into adult life, it is useful to know the problems that they could face. The aim of this study is to evaluate their activities and to assess their insertion problems in the professional world. It is based on medical records of patients, aged 16 to 25 years, followed in the transition clinic of young adults in the Neurorehabilitation services of a tertiary centre. From 387 patients of the paediatric consultation, there are 267 patients (69%), included 224 with neurodevelopmental diseases and 43 with neuromuscular diseases. Nearly half of them (46.8%) were in a protected environment, 37.08% studied and 3.4% worked. Paradoxically, only 29.2% reported work problems. These results highlight the need to increase the integration of young adults with neuromotor disorders in the labor market

A possible signature of terrestrial planet formation in the chemical composition of solar analogs

Recent studies have shown that the elemental abundances in the Sun are anomalous when compared to most (about 85%) nearby solar twin stars. Compared to its twins, the Sun exhibits a deficiency of refractory elements (those with condensation temperatures Tc>900K) relative to volatiles (Tc<900K). This finding is speculated to be a signature of the planet formation that occurred more efficiently around the Sun compared with the majority of solar twins. Furthermore, within this scenario, it seems more likely that the abundance patterns found are specifically related to the formation of terrestrial planets. In this work we analyze abundance results from six large independent stellar abundance surveys to determine whether they confirm or reject this observational finding. We show that the elemental abundances derived for solar analogs in these six studies are consistent with the Tc trend suggested as a planet formation signature. The same conclusion is reached when those results are averaged heterogeneously. We also investigate the dependency of the abundances with first ionization potential (FIP), which correlates well with Tc. A trend with FIP would suggest a different origin for the abundance patterns found, but we show that the correlation with Tc is statistically more significant. We encourage similar investigations of metal-rich solar analogs and late F-type dwarf stars, for which the hypothesis of a planet formation signature in the elemental abundances makes very specific predictions. Finally, we examine a recent paper that claims that the abundance patterns of two stars hosting super-Earth like planets contradict the planet formation signature hypothesis. Instead, we find that the chemical compositions of these two stars are fully compatible with our hypothesis.Comment: To appear in Astronomy and Astrophysic

Study of shell supported ring frames with out- of-plane loading Final report, 24 Jun. - 28 Dec. 1965

Deflections and internal loading distribution of circular cylindrical shell supported ring frames with out-of-plane loading

Desensitizing Inflation from the Planck Scale

A new mechanism to control Planck-scale corrections to the inflationary eta parameter is proposed. A common approach to the eta problem is to impose a shift symmetry on the inflaton field. However, this symmetry has to remain unbroken by Planck-scale effects, which is a rather strong requirement on possible ultraviolet completions of the theory. In this paper, we show that the breaking of the shift symmetry by Planck-scale corrections can be systematically suppressed if the inflaton field interacts with a conformal sector. The inflaton then receives an anomalous dimension in the conformal field theory, which leads to sequestering of all dangerous high-energy corrections. We analyze a number of models where the mechanism can be seen in action. In our most detailed example we compute the exact anomalous dimensions via a-maximization and show that the eta problem can be solved using only weakly-coupled physics.Comment: 34 pages, 3 figures

A Field Range Bound for General Single-Field Inflation

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models. This shows that non-trivial dynamics can't evade the Lyth bound. We also present a weaker, but completely universal bound that holds whenever the Null Energy Condition (NEC) is satisfied at horizon crossing.Comment: 16 page