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128 results on '"Colin, Mathieu"'

1. Stable standing waves for Nonlinear Schr\'odinger-Poisson system with a doping profile

Author

Colin, Mathieu and Watanabe, Tatsuya

Subjects
Mathematics - Analysis of PDEs, Mathematical Physics, 35J20, 35B35, 35Q55
Abstract

This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a doping profile causes a difficulty in the proof of the strict sub-additivity. A key ingredient is to establish the strict sub-additivity by adapting a scaling and an iteration argument, which is inspired by \cite{ZZou}. When the doping profile is a characteristic function supported on a bounded smooth domain, smallness of some geometric quantity related to the domain ensures the existence of stable standing waves.

Published
2024

2. Solitary wave solutions to the Isobe-Kakinuma model for water waves

Author

Colin, Mathieu and Iguchi, Tatsuo

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider the Isobe-Kakinuma model for two-dimensional water waves in the case of the flat bottom. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves. We show theoretically the existence of a family of small amplitude solitary wave solutions to the Isobe-Kakinuma model in the long wave regime. Numerical analysis for large amplitude solitary wave solutions is also provided and suggests the existence of a solitary wave of extreme form with a sharp crest., Comment: 25 pages, 6 figures

Published
2019

3. BD Entropy and Bernis-Friedman Entropy

Author

Bresch, Didier, Colin, Mathieu, Msheik, Khawla, Noble, Pascal, and Song, Xi

Subjects
Mathematics - Analysis of PDEs, Mathematical Physics, Mathematics - Dynamical Systems
Abstract

In this note, we propose in the full generality a link between the BD entropy introduced by D. Bresch andB. Desjardins for the viscous shallow-water equations and the Bernis-Friedman (called BF) dissipative entropyintroduced to study the lubrications equations. Dierent dissipative entropies are obtained playing with the dragterms on the viscous shallow water equations. It helps for instance to prove global existence of nonnegativeweak solutions for the lubrication equations starting from the global existence of nonnegative weak solutions forappropriate viscous shallow-water equations.

Published
2018

8. Lubrication and shallow-water systems Bernis-Friedman and BD entropies

Author

Bresch Didier, Colin Mathieu, Msheik Khawla, Noble Pascal, and Song Xi

Subjects
lubrication and shallow-water models, bd and bf entropies, global weak solutions, Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

This paper concerns the results recently announced by the authors, in C.R. Acad. Sciences Maths volume 357, Issue 1, 1-6 (2019), which make the link between the BD entropy introduced by D. Bresch and B. Desjardins for the viscous shallow-water equations and the Bernis-Friedman (called BF in our paper) dissipative entropy introduced to study the lubrication equations. More precisely different dissipative BF entropies are obtained from the BD entropies playing with drag terms and capillarity formula for viscous shallow water type equations. This is the main idea in the paper which makes the link between two communities. The limit processes employ the standard compactness arguments taking care of the control in the drag terms. It allows in one dimension for instance to prove global existence of nonnegative weak solutions for lubrication equations starting from the global existence of nonnegative weak solutions for appropriate viscous shallow-water equations (for which we refer to appropriate references). It also allows to prove global existence of nonnegative weak solutions for fourth-order equation including the Derrida-Lebowitz-Speer-Spohn equation starting from compressible Navier-Stokes type equations.

Published
2020
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9. Lubrication Theory and Viscous Shallow-Water Equations

Author

Bresch, Didier, Colin, Mathieu, Lin, Xi, Noble, Pascal, Formaggia, Luca, Editor-in-Chief, Larson, Mats G., Series Editor, Martínez-Seara Alonso, Tere, Series Editor, Parés, Carlos, Series Editor, Pareschi, Lorenzo, Series Editor, Pedregal, Pablo, Editor-in-Chief, Tosin, Andrea, Series Editor, Vazquez, Elena, Series Editor, Zubelli, Jorge P., Series Editor, Zunino, Paolo, Series Editor, Doubova, Anna, editor, González-Burgos, Manuel, editor, Guillén-González, Francisco, editor, and Marín Beltrán, Mercedes, editor

Published
2018
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11. Bifurcation from semi-trivial standing waves and ground states for a system of nonlinear Schr\'{o}dinger equations

Author

Colin, Mathieu and Ohta, Masahito

Subjects
Mathematics - Analysis of PDEs
Abstract

We consider a system of nonlinear Schr\"{o}dinger equations related to the Raman amplification in a plasma. We study the orbital stability and instability of standing waves bifurcating from the semi-trivial standing wave of the system. The stability and instability of the semi-trivial standing wave at the bifurcation point are also studied. Moreover, we determine the set of the ground states completely., Comment: 25 pages, 2 figures

Published
2011

12. Stability and instability results for standing waves of quasi-linear Schr\'odinger equations

Author

Colin, Mathieu, Jeanjean, Louis, and Squassina, Marco

Subjects
Mathematics - Analysis of PDEs, 35J40, 58E05
Abstract

We study a class of quasi-linear Schr\"odinger equations arising in the theory of superfluid film in plasma physics. First, using gauge transforms and a derivation process we solve, under some regularity assumptions, the Cauchy problem. Then, by means of variational methods, we study the existence, the orbital stability and instability of standing waves which minimize some associated energy., Comment: 40 pages

Published
2009

13. Short Pulses Approximations in Dispersive Media

Author

Colin, Mathieu and Lannes, David

Subjects
Mathematics - Analysis of PDEs
Abstract

We derive various approximations for the solutions of nonlinear hyperbolic systems with fastly oscillating initial data. We first provide error estimates for the so-called slowly varying envelope, full dispersion, and Schr\"odinger approximations in a Wiener algebra; this functional framework allows us to give precise conditions on the validity of these models; we give in particular a rigorous proof of the ``practical rule'' which serves as a criterion for the use of the slowly varying envelope approximation (SVEA). We also discuss the extension of these models to short pulses and more generally to large spectrum waves, such as chirped pulses. We then derive and justify rigorously a modified Schr\"odinger equation with improved frequency dispersion. Numerical computations are then presented, which confirm the theoretical predictions.

Published
2007

15. Stable standing waves for a Schrödinger system with nonlinear χ3 response.

Author

Colin, Mathieu and Watanabe, Tatsuya

Subjects
*STANDING waves, *NONLINEAR systems, *NONLINEAR optics, *NONLINEAR waves
Abstract

In this paper, we consider standing waves for a nonlinear Schrödinger system which appears in nonlinear optics. This two-component system contains a cubic nonlinear term which is called χ3-interaction, and has a strong coupling on one side only. Oliveira and Pastor [Anal. Math. Phys. 11, 123 (2021)] showed the existence of ground states solutions for the corresponding stationary problems and investigated their stability. In our study, by considering the solvability of a constraint minimization problem, we show the existence of stable standing wave solutions. We also investigate the correspondence between minimizers and ground state solutions. [ABSTRACT FROM AUTHOR]

Published
2023
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18. Endoctriner et radicaliser sur la Toile

Author

Colin, Mathieu, Lefebvre, Solange, and Casoni, Dianne

Subjects
sitios internet, violencia, extrema derecha, radicalisation, radicalización, médias, political far right, media, sites internet, violence, websites, radicalization, extrême-droite, medios de comunicación
Abstract

Cet article s’appuie sur les résultats d’une recherche portant sur l’extrême-droite et qui visait à analyser les liens multiples existant entre les médias et la radicalisation menant à la violence. L’équipe de recherche a recouru à plusieurs types de méthodologies aussi bien quantitatives que qualitatives découlant d’entretiens menés avec près de 70 individus radicalisés, et d’observations directes d’événements réunissant leurs groupes Le présent article retient les propos explicites de deux individus radicalisés et s’attèle en particulier à l’analyse de centaines de sites consultés sur une période de plusieurs mois, entre 2018 et 2020 This paper discusses the findings of research on the political far right aimed at analyzing the multiple links between the media and radicalization leading to violence. The research team used a number of quantitative and qualitative methodologies based on interviews with some 70 radicalized individuals and direct observations of events that bring their groups together. The paper examines the explicit statements of two radicalized individuals and presents an analysis of the hundreds of sites visited over many months between 2018 and 2020. Este artículo se apoya en los resultados de una investigación referente a la extrema derecha, que tenía como objetivo analizar los múltiples vínculos existentes entre los medios de comunicación y la radicalización que conducen a la violencia. El equipo de investigación recurrió a diversos tipos de metodologías tanto cuantitativas como cualitativas empleadas en entrevistas llevadas a cabo con 70 personas radicalizadas, y observaciones directas de eventos que congregan sus grupos. El artículo se refiere a las declaraciones explícitas de dos personas radicalizadas y se centra en particular en el análisis de centenares de sitios consultados durante un periodo de varios meses, entre 2018 y 2020

Published
2022

19. In Satan we trust : le temple satanique entre mouvement social et religion

Author

Colin, Mathieu and Lefebvre, Solange

Subjects
Satanisme, Ultramodernity, Politics, The Satanic Temple, États-Unis, Atheism, Aesthetics, United-States, Non-religious, sans religion, athéisme, politique, Religion, Social media, Satanism, ultramodernité, mythe, Temple Satanique, médias sociaux, esthétique, Myth
Abstract

Fondé aux États-Unis fin 2012 par Malcolm Jarry et Lucien Greaves et se voyant comme une évolution de l’Église de Satan, groupe fondé par Anton LaVey en 1966, le Temple Satanique est à la croisée entre satanisme, sécularisme et religion non-théiste, en plus de s’appuyer sur un activisme politique explicite en faveur de la séparation entre Églises et État. Il s’appuie sur une lecture non-théiste de la figure de Satan comme symbole de libre-pensée et de compassion, inspirée notamment des lectures romantiques et de La Révolte des anges (1914) d’Anatole France. En se positionnant comme religion dans la sphère publique, l’organisation souhaite contrer l’hégémonie du christianisme et assurer le respect d’un réel pluralisme religieux, qui prendrait en compte les récentes mutations démographiques et culturelles américaines. Cette thèse emploie une approche interdisciplinaire. Sur le plan théorique, elle analyse ce groupe se disant religieux à l’aide de l’histoire des idées ainsi que d’une analyse sociologique, politique et médiatique. Elle met en œuvre une méthodologie qualitative et quantitative, documentant plusieurs aspects du groupe à l’aide d’entretiens et d’un questionnaire qualitatif en ligne. Les principales innovations de cette thèse sont les suivantes. Nous analysons le Temple Satanique comme un mouvement social mettant en avant le concept de communauté, et nous situons l’organisation dans un paradigme ultramoderne (concept de Jean-Paul Willaime), selon lequel un certain nombre de sous-cultures sont générées, cherchant à créer des ressources de sens. Ces sous-cultures émergent comme des systèmes de sens identitaires et politiques s’alimentant à des sources mythiques et esthétiques pour élaborer du sens, puisant largement dans les domaines religieux et spirituels. Il s’agit d’un laboratoire d’étude de la complexification du milieu séculariste et de ses profondes divisions, ainsi que du satanisme moderne et contemporain. Sa particularité est de proposer un satanisme politique rationaliste. Notre recherche se situe au croisement de trois champs d’études : celui des nouveaux mouvements religieux, celui du satanisme et de l’ésotérisme, ainsi que celui de la religion digitale. Cette religiosité, largement diffusée sur Internet, redéfinit les cadres institutionnels et de croyances, les adeptes ayant accès à des ressources presque illimitées, informant un mode du croire caractérisé par son individualité et sa méfiance institutionnelle, mettant en exergue une tension constante entre individualité et communauté. Par ses procédés ultramodernes, le groupe se pose en contre-mythe, afin de questionner l’héritage chrétien américain revendiqué par la Droite chrétienne comme une religion civile. En effet, par l’usage du symbole de Satan, l’organisation met en tension l’identité nationale américaine en posant la question de l’intégration des populations non-chrétiennes au sein d’un cadre culturel fortement imprégné de christianisme. Le Temple Satanique pose ainsi la question de l’intégration des communautés marginalisées, comme les athées, ou la population des sans-religion, dans la sphère publique, à l’heure où elles deviennent des forces politiques potentielles. C’est sans doute pour cette raison qu’il compte déjà des antennes dans d’autres pays. Le Temple essaye de dépasser l’aporie entre religion et mode de vie séculariste, en mettant en avant une religion non-théiste s’appuyant sur des valeurs partagées au sein d’une communauté., Founded in the US by Malcolm Jarry and Lucien Greaves at the very end of the year 2012 and thought as an evolution of The Church of Satan, the first satanic organization created by Anton LaVey in 1966, The Satanic Temple is both a non-theistic religion, a secularist group and a satanic group fighting for the strict separation of Church and State. Drawing especially on romantic and Anatole France’s Revolt of the Angels (1914) readings of Satan as an embodiment of freedom, justice and science, The Satanic Temple uses its position as a religion in the public sphere to denounce what is considers the marks of Christian hegemony within public institutions or places, and stands for other discriminated groups by defending a respectful and inclusive religious pluralism for all faiths, and taking into account the recent cultural and demographic changes in the US. This dissertation uses an interdisciplinary approach. In order to analyze this aspiring religious group, it combines a sociological analysis, the study of history of ideas as well as political and media studies. It also uses a quantitative and qualitative methodology to understand several dimensions of the group, with interviews and an online survey. The main innovations of the dissertation are the following. The Satanic Temple is a social movement building a community of like-minded people and transforming the concept of religion. I consider it a direct result of the ultramodern paradigm described by Jean-Paul Willaime that gives birth to a number of subcultural movements that struggle to create sense for their members. I analyze these subcultural movements as political meaning systems creating a sense of identity. They draw on mythical and aesthetical sources to create meaning by using religious and spiritual resources. This paradigm enables us to analyze the increasingly complex secular milieu and its divisions, as well as the evolution of modern and contemporary Satanism. Political rationalist Satanism is one of its new developments. Our research stands at the crossroad of three areas of studies: new religious movements studies, esoteric and satanic studies, and digital religion studies. I shall analyze the individualization of religious beliefs on the Internet, and the growing mistrust towards institutions or the process of formalization, perceived as threats to the unlimited religious resources offered by digital platforms. The tension between individuality and community is constantly at stake for a group such as The Satanic Temple. As an ultramodern movement, The Satanic Temple takes the stance as a counter-myth in order to question the Christian legacy of the country claimed by movements, such as the Christian Right, that want to turn it into the one and only possible civil religion. Indeed, The Satanic Temple aims at raising the question of the integration of non-Christians as respectful and respected citizens within the public sphere, thus negotiating the tensions at the core of the American national identity and of its civil religion, both heavily influenced by Christianity, with the help of Satan’s symbol. The rise of the « nones » as a new political force also raises the issue of their integration, as The Satanic Temple asks the tough question of taking into account marginalized communities that want their voice to be heard in a changing public sphere. Despite being primarily US-based, the organization has chapters in other countries such as Canada, and in Europe.

Published
2022

21. An Enriched Shifted Boundary Method to Account For Moving Fronts

Author

Carlier, Tiffanie, Nouveau, Léo, Beaugendre, Heloise, Colin, Mathieu, Ricchiuto, Mario, CARLIER, Tiffanie, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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, and 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)

Subjects
Finite element method, Stefan mixed formulation, Temperature enrichment, Moving front, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH] Mathematics [math], [MATH]Mathematics [math], Jump condition, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Enriched shifted boundary method
Abstract

We present an extension of the shifted boundary method to simulate partial differential equations with moving internal interfaces. The objective is to apply the method to phase change problems modelled by the Stefan equation : the parabolic heat equation with a discontinuity separating the two phases, moving at a speed given by the normal flux jump. To obtain an accurate prediction of the temperature field on both sides of the discontinuity, and of the position of the discontinuity itself, we propose an enhanced variant of the shifted boundary method. This method is based on an enriched mixed form proposed by some of the present authors, which allows a uniform second order accuracy in space and time. Stabilization terms are added on the whole domain to ensure convergence. The specificities generated by the interface displacement are handled by a particular construction, with a double nodal points structure at the surrogate interface. Several recovering techniques based on Taylor developments from the interface to its surrogate, and a least square minimization method for node initialization are performed to recover the missing values generated by the moving interface and the phase structure of the model.

Published
2022

23. Dix regards prospectifs sur huit années de pontificat

Author

Souletie, Jean-Louis, primary, Maalouf, Charbel, additional, Soleil, Narsay, additional, Oiry, Béatrice, additional, Bada Silas, Silas, additional, Drouin, Gilles, additional, Capul, Hélène, additional, Kerdraon, Anne-Solen, additional, Colin, Mathieu, additional, Trébuchet, Marie-Dominique, additional, Rouyrre, Jeanne-Marie, additional, Pisani, Emmanuel, additional, Schneider, Dominique, additional, Cholvy, Brigitte, additional, Beffa, Sébastien, additional, Molinario, Joël, additional, Airault, Jennifer, additional, Forestier, Luc, additional, Karerakkattil, Aljo, additional, Moog, François, additional, and Ndangha Mbome Ndong, Jean Davy, additional

Published
2021
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24. Conception d'un nano-drone à ailes vibrantes

Author

Colin, Mathieu, Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), HESAM Université, Olivier Thomas, and Sébastien Grondel

Subjects
Aerodynamics, Résonance, Nano-Drone, Aerodynamique, Dynamique de structures, Structural dynamics, Nonlinear damping, Microfabrication, Nav, [SPI.GCIV.EC]Engineering Sciences [physics]/Civil Engineering/Eco-conception
Abstract

The objective of this PhD is to review the design of the current prototype in order to increase its lift, so as to take off.; L’objectif de cette thèse est de revoir la conception du prototype actuel pour accroître sa portance, dans l’idée de procéder au décollage du nano drone.

Published
2021

26. A diptera-inspired vibrating-wing nano drone

Author

Colin, Mathieu, Cattan, Eric, Grondel, Sébastien, Thomas, Olivier, Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN), Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Matériaux et Acoustiques pour MIcro et NAno systèmes intégrés - IEMN (MAMINA - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - Département Opto-Acousto-Électronique - UMR 8520 (IEMN-DOAE), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Institut National des Sciences Appliquées (INSA), and Renatech Network

Subjects
[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph], [SPI]Engineering Sciences [physics], [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, ComputingMilieux_MISCELLANEOUS, [SPI.MAT]Engineering Sciences [physics]/Materials
Abstract

International audience

Published
2020

29. Diptera-inspired vibrating-wing nano drone

Author

Colin, Mathieu, Faux, Damien, Cattan, Eric, Grondel, Sébastien, Thomas, Olivier, Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN), Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Matériaux et Acoustiques pour MIcro et NAno systèmes intégrés - IEMN (MAMINA - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - Département Opto-Acousto-Électronique - UMR 8520 (IEMN-DOAE), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Institut National des Sciences Appliquées (INSA), and TORCK, Kathleen

Subjects
[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph], [SPI.ACOU] Engineering Sciences [physics]/Acoustics [physics.class-ph], [SPI]Engineering Sciences [physics], [SPI] Engineering Sciences [physics], [SPI.NANO] Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, [SPI.MAT] Engineering Sciences [physics]/Materials, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, ComputingMilieux_MISCELLANEOUS, [SPI.MAT]Engineering Sciences [physics]/Materials
Abstract

International audience

Published
2019

34. Vibrations de structures flexibles en très grande amplitude - Application à un nano drone

Author

Colin, Mathieu, Givois, Arthur, Guillot, Vinciane, Cattan, Eric, Grondel, Sébastien, Ture Savadkoohi, Alireza, Lamarque, Claude-Henri, Thomas, Olivier, Laboratoire d’Ingénierie des Systèmes Physiques et Numériques (LISPEN), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne-Centre National de la Recherche Scientifique (CNRS), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), and Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)

Subjects
Amortissement aérodynamique, [SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph], [SPI]Engineering Sciences [physics], Dynamique non-linéaire, Identification paramétrique, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, [SPI.MAT]Engineering Sciences [physics]/Materials
Abstract

National audience; L’objectif de cette étude est la meilleure compréhension des vibrations de structures flexibles en très grande amplitude et basse fréquence. Cette démarche s’inscrit dans l’optimisation de la conception d’un nano drone à ailes vibrantes, pour lequel on cherche à obtenir un grand débattement des ailes dans la perspective d’augmenter la force de portance. Il s’agit d’identifier les paramètres déterminant la grande amplitude de vibration et d’évaluer l’effet des non-linéarités sur celle-ci.

Published
2019

35. A refined stability result for standing waves of the Schrodinger-Maxwell system

Author

Watanabe, Tatsuya, Colin, Mathieu, Kyoto Sangyo University, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2019

37. Lubrication theory and viscous shallow-water equations

Author

Colin, Mathieu, Bresch, Didier, NOBLE, Pascal, Lin, Xi, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2018

43. On the existence of solitary waves for Boussinesq type equations and a new conservative model

Author

Bellec, Stevan, Colin, Mathieu, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Bordeaux (Bordeaux INP), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; In this paper, we present a long time existence theory for a new enhanced Boussinesq-type system with constant bathymetry written in a conservative form. We also prove the existence of solitary wave for a large class of asymptotic models, including Beji-Nadaoka, Madsen-Sorensen and Nwogu equations. Furthermore, we give a procedure to calculate numerically these particular solutions and we present some effective computations.

Published
2016

44. Discrete asymptotic equations for long wave propagation

Author

Bellec, S, Colin, Mathieu, Ricchiuto, Mario, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Inria Bordeaux Sud-Ouest, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
[SDU.OCEAN]Sciences of the Universe [physics]/Ocean, Atmosphere, Wave propagation, asymptotic equations, Boussinesq models, finite elements, AMS: 35Q31, 35Q35, 65M60, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], discrete asymptotics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this paper, we present a new systematic method to obtain some discrete numerical models for incompressible free-surface flows. The method consists in first discretizing the Euler equations with respect to one variable, keeping the other ones unchanged and then performing an asymptotic analysis on the resulting system. For the sake of simplicity, we choose to illustrate this method in the context of the Peregrine asymptotic regime, that is we propose an alternative numerical scheme for the so-called Peregrine equations. We then study the linear dispersion characteristics of our new scheme and present several numerical experiments to measure the relevance of the method.

Published
2015

46. On the nonlinear behavior of Boussinesq type models: amplitude-velocity vs amplitude-flux forms

Author

Filippini, Andrea Gilberto, Bellec, Stevan, Colin, Mathieu, Ricchiuto, Mario, Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems (BACCHUS), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), and INRIA

Subjects
[PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], [PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [SDU.OCEAN]Sciences of the Universe [physics]/Ocean, Atmosphere, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], [SDE.IE]Environmental Sciences/Environmental Engineering, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [SDU.STU.OC]Sciences of the Universe [physics]/Earth Sciences/Oceanography, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract

In this paper we consider the modeling of nonlinear wave transformation by means of weakly nonlinear Boussinesq models. We show that for a given linear dispersion relation and linear shoaling parameter one can derive, within the same asymptotic truncation, two system of PDEs differing only in the form of the linear dispersive operators. In particular, these can either be formulated in terms of derivatives of the velocity, or in terms of derivatives of the flux. In the first case we speak of amplitude-velocity form of the model, in the second case of amplitude flux form. We show examples of these couples for several linear relations, including a new amplitude-flux variant of the model of Nwogu. We then show, both analytically and by numerical nonlinear shoaling tests, that while for small amplitude waves it is important to have accurate linear dispersion and shoaling characteristics, when approaching breaking conditions it is only the amplitude-velocity or amplitude-flux form of the equations which determines the behavior of the model, and in particular the shape and the height of the waves. This knowledge has tremendous importance when considering the use of these models in conjunction with wave breaking detection and dissipation mechanisms.

Published
2014

47. On shoaling properties of enhanced Boussinesq models

Author

Filippini, Andrea Gilberto, Bellec, Stevan, Colin, Mathieu, Ricchiuto, Mario, Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems (BACCHUS), Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Bordeaux (Bordeaux INP), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; In this paper, we investigate the nonlinear properties of Boussinesq models.In particular, we consider the wave shoaling obtained in physical regimes whichgo from linear to weakly nonlinear, to the wave breaking limit. For a given asymptoticaccuracy in terms of dispersion and nonlinearity, we consider two families ofmodels: the first depending on derivatives of the velocity, the second on derivativesof the volume flux. Ww show that, while linear dispersion and linear shoaling characteristicsare strongly dependent on the type of dispersive terms introduced, whenapproaching the nonlinear regime the only influencing factor is whether the model isin amplitude-velocity of amplitude-flux form. We investigate these two alternativeformulations of several known models, and propose a new model with a compactdifferential form, and the same linear characteristics of the model of Nwogu. Thenonlinear shoaling properties of the models are investigated numerically showingthat inside one given family, all the models have almost identical behaviour.

Published
2014

48. Conservative and non-conservative variants of weakly nonlinear Boussinesq models: derivation and numerical assessment

Author

Filippini, Andrea Gilberto, Bellec, Stevan, Colin, Mathieu, Ricchiuto, Mario, Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems (BACCHUS), Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2014

49. Instability of ground states for a quasilinear Schrödinger equation

Author

Colin, Mathieu, Ohta, Masahito, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Bordeaux (Bordeaux INP), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Tokyo University of Science [Tokyo], Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
35Q55, Applied Mathematics, schrodinger, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 35B35, Analysis
Abstract

International audience; We study a class of one parameter (denoted by κ) family of quasi-linear Schrödinger equations arising in the theory of superfluid film in plasma physics. Using variational techniques, we prove the orbital instability of solitary waves for small values of the parameter κ, which gives an answer to a question raised in [9].

Published
2014

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