A posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions

[Abstract] We develop a residual-based a posteriori error analysis for the augmented mixed methods introduced in and for the problem of linear elasticity in the plane. We prove that the proposed a posteriori error estimators are both reliable and efficient. Numerical experiments confirm these theoretical properties and illustrate the ability of the corresponding adaptive algorithms to localize the singularities and large stress regions of the solutions

Augmented mixed finite element method for the Oseen problem: A priori and a posteriori error analyses

We propose a new augmented dual-mixed method for the Oseen problem based on the pseudostress–velocity formulation. The stabilized formulation is obtained by adding to the dual-mixed approach suitable least squares terms that arise from the constitutive and equilibrium equations. We prove that for appropriate values of the stabilization parameters, the new variational formulation and the corresponding Galerkin scheme are well-posed, and a Céa estimate holds for any finite element subspaces. We also provide the rate of convergence when each row of the pseudostress is approximated by Raviart–Thomas or Brezzi–Douglas–Marini elements and the velocity is approximated by continuous piecewise polynomials. Moreover, we derive a simple a posteriori error estimator of residual type that consists of two residual terms and prove that it is reliable and locally efficient. Finally, we include several numerical experiments that support the theoretical results.Dirección de Investigación of the Universidad Católica de la Santísima Concepción (Chile) y CONICYT-Chile FONDECYT; Ministerio de Ciencia e Innovación del Gobierno de España

Enabling propagation of anisotropic polaritons along forbidden directions via a topological transition

Polaritons with directional in-plane propagation and ultralow losses in van der Waals (vdW) crystals promise unprecedented manipulation of light at the nanoscale. However, these polaritons present a crucial limitation: their directional propagation is intrinsically determined by the crystal structure of the host material, imposing forbidden directions of propagation. Here, we demonstrate that directional polaritons (in-plane hyperbolic phonon polaritons) in a vdW crystal (α-phase molybdenum trioxide) can be directed along forbidden directions by inducing an optical topological transition, which emerges when the slab is placed on a substrate with a given negative permittivity (4H–silicon carbide). By visualizing the transition in real space, we observe exotic polaritonic states between mutually orthogonal hyperbolic regimes, which unveil the topological origin of the transition: a gap opening in the dispersion. This work provides insights into optical topological transitions in vdW crystals, which introduce a route to direct light at the nanoscale

Emission polarization control in semiconductor quantum dots coupled to a photonic crystal microcavity

8 páginas, 5 figuras.-- OCIS codes: (160.4760) Optical properties; (230.5298) Photonic crystals; (230.5590) Quantumwell, -wire and –dot devices.We study the optical emission of single semiconductor quantum dots weakly coupled to a photonic-crystal micro-cavity. The linearly polarized emission of a selected quantum dot changes continuously its polarization angle, from nearly perpendicular to the cavity mode polarization at large detuning, to parallel at zero detuning, and reversing sign for negative detuning. The linear polarization rotation is qualitatively interpreted in terms of the detuning dependent mixing of the quantum dot and cavity states. The present result is relevant to achieve continuous control of the linear polarization in single photon emitters.This work has been supported by research contracts of the Spanish Ministry of Education Grants MAT2008-01555/NAN, Consolider CSD 2006-19 and Naninpho-QD TEC2008-06756-C03- 01, and the Community of Madrid Grant Grant CAM (S2009/ESP-1503).Peer reviewe

Clinical narrative analytics challenges

Precision medicine or evidence based medicine is based on the extraction of knowledge from medical records to provide individuals with the appropriate treatment in the appropriate moment according to the patient features. Despite the efforts of using clinical narratives for clinical decision support, many challenges have to be faced still today such as multilinguarity, diversity of terms and formats in different services, acronyms, negation, to name but a few. The same problems exist when one wants to analyze narratives in literature whose analysis would provide physicians and researchers with highlights. In this talk we will analyze challenges, solutions and open problems and will analyze several frameworks and tools that are able to perform NLP over free text to extract medical entities by means of Named Entity Recognition process. We will also analyze a framework we have developed to extract and validate medical terms. In particular we present two uses cases: (i) medical entities extraction of a set of infectious diseases description texts provided by MedlinePlus and (ii) scales of stroke identification in clinical narratives written in Spanish

Theoretical modelling of quaternary GaInAsSb/GaAs self-assembled quantum dots

Trabajo presentado al "Quantum Dot", celebrado en Nottingham (UK) del 26 al 30 de Abril de 2010.InAs/GaAs quantum dots exposed to Sb after growth exhibit spectral changes. We study in the present paper an idealized nanostructure consisting of a homogeneous distribution of the quaternary GaInAsSb surrounded by a barrier of GaAs. We nd that the valence band o set is a critical parameter in modelling its electronic structure. Depending on this value, we predict a transition from type-I to type-II band alignment at a di erent Sb concentration. The addition of Sb to reduce the transition energy while keeping a type-I alignment is only of bene t at low Sb concentrationThis work was supported by the Spanish MICINN (projects TEC2008-06756-C03-01/02/TEC, CONSOLIDER INGENIO 2010 CSD2006-0019 and CSD2009-00013), the Junta de Andalucía (PAI research groups TEP-120 and TIC-145; project P08-TEP-03516) and Comunidad Autónoma de Madrid S2009ESP-1503.Peer reviewe

Planar refraction and lensing of highly confined polaritons in anisotropic media

Refraction between isotropic media is characterized by light bending towards the normal to the boundary when passing from a low- to a high-refractive-index medium. However, refraction between anisotropic media is a more exotic phenomenon which remains barely investigated, particularly at the nanoscale. Here, we visualize and comprehensively study the general case of refraction of electromagnetic waves between two strongly anisotropic (hyperbolic) media, and we do it with the use of nanoscale-confined polaritons in a natural medium: alpha-MoO3. The refracted polaritons exhibit non-intuitive directions of propagation as they traverse planar nanoprisms, enabling to unveil an exotic optical effect: bending-free refraction. Furthermore, we develop an in-plane refractive hyperlens, yielding foci as small as lambdap/6, being lambdap the polariton wavelength (lambda0/50 compared to the wavelength of free-space light). Our results set the grounds for planar nano-optics in strongly anisotropic media, with potential for effective control of the flow of energy at the nanoscale.G.Á.-P. and J.T.-G. acknowledge support through the Severo Ochoa Program from the Government of the Principality of Asturias (nos. PA-20-PF-BP19-053 and PA-18-PF-BP17-126, respectively). S.X. acknowledges the support from Independent Research Fund Denmark (Project No. 9041-00333B). B.C. acknowledges the support from VILLUM FONDEN (No. 00027987). The Center for Nanostructured Graphene is sponsored by the Danish National Research Foundation (Project No. DNRF103.) K.V.V. and V.S.V. gratefully acknowledge the financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2021-606). J.M.-S. acknowledges financial support through the Ramón y Cajal Program from the Government of Spain (RYC2018-026196-I). A.Y.N. and J.I.M. acknowledge the Spanish Ministry of Science, Innovation and Universities (national projects MAT201788358-C3-3-R and PID2019-104604RB/AEI/10.13039/501100011033). R.H. acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities (national project RTI2018-094830-B-100 and the project MDM-2016-0618 of the Marie de Maeztu Units of Excellence Program) and the Basque Government (grant No. IT1164-19). A.Y.N. also acknowledges the Basque Department of Education (grant no. PIBA-2020-1-0014). P.A.-G. acknowledges support from the European Research Council under starting grant no. 715496, 2DNANOPTICA and the Spanish Ministry of Science and Innovation (State Plan for Scientific and Technical Research and Innovation grant number PID2019-111156GB-I00)

All-particle cosmic ray energy spectrum measured by the HAWC experiment from 10 to 500 TeV

We report on the measurement of the all-particle cosmic ray energy spectrum with the High Altitude Water Cherenkov (HAWC) Observatory in the energy range 10 to 500 TeV. HAWC is a ground based air-shower array deployed on the slopes of Volcan Sierra Negra in the state of Puebla, Mexico, and is sensitive to gamma rays and cosmic rays at TeV energies. The data used in this work were taken from 234 days between June 2016 to February 2017. The primary cosmic-ray energy is determined with a maximum likelihood approach using the particle density as a function of distance to the shower core. Introducing quality cuts to isolate events with shower cores landing on the array, the reconstructed energy distribution is unfolded iteratively. The measured all-particle spectrum is consistent with a broken power law with an index of $-2.49\pm0.01$ prior to a break at $(45.7\pm0.1$) TeV, followed by an index of $-2.71\pm0.01$. The spectrum also respresents a single measurement that spans the energy range between direct detection and ground based experiments. As a verification of the detector response, the energy scale and angular resolution are validated by observation of the cosmic ray Moon shadow's dependence on energy.Comment: 16 pages, 11 figures, 4 tables, submission to Physical Review