Integral Methods in Science and Engineering: Theoretical and Computational Advances

706 Pages·2015·9.945 MB·English

by  Christian Constanda, Andreas Kirsch (eds.)

Christian Constanda
Andreas Kirsch
Editors
Integral Methods
in Science and
Engineering
Theoretical and Computational
Advances

Christian Constanda • Andreas Kirsch
Editors
Integral Methods in Science
and Engineering
Theoretical and Computational Advances
Editors
ChristianConstanda AndreasKirsch
DepartmentofMathematics DepartmentofMathematics
TheUniversityofTulsa KarlsruheInstituteofTechnology
Tulsa,OK,USA Karlsruhe,Germany
ISBN978-3-319-16726-8 ISBN978-3-319-16727-5 (eBook)
DOI10.1007/978-3-319-16727-5
LibraryofCongressControlNumber:2015949822
MathematicsSubjectClassification(2010):00B25,35-06,41-06,44-06,45-06,65-06,76-06,86-06,
86A10
SpringerChamHeidelbergNewYorkDordrechtLondon
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Preface
Since 1985, the international conferences on Integral Methods in Science and
Engineering (IMSE) have brought together researchers in various theoretical and
applied areas, whose work makes use, in one form or another, of integration tech-
niques. This type of mathematical procedures are efficient, elegant, and powerful
intheirdiversity,offeringacommongroundto,andservingasalinchpinbetween,
manyareasofacademicendeavor.
The first 12 IMSE conferences took place in a variety of venues all over the
world:
1985,1990: UniversityofTexas–Arlington,USA;
1993: TohokuUniversity,Sendai,Japan;
1996: UniversityofOulu,Finland;
1998: MichiganTechnologicalUniversity,Houghton,MI,USA;
2000: Banff,AB,Canada(organizedbytheUniversityofAlberta,Edmonton);
2002: UniversityofSaint-Étienne,France;
2004: UniversityofCentralFlorida,Orlando,FL,USA;
2006: NiagaraFalls,ON,Canada(organizedbytheUniversityofWaterloo);
2008: UniversityofCantabria,Santander,Spain;
2010: UniversityofBrighton,UK;
2012: BentoGonçalves,Brazil(organizedbytheFederalUniversityofRioGrande
doSul).
The 2014 meeting, hosted by Karlsruhe Institute of Technology, July 21–25,
and attended by participants from 11 countries on 4 continents, continued and
strengthened the well-established IMSE reputation as an important international
forum where scientists and engineers from all over the world have a fruitful and
stimulatingexchangeofnovelresearchideasandprojects.
IMSE 2014 was, as expected, organized to a very high standard, and the
participantswishtothankDeutscheForschungsgemeinschaftandtheDepartmentof
v
vi Preface
MathematicsatKarlsruheInstituteofTechnologyfortheirfinancialsupport.Special
thanksareduetothemembersoftheLocalOrganizingCommittee:
AndreasKirsch(KarlsruheInstituteofTechnology),Chairman,
TiloArens(KarlsruheInstituteofTechnology),
FrankHettlich(KarlsruheInstituteofTechnology).
A new feature of IMSE 2014 was the inclusion of three minisymposia—on
AsymptoticAnalysis:HomogenizationandThinStructures,WavePhenomena,and
InverseProblems.
ThenextIMSEconferencewillbehostedbytheUniversityofPadova,Italy,in
July2016.Furtherdetailswillbepostedinduecourseontheconferencewebsite.
The peer-reviewed chapters of this volume, arranged alphabetically by first
author’s name, are based on 58 papers from among those presented in Karlsruhe.
The editors would like to thank the staff at Birkhäuser for their courteous and
professionalhandlingofthepublicationprocess.
Tulsa,OK,USA ChristianConstanda
January2015
TheInternationalSteeringCommitteeofIMSE:
C.Constanda(TheUniversityofTulsa),Chairman
B.Bodmann(FederalUniversityofRioGrandedoSul)
H.deCamposVelho(INPE,SaõJosédosCampos)
P.J.Harris(UniversityofBrighton)
A.Kirsch(KarlsruheInstituteofTechnology)
M.LanzadeCristoforis(UniversityofPadova)
S.Mikhailov(BrunelUniversity)
D.Mitrea(UniversityofMissouri-Columbia)
M.Mitrea(UniversityofMissouri-Columbia)
D.Natroshvili(GeorgianTechnicalUniversity)
M.E.Pérez(UniversityofCantabria)
O.Shoham(TheUniversityofTulsa)
I.W.Stewart(UniversityofStrathclyde)
Contents
1 SolvabilityofaNonstationaryProblemofRadiative–Conductive
HeatTransferinaSystemofSemi-transparentBodies................ 1
A.Amosov
1.1 Introduction........................................................... 1
1.2 PhysicalStatementoftheProblem.................................. 1
1.3 BoundaryValueProblemfortheRadiativeTransfer
EquationwithReflectionandRefractionConditions............... 3
1.3.1 SomeNotationsandFunctionSpaces ..................... 4
1.3.2 BoundaryOperators........................................ 5
1.3.3 StatementoftheReflectionandRefractionConditions... 8
1.3.4 Boundary Value Problem for Radiative
Transfer Equation with Reflection and
RefractionConditions...................................... 9
1.4 MathematicalStatementoftheProblemandMainResults........ 10
References.................................................................... 13
2 TheNonstationaryRadiative–ConductiveHeatTransfer
Problem in a Periodic System of Grey Heat Shields.
SemidiscreteandAsymptoticApproximations.......................... 15
A.Amosov
2.1 Introduction........................................................... 15
2.2 Statement and Some Properties
of the Radiative–Conductive Heat Transfer
ProbleminaPeriodicSystemofGreyShields ..................... 16
2.2.1 PhysicalStatementoftheProblem ........................ 16
2.2.2 Well-KnownAsymptoticApproximations ................ 17
2.2.3 MathematicalStatementoftheOriginalProblem......... 18
2.3 SemidiscreteApproximations ....................................... 19
2.3.1 Grids,GridFunctions,andGridoperators ................ 19
2.3.2 TheBasicSemidiscreteProblem .......................... 20
vii
viii Contents
2.3.3 TheFirstSemidiscreteProblem............................ 21
2.3.4 TheSecondSemidiscreteProblem ........................ 21
2.4 AsymptoticApproximations......................................... 23
2.4.1 TheFirstHomogenizedProblem .......................... 23
2.4.2 TheSecondHomogenizedProblem ....................... 23
2.5 SemidiscreteProblems.ExistenceandUniqueness
ofaSolution.APrioriEstimatesforSolutions..................... 24
2.6 ErrorEstimatesforSolutionstoSemidiscreteProblems........... 24
2.7 HomogenizedProblems.ExistenceandUniqueness
ofaSolution.APrioriEstimatesandComparisonTheorem....... 25
2.8 ErrorEstimatesforSolutionstotheHomogenizedProblems...... 26
References.................................................................... 27
3 AMixedImpedanceScatteringProblemforPartially
CoatedObstaclesinTwo-DimensionalLinearElasticity............... 29
C.E.Athanasiadis,D.Natroshvili,V.Sevroglou,
andI.G.Stratis
3.1 Introduction........................................................... 29
3.2 TheDirectScatteringProblem ...................................... 30
3.3 TheInverseScatteringProblem ..................................... 33
References.................................................................... 41
4 Half-Life Distribution Shift of Fission Products by
CoupledFission–FusionProcesses........................................ 43
J.B.Bardaji,B.E.J.Bodmann,M.T.Vilhena,
andA.C.M.Alvim
4.1 Introduction........................................................... 43
4.2 TheCoulombBarrier................................................. 45
4.3 ParticleStoppinginNuclearFuel ................................... 47
4.4 FusionFollowingFission............................................ 50
4.5 Conclusions........................................................... 53
References.................................................................... 54
5 DRBEM Simulation on Mixed Convection
withHydromagneticEffect................................................ 57
C.Bozkaya
5.1 Introduction........................................................... 57
5.2 ProblemFormulationandGoverningEquations.................... 58
5.3 MethodofSolution................................................... 61
5.4 NumericalResultsandDiscussion .................................. 63
5.5 Conclusions........................................................... 67
References.................................................................... 68
Contents ix
6 NonlinearMethodofReductionofDimensionalityBased
onArtificialNeuralNetworkandHardwareImplementation ........ 69
J.R.G.Braga,V.C.Gomes,E.H.Shiguemori,H.F.C.Velho,
A.Plaza,andJ.Plaza
6.1 Introduction........................................................... 69
6.2 Methodology ......................................................... 70
6.2.1 PrincipalComponentAnalysis............................. 70
6.2.2 ArtificialNeuralNetwork.................................. 71
6.2.3 Self-AssociativeArtificialNeuralNetwork ............... 72
6.2.4 Multi-ParticleCollisionAlgorithm........................ 73
6.3 Results ................................................................ 74
6.3.1 ExecutionofNLPCAinHardware ........................ 76
6.4 Conclusions........................................................... 78
References.................................................................... 78
7 OntheEigenvaluesofaBiharmonicSteklovProblem................. 81
D.BuosoandL.Provenzano
7.1 Introduction........................................................... 81
7.2 AsymptoticBehaviorofNeumannEigenvalues.................... 83
7.3 IsovolumetricPerturbations.......................................... 84
7.4 TheIsoperimetricInequality......................................... 86
References.................................................................... 88
8 ShapeDifferentiabilityoftheEigenvaluesofEllipticSystems ........ 91
D.Buoso
8.1 AnalyticityResults................................................... 93
8.2 IsovolumetricPerturbations.......................................... 95
References.................................................................... 97
9 Pollutant Dispersion in the Atmosphere: A Solution
ConsideringNonlocalClosureofTurbulentDiffusion ................. 99
D.Buske,M.T.B.Vilhena,B.E.J.Bodmann,R.S.Quadros,
andT.Tirabassi
9.1 Introduction........................................................... 99
9.2 TheAdvection-DiffusionEquationandthe3D-GILTTMethod... 100
9.3 TurbulentParameterization .......................................... 104
9.4 ApplicationtoaMeteorologicalScenario........................... 106
9.5 Conclusions........................................................... 107
References.................................................................... 108
10 The Characteristic Matrix of Nonuniqueness
forFirst-KindEquations .................................................. 111
C.ConstandaandD.R.Doty
10.1 Introduction........................................................... 111
10.2 PlaneElasticStrain................................................... 112
10.3 NumericalExamples................................................. 115
References.................................................................... 117