物理中三個逆問題的多種嚴格解方法的探求研究及具體實現(xiàn).pdf

1、復旦大學博士學位論文物理中三個逆問題的多種嚴格解方法的探求研究及具體實現(xiàn)姓名：溫濤申請學位級別：博士專業(yè)：理論物理指導教師：戴顯熹2001.4.1————塑型塵竺些型些塑蘭!!!蘭堡堅塑!：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