Integral Methods in Science and Engineering: Applications in Theoretical and Practical Research

361 Pages·2022·8.777 MB·English

by  Christian Constanda, Bardo E.J. Bodmann, Paul J. Harris

Christian Constanda
Bardo E. J. Bodmann
Paul J. Harris
Editors
Integral Methods
in Science and
Engineering
Applications in Theoretical
and Practical Research

Christian Constanda • Bardo E. J. Bodmann (cid:129)
Paul J. Harris
Editors
Integral Methods in Science
and Engineering
Applications in Theoretical and Practical
Research
Editors
ChristianConstanda BardoE.J.Bodmann
DepartmentofMathematics EngineeringSchool
TheUniversityofTulsa FederalUniversityofRioGrandedoSul
Tulsa,OK,USA PortoAlegre,RioGrandedoSul,Brazil
PaulJ.Harris
DepartmentofMathematics
UniversityofBrighton
Brighton,UK
ISBN978-3-031-07170-6 ISBN978-3-031-07171-3 (eBook)
https://doi.org/10.1007/978-3-031-07171-3
MathematicsSubjectClassification:45Exx,45E10,65R20,45D05
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Preface
The international conferences on Integral Methods in Science and Engineering
(IMSE) started in 1985 at the University of Texas–Arlington, and continued
bienniallyinavarietyofvenuesaroundtheworld,bringingtogetherspecialistswho
employintegrationtechniquesasessentialtoolsintheirresearch.Theseprocedures
exhibitgenerality,elegance,andefficiency,allofwhichareessentialingredientsin
theworkofawidecategoryofpractitioners.
Thedatesandvenuesofthefirst15IMSEconferencesarelistedbelow.
1985,1990:UniversityofTexas–Arlington,TX,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: Bento Gonçalves, Brazil (organized by the Federal University of Rio
GrandedoSul)
2014:KarlsruheInstituteofTechnology,Germany
2016:UniversityofPadova,Italy
2018:UniversityofBrighton,UK
Duetotheunfavorableworldhealthconditions,the2020conference,scheduled
to be held at the Steklov Mathematical Institute in St. Petersburg, Russia, had to
be postponed. However, as an intermediate solution, a Symposium on the Theory
and Applications of Integral Methods in Scientific Research was held online in
July 2021. By making public their latest results, the participants in this event, all
withlong-standingIMSEcredentials,havekepttheflamesofourcommonresearch
interests burning bright, in anticipation of the more inclusive in-person meeting
expectedtotakeplace,asplanned,inSt.Petersburginthesummerof2022.
v
vi Preface
The peer-reviewed chapters of this volume, arranged alphabetically by first
author’s name, consist of 22 of the papers presented at the 2021 symposium. The
editors would like to thank the reviewers for their help, Christopher Tominich at
Birkhäuser–New York for his support of this project, and Saveetha Balasundaram
and her production team for their courteous and professional handling of the
publicationprocess.
Tulsa,OK,USA ChristianConstanda
PortoAlegre,Brazil BardoE.J.Bodmann
Brighton,UK PaulJ.Harris
January2022
The International Steering Committee
of IMSE
Christian Constanda (The University of Tulsa), Chairman; Bardo E.J. Bodmann
(FederalUniversityofRioGrandedoSul);PaulJ.Harris(UniversityofBrighton);
MirelaKohr(Babes–BolyaiUniversityofCluj–Napoca);MassimoLanzadeCristo-
foris(UniversityofPadova);SergeyMikhailov(BrunelUniversityLondon);Dorina
Mitrea (Baylor University); Marius Mitrea (Baylor University); David Natroshvili
(Georgian Technical University); Maria Perel (St. Petersburg State University);
Maria Eugenia Pérez–Martínez (University of Cantabria); Ovadia Shoham (The
UniversityofTulsa).
vii
Contents
1 ApproximateSolutionforOne-DimensionalCompressible
Two-PhaseImmiscibleFlowinPorousMediaforVariable
BoundaryConditions ...................................................... 1
W.Q.Barros,A.P.Pires,andÁ.M.M.Peres
2 On Pseudo-Cross Sections for Neutron Escape from a
DomainbyaPhysicalMonteCarloSimulation......................... 19
D.G.Benvenutti,L.F.F.C.Barcellos,andB.E.J.Bodmann
3 From a Unitary Symmetry Hypothesis to Dynamical
StructuresinQuantumMechanicsModels.............................. 35
B.E.J.Bodmann
4 TheTractionBoundaryValueProblemforThinElasticStructures.. 51
C.ConstandaandD.Doty
5 MappingPropertiesofPotentialOperatorsRelatedtothe
2DCompressibleStokesSysteminWeightedSobolevSpaces......... 67
M.A.DagnawandC.Fresneda-Portillo
6 Stochastic Effects of the Meander on the Dispersion of
PollutantsinthePlanetaryBoundaryLayerUnderLow
WindConditions............................................................ 85
C.Fávero,G.A.Gonçalves,D.Buske,andR.S.Quadros
7 Asymptotics for the Spectrum of a Floquet-Parametric
Family of Homogenization Problems Associated with a
DirichletWaveguide........................................................ 95
D.Gómez,S.A.Nazarov,R.Orive-Illera,andM.-E.Pérez-Martínez
8 TheWavelet-BasedIntegralFormulafortheSolutionsofthe
WaveEquationinanInhomogeneousMedium:Convergence
ofIntegrals .................................................................. 113
E.A.GorodnitskiyandM.V.Perel
ix
x Contents
9 ModellingtheSpreadofaDiseaseinanEpidemicThrough
aCountryDividedintoGeographicalRegions.......................... 127
P.J.HarrisandB.E.J.Bodmann
10 ComputingElasticInteriorTransmissionEigenvalues................. 139
A.KleefeldandM.Zimmermann
11 ANovelSolutionoftheMulti-GroupNeutronDiffusion
EquationbytheHankelTransformFormalism......................... 157
R.A.S.KleinandJ.C.L.Fernandes
12 ASimple Numerical Scheme toObtainReflectivity and
TransmissivityofanIsotropicallyScatteringSlab...................... 169
C. A. Ladeia, H. R. Zanetti, D. L. Gisch, M. Schramm,
andJ.C.L.Fernandes
13 A Unified Integral Equation Formulation for Linear
and Geometrically Nonlinear Analysis of Thick Plates:
DerivationofEquations.................................................... 179
R.J.Marczak
14 OnViscousFluidFlowinCurvilinearCoordinateSystems ........... 197
A.Meneghetti,B.E.J.Bodmann,andM.T.M.B.Vilhena
15 Impact Loading of Interface Cracks: Effects of Cracks
ClosureandFriction ....................................................... 213
O.Menshykov,M.Menshykova,andI.A.Guz
16 PeriodicSolutionsinRn forStationaryAnisotropicStokes
andNavier-StokesSystems................................................ 227
S.E.Mikhailov
17 Null-SolutionsofEllipticPartialDifferentialEquationswith
PowerGrowth............................................................... 245
D.Mitrea,I.Mitrea,andM.Mitrea
18 OntheUseoftheAdjointTechniquetotheEstimationof
NeutronSourceDistributionsintheContextofSubcritical
NuclearReactors ........................................................... 261
L.R.C.MoraesandR.C.Barros
19 The Nodal LTS Solution and a New Approach to
N
DeterminetheOutgoingAngularFluxattheBoundaryina
RectangularDomain ....................................................... 277
A.R.Parigi,C.F.Segatto,B.E.J.Bodmann,andF.C.daSilva
20 A Numerical Study of the Convergence of Two Hybrid
ConvolutionQuadratureSchemesforBroadbandWaveProblems... 291
J.RowbottomandD.J.Chappell
Contents xi
21 Analytical Reconstruction of the Nonlinear Transfer
FunctionforaWiener–HammersteinModel............................ 307
J.Schmith,A.SchuckJr.,B.E.J.Bodmann,andP.J.Harris
22 Variation of Zero-Net Liquid Holdup in Gas–Liquid
CylindricalCyclone(GLCC©)............................................ 323
M.Shah,H.Zhao,R.Mohan,andO.Shoham
23 OntheMono-EnergeticNeutronSpaceKineticsEquationin
CartesianGeometry:AnAnalyticSolutionbyaSpectralMethod ... 343
F.Tumelero,M.T.Vilhena,andB.E.J.Bodmann
Index............................................................................... 359