Consistent Discretizations for Vanishing Regularization Solutions to Image Processing Problems

A model problem is used to represent a typical image processing problem of reconstructing an unknown in the face of incomplete data. A consistent discretization for a vanishing regularization solution is defined so that, in the absence of noise, limits first with respect to regularization and then with respect to grid refinement agree with a continuum counterpart defined in terms of a saddle point formulation. It is proved and demonstrated computationally for an artificial example and for a realistic example with magnetic resonance images that a mixed finite element discretization is consistent in the sense defined here. On the other hand, it is demonstrated computationally that a standard finite element discretization is not consistent, and the reason for the inconsistency is suggested in terms of theoretical and computational evidence

On the Optimal Taxation of Common-Pool Resources

Recent research developments in common-pool resource models emphasize the importance of links with ecological systems and the presence of non-linearities, thresholds and multiple steady states. In a recent paper Kossioris et al. (2008) develop a methodology for deriving feedback Nash equilibria for non-linear differential games and apply this methodology to a common-pool resource model of a lake where pollution corresponds to benefits and at the same time affects the ecosystem services. This paper studies the structure of optimal state- dependent taxes that steer the combined economic-ecological system towards the trajectory of optimal management, and provides an algorithm for calculating such taxes.Differential Games, non-linear Feedback Nash Equilibria, Ecosystems, Optimal State-dependent Tax

Evaluation of WRF performance for the analysis of surface wind speeds over various Greek regions

In this study we analyze the surface wind variability over selected areas of the Greek territory by comparing a 3-Km spatial resolution simulation performed with the Weather Research and Forecasting (WRF) model for the summer months of 2013 with actual surface measurements. Daily 36hrs runs at 12 UTC were driven by FLN (1 deg x 1 deg) data for the period of 11 July 2013 to 17 July 2013. Various verification statistics such as BIAS, RMSE and DACC for wind speed and direction were used to gauge the mesoscale model performance

A Posteriori Analysis for Space-Time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain

This paper presents an a posteriori error analysis for the discontinuous in time space-time scheme proposed by Jamet for the heat equation in multi-dimensional, non-cylindrical domains [25]. Using a Cl ement-type interpolant, we prove abstract a posteriori error bounds for the numerical error. Furthermore, in the case of two-dimensional spatial domains we transform the problem into an equivalent one, of parabolic type, with space-time dependent coe cients but posed on a cylindrical domain. We formulate a discontinuous in time space{time scheme and prove a posteriori error bounds of optimal order. The a priori estimates of [19] for general parabolic initial and boundary value problems are used in the derivation of the upper bound. Our lower bound coincides with that of Picasso [36], proposed for adaptive, Runge-Kutta finite element methods for linear parabolic problems. Our theoretical results are verified by numerical experiments

Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain

First published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical SocietyMotivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundary-value problem for a general Schr¨odinger-type equation posed on a two space-dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain, and we approximate its solution by a Crank–Nicolson finite element method. For the proposed numerical method, we derive an optimal order error estimate in the L2 norm, and to support the error analysis we prove a global elliptic regularity theorem for complex elliptic boundary value problems with mixed boundary conditions. Results from numerical experiments are presented which verify the optimal order of convergence of the method

ELGAR—a European Laboratory for Gravitation and Atom-interferometric Research

Gravitational waves (GWs) were observed for the first time in 2015, one century after Einstein predicted their existence. There is now growing interest to extend the detection bandwidth to low frequency. The scientific potential of multi-frequency GW astronomy is enormous as it would enable to obtain a more complete picture of cosmic events and mechanisms. This is a unique and entirely new opportunity for the future of astronomy, the success of which depends upon the decisions being made on existing and new infrastructures. The prospect of combining observations from the future space-based instrument LISA together with third generation ground based detectors will open the way toward multi-band GW astronomy, but will leave the infrasound (0.1–10 Hz) band uncovered. GW detectors based on matter wave interferometry promise to fill such a sensitivity gap. We propose the European Laboratory for Gravitation and Atom-interferometric Research (ELGAR), an underground infrastructure based on the latest progress in atomic physics, to study space–time and gravitation with the primary goal of detecting GWs in the infrasound band. ELGAR will directly inherit from large research facilities now being built in Europe for the study of large scale atom interferometry and will drive new pan-European synergies from top research centers developing quantum sensors. ELGAR will measure GW radiation in the infrasound band with a peak strain sensitivity of $3.3{\times}1{0}^{-22}/\sqrt{\text{Hz}}$ at 1.7 Hz. The antenna will have an impact on diverse fundamental and applied research fields beyond GW astronomy, including gravitation, general relativity, and geology.AB acknowledges support from the ANR (project EOSBECMR), IdEx Bordeaux—LAPHIA (project OE-TWR), theQuantERA ERA-NET (project TAIOL) and the Aquitaine Region (projets IASIG3D and USOFF).XZ thanks the China Scholarships Council (No. 201806010364) program for financial support. JJ thanks ‘AssociationNationale de la Recherche et de la Technologie’ for financial support (No. 2018/1565).SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grants No. DLR∼50WM1641 (PRIMUS-III), 50WM1952 (QUANTUS-V-Fallturm), and 50WP1700 (BECCAL), 50WM1861 (CAL), 50WM2060 (CARIOQA) as well as 50RK1957 (QGYRO)SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by ‘Niedersächsisches Vorab’ through the ‘Quantum- and Nano-Metrology (QUANOMET)’ initiative within the project QT3, and through ‘Förderung von Wissenschaft und Technik in Forschung und Lehre’ for the initial funding of research in the new DLR-SI Institute, the CRC 1227 DQ-mat within the projects A05 and B07DS gratefully acknowledges funding by the Federal Ministry of Education and Research (BMBF) through the funding program Photonics Research Germany under contract number 13N14875.RG acknowledges Ville de Paris (Emergence programme HSENS-MWGRAV), ANR (project PIMAI) and the Fundamental Physics and Gravitational Waves (PhyFOG) programme of Observatoire de Paris for support. We also acknowledge networking support by the COST actions GWverse CA16104 and AtomQT CA16221 (Horizon 2020 Framework Programme of the European Union).The work was also supported by the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grant Nos.∼50WM1556, 50WM1956 and 50WP1706 as well as through the DLR Institutes DLR-SI and DLR-QT.PA-S, MN, and CFS acknowledge support from contracts ESP2015-67234-P and ESP2017-90084-P from the Ministry of Economy and Business of Spain (MINECO), and from contract 2017-SGR-1469 from AGAUR (Catalan government).SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967 (B2) andCRC1227 ‘DQ-mat’ within projects A05, B07 and B09.LAS thanks Sorbonne Universités (Emergence project LORINVACC) and Conseil Scientifique de l'Observatoire de Paris for funding.This work was realized with the financial support of the French State through the ‘Agence Nationale de la Recherche’ (ANR) in the frame of the ‘MRSEI’ program (Pre-ELGAR ANR-17-MRS5-0004-01) and the ‘Investissement d'Avenir’ program (Equipex MIGA: ANR-11-EQPX-0028, IdEx Bordeaux—LAPHIA: ANR-10-IDEX-03-02).Peer Reviewe

High order finite volume element approximations of one dimensional indefinite elliptic problems

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Error control for time-splitting spectral approximations of the semiclassical Schrödinger equation

We prove a posteriori error estimates of optimal order in the L ∞(L2)-norm for time-splitting spectral methods applied to the linear Schrödinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.</p

On the Optimal Taxation of Common-Pool Resources

Recent research developments in common-pool resource models emphasize the importance of links with ecological systems and the presence of non-linearities, thresholds and multiple steady states. In a recent paper Kossioris et al. (2008) develop a methodology for deriving feedback Nash equilibria for non-linear differential games and apply this methodology to a common-pool resource model of a lake where pollution corresponds to benefits and at the same time affects the ecosystem services. This paper studies the structure of optimal state- dependent taxes that steer the combined economic-ecological system towards the trajectory of optimal management, and provides an algorithm for calculating such taxes