Active Particles, Volume 1 : Advances in Theory, Models, and Applications PDF
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Modeling and Simulation in Science, Engineering and Technology Nicola Bellomo Pierre Degond Eitan Tadmor Editors Active Particles, Volume 1 Advances in Theory, Models, and Applications Modeling and Simulation in Science, Engineering and Technology Series editors NicolaBellomo TayfunE.Tezduyar DepartmentofMathematics DepartmentofMechanicalEngineering FacultyofSciences RiceUniversity KingAbdulazizUniversity Houston,TX,USA Jeddah,SaudiArabia Editorial Advisory Board K.Aoki P.Koumoutsakos KyotoUniversity ComputationalScience&Engineering Kyoto,Japan Laboratory ETHZürich K.J.Bathe Zürich,Switzerland DepartmentofMechanicalEngineering MassachusettsInstituteofTechnology H.G.Othmer Cambridge,MA,USA DepartmentofMathematics UniversityofMinnesota Y.Bazilevs Minneapolis,MN,USA DepartmentofStructuralEngineering UniversityofCalifornia,SanDiego K.R.Rajagopal LaJolla,CA,USA DepartmentofMechanicalEngineering TexasA&MUniversity M.Chaplain CollegeStation,TX,USA DivisionofMathematics UniversityofDundee K.Takizawa Dundee,Scotland,UK DepartmentofModernMechanical Engineering P.Degond WasedaUniversity DepartmentofMathematics Tokyo,Japan ImperialCollegeLondon London,UK Y.Tao DongHuaUniversity A.Deutsch Shanghai CenterforInformationServices China andHigh-PerformanceComputing TechnischeUniversitätDresden Dresden,Germany M.A.Herrero DepartamentodeMatematicaAplicada UniversidadComplutensedeMadrid Madrid,Spain More information about this series at http://www.springer.com/series/4960 Nicola Bellomo Pierre Degond (cid:129) Eitan Tadmor Editors Active Particles, Volume 1 Advances in Theory, Models, and Applications Editors NicolaBellomo EitanTadmor Department ofMathematical Sciences CSCAMM KingAbdulaziz University University of Maryland Jeddah CollegePark SaudiArabia USA Pierre Degond Department ofMathematics Imperial CollegeLondon London UK ISSN 2164-3679 ISSN 2164-3725 (electronic) Modeling andSimulationin Science, Engineering andTechnology ISBN978-3-319-49994-9 ISBN978-3-319-49996-3 (eBook) DOI 10.1007/978-3-319-49996-3 LibraryofCongressControlNumber:2016961339 Mathematics Subject Classification (2010): 35K55, 35Q92, 35Q70, 37N40, 60H10, 49J15, 74A25, 70F45,76N10,82D99,91A26,92D25,91C20,82B21,35Q91,49J45 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisbookispublishedunderthetradenameBirkhäuser TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland (www.birkhauser-science.com) Preface This edited book collects ten surveys on modeling, simulation, and applications of active matter by various types of methods spanning from mathematical kinetic theorytononequilibriumstatisticalmechanics.Thecontributionsdevelopavariety of different viewpoints, such as individual-based models, evolutive games, Brownian particles, kinetic theory, and continuum theories, as well as a combina- tion of these, such as kinetic theory and evolutive games or individual-based and continuummodels.Theauthorsofeachchapterhavebeenselectedamongthemost active mathematicians operating on the aforementioned challenging field. The contents provide a survey of recent results of the various teams and look ahead to research perspectives. Hence, this book is just timely to provide the scientific community with an up-to-date overview of current research conducted by leading experts in this field. Indeed, this book covers a broad range of applications, such as biological net- work formation and network theory in the chapters “Continuum Modeling of BiologicalNetworkFormation”and“InteractionNetwork,StateSpace,andControl inSocialDynamics”;opinionformationandsocialsystemsinthechapters“Recent Advances in Opinion Modeling: Control and Social Influence,” “Interaction Network, State Space, and Control in Social Dynamics,” “Sparse Control of MultiagentSystems,” and“AReview onAttractive–Repulsive Hydrodynamicsfor ConsensusinCollectiveBehavior”;controltheoryofsparsesystemsinthechapters “Recent Advances in Opinion Modeling: Control and Social Influence,” “Interaction Network, State Space and Control in Social Dynamics,” and “Sparse ControlofMultiagentSystems”;theoryandapplicationsofmeanfieldgamesinthe chapter “Variational Mean Field Games;” population learning in the chapter “Sparse Control of Multiagent Systems”; dynamics of flocking systems in the chapter “Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants”; vehicular traffic in the chapter “Follow-the-Leader Approximations of Macroscopic Models for Vehicular and Pedestrian Flows”; and stochastic particles and mean field approximation in the chapter “Mean Field Limit for Stochastic Particle Systems.” v vi Preface Differentmathematicaltoolshavebeenusedfrommethodsofgeneralizedkinetic theory and statistical dynamics to stochastic evolutive games, mean field games, and stochastic differential systems. Control theory, flocking analysis, and network theory contribute and enrich the application of the aforementioned mathematical tools. The variety of applications and the interdisciplinary use of different mathemat- ical tools witness the interest of applied mathematicians toward modeling, quali- tativeanalysis,andcomputingoflargesystemsofactiveparticlesviewedasliving, hence complex, systems. This new frontier of science offers to applied mathe- maticians a broad variety of new challenging problems. The research activity in the field meets an equally productive scientific envi- ronment. In particular,we mentionthe Ki-Net, anNSF Research Networkfocused on “Kinetic description of emerging challenges in multiscale problems of natural sciences” (www.ki-net.umd.edu). The Ki-Net, through its main three hubs in the UniversityofMaryland,UniversityofWisconsin,andUTAustinandaninterlinked networkof20+nodes,fostersaseriesofactivitieswithamainintellectualfocuson development, analysis, computation, and application of quantum dynamics, net- work dynamics, and kinetic models of biological processes. As such, Ki-Net is a primary outlet for presentation of recent activities in the above areas of active matter.Indeed,manyoftheauthorsinthisspecialvolumewereinvolvedinKi-Net activities.WementioninthiscontexttherecentexamplesofKi-Networkshopson modeling and control in social dynamics (October 2014), on groups and interac- tions in data, networks and biology (May 2015), and on collective dynamics in biologicalandsocialsystems(November2015).Acompletelistofactivitiescanbe found at www.ki-net.umd.edu/content/activities, and we use this opportunity to acknowledge the NSF support of Ki-Net Grant #1107444 for funding these activities. Jeddah, Saudi Arabia Nicola Bellomo London, UK Pierre Degond College Park, USA Eitan Tadmor Contents Continuum Modeling of Biological Network Formation. .... ..... .... 1 Giacomo Albi, Martin Burger, Jan Haskovec, Peter Markowich and Matthias Schlottbom Recent Advances in Opinion Modeling: Control and Social Influence...... 49 Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani and Mattia Zanella Interaction Network, State Space, and Control in Social Dynamics........ 99 Aylin Aydoğdu, Marco Caponigro, Sean McQuade, Benedetto Piccoli, Nastassia Pouradier Duteil, Francesco Rossi and Emmanuel Trélat Variational Mean Field Games .... .... .... .... .... .... ..... .... 141 Jean-David Benamou, Guillaume Carlier and Filippo Santambrogio Sparse Control of Multiagent Systems... .... .... .... .... ..... .... 173 Mattia Bongini and Massimo Fornasier A Kinetic Theory Approach to the Modeling of Complex Living Systems .. .... .... .... .... ..... .... .... .... .... .... ..... .... 229 Diletta Burini, Livio Gibelli and Nisrine Outada A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior... .... ..... .... .... .... .... .... ..... .... 259 José A. Carrillo, Young-Pil Choi and Sergio P. Perez Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants ... .... .... ..... .... .... .... .... .... ..... .... 299 Young-Pil Choi, Seung-Yeal Ha and Zhuchun Li Follow-the-Leader Approximations of Macroscopic Models for Vehicular and Pedestrian Flows. .... .... .... .... .... ..... .... 333 M. Di Francesco, S. Fagioli, M.D. Rosini and G. Russo Mean Field Limit for Stochastic Particle Systems . .... .... ..... .... 379 Pierre-Emmanuel Jabin and Zhenfu Wang vii Contributors Giacomo Albi Applied Numerical Analysis, Technical University of Munich, Garching bei München, Germany Aylin Aydoğdu Rutgers University, Camden, NJ, USA Jean-David Benamou INRIA-MOKAPLAN, Paris, France Mattia Bongini Technische Universität München, Garching, Germany Martin Burger Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany Diletta Burini Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy Marco Caponigro Conservatoire National des Arts et Métiers, Paris, France Guillaume Carlier Ceremade Univ. Paris Dauphine and INRIA-MOKAPLAN, Paris, France José A. Carrillo Department of Mathematics, Imperial College London, South Kensington, UK Young-Pil Choi Fakultät für Mathematik, Technische Universität München, Garching bei München, Germany Nastassia Pouradier Duteil Rutgers University, Camden, NJ, USA S. Fagioli DISIM, Università degli Studi dell’Aquila, L’Aquila (AQ), Italy Massimo Fornasier Technische Universität München, Garching, Germany M.DiFrancesco DISIM,UniversitàdegliStudidell’Aquila,L’Aquila(AQ),Italy LivioGibelli DepartmentofMathematicalSciences,PolitecnicodiTorino,Turin, Italy ix x Contributors Seung-Yeal Ha Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Republic of Korea Jan Haskovec Mathematical and Computer Sciences and Engineering Division, KingAbdullahUniversityofScienceandTechnology,Thuwal,KingdomofSaudi Arabia Pierre-Emmanuel Jabin CSCAMM and Department of Mathematics, University of Maryland, College Park, MD, USA ZhuchunLi DepartmentofMathematics,HarbinInstituteofTechnology,Harbin, People’s Republic of China Peter Markowich Mathematical and Computer Sciences and Engineering Division,KingAbdullahUniversityofScienceandTechnology,Thuwal,Kingdom of Saudi Arabia Sean McQuade Rutgers University, Camden, NJ, USA NisrineOutada FacultédesSciencesSemlalia,Marrakesh,Morocco;Laboratoire Jacques Louis-Lions, Université Pierre et Marie Curie, Paris, France Lorenzo Pareschi University of Ferrara, Ferrara, Italy Sergio P. Perez ETSIAE, Technical University of Madrid, Madrid, Spain Benedetto Piccoli Rutgers University, Camden, NJ, USA M.D.Rosini InstytutMatematyki,UniwersytetMariiCurie-Skłodowskiej,Lublin, Poland Francesco Rossi Aix Marseille Université, CNRS, ENSAM, Université de Toulon, Marseille, France G. Russo Dipartimento di Matematica ed Informatica, Università di Catania, Catania, Italy Filippo Santambrogio Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, Orsay Cedex, France MatthiasSchlottbom MultiscaleModelingandSimulation,UniversityofTwente, AE Enschede, The Netherlands Giuseppe Toscani University of Pavia, Pavia, Italy Emmanuel Trélat Sorbonne Universités, Paris, France; Laboratoire Jacques-Louis Lions, Institut Universitaire de France, Paris, France Zhenfu Wang CSCAMM and Department of Mathematics, University of Maryland, College Park, MD, USA Mattia Zanella University of Ferrara, Ferrara, Italy
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