MATHKNOW
MS&ASeries Editors:
Alfio Quarteroni (Editor-in-Chief ) • Tom Hou • Claude Le Bris • Anthony T. Patera • Enrique Zuazua
Michele Emmer, Alfio Quarteroni (Eds.)
MATHKNOW
Mathematics, Applied Sciences
and Real Life
Michele EmmerUniversità degli studi “La Sapienza”Dipartimento di Matematica “G. Castelnuovo”Roma, Italy
Alfio QuarteroniMOX, Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilan, ItalyandCMCS-IACSEcole Polytechnique Fédérale de LausanneLausanne, Switzerland
On the cover:Anelli borromei. BibliotecaAmbrosiana,Milano.©SabrinaProvenzi
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ISBN 978-88-470-1121-2 Springer Milan Berlin Heidelberg New Yorke-ISBN 978-88-470-1122-9 Springer Milan Berlin Heidelberg New York
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII
The misuse of mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Ralph Abraham
Mathematics and literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Andrew Crumey
Applied partial differential equations: visualizationby photography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Peter Markowich
The spirit of algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Claudio Procesi
Theory and applications of Raptor codes . . . . . . . . . . . . . . . . . . . 59Amin Shokrollahi
Other geometries in architecture: bubbles, knots andminimal surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Tobias Wallisser
Soft matter: mathematical models of smart materials . . . . . . . 113Paolo Biscari
Soap films and soap bubbles: from Plateau to the olympicswimming pool in Beijing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Michele Emmer
Games suggest how to define rational behavior. Surprisingaspects of interactive decision theory . . . . . . . . . . . . . . . . . . . . . . . 131Roberto Lucchetti
VI Contents
Archaeoastronomy at Giza: the ancient Egyptians’mathematical astronomy in action . . . . . . . . . . . . . . . . . . . . . . . . . . 147Giulio Magli
Mathematics and food: a tasty binomium . . . . . . . . . . . . . . . . . . . 157Luca Paglieri and Alfio Quarteroni
Detecting structural complexity: from visiometrics togenomics and brain research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Renzo L. Ricca
Recreative mathematics: soldiers, eggs and a pirate crew . . . 183Nadia Ambrosetti
Mathematical magic and society . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193Fernando Blasco
Little Tom Thumb among cells: seeking the cues of life . . . . . 201Giacomo Aletti, Paola Causin, Giovanni Naldi and Matteo Semplice
Adam’s Pears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215Guido Chiesa
Mathematics enters the picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Massimo Fornasier
Multi-physics models for bio-hybrid device simulation . . . . . . 229Riccardo Sacco
Stress detection: a sonic approach . . . . . . . . . . . . . . . . . . . . . . . . . . 241Laura Tedeschini Lalli
Vulnerability to climate change: mathematics as a languageto clarify concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Sarah Wolf
Preface
Mathematics 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 fulfilling
very 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 been
organized 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, when
mathematical 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 sciences
in 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 merely
museum-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 scientists
from 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 how
mathematics 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 Contributors
Ralph AbrahamUniversity of CaliforniaSanta Cruz, CA, [email protected]
Giacomo AlettiDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, [email protected]
Nadia AmbrosettiDipartimento di Informatica eComunicazioneFacolta di Scienze Matematiche,Fisiche e NaturaliUniversita degli Studi di MilanoMilano, [email protected]
Paolo BiscariDipartimento di MatematicaPolitecnico di MilanoMilano, [email protected]
Fernando BlascoDepartamento de MatematicaAplicada a los Recursos NaturalesETSI MontesUniversidad Politecnica de MadridMadrid, [email protected]
Paola CausinDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, [email protected]
Andrew CrumeySchool of English Literature,Language and LinguisticsNewcastle UniversityNewcastle upon Tyne, [email protected]
Guido ChiesaMovie DirectorPadova, [email protected]
X List of Contributors
Michele EmmerUniversita degli studi “La Sapienza”Dipartimento di Matematica“G. Castelnuovo”Roma, [email protected]
Massimo FornasierJohann Radon Institute forComputational and AppliedMathematics (RICAM)Linz, [email protected]
Roberto LucchettiDipartimento di MatematicaPolitecnico di MilanoMilano, Italy
Giulio MagliFacolta di Architettura CivilePolitecnico di MilanoMilano, Italy
Peter MarkowichDAMTPCentre for Mathematical SciencesCambridge, UK
Giovanni NaldiDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, [email protected]
Luca PaglieriMOX, Dipartimento di Matematica“F. Brioschi”Politecnico di MilanoMilano, Italy
Claudio ProcesiUniversita degli studi “La Sapienza”Istituto di Matematica“G. Castelnuovo”Roma, Italy
Alfio QuarteroniMOX, Dipartimento di Matematica“F. Brioschi”Politecnico di MilanoMilano, ItalyandCMCS-IACSEcole Polytechnique Federale deLausanneLausanne, Switzerland
Renzo L. RiccaDipartimento di MatematicaApplicataUniversita Milano-BicoccaMilano, ItalyandInstitute for Scientific InterchangeTorino, [email protected]
www.matapp.unimib.it/~ricca
Riccardo SaccoDipartimento di Matematica“F. Brioschi”Politecnico di MilanoMilano, [email protected]
Matteo SempliceDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, [email protected]
List of Contributors XI
Amin ShokrollahiEcole Polytechnique Federale deLausanneLausanne, [email protected]
Laura Tedeschini LalliDipartimento di MatematicaUniversita Roma TreRoma, Italy
Tobias WallisserStaatliche Akademie der BildendenKunste StuttgartStuttgart, Germany
Sarah WolfPotsdam Institute for ClimateImpact Research (PIK)Potsdam, [email protected]