Mathematical and Computational Approaches in Advancing Modern Science and Engineering

777 Pages·2016·22.89 MB·English

by  Jacques Bélair

Jacques Bélair · Ian A. Frigaard
Herb Kunze · Roman Makarov
Roderick Melnik · Raymond J. Spiteri Editors
Mathematical
and Computational
Approaches
in Advancing
Modern Science
and Engineering
Mathematical and Computational Approaches in
Advancing Modern Science and Engineering

Jacques Bélair (cid:129) Ian A. Frigaard (cid:129) Herb Kunze
Roman Makarov (cid:129) Roderick Melnik
Raymond J. Spiteri
Editors
Mathematical and
Computational Approaches
in Advancing Modern
Science and Engineering
123
Editors
JacquesBélair IanA.Frigaard
DepartmentofMathematicsandStatistics DepartmentofMathematics
UniversityofMontreal UniversityofBritishColumbia
Montreal,QC Vancouver,BC
Canada Canada
HerbKunze RomanMakarov
DepartmentofMathematicsandStatistics DepartmentofMathematics
UniversityofGuelph WilfridLaurierUniversity
Guelph,ON Waterloo,ON
Canada Canada
RoderickMelnik RaymondJ.Spiteri
MS2DiscoveryInstitute DepartmentofComputerScience
WilfridLaurierUniversity UniversityofSaskatchewan
Waterloo,ON Saskatoon,SK
Canada Canada
ISBN978-3-319-30377-2 ISBN978-3-319-30379-6 (eBook)
DOI10.1007/978-3-319-30379-6
LibraryofCongressControlNumber:2016943639
Mathematics Subject Classification (2010): 00A69, 00A71, 00A79, 92-XX, 35Qxx, 81T80, 97M10,
47N60,49-xx,91Axx,62Pxx,97Pxx,70-xx
©SpringerInternationalPublishingSwitzerland2016
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland
Preface
This book consists of five parts covering a wide range of topics in applied
mathematics,modeling,andcomputationalscience(AMMCS).Itresultedfromtwo
highlysuccessfulmeetingsheldjointlyin Waterloo(Canada)onthe maincampus
ofWilfridLaurierUniversity.ItistheoldestuniversityintheCambridge-Kitchener-
Waterloo-Guelpharea,abeautifulpartofCanada,justwestofthecityofToronto.
The main campus of the university is located in a comfortable driving distance
fromsomeofNorthAmerica’smostspectaculartouristdestinations,includingthe
NiagaraEscarpment,aUNESCOWorldBiosphereReserve.Overtheyears,thisuni-
versityhasbecomeatraditionalvenuefortheInternationalConferenceonApplied
Mathematics,ModelingandComputationalScience,andin2015itwasheldjointly
with the annual meeting of the Canadian Applied and Industrial Mathematics
(CAIMS)fromJune7–12,2015.TheAMMCSinterdisciplinaryconferenceseries
runs biannually. Focusing on recent advances in applied mathematics, modeling,
andcomputationalscience,the2015AMMCS-CAIMSCongressdrewsomeofthe
topscientists,mathematicians,engineers,andindustrialistsfromallovertheworld
andwasatruecelebrationofinterdisciplinaryresearchandcollaborationinvolving
mathematical, statistical, and computational sciences within a larger international
community.
The book clearly demonstrates the importance of interdisciplinary interactions
between mathematicians,scientists, engineers,and representativesfromother dis-
ciplines. It is a valuable source of the methods, ideas, and tools of mathematical
modeling,computationalscience,andappliedmathematicsdevelopedforavariety
of disciplines, including natural and social sciences, medicine, engineering, and
technology. Original results are presented here on both fundamental and applied
levels,withanamplenumberofexamplesemphasizingtheinterdisciplinarynature
anduniversalityofmathematicalmodeling.
The book contains 70 articles, arranged according to the following topics
representedbyfiveparts:
(cid:129) Theory and Applications of Mathematical Models in Physical and Chemical
Sciences
v
vi Preface
Fig.1 Participantsofthe2015InternationalAMMCS-CAIMSCongress,Canada(Phototakenby
TomaszAdamskiontheWaterlooCampusatWilfridLaurierUniversity)
(cid:129) MathematicalandComputationalMethodsinLifeSciencesandMedicine
(cid:129) ComputationalEngineeringandMathematicalFoundation,NumericalMethods,
andAlgorithms
(cid:129) MathematicsandComputationinFinance,Economics,andSocialSciences
(cid:129) New Challenges in Mathematical Modeling for Scientific and Engineering
Applications
These chapters are based on selected refereed contributions made by the
participants of both meetings. The AMMCS-CAIMS Congress featured over 30
special and contributed sessions with mini-symposia ranging from mathematical
modelsinnanoscienceandnanotechnologytostatisticalequilibriumineconomics
andtomathematicalneuroscience,theembeddedConferenceoftheComputational
FluidDynamicsSocietyofCanada,andthe2ndCanadianSymposiumonScientific
Computing and Numerical Analysis, as well as larger sessions around such sci-
entific themesas appliedanalysis and dynamicalsystems, industrialmathematics,
mathematicalbiology,financialmathematics,andmuchmore.Over600participants
from all continents attended the Congress and shared the latest achievements,
ideas, insights, and theories about modern problems in science, engineering, and
society that can be approachedwith new advancesin mathematicalmodeling and
mathematical,computational,andstatisticalmethods.
This book presents a selected sample of the above topics and can serve as a
referencetosomeofthestate-of-the-artoriginalworksonarangeofsuchtopics.It
Preface vii
Fig.2 Members of thelocal organizing committeeand student volunteers (Photo taken byDr.
ShyamBaduontheWaterlooCampusatWilfridLaurierUniversity)
has a strong multidisciplinary focus, supported by fundamentaltheories, rigorous
procedures, and examples from applications. Furthermore, the book provides a
multitude of examples accessible to graduate students and can serve as a source
forgraduatestudentprojects.
Takingthisopportunity,wewouldliketothankourcolleaguesontheAMMCS-
CAIMSCongressorganizingteam,aswellasoursponsorsandpartners,inparticu-
lartheFieldsInstituteandPIMS,andtheCentredeRecherchesMathématiques,as
wellasWilfridLaurierUniversity,NSERC,andtheGovernmentofOntario.Among
others, traditional supporters of the AMMCS Interdisciplinary Conference series
wereMaplesoftandSHARCNET,aswellasSpringer,DeGruyter,andCRCPress.
The Congress was held under the auspices of the MS2DiscoveryInterdisciplinary
Research Institute based at Wilfrid Laurier University and in cooperation with
the Society of Industrial and Applied Mathematics and the American Institute of
MathematicalSciences.
The Congress scientific committee included 15 internationally known
researchers.We wouldlike to thankthem,aswellas theCongressrefereeswhose
help in the refereeing process was invaluable. Among them we had some of the
leadingresearchersfromallpartsoftheworld,andtheirassistancewasdecisivein
completingthisproject.Ourtechnicalsupportcommitteeandstudents’teamwere
exemplary, and we are truly grateful for their efforts. Last but not least, we are
viii Preface
alsogratefultotheeditorialteamatSpringer,inparticularMartinPetersandRuth
Allewelt, whose continuous support during the entire process was at the highest
professionallevel.
We believe that the book will be a valuable addition to the libraries, as well
as to private collections of university researchers and industrialists, scientists and
engineers, graduate students, and all of those who are interested in the recent
progressinmathematicalmodelingandmathematical,computational,andstatistical
methodsappliedininterdisciplinarysettings.
Montreal,Canada JacquesBélair
Vancouver,Canada IanFrigaard
Guelph,Canada HerbKunze
Waterloo,Canada RomanMakarov
Waterloo,Canada RoderickMelnik
Saskatoon,Canada RaymondSpiteri
Contents
PartI TheoryandApplicationsofMathematicalModels
inPhysicalandChemicalSciences
CompressibilityCoefficientsinNonlinearTransportModels
inUnconventionalGasReservoirs ............................................. 3
IftikharAli,BilalChanane,andNadeemA.Malik
Solutions of Time-Fractional Diffusion Equation
withReflectingandAbsorbingBoundaryConditionsUsingMatlab ...... 15
IftikharAli,NadeemA.Malik,andBilalChanane
HomoclinicStructureforaGeneralizedDavey-StewartsonSystem ....... 27
CeniBabaogluandIrmaHacinliyan
NumericalSimulationsofthe DynamicsofVortexRossby
WavesonaBeta-Plane........................................................... 35
L.J.Campbell
OntheProblemofSimilar MotionsofaChainofCoupled
HeavyRigidBodies .............................................................. 47
DmitriyChebanov
OnStabilizationofanUnbalancedLagrangeGyrostat...................... 59
DmitriyChebanov,NataliaMosina,andJoseSalas
ApproximateSolutionofSomeBoundaryValue Problems
ofCoupledThermo-Elasticity .................................................. 71
MananaChumburidze
Symmetry-Breaking Bifurcations in Laser Systems
withAll-to-AllCoupling......................................................... 81
JuanchoA.Collera
ix