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1. Stability of optimal traffic plans in the irrigation problem

Author

Antoine Prouff, Antonio De Rosa, Andrea Marchese, Maria Colombo, Paul Pegon, Ecole Polytechnique Fédérale de Lausanne (EPFL), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Department of mathematics/Dipartimento di Matematica [Univ. Trento], Università degli Studi di Trento (UNITN), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), Maria Colombo was partially supported by the Swiss National Science Foundation grant 200021_182565. Antonio De Rosa has been supported by the NSF DMS Grant No. 1906451. Andrea Marchese acknowledges partial support from GNAMPA-INdAM., Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University [Milan, Italy], Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, M. C. was partially supported by the Swiss National Science Foundation grant 200021_182565. A. D. R. has been supported by the NSF DMS Grant No. 1906451 and the NSF DMS Grant No. 2112311. A. M. acknowledges partial support from GNAMPA-INdAM. A.P. was supported by the Fondation Mathématiques Jacques Hadamard. P.P and A.P. both acknowledge EPFL for hosting them during the semester this paper was prepared., Inria de Paris, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)

Subjects
BRANCHED TRANSPORT, Mathematical optimization, Irrigation, TRAFFIC PLANS, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 01 natural sciences, Stability (probability), symbols.namesake, Mathematics - Analysis of PDEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Computer Science::Networking and Internet Architecture, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete Mathematics and Combinatorics, Limit (mathematics), 0101 mathematics, Mathematics - Optimization and Control, Mathematics, TRANSPORTATION NETWORK, BRANCHED TRANSPORT, IRRIGATION PROBLEM, TRAFFIC PLANS, STABILITY, STABILITY, IRRIGATION PROBLEM, Applied Mathematics, TRANSPORTATION NETWORK, 010102 general mathematics, Eulerian path, Flow network, 010101 applied mathematics, Optimization and Control (math.OC), Mathematics - Classical Analysis and ODEs, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis, Lagrangian, Analysis of PDEs (math.AP)
Abstract

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [7], extending it to the Lagrangian framework.

Published
2022

2. Large deviations for the dynamic $\Phi^{2n}_d$ model

Author

Cerrai, Sandra, Debussche, Arnaud, Department of Mathematics, University of Maryland, Multi-scale numerical geometric schemes (MINGUS), 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), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), 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 ), ANR-11-LABX-0020/11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation ( 2011 ), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, 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), 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)-Inria Rennes – Bretagne Atlantique

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability
Abstract

We are dealing with the validity of a large deviation principle for a class of reaction-diffusion equations with polynomial nonlinearity, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength of the noise and its correlation are vanishing, on a length scale $\epsilon$ and $\delta(\epsilon)$, respectively, with $0

Published
2019

3. Large deviations for the two-dimensional stochastic Navier–Stokes equation with vanishing noise correlation

Author

Arnaud Debussche, Sandra Cerrai, Department of Mathematics, University of Maryland, 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), Multi-scale numerical geometric schemes (MINGUS), 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), École normale supérieure - Rennes (ENS Rennes), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, 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), 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, 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 ), ANR-11-LABX-0020/11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation ( 2011 ), and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

Subjects
Statistics and Probability, Length scale, Weak convergence approach to large deviations, Gaussian, 01 natural sciences, Noise (electronics), 010104 statistics & probability, symbols.namesake, FOS: Mathematics, Periodic boundary conditions, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Navier stokes, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematical physics, Mathematics, Stochastic Navier–Stokes equation, Probability (math.PR), 010102 general mathematics, Noise correlation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Large deviations, 35Q30, symbols, 60H15, Large deviations theory, Statistics, Probability and Uncertainty, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Rate function, Mathematics - Probability, Rough noise, 60F10
Abstract

We are dealing with the validity of a large deviation principle for the two-dimensional Navier–Stokes equation, with periodic boundary conditions, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength of the noise and its correlation are vanishing, on a length scale $\epsilon$ and $\delta(\epsilon)$, respectively, with $0

Published
2019

4. Strong solutions to stochastic differential equations with rough coefficients

Author

Pierre Emmanuel Jabin, Nicolas Champagnat, TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, and Department of Mathematics, University of Maryland

Subjects
Statistics and Probability, MSC 2000 subject classifications: 60J60, 60H10, 35K10, rough drift, 60J60, 60H10, 35K10, 01 natural sciences, degenerate diffusion matrix, Mathematics::Numerical Analysis, Strong solutions, 010104 statistics & probability, Stochastic differential equation, Mathematics::Probability, FOS: Mathematics, Maximal operator, rough diffusion matrix, Uniqueness, 0101 mathematics, Mathematics, 60J60, Probability (math.PR), 010102 general mathematics, Mathematical analysis, Fokker-Planck equation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], kinetic stochastic differential equations, Stochastic differential equations, Fokker–Planck equation, strong solutions, Statistics, Probability and Uncertainty, maximal operator, Mathematics - Probability, pathwise uniqueness
Abstract

International audience; We study strong existence and pathwise uniqueness for stochastic differential equations in $\RR^d$ with rough coefficients, and without assuming uniform ellipticity for the diffusion matrix. Our approach relies on direct quantitative estimates on solutions to the SDE, assuming Sobolev bounds on the drift and diffusion coefficients, and $L^p$ bounds for the solution of the corresponding Fokker-Planck PDE, which can be proved separately. This allows a great flexibility regarding the method employed to obtain these last bounds. Hence we are able to obtain general criteria in various cases, including the uniformly elliptic case in any dimension, the one-dimensional case and the Langevin (kinetic) case.

Published
2018

5. Modeling crowd dynamics through coarse-grained data analysis

Author

Elsa G. Guillot, Julien Pettré, Guy Theraulaz, Mathieu Moreau, Sebastien Motsch, Pierre Degond, Cécile Appert-Rolland, Mehdi Moussaïd, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Center for Adaptive Behavior and Cognition (ABC), Max Planck Institute for Human Development, Max-Planck-Gesellschaft-Max-Planck-Gesellschaft, Centre de Recherches sur la Cognition Animale - UMR5169 (CRCA), Institut des sciences du cerveau de Toulouse. (ISCT), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre de Biologie Intégrative (CBI), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Institut de Chimie Moléculaire de l'Université de Bourgogne [Dijon] (ICMUB), Université de Bourgogne (UB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Sensor-based and interactive robotics (RAINBOW), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Imperial College London], Imperial College London, 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), Centre de Recherches sur la Cognition Animale (CRCA), Centre National de la Recherche Scientifique (CNRS)-Institut des sciences du cerveau de Toulouse. (ISCT), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-CHU Toulouse [Toulouse]-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-CHU Toulouse [Toulouse]-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre de Biologie Intégrative (CBI), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), Analysis-Synthesis Approach for Virtual Human Simulation (MIMETIC), Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-MEDIA ET INTERACTIONS (IRISA-D6), 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)-Université de Rennes (UNIV-RENNES)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Centre National de la Recherche Scientifique (CNRS)-Université de Bourgogne (UB), Department of Mathematics, University of Maryland, Centre de Biologie Intégrative (CBI), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut des sciences du cerveau de Toulouse. (ISCT), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-CHU Toulouse [Toulouse]-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse - Jean Jaurès (UT2J)-CHU Toulouse [Toulouse]-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Bourgogne (UB)-Institut de Chimie du CNRS (INC), Université de Bretagne Sud (UBS)-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)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-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)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), The Royal Society, Engineering & Physical Science Research Council (EPSRC), Pettré, Julien, Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre de Biologie Intégrative (CBI)

Subjects
Data Analysis, Operations research, Computer science, FLOW, [INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR], macroscopic model, 0904 Chemical Engineering, Transportation, 02 engineering and technology, computer.software_genre, 01 natural sciences, 010305 fluids & plasmas, [SHS]Humanities and Social Sciences, [SCCO]Cognitive science, Crowds, 0903 Biomedical Engineering, 0102 Applied Mathematics, 11. Sustainability, 0202 electrical engineering, electronic engineering, information engineering, Cluster Analysis, Applied Mathematics, bi-directional flux, collective behaviour, General Medicine, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Computational Mathematics, Core (game theory), Modeling and Simulation, [SCCO.PSYC]Cognitive science/Psychology, 020201 artificial intelligence & image processing, General Agricultural and Biological Sciences, Life Sciences & Biomedicine, BEHAVIOR, Crowd dynamics, Relation (database), Bioinformatics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Bioengineering, Pedestrian, Models, Psychological, Machine learning, Advanced Traffic Management System, Pedestrian traffic, 0103 physical sciences, Humans, Computer Simulation, [NLIN.NLIN-AO]Nonlinear Sciences [physics]/Adaptation and Self-Organizing Systems [nlin.AO], Block (data storage), Science & Technology, business.industry, Mathematical Concepts, SIMULATIONS, data-based modeling, Crowding, Key (cryptography), Artificial intelligence, Mathematical & Computational Biology, business, computer
Abstract

International audience; Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.

Published
2018

6. Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

Author

Thomas Rey, Pierre Emmanuel Jabin, Department of Mathematics, University of Maryland, Reliable numerical approximations of dissipative systems (RAPSODI ), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, NSF Grant 1312142, NSF Grant RNMS (Ki-Net) 1107444, ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Université de Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematics::Analysis of PDEs, pressureless Euler, Space (mathematics), Kinetic energy, 01 natural sciences, symbols.namesake, Mathematics - Analysis of PDEs, Dimension (vector space), hydrodynamic limit, Convergence (routing), Oleinik property, Primary: 76P05, 82C40, Secondary: 35P20, 76T25, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Limit (mathematics), 0101 mathematics, Physics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, granular gases, Euler system, 010101 applied mathematics, Euler's formula, symbols, Knudsen number, Analysis of PDEs (math.AP)
Abstract

We investigate the behavior of granular gases in the limit of small Knudsen number, that is very frequent collisions. We deal with the strongly inelastic case, in one dimension of space and velocity. We are able to prove the convergence toward the pressureless Euler system. The proof relies on dispersive relations at the kinetic level, which leads to the so-called Oleinik property at the limit., Comment: 23 pages, 1 figure

Published
2017

7. Isogenies for Point Counting on Genus Two Hyperelliptic Curves with Maximal Real Multiplication

Author

Ballentine, S., Guillevic, A., Lorenzo-Garcia, E., Martindale, C.R., Maisserer, M., Smith, B., Top, J., Howe, E.W., Lauter, K.E., Walker, J.L., Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, University of Calgary, Pacific Institute for the Mathematical Sciences (PIMS), University of Calgary-Centre National de la Recherche Scientifique (CNRS), 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), Universiteit Leiden, Lithe and fast algorithmic number theory (LFANT), 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), University of New South Wales [Sydney] (UNSW), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Geometry, arithmetic, algorithms, codes and encryption (GRACE), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence, University of Groningen [Groningen], Institute for Pure and Applied Mathematics (IPAM), University of California, Los Angeles (UCLA), E. W. Howe, K. E. Lauter, J. L. Walker, ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Department of Mathematics, University of Maryland, Pacific Institute for the Mathematical Sciences ( PIMS ), 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 ), Universiteit Leiden [Leiden], University of New South Wales [Sydney] ( UNSW ), Laboratoire d'informatique de l'École polytechnique [Palaiseau] ( LIX ), Centre National de la Recherche Scientifique ( CNRS ) -École polytechnique ( X ), Geometry, arithmetic, algorithms, codes and encryption ( GRACE ), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Johann Bernoulli Institute for Mathematics and Computer Science ( JBI ), 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), 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, Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Inria Saclay - Ile de France, Discrete Mathematics, Coding Theory and Cryptology, and Algebra

Subjects
FOS: Computer and information sciences, Computer Science - Cryptography and Security, Mathematics::Number Theory, [ INFO.INFO-CR ] Computer Science [cs]/Cryptography and Security [cs.CR], 010103 numerical & computational mathematics, 01 natural sciences, [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT], [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], cs.CR, Mathematics::Algebraic Geometry, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Mathematics, Discrete mathematics, Mathematics - Number Theory, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], 010101 applied mathematics, Schoof–Elkies–Atkin algorithm, math.NT, Elliptic curve, Finite field, Discriminant, Counting points on elliptic curves, Multiplication, Schoof's algorithm, Cryptography and Security (cs.CR), Division polynomials
Abstract

Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit isogenies. Moving to Jacobians of genus-2 curves, the current state of the art for point counting is a generalization of Schoof's algorithm. While we are currently missing the tools we need to generalize Elkies' methods to genus 2, recently Martindale and Milio have computed analogues of modular polynomials for genus-2 curves whose Jacobians have real multiplication by maximal orders of small discriminant. In this article, we prove Atkin-style results for genus-2 Jacobians with real multiplication by maximal orders, with a view to using these new modular polynomials to improve the practicality of point-counting algorithms for these curves., Comment: 31 pages

Published
2017

8. Electrified thin films: Global existence of non-negative solutions

Author

Antoine Mellet, Cyril Imbert, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Department of Mathematics, University of Maryland, ANR-08-BLAN-0242,EVOL,Dissipative Evolutions and Convergence to Equilibrium(2008), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Substrate (electronics), Viscous liquid, 01 natural sciences, Domain (mathematical analysis), Non-local equation, Physics::Fluid Dynamics, Mathematics - Analysis of PDEs, Electric field, Higher order equation, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Thin film, MSC: 35G25, 35K25, 35A01, 35B09, Mathematical Physics, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Non-negative solutions, 010101 applied mathematics, Thin film equation, Bounded function, Wetting, Energy (signal processing), Analysis, Analysis of PDEs (math.AP)
Abstract

We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined globally in time for general initial data (with finite energy)., To appear in Annales de l'IHP, analyse non-lin\'eaire. Minor modifications after reading proofs

Published
2012
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9. Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach

Author

Marjolaine Puel, Naoufel Ben Abdallah, Antoine Mellet, 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), Department of Mathematics, University of Maryland, 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Computer Science::Computer Science and Game Theory, Numerical Analysis, 010102 general mathematics, Mathematical analysis, 76P05, 26A33, 22E46, 53C35, 57S20, 01 natural sciences, 010305 fluids & plasmas, Kinetic equations, Heavy-tailed distribution, Modeling and Simulation, 0103 physical sciences, Fractional diffusion, Limit (mathematics), 0101 mathematics, Linear boltzmann equation, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.

Published
2011

10. Existence and regularity of extremal solutions for a mean-curvature equation

Author

Antoine Mellet, Julien Vovelle, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, University of Maryland, 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), and Reymond, Aurélie

Subjects
Minimal solution, Pure mathematics, Class (set theory), regularity, Existential quantification, 2000 MSC: 49F10, (35J60), 01 natural sciences, mean curvature operator, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Mean curvature, Applied Mathematics, Operator (physics), 010102 general mathematics, minimal solutions, 53A10, Semi-stable solution, Symmetric case, semilinear equation, 010101 applied mathematics, Extremal solution, Analysis, Analysis of PDEs (math.AP)
Abstract

We study a class of mean curvature equations $-\mathcal Mu=H+\lambda u^p$ where $\mathcal M$ denotes the mean curvature operator and for $p\geq 1$. We show that there exists an extremal parameter $\lambda^*$ such that this equation admits a minimal weak solutions for all $\lambda \in [0,\lambda^*]$, while no weak solutions exists for $\lambda >\lambda^*$ (weak solutions will be defined as critical points of a suitable functional). In the radially symmetric case, we then show that minimal weak solutions are classical solutions for all $\lambda\in [0,\lambda^*]$ and that another branch of classical solutions exists in a neighborhood $(\lambda_*-\eta,\lambda^*)$ of $\lambda^*$., Comment: v2: Typos corrected. Proof of Theorem 2.11 added.

Published
2010

11. A HELE-SHAW problem for tumor growth

Author

Mellet, Antoine, Perthame, Benoît, Quirós , Fernando, Department of Mathematics, University of Maryland, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Modelling and Analysis for Medical and Biological Applications (MAMBA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Departamento de Matemáticas [Madrid], Universidad Autonoma de Madrid (UAM), ANR-13-BS01-0004,KIBORD,Modèles cinétiques en biologie et domaines connexes(2013), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, and Universidad Autónoma de Madrid (UAM)

Subjects
Mathematics - Analysis of PDEs, tumor growth, porous medium equation, free boundary problems, Mathematical biology, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Hele-Shaw equation, 35K55, 35B25, 76D27, 92C50, Analysis of PDEs (math.AP)
Abstract

International audience; We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka-Volterra source term describing the evolution of the number density of cancerous cells. We prove that such limit solutions solve a free boundary problem of Hele-Shaw type. We also obtain regularity properties, both for the solution and for its free boundary. The main new difficulty arises from the competition between the growth due to the source, which keeps the initial singularities, and the free boundary which invades the domain with a regularizing effect. New islands can be generated at singular times.

Published
2015
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12. Self-similar solutions for a fractional thin film equation governing hydraulic fractures

Author

Antoine Mellet, Cyril Imbert, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, University of Maryland, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Toughness, Materials science, self-similar solutions, Mathematical analysis, Zero (complex analysis), Statistical and Nonlinear Physics, Injection rate, free boundary condition, Contact angle, Mathematics - Analysis of PDEs, thin films, higher order equation, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Hydraulic fractures, Thin-film equation, Boundary value problem, fractional Laplacian, Constant (mathematics), Mathematical Physics, Energy (signal processing), Analysis of PDEs (math.AP), AMS 35G30, 35R11, 35C06
Abstract

In this paper, self-similar solutions for a fractional thin film equation governing hydraulic fractures are constructed. One of the boundary conditions, which accounts for the energy required to break the rock, involves the toughness coefficient $K\geq 0$. Mathematically, this condition plays the same role as the contact angle condition in the thin film equation. We consider two situations: The zero toughness ($K=0$) and the finite toughness $K\in(0,\infty)$ cases. In the first case, we prove the existence of self-similar solutions with constant mass. In the second case, we prove that for all $K\textgreater{}0$ there exists an injection rate for the fluid such that self-similar solutions exist.

Published
2015

13. The coffee genome provides insight into the convergent evolution of caffeine biosynthesis

Author

Giorgio Graziosi, Maria Bernard, Michel Rigoreau, Adriana Muñoz, Olivier Garsmeur, Alan Carvalho Andrade, Qiong Zhang, Priyono, Xavier Argout, Lorenzo Carretero-Paulet, Thomas Gayraud, Giovanni Giuliano, Alexandre de Kochko, Steve Rounsley, Alberto Pallavicini, Benoît Bertrand, David Sankoff, Claudine Campa, Dominique Crouzillat, Patrick Wincker, Loretta Daddiego, François Anthony, Marie Christine Combes, Romain Guyot, Valentin Guignon, Katharina Jahn, Loredana Lopez, Pascal Bento, Stéphane Dussert, Christine Tranchant-Dubreuil, Maud Lepelley, Tianying Lan, Ray Ming, Thierry Joët, Gaëtan Droc, G. Aprea, Corinne Da Silva, Julio Rozas, David Pot, Véronique Jamilloux, Thierry Leroy, Benjamin Noel, Valérie Poncet, Pablo Librado, Adriana Alberti, Victor A. Albert, Jean-Marc Aury, Gaetano Perrotta, Philippe Lashermes, Robert VanBuren, Chunfang Zheng, Robert J Henry, Leiting Li, Julie Leclercq, Chifumi Nagai, Marco Pietrella, Karine Labadie, Jayarama, Stéphanie Bocs, Alberto Cenci, Fabien De Bellis, Mathieu Rouard, Alexis Dereeper, Génomique métabolique (UMR 8030), Genoscope - Centre national de séquençage [Evry] (GENOSCOPE), Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Université d'Évry-Val-d'Essonne (UEVE), Institut de Génomique d'Evry (IG), Université Paris-Saclay-Institut de Biologie François JACOB (JACOB), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), University at Buffalo [SUNY] (SUNY Buffalo), State University of New York (SUNY), Institut de Recherche pour le Développement (IRD), Résistance des plantes aux bio-agresseurs (UMR RPB), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Université Montpellier 2 - Sciences et Techniques (UM2), Amélioration génétique et adaptation des plantes méditerranéennes et tropicales (UMR AGAP), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut National de la Recherche Agronomique (INRA)-Centre international d'études supérieures en sciences agronomiques (Montpellier SupAgro)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Diversité, adaptation, développement des plantes (UMR DIADE), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Agenzia Nazionale per le nuove Tecnologie, l’energia e lo sviluppo economico sostenibile = Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Department of Mathematics and Statistics [Ottawa], University of Ottawa [Ottawa], Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Bioversity, Parc Scientifique Agropolis II, Nestlé France, Center for Biotechnology (CeBiTec), Universität Bielefeld = Bielefeld University, Unité de Recherche Génomique Info (URGI), Institut National de la Recherche Agronomique (INRA), Chongqing University of Science & Technology, University of Illinois at Urbana-Champaign [Urbana], University of Illinois System, Institut de Recerca de la Biodiversitat - Biodiversity Research Institute [Barcelona, Spain] (IRBio UB), Universitat de Barcelona (UB), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Università degli studi di Trieste = University of Trieste, Indonesian Coffee and Cocoa Research Institute, Partenaires INRAE, Embrapa Recursos Genéticos e Biotecnologia [Brasília], Queensland Alliance for Agriculture and Food Innovation (QAAFI), University of Queensland [Brisbane], Hawaii Agriculture Research Center, University of Arizona, Australian Research Council, Natural Sciences and Engineering Research Council of Canada, CNR-ENEA Agrifood Project A2 C44 L191, FINEP-Qualicafe, NSF 0922742 0922545, College of Arts and Sciences, University at Buffalo, SouthGreen Bioinformatics platform (UMR AGAP), CIRAD, INCT-CAFE, ANR-08-GENM-022-001, ANR-09-GENM-014-002, ANR-08-GENM-0022,GénomeCafé,Analyses de séquences d'extrémités de clones BAC comme étape préliminaire au séquençage du génome des caféiers(2008), ANR-09-GENM-0014,COFFEASEQ,Séquençage du génome du caféier (Coffea canephora)(2009), Institut de Biologie François JACOB (JACOB), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Université Montpellier 2 - Sciences et Techniques (UM2)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad), 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 de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad), Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Department of Mathematics, University of Maryland, University of Trieste, Giuliano, G., Perrotta, G., Lopez, Daddiego, L., Aprea, G., Pietrella, M., Denoeud, France, Carretero Paulet, Lorenzo, Dereeper, Alexi, Droc, Gaëtan, Guyot, Romain, Pietrella, Marco, Zheng, Chunfang, Alberti, Adriana, Anthony, Françoi, Aprea, Giuseppe, Aury, Jean Marc, Bento, Pascal, Bernard, Maria, Bocs, Stéphanie, Campa, Claudine, Cenci, Alberto, Combes, Marie Christine, Crouzillat, Dominique, Da Silva, Corinne, Daddiego, Loretta, De Bellis, Fabien, Dussert, Stéphane, Garsmeur, Olivier, Gayraud, Thoma, Guignon, Valentin, Jahn, Katharina, Jamilloux, Véronique, Joët, Thierry, Labadie, Karine, Lan, Tianying, Leclercq, Julie, Lepelley, Maud, Leroy, Thierry, Li, Lei Ting, Librado, Pablo, Lopez, Loredana, Muñoz, Adriana, Noel, Benjamin, Pallavicini, Alberto, Perrotta, Gaetano, Poncet, Valérie, Pot, David, Priyono, P., Rigoreau, Michel, Rouard, Mathieu, Rozas, Julio, Tranchant Dubreuil, Christine, Vanburen, Robert, Zhang, Qiong, Andrade, Alan C., Argout, Xavier, Bertrand, Benoît, De Kochko, Alexandre, Graziosi, Giorgio, Henry, Robert J., Jayarama, J., Ming, Ray, Nagai, Chifumi, Rounsley, Steve, Sankoff, David, Giuliano, Giovanni, Albert, Victor A., Wincker, Patrick, and Lashermes, Philippe

Subjects
Phylogénie, [SDV]Life Sciences [q-bio], Coffea, Évolution, biosynthèse, Genome, Camellia sinensis, F30 - Génétique et amélioration des plantes, chemistry.chemical_compound, Solanum lycopersicum, genetics, Methyltransferase, Phylogeny, Plant Proteins, caffeine, 2. Zero hunger, Genetics, Multidisciplinary, Medicine (all), Plant Protein, food and beverages, F70 - Taxonomie végétale et phytogéographie, Caféine, Caffeine, Genome, Plant, coffea, Canephora, F60 - Physiologie et biochimie végétale, Biology, Transférase, Coffea canephora, Evolution, Molecular, Phylogenetics, evolution, Methyltransferases, Gene family, [SDV.BV]Life Sciences [q-bio]/Vegetal Biology, Theobroma cacao, Gene, genome, Génome, Molecular, Plant, biology.organism_classification, chemistry, Angiosperme
Abstract

Coffee, tea, and chocolate converge Caffeine has evolved multiple times among plant species, but no one knows whether these events involved similar genes. Denoeud et al. sequenced the Coffea canephora (coffee) genome and identified a conserved gene order (see the Perspective by Zamir). Although this species underwent fewer genome duplications than related species, the relevant caffeine genes experienced tandem duplications that expanded their numbers within this species. Scientists have seen similar but independent expansions in distantly related species of tea and cacao, suggesting that caffeine might have played an adaptive role in coffee evolution. Science , this issue p. 1181 ; see also p. 1124

Published
2014

14. Existence and asymptotics of fronts in non local combustion models

Author

Yannick Sire, Antoine Mellet, Jean-Michel Roquejoffre, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, University of Maryland, 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), and Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)

Subjects
Physics, Applied Mathematics, General Mathematics, 35A01, 35B08, 010102 general mathematics, Mathematical analysis, Mathematics::History and Overview, asymptotic behaviour, fractional laplacian, Non local, Combustion, 01 natural sciences, Computer Science::Computers and Society, 010101 applied mathematics, Physics::Popular Physics, Mathematics - Analysis of PDEs, reaction-diffusion equations, Homogeneous, Reaction–diffusion system, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Fractional Laplacian, Nonlinear Sciences::Pattern Formation and Solitons, Analysis of PDEs (math.AP)
Abstract

International audience; We prove the existence and provide the asymptotics for non local fronts in homogeneous media.

Published
2014

15. Zero Lyapunov exponents of the Hodge bundle

Author

Anton Zorich, Giovanni Forni, Carlos Matheus, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), 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), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Department of Mathematics, University of Maryland, Laboratoire Analyse, Géométrie et Applications ( LAGA ), Université Paris 8 Vincennes-Saint-Denis ( UP8 ) -Université Paris 13 ( UP13 ) -Université Sorbonne Paris Cité ( USPC ) -Institut Galilée-Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Jussieu - Paris Rive Gauche ( IMJ-PRG ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Université Paris Diderot - Paris 7 ( UPD7 ) -Centre National de la Recherche Scientifique ( CNRS ), 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 Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), 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), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)

Subjects
Pure mathematics, Kontsevich-Zorich cocycle, Mathematics::Dynamical Systems, moduli spaces of Abelian and quadratic differentials, General Mathematics, [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], Hodge bundle, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Lyapunov exponent, symbols.namesake, Mathematics::Algebraic Geometry, Teichmüller flow, FOS: Mathematics, Geodesic flow, Mathematics - Dynamical Systems, Invariant (mathematics), Abelian group, Hodge dual, Mathematics::Symplectic Geometry, Mathematics, Probability measure, Mathematical analysis, 37D25, 37D40, 32G15, Lyapunov exponents, Mathematics::Geometric Topology, Monodromy, symbols, groups of pseudo-unitary complex matrices
Abstract

By the results of G. Forni and of R. Trevi\~no, the Lyapunov spectrum of the Hodge bundle over the Teichm\"uller geodesic flow on the strata of Abelian and of quadratic differentials does not contain zeroes even though for certain invariant submanifolds zero exponents are present in the Lyapunov spectrum. In all previously known examples, the zero exponents correspond to those PSL(2,R)-invariant subbundles of the real Hodge bundle for which the monodromy of the Gauss-Manin connection acts by isometries of the Hodge metric. We present an example of an arithmetic Teichm\"uller curve, for which the real Hodge bundle does not contain any PSL(2,R)-invariant, continuous subbundles, and nevertheless its spectrum of Lyapunov exponents contains zeroes. We describe the mechanism of this phenomenon; it covers the previously known situation as a particular case. Conjecturally, this is the only way zero exponents can appear in the Lyapunov spectrum of the Hodge bundle for any PSL(2,R)-invariant probability measure., Comment: 47 pages, 10 figures. Final version (based on the referee's report). A slightly shorter version of this article will appear in Commentarii Mathematici Helvetici. A pdf file containing a copy of the Mathematica routine "FMZ3-Zariski-numerics_det1.nb" is available at this link here: http://w3.impa.br/~cmateus/files/FMZ3-Zariski-numerics_det1.pdf

Published
2014

16. Hydrodynamic models of self-organized dynamics: derivation and existence theory

Author

Sebastien Motsch, Jian-Guo Liu, Pierre Degond, Vladislav Panferov, 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), Duke Physics, Duke University [Durham], Department of Mathematics, University of Maryland, Department of Mathematics [CSUN], California State University [Northridge] (CSUN), 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Capillary action, Self-propelled particles, Dynamics (mechanics), Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Mathematical Physics (math-ph), Physics - Fluid Dynamics, 01 natural sciences, Term (time), 010101 applied mathematics, Viscosity, Classical mechanics, Inviscid flow, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 0103 physical sciences, Limit (mathematics), 0101 mathematics, Variety (universal algebra), 010306 general physics, Mathematical Physics, Mathematics
Abstract

International audience; This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. The starting point is the kinetic model considered in earlier work of Degond & Motsch with the addition of an attraction-repulsion interaction potential. Introducing different scalings than in Degond & Motsch, the non-local effects of the alignment and attraction-repulsion interactions can be kept in the hydrodynamic limit and result in extra pressure, viscosity terms and capillary force. The systems are shown to be symmetrizable hyperbolic systems with viscosity terms. A local-in-time existence result is proved in the 2D case for the viscous model and in the 3D case for the inviscid model. The proof relies on the energy method.

Published
2013

17. Traveling waves for a boundary reaction–diffusion equation

Author

Antoine Mellet, Yannick Sire, Luis A. Caffarelli, University of Texas at Austin [Austin], Department of Mathematics, University of Maryland, Laboratoire d'Analyse, Topologie, Probabilités (LATP), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), L. C. partially supported by NSF Grant.A. M. partially supported by NSF Grant DMS-0901340., Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Mathematics(all), 35K60, 35C07, 35K05, 35K57, 35R35, 80A25, General Mathematics, 010102 general mathematics, Mathematical analysis, Boundary (topology), Activation energy, Term (logic), 01 natural sciences, boundary reaction–diffusion equation, free boundary problem, 010101 applied mathematics, Nonlinear system, traveling waves, Mathematics - Analysis of PDEs, Reaction–diffusion system, FOS: Mathematics, Free boundary problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Limit (mathematics), 0101 mathematics, Exponential decay, Analysis of PDEs (math.AP), Mathematics
Abstract

International audience; We prove the existence of a traveling wave solution for a boundary reaction–diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for traveling wave solutions of a free boundary problem obtained as singular limit for the reaction–diffusion equation (the so-called high energy activation energy limit). This explicit formula, which is interesting in itself, also allows us to get an estimate on the decay at infinity of the traveling wave (which turns out to be faster than the usual exponential decay).

Published
2012

18. Convergence rates for AFEM with H-1 data

Author

Cohen, Albert, Devore, Ronald, Nochetto, Ricardo H., Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), University of South Carolina [Columbia], Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, and Department of Mathematics, University of Maryland

Subjects
ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience

Published
2012

19. Finiteness of central configurations of five bodies in the plane

Author

Alain Albouy, Vadim Kaloshin, Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), and Department of Mathematics, University of Maryland

Subjects
[PHYS]Physics [physics], Pure mathematics, Subvariety, Plane (geometry), 010102 general mathematics, Geometry, Codimension, Isometry (Riemannian geometry), Space (mathematics), 01 natural sciences, Mathematics (miscellaneous), Planar, 0103 physical sciences, Mathematics::Metric Geometry, Relative equilibria, 0101 mathematics, Statistics, Probability and Uncertainty, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], 010303 astronomy & astrophysics, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses belongs to a given codimension 2 subvariety of the mass space.

Published
2012

20. Measurement of Separate Cosmic-Ray Electron and Positron Spectra with the Fermi Large Area Telescope

Author

The, Fermi-LAT Collaboration, Ackermann, M., Ajello, M., Allafort, A., Atwood, W. B., Baldini, L., Barbiellini, G., Bastieri, D., Bechtol, K., Bellazzini, R., Berenji, B., Blandford, R. D., Bloom, E. D., Bonamente, E., Borgland, A. W., Bouvier, A., Bregeon, J., Brigida, M., Bruel, P., Buehler, R., Buson, S., Caliandro, G. A., Cameron, R. A., Caraveo, P. A., Casandjian, J. M., Cecchi, C., Charles, E., Chekhtman, A., Cheung, C. C., Chiang, J., Ciprini, S., Claus, R., Cohen-Tanugi, J., Conrad, J., Cutini, S., de, Angelis A., de, Palma F., Dermer, C. D., Digel, S. W., do, Couto e Silva E., Drell, P. S., Drlica-Wagner, A., Favuzzi, C., Fegan, S. J., Ferrara, E. C., Focke, W. B., Fortin, P., Funk, S., Fusco, P., Gargano, F., Gasparrini, D., Germani, S., Giglietto, N., Giommi, P., Giordano, F., Giroletti, M., Glanzman, T., Godfrey, G., Grenier, I. A., Grove, J. E., Guiriec, S., Gustafsson, M., Hadasch, D., Harding, A. K., Hughes, R. E., Johannesson, G., Johnson, A. S., Knodlseder, J., Kuss, M., Lande, J., Latronico, L., Lemoine-Goumard, M., Llena, Garde M., Longo, F., Loparco, F., Lovellette, M. N., Lubrano, P., Madejski, G. M., Mazziotta, M. N., McEnery, J. E., Michelson, P. F., Mitthumsiri, W., Moiseev, A. A., Monte, C., Monzani, M. E., Morselli, A., Moskalenko, I. V., Murgia, S., Nakamori, T., Nolan, P. L., Norris, J. P., Nuss, E., Omodei, N., Orlando, E., Ormes, J. F., Paneque, D., Parent, D., Pesce-Rollins, M., Pierbattista, M., Piron, F., Pivato, G., Porter, T. A., Raino, S., Rando, R., Razzano, M., Razzaque, S., Reimer, A., Reimer, O., Reposeur, T., Ritz, S., Romani, R. W., Roth, M., Sadrozinski, H. F.-W., Sbarra, C., Schalk, T. L., Sgro, C., Siskind, E. J., Spandre, G., Spinelli, P., Strong, A. W., Fukazawa, Y., Hayashida, M., Kamae, T., Katagiri, H., Kataoka, J., Mizuno, T., Ohno, Masanori, Ohsugi, T., Okumura, Akira, Ozaki, Masanobu, Takahashi, H., Takahashi, Tadayuki, Ackermann, M., Ajello, M., Allafort, A., Atwood, W. B., Baldini, L., Barbiellini, G., Bastieri, D., Bechtol, K., Bellazzini, R., Berenji, B., Blandford, R. D., Bloom, E. D., Bonamente, E., Borgland, A. W., Bouvier, A., Bregeon, J., Brigida, M., Bruel, P., Buehler, R., Buson, S., Caliandro, G. A., Cameron, R. A., Caraveo, P. A., Casandjian, J. M., Cecchi, C., Charles, E., Chekhtman, A., Cheung, C. C., Chiang, J., Ciprini, S., Claus, R., Cohen Tanugi, J., Conrad, J., Cutini, S., Angelis, A., Palma, F., Dermer, C. D., Digel, S. W., Couto, E., Drell, P. S., Drlica Wagner, A., Favuzzi, C., Fegan, S. J., Ferrara, E. C., Focke, W. B., Fortin, P., Fukazawa, Y., Funk, S., Fusco, P., Gargano, F., Gasparrini, D., Germani, S., Giglietto, N., Giommi, P., Giordano, F., Giroletti, M., Glanzman, T., Godfrey, G., Grenier, I. A., Grove, J. E., Guiriec, S., Gustafsson, M., Hadasch, D., Harding, A. K., Hayashida, M., Hughes, R. E., Johannesson, G., Johnson, A. S., Kamae, T., Katagiri, H., Kataoka, J., Kn\odlseder, J., Kuss, M., Lande, J., Latronico, L., Lemoine Goumard, M., Garde, M., Longo, Francesco, Loparco, F., Lovellette, M. N., Lubrano, P., Madejski, G. M., Mazziotta, M. N., Mcenery, J. E., Michelson, P. F., Mitthumsiri, W., Mizuno, T., Moiseev, A. A., Monte, C., Monzani, M. E., Morselli, A., Moskalenko, I. V., Murgia, S., Nakamori, T., Nolan, P. L., Norris, J. P., Nuss, E., Ohno, M., Ohsugi, T., Okumura, A., Omodei, N., Orlando, E., Ormes, J. F., Ozaki, M., Paneque, D., Parent, D., Pesce Rollins, M., Pierbattista, M., Piron, F., Pivato, G., Porter, T. A., Rain\`o, S., Rando, R., Razzano, M., Razzaque, S., Reimer, A., Reimer, O., Reposeur, T., Ritz, S., Romani, R. W., Roth, M., Sadrozinski, H. F., Sbarra, C., Schalk, T. L., Sgr\`o, C., Siskind, E. J., Spandre, G., Spinelli, P., Strong, A. W., Takahashi, H., Takahashi, T., Tanaka, T., Thayer, J. G., Thayer, J. B., Tibaldo, L., Tinivella, M., Torres, D. F., Tosti, G., Troja, E., Uchiyama, Y., Usher, T. L., Vandenbroucke, J., Vasileiou, V., Vianello, G., Vitale, V., Waite, A. P., Winer, B. L., Wood, K. S., Wood, M., Yang, Z., Zimmer, S., Laboratoire Leprince-Ringuet (LLR), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Astrophysique Interprétation Modélisation (AIM (UMR_7158 / UMR_E_9005 / UM_112)), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire Univers et Particules de Montpellier (LUPM), Université de Montpellier (UM)-Université Montpellier 2 - Sciences et Techniques (UM2)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), GLAST, Centre d'Etudes Nucléaires de Bordeaux Gradignan (CENBG), Université Sciences et Technologies - Bordeaux 1-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Fermi-LAT, Deutsches Elektronen-Synchrotron [Zeuthen] (DESY), Helmholtz-Gemeinschaft = Helmholtz Association, Kavli Institute for Particle Astrophysics and Cosmology (KIPAC), Stanford University, Santa Cruz Institute for Particle Physics (SCIPP), University of California [Santa Cruz] (UCSC), University of California-University of California, Istituto Nazionale di Fisica Nucleare [Pisa] (INFN), Istituto Nazionale di Fisica Nucleare (INFN), Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (INFN, Sezione di Trieste), Istituto Nazionale di Fisica Nucleare, Sezione di Padova (INFN, Sezione di Padova), Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (INFN, Sezione di Perugia), Dipartimento di Fisica \M. Merlin' dell'Universita e del Politecnico di Bari, Istituto Nazionale di Fisica Nucleare, sezione di Bari (INFN, sezione di Bari), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Institut de Ciencies de l'Espai [Barcelona] (ICE-CSIC), Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), INAF - Osservatorio Astronomico di Milano (OAM), Istituto Nazionale di Astrofisica (INAF), ARTEP, inc, National Research Council Washington, National Academy of Sciences Washington, Istituto di Scienza e Tecnologie dell'Informazione - Università degli Studi di Perugia, Università degli Studi di Perugia (UNIPG), Université Montpellier 2 - Sciences et Techniques (UM2)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), The Oskar Klein Centre for Cosmoparticle Physics and Department of Physics, Stockholm University, Agenzia Spaziale Italiana (ASI), Space Science Division [Washington], Naval Research Laboratory (NRL), NASA Goddard Space Flight Center (GSFC), Hiroshima City University, INAF - Osservatorio Astronomico di Bologna (OABO), Center for Space Plasma and Aeronomic Research [Huntsville] (CSPAR), University of Alabama in Huntsville (UAH), Kyoto University [Kyoto], Center for Cosmology & AstroParticle Physics, Ohio State University [Columbus] (OSU), University of Iceland [Reykjavik], Ibaraki University, Waseda University, Institut de recherche en astrophysique et planétologie (IRAP), Institut national des sciences de l'Univers (INSU - CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Observatoire Midi-Pyrénées (OMP), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS), Galaxies, Astrophysique des Hautes Energies et Cosmologie (GAHEC), Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Météo France-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Toulouse III - Paul Sabatier (UT3), Istituto Nazionale di Fisica Nucleare, Sezione di Torino (INFN, Sezione di Torino), Université Sciences et Technologies - Bordeaux 1-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Stockholm University Astrobiology Centre, Stockholm University, Department of Mathematics, University of Maryland, Center for Research and Exploration in Space Science and Technology [GSFC] (CRESST), George Mason University [Fairfax], University of California [Santa Cruz] (UC Santa Cruz), University of California (UC)-University of California (UC), Dipartimento di Fisica 'M. Merlin' dell'Università e del Politecnico di Bari, Politecnico di Bari, Astrophysique Interprétation Modélisation (AIM (UMR7158 / UMR_E_9005 / UM_112)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), CNR Istituto di Scienza e Tecnologie dell’Informazione 'A. Faedo' [Pisa] (CNR | ISTI), National Research Council of Italy | Consiglio Nazionale delle Ricerche (CNR), Université Montpellier 2 - Sciences et Techniques (UM2)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Kyoto University, Waseda University [Tokyo, Japan], Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire Midi-Pyrénées (OMP), Institut de Recherche pour le Développement (IRD)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS)-Météo-France -Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Sciences et Technologies - Bordeaux 1 (UB)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Perugia = University of Perugia (UNIPG), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
[PHYS.ASTR.HE]Physics [physics]/Astrophysics [astro-ph]/High Energy Astrophysical Phenomena [astro-ph.HE], Proton, Astrophysics::High Energy Astrophysical Phenomena, Dark matter, FOS: Physical sciences, General Physics and Astronomy, Cosmic ray, Electron, Astrophysics, 01 natural sciences, Spectral line, law.invention, Telescope, Physics and Astronomy (all), Positron, Cosmic rays, law, 0103 physical sciences, ddc:550, Nuclear Experiment, 010306 general physics, High Energy Astrophysical Phenomena (astro-ph.HE), Physics, 010308 nuclear & particles physics, [SDU.ASTR.HE]Sciences of the Universe [physics]/Astrophysics [astro-ph]/High Energy Astrophysical Phenomena [astro-ph.HE], High Energy Physics::Experiment, Astrophysics - High Energy Astrophysical Phenomena, Fermi Gamma-ray Space Telescope
Abstract

We measured separate cosmic-ray electron and positron spectra with the Fermi Large Area Telescope. Because the instrument does not have an onboard magnet, we distinguish the two species by exploiting the Earth's shadow, which is offset in opposite directions for opposite charges due to the Earth's magnetic field. We estimate and subtract the cosmic-ray proton background using two different methods that produce consistent results. We report the electron-only spectrum, the positron-only spectrum, and the positron fraction between 20 GeV and 200 GeV. We confirm that the fraction rises with energy in the 20-100 GeV range. The three new spectral points between 100 and 200 GeV are consistent with a fraction that is continuing to rise with energy., 5 figures, 1 table, revtex 4.1, updated to match PRL published version

Published
2012

21. Trail formation based on directed pheromone deposition

Author

Pierre Degond, Emmanuel Boissard, Sebastien Motsch, 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), Department of Mathematics, University of Maryland, 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Fluid models, Quantitative Biology - Quantitative Methods, Models, Biological, 01 natural sciences, ComputingMethodologies_ARTIFICIALINTELLIGENCE, Pheromones, 03 medical and health sciences, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Animals, Deposition (phase transition), Computer Simulation, 0101 mathematics, TRAIL formation, Quantitative Methods (q-bio.QM), 030304 developmental biology, 0303 health sciences, Behavior, Animal, Ants, Chemistry, Applied Mathematics, 010102 general mathematics, Mathematical Concepts, Agricultural and Biological Sciences (miscellaneous), Insect Hormones, Modeling and Simulation, Sex pheromone, FOS: Biological sciences, Pheromone, Biological system, Locomotion
Abstract

International audience; We propose an Individual-Based Model of ant-trail formation. The ants are modeled as self-propelled particles which deposit directed pheromones and interact with them through alignment interaction. The directed pheromones intend to model pieces of trails, while the alignment interaction translates the tendency for an ant to follow a trail when it meets it. Thanks to adequate quantitative descriptors of the trail patterns, the existence of a phase transition as the ant-pheromone interaction frequency is increased can be evidenced. Finally, we propose both kinetic and fluid descriptions of this model and analyze the capabilities of the fluid model to develop trail patterns. We observe that the development of patterns by fluid models require extra trail amplification mechanisms that are not needed at the Individual-Based Model level.

Published
2011
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22. Two-way multi-lane traffic model for pedestrians in corridors

Author

Pierre Degond, Cécile Appert-Rolland, Sebastien Motsch, Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), 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), and Department of Mathematics, University of Maryland

Subjects
Statistics and Probability, Physics - Physics and Society, Computer science, Macroscopic model, Traffic model, FOS: Physical sciences, Pedestrian, Physics and Society (physics.soc-ph), 01 natural sciences, Compressible flow, Instability, 010305 fluids & plasmas, Incompressible flow, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 11. Sustainability, 0103 physical sciences, Limit (mathematics), 0101 mathematics, Mathematical Physics, Applied Mathematics, Mathematical analysis, General Engineering, Mathematical Physics (math-ph), Nonlinear Sciences - Adaptation and Self-Organizing Systems, Computer Science Applications, 010101 applied mathematics, Constraint (information theory), Adaptation and Self-Organizing Systems (nlin.AO)
Abstract

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability.

Published
2011

23. Anomalous diffusion limit for kinetic equations with generate collision frequency

Author

Antoine Mellet, Marjolaine Puel, Naoufel Ben Abdallah, 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), Department of Mathematics, University of Maryland, 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
Physics, Asymptotic analysis, Anomalous diffusion, Mean free path, Applied Mathematics, 010102 general mathematics, Degenerate energy levels, 01 natural sciences, Collision operator, 010101 applied mathematics, Classical mechanics, Collision frequency, Kinetic equations, Modeling and Simulation, 76P05 26A33 22E46 53C35 57S20, 0101 mathematics, Degeneracy (mathematics), ComputingMilieux_MISCELLANEOUS
Abstract

This paper is devoted to hydrodynamic limits for collisional linear kinetic equations. It is a classical result that under certain conditions on the collision operator, the long time/small mean free path asymptotic behavior of the density of particles can be described by diffusion-type equations. We are interested in situations in which the degeneracy of the collision frequency for small velocities causes this limit to break down. We show that the appropriate asymptotic analysis leads to an anomalous diffusion regime.

Published
2011

24. Generalized fronts for one-dimensional reaction-diffusion equations

Author

Antoine Mellet, Yannick Sire, Jean-Michel Roquejoffre, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Analyse, Topologie, Probabilités (LATP), Université Paul Cézanne - Aix-Marseille 3-Université de Provence - Aix-Marseille 1-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, University of Maryland, 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), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Class (set theory), Diffusion equation, Differential equation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, 01 natural sciences, Upper and lower bounds, 35K57 (35B40), 010101 applied mathematics, chemistry.chemical_compound, chemistry, Reaction–diffusion system, Time derivative, Discrete Mathematics and Combinatorics, 0101 mathematics, Analysis, Derivative (chemistry), ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

For a class of one-dimensional reaction-diffusion equations, we establish the existence of generalized fronts, as recently defined by Berestycki and Hamel. We also prove uniform nondegeneracy estimates, such as a lower bound on the time derivative on some level sets, as well as a lower bound on the spatial derivative.

Published
2010

25. Stability of generalized transition fronts

Author

Antoine Mellet, Lenya Ryzhik, Jean-Michel Roquejoffre, James Nolen, Department of Mathematics, University of Maryland, Department of Mathematics [Stanford], Stanford University, 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), Department of Mathematics [Chicago], University of Chicago, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, 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, 010102 general mathematics, Mathematical analysis, Type (model theory), 35B35 (35K57, 35K15, 35K55), Translation (geometry), 01 natural sciences, Stability (probability), 010101 applied mathematics, Reaction rate, Nonlinear system, Exponential stability, Bounded function, Initial value problem, 0101 mathematics, Analysis, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

We study the qualitative properties of the generalized transition fronts for the reaction–diffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transition fronts are unique up to translation in time and are globally exponentially stable for the solutions of the Cauchy problem. The results hold for reaction rates that have arbitrary spatial variations provided that the rate is uniformly positive and bounded from above.

Published
2009

26. Computing Hilbert Class Polynomials

Author

Reinier Bröker, Juliana Belding, Andreas Enge, Kristin E. Lauter, Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Microsoft Research [Redmond], Microsoft Corporation [Redmond, Wash.], Algorithmic number theory for cryptology (TANC), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Alfred J. van der Poorten, Andreas Stein

Subjects
Discrete mathematics, Polynomial, algorithm, Mathematics - Number Theory, Quaternion algebra, Group (mathematics), [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Combinatorics, Elliptic curve, Finite field, Discriminant, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, Order (group theory), Number Theory (math.NT), Remainder, complexity, class polynomial, Mathematics, p-adic lifting
Abstract

International audience; We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$ , and we show that all methods have comparable run times.

Published
2008

27. Numerical comparison between two Spherical Harmonics Expansion models and a kinetic equation

Author

Antoine Mellet, J. P. Bourgade, Luc Mieussens, 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), Department of Mathematics, University of Maryland, 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 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), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, 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
Kinetic model, 010102 general mathematics, Spherical harmonics, Collision, 01 natural sciences, Boltzmann equation, Computer Science Applications, 010101 applied mathematics, Kinetic equations, Modelling and Simulation, Modeling and Simulation, Transient (oscillation), Statistical physics, 0101 mathematics, Diffusion (business), Convection–diffusion equation, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

In this paper, we investigate the reliability of two diffusion models, the SHE andcoupled SHE models, by accurate numerical comparisons with a Boltzmann-like equation. These models describe the transport of particles subject to collisions with the medium. Comparisons are given at three levels of description: at small times (transient regime), at the diffusion time (diffusion regime), and for long times (stationary regime). The three regimes are well described by both SHE models. A discussion of the main benefits and drawbacks of each of the SHE models is given, according to the regime.

Published
2004

28. Study of a system for the isothermal separation of components in a binary alloy with change of phase

Author

Ulisse Stefanelli, Daniel Kessler, Giulio Schimperna, Jean-François Scheid, Department of Mathematics, University of Maryland, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Matematica - Università di Pavia, Università degli Studi di Pavia, Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R., Consiglio Nazionale delle Ricerche (CNR), The work of Daniel Kessler is supported by the Swiss National Science Foundation., Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Dipartimento di Matematica 'Felice Casorati' Department of Mathematics [Univ Pavia] (UNIPV), Università degli Studi di Pavia = University of Pavia (UNIPV), and National Research Council of Italy | Consiglio Nazionale delle Ricerche (CNR)

Subjects
variational formulation, Asymptotic analysis, Phase transition, Partial differential equation, Component (thermodynamics), constraint, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Stefan problem, fourth-order parabolic system, 01 natural sciences, Isothermal process, binary alloy, 010101 applied mathematics, Faedo–Galerkin scheme, maximum principle, phase transition, Phase (matter), [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Cahn–Hilliard equation, Mathematics
Abstract

International audience; An isothermal model describing the separation of the components of a binary metallic alloy is considered. A process of phase transition is also assumed to occur in the solder; hence, the state of the material is described by two order parameters, i.e. the concentration c of the first component and the phase field ϕ. A physical derivation is provided starting from energy balance considerations. The resulting system of PDEs consists of a rather regular second-order parabolic equation for ϕ coupled with a fourth-order relation of Cahn-Hilliard type for c with constraint and solution-dependent mobility. Global existence of solutions is proved and several regularity properties are discussed under more restrictive assumptions on the physical parameters. Continuous dependence on data is shown in a special case. An asymptotic analysis of the model is also performed, yielding at the limit step a coupling of the original phase field equation with a Stefan-like system for c.

Published
2004

29. Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem

Author

Marcel Guardia, Jacques Féjoz, Vadim Kaloshin, Pablo Roldan, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC, Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Department of Mathematics, University of Maryland, ANR-12-BS01-0020,WKBHJ,KAM faible au-delà de Hamilton-Jacobi(2012), ANR-10-BLAN-0102,DynPDE,Dynamique et EDP(2010), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [College Park], University of Maryland [College Park], and University of Maryland System-University of Maryland System

Subjects
General Mathematics, Kirkwood gap, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), 01 natural sciences, 0103 physical sciences, Three-body problem, FOS: Mathematics, 0101 mathematics, Mathematics - Dynamical Systems, Arnold diffusion, Mathematics, Mathematical physics, Problema dels tres cossos, Applied Mathematics, 010102 general mathematics, Matemàtiques i estadística [Àrees temàtiques de la UPC], Mass ratio, Sistemes dinàmics diferenciables, Dynamics, Mean motion, Physics::Space Physics, Asteroid belt, 010307 mathematical physics, Astrophysics::Earth and Planetary Astrophysics, Eccentricity (mathematics), Osculating circle
Abstract

International audience; We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun--Jupiter--asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio $\mu=10^{-3}$ and a small eccentricity $e_0>0$. The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. We verify certain non-degeneracy conditions numerically. Based on the work of Treschev, it is natural to conjecture that diffusion time for this problem is $\sim \frac{-\ln (\mu e_0)}{\mu^{3/2} e_0}$. We expect our instability mechanism to apply to realistic values of $e_0$ and we give heuristic arguments in its favor. If so, the applicability of Nekhoroshev theory to the three-body problem as well as the long time stability become questionable. It is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. Our mechanism gives a possible explanation of their existence. To relate the existence of Kirkwood gaps with Arnold diffusion, we state a conjecture on its existence for a typical $\eps$-perturbation of the product of a pendulum and a rotator. Namely, we predict that a positive conditional measure of initial conditions concentrated in the main resonance exhibits Arnold diffusion on time scales $\frac{- \ln \eps}{\eps^{2}}$.

30. Compressed Sensing Electron Tomography for Determining Biological Structure.

Author

Guay MD, Czaja W, Aronova MA, and Leapman RD

Subjects
Animals, Artifacts, Electron Microscope Tomography instrumentation, Image Processing, Computer-Assisted statistics & numerical data, Islets of Langerhans ultrastructure, Mice, Phantoms, Imaging, Algorithms, Data Compression methods, Electron Microscope Tomography methods, Image Processing, Computer-Assisted methods
Abstract

There has been growing interest in applying compressed sensing (CS) theory and practice to reconstruct 3D volumes at the nanoscale from electron tomography datasets of inorganic materials, based on known sparsity in the structure of interest. Here we explore the application of CS for visualizing the 3D structure of biological specimens from tomographic tilt series acquired in the scanning transmission electron microscope (STEM). CS-ET reconstructions match or outperform commonly used alternative methods in full and undersampled tomogram recovery, but with less significant performance gains than observed for the imaging of inorganic materials. We propose that this disparity stems from the increased structural complexity of biological systems, as supported by theoretical CS sampling considerations and numerical results in simulated phantom datasets. A detailed analysis of the efficacy of CS-ET for undersampled recovery is therefore complicated by the structure of the object being imaged. The numerical nonlinear decoding process of CS shares strong connections with popular regularized least-squares methods, and the use of such numerical recovery techniques for mitigating artifacts and denoising in reconstructions of fully sampled datasets remains advantageous. This article provides a link to the software that has been developed for CS-ET reconstruction of electron tomographic data sets.

Published
2016
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