MFNWtKUb<ob<R=MDLCdNFZ;]j?[=ZK_junQ@j?<O`Lo\\xyyyyKxKJB:yyoYdlDn`Qk[xYg=oyiwa@wbAWHXKFXWUINquXqyyhyNJlkHLKAxj\\MV\\mv_iVeHOdd:iywiIEMSDohpoHMMdLoB?gBwcIw?Yr=ydOgdYr;Mb`mV`KItKyy=INkwgiGW_uVwUYuEJwcIsylWT\\IF\\SeTOuv[GMkxMGTHgcGoYkWTy[xM_ydSttgfLqXPGTasFaiIiUtrsELYYbQdsCVLwxSItnaCKkIjUdR;URgxJETqCuK]hCCdrcELKI]MD^Yv]UIaQDXguWagfagcSvFeW`kC\\aeDmcEXLO<MbyTZ`wcTNpYv^hrtdLFLK>Dxv\\NF=rQxphtkSYsUpLMtjWDmCHpcxKwTpLXnWhjI\\K:B?]tJYrFKKEdkLdNXTj@UK=l;qRCMDK=DOkEaUYQMfW?iKghGEgJ_cK_bKwDpSU:GHZ]BRSbS]CrESaCwpMtWIStWY`SHyYyyCsyUWMOSe[r@YdXWHtqS\\qb<=WcwghigugTkwhQOF?McNCGL]fBEd\\cRD::frq_j]Xrwiu[ApvHxlgj<Gv^^xL>d;xhvifSneP_qi@ruhiqicWYaFp]q?_yHh[iiuwmq`]twdL>avpqyxoQ_iGoqEg]Dyff^]kprv`i=>xlpmjarOPw_ivwYdXytpO^YXh]wgggjm_pE_\\pfehv[Afetwdxxhy>qqquO?v_gtuQ[vXaowuNFvW@fgQ]XweEx[H_vUAamwkiWiGxkxp[e^tJgoPWbbQbxhfYinh`iIohhfplYmePrEQffYlhym\\VsnFvDVhs_lvNsaa[IPoQ@^Ipir>uOnushmU@hs`kCIktvbSPmAAvSg_MHv=>n<P`P`rZg_MXxtIOyxU[yoiRhSbVmTH=T`SVj=Yvowo[SPaeCaVdmf^kCo]V^MX`mCxAS]?WisVBud<Wtu?HVmB[qvFkXOQXGAHFui>GSrwRjixVECxad^IvRaH_WuViC=gVnqSQuUEcUQAvioX:oxqcUHmVJQCl;WR]h=MdR[bHmHD]cp;vFaYnUu[iek]Y?AXfiYU;Enkc;kFjkVDufCAESSgRAeUod[eeuegxmB;]bFMRw[y]MiFkwWYUv]CwKeSCeUsIhIV:EePEXxERB_RImWu;Hb=c[Eh]kBqAtucTK]Tryu?;D<[XbSE;mc]uGXktWcExIIRaYIEcl;ecCTWkdBAFVsru[vLKYJYEkHrT]RymP:XJRlLAuRo=lqtk@hYrLmBLWsQUdiu:TjAevlEYihUDatDaxOXke`MwpOVPnNTo=uK;@RNaN]Ix^@U=DnoeRO<M>ev]lkrxWyiRZxundRgaxoqLaiRQyVeXmKAWgHS>EKd@uuetwlWLQtotRKUqRTvCpSR\\ofMqTMnFlVllLSXNMDM>lum]laYnFHlu@xTySvyUL<NFLpXyqhhVvHWtpk>YMYPMnIPBEJFLU;XT<dX^Qr>ujYxw?Avntlk`rmhLEEMmHOx<NFlrwEw_@Ry<WDXjkUg=pcSHeIwngH^__jmNaTghuXoxPnmOcOItR`i^aunw\\gh\\xAprXpa>aUhs\\ql\\pqIxi^Fj>oZE?`jWwU>]VYmQP`n?nN^yAgg^?p:`^@v[CpsGVmWWek>qQa^d?nDvnuV[xO^JGf^V`:Y^Uf^[vgigrZpuCqhQXd<ykppqS^hiwlrG^>?dyAkSnguq[[ocqxtrxocOiag`Xgcko\\IWet>kZ>`rVdoxxbnh\\wlXv^PWk`qmZIegPs@nZ;HkTFwtNr^`nA@j;aekHyB?tJ`wcNrZVadH_efu]>gp>\\dwdwy`vh]=xbZgjVVjG^hOVyNxcVGcuxvjwnQ>qEVwCXfaOenYlhpkP@bK>l`HwtXfUiiZ^fTQyBgjJwq_NZ@?ZA_hOgbyApV?vAfij>eWihNNbVwrKyN=h:IUZuyWyU]=HbSbPmyTCdxES`=XiAujKXjMFEmh]=egKemCG^Uy<?HrwYlMXlwu^KdZihQ;TC_suoDTWsdUVukBCAFlKDGCduEU]UtcWUvWFp?g??d?;uVIUUMBR[TnGCBWTPItXkD:YtfWR>UW>gE<=vRSCtAHxACM;fpABiwFpagu_igIIj]UPEedeu;gI=YGRwBYIfGoIdMF=wvuUXmSTe]eaSHreW_=reEgTmyh[c_=dBQMsyphdMYEm]To>\\QRPpwaq_Tj>mymdpEAya`S`=TrTLuTVjyLJlPWUw]]QJilxYRahtuAjkQpoILI<k\\dU<DSM]kQUjOQqAqV@IKn`s:iYbek:pwupuDtxPUJwXjuMo\\pyphM=poAusNInuAm:AvKIPR@JQhn>mJmatVxqBIsp]KMQnmYSDpnIUkLqM]pOW=VT`Qippm]re\\QpQmphVj`S`Ht>xn>Hv_DWKqjYUkT\\uaIsgak;yMcTPpiO[lROaxUht^=tkXQR@SOpP@Dj=To_]uOAqsLogHx\\MjkuUQYQMXmoAKN`OXhkY\\xoALHMnwAp?Tj`HTdUpQXyxDT]]K<DL@DPbMlR\\nwblkIy\\q_TJ`TWc`TDATaPN>PJFyVL@OiUsZ<qMHqMAk`Ew`]Kq]YKtsYyVCawdmyM<yayTDAntTq=IuH<t>lo=hoVAj<`wdQkxujiaW\\`SWtRrPLWHk]UJiXrX\\M`hK:mMkuoOypAhMgUQ@txh\\KK<S[lyVxNg\\m;iQjHxlTMR\\n@`NFmjxXk_<u\\xv_YN\\hmihvpQPQAooUSxHkgHMnLlS\\NhpjeiSnhsqlx`lyG=M>tMIet:amshmK@JGQQE]WNXQZ=XDXU;tuX<w_dsRtkgqyLpSLpkTQtaPSEPPrHYrEJien\\Dwu=XCakVxXv@VjuwkppCHrwXOj\\N_pU[@SpqNliN=yQgmLKUvVxuH`v>qwFHr<dxbIs]mvUqlNTluULS\\ysYPRANWpKMEmRtSWpuNPL=mv;eYkIrhio_MKoitT<KYhKjmpopVAhOnMNyXvX\\YpIWEXm=HuI\\S:QVuQkvTnNLlnEM^HxBaV@DrPHKSPj>EXWeml\\UruvOlyZeMsaoyyRRpkKEpsEUn`YGYQ]=lV=N]MUmqRK@uvpybPuHIMvPJ@dxoDP]]X_eK@tVETXmYp?]m;itFtOoEk:qMFYYZtotUWnpvAhuJlwQTKO@PrysglWhPKmdU`tRFAR^tX<xrZIQV<lFAVS@uWHjX\\nKhwVTRGYLIut]xJWmVsmt]YLRqn>aXGIjv=SHhyhAM>LK[IKEETKhwWXPrMySuTa=VJ@OTDXXlrDQjmTtoHs^AQgQvHxLKUX`dm[DvT\\P`ujuIkrIJ>ex@@S\\PnyQxiiWh<Uj<TG@uvAsamkYHYS\\m<MRpEk[hkdmYulNJhUt]lH`RvTlJMllQTZ`uT@kViRGdv\\UpE]Lm=WD@Y@<Ww@kbmlK=Q`xkcEn\\`of<SpEWQaKHyqbQYQ@MhdMG@MadQ;asDuVPLwDqx^<XBlUwlnKyPweJ\\PSyYwe`vGalBAvitQiuXCYruyrAYsZMwmpUbXkAUONivFYWwpUIlryPOqyVqIjx=Oydtw<YFewQiR<mlV=rqmm<IUmHYiyQm=yLujJaLkaJ?PRbqm<AuypYf]PepyJExxeqxaLm=yEHtxyQJlqxDm<tlqUoITlxdKlMjEuQ?pvPAJrHxN@ObUSR@J;qjKaTjAPP<nkUYHuY^PLS\\U<HpdxYGxkmdnrUQvlyEeNkXphaLM@tTQixafANsAgf^Aj[VZixlX`[dNmpPj@^iqngcnphpkt?nkGcjicAx_KHemYx@Hq[frU@nsY_Ro^wIpXyeeVpoAhvp]hxrgvfNyyJQj`IlmprYf^=obWFjGNoKve\\OqjonwO^exhtVg`N`ryfvgs;OKAXC?CoKEwyCvGySoIU=tb;w:OiCOylwGasYOgd]Ogw;X^IxNGuf?yP_B]MUnCE_wynsyuwE`yYLsVBmVBetgycFqdSOH`qdgsi=uSIGX:iVNEgysS\\sHdAg=gErKuxyRuywx=eyISNEI=OE[]SgeS@qx=Qd`[yh]W\\aHf[W_[COuwqUI]KG>WSAeX:MVCWs[Uf`qvEifRIIdAwSOitUbKCcw?TwAWIoIJKCaKihaVswHboBr[tnuRieScMbJue[ixJ[yt=VjqYmivL]wVsbbAbrQXM[cuMgDki>kebsCMoIoECaWGvoVp]cx=f@CI>oRO;c@GcJUeRiG\\IteCx_WUckuJSybiICaupOirIBV[BFkr_Ch^=G=wh]qDEYUbyeJyeD=gteWVYhiAHcsg:sX^MuL]ta]D_ay`?Ye]TJYIGEt@Gu?kUn_dHkrwIhUuTkSvsCR_YC<=wQYB[qTb_HOaR<[HWKrpCGcGtQSFOeIRaUlge\\iCJmF?SfdkwhCVD[FxcYa=r=SfSIBQAfIyyZEt@yXfiipAba_IwuilwRNucdkH[=xw=FW=TbMhVGy_=Fe=USwhCkEwiguub\\AXsGx^GsZYImIY[CDvQwkAXeQGlIfIoCIMfL]e\\EC?qfnPsMUXxEXo]YK]WYhNQqQaYKQXxMYo]YoMqxwqKPuSZxSZIKpQYRtouAn=uW@atKYr]ql<IKvuv@\\ky]npQoxLm\\Ild@QE]QNmTMMm?ApA]nJIORMopMjreuD=Rspm[PL;=pnDXHqKAeKsHp;YMwmm`eQsEx@TQBaky<rwDu[]taHmp=oD`wnUm?pK_Ywe\\VShnVHVRDqLeKSukk`NxdLKLxH\\RmytHmQBpnremOaRmmtDpoePUI`lIlOWdkGEjyLSItxA<qwMWA`TgHutXjmPUQxnBtwjuR]DKXArSHyDYJqEn=trOToutxadsqQs_ltfYUuElq`R?PqFuXWdV\\IVR\\wZXV]lwBPl>AVNIKD=Ob]TQTXUXs^ywKesqeR=aRaHlVlTG\\lmiUj`jHxUAIvOyLPuTBMje\\uUYWomlrEQ]dtrQsqlrWYLYEsm=nehqhQNExQFXqrqS[QypeP`\\Xeyq>DM^eXRAxflqPQKiqp:mjg@rThyO\\RvaKSDqdhwgHM^<pFtMSUmS\\ORhpjIUl=OrTT:YtYEnjikS<wniP_uSGxWxTOmxnePowTJQMVFlN`IJMiRAyvhQQhxMfeS[erAXs[ts>EvHTM<tm=HOmDrOxYCUlEQkYekxLmnHtniS=pOGljvLQXqm;=qX`YIYMS\\qF@n?@npeLRPOdIJsYXiIopQKe<xXmKeHj?HqhekP=QuAncMkxYJ]ek?Tsd`wGyV?Umrdo[uUKO[WH`;alkHwvAyM?_bp^NAw__b]^[nwmTf`rP\\Oh`I`bO`mKiyI>`bvtp`g`?pKViX`eHyxWPgFVtS@boVwYWbOFaLfjeO_YWbAwdNgweVvF_hnvmqyyrop;GtLnsnpsnGaW_cCgvT_hJgwTXoKamNqdkwmPyn@wxsP\\oinRvcwHZevdAptK@e<xvoyj[IjW^^R^s?@dEV`b_jI?_i^cTArZYnA?nKOoSodg`vWp^a?c]FvCOajvZANe``XYswEhwMENGvhoUPwFV[T?UYxYbkkFOoFV=hPwxhwVbWGTgg<CwSeFl[FmmGNAgnAwamu>GFISxEAC_KiisCgESrCROCCrOUP]tBavD]Yr?X@SX?ADHeuKovl;Y_kTXKEBacr?VlSbOuxpcCNGeYuTewtIwrXOhfCY=uWYid:UrlScqitaOw_idqeI]UxtGfR;TQoUZqhE]u<MVQ_ia]WW=y`?u`SWvav_aC;ABlwb^?s<[EtAxDkUh[RLeWp_GQMXwSDiAXYuFo[uaWFwCvcAWloeIWbm=ducdTaya[St]XkiWI]uDYyGEtGQTsSV\\SbXOTkogVeSr=UnQUWIRSGDIoUdcUEoWwCYnEWGiWdciCgBk=CWAXEmDiwEtKgucBpKBAqIkoviKFNigXqudOygCS=sRhWY[QWNMtQgDCmg<isxcFTmvAOXXSFA?wCKCXGS:=HR_vjsbS[xTSH@mrgMS^=tWKdxQtgwFQGEK=dtuGVUFemGu[euqRC]ErQtrOxIyUVEdLuV=yc^eRocc]GFNCXDmUMkxeYHuqSe=caMGg?RFSIMSYLOEoEswSdgoWI_DHehIIWZybTuxKsesuhmWX@CUsKgiqfM?Ef;c[CEfoeUyhrcbVQXDYiAkBfibliDYSBxSY[ygZGxisSEOg>iGNyeyuC>AFHOuXYs\\SyForRatHybfuhEQWGSRHaB;sEZoex_dqyDJOeIUFtAcSYBJiifEws?UB;w=YUj;YNKewWdR[D\\;EXuCdqsl_SBsGsAuoSRO_CsEVsaiN=CiGU@?tUOur]EgatgIhDmBCUFfqew]S\\]WtQch_S]cfPKgOcdYigTMxj[dVIYyuraYFN?GqImOhs?@Pr<sClu<HRxLV^tPpDj;YLkARKTvQivFPWIlWaQMP=yH`jVtJi]VU=s@AOcDmsijk\\vceXPtjnAKd<p=lyn]PL]v>xWtxKZ\\rH]TATqdXRn]NQqlAQnI=qTdY\\]REqLItMVa^aauDhw^x`[?xr>wTDFKcSEFdUEIWFXsV]GX`CFKghbghUiR[;siSCGavCQRfEBGEyMGx]IIRwdvKGtMwpmBKGS>UDHMWa=ipWY>?yZmV<WRbwRxMI`_RmUXxaI<ecHYSLOi[=vVAtSySv]EhifGaC`cTBurj;G@eeuuHC[ClycF?sLEuEEsBSiQ[TAeCcCF>wGoUwCQvQCf;uCRMGcSvXiYS]B`IBXuCHIU=yWtCerCW>mvM]hWqGNAW=oi]QSN[rOGwNkumyRKKSNwRSAgNOxXoG?WGcoHl;ElyBIeFAIITGRKKxkqEbke;QHQicKOd_QIn_rSuv]?H@ETlEWoSDPkBaCvkyT[SbpyWFGEiQHxgxBKt`ESvMHvQgkeBfXPTYm[Iu?lW@@X_LKMERMMNB]K;EQUErOyOY@RsMQ]\\wJ]W^=PNTlKhlw]N=HyFHLfeka=tolp]xXmPLTXxTYsBaRi=j;yoJMY[eq`YLtmTSHNDYvbmmWqs=HnY]TY=kN@nZLVf]mwAqltNkaxnILSYVJXynIoKENiMlLdvmYKIdPkUJy\\wJ]W`=PBDUKeRk<yNXLmMla=M@YPrxMLAqKuP;Lno]rgiSeLYSaJQypidP_msKyWn\\sSlk]Hk>`jHLwOhqvlXaQuvtSrDtRTU^]R@PjAQJGmqQykUIkVekLEsGASihYIqOnQOqmwGPUjawuDVJAqt`v_@JI@vdDxiIsSAlrmJ?aJPUkH@kkUO:aWtmOD]XnYxf\\LtAye=nMDnBXnsEKKtQAMjYuwPLMVxUuDWoyVXaxr@fbHfKXbsAo]ntQqqYao[>vmGlUpqJNdT^];Ya[?\\Fne;vsUglif\\IAv[qtFNkjFrUA`RabTP]HXnsHqBnmrid]ahfyfJyqYQfih_FFsMvdCPtE?cnheDYh\\`ybqjc^[qFrN?hlhuGVjKwjo^nmgrm>iL`o?GyNP[TyuOQnKqcuWxoOeN^h;IjtImkH^gq_;igONecNo<hr\\PuVitqQrtWy<`fanaV@r?I[`@h[`bENtMIluoqLhwLO[;_sv`iHAly@kBw]hig=A^DN^fGs>HfrYZ<IxFNqxqgnX]:ya_VlYvIachWWQKrTAcvaXmkcJytyKbxQbqcBLOVEGxrgfrSFwAvQMubCyTsDVwvriSkQs`?e_abLcVgQFLQdi_bO?gBQS^auxuDkkr:WRkGuY[GVKyK=d^cIHGRMyevmSZ=xBWSSGEhwfJosI]W>kgD_frEivMEhWV=ch=uY;[uwWijaYpYVTArD_RooUqMH;IUVIT][ywmejMSRAFagshiuDYh;oF@EFiaYeIgDIgnQipseZgu<gxjUeR[u<YfICfS;eOQDvKY;]SgKwtsc<YfyKXWCgBAvGwv<oWVAfokCfkW`ic]kwd[Y]ostWH?AYLirr=VEeheMxhOBxIskkwpaSXkFnecPmtAIisSwY?r`Kfk=Cr[DuCcdGxGWi>mTp[Er;SZ=T^KHf?CcID=CdxKejYI\\cUxkeW?HFydiGhqySJ[IHox]Cg_?tgIDckFGqVkOH^oSy?cuUYlQSX<uS]T>xJGmYQPnW]NITrM]qOTV?`VvPPRlkW@Pb]UjhvqqWTHNbEx`<Pb\\UtAoEdpGEyvmw>aMppR?mlyLUQtWApJDajmyR>YSJyWCqPs]VwLurxSDdY]TXIer^imWLM\\djCuwLilXQkIujCMwkDpLHOnHMQYwS\\L\\yYhQk^qxT]TbHtBXUrMXIuRYqmkEWoLX;us]arWdJi@uqHyJYMStNFunvqKM=n]xXi]pHUSu=rEiPSYQI`wt=neMUbtyummV@ud<sF@SdpUd<qjIOQluh]JJdtMUqGiSBDUBlWy`m>AnU]sMUKvEsWtjPTK^HKYpQMXQpYTrMNXdOxutaiWZql\\Xqo]LTPQGQjjixndYjUuKMQ^enSuSOmtqTVO`o_MxG]mqYMp\\TM`p\\`UKYUo`u`EUnpS>ewiijYLREDsmhyHXXMdRh<TbUUU]LjtLOaQ`ijnuVAO\\LwttaqpG_FIsxxbOiooquvHsoO\\hHqPVvy>kjI[`@boY^Xpu\\I\\SawcY^WotUhhbqixXdAg[NIb?PscOZr_xDol^Wc^ae`?pV^at^`UFhE?sNh[GhsFnvIPrJvr>@]vvv]gsjyh`@fj@dC>jham`ildFnpI^uvhxQyRi`@aagqh[nfMVZWPxYP]cvaW?qYwpX?mR@vbVdeOdrxhfnkpNmJhZNVjXXrp@rEq_ngZXY_=HgZp\\kIgMpyP`opwyxahXgcXxbE@sQyj\\?n\\ouNxiY?fmxbiot<?h_Q`VFuPNiNy]vIhM>pKHt;FgTq_[PdkhuRxeBWgb^^ehyVYt??vbqmpX]gYd^il_NmihuEin;vs?YbfvqyVg^oqMIjyNpT^dcQxdQyuNrZnmdXl;pv?Au:wuRV]ihwxVnyxfvPcEGs;avh`b>OoFX]GNpRvyoAoT`gmxb^q^VgadVigfrV_xS@yWweEWxvfuGadt``Lh`@InVOpWX_Sh^caq`itewheQoZXgKnv^FhnXufweY`uHa`Vh]nir@geMfeaVitfud_hGipgN\\HgxGit@ic[pbwIbAvsmwlLFZ<gy?x^?FprnbdFwTIa=xv<Oi^gfkHj;iqm@u\\Oi^yxgV[kVs`>n]o_XwqH@lAifbOo;gpyNfFwxoimcqxj_[T_hCoxe`nOiqrgfqGudneX@hDOkAAyuP_NXnOnnr`n>GqHOknXs>Fq[VoawhFNix>jNnyTarZ^unG_dYxV?_JIdsnkFndR>gQV]s@xf_y;fu^Hou^^uyncQmdXlWW_:qyVNjjioCquk^fgAvAnpaqpdApoHgU_\\vYhqhaRYth_`CYa?@_fHktFoBIrrOorwxFNqphfg^dmh]IAvXIik^_WoZtPkBNlwnjCq`dgnWagQxb\\GuYAgppmfwmGox_FmFXaWpy:IqwH]Xqsrq[Vo`jAogNeWp\\eXg]F`phgpYru`okhyWYZxWvKhrqiiqWepIudplV_nVwvsQlQvs[@igVjnahxGiIyt>qfnqeoHf^`jsY`LfjM_^gXf[VwBwo\\hm^YlsNoCyaDil=GquiuvqkWFkHHpootDPuYw_jafDqid^fsN^yw]t>iwIlfomp^dnw^uwjsqfW_np`h]y[XhwKNfRQseAfofe=Q^Gqd=igbWefArbQhLnychvdamwopDWuDvr>P`oV@_VEOtMiBvExaktTMHGCtkwfP]sC_Yscf=qvkCun_h^MeoSCScwresNEI=SdYkSSMFAKe?QwH?yUYFcmbaeTNaE`UhTaVoKE;ahAgEtoecWvjgbXOcm[wDuIdYfvQiW=F[sSKKiQYFPqYN;IhsEMuHs]DtAIpAyvMB<wBOWVxOYnGwVERmIhLuihmHTcsmwfMgC@gvsEftEyRqWXyTIsXoYe?[D_]x?]w;ifHQUdofeOgxSeFuEh=G?wH^uBD=yZeI_WeBAxLchYmUQ;SBEhU]Tcqw:]c<uX[cbgAhWotRqvcMWPovc[r`eUIAwoEb>_Dukr?wW]WR@wcquCtgu[SEssxCqSPScKiGHqX>EbjySusyoabNsg<eBwexgkw^UEdUdFaBsIeJGh`?GwcRiEdREGuKvA_XUsfiiCa=wwWi@OVouRBMF[cHvKUisIf;sISDJSGawYEIC>cETowbKyWIv<=u]OwfESpGEKAsxWU=MhaIFWYSN?XtPLE<YyipGyKF]nrys\\tkxHXxmte]qfYQHDy;=tOTueeKy=X:UpHdjaDnyeuOyW;tnRiND\\Wd\\NUxWkyuW\\rrMQ]`KhtTEIvjEQkqN;aXyDtiQLQaPphonPQqPvqYUAiMAPK[lwcYnKPNB\\YyHOiXm\\yw<UlgHlqxWkan_uXi]MW`OqpMKtQxEntxQDhK>lnyhSjiu\\mSc\\TAyK^`t<xWdLoUiyc<oMqKq`ToYjGxQv\\l\\yW>tnJMu\\QVvpXnelbhTPlS]\\J`pVbyxFHQUuO[<nSYRjmJoqQsIyPmo<UT<tqm]QlPjgmSZAVkUmW=wdQja`N:QKGuv:ywXtVLqsUUNFxlZmrnExJPySLwIHoOLyYAjtLyAtusUSKQUwXQvPm\\qOwUxviO`dyTPvuTR_pjxUpsmNxXkQqxZIjrHkpYygQllIOxxJnHtY`SFdm?Ap_@W^yJEilIQt\\hnNtuwLwnusYLPqIxyxwKLYkQOMaLyuJDiWnYt;hOdLOXxqZXkQpw=Um\\yw<IvIAwmYPWEKdayBPNqtqEExwXvTDnixspPxCDnEatExyiaRsqM[xsBdPLeJtyuE<vjdvidRD`Lc>C?SKOF?M;]yACxyABrsrdCDnGH>qD:<J:`n\\tN\\tT[<P;;2:\"\{\}LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVIkRiotJS5CT1VORFNfSEVJR0hURzYjJCIkcSlGKi0lKUNISUxEUkVORzYiBurgers' VortexDepartment of Applied MathematicsUniversity of Waterloo, CanadaCreated for: AMATH 463Created by: Marek Stastna and Emilee CarsonThe Burgers vortex is a well known solution of the Navier Stokes equations that combines vorticity and shear. It allows for the study of a realistic flow in analytical form, thereby offering intuition for more complex flows. However, the cylindrical coordinate system makes certain calculations cumbersome to carry out by hand. This worksheet allows the user to explore aspects of the flow without having to carry out the calculations.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
CommentsCalculationsThese are the three componenets of the Burgers vortex.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print(); # input 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print(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0Zmbi8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0YrLUY2NiQtRiM2Iy1GLDYlUSZwbG90c0YnRi9GMkY9Rj9GV0YrLUY2NiQtRiM2Iy1GLDYlUShERXRvb2xzRidGL0YyRj1GP0ZXRistRjY2JC1GIzYkLUYsNiVRKFN0dWRlbnRGJ0YvRjItRjY2Ji1GIzYjLUYsNiVRL1ZlY3RvckNhbGN1bHVzRidGL0YyRj0vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGPUY/RlctRkA2LVEifkYnRj1GQ0ZGRkhGSkZMRk5GUC9GU0Zpbi9GVkZpbg==JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjdjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSxWZWN0b3JGaWVsZEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUZTNiYtRiM2Jy1GLDYlUSN1ckYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRJ3V0aGV0YUYnRi9GMkZobi1GLDYlUSN1ekYnRi9GMkY5LyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0Zobi1GLDYlUSxjeWxpbmRyaWNhbEYnRi9GMkY5print(); # input 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(); # input 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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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%;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%;JSFHThis is the divergence as a sanity check. 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Here is the vorticity.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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEsbXl2b3J0dGhldGFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSVkaWZmRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEjdXJGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ6RidGL0YyRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZjb0ZPLUZTNiQtRiM2JS1GLDYlUSN1ekYnRi9GMkZaLUYsNiVRInJGJ0YvRjJGOQ==print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=These are the components of the rate of strain tensor.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(); # input 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(); # input 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(); # input 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print(); # input 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(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=This is the only non-zero shear component for a sample parameter set.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqbXlzaGVhcmV4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVElc3Vic0YnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYvLUYsNiVRI0cwRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkjbW5HRiQ2JFEiMUYnRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSZhbHBoYUYnL0YwRj1GOUZaRmduRltvLUYsNiVRI251RidGZm9GOUZaLUZobjYkUSsxZSZtaW51czs2RidGOUZbby1GLDYlUShlcnRoZXRhRidGL0YyRjk=print(); # input 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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Now I define the actual rate of strain as a matrix then use the Maple linear algebra package to define the second invariant (I used the wiki page for the scaling)And here is a plot of the example showing that the second invariant has a local extremum for r>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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmdHJhY2VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJlRidGL0YyL0YzUSdub3JtYWxGJw==print(); # input 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(); # input 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(); # input 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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Now I define the enstrophy and plot a sample to show that in fact it is monotonically decreasing. 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print(); # input 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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=