chapter3 - Fkdswhu 6 WKH KDUPRQLF RVFLOODWRU Zh qrz...

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Fkdswhu 6 WKH KDUPRQLF RVFLOODWRU Zh qrz frqvlghu dq h{whqghg h{dpsoh zklfk doorzv xv wr dsso| wkh wkhruhwlfdo dssdudwxv frqvwuxfwhg lq suhylrxv vhfwlrqv1 Wkh h{dpsoh zh fkrrvh/ wkdw ri d sduwlfoh vxemhfwhg wr d olqhdu uhvwrulqj irufh 0 wkh vr0fdoohg kduprqlf rvfloodwru 0 lv lpsruwdqw iru vhyhudo uhdvrqv1 Iluvw/ lw lv rqh ri wkh uhodwlyho| vpdoo qxpehu ri txdqwxp phfkdqlfdo sureohpv wkdw fdq eh vroyhg h{dfwo| dqg frpsohwho|1 Lq dgglwlrq/ wkh sureohp surylghv d edvlv iru rxu xqghuvwdqglqj ri pdq| lpsruwdqw sk|vlfdo sureohpv/ lqfoxglqj prohfxodu yleudwlrqv/ wkh yleudwlrqdo h{flwdwlrqv ri vrolgv +l1h1/ skrqrqv,/ dqg wkh txdqwl}dwlrq ri wkh hohfwur0 pdjqhwlf ±hog +skrwrqv,1 Lq d uhdo vhqvh/ wkh rqh0glphqvlrqdo kduprqlf rvfloodwru lv wkh pdlq exloglqj eorfn ri d juhdw ghdo ri txdqwxp ±hog wkhru|1 614 Vwdwhphqw ri wkh Sureohp Zh frqvlghu d sduwlfoh ri pdvv p vxemhfw wr d olqhdu uhvwrulqj irufh I @ ± n{ /fruuhvsrqg0 lqj wr wkh txdgudwlf srwhqwldo Y + { ,@ 4 5 5 @ 4 5 p$ 5 { 5 +614, zkhuh $ @ s [email protected] 1 Lq wkh Kdplowrqldq ghvfulswlrq ri fodvvlfdo phfkdqlfv/ wkh v|vwhp lv ghvfulehg e| wkh g|qdplfdo yduldeohv i {> s j / dqg wkh hyroxwlrq lv jryhuqhg e| wkh Kdplowrqldq K @ W . Y @ s 5 5 p . 4 5 p$ 5 { 5 = +615, Kdplowrq*v htxdwlrqv ri prwlrq b { @ CK Cs @ s p +616, b s @ ± C{ @ ± p$ 5 { +617, duh/ xsrq wdnlqj d vhfrqg ghulydwlyh/ htxlydohqw wr wkh idploldu Qhzwrqldq htxdwlrqv ± { . $ 5 { @3 ± s . $ 5 s +618, zkrvh vroxwlrqv ohdg wr wkh idploldu rvfloodwru| ehkdylru { + w D vlq+ $w . ± , +619, s + w Dp$ frv+ . ± , = +61:,
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437 Wkh Kduprqlf Rvfloodwru Lq sdvvlqj iurp d fodvvlfdo wuhdwphqw wr d txdqwxp phfkdqlfdo rqh/ wkh g|qdplfdo ydul0 deohv duh uhsodfhg e| rshudwruv { $ [ s $ S @ | N +61;, zklfk reh| wkh fdqrqlfdo frppxwdwlrq uhodwlrqv ^ [>S `@ l | = +61<, Hyroxwlrq ri wkh txdqwxp phfkdqlfdo v|vwhp lv jryhuqhg e| wkh dvvrfldwhg Kdplowrqldq rshudwru K @ S 5 5 p . 4 5 p$ 5 [ 5 = +6143, Vlqfh wkh v|vwhp lv frqvhuydwlyh + [email protected] @3 , /wk l vhyr ox w lrql veh v wfrq v lgh uhglqwkh edvlv ri wkh hljhqvwdwhv m ! q l ri wkh Kdplowrqldq/ zklfk duh dvvxphg wr vsdq wkh vsdfh ri d vlqjoh sduwlfoh prylqj lq rqh0glphqvlrq/ dqg zklfk reh| wkh hqhuj| hljhqydoxh htxdwlrq + K ± H q , m ! q l = +6144, Dv zlwk dq| hljhqydoxh sureohp/ zh qhhg dq lqlwldo uhsuhvhqwdwlrq lq zklfk wr zrun1 Lq wkh m { l uhsuhvhqwdwlrq/ dvvrfldwhg zlwk wkh hljhqvwdwhv ri wkh srvlwlrq rshudwru [> wklv ehfrphv d gl±huhqwldo htxdwlrq ± | 5 5 p g 5 ! q g{ 5 . ± 4 5 p$ 5 { 5 ± H q ² ! q + { ,@3 +6145, iru wkh hljhqixqfwlrqv ! q + { ,@ k { m ! q l 1 Wkh qrwdwlrq wkdw zh kdyh lqwurgxfhg vxjjhvwv d glvfuhwh vshfwuxp/ dqg/ lqghhg lw fdq eh dqwlflsdwhg wkdw doo ri wkh hljhqvwdwhv ri wkh kduprqlf srwhqwldo pxvw eh erxqg vwdwhv1 Wklv iroorzv iurp wkh revhuydwlrq wkdw wkh srwhqwldo hqhuj| ri wkh rvfloodwru ehfrphv lq²qlwh dv m { m$4 1D vdu h v x o w /w k hz d y h ixqfwlrq pxvw jr wr }hur dw odujh glvwdqfhv iurp wkh ruljlq lq rughu iru wkh hqhuj| ri wkh v|vwhp wr uhpdlq ²qlwh1 Wkxv/ wkh deryh htxdwlrq lv wr eh vroyhg zlwk wkh erxqgdu| frqglwlrq !
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chapter3 - Fkdswhu 6 WKH KDUPRQLF RVFLOODWRU Zh qrz...

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