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1、THETHIRDBRANCHOFPHYSICSEssaysonScienti¯cComputingNorbertSchÄorghoferJune26,2005Copyright°c2005byNorbertSchÄorghoferContentsAboutThisManuscriptv1AnalyticandNumericSolutions;Chaos12ThemesofNumericalAnalysis43Roundo®andNumberRepresentation104ProgrammingTools165Physic
2、sSampler216DiscreteApproximationsoftheContinuum297FromProgramstoDataAnalysis368PerformanceBasics419BytesatWork4710CountingOperations5211RandomNumbersandStochasticMethods5812Algorithms,DataStructures,andComplexity6213SymbolicComputation6814ACrashCourseonPartialDi®e
3、rentialEquations7215LessonfromDensityFunctionals79AnswerstoProblems83iiiivAboutThisManuscriptFundamentalscienti¯cdiscoverieshavebeenmadewiththehelpofcom-putationalmethodsand,undoubtedly,morearetocome.Forexample,commonalities(universality)inthebehaviorofchaoticsyst
4、emshadnotbeendiscoveredorunderstoodwithoutcomputers.Onlywithnumericalcomputationsisitpossiblepredictthemassoftheprotonsoaccuratelythatfundamentaltheoriesofmattercanbeputtotest.Andnumericsisnotonlyusedtodeterminethebindingbetweenatomsandmolecules,buthasalsoledtonew
5、quantum-mechanicalmethodsthatrevolutionizedchemistryandmaterialsscience.Suchexampleshighlighttheenormousroleofnumericalcalculationsforbasicscience.Manyresearchers¯ndthemselvesspendingmuchtimewithcomputa-tionalwork.Whiletheyaretrainedinthetheoreticalandexperimental
6、methodsoftheir¯eld,comparativelylittlematerialiscurrentlyavailableaboutthecomputationalbranchofscienti¯cinquiry.Thismanuscriptisintendedforresearchersandstudentswhoembarkonresearchinvolv-ingnumericalcomputations.Itisacollectionofconcisewritingsinthestyleofsummarie
7、s,discussions,andlectures.Itusesaninterdisciplinaryapproach,wherecomputertechnology,numericalmethodsandtheirin-terconnectionsaretreatedwiththeaimtofacilitatescienti¯cresearch.Itdescribesconceptualideasaswellaspracticalissues.Theaimwastoproduceashortmanuscriptworth
8、reading.Oftenwhenworkingonthemanuscriptitgrewshorterandshorter,bydiscardinglessrelevantmaterial.Itiswrittenwithaneyeonusefulness,longevity,andbreadth.Th