Association for Women in Mathematics Series Malena I. Español Marta Lewicka Lucia Scardia Anja Schlömerkemper Editors Research in Mathematics of Materials Science Association for Women in Mathematics Series Volume 31 SeriesEditor KristinLauter Facebook Seattle,WA,USA Focusingonthegroundbreakingworkofwomeninmathematicspast,present,and future,Springer’sAssociationforWomeninMathematicsSeriespresentsthelatest research and proceedings of conferences worldwide organized by the Association forWomeninMathematics(AWM).Allworksarepeer-reviewedtomeetthehighest standardsofscientificliterature,whilepresentingtopicsatthecuttingedgeofpure and applied mathematics, as well as in the areas of mathematical education and history. Since its inception in 1971, The Association for Women in Mathematics has been a non-profit organization designed to help encourage women and girls to study and pursue active careers in mathematics and the mathematical sciences and to promote equal opportunity and equal treatment of women and girls in the mathematical sciences. Currently, the organization represents more than 3000 members and 200 institutions constituting a broad spectrum of the mathematical communityintheUnitedStatesandaroundtheworld. TitlesfromthisseriesareindexedbyScopus. Malena I. Español (cid:129) Marta Lewicka (cid:129) Lucia Scardia (cid:129) Anja Schlömerkemper Editors Research in Mathematics of Materials Science Editors MalenaI.Español MartaLewicka SchoolofMathematicalandStatistical MathematicsDepartment Sciences UniversityofPittsburgh ArizonaStateUniversity Pittsburgh,PA,USA Tempe,AZ,USA LuciaScardia AnjaSchlömerkemper DepartmentofMathematics InstituteofMathematics Heriot-WattUniversity UniversitätWürzburg Edinburgh,UK Würzburg,Germany ISSN2364-5733 ISSN2364-5741 (electronic) AssociationforWomeninMathematicsSeries ISBN978-3-031-04495-3 ISBN978-3-031-04496-0 (eBook) https://doi.org/10.1007/978-3-031-04496-0 Mathematics Subject Classification: 35Qxx, 49Jxx, 49Nxx, 49Sxx, 70Bxx, 70Cxx, 70Exx, 70Fxx, 70Hxx,70Jxx,70Kxx,70Lxx,70Qxx,74Bxx,74Cxx,74Dxx,74Hxx,74Jxx,74Kxx,74Nxx,74Pxx, 74Qxx,74Rxx,74Sxx ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Materialsscienceisaninterdisciplinaryresearchfieldthatincorporatestheanalyti- calandexperimentaltechniquesofengineering,physics,andchemistry.Itsgoalisto develop a comprehensive understanding of material characteristics and properties, andtogainadeeperinsightintothematerialbehavioracrossseverallengthscales, from atomistic to macroscopic. Such insight is key to the design and discovery of new materials, as well as to the development of new technologies. In this context, Research in Mathematics of Materials Science seeks to provide a rigorous basis for future technological advances by developing tools for the accurate modeling of multi-scale phenomena. In the past decades, this field has seen rapid progress with an impressive level of success. Mathematics and materials science have thus developedstrongtiesandformedapartnershipofmutualbenefit. ThisAWMSpringerVolumehighlightscontributionsofwomenmathematicians in the study of complex materials. The collected papers are both original research and reviews. The featured topics and methods draw on the fields of calculus of variations, partial differential equations, functional analysis, differential geometry andtopology,aswellasnumericalanalysisandmathematicalmodelling.Areasof applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homoge- nization,crystallization,graingrowth,andphase-fieldmodels. We hope that gathering such multifaceted scientific output in a single volume will facilitate knowledge exchange and help to identify new research problems. A parallelgoalistogivevisibilitytotheresultsofwomenresearchers,andultimately helpaddressthegendergapinmathematicsandscience. Tempe,AZ,USA MalenaI.Español Pittsburgh,PA,USA MartaLewicka Edinburgh,UK LuciaScardia Würzburg,Germany AnjaSchlömerkemper December2021 v Acknowledgements We express gratitude to the authors who contributed their manuscripts and to the refereeswhoprovidedvaluablefeedback.Allarticlesinthisvolumehavebeenpeer reviewed.AnacknowledgmentextendstoKristinLauter,editoroftheAWMSeries, for the opportunity of publishing this volume, and to Saveetha Balasundaram, our editoratSpringer,forherguidancealongtheway. vii Contents PartI ResearchPapers InteractionBetweenOscillationsandSingularPerturbationsina One-DimensionalPhase-FieldModel.......................................... 3 Annika Bach, Teresa Esposito, Roberta Marziani, andCaterinaIdaZeppieri GrainGrowthandtheEffectofDifferentTimeScales...................... 33 Katayun Barmak, Anastasia Dunca, Yekaterina Epshteyn, Chun Liu, andMasashiMizuno RegularityofMinimizersforaGeneralClassofConstrained Energies in Two-Dimensional Domains with Applications to LiquidCrystals................................................................... 59 PatriciaBaumanandDanielPhillips OnSomeModelsinRadiationHydrodynamics .............................. 79 XavierBlanc,BernardDucomet,andŠárkaNecˇasová Poro-Visco-ElasticityinBiomechanics:OptimalControl ................... 103 LorenaBociuandSarahStrikwerda Global Gradient EstimateforaDivergence Problem and Its ApplicationtotheHomogenizationofaMagneticSuspension ............. 133 ThuyenDang,YuliyaGorb,andSilviaJiménezBolaños OnStaticandEvolutionaryHomogenizationinCrystalPlasticity forStratifiedComposites........................................................ 159 ElisaDavoliandCarolinKreisbeck On the Prescription of Boundary Conditions for Nonlocal Poisson’sandPeridynamicsModels ........................................... 185 MartaD’EliaandYueYu ix x Contents ExistenceofGlobalSolutionsfor2DFluid–ElasticInteraction withSmallData .................................................................. 209 KarolineDisserandMichelleLuckas DoublyNonlocalCahn–HilliardEquations................................... 239 MikilD.Foss,PetronelaRadu,andLauraWhite 3DImage-BasedStochasticMicro-structureModellingofFoams forSimulatingElasticity......................................................... 257 AnneJung,ClaudiaRedenbach,KatjaSchladitz,andSarahStaub Machine Learning for Failure Analysis: A Mathematical ModellingPerspective ........................................................... 283 JudithPérez-Velázquez,MeltemGölgeli,andCarlosAlfonsoRuizGuido InvertibilityofOrlicz–SobolevMaps .......................................... 297 GiovanniScillaandBiancaStroffolini GlobalExistenceofSolutionsfortheOne-DimensionalResponse ofViscoelasticSolidsWithintheContextofStrain-LimitingTheory...... 319 YaseminS¸engül GENERICforDissipativeSolidswithBulk–InterfaceInteraction......... 333 MaritaThomasandMartinHeida PartII ReviewPapers PhaseSeparationinHeterogeneousMedia.................................... 367 RiccardoCristoferi,IreneFonseca,andRaghavendraVenkatraman Some Recent Results on 2D Crystallization for Sticky Disc ModelsandGeneralizationsforSystemsofOrientedParticles............. 383 LuciaDeLuca PatternFormationforNematicLiquidCrystals—Modelling, Analysis,andApplications...................................................... 399 YucenHanandApalaMajumdar OnApplicationsofHerglotz-NevanlinnaFunctionsinMaterial Sciences,I:ClassicalTheoryandApplicationsofSumRules .............. 433 AnnemarieLugerandMiao-JungYvonneOu OnApplicationsofHerglotz–NevanlinnaFunctionsinMaterial Sciences,II:ExtendedApplicationsandGeneralizedTheory .............. 461 Miao-JungYvonneOuandAnnemarieLuger RigidityandFlexibilityintheModellingofShape-MemoryAlloys........ 501 AngkanaRüland About the Editors Malena I. Español is an Argentine-American applied mathematician specializing in numerical analysis and numerical linear algebra. Her research involves devel- oping, analyzing, and applying mathematical models andnumericalmethodstoproblemsarisinginmaterials scienceandimageprocessing.Sheisafacultymember in the School of Mathematical and Statistical Sciences atArizonaStateUniversity,USA. Marta Lewicka is a mathematician specializing in analysis and PDEs. She has contributed results in the theory of nonlinear elasticity, hyperbolic systems of conservation laws, fluid dynamics, calculus of varia- tions, potential theory, and differential games. She is a fellowoftheAmericanMathematicalSocietyandholds Professor’s scientific title awarded by the President of theRepublicofPoland.SheworksattheUniversityof Pittsburgh,USA. xi