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01 mathknow front matter 01 mathknow front matter Document Transcript

  • MATHKNOW
  • MS&ASeries Editors:Alfio Quarteroni (Editor-in-Chief ) • Tom Hou • Claude Le Bris • Anthony T. Patera • Enrique Zuazua
  • Michele Emmer, Alfio Quarteroni (Eds.)MATHKNOWMathematics, Applied Sciencesand Real Life
  • Michele EmmerUniversità degli studi “La Sapienza”Dipartimento di Matematica “G. Castelnuovo”Roma, ItalyAlfio QuarteroniMOX, Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilan, ItalyandCMCS-IACSEcole Polytechnique Fédérale de LausanneLausanne, SwitzerlandOn the cover: Anelli borromei. Biblioteca Ambrosiana, Milano. © Sabrina ProvenziLibrary of Congress Control Number: 2009922761ISBN 978-88-470-1121-2 Springer Milan Berlin Heidelberg New Yorke-ISBN 978-88-470-1122-9 Springer Milan Berlin Heidelberg New YorkSpringer-Verlag is a part of Springer Science+Business Mediaspringer.comc Springer-Verlag Italia, Milan 2009This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication orparts thereof is permitted only under the provisions of the Italian Copyright Law in its current version, andpermissions for use must always be obtained from Springer. Violations are liable to prosecution under theItalian Copyright Law.9 8 7 6 5 4 3 2 1Typesetting with Latex: PTP-Berlin, Protago TEX-Production GmbH, Germany (www.ptp-berlin.eu)Cover-Design: Francesca Tonon, MilanPrinting and Binding: Grafiche Porpora, Cernusco S/N (MI)Printed in ItalySpringer-Verlag Italia Srl – Via Decembrio 28 – 20137 Milano
  • ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIIThe misuse of mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Ralph AbrahamMathematics and literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Andrew CrumeyApplied partial differential equations: visualizationby photography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Peter MarkowichThe spirit of algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Claudio ProcesiTheory and applications of Raptor codes . . . . . . . . . . . . . . . . . . . 59Amin ShokrollahiOther geometries in architecture: bubbles, knots andminimal surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Tobias WallisserSoft matter: mathematical models of smart materials . . . . . . . 113Paolo BiscariSoap films and soap bubbles: from Plateau to the olympicswimming pool in Beijing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Michele EmmerGames suggest how to define rational behavior. Surprisingaspects of interactive decision theory . . . . . . . . . . . . . . . . . . . . . . . 131Roberto Lucchetti
  • VI ContentsArchaeoastronomy at Giza: the ancient Egyptians’mathematical astronomy in action . . . . . . . . . . . . . . . . . . . . . . . . . . 147Giulio MagliMathematics and food: a tasty binomium . . . . . . . . . . . . . . . . . . . 157Luca Paglieri and Alfio QuarteroniDetecting structural complexity: from visiometrics togenomics and brain research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Renzo L. RiccaRecreative mathematics: soldiers, eggs and a pirate crew . . . 183Nadia AmbrosettiMathematical magic and society . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193Fernando BlascoLittle Tom Thumb among cells: seeking the cues of life . . . . . 201Giacomo Aletti, Paola Causin, Giovanni Naldi and Matteo SempliceAdam’s Pears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215Guido ChiesaMathematics enters the picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Massimo FornasierMulti-physics models for bio-hybrid device simulation . . . . . . 229Riccardo SaccoStress detection: a sonic approach . . . . . . . . . . . . . . . . . . . . . . . . . . 241Laura Tedeschini LalliVulnerability to climate change: mathematics as a languageto clarify concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Sarah Wolf
  • PrefaceMathematics is the oldest of all sciences. Its foundations are visible in math-ematical texts originating in the ancient Egyptian, Mesopotamian, Indian,Chinese, Greek and Islamic worlds. Since the very beginning, when mathematics was conceived for fulfillingvery basic needs like numbering, counting and measuring simple-shaped ar-eas, this discipline has evolved in a boisterous way thus producing significantresults that have strongly marked the evolution of mankind. Through the centuries, mathematical ideas and achievements have beenorganized and shaped into fundamental branches like arithmetic, numbertheory, algebra, geometry, and trigonometry, as well as related sciences likeastronomy, mechanics and physics. The development of the discipline then bloomed in the 16th century, whenmathematical innovations started to interact with new scientific discoveries;and its growth has never ceased thereafter. Nowadays, mathematics is the most influential and pervasive of all sciencesin our society, because of its exclusive potential of establishing connectionsamong virtually all possible manifestation of our knowledge. As a matter offact, it is used throughout the world as an essential tool in many fields. Inparticular, applied mathematics tranfers mathematical knowledge into otherfields, offering new possibilities to manage the growing complexity of our realworld. Beautiful though they may be, mathematical results are not merelymuseum-pieces, but form a vital underpinning for every branch of quanti-tative knowledge, including all domains of science and engineering. Mathe-matics is in constant and vigorous development, driven both by its internaldynamics and by the demands of other disciplines, henceforth impacting thewhole of our daily life. By gathering different contributions from several world-famous scientistsfrom mathematics and related sciences, this book highlights the way mathe-matics deeply permeates and fertilizes our society.
  • VIII Preface In particular, here will we face the role of mathematics in applied sciencesshowing results in different fields in industry, environment, life sciences andarchitecture. This book has the ambition to excite the readers interest showing howmathematics is also hidden in the natural world around us, independentlyof mankind presence and interference: there are maths schemes in any prey-predator interaction, Boltzmanns equations hidden in clouds, Navier-StokesEquations concealed in a waterfall, free boundary problems to be solved in amelting iceberg. Though this work will face maths problems that are not always elemen-tary, yet it is not intended for mathematicians only. The rigorous, nonethelessreadable, exposition, the intriguing examples, the stimulating demonstrationsof the deep connections among science, technology, architecture, human sci-ences and mathematics will fascinate even those who, not being scientists orexperts of this discipline, have always felt attracted by the noblest and mostfundamental of modern sciences.The Editors, and the Publisher as well, would like to thank all the authors andthe people who actively contributed to the success of this project, in particularLuca Paglieri, for his accuracy and concern in supporting the MATHKNOWexperience since the very beginning.
  • List of ContributorsRalph Abraham Fernando BlascoUniversity of California Departamento de Matem´tica aSanta Cruz, CA, USA Aplicada a los Recursos Naturalesrha@ucsc.edu ETSI Montes Universidad Polit´cnica de Madrid e Madrid, Spain fernando.blasco@upm.esGiacomo AlettiDipartimento di Matematica“F. Enriques”Universit` degli Studi di Milano a Paola CausinMilano, Italy Dipartimento di Matematicaaletti@mat.unimi.it “F. Enriques” Universit` degli Studi di Milano a Milano, Italy causin@mat.unimi.itNadia AmbrosettiDipartimento di Informatica eComunicazioneFacolt` di Scienze Matematiche, a Andrew CrumeyFisiche e Naturali School of English Literature,Universit` degli Studi di Milano a Language and LinguisticsMilano, Italy Newcastle Universitynadia.ambrosetti@unimi.it Newcastle upon Tyne, UK Andrew.Crumey@ncl.ac.ukPaolo BiscariDipartimento di Matematica Guido ChiesaPolitecnico di Milano Movie DirectorMilano, Italy Padova, Italypaolo.biscari@polimi.it guido.chiesa@fastwebnet.it
  • X List of ContributorsMichele Emmer Claudio ProcesiUniversit` degli studi “La Sapienza” a Universit` degli studi “La Sapienza” aDipartimento di Matematica Istituto di Matematica“G. Castelnuovo” “G. Castelnuovo”Roma, Italy Roma, Italyemmer@mat.uniroma1.it Alfio QuarteroniMassimo Fornasier MOX, Dipartimento di MatematicaJohann Radon Institute for “F. Brioschi”Computational and Applied Politecnico di MilanoMathematics (RICAM) Milano, ItalyLinz, Austria andmassimo.fornasier@oeaw.ac.at CMCS-IACS Ecole Polytechnique F´d´rale de e eRoberto Lucchetti LausanneDipartimento di Matematica Lausanne, SwitzerlandPolitecnico di MilanoMilano, Italy Renzo L. Ricca Dipartimento di MatematicaGiulio Magli ApplicataFacolt` di Architettura Civile a Universit` Milano-Bicocca aPolitecnico di Milano Milano, ItalyMilano, Italy and Institute for Scientific Interchange Torino, ItalyPeter Markowich renzo.ricca@unimib.itDAMTP www.matapp.unimib.it/~riccaCentre for Mathematical SciencesCambridge, UK Riccardo SaccoGiovanni Naldi Dipartimento di MatematicaDipartimento di Matematica “F. Brioschi”“F. Enriques” Politecnico di MilanoUniversit` degli Studi di Milano a Milano, ItalyMilano, Italy riccardo.sacco@polimi.itnaldi@mat.unimi.it Matteo SempliceLuca Paglieri Dipartimento di MatematicaMOX, Dipartimento di Matematica “F. Enriques”“F. Brioschi” Universit` degli Studi di Milano aPolitecnico di Milano Milano, ItalyMilano, Italy semplice@mat.unimi.it
  • List of Contributors XIAmin Shokrollahi Tobias WallisserEcole Polytechnique F´d´rale de e e Staatliche Akademie der BildendenLausanne K¨nste Stuttgart uLausanne, Switzerland Stuttgart, Germanyamin.shokrollahi@epfl.ch Sarah WolfLaura Tedeschini Lalli Potsdam Institute for ClimateDipartimento di Matematica Impact Research (PIK)Universit` Roma Tre a Potsdam, GermanyRoma, Italy sarah.wolf@pik-potsdam.de