Table Of ContentAssociation 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
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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
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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
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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.
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