Characteristics of bound modes in coupled dielectric waveguides containing negative index media

We investigate the characteristics of guided wave modes in planar coupled waveguides. In particular, we calculate the dispersion relations for TM modes in which one or both of the guiding layers consists of negative index media (NIM)-where the permittivity and permeability are both negative. We find that the Poynting vector within the NIM waveguide axis can change sign and magnitude, a feature that is reflected in the dispersion curves

Radiative Inflation and Dark Energy

We propose a model based on radiative symmetry breaking that combines inflation with Dark Energy and is consistent with the WMAP 7-year regions. The radiative inflationary potential leads to the prediction of a spectral index 0.955 \lesssim n_S \lesssim 0.967 and a tensor to scalar ratio 0.142 \lesssim r \lesssim 0.186, both consistent with current data but testable by the Planck experiment. The radiative symmetry breaking close to the Planck scale gives rise to a pseudo Nambu-Goldstone boson with a gravitationally suppressed mass which can naturally play the role of a quintessence field responsible for Dark Energy. Finally, we present a possible extra dimensional scenario in which our model could be realised.Comment: 15 pages, 4 figures; v2: references added, appendix added, Section 5 slightly modified; content matches published versio

On Singularity formation for the L^2-critical Boson star equation

We prove a general, non-perturbative result about finite-time blowup solutions for the $L^2$-critical boson star equation $i\partial_t u = \sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under the sole assumption that the solution blows up in $H^{1/2}$ at finite time, we show that $u(t)$ has a unique weak limit in $L^2$ and that $|u(t)|^2$ has a unique weak limit in the sense of measures. Moreover, we prove that the limiting measure exhibits minimal mass concentration. A central ingredient used in the proof is a "finite speed of propagation" property, which puts a strong rigidity on the blowup behavior of $u$. As the second main result, we prove that any radial finite-time blowup solution $u$ converges strongly in $L^2$ away from the origin. For radial solutions, this result establishes a large data blowup conjecture for the $L^2$-critical boson star equation, similar to a conjecture which was originally formulated by F. Merle and P. Raphael for the $L^2$-critical nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704]. We also discuss some extensions of our results to other $L^2$-critical theories of gravitational collapse, in particular to critical Hartree-type equations.Comment: 24 pages. Accepted in Nonlinearit

Wave equation with concentrated nonlinearities

In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of \CO^n and a discrete set Y\subset\RE^3 with $n$ elements, we define a nonlinear operator $\Delta_{V,Y}$ on L^2(\RE^3) which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean matrix. We then consider the nonlinear wave equation $\ddot \phi=\Delta_{V,Y}\phi$ and study the corresponding Cauchy problem, giving an existence and uniqueness result in the case $V$ is Lipschitz. The solution of such a problem is explicitly expressed in terms of the solutions of two Cauchy problem: one relative to a free wave equation and the other relative to an inhomogeneous ordinary differential equation with delay and principal part $\dot\zeta+V(\zeta)$. Main properties of the solution are given and, when $Y$ is a singleton, the mechanism and details of blow-up are studied.Comment: Revised version. To appear in Journal of Physics A: Mathematical and General, special issue on Singular Interactions in Quantum Mechanics: Solvable Model

The Carina Project. V. The impact of NLTE effects on the iron content

We have performed accurate iron abundance measurements for 44 red giants (RGs) in the Carina dwarf spheroidal (dSph) galaxy. We used archival, high-resolution spectra (R~38,000) collected with UVES at ESO/VLT either in slit mode (5) or in fiber mode (39, FLAMES/GIRAFFE-UVES). The sample is more than a factor of four larger than any previous spectroscopic investigation of stars in dSphs based on high-resolution (R>38,000) spectra. We did not impose the ionization equilibrium between neutral and singly-ionized iron lines. The effective temperatures and the surface gravities were estimated by fitting stellar isochrones in the V, B-V color-magnitude diagram. To measure the iron abundance of individual lines we applied the LTE spectrum synthesis fitting method using MARCS model atmospheres of appropriate metallicity. We found evidence of NLTE effects between neutral and singly-ionized iron abundances. Assuming that the FeII abundances are minimally affected by NLTE effects, we corrected the FeI stellar abundances using a linear fit between FeI and FeII stellar abundance determinations. We found that the Carina metallicity distribution based on the corrected FeI abundances (44 RGs) has a weighted mean metallicity of [Fe/H]=-1.80 and a weighted standard deviation of sigma=0.24 dex. The Carina metallicity distribution based on the FeII abundances (27 RGs) gives similar estimates ([Fe/H]=-1.72, sigma=0.24 dex). The current weighted mean metallicities are slightly more metal poor when compared with similar estimates available in the literature. Furthermore, if we restrict our analysis to stars with the most accurate iron abundances, ~20 FeI and at least three FeII measurements (15 stars), we found that the range in iron abundances covered by Carina RGs (~1 dex) agrees quite well with similar estimates based on high-resolution spectra.Comment: Accepted for publication in PASP, 16 pages, 7 figures, 3 tables, 1 MR table Note: the electronic version of Table1 is included, but commented, in the tex fil

Reactor Neutrino Experiments with a Large Liquid Scintillator Detector

We discuss several new ideas for reactor neutrino oscillation experiments with a Large Liquid Scintillator Detector. We consider two different scenarios for a measurement of the small mixing angle $\theta_{13}$ with a mobile $\bar{\nu}_e$ source: a nuclear-powered ship, such as a submarine or an icebreaker, and a land-based scenario with a mobile reactor. The former setup can achieve a sensitivity to $\sin^2 2\theta_{13} \lesssim 0.003$ at the 90% confidence level, while the latter performs only slightly better than Double Chooz. Furthermore, we study the precision that can be achieved for the solar parameters, $\sin^2 2\theta_{12}$ and $\Delta m_{21}^2$, with a mobile reactor and with a conventional power station. With the mobile reactor, a precision slightly better than from current global fit data is possible, while with a power reactor, the accuracy can be reduced to less than 1%. Such a precision is crucial for testing theoretical models, e.g. quark-lepton complementarity.Comment: 18 pages, 3 figures, 2 tables, revised version, to appear in JHEP, Fig. 1 extended, Formula added, minor changes, results unchange

The Orbital Stability of the Ground States and the Singularity Formation for the Gravitational Vlasov Poisson System

International audienceWe study the gravitational Vlasov Poisson system $f_t+v\cdot\nabla_x f-E\cdot\nabla_vf=0$ where $E(x)=\nabla_x \phi(x)$, $\Delta_x\phi=\rho(x)$, \rho(x)=\int_{\RR^N} f(x,v)dxdv, in dimension $N=3,4$. In dimension $N=3$ where the problem is subcritical, we prove using concentration compactness techniques that every minimizing sequence to a large class of minimization problems attained on steady states solutions are up to a translation shift relatively compact in the energy space. This implies in particular the orbital stability {\it in the energy space} of the spherically symmetric polytropes what improves the nonlinear stability results obtained for this class in \cite{Guo,GuoRein,Dol}. In dimension $N=4$ where the problem is $L^1$ critical, we obtain the polytropic steady states as best constant minimizers of a suitable Sobolev type inequality relating the kinetic and the potential energy. We then derive using an explicit pseudo-conformal symmetry the existence of critical mass finite time blow up solutions, and prove more generally a mass concentration phenomenon for finite time blow up solutions. This is the first result of description of a singularity formation in a Vlasov setting. The global structure of the problem is reminiscent to the one for the focusing non linear Schrödinger equation $iu_t=-\Delta u-|u|^{p-1}u$ in the energy space $H^1(\R^N)$