物理中三個(gè)逆問題的多種嚴(yán)格解方法的探求研究及具體實(shí)現(xiàn).pdf

1、復(fù)旦大學(xué)博士學(xué)位論文物理中三個(gè)逆問題的多種嚴(yán)格解方法的探求研究及具體實(shí)現(xiàn)姓名：溫濤申請學(xué)位級別：博士專業(yè)：理論物理指導(dǎo)教師：戴顯熹2001.4.1————塑型塵竺些型些塑蘭!!!蘭堡堅(jiān)塑!：塑叢查絲塾笪璺塑L—————————一AbstractAsanimportantpartofphysics，inverseproblemisrelatedwithltssomeimportantdevelopmentsManyphysicistsha

2、vepaidattentiontothespecificheat—phononspectruminversionDrobleIn(SPl)fortenyearsbecauseoftheneedforstudyingthemechanismofHighTernperatureSuperconductivityThoughtheexactformulaoftheinverseproblemwasdevelopedatthattinlet11

3、einversionresultscouldn’ibeobtainedbyitinpracticeTherearemanydifficultiessuchasthei一posedproblem，theincompletenessofdataetal，whichblocktheimplementationoftheinverseproblemTheyalsoexistinsomeotherinverseproblemsOneofourob

4、jectsistea】izeaconcreteinverseproblem(SPI)byconqueringmanyproblemsinprincipleandinpracticeAccordingtotheexactinversionformulawitheliminatingdivergenceparameterinSPI，theuniqueexistencetheoremwasstudiedanddevelopedThecondi

5、tionofuniqueexistencetheoremcouldn’tbesatisfied，whichresultsinthatsomemethodscouldn’tobtainthecorrectinversionresultsinconcreteproblemsWedevelopedtheasymptoticbehaviorcontroltheory(ABe)，anditisprovedtobehighlyeffectivein

6、practiceTheuniversalfunctionsetmethod(UFS)isdevelopedbyselectingpropercompletesetwhichsatisfiestheasymptoticbehaviornaturallyItisthefirsttimethataphononspectrumofYBCOisobtainedfromitsexperimentalspecificheatdatabyUFSmeth

7、odandtheresultsarecomparabletothatfromneutroninelasticscatteringWealsodevelopedanotherexactformulainSPI，RiemannLaguerrerepresentationoftheexactsolutionIthasmoreadvantagesthanUFSmethodasapurerealrepresentationThebetterpho

8、nonspectrumcanbeobtainedfromYBCOexperimentaldatabyusingthismethodWealsoproveditbyMObiusinversionmethodanditbecomesanewapplicationtoMObiusinversionmethodInourthesis，anewinverseproblem，aninverseemissivityproblem，wassuggest

9、edItwillhaveimportantapplicationsinantiremotesensingandhiddentechnologyItisproposedfirstlyandwegivemanyexactsolutionsaccordingtotheseinversionmethods：theexactsolutionwitheliminatingdivergenceparameteranduniqueexistenceth

10、eorem；UniversalFunctionSetMethod；Riemann—LaguerrerepresentationmethodandMObiusinversionmethodItisshowntobeveryusefulinanumericalcalculationsbyusingUFSmethodTheUFSmakesthisinversionmethodpracticalandconvenientforrealistic

11、calculationsThisworkis“highlyoriginal’’ashighlyappreciatedbyrefereeofPhysicalReviewE(seeAppendix)Theinverseproblemofblack—bodyradiation(BRI)becameahotfieldafteritwasproposedbyBojarskiinI982Italsomeetsmanydifficultieswhil

12、eitisappliedtoconcreteproblemTheexactformulaofUFSmethodisobtainedintheBRIUFSmethodisappliedtocalculateanumericalexample，thenumericalresultsagreewiththetheoreticalresultsItprovestheadaptabilityinpracticeTheRiemann—Laguerr

13、erepresentationmethodisalsoprovedbyMObiusjnverseformtl]aThestudiesofthesethreeproblemsaresignificantinthefundamentalresearchaswellasthepracticalapplicationsofinverseproblemsKeyWords：Inverseproblem；exactsolution；Universal