About the connection between the CℓC_{\ell} power spectrum of the Cosmic Microwave Background and the Γm\Gamma_{m} Fourier spectrum of rings on the sky

In this article we present and study a scaling law of the $m\Gamma_m$ CMB Fourier spectrum on rings which allows us (i) to combine spectra corresponding to different colatitude angles (e.g. several detectors at the focal plane of a telescope), and (ii) to recover the $C_l$ power spectrum once the $\Gamma_m$ coefficients have been measured. This recovery is performed numerically below the 1% level for colatitudes $\Theta> 80^\circ$ degrees. In addition, taking advantage of the smoothness of the $C_l$ and of the $\Gamma_m$, we provide analytical expressions which allow to recover one of the spectrum at the 1% level, the other one being known.Comment: 8 pages, 8 figure

Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

Analysis of a diffusive effective mass model for nanowires

We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking in account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a drift-diffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

First Detection of Polarization of the Submillimetre Diffuse Galactic Dust Emission by Archeops

We present the first determination of the Galactic polarized emission at 353 GHz by Archeops. The data were taken during the Arctic night of February 7, 2002 after the balloon--borne instrument was launched by CNES from the Swedish Esrange base near Kiruna. In addition to the 143 GHz and 217 GHz frequency bands dedicated to CMB studies, Archeops had one 545 GHz and six 353 GHz bolometers mounted in three polarization sensitive pairs that were used for Galactic foreground studies. We present maps of the I, Q, U Stokes parameters over 17% of the sky and with a 13 arcmin resolution at 353 GHz (850 microns). They show a significant Galactic large scale polarized emission coherent on the longitude ranges [100, 120] and [180, 200] deg. with a degree of polarization at the level of 4-5%, in agreement with expectations from starlight polarization measurements. Some regions in the Galactic plane (Gem OB1, Cassiopeia) show an even stronger degree of polarization in the range 10-20%. Those findings provide strong evidence for a powerful grain alignment mechanism throughout the interstellar medium and a coherent magnetic field coplanar to the Galactic plane. This magnetic field pervades even some dense clouds. Extrapolated to high Galactic latitude, these results indicate that interstellar dust polarized emission is the major foreground for PLANCK-HFI CMB polarization measurement.Comment: Submitted to Astron. & Astrophys., 14 pages, 12 Fig., 2 Table

Les Houches 2015: Physics at TeV colliders - new physics working group report

We present the activities of the 'New Physics' working group for the 'Physics at TeV Colliders' workshop (Les Houches, France, 1-19 June, 2015). Our report includes new physics studies connected with the Higgs boson and its properties, direct search strategies, reinterpretation of the LHC results in the building of viable models and new computational tool developments. Important signatures for searches for natural new physics at the LHC and new assessments of the interplay between direct dark matter searches and the LHC are also considered.Comment: Proceedings of the New Physics Working Group of the 2015 Les Houches Workshop, Physics at TeV Colliders, Les Houches 1-19 June 2015. 197 page

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Effects of CO₂, continental distribution, topography and vegetation changes on the climate at the Middle Miocene: a model study

The Middle Miocene was one of the last warm periods of the Neogene, culminating with the Middle Miocene Climatic Optimum (MMCO, approximatively 17–15 Ma). Several proxy-based reconstructions support warmer and more humid climate during the MMCO. The mechanisms responsible for the warmer climate at the MMCO and particularly the role of the atmospheric carbon dioxide are still highly debated. Here we carried out a series of sensitivity experiments with the model of intermediate complexity Planet Simulator, investigating the contributions of the absence of ice on the continents, the opening of the Central American and Eastern Tethys Seaways, the lowering of the topography on land, the effect of various atmospheric CO2 concentrations and the vegetation feedback. Our results show that a higher than present-day CO2 concentration is necessary to generate a warmer climate at all latitudes at the Middle Miocene, in agreement with the terrestrial proxy reconstructions which suggest high atmospheric CO2 concentrations at the MMCO. Nevertheless, the changes in sea-surface conditions, the lowering of the topography on land and the vegetation feedback also produce significant local warming that may, locally, even be stronger than the CO2 induced temperature increases. The lowering of the topography leads to a more zonal atmospheric circulation and allows the westerly flow to continue over the lowered Plateaus at mid-latitudes. The reduced height of the Tibetan Plateau notably prevents the development of a monsoon-like circulation, whereas the reduction of elevations of the North American and European reliefs strongly increases precipitation from northwestern to eastern Europe. The changes in vegetation cover contribute to maintain and even to intensify the warm and humid conditions produced by the other factors, suggesting that the vegetation-climate interactions could help to improve the model-data comparison