Boundary Integral Equations for the Laplace-Beltrami Operator

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere $\S$ in $\mathbb{R}^3$. We consider a closed curve ${\cal C}$ on ${\cal S}$ which divides ${\cal S}$ into two parts ${\cal S}_1$ and ${\cal S}_2$. In particular, ${\cal C} = \partial {\cal S}_1$ is the boundary curve of ${\cal S}_1$. We are interested in solving a boundary value problem for the Laplace-Beltrami operator in $\S_2$, with boundary data prescribed on \C

The HADES RV Programme with HARPS-N@TNG II. Data treatment and simulations

The distribution of exoplanets around low-mass stars is still not well understood. Such stars, however, present an excellent opportunity of reaching down to the rocky and habitable planet domains. The number of current detections used for statistical purposes is still quite modest and different surveys, using both photometry and precise radial velocities, are searching for planets around M dwarfs. Our HARPS-N red dwarf exoplanet survey is aimed at the detection of new planets around a sample of 78 selected stars, together with the subsequent characterization of their activity properties. Here we investigate the survey performance and strategy. From 2700 observed spectra, we compare the radial velocity determinations of the HARPS-N DRS pipeline and the HARPS-TERRA code, we calculate the mean activity jitter level, we evaluate the planet detection expectations, and we address the general question of how to define the strategy of spectroscopic surveys in order to be most efficient in the detection of planets. We find that the HARPS-TERRA radial velocities show less scatter and we calculate a mean activity jitter of 2.3 m/s for our sample. For a general radial velocity survey with limited observing time, the number of observations per star is key for the detection efficiency. In the case of an early M-type target sample, we conclude that approximately 50 observations per star with exposure times of 900 s and precisions of about 1 m/s maximizes the number of planet detections

HADES RV Programme with HARPS-N at TNG VI. GJ 3942 b behind dominant activity signals

Short- to mid-term magnetic phenomena on the stellar surface of M-type stars cannot only resemble the effects of planets in radial velocity data, but also may hide them. We analyze 145 spectroscopic HARPS-N observations of GJ 3942 taken over the past five years and additional photometry to disentangle stellar activity effects from genuine Doppler signals as a result of the orbital motion of the star around the common barycenter with its planet. To achieve this, we use the common methods of pre-whitening, and treat the correlated red noise by a first-order moving average term and by Gaussian-process regression following an MCMC analysis. We identify the rotational period of the star at 16.3 days and discover a new super-Earth, GJ 3942 b, with an orbital period of 6.9 days and a minimum mass of 7.1 Me. An additional signal in the periodogram of the residuals is present but we cannot claim it to be related to a second planet with sufficient significance at this point. If confirmed, such planet candidate would have a minimum mass of 6.3 Me and a period of 10.4 days, which might indicate a 3:2 mean-motion resonance with the inner planet

Asymmetric Dark Matter and Dark Radiation

Asymmetric Dark Matter (ADM) models invoke a particle-antiparticle asymmetry, similar to the one observed in the Baryon sector, to account for the Dark Matter (DM) abundance. Both asymmetries are usually generated by the same mechanism and generally related, thus predicting DM masses around 5 GeV in order to obtain the correct density. The main challenge for successful models is to ensure efficient annihilation of the thermally produced symmetric component of such a light DM candidate without violating constraints from collider or direct searches. A common way to overcome this involves a light mediator, into which DM can efficiently annihilate and which subsequently decays into Standard Model particles. Here we explore the scenario where the light mediator decays instead into lighter degrees of freedom in the dark sector that act as radiation in the early Universe. While this assumption makes indirect DM searches challenging, it leads to signals of extra radiation at BBN and CMB. Under certain conditions, precise measurements of the number of relativistic species, such as those expected from the Planck satellite, can provide information on the structure of the dark sector. We also discuss the constraints of the interactions between DM and Dark Radiation from their imprint in the matter power spectrum.Comment: 22 pages, 5 figures, to be published in JCAP, minor changes to match version to be publishe

Deep Eyedentification: Biometric Identification using Micro-Movements of the Eye

We study involuntary micro-movements of the eye for biometric identification. While prior studies extract lower-frequency macro-movements from the output of video-based eye-tracking systems and engineer explicit features of these macro-movements, we develop a deep convolutional architecture that processes the raw eye-tracking signal. Compared to prior work, the network attains a lower error rate by one order of magnitude and is faster by two orders of magnitude: it identifies users accurately within seconds

Critical properties of the optical field localization in a three-dimensional percolating system: Theory and experiment

We systematically study the optical field localization in an active three-dimensional (3D) disordered percolating system with light nanoemitters incorporated in percolating clusters. An essential feature of such a hybrid medium is that the clusters are combined into a fractal radiation pattern, in which light is simultaneously emitted and scattered by the disordered structures. Theoretical considerations, based on systematic 3D simulations, reveal nontrivial dynamics in the form of propagation of localized field bunches in the percolating material. We obtain the length of the field localization and dynamical properties of such states as functions of the occupation probability of the disordered clusters. A transition between the dynamical states and narrow point-like fields pinned to the emitters is found. The theoretical analysis of the fractal field properties is followed by an experimental study of the light generation by nanoemitters incorporated in the percolating clusters. The experimental results corroborate theoretical predictions.Comment: 10 pages, 14 figures, to be published Chaos, Solitons & Fractal

Quenching of Weak Interactions in Nucleon Matter

We have calculated the one-body Fermi and Gamow-Teller charge-current, and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter at densities of 0.08, 0.16 and 0.24 fm$^{-3}$ and proton fractions ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained by operating on Fermi-gas states by a symmetrized product of pair correlation operators determined from variational calculations with the Argonne v18 and Urbana IX two- and three-nucleon interactions. The squares of the charge current matrix elements are found to be quenched by 20 to 25 % by the short-range correlations in nucleon matter. Most of the quenching is due to spin-isospin correlations induced by the pion exchange interactions which change the isospins and spins of the nucleons. A large part of it can be related to the probability for a spin up proton quasi-particle to be a bare spin up/down proton/neutron. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions which give the variational energies in the Hartree-Fock approximation. The calculated two-nucleon effective interaction describes the spin-isospin susceptibilities of nuclear and neutron matter fairly accurately. However $\geq$ 3-body terms are necessary to reproduce the compressibility. All presented results use the simple 2-body cluster approximation to calculate the correlated basis matrix elements.Comment: submitted to PR