分形渗流中若干问题探究

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1、分翳罐鼬B印M架曲审％引&痂来歯嬴糜J.Tpq聽?條aIconer,和fF.MP咕顾gikERprig呻！等人深AM究・t琴把瞬縣期凶娅棒加肿擒de1b「ois渗淹过程.Wad»lbr®fi潘it模型和隱梳flWHOLft毯模型J&分形渗tt射阳鶴分形渗流屮的I丙个宴摸型.它们的建立.一方面大大扩充了槪率论的研究领域；另一方面为统计物理提供顽严格的散堂根搦匸方面大大扩充了概率论的研究领域：另一方而为统计物理提供稔过押侮她硼.等人的努力.分形的研究已取得大最重耍成果・本文构遗了一种無的英似予随机Bibrpirwld地毯模塑的渗储模塑圳建剛M

2、izMbtfe跆桝鄭文构造了型利彌的类顒这荫秧随机分形比的潘施何题也冊豹曲删瞬界值縮标乔等或关1brofs渗流模kM：赫魏叢船赢朮蕊i%僅麻］由，常鼬翩鵜涵］鶴来複妄+.1,再急合已有结论，得出当W充分大a-nde】"讐粋‘8勰跚勺喘•界值用R(IV)表示.时・几(N)<耳(N),其中Mandelbrot匕潘负模型的临界值用R(N)表示.索・术文得出当IV?ogt，夏.(IV).关键词:Mandelbrot'sM,R(IV)

3、act曲耐乩RCfCpb坡珂呻购坏Qduqfxjb*・

4、BBSUldrandsubsequent1ystud—_icdbyJ.TChayes,KJTalconer,FMDckkingandG.R.GrimmcUetc.TheycallediedbyJ.T.Chayes,K.J.Falconer,F.M.DekkingandG・R.Grimmettetc.Theycthisprocess"MandelbrotMpercolationprocess^JBcsadtothismodel,wealsohaveRAiidoArgi&f)i试Woaw

5、：tb^t^d1出6世firi[iortUf融詡Usm°de1•weafr^Aai^r^olation.Onehand,theconstructionofthesetwomodelsextendsthee1.TheyelsinStatisticalPhysics.,fractalpercolation・0nehand,o*thesetwomodelsextend*hcBytheeffortofB.B.Mandelbrotandotherscientists,theymadegreatachieve-mentsonliiestu^yo!tf

6、ractalpercoiatioi'Inthiuarticle1,weWristrucianewpercofflk1a11ca1_"tk>nmodelwhichistdmilartoRandomSicrpin^kiCarpetmodel,withMandelbrot's{ybi^cdlatioiimode)Wcoiisbderthepercolationproblemsonthesetwomodels,andc」4l-ACr&LL。P丄of1Ik.B・NlaJidelbi«o.tan,cLo^lhr%ci^.nILsIs.theymade

7、grcanndthestrictinequalityrelationofthepercolationcnticalv^Iue.Inthisarticle.we口胛吩杓代^J7PPTWC耶普乃E「张1?邛曲讣叭N辭哄rco1a-enough,R(加'<巴(")•weusePC(N)todenotethecriticalvalueofMandelbrot'stionfmade1.wki.chissimilartoRandomSierpinskiCarpetmanc1brot'S严皿l丹”虫和M饨d

8、qpKSierpiunkiCarppfe戾叙,andderm$°probability,opencluster.findthestrictinequalityrelationofthepercolationcriticalvalue・Inthisarticle,weimprove：whenN—Ohave只(IV)一宇1・Thenweconclude：w?i($largeo,wehenenough,Pc(NXKW).weusePc(N)todenoteth训川va1ue°fMandelbrofSepercolationmodel・Keywo

9、rds：Mancie1brot'8percolationmodeI,RandomSierpinskiCarpet,probabiIity,openduster.首都师范夫学単俺论袁原创桂声明奈