Singular Phenomena and Scaling in Mathematical Models PDF
Preview Singular Phenomena and Scaling in Mathematical Models
Michael Griebel Editor Singular Phenomena and Scaling in Mathematical Models Singular Phenomena and Scaling in Mathematical Models Michael Griebel Editor Singular Phenomena and Scaling in Mathematical Models 123 Editor MichaelGriebel Institutfu¨rNumerischeSimulation Universita¨tBonn Bonn Germany ISBN978-3-319-00785-4 ISBN978-3-319-00786-1(eBook) DOI10.1007/978-3-319-00786-1 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013948877 Math.Subj.Class.(2010):00B15,00A69,00A71,00A99,26A30,35A20,35B65,60J60,65N12,65Z05 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface The success of quantitative modeling in the rapidly expanding areas of the naturalsciences, such asmaterialsscience andbiology,producesa varietyofnew mathematicalmodels. The predictive power of these models has to be tested, and methodsfortheireffectivetreatmenthavetobedeveloped.Thismajoropportunity for mathematics led to the foundation of the Collaborative Research Center SFB 611 entitled ‘Singular Phenomena and Scaling in Mathematical Models’ at the University of Bonn in 2002. One of its major goals was the efficient handling of new types of models through the close combination of theoretical and numerical methods. Funded by the Deutsche Forschungsgesellschaft, we progressively integrated theoretical analysis, numerical simulation and modeling approaches for the treat- ment of singular phenomena in three consecutive phases until the end of 2012. Ourparticularprojectswerefocusedonactualappliedproblems,andwedeveloped qualitatively new and mathematically challenging methods for various problems fromthenaturalsciences. Our Collaborative Research Center was organized in the following three divi- sions ranging from stochastic and geometric analysis over nonlinear analysis and modelingtonumericalanalysisandscientificcomputation: (cid:129) PartI:ScalingLimitsofDiffusionProcessesandSingularSpaces (cid:129) Part II: Multiple Scales in Mathematical Models of Materials Science and Biology (cid:129) PartIII:NumericsforMultiscal eModelsandSingularPhenomena All the three divisions addressed, in their specific way, the key aspects of the SFB611, namely, multiple scales and model hierarchies, singularities and degeneracies and scaling laws and self-similarity. These subjects proved to be timely, challenging and at the forefront of international research. While taking on these topics, the SFB611 acted as a bridge between analysis, modeling and numericalsimulation. v vi Preface A total number of 19 principal investigators and more than 45 other scientists participatedintheresearchofthelastfundingperiodoftheSFBfrom2009to2012. Thisvolumenowcomprisesourfinalandlatestcontributionstotheexcitingfieldof ‘SingularPhenomenaandScalinginMathematicalModels’. At this place, we want to thank the Deutsche Forschungsgesellschaft and the UniversityofBonnfortheirongoingsupport. Bonn,Germany MichaelGriebel January2013 Contents PartI ScalingLimitsofDiffusionProcessesandSingular Spaces RicciBoundsforEuclideanandSphericalCones............................ 3 KathrinBacherandKarl-TheodorSturm AMonotoneApproximationtotheWassersteinDiffusion .................. 25 Karl-TheodorSturm AdaptedFunctionSpacesforDispersiveEquations.......................... 49 HerbertKoch ANoteonMetastableBehaviourintheZero-RangeProcess ............... 69 AntonBovierandRebeccaNeukirch ConvergenceoftheTwo-PointFunctionoftheStationaryTASEP......... 91 JinhoBaik,PatrikLinoFerrari,andSandrinePe´che´ PartII MultipleScalesinMathematicalModelsofMaterials ScienceandBiology VortexMotionfor the Landau-Lifshitz-GilbertEquation withAppliedMagneticField.................................................... 113 MatthiasKurzke,ChristofMelcher,andRogerMoser OnPrandtl-ReussMixtures..................................................... 133 JensFrehseandJosefMa´lek ModelingandSimulationofLipidMonolayersasSurfactant inLungAlveoli................................................................... 171 AnneleneWittenfeld,AndreyRyskin,andWolfgangAlt FluidMixturesandApplicationstoBiologicalSystems ..................... 191 HansWilhelmAltandWolfgangAlt vii viii Contents A Nested VariationalTime Discretizationfor Parametric AnisotropicWillmoreFlow ..................................................... 221 RicardoPerl,PaolaPozzi,andMartinRumpf EnergyScalingandDomainBranchinginSolid-SolidPhase Transitions........................................................................ 243 AllanChanandSergioConti PartIII Numerics for Multiscale Models and Singular Phenomena OnaMultilevelPreconditioneranditsConditionNumbers fortheDiscretizedLaplacianonFullandSparseGridsinHigher Dimensions........................................................................ 263 MichaelGriebelandAlexanderHullmann SimulationofDropletImpactwithDynamicContactAngle BoundaryConditions............................................................ 297 MichaelGriebelandMargritKlitz A Parallel Multiscale Simulation Toolbox for Coupling MolecularDynamicsandFiniteElements..................................... 327 DorianKrause,KonstantinFackeldey,andRolfKrause A Moving Least Squares Approachto the Construction ofDiscontinuousEnrichmentFunctions ...................................... 347 MarcAlexanderSchweitzerandSaWu SecondMomentAnalysisforRobinBoundaryValueProblems onRandomDomains............................................................. 361 HelmutHarbrecht SimulationofQ-TensorFieldswithConstantOrientational OrderParameterintheTheoryofUniaxialNematicLiquidCrystals..... 383 So¨renBartelsandAlexanderRaisch AFastandAccurateNumericalMethodfortheComputation ofUnstableMicromagneticConfigurations................................... 413 So¨renBartels,MarioBebendorf,andMichaelBratsch Part I Scaling Limits of Diffusion Processes and Singular Spaces
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