Mathematics for Industry 26 Hiromichi Itou Masato Kimura Vladimír Chalupecký Kohji Ohtsuka Daisuke Tagami Akira Takada E ditors Mathematical Analysis of Continuum Mechanics and Industrial Applications Proceedings of the International Conference CoMFoS15 Mathematics for Industry Volume 26 Editor-in-Chief MasatoWakayama(KyushuUniversity,Japan) ScientificBoardMembers RobertS.Anderssen(CommonwealthScientificandIndustrialResearchOrganisation,Australia) HeinzH.Bauschke(TheUniversityofBritishColumbia,Canada) PhilipBroadbridge(LaTrobeUniversity,Australia) JinCheng(FudanUniversity,China) MoniqueChyba(UniversityofHawaiiatMānoa,USA) Georges-Henri Cottet (Joseph Fourier University, France) JoséAlbertoCuminato(UniversityofSãoPaulo,Brazil) Shin-ichiro Ei (Hokkaido University, Japan) YasuhideFukumoto(KyushuUniversity,Japan) JonathanR.M.Hosking(IBMT.J.WatsonResearchCenter,USA) AlejandroJofré(UniversityofChile,Chile) KerryLandman(TheUniversityofMelbourne,Australia) RobertMcKibbin(MasseyUniversity,NewZealand) AndreaParmeggiani(UniversityofMontpellier2,France) JillPipher(BrownUniversity,USA) KonradPolthier(FreeUniversityofBerlin,Germany) OsamuSaeki(KyushuUniversity,Japan) WilSchilders(EindhovenUniversityofTechnology,TheNetherlands) ZuoweiShen(NationalUniversityofSingapore,Singapore) Kim-Chuan Toh (National University of Singapore, Singapore) EvgenyVerbitskiy(LeidenUniversity,TheNetherlands) NakahiroYoshida(TheUniversityofTokyo,Japan) Aims&Scope The meaning of “Mathematics for Industry” (sometimes abbreviated as MI or MfI) is different fromthatof“MathematicsinIndustry”(orof“IndustrialMathematics”).Thelatterisrestrictive:it tendstobeidentifiedwiththeactualmathematicsthatspecificallyarisesinthedailymanagement andoperationofmanufacturing.Theformer,however,denotesanewresearchfieldinmathematics thatmayserveasafoundationforcreatingfuturetechnologies.Thisconceptwasbornfromthe integrationandreorganizationofpureandappliedmathematicsinthepresentdayintoafluidand versatileformcapableofstimulatingawarenessoftheimportanceofmathematicsinindustry,as well as responding to the needs of industrial technologies. The history of this integration and reorganizationindicatesthatthisbasicideawillsomedayfindincreasingutility.Mathematicscan beakeytechnologyinmodernsociety. Theseriesaimstopromotethistrendby(1)providingcomprehensivecontentonapplicationsof mathematics, especially to industry technologies via various types of scientific research, (2) introducingbasic,useful,necessaryandcrucialknowledgeforseveralapplicationsthroughcon- crete subjects, and (3) introducing new research results and developments for applications of mathematicsintherealworld.Thesepointsmayprovidethebasisforopeninganewmathematics orientedtechnologicalworldandevennewresearchfieldsofmathematics. More information about this series at http://www.springer.com/series/13254 Hiromichi Itou Masato Kimura (cid:129) í ý Vladim r Chalupeck Kohji Ohtsuka (cid:129) Daisuke Tagami Akira Takada (cid:129) Editors Mathematical Analysis of Continuum Mechanics and Industrial Applications Proceedings of the International Conference CoMFoS15 123 Editors Hiromichi Itou KohjiOhtsuka Tokyo University of Science Hiroshima Kokusai GakuinUniversity Tokyo,Tokyo Hiroshima Japan Japan Masato Kimura Daisuke Tagami Institute of Science andEngineering Kyushu University Kanazawa University Fukuoka Kanazawa Japan Japan AkiraTakada Vladimír Chalupecký AsahiGlass Co.,Ltd. Fujitsu Ltd. Tokyo Tokyo Japan Japan ISSN 2198-350X ISSN 2198-3518 (electronic) Mathematics for Industry ISBN978-981-10-2632-4 ISBN978-981-10-2633-1 (eBook) DOI 10.1007/978-981-10-2633-1 LibraryofCongressControlNumber:2016952521 ©SpringerNatureSingaporePteLtd.2017 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 foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #22-06/08 Gateway East, Singapore 189721, Singapore Preface The international conference CoMFoS15 was held in Fukuoka, Japan, at the Nishijin Plaza of Kyushu University, November 16–18, 2015. The name “CoMFoS” is derived from the research topics called “Continuum Mechanics Focusing on Singularities.” The founding members held the first meeting, “Workshop on Fracture Criterion Viewed from Mathematics”, in Ishikawa, Japan, January 27–29, 1995, to foster research cooperation among the mathematics, computer simulation, and continuum mechanics communities. The research group subsequently organized a series of CoMFoS conferences. In 2004 those activities blossomed into the foundation of a new division under the Japan Society for Industrial and Applied Mathematics (JSIAM). Finally, in 2010, the name of the divisionwasrenamed“MathematicalSciencesonContinuumMechanics”,aimedat broader exchanges among scientists and engineers, and subsequently the division has been steadily hosting a series of CoMFoS conferences. TheCoMFoS15conferencesucceededinbringingtogetheranumberofleading scientists in the field of mathematical and computational research on continuum mechanics as well as its peripheral domains such as physics, engineering, infor- mation, and experimentation. In consequence, academic scientists provided cutting-edge mathematical descriptions of phenomena in continuum mechanics for those working in industry and, in contrast, industrial researchers offered crucial aspectsofcoremanufacturingtechnologytoacademics.Inaddition,theconference covered various technological aspects: fracture mechanics, shape optimization for product design, phenomena of earthquakes and tsunamis, viscoelasticity, materials science, interface mechanics, and industrial applications. It is a particular pleasure to shed light on the important future prospects of the fieldsdealtwithintheconference.First,severalmathematicaltechniquesdeveloped in one field are applicable in another field. The theory and techniques either on shape optimization or on eigenvalue will be applied in a wider range of industrial problems.Second,cutting-edgemathematicaltheoryandtechniqueswillcontribute to solving complex industrial problems in the near future. Several examples of complex industrial problems were discussed at the conference: (1) crack growth, propagation, or dislocation; (2) brittle, fragile, or viscoelastic behaviors of v vi Preface materials;and(3)phasetransitionorphaseseparation.Multiscaleandmultiphysics techniques, in particular, are becoming increasingly useful in industry. Third, it is important to nurture scientists and engineers who can translate from industrial problems to mathematical requirements and vice versa. We would like to thank the Institute of Mathematics for Industry (IMI) of Kyushu University for operational support for organization, and for financial sup- port of the IMI workshop of the Joint Research Projects. Tokyo, Japan, May 2016 Akira Takada On behalf of the Organizing Committee of CoMFoS15 Contents Part I Fracture Mechanics Strong but Slippery Adhesion of Mushroom-Shaped Polysaccharide Gels .... .... ..... .... .... .... .... .... ..... .... 3 Yoshimi Tanaka and Teppei Nakamichi Bridging the Scales Between Discrete and Continuum Dislocation Models... .... .... .... .... ..... .... .... .... .... .... ..... .... 15 Patrick van Meurs Phase Field Crack Growth Model with Hydrogen Embrittlement.. .... 27 Takeshi Takaishi On Singularities in 2D Linearized Elasticity.. .... .... .... ..... .... 35 Hiromichi Itou Part II Shape Optimization Two-Parameter Topological Expansion of Helmholtz Problems with Inhomogeneity. .... .... ..... .... .... .... .... .... ..... .... 51 Victor A. Kovtunenko Solution of Shape Optimization Problem and Its Application to Product Design.. .... .... ..... .... .... .... .... .... ..... .... 83 Hideyuki Azegami Shape Optimization by GJ-Integral: Localization Method for Composite Material.. .... ..... .... .... .... .... .... ..... .... 99 Kohji Ohtsuka Shape Optimization Approach by Traction Method to Inverse Free Boundary Problems .... ..... .... .... .... .... .... ..... .... 111 Shogen Shioda, Ahsani Ummi Maharani, Masato Kimura, Hideyuki Azegami and Kohji Ohtsuka vii viii Contents Part III Earthquakes and Inverse Problems Synthesis of Seismic Wave Envelopes Based on the Markov Approximation .... .... .... ..... .... .... .... .... .... ..... .... 127 Kentaro Emoto Propagation Velocity of Pulse-Like Rupture Along Earthquake Faults.... ..... .... .... .... .... .... ..... .... 143 Shiro Hirano Inverse Source Problem for a Wave Equation with Final Observation Data .. .... .... ..... .... .... .... .... .... ..... .... 153 Daijun Jiang, Yikan Liu and Masahiro Yamamoto Part IV Fluid Mechanics and Interface Dynamics The Contribution of Kawada to the Analytical Solution for the Velocity Induced by a Helical Vortex Filament and Modern Applications of Helical Vortices. .... .... .... ..... .... 167 Yasuhide Fukumoto, Valery L. Okulov and David H. Wood A New Model for Fungal Hyphae Growth Using the Thin Viscous Sheet Equations.... .... .... ..... .... .... .... .... .... ..... .... 175 Thomas de Jong, Georg Prokert and Joost Hulshof On Boundary Conditions for Hele-Shaw Problem . .... .... ..... .... 185 Hisasi Tani Part V Industrial Applications Computer Simulation of the Phase Separation of Polymeric Materials for Industrial Applications.... .... .... .... .... ..... .... 197 Takeshi Aoyagi Highly Parallel Computation of Generalized Eigenvalue Problem in Vibration for Automatic Transmission of Vehicles Using the Sakurai–Sugiura Method and Supercomputers... ..... .... 207 Takanori Ide, Yuto Inoue, Yasunori Futamura and Tetsuya Sakurai Mathematical Analysis of Synchronization from the Perspective of Network Science. .... .... ..... .... .... .... .... .... ..... .... 219 Hirotada Honda and Atusi Tani Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 229 Part I Fracture Mechanics