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1. Laboratory studies of ship hull’s material degradation scenarios to optimize a cathodic protection modelling software

Author

Marie Minola, Virginie Roche, Laure-Line Rouve, Olivier Pinaud, Olivier Chadebec, Michaël Nale, Cédric Goëau, and Jean-Claude Lepretre

Subjects
Materials of engineering and construction. Mechanics of materials, TA401-492
Abstract

Abstract This work presents the experimental research carried out to optimize a current computational software “CorOns”, to obtain a better ship hull electrical signature modelling. Middle-term ageing (597 days) of anticorrosion paints, highlights the appearance of additional corrosion processes, despite an absence of visual defects. A specific model is proposed for an aged surface in seawater based on Electrochemical Impedance Spectroscopy (“EIS”) data analysis. We also investigate the impact of the interruption of cathodic protection on the corrosion process, with the objective of modelling the electrical signature in real conditions that could be encountered. These studies’ interruption of the cathodic protection during 24 h, do not seem to have an impact on the current densities. However, EIS studies, highlight that the protection interruptions damage the calcareous deposit, well-known for it is protective effect once formed.

Published
2023
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2. A priori Bayesian Information for Inverse Resolution of Integral Formulation applied to Thin Regions Magnetization Identification

Author

Gireg Chavin-Collin, Didier Cavallera, Olivier Chadebec, Gérard Meunier, Olivier Pinaud, Nicolas Galopin, Laure Line Rouve, Laboratoire de Génie Electrique de Grenoble (G2ELab ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and Naval Group

Subjects
magnetostatic inverse problem, thin magnetic region, magnetization identification, Bayesian inference, [SPI.NRJ]Engineering Sciences [physics]/Electric power, volume integral method
Abstract

International audience; An algorithm for the reconstruction of the magnetization inside an iron sheet is proposed. The magnetization distribution is reconstructed from magnetic measurements made on sensors placed in the surrounding air region. The problem consists in identifying magnetic charges thanks to Bayesian a priori information. The charges derive from the divergence of the flux density through element facets. The efficiency of the method is demonstrated with a numerical application.

Published
2020

3. Cathodic protection modeling of a covered and uncovered steel immersed in seawater : Corrosion characterizations

Author

Virginie Roche, Michael Nale, Olivier Pinaud, Laure-Line Rouve, Cédric Goeau, Marie Minola, Jean-Claude Leprêtre, Olivier Chadebec, Electrochimie Interfaciale et Procédés (EIP), Laboratoire d'Electrochimie et de Physico-chimie des Matériaux et des Interfaces (LEPMI), Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut de Chimie du CNRS (INC)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Matériaux Interfaces ELectrochimie (MIEL), Délégation générale de l'armement (DGA), Ministère de la Défense, Laboratoire de Génie Electrique de Grenoble (G2ELab ), and Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )

Subjects
[SPI]Engineering Sciences [physics], Materials science, Metallurgy, Seawater, ComputingMilieux_MISCELLANEOUS, Cathodic protection, Corrosion, Characterization (materials science)
Abstract

As underwater structure, ships are protected by a suitable cathodic protection system to prevent and reduce significantly corrosion phenomenon. This protective system, called Impressed Current Cathodic Protection (ICCP), creates an underwater electrical current. Then, this current generates an electromagnetic field also referred as electrical signature that could be detectable by sensors [1-2]. Therefore, this work refers to the electrochemical characterization of the materials used in naval framework in addition to a better comprehension of the corrosion phenomenon. The final goal is to predict electrical signatures of ships under different corrosion conditions as illustrated on figure 1: Electrical fields induce by natural corrosion or ICCP. These predictions will be done by including the obtained models of material in numerical simulation tools based on the boundary element method. In a first time, polarization laws of different materials present on the immersed hull and electrically connected are obtained: the hull material (coated and uncoated), the propeller material and zinc for sacrificial anodes to complete the cathodic protection system. One part of this project is to be able to model the metal/electrolyte interface in different operating conditions: speed, temperature, polarization state, ageing of the coating and galvanic coupling between the different metals. The second part of this project is to integrate these laboratory data in simulation tools to optimize it. In these simulation tools, the hull is discretized by a surface mesh. Each element of the mesh is being associated to local polarization laws obtained during the laboratory test. Then laboratory models and simulation tools will be tested at a bigger scale on a mockup. To achieve these goals, it’s important to understand what happens physically at the interface and modeling the different corrosion phenomena which take place at the interface. To model the interface experimentally, Electrical Equivalent Circuits are used. These Electrical Equivalent Circuits, commonly called EEC, are deduced considering physical phenomenon happening at the interface by fitting Electrochemical Impedance Spectroscopy (EIS) data. To complete EIS investigations and confirm the different models, potentiodynamic curves and Scanning Electron Microscopy with EDX analyses were also performed. From the first results, Electrical Equivalent Circuits (EEC) of the metallic interface behavior (hull) are proposed for different polarizations conditions: anodic, corrosion potential and cathodic (ICCP potential: -0,8 VECS) in order to understand more deeply the corrosion phenomenon following the polarization state of the steel. In complement EEC investigations will be made under different temperatures and in electrolyte dynamic conditions (thanks to a rotating electrode) for hull steel samples at corrosion potential. The propeller material will also be characterized following speed influence of the solution and temperature. Simultaneously painted hull steel is also investigated in regards to temperature, polarization state and mechanical ageing. Transition state (ICCP turn on/off) and galvanic coupling between propeller and hull materials coated or not will be investigated to complete elementary investigations. Painted hull steel samples give equivalent result whatever experimental conditions. Indeed freshly painted hull steel samples show an almost pure capacitance behavior if we refer to the (Loveday et al.; 2004) [1] work’s suggesting a strong protective behavior of freshly painted sample. To model this behavior a simple Randle circuit,which only take into account the impedance of the paint, is used. The impact of mechanical defects will be presented to simulate paint degradation and investigate evolution of polarization law. In case of uncoated hull steel, EEC are more complex and change following the polarization and experimental conditions. In all cases, a deposit is formed but its nature and protective behavior change with polarization: a formation of calcareous deposit under cathodic polarization and corrosion products deposit under anodic polarization. That requires in consequence to include additional impedances in the EEC modeling: impedance of a deposit or diffusion impedance for example. Temperature variation and dynamic conditions influence also the kinetic of the different interfacial phenomena. Simultaneously some results of simulation obtain with the use of this first result give encouraging results with good correlations between data obtain in at laboratory scale and simulations. (C Rannou and JL Coulomd; 2008 ) : Optimization of the cathodic protection system of military ships with respect to the double constraint:cathodic protection and electromagnetic silencing ; HAL ; MARELEC 2006; Amesterdam; Netherlands; 2004 (A.Guibert ) : Diagnostique de corrosion et prédiction de signature électromagnétique de structures sous-marines sous protection cathodique ; Science de l’ingénieur ; Institut National Polytechnique de Grenoble-INPG ; HAL ; 2009 (Loveday et al.; 2004) : Evaluation of organic Coatings with Electrochemical Impedance Spectroscopy, part 2; Gamy Instruments; JCT Coating tech; 2004 Figure 1

Published
2020

4. On local quantum Gibbs states

Author

Romain Duboscq and Olivier Pinaud

Subjects
FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Mathematical Physics
Abstract

We address in this work the problem of minimizing quantum entropies under local constraints. We suppose that macroscopic quantities, such as the particle density, current, and kinetic energy, are fixed at each point of [Formula: see text] and look for a density operator over [Formula: see text], minimizing an entropy functional. Such minimizers are referred to as local Gibbs states. This setting is in contrast with the classical problem of prescribing global constraints, where the total number of particles, total current, and total energy in the system are fixed. The question arises, for instance, in the derivation of fluid models from quantum dynamics. We prove, under fairly general conditions, that the entropy admits a unique constrained minimizer. Due to a lack of compactness, the main difficulty in the proof is to show that limits of minimizing sequences satisfy the local energy constraint. We tackle this issue by introducing a simpler auxiliary minimization problem and by using a monotonicity argument involving the entropy.

Published
2020

5. Constrained minimizers of the von Neumann entropy and their characterization

Author

Olivier Pinaud, Romain Duboscq, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Colorado State University [Fort Collins] (CSU), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Current (mathematics), Applied Mathematics, Operator (physics), 010102 general mathematics, Feasible region, FOS: Physical sciences, Mathematical Physics (math-ph), Von Neumann entropy, 01 natural sciences, 010101 applied mathematics, Nonlinear system, Optimization and Control (math.OC), Position (vector), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Trace class, Mathematics - Optimization and Control, Mathematical Physics, Analysis, Eigenvalues and eigenvectors, Mathematics
Abstract

We consider in this work the problem of minimizing the von Neumann entropy under the constraints that the density of particles, the current, and the kinetic energy of the system is fixed at each point of space. The unique minimizer is a self-adjoint positive trace class operator, and our objective is to characterize its form. We will show that this minimizer is solution to a self-consistent nonlinear eigenvalue problem. One of the main difficulties in the proof is to parametrize the feasible set in order to derive the Euler–Lagrange equation, and we will proceed by constructing an appropriate form of perturbations of the minimizer. The question of deriving quantum statistical equilibria is at the heart of the quantum hydrodynamical models introduced by Degond and Ringhofer (J Statist Phys 112:(3–4), 587-628, 2003). An original feature of the problem is the local nature of constraints, i.e. they depend on position, while more classical models consider the total number of particles, the total current and the total energy in the system to be fixed.

Published
2019

6. A constrained optimization problem in quantum statistical physics

Author

Romain Duboscq, Olivier Pinaud, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Colorado State University [Fort Collins] (CSU), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)

Subjects
Operator (physics), Feasible region, FOS: Physical sciences, Mathematical Physics (math-ph), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, 010305 fluids & plasmas, Functional Analysis (math.FA), 010101 applied mathematics, Constraint (information theory), Mathematics - Functional Analysis, Nonlinear system, Position (vector), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 0103 physical sciences, FOS: Mathematics, Point (geometry), Statistical physics, 0101 mathematics, Trace class, Quantum, Analysis, Mathematical Physics, Mathematics
Abstract

In this paper, we consider the problem of minimizing quantum free energies under the constraint that the density of particles is fixed at each point of R d , for any d ≥ 1 . We are more particularly interested in the characterization of the minimizer, which is a self-adjoint nonnegative trace class operator, and will show that it is solution to a nonlinear self-consistent problem. This question of deriving quantum statistical equilibria is at the heart of the quantum hydrodynamical models introduced by Degond and Ringhofer in [4] . An original feature of the problem is the local nature of constraint, i.e. it depends on position, while more classical models consider the total number of particles in the system to be fixed. This raises difficulties in the derivation of the Euler-Lagrange equations and in the characterization of the minimizer, which are tackled in part by a careful parameterization of the feasible set.

Published
2019

7. A backscattering model based on corrector theory of homogenization for the random Helmholtz equation

Author

Olivier Pinaud and Wenjia Jing

Subjects
Physics, geography, geography.geographical_feature_category, Helmholtz equation, Wave propagation, Applied Mathematics, Mathematical analysis, Detector, 35J05, 35R30, 86A22, 60F99, Random media, Homogenization (chemistry), Quadratic equation, Mathematics - Analysis of PDEs, Orders of approximation, FOS: Mathematics, Sea ice, Discrete Mathematics and Combinatorics, Physics::Atmospheric and Oceanic Physics, Analysis of PDEs (math.AP)
Abstract

This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above the sea ice layer, the main objective of this work is to derive a model for the backscattered signal measured at the source/detector location. The problem is difficult in that, in the practical configuration we consider, the wave impinges on the layer with a non-normal incidence. Since the sea ice is seen by the pulse as an effective (homogenized) medium, the energy is specularly reflected and the backscattered signal vanishes in a first order approximation. What is measured at the detector consists therefore of corrections to leading order terms, and we focus in this work on the homogenization corrector. We describe the propagation by a random Helmholtz equation, and derive an expression of the corrector in this layered framework. We moreover obtain a transport model for quadratic quantities in the random wavefield in a high frequency limit., 30 pages

Published
2018

8. Monte Carlo methods for radiative transfer with singular kernels

Author

Olivier Pinaud, Christophe Gomez, Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Colorado State University [Fort Collins] (CSU), NSF CAREER grant DMS-1452349, and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Work (thermodynamics), Mathematical optimization, Wave propagation, Applied Mathematics, Quantum Monte Carlo, 010102 general mathematics, Monte Carlo method, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], 01 natural sciences, 010101 applied mathematics, Hybrid Monte Carlo, Computational Mathematics, radiative transfer, Radiative transfer, Dynamic Monte Carlo method, Statistical physics, singular kernels, 0101 mathematics, Monte Carlo, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Monte Carlo molecular modeling, Mathematics
Abstract

International audience; This work is devoted to Monte Carlo methods for radiative transfer equations with singular kernels, and is motivated by the study of wave propagation in random media with long-range dependence. As opposed to the short-range case where the collision cross section is integrable and leads to a non-zero mean free time, the cross section is not integrable in the long-range situation and yields a vanishing mean free time. For computational efficiency, a particular care is then required in the construction of the stochastic processes used in the Monte Carlo methods. For this, we adapt a method of Asmussen-Rosi´nskiRosi´nski and Cohen-Rosi´nskiRosi´nski based on a small jumps/large jumps decomposition of the generator. We compare this method with another approach based on alpha-stable processes, and show the superiority of the first one. We consider various algorithms for the simulation of the jump distribution, and underline the efficiency of an appropriate stochastic collocation method. Comparisons between integrable and singular kernel solutions are given.

Published
2018
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9. Optimization-based ambient field compensation applied to fast-field cycling nuclear magnetic resonance experiments

Author

Lucas Blattner Martinho, Olivier Chadebec, Olivier Pinaud, Laure-Line Rouve, Jean-Louis Coulomb, Antoine Viana, Pascal Henry Fries, Gianni Ferrante, Laboratoire de Génie Electrique de Grenoble (G2ELab), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut Nanosciences et Cryogénie (INAC), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Stelar, European Physical Society, and Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power
Abstract

International audience; Fast-field cycling (FFC) nuclear magnetic resonance applications require compensation of the ambient magnetic field. This compensation may be stated in terms of a multi-objective optimization problem involving the spherical harmonics decomposition of the field generated by a set ofcompensation coils. In this article, this optimization-based approach is detailed and applied to the particular case of a FFC relaxometer.

Published
2017

10. On the minimization of quantum entropies under local constraints

Author

Olivier Pinaud, Romain Duboscq, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Colorado State University [Fort Collins] (CSU), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Applied Mathematics, General Mathematics, 010102 general mathematics, FOS: Physical sciences, Monotonic function, Mathematical Physics (math-ph), 01 natural sciences, 010101 applied mathematics, Compact space, Moment closure, Optimization and Control (math.OC), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, Statistical physics, Minification, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Quantum, Mathematics - Optimization and Control, Entropy minimization, Mathematical Physics, Mathematics, Energy constraint
Abstract

This work is concerned with the minimization of quantum entropies under local constraints of density, current, and energy. The problem arises in the work of Degond and Ringhofer about the derivation of quantum hydrodynamical models from first principles, which is an adaptation to the quantum setting of the moment closure strategy by entropy minimization encountered in kinetic theory. The main mathematical difficulty is the lack of compactness needed to recover the energy constraint. We circumvent this issue by a monotonicity argument involving energy, temperature and entropy, that is inspired by some thermodynamical considerations.

Published
2017

11. Multipolar Harmonic Model applied to UEP Source Identification'

Author

Olivier Pinaud, Laure-Line Rouve, Olivier Chadebec, Goëau, C., Arnaud Guibert, Laboratoire de Génie Electrique de Grenoble (G2ELab), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), DGA TN F, and 1) DGA TN F-29200 Brest

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power
Abstract

International audience; Corrosion or adapted cathodic protection is responsible for UEP (underwater electricpotential) generation that may cause ship detection. As a consequence, ship electricsignatures are measured on dedicated ranges at given depth. Nevertheless, to assessthe threat, the signature must be known at larger distances and for differentparameters (conductivity, water depth, number of conductive layers) depending onship operation zone. In previous work, a dipolar model has been proposed torepresent the electric field sources and exhibited good agreement with experiment. Itwas based on ellipsoidal harmonic decomposition and the use of image methods.The present paper deals with the generalization of the model to its multipolarcomponents. After presenting the model elaboration, the approach is tested onnumerical cases computed by CorOnS software, developed by the G2Elab incooperation with the DGA (Direction Générale de l’Armement).

Published
2017

12. The quantum Liouville-BGK equation and the moment problem

Author

Florian Méhats, Olivier Pinaud, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Invariant Preserving SOlvers ( IPSO ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique ( Inria ), Department of Mathematics [Fort Collins], College of Natural Sciences [Fort Collins], Colorado State University [Fort Collins] ( CSU ) -Colorado State University [Fort Collins] ( CSU ), ANR-14-CE23-0007,MOONRISE,MOdèles, Oscillations et SchEmas NUmeriques ( 2014 ), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Invariant Preserving SOlvers (IPSO), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Colorado State University [Fort Collins] (CSU)-Colorado State University [Fort Collins] (CSU), DMS-1452349, National Science Foundation, ANR-14-CE23-0007-01, Agence Nationale de la Recherche, ANR-14-CE23-0007,MOONRISE,MOdèles, Oscillations et SchEmas NUmeriques(2014), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

Subjects
Work (thermodynamics), Closure (topology), Mathematical proof, 01 natural sciences, Hydrodynamic equations, Mathematics - Analysis of PDEs, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], minimization, 0101 mathematics, Quantum, Mathematics, Mathematical physics, diffusion-models, Applied Mathematics, 010102 general mathematics, Entropy principle, Term (logic), energy-transport, 010101 applied mathematics, Constraint (information theory), Moment problem, Minification, Derivation, Analysis, Analysis of PDEs (math.AP)
Abstract

International audience; This work is devoted to the analysis of the quantum Liouville-BGK equation. This equation arises in the work of Degond and Ringhofer on the derivation of quantum hydrodynamical models from first principles. Their theory consists in transposing to the quantum setting the closure strategy by entropy minimization used for kinetic equations. The starting point is the quantum Liouville-BGK equation, where the collision term is defined via a so-called quantum local equilibrium, defined as a minimizer of the quantum free energy under a local density constraint. We then address three related problems: we prove new results about the regularity of these quantum equilibria; we prove that the quantum Liouville-BGK equation admits a classical solution; and we investigate the long-time behavior of the solutions. The core of the proofs is based on a fine analysis of the properties of the minimizers of the free energy.

Published
2017
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13. Magnetic field exposure assessment in electric vehicles

Author

Meinhard Schilling, Alain Ferber, Christof Wehrmann, Olivier Pinaud, Andrea Vassilev, Alastair R. Ruddle, Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), and Chadebec, Olivier

Subjects
Battery (electricity), Engineering, business.industry, Powertrain, Magnetic field exposure, Direct current, [SPI.NRJ]Engineering Sciences [physics]/Electric power, Electrical engineering, Condensed Matter Physics, Atomic and Molecular Physics, and Optics, Frequency spectrum, Automotive engineering, Magnetic field, Magnet, Fuel cells, Electrical and Electronic Engineering, business, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

This article describes a study of magnetic field exposure in electric vehicles (EVs). The magnetic field inside eight different EVs (including battery, hybrid, plug-in hybrid, and fuel cell types) with different motor technologies (brushed direct current, permanent magnet synchronous, and induction) were measured at frequencies up to 10 MHz. Three vehicles with conventional powertrains were also investigated for comparison. The measurement protocol and the results of the measurement campaign are described, and various magnetic field sources are identified. As the measurements show a complex broadband frequency spectrum, an exposure calculation was performed using the ICNIRP “weighted peak” approach. Results for the measured EVs showed that the exposure reached 20% of the ICNIRP 2010 reference levels for general public exposure near to the battery and in the vicinity of the feet during vehicle start-up, but was less than 2% at head height for the front passenger position. Maximum exposures of the order of 10% of the ICNIRP 2010 reference levels were obtained for the cars with conventional powertrains.

Published
2015

14. Introducing a priori Information into Magnetostatic Inverse Problem

Author

Olivier Pinaud, Olivier Chadebec, Laure-Line Rouve, Jean-Michel Guichon, Andrea Vassilev, Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

International audience; This paper deals with the use of the Bayesian approach to bring a priori information into spherical harmonic coefficients identification to inverse an under determined magnetostatic problem.

Published
2014

15. Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations

Author

Christophe Gomez, Olivier Pinaud, Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)

Subjects
Numerical Analysis, Asymptotic analysis, Oscillation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Paraxial approximation, Random Schrödinger equation / long-range correlations / high frequency asymptotics / splitting scheme, 010103 numerical & computational mathematics, 01 natural sciences, Schrödinger equation, Computational Mathematics, symbols.namesake, Amplitude, Modeling and Simulation, symbols, Range (statistics), Initial value problem, Limit (mathematics), 0101 mathematics, [MATH]Mathematics [math], Analysis, Mathematics
Abstract

International audience; This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial condition, and the statistical properties of the random medium. We show that the splitting scheme captures these regimes in a statistical sense for a time stepsize independent of the frequency.

Published
2014
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16. Forward Model Computation of Quasi-static Magnetic Fields inside Electric Vehicles

Author

Olivier Pinaud, Olivier Chadebec, Laure-Line Rouve, Jean-Michel Guichon, Andrea Vassilev, Laboratoire de Génie Electrique de Grenoble (G2ELab), Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology, Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)

Subjects
magnetic field measurement, magnetostatics, [SPI.NRJ]Engineering Sciences [physics]/Electric power, Electric vehicle, magnetic field simulation, magnetic shielding
Abstract

International audience; Magnetostatic field inside a simplified electric vehicle-like geometry is analyzed. The developed model allows evaluation of the shielding effect of the magnetic chassis and frame. It also proposes an equivalent model for the power battery and cables. The study of different configurations leads to the field reduction inside the car.

Published
2014
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17. A problem of moment realizability in quantum statistical physics

Author

Olivier Pinaud, Florian Méhats, Invariant Preserving SOlvers (IPSO), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Inria Rennes – Bretagne Atlantique, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Invariant Preserving SOlvers ( IPSO ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique ( Inria ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Institut Camille Jordan [Villeurbanne] ( ICJ ), École Centrale de Lyon ( ECL ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), and Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
Quantum hydrodynamics, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Second moment of area, 01 natural sciences, Theoretical physics, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Realizability, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Numerical Analysis, Quantum discord, Entropy (statistical thermodynamics), 010102 general mathematics, Mathematical analysis, [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph], Hartree, 010101 applied mathematics, Moment problem, Moment (mathematics), Modeling and Simulation, quantum entropy minimization under contraints, [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph], moment problem, Joint quantum entropy
Abstract

International audience; This work is a generalization of the results previously obtained in [17] in a one-dimensional setting: we revisit the problem of the minimization of the quantum free energy (entropy + energy) under local constraints (moments) and prove the existence of minimizers in various configurations. While [17] addressed the 1D case on bounded domains, we treat in the present paper the multi-dimensional case as well as unbounded domains and non-linear interactions as Hartree/Hartree-Fock. Moreover, whereas [17] dealt with the first moment only, namely the charge density, we extend the results to the second moment, the current density.

Published
2011
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18. Uniform bounds and weak solutions to an open Schrödinger-Poisson system

Author

Olivier Pinaud

Subjects
Applied Mathematics, General Mathematics, Mathematical analysis, non-linear Schrödinger equation, semiconductors, Robin boundary condition, Poincaré–Steklov operator, Domain (mathematical analysis), open boundary conditions, 35Q55, symbols.namesake, 35Q40, Bounded function, Dirichlet boundary condition, Neumann boundary condition, symbols, Free boundary problem, Uniqueness, uniform estimates, Mathematics
Abstract

This paper is concerned with the derivation of uniform bounds with respect to the scaled Planck constant ${\cal E}$ for solutions to the open transient Schrodinger-Poisson system introduced by Ben Abdallah et al in [Math.Meth.Mod. in App. Sci., 15, 667-688, 2005]. The uniform estimates stem from a careful analysis of the non-local in time transparent boundary conditions which allow to restrict the original problem posed on an unbounded domain to a bounded domain of interest. These bounds can be used to obtain the semi-classical limit of the system. The paper also gives an existence and uniqueness result for weak solutions while they were previously defined in a strong sense.

Published
2007

19. On an open transient Schrödinger-Poisson system

Author

Naoufel Ben Abdallah, Florian Méhats, Olivier Pinaud, Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Applied Mathematics, 010102 general mathematics, Electron, 01 natural sciences, 010101 applied mathematics, symbols.namesake, Classical mechanics, Character (mathematics), Dimension (vector space), Modeling and Simulation, Dissipative system, symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Transient (oscillation), Boundary value problem, 0101 mathematics, Quantum, Schrödinger's cat
Abstract

International audience; A mathematical model of quantum transient transport in dimension d = 2, 3 is derived and analyzed. The model describes the evolution of electrons injected into the device by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy non homogeneous open boundary conditions at the device edges. A priori estimates are deduced from the “dissipative properties” of the boundary conditions and from the repulsive character of the electrostatic interaction.

Published
2005
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20. Adiabatic approximation of the Schrödinger-Poisson system with a partial confinement

Author

Olivier Pinaud, Naoufel Ben Abdallah, Florian Méhats, Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Singular perturbation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Eigenfunction, 01 natural sciences, Schrödinger equation, 010101 applied mathematics, Adiabatic theorem, Computational Mathematics, symbols.namesake, Quantum mechanics, symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Limit (mathematics), 0101 mathematics, Poisson's equation, Adiabatic process, Wave function, Analysis, Mathematical physics, Mathematics
Abstract

International audience; Asymptotic quantum transport models of a two-dimensional electron gas are presented. The starting point is a singular perturbation of the three- dimensional Schrödinger-Poisson system. The small parameter $\varepsilon$ is the scaled width of the electron gas and appears as the lengthscale on which a one dimensional confining potential varies. The rigorous $\varepsilon \to 0$ limit is performed by projecting the three dimensional wavefunction on the eigenfunctions corresponding to the confining potential. This leads to a two-dimensional Schrödinger- Poisson system with a modified Poisson equation keeping track of the third dimension. This limit model is proven to be a first-order approximation of the initial model. An intermediate model, called the “2.5D adiabatic model” is then introduced. It shares the same structure as the limit model but is shown to be a second-order approximation of the 3D model

Published
2005
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