• No results found

Numerical determination of flow corrective inserts for granual materials in conical hoppers

N/A
N/A
Protected

Academic year: 2020

Share "Numerical determination of flow corrective inserts for granual materials in conical hoppers"

Copied!
17
0
0

Loading.... (view fulltext now)

Full text

(1)

&')('(*+,.-/ 102 (3 2"$ 457688)9(:

;/<>=?9?@='A BDC'E<>FHG?9=IJEK@LNMPORQETSN<>LUG*VRW5XY9E9=Z'Z'=?N[\ONE@F9L^]^<>XY9E@=_C`W5Y9=E9?@=_?M

a3bc+dfe+ghTd'i)jk9l*m9nfonfpqfrsftuvwsfrx`s'y lr zwsfvw{|z>t^k9nf}}Nl~r4{zw{{ yu9zwl€H‚ƒt^z>t9u9{y„r zwsfv,sf}}v>zw…€s'yzwnPt\{€†

z>t9{ lry{nfp‡fsfr zwnfu9{{zwˆ€lsft9{„k9sf}Nlsfrl,nPp‰y lt/u9{ l+y nz>xŠ}r4nf‡'ly„k9lm9nfo3}rnf}Nl~r4y„zwl+{sft9q'l+y5rzwnfput9l+{„z>rsf‹vwl

lŒl+…€y{{„u9… k$sT{x`s'y lr zwsfv{y„zw… z>t9qy nyk9l|o,sfv>vw{€†fpwutt9l~vm9nfo†_sfr… kz>t9q†fl+y …'ŽHl{y„u9Dy„k9l/…€s'{ l/nfpz>t‡'lryl€

…+nPtzw…+sfvz>t9{l~r4y {z>t…+nftzw…€sfv,k9nP}}Nlr{€‘‚’t“{„}zwylŠnfp)y„k9l`…€nfxŠ}vwl+”Tzwy3nfp)yk9l•}k9lt9nfx`l~t9n€t1s'{Šnf‹9{ lr‡'l+–z>t

}rs'…+y„zw…+lT†\l€”'zw{ y„z>t9q)x`l€yk9n{/s'{ {„ux`lz>t1q'l~t9lrsfvsŠrs'zwsfv{y„r u9…+y„ur4lnfp/y„k9lD{ y„r4l€{{|sft9H‡'l~vwn_…~zwy—9lvw{€D˜

t9l+o™tux`lr zw…+sfvsf}}rn's'… kHy n$y„k9l}rnf‹vwlxšnfp/l€{zwqftz>t9q1›4nf}9yz>x`sPvwœ)z>t9{ lry{|zw{}r4nP}Nn'{ l+3sft9Hy l+{ y l+`‚y

sfv>vwnfoJ{p‰nPr/t9nft*}ur4l~vw)rs'zwsfv9{ nfv>u9y„zwnft9{+jk9lt9l€o“…~rzwy lr zwnftŠzw{pƒnfut9`y n)‹lx`nfrl/{ yr z>t9q'l~t\yyk9sPt`…r zwyl~rzws

‹9s'{ l+nft)puv>vw|r4s'zwsPvP…€nft9{ yr u9…+y„zwnft{+9žnfxŠ}9sfr zw{ nft9{ozwykŠl+”T}Nl~rz>x`l~t_y {s'{o,l~v>v\s'{q'l~t9lrsfv'…+nfxŠx`l~t\y {sf‹nfu9y

y„k9lnf‡'l~r4sPv>v9sf}}r4nTs'… kDsfrlnfŒNl~r4l€

Ÿ* ¡1¢)£9e€¤cTiŠqfr4sPt_uvwsfrm9n¥o†‹nfut9sfr‡fsfv>u9l|}rnf‹vwlxH†fTzwlvwŠ…+nPt9zwyzwnft†€m9nfo^r uvwl

a3¦¨§©4¦™ª`§«c¥¬b@­ h'dh'®wgc€c+¯>°h'gd+¯£9±c'i²_³f´µf¶†·f¸'¹¶_³†'¸_³'º·'»

¼½

&T//¾/)5_ ,

½$¿ÀÁ+ÂÃ^ÄÅ9Æ9ÇÈÉ_ÊË@Ã'À̃Í9Ã^Î>ÏÐ,ÑÒ+Ó9ÑÓ9ɀÃ_Ô.ÕHɀÑ,ÃÖfÌÕ×JÉ+Ó@׃ØÁ+̃Ó9À^Ó5ÙɀÁ+Ã_Õ@ÔÚ

É+ÁfÕÁ€Ã“ÃÛ9ØÕÁ+̃Ó@ÀÉÔÃ'ÉfÖfÒ+̃Ü̃ÀÝÁ€ÂÃÞ,ÓßàÓÙHÕÖPÓ9ÂÃ'ɀ̃Ó9À׃Ã'ɀÉ^Ý9Ò¥Õ5ÀØ×ÕÒUá“ÕÁ€Ã'Ò+ÌÕ5×D̃ÀâÕãÖfÓ@ÀÌÖ'Õ×

ÂÓ@ÑÑ,ÃTÒ_ä)åŠẨɐÉ+Ó9׃ØÁ€ÌƒÓ9À/Ê@Á+ÂÃ3ɀÓæ+Ö'Õ׃׃Ã_Ô^çTè9é9ê èë,ì,íîãïfíëðñêí5ò^̉ÉÁ+ÂÃ$ÜÕÉ+̃ɐÙÓ9Òá^Ø,րÂ^ßÓ9Ò+ÍUÓ9À

Á+ÂÑÔÃTÉ+̃Ý9À¨Ó5ÙD̃À,ÔØɀÁ+Ҁ̒Õ5×/ÂÓ@ÑÑÃ'Ò+É3Ù Ó9ҊÁ+ÂÃ1Â,Õ5À,Ô׃̃ÀÝ^ÓÙá“ÕÀÚÔ̝óJÃ'Ò+ÃTÀNÁ3Í̃À,ÔÉ*ÓÙDÝ@Ò¥ÕÀØ×Õ5Ò

á“Õ5Á+Ã'ҀÌÕ׃ɊÎô\Ð+äõ.ØÖ+ÂÒ+Ã'á.Õ̃ÀÉ)Á€ÓHÜÃ$ØÀ,ÔÃ'ҀÉ+Á+ÓÓÔ.ÕÜÓ9ØÁÁ+ÂÃ3Ò¥Õ@ÔÌÕ×ɀÓ9׃ØÁ€Ì‰Ó@À/Ê@Ã'É+ÑÃ_ÖfÌÕ׃׃Ú^̃Á+É

É+ÁfÕÜ̃׃̃ÁÚÎ>öÊ9÷\Ð+Ê9ÕÀ,ԖÁ+ÂÃ`̃áÑÓ9ҀÁ¥ÕÀÖfÃDÓ5ÙøÁ€ÂÊÉ+̃áÑ׃ÌwÙ ÚÑÀ݊ÕɀÉ+ØáÑÁ+̃Ó@ÀÉÃ'áÑ׃ÓÚ@Ã_Ô3ÜÚ1Ë@Ã'À̃Í9Ã

Î>ÅÐ+ä

¿ÀÁ+ẪɊÑ,Õ5Ñ,Ã'ÒÊßDÃ3ÜÃ'Ý9̃À.ÕÀ“Õ5À,Õ׃ÚÉ+̃ÉÓÙՖÒ+Ã'×Õ5Á+Ã_ÔÜØÁŠáÓ9ҀỂÀÁ€Ò+ÌÖ'ÕÁ€Ã`ÑҀÓ9Ü׃Ã'áùÓÙ̃Àæ

ÔØɀÁ+Ҁ̒Õ5×̃áÑÓ9ҀÁ¥ÕÀÖfÃ9ÊØɀ̃ÀÝ3Ë9Ã'À̃Í@Ã9ÈÉúÕ5ÑÑҀÓNÕ9րÂ^Á€Ó$Á€ÂÊÃ_Û@Ø,Õ5Á+̃Ó9ÀÉÓ5ÙøáÓ9Á+̃Ó@À/äåŠÂÊÑÒ+Ó@Ü׃Ã'á

Õ9ÔÔÒ+Ã'ɀÉ+Ã_ԙÂÃ'ҀÃ3̉ɊÁ€Â,ÕÁŠÓ5ÙÁ€ÂÃ*Þ,Óߚ̃À.Á+ÂÃ3É+ÑÕ9ÖfÃHÜÃ'ÁßÃ'Ã'ÀÕ5À̃Àû9Ã'ҀÁ+Ã_ԙÖfÓ9ÀÌÖ'Õ5×J̃ÀÉ+Ã'ҀÁ`ÕÀ,Ô

Á+ÂÃ1ÂÓ@ÑÑÃ'Ò3ß7Õ5׉×ä`õüÓ9Ò+ÃUÉ+ÑÃ_Öf̝ýøÖTÕ׃׃ÚNÊßÑÖfÓ@ÀÉ+ÌÔÃTÒ$Á€ÂÒ+ÃTÃỖáÃ'Àɀ̃Ó9À,Õ5×/Õþ̃É+Úáá^Ã'Á€Ò+Ì֕Þ,Óß

ÜÃ'ÁßDÃTÃ'À“Õ3ɀá“Õ5׉×@̃ÀNû@Ã'Ò+Á€Ã_Ô^ÖfÓ@ÀÃHÿ Á+ÂỄÀɀÃ'Ò+ÁDÕ5À,Ô^Õ*גÕ5Ò+Ý@Ã`ÖfÓ9ÀÃ3ÿ Á+ÂÊÂÓ9ÑÑÃ'ҐÁ+ÂÕÁ)Â,Õû@ÊÁ+ÂÃ

É¥Õ5áÃ`Õ\þR̃ÉÓÙ/ҀÓ9Á¥Õ5Á+̃Ó9À|Ê9ɀÃ'Ã|̃Ý9ØҀÃ1Ä9äƒÄ@äÓ9ÀÌÖ'Õ5×J̃ÀÉ+Ã'ҀÁ+ɊÂ,Õû@Ã`ÜÃ'Ã'À.É+Á€Ø,ỖÃ_ÔÕÀ,Ô ØÉ+Ã_Ô.Õ5É7Õ

áÃÕÀÉÁ+ÓŨáÑҀÓû9ÃÞÓß Ö€Â,Õ5Ò¥Õ@ÖfÁ+Ã'Ҁ̃É+Á+ÌÖfɊ̃À^ÂÓ@ÑÑÃ'Ò+ÉÊÃ'É+ÑÃ_ÖfÌÕ׃׃ÚUÁ+ÂÓ@É+Ê٠Ó9Ò)ߊÂÌրÂ^Á+ÂÃ`Ò¥Õ@ÔÌÕ×

É+Ó@׃ØÁ+̃Ó9À^ÕÑÑ,Ã_Õ5Ò+ÉÀÓ9ÁÁ+ӖÜ,Ã*û9Õ׃ÌÔJÊÕÀ,ÔUÁ€ÂÊÞ,Óß ÌƒÉ)̃ÀɀÁ+Ã_Õ@Ô+ðòò fëì,íîŠỄÀ^ߊÂÌրÂ^á“ÕÁ€Ã'Ò+ÌÕ5×

Þ,ÓߊÉ1ÔRÓߊÀ ՓÖPÃ'ÀÁ+Ò¥Õ5×ÙØÀÀÃ'×Ê/׃Ã_Õû̃ÀݨÕÉ+Á¥Õ5Ý9À,Õ5ÀÁHÒ+Ã'Ý@̃Ó9À Õ9Ô'Õ9ÖfÃTÀNÁ–Á+Ó¨Á€ÂÃ^ÂÓ9ÑÑ,Ã'ÒUߊÕ׃×ä

¿À,ÖfÌÔÃTÀNÁfÕ׃׃ÚNÊÁ€ÂÊÁ+ÒfÕÀɀ̉Á€ÌƒÓ9ÀHÜÃ'ÁßÃ'Ã'Àá.ÕɀÉJÞ,ÓßHỄÀHߊÂ̒րÂ^Õ׃×Á+ÂÊá.ÕÁ€Ã'Ò+ÌÕ×@̃ÉáÓ9Ü̃׃Ì'Ã_Ô*̃À

Õ3ɀÁ+Ã_Õ@ÔÚ^É+áÓNÓ@Á+–Þ,ÓßHÊ9Õ5À,ÔUÙØÀÀÃ'×Þ,Óß ÌƒÉ)Á€ÂÓ9ØÝ9ÂÁ)Á+ÓUÜÃ`ÕÉ+ɀÓÖfÌÕÁ+ÃÔ^ߊ̃Á+Â^Á€ÂÃ`ÜҀÃ_ÕÍÔÓߊÀ

ÓÙÁ+ÂÃ3ÒfÕ9ÔÌÕ×Þ,ÓߚɀÓ9׃ØÁ€Ì‰Ó@À“Õ5ÉDÁ€ÂÃ3á“ÕÁ€Ã'Ò+ÌÕ5×,Ó@ÒDÂÓ@ÑÑÃ'ҊÑ,ÕÒfÕáÃ'Á+Ã'ҀÉ`ÕҀÃ$րÂ,ÕÀÝ9Ã_ÔJ䐿À,ÔÃ'ÃÔJÊ

Á+ẨÉ`Õ5É+ɀÓRÖP̒Õ5Á+̃Ó9ÀÂ,ÕɊÜÃ'Ã'À™Á+ÂÃHÜÕÉ+̃ÉÙÓ@ÒDá^ØÖ+ÂÓÙÁ+ÂÃ1ÔRÃ'É+̃Ý9À.Ó5Ùá“Õ5É+É~æÞ,Óß ÂÓ9ÑÑÃ'ҀÉ_ä

Ó@ÀÉ+ÌÔÃ'ÒÁ+ÂÃÞ,Óß Ü,Ã'ÁßÃ'Ã'ÀÁ+ÂÃ*̃ÀÉ+Ã'ҀÁ7Õ5À,ÔUÁ+ÂÃ`ÂÓ@ÑÑ,ÃTÒDÕÉÉ+ÂÓߊÀ^̃À|̉Ý@ØÒ+ÃUÄ9äƒÄ9Êߊ̃Á+Â

Á+Ó@Ò+Ó@̒ÔÕ×ÖPÓNÓ@Ò¥ỖÀ,Õ5Á+Ã'É ÿ̃À¨ßŠÂÌրÂã̉É*Á+ÂÃ^ÕÀÝ9׃Ã1Ó5ÙDÒ+Ó@Á¥Õ5Á+̃Ó9ÀÕ5Ü,Ó@ØÁ`Á€ÂÃ^Õþ̃É_ÊJÕÀ,Ô

3ÕÒ+Ã*Ñ×ÕÀÊÑÓ9×Õ5ÒDÖfÓÓ9ÒfỖÀ,ÕÁ€Ã'Ɋ̃À^Á+ÂÃ*Ñ×ÕÀà "!#ÖfÃ'ÀÁ€Ã'Ò+Ã_Ô.Õ5ÁDÁ€ÂÃ`ÑÓ9̃ÀÁDÕÁßŠÂÌÖ+Â

Á+ÂÃ̃ÀÉ+ÃTÒ+Á^ßÓ9Ø×Ôã̃ÀÁ+Ã'ҀÉ+Ã_ÖfÁ^Á€ÂÃ.ÂÓ9ÑÑ,Ã'ÒU̝Ù`Á+ÂÃ.̃ÀɀÃ'Ò+ÁUßDÃTÒ+èÖfÓ9ÀÁ€Ì‰ÀØÃÔ ÕÉUÉ+ÂÓߊÀ ÜÚÁ+ÂÃ

$ jk9lŠ—r{ysfu9y„k9nfrDos'{{u}}nfr4y l+‹\Uyk9l*˜Jr x7&%/l€{l€sfr… k('*)Š…+l3ykrnfu9qfkUqfr4sPt\y {,+/˜|˜-|¶./10_³2/

µ2/¶._µ"0$sPt9+|˜/˜-|¶./10'²/µ2/¶'¶0_·†sft9H‹Uyk9l43/nfryk“žsPr4nfv>z>t9s65Tu}lr…+nfxŠ}u9yz>tq`žlty lrf‘jk9l*{l€…+nft9

sfu9y„k9nfrf>>>9jk9l/y„kz>r4ŠsPu9yk9nfro,s'{J{„u}}NnPr4y l+‹73/s'y„zwnft9sfv85…zwl~t9…+l9nfut9s'y„zwnftDqPr4sfty:+<;65=0_³P¶._³>'¸5†+sft9

‹Š˜Jr x7=%|l+{ l+sfr… k?'*)7…€l)qfrsft\yA@+/˜/˜A-/¶=0>tuxD‹lr{,y nD…€nfx`lB~

Mžlty lr/pƒnfrC%|l+{ l+sfr… k3z>t5…zwlty„z>—9…úžnPxŠ}u9ys'y„zwnft`sft9D+l}9sPr4y„x`ltyJnfp;3s'y„k9lx`s'y„zw…+{€†#3|nfryk‘žsPrE/

nfv>z>t9sF5y s'y lG tzw‡'lr{zwy„'†%/sPvwlzwqfk†3ž“»T·f²0_³2/1>_»P¶_³

(2)

ÔÕ5É+ÂÃ_ԙ׃̃ÀÃH̃ÀJ/̃Ý@ØÒ+ÃÄ@äƒÄ9äK•Ù7ÖfÓ@ØÒ+ɀÃ9ÊJÁ€ÂÃHÞÓß Ì‰À™Á+ẪÉ`ɀÑ,Õ9ÖPÃ1ߊ̃׃×/ÜÃH̃ÀÞ,ØÃTÀ,ÖfÃ_ÔãÜÚ.Á+ÂÃ

Þ,Óß Õ5Ü,Óû@ÊÁ+ÂÃ3̃ÀɀÃ'Ò+ÁÊ,ÕÀÔUÑ,Ó@É+É+̃Ü׃Ú^ÜÚ^Á+ÂÃ`ÞÓßâÜÃ'׃ÓߚÁ€ÂÃ3̉ÀÉ+Ã'ҀÁ_ä,LŠÓ@ÀÃ'Á€ÂÃ'׃Ã'É+ÉÊßDÃ*É+Ã'Ã'Í

É+ÑÃ_ÖfÌÕ5×DɀÓ9׃ØÁ+̃Ó@ÀÉHÁ+ÂÕÁHá.ÕÚüÔRÃ'É¥ÖfҀ̃Ü,Ã.Á+ÂÃUÞ,Óß Ì‰ÀÕ.ҀÃ'Ý9̃Ó9ÀÜÃ'ÁßÃ'Ã'À Á+ÂÃ̉ÀÉ+Ã'ҀÁ‘Õ5À,ÔãÁ+ÂÃ

ÂÓ@ÑÑ,ÃTÒ_ÊfØÉ+ÁÕÉ)Á€ÂÃ`ÒfÕ9ÔÌÕ×@Þ,Óß É€Ó9׃ØÁ+̃Ó@À1̃À^Õ`ÂÓ9ÑÑÃ'ÒÑÒ+ÓûÌÔÃ'ÉDÕ5À‘Õ@Ö'ÖfØÒfÕÁ€Ã$ÔÃ'ÉfÖfÒ+̃ÑÁ€ÌƒÓ9ÀÓ5Ù

Þ,Óß Ã'û@Ã'À̃ÀÖf̃ҥÖPØáɀÁ¥ÕÀÖfÃ'Ɋ̃À^ߊÂÌրÂ^Á+ÂÕÞ,ÓߚÕÜÓû9Ã`Á€ÂÃ`ÂÓ9ÑÑÃ'Ò̉ÉÔÃ_ÖfÌÔÃ_ÔR׉Ú^ÀÓ9ÁÒ¥Õ9ÔR̒Õ5×ä

åŠÂÃUÁ+ẪÀÍ̃ÀÝ^ÂÃTÒ+Ã^̃É`Á€Â,ÕÁ3Á+ÂÃ'Ò+ÃUá“ÕÚÜ,Ã^Õ^ɀá“Õ׃×JÁ€Ò¥ÕÀÉ+̃Á+̃Ó9À™Ò+Ã'Ý@̉Ó@À¨ÀÃ_Õ5Ò3Á+ÂÃU׃Ã'û9Ã'×ÿ Ì4äÃ9äƒÊ

û9Õ׃ØÃTÉ)ÓÙCÓÙJÁ+ÂÃ3û@Ã'Ò+Á€ÃfþÓÙ/Á€ÂÃ`̃ÀɀÃ'Ò+Á̃À^ߊÂÌÖ+ÂÁ+ÂÕÞ,ÓߚÕ9ÔPØÉ+Á€ÉDÁ€ÓHÁ+ÂÃ*É+ÑÃ_ÖfÌÕ×JɀÓ9׃ØÁ€Ì‰Ó@À

ßÊÉ+Ã'Ã'ÍJäåŠÂÊɀÑ,ÃÖfÌÕ×É+Ó9׃ØÁ€ÌƒÓ9À^Ö'ÕÀ^Á€ÂÃ'ÀÜÊØɀÃ_ÔUÁ+ÓHØÀ,ÔÃ'ҀÉ+Á¥Õ5À,Ô^ÂÓß Á+ÂỂÀÉ+Ã'ҀÁDáÓ9Ü̃׃Ì'Ã'É

á“Õ5Á+Ã'ҀÌÕ×Ó9À.Á+ÂÃ3ÂÓ@ÑÑÃ'Ò`ߊÕ׃×Ê9׃Ã_Õ@ỖÀÝUÁ+Ó^ÕUáÓ9ҀÃ`ҀÃfý,ÀÃ_ԙÔÃ'É+̃Ý@À“Ó5ÙÂÓ@ÑÑÃ'Ò`̃ÀɀÃ'Ò+Á€É_ä

hopper

insert

planar cross section

r

θ

a

MJ<ONK9?@=PVQPSRUT2VWXEYZH[\T^]]#_`=aWcbd[Y"V6WQVe_f`gbE_1hDXgT2Vi_jWQVk_`gbl

åŠÂÃ3׃̃Á+Ã'ÒfÕÁ€ØÒ+ÃHÓ@ÀÁ€ÂÃ*Þ,Óß Ó5ÙÝ@Ò¥ÕÀØ×Õ5ÒDá.ÕÁ+ÃTÒ+ÌÕ׃ÉDÕ5Ò+Ó9ØÀ,ÔÓ9ÜɀÁ¥Õ9ÖP׉ÃTɊ̉À.Ý@Ã'ÀÃ'ÒfÕ×ÊÕÀ,Ô

Ó9ÀÁ+ÂÃ3ɀØÜ8fÃ_ÖfÁ*ÓÙÒ+̃Ý9ÌÔ^̃ÀɀÃ'Ò+Á€ÉŠÌƒÀÑ,Õ5Ò+Á+ÌÖfØגÕ5ÒD̃ɊÒfÕÁ+ÂÃ'ҊɥÖ'Õ5Ò¥ÖfÃ@ÊøÕ5À,Ô^áÓ9ɀÁ+׃Ú1ÃTáÑ̃Ò+ÌÖ'Õ5×äJåÓ

Á+ÂÃ$ÕØÁ+ÂÓ@Ò+É_È@ÍÀÓߊ׃Ã_ÔÝ@Ã9Ê9Á€ÂÃ`ÃÕÒ+׃̃Ã'ɀÁDßÓ9ҀÍ^̉ɐÜNÚUË9Ó@Â,ÕÀÉ+Ó9ÀãÎOmÐ,ߊÂÃTÒ+Ã$ÕUÔÃ'ɀ̃Ý9À^ÑҀÓRÖPÃ_ÔØҀÃ

ÙÓ@Ò7ÖfÓ@ÀÌÖ'Õ×J̃ÀɀÃ'Ò+Á€É`̃ÉגÕ5ÌÔ^Ó9ØÁ_ä<n`ɊҀÃ'ÑÓ9Ò+Á€Ã_Ô.̃ÀÎOm\Ð~Ê@Á+ÂÃ`ÞÓߚá“ÕÚUÜ,Ã3Á€ÂÓ9ØÝ@ÂÁŠÓÙúÕ5ÉDÜÃ'̃ÀÝ

Ò+Ó@ØÝ9Â׉ÚÑ×ÕÀ,Õ5Ò`ÕÀ,ÔüÒ¥Õ9ÔR̒Õ5×ÊÕÁ`׃Ã_Õ5É+Á3Õß7ÕÚ ÙÒ+Ó@á Á€ÂÃHû9ÃTÒ+Á+ÃPþÓÙ)Á+ÂÃ1̃ÀɀÃ'Ò+ÁäŠåŠÂÃỦÀÁ€Ø̃Á+̃Ó9À

ÂÃ'ҀÃ`̃ÉÁ+Â,Õ5Á׉ÓÖ'Õ5׃׉Ú3Á€ÂÊÉ+Ñ,Õ@ÖfÊÜÃ'ÁßDÃTÃ'ÀÁ€ÂÊÂÓ9ÑÑ,Ã'Ґß7Õ5׉×Õ5À,ÔHÁ€ÂỄÀÉ+ÃTÒ+Á̉ÉÀÃÕÒ+׃Ú1Õ*ßÃ_ÔÝ@Ã9Ê

ÿÌäÃ9äƒÊ@ߊ̉Á€Âɀ׉̃Ý@ÂNÁ€×ƒÚ1ÖfØҀû9Ã_ÔߊÕ׃׃É'Ê@É+ÓUÁ+ÂÕÁÁ+ÂÃHÖfØҀû9ÕÁ€ØÒ+Ã3ÓÙ/Á€ÂÃ3ÂÓ9ÑÑ,Ã'Ò`Õ5À,ÔUÓÙÁ+ÂÃ*̃ÀÉ+Ã'ҀÁ

É+ÂÓ9Ø×ÔãÒ+ÃTÑÒ+Ã'ɀÃ'ÀÁÕ.ẪÝ9ÂÃ'Ò1Ó@Ò¥ÔÃTÒ1ÖfÓ9ҀÒ+Ã_ÖPÁ+̃Ó9À Á+ÓãÕ.Ñ×ÕÀ,Õ5Ò3Ò¥Õ9ÔR̒Õ5×)É+Ó@׃ØÁ+̃Ó9À|Ê/̃ÀߊÂÌրÂÁ+ÂÃ

Ó9Ҁ̃Ý9̃À̃É?D Çopq "!ro!#s:tÃ3ÃfþÑ׃Ó9ҀÃHÁ+ẪÉ*̉ÀÁ€Ø̃Á+̃û9Ã3ÌÔÃ_ÕUÜÚߊҀ̃Á+̃ÀÝ^Á+ÂÃHÃ_Û@Ø,ÕÁ€ÌƒÓ9ÀÉ

ÓÙ`áÓ9Á€Ì‰Ó@À̃ÀÁ€ÂèÖfÓÓ9Ò¥ÔR̉ÀÕÁ+ÃTÉ1Ó5Ù?/̃Ý@ØÒ+ÃãÄ9äƒÄ9Ê)Õ5À,ÔãÉ+Ã'ÃTÍÑÀÝɀÓ9׃ØÁ€Ì‰Ó@ÀÉ1Õ5ɑÕ5À ÕÉ+ÚáÑÁ+Ó@Á+ÌÖ

É+ÃTÒ+̃Ã'ÉỦÀãÑÓßDÃ'ҀÉ1Ó5ÙuvHrwJá^Ø,րÂÕɖË9Ã'À̃Í@Ã9ÈÉHÉ+Ó@׉ØÁ+̃Ó9ÀãÃ'áÑ׉ÓÚÉ*É¥Ö'Õ5׉̃ÀÝ.Ó5Ù7Á€ÂÃÔÃ'ÑÃ'À,ÔÃTÀNÁ

û9ÕҀÌÕÜ׃Ã'ɊÓ5ÙÉ+Á€Ò+Ã'ɀÉHÕÀ,Ôû9ÃT׉ÓÖf̃ÁÚÜNÚÑ,ÓßÃ'ҀÉ`ÓÙFx&Á+ÂÃ1ỖÉ+ÁfÕÀ,ÖfÖÓÙDÕUá“Õ5Á+Ã'Ҁ̒Õ5×,ÑÓ9̃ÀÁÙҀÓ9á

Á+ÂÃ$û@Ã'Ò+Á€Ãfþ¨ÓÙ)Á+ÂÃ$ÂÓ9ÑÑÃ'Ò_ä

tšÌƒÁ€Â^Á+ẪÉÀÃ'ß ÕÑÑҀÓNÕ@Ö+Â|Ê9ßÃ3ÃfþÁ+Ò¥Õ@ÖfÁŠÁ+ÂÃ`Ò¥Õ@ÔÌÕ×É+Ó@׉ØÁ+̃Ó9ÀÕ5ÉDÁ€ÂÃ3׉ÃÕ9ỖÀÝHÓ@Ò¥ÔÃTҊÁ+Ã'Ҁá

̃ÀÁ€ÂÃ`ÃfþÑ,Õ5ÀÉ+̃Ó@À/ä<tÃ`Á€ÂÃ'ÀÙÓ9Ҁá^Ø×ÕÁ€ÃDÃ_Û@Ø,Õ5Á+̃Ó9ÀÉ)ÙÓ@ÒDÁ€ÂÃ`ÀÃfþÁŠÓ9Ò¥ÔRÃ'ҊÁ+Ã'ҀáÉÊÒ+Ã'ÑҀÃ'É+ÃTÀNÁ€ÌƒÀÝ

Õ3ÖfÓ9ҀÒ+Ã_ÖPÁ+̃Ó9À^Á€ÓHÁ+ÂÊÑגÕ5ÀÃÒ¥Õ9ÔR̒Õ5×É+Ó9׃ØÁ€ÌƒÓ9À/äJåŠẨÉÖfÓ9ҀÒ+Ã_ÖfÁ€ÌƒÓ9À^̃ÉÂÓ9ÑÃ_ÔUÁ+Ó3Ñ,Õ5Ò+Á€Ì’Õ5׃׉ÚHÕ5׉׃Ã'ûÌÕÁ€Ã

É+Ó@áÃÓÙ/Á€ÂÃ`Ó@ÜNû̃Ó9ØÉ)É+ÂÓ@Ò+ÁfÖfÓ9á̉ÀÝ9Ɋ΃Ä_ÇÊ5Ñ/ä>ô9Ï9ö\Ð,ÓÙ/Á€ÂÃ`ÑØÒ+Ã'׃ÚUÒ¥Õ@ÔÌÕ×,Õ5ÑÑÒ+ÓÕ9րÂÓ5Ù`Îm\Ð+ä/åŠÂÃ

Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ3ÿÕÁÜ,Ó@Á+Â.Ó9ÒfÔÃ'ҀÉ`Õ5Ò+Ã3É+Ó@׃û9Ã_Ô ÀNØáÃ'Ҁ̒ÖTÕ׃׃ÚHÙÓ@ÒDҀÃ'ÑҀÃ'É+Ã'ÀÁfÕÁ+̃û@ÃHÑÂÚÉ+ÌÖ'Õ×|Ñ,ÕÒfÕáÃfæ

Á+ÃTÒ+É_äåŠÂÃ3Ó9ØÁ€×ƒÌ‰ÀÃ$Ó5ÙÁ€ÂÃ3Ñ,ÕÑÃ'Ò`̃ɊÕÉÙÓ@׃׉ÓߊÉä/¿ÀJyÃÖfÁ+̃Ó9À¨ÏÊÁ+ÂÃ3Ã_Û@Ø,Õ5Á+̃Ó9ÀɊÓ5ÙáÓ9Á+̃Ó@ÀÕÒ+Ã

ÔÃ'Ҁ̃û9Ã_ÔÕÀ,ÔỖɥÖfØɀÉ+Ã_Ô äFyÃ_ÖPÁ+̃Ó9À.ô3̃ÉDÔÃ'û@Ó9Á+Ã3Á€ÓHÁ+ÂÃ3ÖfÓ9ÀÉ+Á+ҀØ,ÖfÁ€Ì‰Ó@À.ÓÙ/Á+ÂÃ$ÕÜÓû9ÊáÃ'ÀÁ+̃Ó9ÀÃ_Ô

ÃfþÑ,Õ5ÀÉ+̃Ó9À|äCL•ØáÃ'ҀÌÖ'Õ×ÃfþÑ,ÃTÒ+̃áÃ'ÀÁ€ÉDÕҀÃ$ỖɥÖPØÉ+ɀÃ_ỔÀzyRÃ_ÖfÁ+̃Ó@Àz{,ä<|̃À,Õ׃׃ÚNÊÖfÓ@À,Öf׃Øɀ̉Ó@ÀɊÕÒ+Ã

ÓóJÃ'ҀÃ_Ô.̃À|yÃÖfÁ+̃Ó9À}mä

(3)

Ñ,Õ5Ò+Á+ÌÖf׃Ã'É*Â,Õû9ÖÀÓ^áÓ@Á+̃Ó9À^̃À¨Á€ÂÃ1ÕþÌÕ×ÿ Ó9ÒD‚C*ỖÒ+Ã_ÖPÁ+̃Ó9À/äåŠÂÃTÀ¨Á+ÂÃUÔÃ'ÑÃ'À,ÔÃ'ÀÁHû9Õ5Ò+ÌÕÜ׉ÃTÉ

Ò+ÃÔØ,ÖfÃUÁ+ӖÙÓ9ØÒ`ÖfÓ9áÑ,Ó@ÀÃ'ÀÁ+ÉÓÙ)É+Á€Ò+Ã'ɀÉHÕÀ,Ô ÁßDÓ^Ó5Ùû9ÃT׉ÓÖf̃Áڃ

„

…†

„‡2‡ „w‡‰ˆ Ç

„‡2ˆ „wˆˆ Ç

Ç Ç „UŠŠ

‹Œ 

…†



‡



ˆ

Ç

‹Œ

s ÿ4ÏäƒÄŽ

åŠÂÃ3Ã_Û@Ø,Õ5Á+̃Ó9ÀɊÓ5ÙáÓ9Á+̃Ó@ÀÕÒ+à ‘

„ “’8”w ÿ4Ïä>ÏH

̃ÀߊÂ̒րÂ}’.̉É3Á€ÂÃÔÃ'Àɀ̃ÁÚNÊJÁfÕÍ@Ã'ÀÁ+Ó.ÜÃÖfÓ9ÀɀÁ¥Õ5ÀNÁÊÕ5À,ԙÁ+ÂÃUû9Ã_ÖPÁ+Ó9ҕ”¨ÌƒÉ$Á€ÂÃÕ9ÖTÖfÃ'׃Ã'Ò¥Õ5Á+̃Ó9À

ÔØÃ3Á€Ó^Ý9Ò¥Õû̃ÁÚÊNÕ5À,Ô ‘



2Ç: ÿ4Ïä>ôH

– Û@Ø,Õ5Á+̃Ó9ÀÉUÿÏä>Ï8•Ò+Ã'ÑҀÃ'É+ÃTÀNÁUÁ+ÂÃ^Ü,Õ×ÕÀÖfÃ1Ó5ÙDÙ Ó9Ò¥ÖPÃ'É3̉ÀãÁ+ÂÃ^á“ÕÁ€Ã'Ò+ÌÕ5×4ÊߊẪ׃ÃHÃ_Û@Ø,ÕÁ€ÌƒÓ9À ÿ4Ïä>ôH

ÃfþÑҀÃ'É+ɀÃ'É3̉ÀÖfÓ9áÑÒ+Ã'ɀÉ+̃Ü̃׃̃ÁÚNäL•Ó9Á€Ã$Á€Â,ÕÁŠÜÃ_Ö'Õ5ØÉ+ÖÝ9Ò¥Õû̃ÁÚ^Â,Õ5ɊÀӑÖPÓ9áÑÓ9ÀÃ'ÀÁD̃ÀÁ€ÂÃ1Õ\þRÌÕ5×

ỖÒ+ÃÖfÁ+̃Ó9À|Ê „ ̃É^̃À,ÔÃTÑ,Ã'ÀÔÃ'ÀÁ.Óـ‚Ê`Õ5À,Ô Ý9̃û9ÃTÀâÁ€ÂÃ.ÙÓ@Ò+á ÿÏäƒÄ#UÓ5Ù$Á€ÂèÉ+Á€Ò+Ã'ɀɨÁ+ÃTÀÉ+Ó@Ò „

Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ*ÿ4Ïä>Ï8Ò+Ã_ÔØÖfÃHÁ+Ó^ÁßÓUÃ_Û@Ø,ÕÁ€Ì‰Ó@ÀÉ_ÊɀÓ1Á€Â,ÕÁŠÁ€ÂÃ3É+ÚÉ+Á€Ã'á#ÿ4Ïä>ÏÊÏä>ô8)ÖfÓ@ÀÉ+̃ɀÁ+ɊÓÙÁ+ÂҀÃ'Ã

Ã_Û@Ø,Õ5Á+̃Ó9ÀɊ̃ÀÁ+ÂÃHɀ̝þØÀÍÀÓߊÀɊÓ5Ù7ÿÏäƒÄ#Tä

n3ÔÔÃ_ÔãÁ€Ó¨Á+ÂÃTÉ+ÃÃÛ9ØÕÁ+̃Ó@ÀÉ1ÕҀÃÖfÓ9ÀÉ+Á+̃Á€ØÁ+̃û9Ã^×ÕߊÉäz—JÃ'Á4˜™ Á+Ò „ v@ôÜÃ^Á+ÂÃ.è8š# fçTè›I

ï_ñ„ç fï€ï_ÊJáÓ9ҀÃ`ÑҀÃ_Öf̃É+Ã'׃Ú.Á+ÂÃ1Õû9Ã'ÒfÕÝ@ÃHÓÙÁ+ÂÃHÑÒ+̃À,Öf̃Ñ,Õ5×/É+Á€Ò+Ã'ɀÉ+Ã'É&œ:‰ž ÄH¥Ïo¥ôo9Á€ÂÃ3Ã'̃Ý9Ã'Àû9Õ5×wæ

ØÃ'ɖÓÙ

„

ä&n`ɀÉ+Øá̃ÀÝÑ×Õ5É+Á+ÌÖUÔÃfÙÓ@Ò+á.ÕÁ+̃Ó@À“ÃTû9Ã'ҀÚNߊÂÃ'Ò+Ã9ÊßÃ^̃áÑÓ9ɀÃHÁ+ÂÃUû9Ó@À õü̉ɀÃ'ÉDŸê1 fë é

 

í5òJé9êñêíò ¡

¢

1£A¤

ÿœo¥p˜‰¦=2ÏUÉ+̃À¦§w˜w¦8 ÿ4Ïä{

ߊÂÃ'Ҁ觖̃É`Á€ÂÃ1ÕÀÝ9׃Ã3ÓÙ)̃ÀNÁ€Ã'Ò+ÀÕ×JÙ Ò+ÌÖfÁ+̃Ó@À/ä=/̃À,Õ5׃׉ÚÊ@ßDÃHÂÕû9Ã3Á+ÂÖì,íî çðë1 ÊߊÂÌր“ҀÃ'×ÕÁ€Ã'É

Á+ÂÃ$ɀÁ+ҀÃ'É+É3Á+Ó^Á€ÂÃ1ÔÃPÙÓ9Ҁá“ÕÁ€ÌƒÓ9ÀUÁ+ÂҀÓ9ØÝ@“Á€ÂÃHïñç'èêƒò“çTèNñf 1ñf fòïfíç©/ÔÃPý,ÀÃ_Ô¨Õ5É

ª «¥

Ä

Ï

ÿ



¬



Ž­

s

åŠÂÃHÖfÓ@À,ỖÁ+̃Ó9À.Ó5ÙDè_ëƒêc›Nòo®| fòJñ+Ê@Á+ÂÃ`ÞÓß Ò€Ø׃Ã$ØÉ+Ã_Ô.ÂÃ'Ò+Ã9ỄɊÁ+ÂÕÁŠÁ+ÂÃ'Ò+ÃHÃPþR̃ɀÁ$ՖɥÖ'Õ5גÕ5Ò?¯€° Ç

É+ØÖ+™Á+Â,Õ5Á

ª ¯@ÿ „ ¥J˜±Hs ÿ4ÏäOmH

¿À¨Ñ,Õ5Ò+Á€Ì’ÖPØ×ÕÒ_Êɀ̉ÀÖfà S

ª

Á+Ò

ª

/ÕÀ,ÔÁ€ÂÃ1Ҁ̃Ý9ÂÁ`Â,Õ5À,Ô.ɀ̒ÔRÃHÓيÿ4ÏäOm8ŠÂÕÉTÃ'Ò+Ó.Á+ÒfÕ9ÖfÃ@ÊJÁ+ÂÃ

Þ,Óß Ò€Ø׃ÃH̃É$ÖfÓ@ÀÉ+̃É+Á€Ã'ÀÁ3ߊ̉Á€Â¨Á+ÂÃH̃À,ÖfÓ9áÑÒ+ÃTÉ+É+̃Ü̃׃̃ÁړÖfÓ@À,ỖÁ+̃Ó@ÀÿÏä>ô8Tä

–

Û@Ø,Õ5Á+̃Ó9Àãÿ4Ïä{iŠÌƒÉ`Õ

É+̃ÀÝ@׃Ã`Õ׃Ý9Ã'ÜÒ¥ÕÌÖÖfÓ9ÀÉ+Á+ÒfÕ̃ÀÁ)Ó9À^Á€ÂÃ`ɀÁ+ҀÃ'É+ÉÊߊẪ׃ÃDÃÛ9ØÕÁ+̃Ó@À.ÿ4ÏäOmH/ҀÃ_ÔØ,ÖPÃ'ɊÁ+ÓHÁßÓ3Ã_Û@Ø,ÕÁ€ÌƒÓ9ÀÉ

Ò+ÃTגÕ5Á+̃ÀÝHÁ€ÂÃ3É+Á€Ò+Ã'ɀÉ$ÕÀÔ^û9ÃT׉ÓÖf̃ÁÚUÝ9ÒfÕ9ỖÃ'ÀÁ+ÉäåŠÂØÉ_ÊÃ_Û@Ø,Õ5Á+̃Ó9ÀÉ`ÿÏä>ώ²ÏäOm8|Ò+ÃTÑÒ+Ã'ɀÃ'ÀÁ$ՖÉ+Ã'ÁŠÓ5Ù

É+̝þ.Ã_Û@Ø,ÕÁ€Ì‰Ó@ÀɊ̃ÀÁ€ÂÃ3É+̝þ“ØÀÍNÀÓߊÀɊÓÙÿ4ÏäƒÄŽ'ä

¿À.Á+ÂÃÖPÓNÓ@Ò¥ỖÀ,Õ5Á+Ã'É*ÓÙ,/̃Ý@ØÒ+Ã^Ä9äƒÄ@ÊÁ+ÂÃ3É+Á€Ò¥Õ5̉À.ÒfÕÁ+ÖÁ+Ã'ÀɀÓ9ҊÜÃ_ÖfÓ@áÃ'É

ª

…³

³

³

³

†

¥u´ ‡



‡ ÿ‰¥

Ä

´ ˆ



‡ ¥µ´ ‡



ˆ

¬



ˆ

‰v@Ï Ç

ÿ‰¥

Ä

´ ˆ



‡ ¥µ´ ‡



ˆ

¬



ˆ

‰v@Ï ¥

Ä

ÿ´ ˆ



ˆ

¬µ

‡ Ç

Ç Ç ¥



‡ É+̃À¶ ¬·

ˆ ÖfÓ9Éw¶

r

¬

|É+̃À¶ ‹¸

¸

¸

¸

Œ

ÕÀÔÁ€ÂÃ3É+̝þ“ÃÛ9ØÕÁ+̃Ó@ÀÉ`ÕҀÃ

´

‡„w‡‰‡

¬

Ä

´

ˆ„w‡‰ˆ

¬

ÿ

Ä

¬

ɀ̃À¶

r

¬

JÉ+̃À¶ „‡2‡

¬

ÖfÓ@ɶ

r

¬

|É+̃À¶ „‡2ˆ

¥

Ä

„wˆˆ

¥

É+̃À¶

¬

„ ŠŠ

(4)

´ ‡„‡2ˆ ¬ Ä ´ ˆ„ˆˆ ¬ ÿ Ï ¬ É+̃À¶ r ¬ |É+̃À¶ „w‡‰ˆ ¬ ÖfÓ@ɶ r ¬ |É+̃À¶ ÿ „wˆˆ ¥ „ ŠiŠ ,“’8”É+̃À=¶< ÿ4Ïä>öH

ÿ„ ‡2‡ ¥p˜

¦

¬

ÿ„ ˆˆ ¥J˜

¦

¬

ÿ„ŠŠ ¥p˜

¦

¬

Ï „

¦

‡‰ˆ

ÏúÉ+̃À ¦ §w˜

¦ ÿ4Ïä>÷H É+̃À¶ r ¬ É+̃À¶  ‡ ¬ ÖfÓ9ɶ r ¬ /ɀ̃À¹¶  ˆ Ä ´ ˆ  ˆ ¬ Ä  ‡ „ŠŠ ¥|˜ „wˆˆ ¥p˜ ÿ4Ïä>ÅH Ä Ï ´ ‡  ˆ ¬ Ä ´ ˆ  ‡ ¥ Ä  ˆ Ä ´ ˆ  ˆ ¬ Ä  ‡ „ ‡‰ˆ „wˆˆ ¥J˜ ÿÏäƒÄ_ÇH ´ ‡  ‡ ¬ Ä ´ ˆ  ˆ ¬ ÿ Ä ¬ ɀ̃À¶ r ¬ /ɀ̃À¶  ‡ ¬ ÖfÓ@ɶ r ¬ |É+̃À¶ 

ˆ 2Ç:s ÿÏäƒÄ9Ď

– Û@Ø,Õ5Á+̃Ó9ÀÉ3ÿÏä>Æ8ÕÀÔ.ÿ4Ïä>ö8ÕÒ+ÖÁ+ÂÃ3É+Á€Ò+Ã'ɀÉ3Ã_Û@Ø̃׉̃ÜҀ̃ØáàÖfÓ9À,ÔR̉Á€ÌƒÓ9ÀÉÊߊẪ׉Öÿ4Ïä÷H̃ÉDÁ€ÂÃHû9Ó@À

õ.̃É+ÃTÉ`Ú̃Ã'×ԓÖPÓ9À,ỖÁ€Ì‰Ó@À/ä – Û9ØÕÁ+̃Ó@ÀÉ3ÿ4ÏäÅHDÕ5À,ԙÿ4Ïä‰ÄÇ8ŠÕ5Ò+Ã1ỖҀÃ_ÖfÁ$ÖPÓ9ÀɀÃ_Û@ØÃ'À,ÖfÃTÉHÓÙ)Á+ÂÃ3Þ,Óß Ò+Ø׉ÃUÿÏäOm8TäC|̃À,Õ׃׃ÚÊÿÏäƒÄ9Ď)̃ÉÁ+ÂÃ1ÖPÓ9ÀÁ+̃ÀØ̃ÁÚ^Ã_Û@Ø,ÕÁ€ÌƒÓ9ÀÃPþRÑÒ+Ã'ɀÉ+̃ÀÝ.̃À,ÖfÓ9áÑÒ+ÃTÉ+É+̃Ü̃׃̃ÁÚNä åŠÂÃHÕ5Ü,Óû@Ã$ɀÚÉ+Á+ÃTá ̉ɊÖfÓ@áÑ׃Ã'Á€Ã_Ôߊ̉Á€ÂÁ€ÂÃ3ÙÓ@׉׃Óߊ̃ÀÝ3ÜÓ9ØÀ,ÔÕÒ+Ú.ÖfÓ9ÀỖÁ+̃Ó9ÀÉ „w‡‰ˆ ÿg¶A¤,“º „ˆˆ ÿg¶A¤" „‡2ˆ ÿ¶ ¦ C»¥=º „ˆˆ ÿ¶ ¦ ÿÏäƒÄ_ÏH  ˆ ÿg¶A¤,2Ç  ˆ ÿ¶ ¦ ,2Ç:s ÿÏäƒÄ_ôH

– Û@Ø,Õ5Á+̃Ó9Àãÿ4ÏäƒÄ_Ï8ÔÃ'ÉfÖfÒ+̃ÜÃ'É3Á+ÂÃÙÒ+ÌÖfÁ€Ì‰Ó@À.ÃfóøÃÖfÁ+É3Ó9À.Á€ÂÃHߊÕ׃׃ÉDÓ5ÙúÜÓ9Á€Â¨Á+ÂÃ$̃ÀɀÃ'Ò+ÁUÿg¶zq¶ ¤

ÕÀÔ^Á+ÂÃ$ÂÓ9ÑÑÃ'Ò'ÿg¶p¶

¦

Tä,Ó@ÒDÁ€ÂÃ3É¥Õ5Í9Ã`Ó5Ùɀ̉áÑ׃ÌÖf̃ÁÚNÊßÃ$ÕɀÉ+ØáÃ`Á€ÂÃ3É¥ÕáÃ$ÖfÓü“ÖP̉ÃTÀNÁŠÓ5Ù

ߊÕ׃×Ù Ò+ÌÖfÁ+̃Ó@À|º™ÙÓ@ÒDÜÓ9Á€Â“̃ÀɀÃ'Ò+Á3ÕÀ,ÔÂÓ@ÑÑÃ'Ò_ä

½ ½?=¾

8)(T U+Š#¿D¿,88)À )(T9(Á/(T_

½1¿À–Á+ÂÃDÖTÕÉ+ÐÓÙÁ+ÂÃÂÓ@ÑÑÃ'ÒÂ5̉ÀÉ+Ã'ҀÁ

ÑҀÓ9Ü׃Ã'áãÊ9Á€ÂÃ'Ò+Ã3̃ÉÀÓ1ɀ̃á̃×ÕÒ+̃ÁÚ3É+Ó@׃ØÁ+̃Ó9À|äCÓ9Ò=rJà ÇÊ:r6ÄÅÊɀÃ'Ã|̃Ý9ØҀÃ1Ä@ä‰Ä@Ê9ßÃ$ÖPÓ9Àɀ̒ÔRÃ'Ò

̃ÀÉ+Á€Ã_Õ9ÔÁ€ÂÃ3ÙÓ@׉׃Óߊ̃ÀÝ3ÃfþÑ,Õ5ÀÉ+̃Ó9À

„ “ „Æ ÿg¶

¬ ¦ „ ¤ ÿg¶ ¬ sŽs#s  Ä  Æ ÿ¶ ¬· ¤ ÿg¶ ¬ sŽsŽss ÿ4ôäƒÄŽ tÃỦÀÁ€Ò+ÓÔØ,ÖfÃ^ÀÃ'ßÇyÓ9Í@Ó9׃ÓûÉ+Í̃Ì/û9ÕҀÌÕÜ׃Ã'É*Á+Ó.Ò+Ã'ߊҀ̃Á+Ã^Á+ÂÃUý,Ò+ɀÁHÁ+ÂҀÃ'ÓÖPÓ9áÑÓ9ÀÃ'ÀÁ+É3ÓيÁ+Âà É+Á€Ò+Ã'ɀÉ3Á+Ã'ÀɀÓ9ÒäFÓ9Ò=È Ço_Ä@Ê9ßÃ3É+Ã'Á É „Ê ‡‰‡ ÿ¶ „Ê ‡‰ˆ ÿ¶ „Ê ‡‰ˆ ÿg¶ „Ê ˆˆ ÿ¶IË «œ Ê ÿg¶gÌ ¬·Í Ê ÿg¶ É

¥üÖfÓ@ÉøÏHÎ Ê ÿ¶Ï¥“ɀ̉À`ÏHÎ Ê ÿg¶

¥.É+̃À`ÏHÎ Ê ÿg¶ ÖPÓ9ÉJÏ8Î Ê ÿg¶

Ë

s ÿ4ôä>ÏH

Ð ÃTגÕ5Á+̃Ó9ÀÉ^ÿ4ôä‰ÄŽ1Õ5À,Ô ÿôä>Ï8–ÕÒ+ÃÁ+ÂÃTÀâɀØÜɀÁ+̃Á+ØÁ€Ã_Ô ÌƒÀ ÿ4Ïä>Ǝ²RÏäƒÄ9Ä#TÊÕ5À,ÔÁ€ÂÓÖPÓNÃ"¼“Öf̃Ã'ÀÁ+ÉÓ5Ù

Ã_Û@Ø,Õ5×/ÑÓßDÃ'ҊÓ5ÙFHÃ_Û@Ø,Õ5Á+Ã_Ô äFK*À׃ÚÁ€Ã'Ò+áɊÓÙÓ@Ò¥ÔÃTÒ$Ç^ÕÀÔÄHÕ5Ò+ÃHÖfÓ@ÀÉ+ÌÔÃ'ҀÃ_ԙÂÃ'Ò+Ã@äFtÃ*Â,Õû9à ÙÓ@ØÀ,Ô^̃Á`ÖfÓ@Àû9Ã'À̃Ã'ÀÁŠÁ€Ó^ßDÓ@Ò+Íߊ̃Á€ÂÁ+ÂÃ3ÙÓ9׃׃Óߊ̃ÀÝ3É+Á€Ò+Ã'ɀÉ$û9Õ5Ò+ÌÕÜ׉ÃTÉ œ Æ Î Æ ÑÒ Í ¤ ÖfÓ@É,Ï8Î ¤ ÓD Í ¤ É+̃ÀŠÏ8Î ¤ É+ÓUÁ+ÂÕÁŠÌƒÀ^ÃfóJÃ_ÖfÁ`Á€Âà Í

û9Õ5Ò+ÌÕÜ׃Ã'ɐÙҀÓ9á ÿ4ôäÏHDÕ5Ò+Ã*ÀÓ9ÁÃfþÑ׃ÌÖf̃Á+׃Ú^ÑÒ+ÃTÉ+Ã'ÀÁ_ä7Ó@ÒDÁ€ÂÃ3û9Ã'׃ÓÖf̃ÁÚÊ

(5)

Õ É€ÌƒÀÝ.ÿ4Ïä÷H'Ê@̃ÁŠÁ+ÂÃ'ÀÙÓ@׃׉ÓߊÉÁ+ÂÕÁ

Í

Æ œ Æ É+̃À§ ÿ4ôä{

Õ É€ÌƒÀÝ^Ò+Ã'×Õ5Á+̃Ó9ÀÉ*ÿ4Ïä>Æ8ŠÕÀÔ.ÿ4Ïä>ö8×‰ÃÕ9ÔÁ+Ó^Á€ÂÃ3É+ÚÉ+Á€Ã'á

É

¥.É+̃À§|É+̃À`Ï8Î Æ ¥`Ï8œ Æ É€ÌƒÀ§ÖPÓ9ÉJÏ8Î Æ

Ä

¬

ɀ̃À§ÖPÓ9É,ÏHÎ

Æ

¥`Ï8œ

Æ

É+̃À§|É+̃À7ÏHÎ

ÆjË

É

œ Æ

Î

ÆË=Ö

¬

É

œ Æ ÿ¥Ä7¥ôÉ+̃À§ÖfÓ9ÉÏ8Î Æ

¥`ôHœ

Æ

É+̃À§|É+̃À`ÏHÎ

Æ×Ë

É

¥¹’H”7ÖPÓ9ɶ

’8”É+̃À¶ØË

¶ÚÙãÿ¶A¤#¶

¦

s ÿ4ôäOmH

åŠÂÃ3É+ÚɀÁ+Ã'á ÿôäOm8ÌƒÉ`ÖfÓ9áÑ׃Ã'Á+Ã_Ô ÜÚÁßÓ1ÜÓ9ØÀÔÕҀړÖfÓ@À,ỖÁ+̃Ó9ÀÉ

„ ‡‰ˆ ÿg¶

¤

,“º „ ˆˆ ÿg¶

¤

„ ‡2ˆ ÿ¶

¦

C»¥=º „ ˆˆ ÿ¶

¦

s

åŠÂÃHÕÜÓû9Ã3Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ`Ö'ÕÀ.ÜÃ$ɀÓ9׃û9ÃԓÕ5À,ÔÚ̉ÃT×’Ô Ü,Ó@ØÀ,ÔÕ5Ò+Ú.ÖfÓ9À,ÔR̉Á€ÌƒÓ9ÀɊÓ@À|Î Æ

Î

Æ

ÿ¶ ¤ ,»¥ÎAÛ Î

Æ

ÿg¶

¦

,«ÎAÛ¹ ÿ4ôä>ÆH

ߊ̃Á+ÂÜÎAÛµ

ÕÒ¥ÖPÁ¥ÕÀ=º

Ï

¬

Ä

Ï

Õ5Ò¥Öfɀ̃À/ÿ

É+̃ÀJÿ4Õ5Ò¥ÖfÁfÕÀ=º

É+̃À§

Ä

Ï

ÿÝ

¬

ÕÒfÖfÉ+̃À|ÿ É+̃ÀÝ

É+̃À§

2ŠßŠÂÃ'ҀèÝ3Êwº

Á¥Õ5ÀÝ3ỂÉ*Á+ÂÃ^ÕÀÝ9׃ÃHÓÙ)ߊÕ׃×JÙ Ò+ÌÖfÁ+̃Ó@À/ä`¿ÀÖfÌÔÃ'ÀÁ¥Õ5׉׃ÚÊÁ+ÂÃ^ÕÜÓû9ÖÒ+Ã'×ÕÁ€ÌƒÓ9À¨á.ÕÍ9ÃTɊÉ+Ã'ÀɀÃ^Ó9À׃Ú

̝ÙDÁ+ÂÃÕÀÝ@׉ÃUÓÙß7Õ5׉×|ÙҀÌÖfÁ+̃Ó9À}Ý ÌƒÉ3׉ÃTÉ+ÉHÓ@Ò$ÃÛ9ØÕ×)Á€Ó“Á€ÂÃ^ÕÀÝ@׉ÃUÓÙ̉ÀÁ€Ã'Ò+À,Õ5×ÙҀ̒ÖPÁ+̃Ó9ÀܧÊ|ÌäÃ9äƒÊ

ÝSÞߧÊ|Ó9Ò3Ã_Û@Ø̃û9Õ׃Ã'ÀÁ€×‰ÚÊwº·Þ Á¥Õ5À§äU¿ÀÑÒfÕ9ÖfÁ€ÌÖfÃ9ÊÁ+ÂÃ^Ò+Ó9ØÝ9ÂÀÃTÉ+ÉHÓ5Ù7Á€ÂÃ^ß7Õ5׃׉É*̃É$ØÉ+Ø,Õ5׉׃Ú

É+ØÖ+ÂÁ€Â,ÕÁ–Á+ÂÃ^ÑҀÃ'û̃Ó9ØÉ1ÖPÓ9À,ỖÁ€Ì‰Ó@À̃É1ÖPÓ9á^Ù Ó9Ò+ÁfÕÜ׃ÚÉ¥ÕÁ€ÌƒÉý,Ã_Ô Î>öÊJÑ/ä{ÆÐ+äUåŠÂÃ^Ò+Ã'×Õ5Á+̃Ó9ÀɀẪÑ

ÜÃ'ÁßDÃTÃ'ÀÜÎ

Û

Õ5À,ԙÿEº,§)̃Ɋ̃׃׉ØÉ+Á+ÒfÕÁ€Ã_ỔÀp|̉Ý@ØÒ+ÃHôä‰Ä@ä

0

0.1

0.2

0.3

0.4

0.5

0

10

20

30

40

50

60

boundary condition

ψ

W

wall friction

µ

δ

= 5,...,50

5

10

15

20

25

30

35

40

45

50

MJ<ONK@?9=,à@VQPâá=_ã]#_fV8hŽ_fV8Xg_FTä*b[\_AåT2æŽV8hY`gç=XgT2V8hWQbW1T2V=èéaWcb[,`_fkE]Ž_1X^bbETAb[\_*aYZQZfäg`gWXgbWêTV

ë

äT2`,eY`gWêTæ#k,eYZæì_k,b[\_7YV#íZO_=Tä<WcVbE_f`gV8YZä^`gWdX^bdW1T2V?îl

L•Ó9Á+ÖÁ+Â,Õ5ÁŠÁ+ÂÃ1Õ5Ü,Óû@ÃHÑҀÓ9Ü׃Ã'á#ÿ4ôämÊôä>Æ8TÊÖfÓ9ҀÒ+Ã'ɀÑ,Ó@À,ỖÀÝ.Á+Ó^Á€ÂÃH׃ÓßÃ'É+ÁŠÓ@Ò¥ÔÃ'Ò*Á+Ã'ҀáÉ

̃À.Ó9ØÒ*ÃfþÑ,ÕÀɀ̃Ó9À/ỂÉ*Ãfþ,Õ9ÖfÁ€×ƒÚ“Ë@Ã'À̃Í9Ã@ÈÉ*Ò¥Õ@ÔÌÕ×JÉ+Ó@׃ØÁ+̃Ó9À.̃À.Á+ÂÃUÑ×ÕÀÕÒ`Ö'Õ5É+Ã9ä=tÃ3ÀÓß Á€ØÒ+À

Á+Ó^Á€ÂÃHÔÃ'Ҁ̉û9Õ5Á+̃Ó9ÀÓÙÁ+ÂÃHÃÛ9ØÕÁ+̃Ó@ÀÉÙÓ9ÒÁ+ÂÃ3ý,Ò+ɀÁ`Ó@Ò¥ÔÃ'ҊÁ€Ã'Ò+áÉ_ä

Õ

É+̃ÀÝ.ÿ4Ïä>Å8'Ê@ßÃ$Ý@Ã'Á

„

¤

ŠŠ Ԙ

¤

¬

É+̃À¶

œ

Æ

ɀ̉À§ÖfÓ@É,Ï8Î

Æ

(6)

ÕÀÔÁ€ÂØÉ_ÊÜNÚÔRÃfý,À̃Á+̃Ó@À“Ó5ÙU˜ ¤ ˜ ¤ «œ ¤ ¬ É+̃À¶ Ï,r

œ Æ É+̃À§ÖfÓ@É,Ï8Î Æ s ÿ4ôä>öH

åŠẪɊ×ÕɀÁDҀÃ'×ÕÁ+̃Ó@À“̃ÉÁ+ÂÃý,Ò+ɀÁ`Ó9ÒfÔÃ'Ò`Õ5À,Õ׃Ó9ÝUÁ+Óÿ4ôä>ô8'äåŠÂÃ'À/ÊJÿÏä>÷8×ƒÃ_Õ9ÔRɊÁ+Ó

Í

Æ

Í

¤

ÖfÓ@É,ÏÿgÎ Æ ¥Î

¤

,šÉ€ÌƒÀ

¦

§<œ Æ ˜

¤ ÕÀÔÁ€ÂØÉ_ÊÜNÚ.ÿôä{iÕÀÔ¨ÿôä>ö8 Í ¤ ÖfÓ9ÉÏÿÎ Æ ¥µÎ ¤ jšÉ€Ì‰À=§ É œ ¤ ¬ ɀ̃À¹¶ Ï,r œ Æ É+̃À§ÖfÓ9É,ÏHÎ Æ Ë s ÿ4ôä>÷H åŠÂÃU×ÕÉ+Á*Ã_Û@Ø,ÕÁ€ÌƒÓ9Àãÿ4ôä÷HŠßŠÌƒ×ƒ×/ÜÃHÒ+ÃTÝNÕÒfÔÃ_ÔÕ5É$ÕÀ™Ã_Û@Ø,ÕÁ€Ì‰Ó@À.ÙÓ@Ò?œ ¤ ÊÓ9ÀÖfèΠ¤ ÕÀ,Ô Í ¤ Â,Õû9Ã

ÜÃ'Ã'À ÔÃ'Á€Ã'Ò+á̃ÀÃ_ÔJä – Û@Ø,ÕÁ€ÌƒÓ9ÀɕÙÓ9ÒDÎ

¤

ÕÀ,Ô

Í

¤

Õ5Ò+ÃUÓ9ÜÁfÕ̃ÀÃ_ԓÙÒ+Ó@á ÿ4Ïä>ÆHŠÕÀ,Ô ÿ4ÏäöH'ÊߊÂÌÖ+Â

Ú̃Ã'×Ô ÿ‰¥ Í ¤ É+̃ÀŠÏ8Î ¤ Ö ¬ ÏHœ ¤ ¥Ü{ Í ¤ ÖfÓ@ÉøÏHÎ ¤ œ Æ r É+̃À§|É+̃ÀJÿg¶ ¬ Ï8Î Æ ÿgœ ¤ ¬µÍ ¤ ÖfÓ9ÉÏ8Î ¤ Ö ¥™{ Í ¤ É+̃À`ÏHÎ ¤ q¥ œ Æ r É+̃À§ÖfÓ9ÉTÿ¶ ¬

ÏHÎ Æ s

ÿ4ôä>ÅH åŠÂÃ*ý,ҀÉ+Á`Ó@Ò¥ÔÃTÒ$ÖfÓ@ØÀÁ+Ã'ҀÑ,ÕҀÁ`Á+ÓUÁ+ÂÃHÜ,Ó@ØÀ,ÔÕ5Ò+Ú.ÖfÓ9À,ÔR̉Á€ÌƒÓ9ÀÉ*ÿ4ôä‰ÄÆ8ÌƒÉÙÓ9ØÀÔÁ€Ó1Üà ¥  ÿ¶A¤,·ºÿï ÿ¶A¤ ¬ Ñÿ¶A¤‰  ÿ¶ ¦ ,·ºÿï ÿ¶ ¦ ¬ Ñÿ¶ ¦ ‰ ߊÂÃ'ҀÃï.̃ɊÔÃ'Á+ÃTÒ+á̃ÀÃÔÜÚ ï Ä É€ÌƒÀ§ É Ñ¨ÖfÓ9ÉÏ8Î Æ ¬

Óɀ̃À`Ï8Î Æ ¥ ŽžE

¦

§

Ï,r

œ Æ É€ÌƒÀ¶$ÖPÓ9É,ÏHÎ Æ

Ë s ÿôäƒÄ_ÇH tÊÀÓß Á+ØÒ+ÀÁ€ÓHÁ+ÂÃ$ÔÃ'Á€Ã'Ò+á̃À,ÕÁ€Ì‰Ó@À1Ó5Ù/Á+ÂÃ*û9Ã'׃ÓÖf̃ÁÚHÃ_Û@Ø,Õ5Á+̃Ó9ÀÉ_Ê@É+Á¥Õ5Ò+Á€Ì‰ÀÝ1ߊ̃Á+Â^Ó@Ò¥ÔÃTÒ7ÇänŠÁ Á+ÂÃ?TÃ'Ò+Ó5æ4Á€Â¨Ó9ÒfÔÃ'Ò_ÊÃ_Û@Ø,ÕÁ€ÌƒÓ9Àãÿ4Ïä‰Ä@Ä#Ò+Ã_ÔRØ,ÖfÃ'É3Á+Ó ´ ˆ  Æ ˆ 2Ç: ÕÀÔÁ€ÂØÉ_ÊÉ+̃À,Öfà  ˆ ÂÕɊÁ+Ó^û9Õ5À̃É+ÂÓ9À.Á+ÂÃ3ÜÓ9ØÀÔÕÒ€Ú 

ƈ¨ð Ç:s ÿôäƒÄ9Ď

åŠÂÃ3Ã_Û@Ø,Õ5Á+̃Ó9ÀÙÓ@Ò



Æ

‡

̃ɊÓ9ÜÁfÕ̃ÀÃ_Ô ÙҀÓ9á ÿÏäƒÄ_ÇH)ߊÂÌրÂ.Ò+Ã_Õ@ÔɊÂÃ'ҀÃ

´ ˆ  Æ ‡ »¥`Ï  Æ ‡ Á¥Õ5À`Ï8Î Æ s ÿôäƒÄ_ÏH LŠÓÜÓ9ØÀ,ÔÕҀÚâÖfÓ@À,ỖÁ+̃Ó@ÀÉÕҀÓ̃áÑ,Ó@É+Ã_Ô Ó9À 

Ƈ äšåŠẪÉ^ÖfÓ9Ø×’Ô ÜÃÔÓ@ÀÃ9ʐÙÓ9Ò^̃ÀɀÁ¥Õ5À,ÖfÃ9ÊÜÚ

̃áÑÓ9ɀ̉ÀÝHÁ+ÂÃ3ߊ̃Á+ÂÔÒ¥ÕߊÕ×JÒfÕÁ+ÃD’Fñ  ‡ ò¶ä åÓUÓ9ÜÁfÕ̃ÀÁ€ÂÃ3ý,ҀÉ+ÁŠÓ9ÒfÔÃ'Ò*Ã_Û@Ø,ÕÁ€Ì‰Ó@ÀÉÙÓ@ÒDÁ€ÂÃHû9ÃT׉ÓÖf̃Á€Ì‰ÃTÉ_ÊßÃ3ý,Ò+ɀÁŠÀÓ9Á€Ã „ ‡‰ˆ „ˆˆ ¥ó˜ „ Æ ‡2ˆ „ Æ ˆˆ ¥p˜ Æ ¬ É „ ¤ ‡2ˆ „ Æ ˆˆ ¥p˜ Æ ¥ „ Æ ‡2ˆ ÿ„ ¤ ˆˆ ¥|˜ ¤ ÿ „ Æ ˆˆ ¥J˜ Æ ¦ Ë ¬ sŽs#s – Û@Ø,Õ5Á+̃Ó9À™ÿ4ÏäƒÄÇ8Á+ÂÃ'À™×‰ÃÕ9ÔɊÁ€Ó ´ ˆ  ¤ ‡ ¬

ÏÁ¥Õ5À`Ï8Î Æ ÿ´ ˆ

 ¤ ˆ ¬ ¤ ‡ *¥  ¤ ˆ »¥ ɀ̉À`ÏHÎ Æ œ Æ É+̃À§ÖfÓ@É ¦ ÏHÎ Æ É Ï8Ñ ¬ ɀ̉À¶ r

œ Æ É+̃À§/ÖPÓ9ÉJÏ8Î Æ

Ë



(7)

K*À.Á+ÂÃHÓ@Á+ÂÃTҊÂ,ÕÀ,Ô Êÿ4ÏäƒÄ@Ä#ÚÑÃ'×ÔɊÁ€ÂÃHÃ_Û@Ø,Õ5Á+̃Ó9À ÙÓ9Ò  ¤ ˆ ÊߊÂÌրÂ.̃ÉÙÓ9ØÀÔ^Á+Ó^Üà ´ ˆ  ¤ ˆ ¬· ¤ ‡ »¥ É+̃À¶ r  Æ ‡ s ÿôäƒÄ{ åŠÂÃÙÕ9ÖfÁ|Á+Â,Õ5Á  ˆ û9ÕÀ̃ɀÂÃ'É/Ó@ÀHÁ+ÂÃ)Ü,Ó@ØÀ,ÔÕ5Ò+Ú3ÑҀÓûNÌÔÃTÉ/Á+ÂÃ7Õ@ÔỖÁ+̃Ó9ÀÕ×9ÖfÓ@À,ỖÁ+̃Ó9ÀÉJÀÃ_ÖfÃ'ɀɥÕ5Ò+Ú Á+ÓÖP׉Ó@É+Ã3Ó9ØҊÉ+ÚÉ+Á€Ã'á  ¤ ˆ ÿ¶ ¤ ,  ¤ ˆ ÿg¶ ¦ <2Ç:s Ó9Ò`ÖfÓ@Àû9Ã'À̃Ã'ÀÖfÃ9ÊÁ€ÂÃHÃ_Û@Ø,Õ5Á+̃Ó9ÀÉ`ÕÒ+Ã3ҀÃ'ߊÒ+̃Á+Á€Ã'À¨ÌƒÀ“ÕUáÓ9ҀÃ$ÖfÓ@áÑ,Õ@ÖfÁ)Ù Ó9Ò+áãä …³ ³ ³ ³ ³ ³ ³ † ô õ Ç Ç Ç Ç Ç ö ÷ Ç Ç Ç Ç Ç Ç Ç Ç ø Ç Ç Ç ù ú û ± Ç Ç Ç Ç Ç Ç Ç Ä Ç Ç Ç Ç Ç Ç Ç Äýü Ç Ç Ç Ç Ç Ç Ä ‹¸ ¸ ¸ ¸ ¸ ¸ ¸ Œ …³ ³ ³ ³ ³ ³ ³ † œ Æ Î Æ Ñ Ó  Ƈ  ¤ ‡  ¤ ˆ ‹¸ ¸ ¸ ¸ ¸ ¸ ¸ Œ Ö ¬ …³ ³ ³ ³ ³ ³ ³ † þÿ ‹¸ ¸ ¸ ¸ ¸ ¸ ¸ Œ …³ ³ ³ ³ ³ ³ ³ † ¥=’8”ŠÖfÓ9ɶ ’8”É+̃À¶ Ç Ç Ç Ç Ç ‹¸ ¸ ¸ ¸ ¸ ¸ ¸ Œ s ÿôäƒÄ#mH

åŠÂÃ3ÕÜÓû9ÊÉ+ÚɀÁ+Ã'á ÓÙCK – É̉ÉÖf׃Ó9É+ÃÔߊ̃Á€Â^Á+ÂÕÙÓ9׃׃Óߊ̃ÀÝ`ÜÓ9ØÀÔÕҀÚÖfÓ9À,ÔR̉Á€ÌƒÓ9ÀÉÊNÔÃTÒ+̃û̉ÀÝ

ÙҀÓ9á ÿÏäƒÄ_ÏÊNÏä‰Äô8

Î

Æ

ÿ¶A¤,q¥Î Û Î

Æ

ÿ¶

¦

jÎ Û ÿôäƒÄ_ÆH

¥  ÿ¶ ¤ ,“ºÿœ ¤ ÿ¶ ¤ ¬

Ñÿ¶ ¤ 2

 ÿg¶ ¦ <“ºÿœ ¤ ÿ¶ ¦ ¬ Ñÿ¶ ¦ ‰ ÿôäƒÄ_öH  ¤ ˆ ÿ¶A¤, Ç  ¤ ˆ ÿ¶ ¦

j Ço ÿôäƒÄ_÷H

ߊÂÃ'ҀÃ3Á+ÂÃ3û9ÕҀ̃Ó9ØɊÛ@Ø,ÕÀÁ+̃Á€Ì‰ÃTÉ7Õ5ÑÑ,ÃÕÒ+̃ÀÝŨÀ.ÿ4ôä‰ÄŽm8)Õ5Ò+ÃHÔÃ'ÉfÖfÒ+̃ÜÃ_Ô.̃ÀÁ€ÂÃDn`ÑÑÃ'À,ÔRÌwþ/ä,L•Ó9Á+Ã

Á+ÂÕÁÁ+ÂÃ'ҀÃ1ÕҀÃ`ÀÓUÜÓ9ØÀ,ÔÕÒ+ÚÖPÓ9À,ỖÁ€Ì‰Ó@ÀÉÓ9À|œ Æ Ê:Ñ2ÕÀ,Ô

 ‡ ¤ äCØÒ+Á€ÂÃ'ÒÊJÿ4ôäƒÄ#m8ú̉É̃À^Ù4Õ@ÖfÁßDÃ'×ƒ× ÑÓ9É+ÃÔJÊ9ÃTû9Ã'ÀUßDÃÂ,Õû@ÃDɀÌwþUÜ,Ó@ØÀ,ÔÕ5Ò+Ú1ÖfÓ@À,ỖÁ+̃Ó@ÀÉÕ5À,ÔHɀÃ'û9ÃTÀ^ØÀÍÀÓߊÀÉÊÉ+̃À,ÖfÊÁßÓ`ÜÓ9ØÀ,ÔÕÒ€Ú ÖfÓ@À,ỖÁ+̃Ó9ÀɊßDÃ'ҀÃHÖ'ÕҀÒ+Ú̃ÀÝ^Ó9À¨ÕÀ.Ã'̃Ý@ÂNÁ€Âû9Õ5Ò+ÌÕÜ׃à  ƈ ÊߊÂÌրẪɊÌÔÃ'ÀÁ+ÌÖ'Õ5׉׃Ú'ÃTÒ+Ó,ä ÚÃfþ,Õ5á̃À̃ÀÝ3Á+ÂÃ3ɀÁ+Ò+ØÖfÁ+ØҀÃ1Ó5ÙÁ€ÂÃ1ÕÜÓû9Ã*É+ÚÉ+Á€Ã'áÊÓ@ÀÃHÖ'ÕÀ.ɀÃ'ÃHÁ+ÂÕÁØÑ,Ó@À¨ÕÑÑҀÓþÌwæ á“Õ5Á+̃Ó9ÀUÜÚÁ€ÂÃ3É+Ã'Ҁ̉ÃTÉHÿ4ôäƒÄ#'Ê@Á+ÂÃHÉ+Á€Ò+Ã'ɀÉ`Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ`ÖTÕÀ.Ü,Ã3ɀÓ9׃û9Ã_Ô Ü,Ó@Á+¨ÕÁŠÁ€ÂÃD'Ã'ҀÓæÁ+¨ÕÀ,Ô

Á+ÂÊý,ҀÉ+ÁÓ9Ò¥ÔRÃ'Ò_ỄÀ,ÔÃTÑ,Ã'ÀÔÃ'ÀÁ+׃Ú^ÓÙJÁ+ÂÃ`û9ÃT׉ÓÖf̃ÁÚUÃ_Û@Ø,ÕÁ€ÌƒÓ9ÀɊÿ Á+ẪÉ̃É)ÀÓ9ÁÁ+Ò+ØÃ`ÓÙ/Á€Âà – ÈÉTä

tÓÖTÕÀ Á+ÂØÉ^ÔÃ_ÖfÓ@áÑÓ9ɀÓÁ€ÂÃJK – ̃ÀÁ+Ó¨Á€ÂÒ+ÃTèÑÒ+Ó@Ü׃Ã'áɖÓÙ$̃À,ÖPÒ+Ã_Õ5É+̃ÀÝ ÖfÓ@áÑ׃Ãfþ̃ÁÚ¨ÜÚ

É+Ó@׃ûÑÀÝ^ՖÑÒ+Ó@Ü׃Ã'áàÙ Ó9ÒÁ+ÂÃD'Ã'ҀÓæÁ+¨Ó@Ò¥ÔÃTÒ`É+Á€Ò+Ã'ɀÉ`Á€Ã'Ò+áÉý,Ò+ɀÁ_ÊÁ€ÂÃ'À.ÜÚɀÓ9׃û̉ÀÝHÙÓ@ÒDÁ€ÂÃ*ý,Ò+ɀÁ

Ó9ÒfÔÃ'ÒHɀÁ+ҀÃ'É+ÉUÁ+Ã'ҀáÉÊøÕ5À,Ôüý,À,Õ׃׃Ú.ÜÚ¨É+Ó@׉ØÁ+̃Ó9À.Ù Ó9Ò`Á€ÂÃÖfÓ@áÑÓ9ÀÃ'ÀÁ€É$Ó5ÙDÁ+ÂÃ^û9Ã'׃ÓÖf̃ÁÚNäDt ̉Á€Â

Á+ÂÃ$ÀÓ9Á¥Õ5Á+̃Ó9À.Ó5ÙDÿ4ôäƒÄ#m8TÊ9Á€ÂÃHÁ€ÂÒ+Ã'ÃUÖfÓ9ҀÒ+Ã'ɀÑ,Ó@À,ỖÀÝá.ÕÁ€Ò+ÌÖfÃ'ɊÕҀÃ$ҀÃ'É+ÑÃ_ÖfÁ€Ìƒû9Ã'×ƒÚ Æ É ô õ ö ÷ Ë ¤ …³ † ô õ Ç Ç ö ÷ Ç Ç Ç Ç Ç ø ù ú û ± ‹¸ Œ …³ ³ ³ ³ ³ ³ ³ † ô õ Ç Ç Ç Ç Ç ö ÷ Ç Ç Ç Ç Ç Ç Ç Ç ø Ç Ç Ç ù ú û ± Ç Ç Ç Ç Ç Ç Ç Ä Ç Ç Ç Ç Ç Ç Ç Ä ü Ç Ç Ç Ç Ç Ç Ä ‹¸ ¸ ¸ ¸ ¸ ¸ ¸ Œ s ÿôäƒÄ_ÅH n`ÝÕ̃À/ÊßÃHÉ+Á€Ò+Ã'ɀÉHÁ+ÂÕÁŠÓ9À׉ÚÁ+ÂÕ'Ã'Ò+Ó5æ4Á€ÂÓ@Ò¥ÔÃTÒ`É+Á€Ò+Ã'ɀÉ3Á+Ã'ҀáÉ$Õ5ÑÑÃ_ÕÒ*̉À.Á€ÂÃHÃ_Û@Ø,Õ5Á+̃Ó9À¨ÖfÓ@Òæ Ò+ÃTÉ+ÑÓ9À,ỖÀÝUÁ+Ó Æ

ä,— ̉Í@Ã'ߊ̃É+Ã9Ê@Á+Âà ¤ æ4Ã_Û@Ø,Õ5Á+̃Ó9À^Ó@À׃ڑÖPÓ9ÀÁ¥Õ5̉ÀÉ,'Ã'ҀӑÕ5À,ÔUý,ҀÉ+ÁÓ9ÒfÔÃ'ÒÉ+Á+ҀÃ'É+É

Á+ÃTÒ+áÉä¨åŠẪÉ3ÙÕ9ÖfÁŨÉ1ØɀÃ_ỖÀÁ€ÂÃÀÃPþRÁUÉ+ÃÖfÁ+̃Ó9À|ä™ØҀÁ+ÂÃ'ÒÊ)ßÃÓ@ÜÉ+Ã'Ҁû9Ã.Á+ÂÕÁHÃ_Õ@րÂâÓ5Ù`Á+ÂÃ

(8)

րÂÃ_րÍÉ

ÔÃ'Á

Æ

ÏHœ Æ É+̃À§@ÿÖfÓ9É,ÏHÎ Æ

¬

É+̃À§

ÔÃ'Á ¤ ÔÃTÁ q¥`Ï8œ Æ É+̃À¦§@ÿÖfÓ9ÉJÏ8Î Æ

¬

ɀ̃À¹§2¦8s

åŠÂÃ'ҀÃfÙÓ@Ò+Ã9Ê3ÑØÁ+Á+̃ÀݚÕ5É+ÌÔÃãÁ+ÂÃãÑ,ÕҀÁ+ÌÖfØ×Õ5ÒüÖTÕÉ+õœ Æ Ç ÕÀ,Ô:Â5Ó9Ò.É+̃À§ ÇÊ`Á€ÂÃãÉ+Á+ҀÃ'É+É

Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ`Õ5Ò+Ã3É+̃ÀÝ@Ø×ÕÒ̝Ù

ÖfÓ9É,ÏHÎ Æ

¬

É+̃À§4 Ço ÿôä>Ï9ÇH

ߊẪ׃Ã`Ã_Õ@ր¨ÓÙÁ+ÂÃHÁ€ÂÒ+ÃTÃHû9Ã'׃ÓÖf̃ÁÚ^Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ3ÿôäƒÄ_Ï\²Rôä‰Ä{iÕҀÃHÉ+̃ÀÝ@Ø×ÕÒߊÂÃ'ÀÃTû9Ã'Ò

Î Æ v{6“{imìs ÿôä>ÏĎ

tÃHߊ̃׃×/ØɀÃ1Á€ẪÉ$ÖfÓ@À,ỖÁ+̃Ó@À¨Á+ÓÀNØáÃ'Ҁ̒ÖTÕ׃׃ÚÔÃ'Á+ÃTÒ+á̃ÀÃUÁ+ÂÃHÉ+ÁfÕÝ9ÀÕÀÁ3Ñ,ÕҀÁ`ÓÙÁ+ÂÖÞ,Óß ÌƒÀ

Á+ÂÃ$ÀÃfþÁ`É+ÃÖfÁ+̃Ó9À|ä

|½ 453R(T( ½HåŠÂÃÀØáÃ'Ò+ÌÖ'Õ5×áÃ'Á+ÂÓRÔã̃ÉHÜÕÉ+ÃÔÓ9ÀÁ€ÂÃÁßÓ.ÙÓ@׃׉Óߊ̃ÀÝ

á“Õ5̃À^É+Á+ÃTÑÉ

ÿ¥ÄŽØÉ+ÃUÓÙDÕ Ð ØÀÝ9ÃPæ*ØÁ€Á¥Õæ‰Ã'Â׃Ü,ÃTÒ+Ýz{ÿmHáÃ'Á€ÂÓÔߊ̃Á€ÂÕØÁ€Ó9á.ÕÁ+Ì֕É+Á+ÃTÑɀÌdTÃHÉ+Ã'׃Ã_Ö¥æ

Á+̃Ó@ÀÙ Ó9Ҋ̃ÀÁ+Ã'Ý@Ò¥ÕÁ€ÌƒÀÝ1Á€ÂÃK – ÉHÿ ÌäÃ@ä‰ÊÕ&{@Á+Â.Ó9ÒfÔÃ'Ò Ð ØÀÝ@Ãfæ`ØÁ+Á¥Õ ߊÂÃ'ҀÃHÁ+ÂÖ׉ÓÖ'Õ5×/Á€Ò+ØÀ,ÖTÕæ

Á+̃Ó@ÀÃ'ҀÒ+Ó@Ò1̃ÉHÃ'ɀÁ+̃á“Õ5Á+Ã_ԙÁ+ÂÒ+Ó9ØÝ9 ÕýÙ Á+ÂãÓ9Ò¥ÔRÃ'ÒHÙ Ó9Ò+á^ØגÕÊ,Õ5À,Ôã̃ÉHÁ+ÂÃTÀØÉ+Ã_Ô ÙÓ9ҖÉ+Á+ÃTÑÉ+Ì'Ã

É+ÃT׉ÃÖfÁ+̃Ó9Àw

ÿ4ÏHØÉ+ÃHÓ5ÙúÕÀ̃ÀÃfþ,Õ9ÖfÁL•Ã'ߊÁ+Ó@À.áÃ'Á€ÂÓÔUÙÓ@ÒDɀÓ9׃û̉ÀÝ1Á€ÂÃ3ÀÓ9À׃̃ÀÃ_Õ5ÒDÑÒ+Ó9Ü׉ÃTáɊÕÒ+̃ɀ̉ÀÝ

ÙҀÓ9áàÁ€ÂÃHÉ+ÂÓNÓ@Á+̃ÀÝUÉ+Á€Ã'ÑÉHÿ É+Ã'ÃUÜÃ'׃Óß'ä

n*É`ÔÃ'É¥ÖPÒ+̃Ü,ÃÔ.̃ÀÁ+ÂÃ$ÑÒ+Ã'û̃Ó9ØɊɀÃ_ÖfÁ€Ì‰Ó@À/ÊßÃ3Â,Õû9Ã*Á+Ó^ɀÓ9׃û9Ã3ÕHÜÓ9ØÀÔÕҀÚû9Õ׃ØÃ*ÑÒ+Ó@Ü׃Ã'á

ÖfÓ@ÀÉ+̃É+Á€ÌƒÀݨÓيÉ+ÃTû9Ã'ÀÀÓ@À׃̃ÀÃ_ÕÒUÖfÓ9ØÑ׉ÃÔK – Éä|L•ØáÃTÒ+ÌÖ'Õ׃׃ÚÊÁ+Ẩɖ̉ÉHÔÓ@ÀÃ^ÜÚɀÓ9׃û̃ÀݓÕ

É+ÃÛ9ØÃ'À,ÖfÃUÓÙ)̃À̃Á+ÌÕ×û9Õ׃ØÃ3ÑҀÓ9Ü׃Ã'áÉDߊÂÃ'Ò+ÃUÁ+ÂÃ+á̃ɀÉ+̃Àݖ̉À̉Á€ÌÕ×û9Õ׃ØÃ'É`Õ5Ò+ÃHɀÓ9ØÝ@ÂNÁŠÉ€ÓÕÉ

Á+Ó.ÉfÕÁ+̃É~ÙÚÁ€ÂÃ^ÑҀÃ'É¥ÖfҀ̃Ü,Ã_Ô Ü,Ó@ØÀ,ÔÕ5Ò+ÚÖfÓ9ÀỖÁ+̃Ó9ÀÉÊJÌäÃ9äƒÊJÁ+ÂÃ^ɀÓæ+Ö'Õ׃׃Ã_ÔãɀÂÓÓ9Á+̃ÀÝ.áÃ'Á+ÂÓÔ.̃É

ØɀÃ_ÔJä

n*É`̃ɊßDÃT׉×JÍÀÓߊÀ|ÊÁ+ÂÃHɀÂÓÓ9Á€Ì‰ÀÝ^áÃ'Á€ÂÓÔÖ'Õ5À“׃Ã_Õ@ÔÁ+Ó^û9ÕҀ̃Ó9ØɊÑҀÓ9Ü׃Ã'áÉD̃À.ÑÒfÕ9ÖfÁ€Ì’ÖPÃ9ä

n`ÉUÕÀ Õ׃Á€Ã'Ò+À,Õ5Á+̃û9Ã^Á€Ó.á^Ø׃Á+̃Ñ׃ÃHÉ+ÂÓNÓ@Á+̃ÀÝÊ/Á€ÂÃ^É+ÂÓÓ@Á+̃ÀݨÑҀÓÖfÃ'É+ÉŨÉ1ÔÓ@ÀÃ^ÂÃ'ҀÃ̃ÀÉ+Ã'û@Ã'Ò¥Õ5×

É+Á€Ã'ÑÉÊD̃ÀÓ@Ò¥ÔÃ'Ò^Á€Ó¨Á¥Õ5Í9Ã.Õ9Ôû9Õ5ÀNÁfÕÝ@Ã^ÓÙ$Á€ÂÃÜ׉ÓրÍãÉ+Á+ҀØ,ÖfÁ€ØÒ+èÓ5Ù$Á€ÂÃɀÚNɀÁ+Ã'á ÿ4ôäƒÄ#m8Tä¨åŠÂÃ

ÕÑÑÒ+ÓÕ9րÂ.̉Ɋɀ̃áÑ׃Ã'Ò)Á€Â,ÕÀ.á^Ø׃Á€Ì‰Ñ׉ÊɀÂÓÓ9Á€Ì‰ÀݑÕ5À,ÔßDÓ@Ò+ÍɊßDÃT׉×J̃ÀÁ+ÂÃHÑÒ+Ã'ɀÃ'ÀÁ$ÖfÓ@ÀNÁ€ÃfþÁ_ä

|̃Ò+ɀÁ_ÊÁ€ÂÃDÃÛ9ØÕÁ+̃Ó@À1ÖfÓ9ҀÒ+Ã'ɀÑ,Ó@À,ỖÀÝHÁ€Ó

Æ

Êÿ4ôäƒÄ_ÅäƒÄŽ'Ê'̃É|É+Ó9׃û@Ã_Ô*ÙÓ@ÒÁ€ÂÊÇÁ+–Ó9Ò¥ÔRÃ'ÒÉ+Á+ҀÃ'É+É

Á+ÃTÒ+áɜ Æ ÕÀ,Ô·Î Æ Ê)̃ÉUÉ+Ó@׉û@Ã_ÔJä åŠÂÃÜÓ9ØÀ,ÔÕҀÚâÖfÓ@À,ỖÁ+̃Ó@ÀÉÿôäƒÄ_ÆHHÕҀèÕ9ÔfØÉ+Á+ÃÔ Á€ÂÒ+Ó@ØÝ9Â

É+ÂÓNÓ@Á+̃ÀÝãÓ9À œä yÃ_ÖPÓ9À,ÔJÊÁ€ÂèÉ+ÚɀÁ+Ã'á ÖfÓ9ҀÒ+Ã'ɀÑ,Ó@À,ỖÀÝ Á+Ó ¤ÊŠÿ4ôäƒÄ_Åä>ÏH'ỄÉ^É+Ó@׉û@Ã_ÔJä åŠÂÃ

ÜÓ9ØÀ,ÔÕÒ+Ú¨ÖfÓ@À,ỖÁ+̃Ó@ÀÉHÿôäƒÄ_öHŠÕÒ+ÃUÕ9ÔfØÉ+Á+ÃÔ¨Á€ÂÒ+Ó@ØÝ9¨ɀÂÓÓ9Á€Ì‰ÀÝ^Ó9ÀÜіä|̉ÀÕ׃׃ÚNÊÁ€ÂÃHÉ+ÚɀÁ+Ã'á

ߊ̃Á+ Ê|ÿ4ôä‰ÄÅä>ô8ÌƒÉ`ɀÓ9׃û9Ã_Ô Ê,ÕÀÔ.Á+ÂÖÜ,Ó@ØÀ,ÔÕ5Ò+Ú¨ÖfÓ9ÀỖÁ+̃Ó9Àɖÿ4ôä‰Ä÷8ÕҀÑÕ@ÔfØɀÁ+Ã_Ô.Á€ÂÒ+Ó@ØÝ9Â

É+ÂÓNÓ@Á+̃ÀÝUÓ9À



¤

‡

ä<tÃ3Ó9á̉ÁÁ+ÂÃHÔÃ'ÁfÕ̃׃É_ä

|½¼ -NŠ88)_ (3HŽ¿)! ½^åÚÑÌÖ'Õ×|É+Ó9׃ØÁ€ÌƒÓ9ÀÉ`Õ5Ò+ÃỦ׃׃ØɀÁ+Ò¥Õ5Á+Ã_ÔüÜ,Ã'׃ÓßHä

LŠÓ@Á+Ã.Á+ÂÕÁUÁ+ÂÃ.Ñ,Õ5Ò¥ÕáÃ'Á+ÃTÒ+Ér,Êj’ ÕÀ,Ô ” Õ5Ò+èÕ׃×É+Ã'Á^ÃÛ9ØÕ׊Á+Ó ÄÁ+ÂҀÓ9ØÝ@ÂÓ9ØÁäåÓ9׃Ã'ÒfÕÀ,ÖfÃ

¤

(9)

−40

0

−30

−20

−10

0

10

20

30

40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

angle

θ

average stress p

0

−40

−30

−20

−10

0

10

20

30

40

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

angle

θ

average stress correction: p

1

−40

0

−30

−20

−10

0

10

20

30

40

0.2

0.4

0.6

0.8

1

angle

θ

T

rr

0

−40

−30

−20

−10

0

10

20

30

40

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

angle

θ

T

rr

1

−40

−30

−20

−10

0

10

20

30

40

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

angle

θ

T

r

θ

0

−40

−30

−20

−10

0

10

20

30

40

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

angle

θ

T

r

θ

1

−40

0

−30

−20

−10

0

10

20

30

40

0.5

1

1.5

2

2.5

3

angle

θ

T

θθ

0

−40

−30

−20

−10

0

10

20

30

40

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

angle

θ

T

θθ

1

MJ<ONK@?9=@VQP bd`g_fkgk?XgT"!,]#T2Vi_Vbk•TêäDb[\_7]Ž`Tå2Z_#! awWQb[XTVWdXfYZAWQVk_f`gb%$YV#íZO_6Tä<äg`gWXgbWêTV

î'&¸'¶)("*<[#YZäDTg]#_VWQV#í&YV#íZO_,+}.'¶-(6YV8hDaYZcZäg`gWXgbWêT2V

ë

&/.10'»f¶321.4&ã¶526766"2·Žl 8gVYZcZ:b[\_

]ŽWXgbæ#`g_fk¹_:9Xg_1]Žb<;>= *

ë

(10)

−40

0

−30

−20

−10

0

10

20

30

40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

angle

θ

radial velocity −v

r

0

−40

−30

−20

−10

0

10

20

30

40

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

angle

θ

correction to radial velocity: v

r

1

−40

−30

−20

−10

0

10

20

30

40

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

angle

θ

angular velocity v

θ

1

MJ<ONK@?9=9VDCFE8_gZOTgX^WQbçXgT"! ]ŽT2Vi_fVbk?Tä7b[\_<]\`Tå‰ZO_G!qawWQb[DXT2VWXEYZwWQVk_f`gb%$YV#íZO_=Tääg`gWXgbWêTV

î&.¸T¶)(H*[#YZäTg]Ž_fVWcV#í6YV#íZ_I+J.'¶)(DY"V8haYZcZä^`gWdX^bdW1T2V

ë

&.10'»f¶321.B&¨¶3276"6762·ŽlJ8^V6b[\_BKw`gkgb

ba*Tj]ŽWdX^bæ#`_kF]ŽWdX^bæ#`_kL*

ë

&™¶XT`g`_fkE]ŽT2V8hk=bETubd[_<AY"bdbE_`¹X^æ#`ge_1Mjb[\_=T2`Eh#_`=WQk7`_fe_f`gk_ãh,äT`

N

=

O

l

L•Ó9Á+ÖÁ+Â,Õ5ÁŠÁ+ÂÃ1Õ5Ü,Óû@Ã3û9Ã'׃ÓÖf̃ÁÚ^ý,ÃTגÔRÉ`Â,Õû@Ã$ÜÃ'Ã'À™ÀÓ9Ҁá“Õ׃Ì'Ã_Ô äåŠÂÃ1ÔÃ'ÑÕÒ+Á€ØÒ+ÖÙҀÓ9á Õ

ÑØҀÃ'׃ÚÒfÕ9ÔÌÕ×JɀÁ+ҀØ,ÖfÁ+ØÒ+ÃH̃Ɋû̃É+̃Ü׃Ã`ÜÚ̃ÀɀÑ,ÃÖfÁ+̃Ó9À.Ó5Ù |̃Ý9ØҀÃ?{äƒÄ$Õ5À,Ô{äÏä/åŠÂÃ$ÜÃ'Â,Õû̃Ó9ҊÓ5Ù

Á+ÂÃ3Þ,Óß Ö'Õ5À¨Õ׃É+Ó^ÜÃH̃׃׉ØÉ+Á+ÒfÕÁ€Ã_Ô^ÜړÕU׃ÓÓ9ÍÕ5ÁŠÁ+ÂÃ3ɀÁ+Ò+ÃÕá׃̃ÀÃ'É`ÖPÓ9Ò+ҀÃ'É+ÑÓ9ÀỖÀÝÁ€Ó^Á+ÂÃ*ÙØ׃×

(11)

|½d~ N ,$Ž¿(T_SR/–8^3#¿)! ½n*É`ÀÓ@Á+Ã_Ô¨Õ5Á`Á€ÂÃHÃ'À,Ô

ÓÙ,yÃ_ÖfÁ€ÌƒÓ9ÀôÊÁ+ÂÃ3ÑҀÓ9Ü׃Ã'á Ü,ÃÖfÓ9áÃ'ɊÉ+̃ÀÝ@Ø×ÕÒߊÂÃ'À

Î

Æ

á̃ÀST

ÕÒ¥ÖTÖfÓ9Éÿ‰¥.É+̃À§

Ï

{,U

{

s

åŠÂÕý,Ò+ɀÁ`ÖfÓ9À,ÔR̉Á€ÌƒÓ9À/ỄÀÁ+ÂÃ*áÌÔÔ׃ÃÁ+Ã'ҀáÊÖfÓ9ҀÒ+Ã'ɀÑ,Ó@À,ÔɊÁ+ÓUÁ+ÂÃ`É+Á€Ò+Ã'ɀÉ`Ã_Û@Ø,Õ5Á+̃Ó9ÀÉ_Ê@ߊẪ׉Ã*Á+ÂÃ

É+ÃÖfÓ9À,ԙ̃ɊÒ+Ã'×Õ5Á+Ã_Ô.Á€Ó^Á+ÂÖû9Ã'׃ÓÖf̃ÁÚÃ_Û@Ø,Õ5Á+̃Ó9ÀÉ_äåŠÂÃ'ҀÃfÙÓ9ҀÃ9ÊÁ+ÂÖû9Ã'׃ÓÖf̃ÁÚÃ_Û@Ø,Õ5Á+̃Ó9ÀɊÜ,Ã_ÖPÓ9áÃ

É+̃ÀÝ@Ø×ÕÒV+ÜÃfÙÓ9ҀÃ.Á+ÂÃUÉ+Á€Ò+Ã'ɀÉHÃ_Û@Ø,Õ5Á+̃Ó9ÀÉä3¿ÀÓ@Á+ÂÃTÒ$ßÓ9ÒfÔÉ_Ê ßDÃ^Ö'ÕÀãÉ+Ó@׃û9ÃHÁ€ÂÃ

Æ

æÉ+ÚÉ+Á€Ã'áÊ

ÖfÓ@Ò+Ò+ÃTÉ+ÑÓ9À,ỖÀݙÁ+Ó.Á+ÂÃTÃ'Ò+Ó5æ4Á€ÂÓ9Ò¥ÔRÃ'ÒHÉ+Á€Ò+Ã'ɀÉ1Á€Ã'Ò+áÉHÕÀ,ÔãÔÃ'Á€Ã'Ò+á̉ÀÃ1ߊÂÃTÒ+ÃÁ€ÂÃ^ÇæÁ+ÂãÓ9Ò¥ÔRÃ'Ò

û9ÃT׉ÓÖf̃ÁÚ¨ÃÛ9ØÕÁ+̃Ó@ÀÜ,Ã_ÖPÓ9áÃTÉHÉ+̃ÀÝ@Ø×ÕÒ_äÓ9׃׃Óߊ̃ÀÝÎ>öÐ+ÊJßÃ^êƒòJñE fçW,ç ñ*Á+ÂÃ^Ñ,ÕҀÁHÓيÁ+Âà Þ,Óß

ÜÃ'Ú9Ó@À,ÔãÁ+ÂÃÑ,Ó@̃ÀNÁ3ߊÂÃTÒ+ÃÁ€ÂÃû@Ã'׃ÓÖf̃ÁÚ.ý,Ã'×ÔãÜÃ_ÖfÓ9áÃ'ÉUÉ+̃ÀÝ9ØגÕ5ÒHÕÉ1ÖfÓ@Ò+ҀÃ'É+ÑÓ9À,ÔR̉ÀÝÁ€Ó¨Á+ÂÃ

ï_ñ~è›òJè_òJñŠÑÓ9ҀÁ+̃Ó9ÀÓ5Ù7Á€ÂÃUÞ,ÓßHäåŠẪÉHß7ÕÚÊ/ÕX€Ñ,ÕҀÁ+ÌÕאá“ÕÑYÓيÁ+ÂÃ^Ù4Õ5̉׃ØҀÃ1áÓÔÃ1Ó5Ù`Á+ÂÃ

̃ÀÉ+ÃTÒ+ÁÉ+Á+ÒfÕÁ€Ã'Ý9Ú̉ɐÓ9ÜÁfÕ̃ÀÃ_ÔJä|åŠÂÃ*ÑÒ+Ã'ɀÃ'ÀÁ`ÕÀ,Õ5׃ÚNɀ̃É)̃áÑ׃ÌÖf̃Á+׃ÚHÕɀÉ+ØáÃ'É)Á+ÂÃ`É+ÁfÕÝ@À,ÕÀÁ,'Ó@ÀÃ

Á+Ó.ÜÃ^Ò¥Õ@ÔÌÕ×ÊߊÂÌÖ+Âã̃É3Ò¥ÕҀÃ'׃ڨÁ+ÂÃÖ'ÕɀÃ^̉ÀãÑÒfÕ9ÖfÁ€Ì’ÖPÃ9ä^åŠÂÃ^ÑÓ9ɀ̉Á€ÌƒÓ9À¨Ó5Ù7Á€ÂÃÖfÒ+̃Á€Ì’ÖTÕ×Ò¥ÕÚÊJ̝Ù

̃Á1ÃPþR̃ɀÁ+É_ÊɀÃ'Ñ,ÕÒfÕÁ€Ì‰ÀÝÁ€ÂÃ.áÓû̃ÀݨÕÀ,Ô É+Á¥Õ5Ý9À,Õ5ÀÁ1Ñ,Õ5Ò+Á€É^ÓÙ$Á€ÂÃÞ,Óßà̃ÉUáÃ_Õ5É+ØҀÃ_Ô Ì‰À Á+ÂÃ

ÖfÓÓ9ÒfỖÀ,ÕÁ€Ã3É+ÚÉ+Á€Ã'á ÓÙ,/̃Ý@ØÒ+Ã^Ä9äƒÄ*ÜړÕUÖfÒ+̃Á+ÌÖ'Õ5×Õ5ÀÝ9׃Ã?¶<Z@ä

¿ÀÜ|̃Ý9ØÒ+Ã&{,ä{,ÊÁ+ÂÃUߊÌÔÁ+¨Ó5ÙDÁ+ÂÃHÞ,Óߊ̃ÀÝ^ÑÕÒ+Á3̃É`ҀÃ'ÑÓ9Ò+Á€Ã_ԙÙÓ@Ò$Õ^ÂÓ9ÑÑÃ'Ò3ߊ̃Á+ÂÕô9Ç

Â,Õ5×wÙJÓ9ÑÃ'À̃ÀÝHÕ5ÀÝ9׃Ã9Ê5ÙÓ9Òû9Õ5Ò+̃Ó9ØÉû9Õ5׉ØÃ'É)ÓÙJÁ+ÂÃ`ÕÀÝ@׉ÃTÉ)ÓÙJß7Õ5׃×9Ù Ò+ÌÖfÁ+̃Ó@À/ÊiÝÔ Õ5Ò¥ÖfÁfÕÀJÿfº'ÊÕÀ,Ô

̃ÀÁ+Ã'ҀÀ,Õ×ÙҀÌÖfÁ+̃Ó9ÀJ§ä

20

22

24

26

28

30

32

34

36

38

40

18

20

22

24

26

28

30

angle of wall friction

Φ

angle of the stagnant zone boundary

θ

*

δ

= 22.5,...,40

MJ<ONK@?9= @V@ á¹_ã]#_V8h#_fV8Xg_DTä,b[\_ kgb1Y‰íV8Y"Vb\[T2Vi_,ågT2æŽV8hY`gçDYV#íZO_jaWcb[YV#íZO_=TäjaUYZcZäg`gWdX]

bWêT2V4WQVDY,[\T^]]#_`CawWQb[=Y^3_7(=[ŽYZäjYV#íZO_äT`eY"`gWêT2æŽk<eYZæì_kFTäAbd[_WcVbE_f`gV8YZHYV#íZO_,Tääg`gWXgbWêTV

î4å_bda_f_fV``l%a(DYV8hcbd_7(Žl

¿Àµ|̃Ý9ØҀÃ{,ä{,ÊÕû9Õ׃ØÃ^Ó5ٕô@Ç

ÖfÓ@Ò+Ò+ÃTÉ+ÑÓ9À,ÔÉ^Á€Ó¨ÀӨɀÁ¥Õ5Ý9À,Õ5ÀNÁ•'Ó9ÀÃ@äJÓ@ÒHû9Õ׃ØÃ'ɖÓÙ§

É+á.Õ׃׃Ã'Ò3Á+Â,Õ5À Á€ÂÓ9ɀÃüÖPÓ9Àɀ̒ÔRÃ'Ò+Ã_Ô ÂÃTÒ+Ã9ʐÀÓɀÁ¥Õ5Ý9À,Õ5ÀNÁ&'Ó@ÀÃߊÕÉUÑÒ+ÃÔÌÖfÁ+Ã_Ô äµK*ÀÃ.Ó9ÜɀÃ'Ò+û@Ã'É

Á+ÂÕÁ–ÙÓ9ÒUÃ_Õ9ր ÖfÓ9ÀɀÌÔÃ'Ò+ÃÔ û9Õ5׃ØÃÓ5Ù`Á+ÂÃ.̃ÀÁ+Ã'ҀÀ,Õ׊ÕÀÝ@׃ÃÓي٠Ò+ÌÖfÁ+̃Ó@Àµ§Ê)Á+ÂÃ'Ò+Ã.̃ɑÕãÖfҀ̉Á€ÌÖ'Õ×

û9Õ׃ØÃ^Ó5Ù`Á+ÂÃß7Õ5׃×ÙÒ+ÌÖfÁ€ÌƒÓ9À/ÊØÀÔÃ'ÒUߊÂÌÖ+ÂÁ€ÂÃ'ҀÓ̃ÉUÀӨɀÁ¥ÕÝ@À,ÕÀÁUÒ+Ã'Ý@̃Ó9À/ÊÕÀ,Ô Óû9Ã'ҖߊÂÌÖ+Â

É+ØÖ+ÂãÕÀ¨ÕҀÃ_ÕÕ5ÑÑ,ÃÕÒ+ÉäåŠẪÉ$ÖfҀ̉Á€ÌÖ'Õ×|û9Õ׃ØÃ3̃À,ÖfÒ+ÃÕÉ+ÃTÉ$ߊ̃Á€Âó§ä7ØÒ+Á+ÂÃ'Ò_ÊÙÓ@Ò`ÕUýþÃ_Ôp§ÊÁ+ÂÃ

ߊÌÔÁ+ÂÓÙ/Á€ÂÃ`ɀÁ¥ÕÝ@À,ÕÀÁÑ,ÕҀÁDÓ5Ù/Á+ÂÃ*Þ,Óß ÌƒÀ,ÖfҀÃ_ÕɀÃ'É`ߊ̃Á€Â^Á+ÂÃ3ߊÕ׃×ÙҀ̒ÖPÁ+̃Ó9À/ä<K*ÀÃ_Õ@րÂüÖPØÒ+û@Ã9Ê

(12)

|½d½fe EÁ/(T (H$Ž¿¨ )(Tg‰(– 4)) ½$åŠÂÃ1ÕÀ,Õ5׃ÚNɀ̃Ɋ̉É*Ü,ÕɀÃ_Ô.Ó@À¨Á+ÂÃUÖ+ÂÕÒ¥Õ@րæ

Á+ÃTÒ+̃É+Á€Ì’Ö^ÖPØÒ+û@Ã'É_ä¿ÀÓ9ÒfÔÃ'ÒHÁ€ÓüÖPÓ9ÀɀÁ+Ò+ØÖfÁ1Á€ÂÃ^û9ÃT׉ÓÖf̃ÁÚրÂ,Õ5Ò¥Õ@ÖfÁ+Ã'Ҁ̃É+Á+ÌÖfÉÊßDÃ^Ý@Ó.Ü,Õ9րͨÁ€Ó¨Á+ÂÃ

Ó9Ҁ̃Ý9̃À,Õ×< – ÉÊ,ÕÀÔҀÃ'ߊÒ+̃Á€Ã^ÿ4Ïä‰ÄÇ8ÕÀ,Ôüÿ4Ïä‰Ä@Ä#ÕÉÙÓ@׃׉ÓߊÉ

h

´

‡

É



‡



ˆ

Ë

¬

Ä

Bi

´

ˆ

É



‡



ˆ

Ë

Pj4

ߊÂÃ'ҀÃ

h

É

Ä Ç

Ç ÄŽv9Ï Ë

i

É

Ç Ä

Ä#v@Ï ¥ „w‡‰ˆ vÿ„wˆˆ ¥|˜w Ë

Á+ÂÃ1ÃfþÑҀÃ'É+ɀ̃Ó9ÀÓÙÁ+ÂÃ^á.ÕÁ+Ҁ̝þkj ̃É`ÀÓ9Á3Ò+Ã'׃Ã'û9Õ5ÀÁ$ÂÃ'Ò+Ã9äUåŠÂÃUû9ÃT׉ÓÖf̃ÁڨրÂ,ÕÒfÕ9ÖfÁ€Ã'Ò+̃ɀÁ+ÌÖfÉ^ÕÒ+Ã

Á+ÂÃ'À

Ä

òi

ò¶ l ¤Hm

¦

ߊÂÃ'ҀÃnl ¤Qm

¦

Õ5Ò+Ã3Á+ÂÖÃ'̃Ý9Ã'Àû9Õ׃ØÃTɊÓÙÁ€ÂÃ3á“Õ5Á+Ò+̝þ

i

¤

h

ä

–

׃Ã'áÃ'ÀÁ¥ÕҀÚÖ'Õ×ÖfØגÕ5Á+̃Ó9ÀÉD׃Ã_Õ@ÔÁ€Ó

Ä

ò

ò¶

„ ‡2ˆ

„ ˆˆ ¥J˜po

q

„

¦

‡‰ˆ

ÿ„ ˆˆ ¥J˜w

¦

¬

Ä ¶óÙÿg¶A¤\¶

¦

s ÿE{,ä{

åŠÂÃHÕÜÓû9Ã3ҀÃ'×ÕÁ+̃Ó@À/ÊÃfþÑÒ+ÃTÉ+É+ÃԨ̃ÀÁ€Ã'Ò+áɊÓÙÁ+ÂÃyRÓ9Í9Ó@׃ÓûNɀÍ̉Ìû9ÕÒ+ÌÕ5Ü׃Ã'É_ÊÜÃ_ÖfÓ@áÃ'É

Ä

ò

ò¶

r™Á¥ÕÀ ÿ

{ o

Îjs ÿE{,äOmH

åÓý,À,Ô*Á+ÂÃ)É+Á€Ò+Ã'ɀÉúրÂ,Õ5Ò¥Õ@ÖfÁ+Ã'Ҁ̃É+Á+ÌÖfÉÊÿ4Ïä>Æ8JÕÀÔHÿÏä>ö8JÕ5Ò+ÃÒ+ÃTߊÒ+̃Á+Á€Ã'á ØÉ+̃ÀÝ`Õ5ÝNÕ5̉À3Á€ÂÃ,yÓ9Í@Ó9׃ÓûÉ+Í̃Ì

û9ÕҀÌÕÜ׃Ã'É s

´

‡

É

œ

Î Ë

¬

Ä

ut

´

ˆ

É

œ

Î Ë Xv6

ߊÂÃ'ҀÃ

s

É

Ä7¥ãÉ+̃À§ÖfÓ9ÉJÏ8Î ÏHœ*É+̃À§|É+̃À7ÏHÎ

¥.É+̃À§|É+̃À`ÏHÎ ¥`Ï8œ3ɀ̉À=§ÖfÓ9ÉJÏ8Î Ë

t

É

¥.É+̃À§|É+̃À`Ï8Î ¥`ÏHœ`ɀ̃À§ÖPÓ9É,ÏHÎ

Ä

¬

ɀ̉À§ÖfÓ@É,Ï8Î ¥`Ï8œ*ɀ̉À§|ɀ̉À`ÏHÎ Ë

v ̃Ɋ̃Ò+ҀÃ'׃Ã'û9ÕÀÁŠÂÃTÒ+Ã9äåŠÂÃ3É+Á+ҀÃ'É+ÉHրÂ,Õ5Ò¥Õ9ÖPÁ+Ã'Ҁ̉ɀÁ+ÌÖfÉHÕҀÃ3Á+ÂÃ'À

Ä

òi

ò¶ º<¤Hm

¦

ߊÂÃ'Ҁú<¤Hm

¦

ÕҀÊÁ+ÂÊÃT̉Ý@Ã'Àû9Õ׃ØÃ'ɐÓÙJÁ+ÂÊá.ÕÁ+Ҁ̝þ

t

¤

s

ä=LŠÓ@Á+ÊÁ€Â,ÕÁ

t

̃ÉÀÓ9ÀÉ+̃ÀÝ9ØגÕ5Ò)ÕÉ)׃Ó9ÀÝ

ÕɊɀ̃À§

¬

ÖfÓ@É,Ï8ΫÃ2ÇÊߊÂÌր¨ÖfÓ9ҀÒ+Ã'ɀÑ,Ó@À,ÔÉ3ÕÝNÕ5̃ÀÁ+Ó.ÿôä>Ï9ÇH'ä<K*ÀÃ3ý,À,ÔRÉ

Ä

ò

ò¶

r¨ÁfÕÀJÿ

{

¥

§

Ï

o

Îjs ÿE{,ä>ÆH

¿À,ÖfÌÔÃTÀNÁfÕ׃׃ÚNÊTßDÃÓ9ÜÉ+Ã'Ҁû9ÐÙÒ+Ó@á ÿf{,äOm8|ÕÀ,ԖÿE{ä>Æ8JÁ€Â,ÕÁ|Á+ÂÃû9ÃT׉ÓÖf̃ÁÚ3ÕÀ,Ô3ɀÁ+ҀÃ'É+ÉDրÂ,Õ5Ò¥Õ@ÖfÁ+Ã'Ҁ̃É+Á+ÌÖfÉ

ÕҀÃҀÃ'É+ÑÃ_ÖfÁ€Ì‰û@Ã'׃ÚâÕ5Á‘Õ5ÀÝ9׃Ã'É

o

vì{ Õ5À,Ô

o

ÿ#v{(¥â§v@Ï8ÙÒ+Ó@á Á€ÂÃá.ÕfÓ@Ò$ÑÒ+̃À,Öf̃Ñ,Õ5×DɀÁ+Ò+ÃTÉ+É_ä

LŠØáÃ'Ҁ̒ÖTÕ׃׃ÚNÊÁ€ÂÃp'Ã'Ò+Ó5æ4Á€Â ÕÀÔýÒ+É+ÁÓ9ÒfÔÃ'Òû@Ã'׃ÓÖf̃ÁÚâրÂ,ÕÒfÕ9ÖfÁ€Ã'Ò+̃ɀÁ+ÌÖfɨÕҀÃüÖPÓ9ÀɀÁ+Ò+ØÖfÁ+Ã_Ô ÜÚ

É+Ó@׃ûÑÀÝ ÿE{,ä{3̃À ÖfÓ9À#PØÀ,ÖfÁ€Ì‰Ó@À ߊ̃Á+ ÿ4ôä‰ÄŽm8TÊ/ߊÂÃTÒ+Ã.Á+ÂÃ.ɀÁ+Ò+ÃTÉ+ÉÖfÓ@áÑÓ9ÀÃ'ÀÁ€É‘Õ5ÑÑ,ÃÕÒ+̃ÀÝã̃À

ÿE{ä{iÕ5Ò+èҀÃ'É+ÑÃ_ÖfÁ€Ìƒû9Ã'׃Ú2Á¥ÕÍ@Ã'À ÕÁÓ@Ò¥ÔÃTÒ|TÃ'Ò+ӚÕÀÔ Ó9ÀÃ@ä åŠÂèÉ+Á€Ò+Ã'É€É Ö€Â,Õ5Ò¥Õ@ÖfÁ+Ã'Ҁ̃É+Á+ÌÖfÉãÕÒ+Ã

Ó9ÜÁ¥Õ̃ÀÃÔ^ÜÚ1ɀÓ9׃û̃ÀÝ^ÿE{ä>Æ8̃ÀÖfÓ@À#fØÀ,ÖPÁ+̃Ó9Àߊ̉Á€Â¨ÿôäƒÄ#mH'ÊߊÂÃTÒ+Ã6Î

Ä

Ï

ÕÒ¥ÖPÁ¥ÕÀ ÿ Ï „w‡‰ˆ

„w‡‰‡ ¥ „wˆˆ 'Ê

ÕÀÔ^ߊ̃Á+Â.Á+ÂÃ$ɀÁ+ҀÃ'É+É3ÖfÓ9áÑ,Ó@ÀÃ'ÀÁ+ÉÜ,ÃT̉ÀÝÕÝNÕ5̃À^Á¥ÕÍ@Ã'À¨ÕÁÓ9ÒfÔÃ'Ò='Ã'ҀӓÕ5À,Ô^Ó@ÀÃ3Ò+Ã'ɀÑ,Ã_ÖPÁ+̃û9Ã'׃Úä

(13)

−40

0

−30

−20

−10

0

10

20

30

40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

angle

radius

0

2

4

0

2

4

−40

0

−30

−20

−10

0

10

20

30

40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

angle

radius

0

2

4

0

2

4

MJ<ONK@?9=@Vw5yx:_Oä^b%$z[_`T"]1b[|{ghYkg[#h#T2bD}<YV8hSKw`gkgb:T2`Eh#_`>{fkTZWdh7}<h#T2awVkgb`_ãYH!e"_^ZT^XgWQbçFX^[#Y`EYX7]

bE_f`gWckgbdWXgkäg`T"!·b[\_AbETg]&Tä<b[\_ WQVk_`gb~MU`gWí[b$<k‰YH!_<X^æ#`ge_fkäT2`,b[\_Akgb`_kgk X^[#Y`EYXgbE_f`gWckgbdWXgkgl>8^V

ågT2b[¹XfYk_fkL*Ubd[_]Y`EYH!_fbE_`gk Y"`_G$,YV#íZ_,Têäiä^`gWdX^bdW1T2V¹î€&¸'¶)(H*o[#YZä,Tg]#_VWQV#í=Y"V#íZO_€+.'¶)(l':[\_

XgæŽ`ge"_k,WQV8hŽ_19#_ãhn_7*z`Q*YbXgT2`g`_kE]#T2V8h4bET7aYZQZä^`gWdXgbW1T2V6eYZæ8_fk¹Têä

ë

&.¶3276»-276.)*U`_fkE]Ž_1X^bdWce"_^Zçl

¿Á̃ÉDÓ@ÜÉ+Ã'Ҁû9Ã_ԓÙÒ+Ó@á |̃Ý9ØÒ+Ã{äOmÊ@Á+Â,Õ5ÁŠÌ‰À^ÀÃ'̃Á+ÂÃ'Ò`ÖTÕÉ+ÃUÖ'ÕÀÁ+ÂÃ*ý,ҀÉ+ÁŠÓ9ÒfÔÃ'Ò`ÖfÓ@Ò+ҀÃ_ÖfÁ+̃Ó@ÀÉ

ÜÃH̃Ý9ÀÓ@Ò+Ã_ÔJä

tÃ*ÀÓß Á+ØҀÀ“Á€Ó1Á€ÂÃ`á.Õ̃À^ÕÑÑ׃ÌÖ'Õ5Á+̃Ó9À^Ó5Ù/Ó9ØÒáÃ'Á€ÂÓԃ|Á+ÂÃHÔÃ'Á€Ã'Ò+á̃À,ÕÁ€Ì‰Ó@À^ÓÙ €Ó9ÑÁ€Ìwæ

á“Õ5×%DÖfÓ9À̒ÖTÕ×9̃ÀɀÃ'Ò+Á€É_Ê9Õ@Ö'ÖfÓ@Ò¥ỖÀÝ*Á+ӊÁ+ÂÃDÖfÒ+̃Á€Ã'Ò+̃Ó9ÀUỖɥÖfØɀÉ+Ã_Ԗ̃À3Á+ÂÃ)¿ÀÁ€Ò+ÓÔØ,ÖfÁ€ÌƒÓ9À/ä<Ó@׃׉Óߊ̃ÀÝ

Ë9Ó@Â,ÕÀÉ+Ó9À ÎOmÐ+ÊJßÃ1ßÓ9Ҁͨߊ̃Á+ÂãÁ+ÂÃ^ɀÁ+ҀÃ'É+ÉրÂ,Õ5Ò¥Õ9ÖPÁ+Ã'Ҁ̉ɀÁ+ÌÖfÉä|L•ØáÃ'ҀÌÖ'Õ׃׃ÚNÊÁ+ÂÃÔRÓߊÀÉ+Á€Ò+Ã_Õ5á

É+Á€Ò+Ã'ɀÉրÂ,ÕÒfÕ9ÖfÁ€Ã'Ò+̃É+Á€Ì֓ÖPØÒ+û@ÓÃTá“ÕÀÕÁ+̃ÀÝ ÙÒ+Ó@á Á+ÂÃÁ+Ó9ÑÓ5Ù`Á+ÂÃÂÓ9ÑÑ,Ã'Ò^̃É3ýÒ+É+Á^ÖfÓ@áÑØÁ€Ã_ÔJä

¿Á+É*̃ÀNÁ€Ã'Ò+ɀÃ_ÖfÁ€Ì‰Ó@Àߊ̃Á€Â“Á€ÂÃHÓ@ØÁ+Ã'Ò*ß7Õ5׃×JÓÙ)Á+ÂÖÂÓ9ÑÑÃ'Ò3̃ɊÒ+Ã_ÖPÓ9Ò¥ÔRÃ_Ôÿ É+Ã'Ã|̃Ý9ØҀÃ6{,ä>Æ8Tä)åŠÂÃTÀ/Ê

ÜÚ Õ™É+ÂÓNÓ@Á+̃ÀݨáÃ'Á+ÂÓRÔ Ê/Á€ÂèỖÉ+Á¥Õ5À,ÖfÃpH‚,ÊáÃ_ÕɀØÒ+Ã_Ô Õ׃Ó9ÀݓÁ€ÂÃ׃̃Àà ÙÒ+Ó@á Á€ÂÃÓ@Ò+̃Ý9̃ÀãÁ+Ó

Á+ÂÃÁ+Ó@ÑÓÙ`Á€ÂÓÖfÓ@ÀÌÖ'Õא̉ÀÉ+Ã'ҀÁÿ É+Ã'èÕÝÕ̃À/̃Ý@ØÒ+Ã{äÆH3̃ÉHÉ+Ó@ØÝ9ÂÁä.åŠÂÓÖfҀ̃Á+ÌÖ'Õ×û9Õ׃ØÃH‚

̃É`ɀӓÁ€Â,ÕÁ*Á+ÂÃ^ØÑÉ+Á€Ò+Ã_Õ5á րÂ,ÕÒfÕ9ÖfÁ€Ã'Ò+̃ɀÁ+ÌÖ^ÖfØҀû9ÖÙÒ+Ó@á Á+ÂÃUÜ,Ó@Á+Á€Ó9á ÓÙÁ+ÂÃŨÀÉ+Ã'ҀÁ3̉ÀÁ€Ã'Ò+ɀÃ_ÖfÁ+É

Á+ÂÃÔÓߊÀÉ+Á€Ò+Ã_Õ5á րÂ,Õ5Ò¥Õ9ÖPÁ+Ã'Ҁ̉ɀÁ+ÌÖÖPØÒ+û@ÃUÙÒ+Ó@á Á+ÂÃ^Á€Ó9ÑãÓيÁ+ÂÃ^̃ÀɀÃ'Ò+ÁHÃPþÕ@ÖfÁ+׃ڨÓ@ÀÁ€ÂÃ^Ó9ØÁ+Ã'Ò

ÂÓ@ÑÑ,ÃTÒ`ߊÕ׃×ä

a

R

W

θ

r*

insert

wall of the

hopper

MJ<ONK9?@=9Vƒ9 „<_ET"!_fb`gç6Tä,b[\_ [\Tg]]#_f`L…\WQVk_f`gbAkgçkgbã_#!Fl

¿À.Á+ÂÃÖTÕ×ÖfØ×ÕÁ€ÌƒÓ9ÀÉ)ÜÃ'׃ÓßHÊÁ+ÂÃ$ҀÃ'É+Ø׉Á€É$Õ5Ò+Ã3ÃfþÑÒ+ÃTÉ+É+ÃԨ̃ÀÁ€Ã'Ò+áÉDÓ5ÙÁ€ÂÃHỖáÃ'Àɀ̃Ó9À׃Ã'ɀÉ

Ñ,Õ5Ò¥ÕáÃ'Á+ÃTÒ,†Üv8xUÊ@ߊÂÃ'Ò+dž ̃É)Á+ÂÃ`ÂÓ@Ò+Ì'Ó9ÀÁfÕ×,ỖɀÁ¥ÕÀÖfÃ`ÜÃ'ÁßÃ'Ã'À.Á+ÂÃ*Ü,Ó@Á+Á€Ó9á ÓÙJÁ+ÂÃ*̃ÀÉ+Ã'ҀÁ

ÓÙ)Á€ÂÃ1ߊÕ׃×JÓ5ÙúÁ€ÂÃUÂÓ9ÑÑÃ'ÒÊ,ߊẨ׃Ãx É+ÁfÕÀ,ÔÉ*ÙÓ@ҊÁ+ÂÃUÒ¥Õ@ỖØÉ`Ó5Ù)Á+ÂÃH̃ÀɀÃ'Ò+ÁÊJÉ+ÃTè|̃Ý9ØҀÃ6{,ä>Æä

– Û@Ø̃û9Õ׃Ã'ÀÁ€×‰ÚÊßÃ$ÂÕû9ÆÜvHxq Ï8H‚)ɀ̃À¹-ˆÜvRÿr€¥ H‚É+̃À-ˆJ'ÊߊÂÃ'ҀÃ1Á€ÂÃHÑ,Õ5Ò¥Õ5áÃ'Á€Ã'ÒrÂ,ÕÉ

(14)

̃À¨|̃Ý9ØÒ+Ã{ä>öäJåŠÂÃ`ÔRÃ'Ñ,ÃTÀ,ÔÃ'À,ÖPÚÓنÜvHxšÓ@À1Á€ÂÃ`ߊÕ׃×@ÙҀ̒ÖPÁ+̃Ó9À^̃É̃׉׃ØɀÁ+ÒfÕÁ+ÃÔỦÀz|̃Ý9ØÒ+Ã={,ä>÷ä

10

15

20

25

30

35

40

0

1

2

3

4

5

6

half opening angle

W/R

x:

δ

= 15

o

o:

δ

= 25

o

+:

δ

= 35

o

*:

δ

= 45

o

MJ<ONK@?9=,@V‰5PŠ]]Ž`gT79W‹!¹YbE_7X^`gWQbWdXfYZHkgW[_,Têä<b[\_<[Tg]]#_`L…ŽWQVk_`gbkgçkgbã_#!ÒåfYk_ãh?T2V6b[\_Ckgbd`g_fkgk

Xg[ŽY`EYX^bã_`gWQkgbWdX^kLMXg`gWcbWdXfYZeYZæ8_<Œ‡0HµY‰íYWQVkgbobd[_[ŽYZä,Tg]Ž_fVWcV#í=YV#íZO_1*AhYkg[Žh#T2bZWQVi_#$CawWQb[\Tæ#b

XgT2`g`_ãXgbWêT2V)*AkT"ZWhZWQVi_G$jaWcbd[XgT2`g`_ãXgbW1T2VlnŽ6YZcZ‰ä^`gWdXgbW1T2V

ë

&6»Žl

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

wall friction

µ

W/R

MJ<ONK@?9=,@V@PŠ]]Ž`gT79W‹!¹YbE_7X^`gWQbWdXfYZHkgW[_,Têä<b[\_<[Tg]]#_`L…ŽWQVk_`gbkgçkgbã_#!ÒåfYk_ãh?T2V6b[\_Ckgbd`g_fkgk

Xg[ŽY`EYX^bã_`gWQkgbWdX^kLMX^`gWQbWdXfYZ*eYZæì_IŒn0HqY‰íYWQVkgbjbd[_=aYZcZäg`gWdX^bWêT2V

ë

*=hY"kg[#h#T2bFZWQVi_#$awWQb[\Tæ#b

XgT2`g`_ãXgbWêT2V)*AkT"ZWhZWQVi_G$jaWcbd[XgT2`g`_ãXgbW1T2Vl|‘,YZä=Tg]#_VWQV#íDYV#íZ_|¸'¶

(

(15)

†Üv8x ÔÃ_ÖfҀÃ_ÕɀÃ'ÉDÕ5É/Á+ÂÃ)Ó9ÑÃ'À̃ÀÝ`Õ5ÀÝ9׃Ã̃À,ÖfÒ+ÃÕÉ+ÃTÉ_ÊÕÉ/ÃPþRÑÃ_ÖfÁ€Ã_ÔJä,ØÒ+Á€ÂÃ'ÒÊÁ+ÂÐû9Õ׃ØÃ'ÉJÓ5ْ†ÜvHx

ÖfÓ@áÑØÁ€Ã_Ô.Á€ÂÒ+Ó@ØÝ9ÂãÓ9ØÒHÕ5À,Õ׃ÚÉ+̃Ɋߊ̃Á+™ý,Ò+ɀÁ3Ó9Ò¥ÔRÃ'Ò1ÖfÓ@Ò+Ò+ÃÖfÁ+̃Ó9ÀÕҀÃ1̃ÀãÃ'û9ÃTÒ+ÚÖ'Õ5É+Ã^ÜÃ'ÁßÃ'Ã'À

{d“ ÕÀ,Ô ô9Ǔ É+á“Õ5׃׉ÃTÒHÁ+Â,Õ5À Á€ÂÓ9ɀèÓ9ÜÁfÕ̃ÀÃ_Ô ßŠÌƒÁ+ÂÓ@ØÁ‘ÖPÓ9Ò+ҀÃ_ÖfÁ€Ì‰Ó@À/ä åŠẪÉÖfÓ@Ò+Ò+ÃTÉ+ÑÓ9À,ÔÉÁ+Ó

Ò+ÃÛ9Ø̉Ҁ̃ÀÝ×ÕÒ+Ý@Ã'Ò^̃ÀÉ+ÃTÒ+Á+Éä2¿ÀâÓ@Á+ÂÃTÒßÓ9Ò¥ÔRÉ_ÊÓ9ØÒ.ÖfÒ+̃Á€Ã'Ò+̃Ó9À ̃É^É+Ó@áÃ'ߊÂÕÁUáÓ9ҀÃ.É+Á+Ҁ̃ÀÝ9Ã'ÀÁ

Á+ÂÕÀãË9Ó9ÂÕÀɀÓ9À/ÈÉ_ä åŠÂÑÔRÌwóJÃ'ҀÃ'À,ÖfÃ.ÜÃ'ÁßDÃTÃ'ÀÁ+ÂÃ^ÁßÓ¨ÕÑÑÒ+ÓNÕ@րÂÃ'ÉH̃ÉHÛ@Ø̃Á+Ã^É+̃Ý@À̝ýøÖ'ÕÀÁ*ÙÓ@Ò

×ÕҀÝ9ÃHÓ@Ñ,Ã'À̉ÀݓÕÀÝ9׃Ã'ÉUÿ#”»{NÇ $Õ5À,Ô.×ÕҀÝ9Ã1Õ5ÀÝ9׃Ã'É3Ó5Ùú̃ÀÁ+ÃTÒ+À,Õ5×/Ù Ò+ÌÖfÁ+̃Ó@Àܧ.ÿg§n”»{im8Ǝ'ÊߊÂÃTÒ+Ã

̃Á$Ö'Õ5À¨Ò+ÃÕ9ր ô@ǓùÓ9Ò*áÓ9ҀÃ9ä=n*׉ɀÓ,ÊßÃHÀÓ9Á€Ã1Á€Â,ÕÁ*Ó9ØÒ*Ò+Ã'ɀØ׃Á+É1Õ5Á`Ó@Ò¥ÔÃ'ÒD'ÃTÒ+Ó,Ê Ì4äÃ9äƒÊߊ̉Á€ÂÓ9ØÁ

ÖfÓ@Ò+Ò+ÃÖfÁ+̃Ó9À|ÊDÕÑÑ,Ã_Õ5Ò1Á€ÓÜÓÛ@Ø̃Á€Ã“ÖfÓ@ÀÉ+̃É+Á€Ã'ÀÁ^ߊ̃Á+ Ë@Ó9Â,Õ5ÀÉ+Ó@À/ÈÉHÒ+ÃTÉ+Ø׃Á+ɨÎOm\Ð~ä}Ó@ÒH̃ÀÉ+ÁfÕÀ,ÖPÃ9Ê

ÙÓ@ґՙÂÓ9ÑÑ,Ã'ÒUߊ̃Á+ ÕôHm

Ó@Ñ,ÃTÀ̃ÀÝ Õ5ÀÝ9׃Ã.ÕÀ,Ô ßŠÌ‰Á€Âá“Õ5Á+Ã'Ҁ̒Õ5×DÑÕÒ¥Õ5áÃ'Á€Ã'Ò+ɧJ {NÇ

ÕÀ,Ô

ºJšÕÒfÖfÁ¥Õ5À/ÿÏ9ô

'ÊÕ5׉×ÓÙÁ+ÂÓ@É+Ã3ÜÃ'̃Àݕ+×ÕҀÝ9ÃUû9Õ׃ØÃTÉ_Ê@Ë9Ó9ÂÕÀɀÓ9À.Ò+Ã'ÑÓ9ҀÁ+É*Á+ÂÃ3ÃfþÑÃ'Ò+̃áÃTÀNÁfÕ×

û9Õ׃ØֆÜv8x«šÇosÆÊ9ÕÀÔ^Õ$ÖPÓ9Ò+ҀÃ'É+ÑÓ9ÀỖÀݑÖPÓ9áÑØÁ+Ã_Ԗû9Õ׃ØÊÓ5Ù Çä>ÆätšÌƒÁ€ÂÓ9ØÁ)ÖfÓ@Ò+ҀÃ_ÖfÁ+̃Ó@À/ÊßDÃ

Ó9ÜÁ¥Õ̃À†Üv8x«qsOm9Å9Æ@ÏÊ@ÜØÁŠßŠÌƒÁ+¨ÖfÓ@Ò+ҀÃ_ÖfÁ+̃Ó@À/ÊÁ+ÂÃHÖfÓ@áÑØÁ€Ã_Ô^û9Õ5׃ØÃ3ÓÙ|†ÜvHx2Ù4Õ5׃׉ɐÁ+Ó¨ä>ô9ö@ô9Ïä

åŠÂÃHỖÉfÖfÒ+Ã'ÑÕÀ,ÖfÚãÖfÓ9Ø×Ô É+Á+ÃTá ÙÒ+Ó@áàÉ+Ã'û@Ã'Ò¥Õ5×/ҀÃ_ÕɀÓ9ÀÉäF|̃Ò+É+ÁÊÓ@ØÒ`ÕÀ,Õ5׃ÚNɀ̃ÉD̃ɊÜ,Õ5É+Ã_ÔÓ9À

Á+ÂÃ`û9Ó@Àõ.̃É+Ã'ÉÚ̃Ã'×Ô^ÖfÓ9À,ÔR̉Á€ÌƒÓ9À/Ê@Ò¥Õ5Á+ÂÃ'ÒÁ+ÂÕÀÁ€ÂÃ`ɀ̃áÑ׃Ã'Ò,Ó9Ø׉Ó@á^ÜHÚ̃Ã'×Ô^ÖfÓ9À,ÔR̉Á€ÌƒÓ9ÀÖfÓ@Ò+Ò+ÃPæ

É+ÑÓ9ÀỖÀÝÁ€ÓÜÓ9Á+™Ë9Ó9ÂÕÀɀÓ9À/ÈÉ$Õ5À,Õ׃ÚÉ+̃É3ÕÀ,Ô.Ó@ØÒ$Õ5ÑÑҀÓNÕ9ր¨ߊ̃Á€ÂÓ9ØÁ3ÖfÓ9ҀÒ+Ã_ÖPÁ+̃Ó9À/ä6yRÃ_ÖfÓ9ÀÔJÊ

ÕɖÃfþÑ×Õ̃ÀÃ_ԙ̃ÀÁ€ÂÿÀÁ+ҀÓÔØ,ÖfÁ€Ì‰Ó@À/Ê|Á+ÂÃ^ɀÁ+Ò+ÃTÉ+É^ÕÀ,Ôãû@Ã'׃ÓRÖP̉ÁÚüý,Ã'×ÔÉ1Õ5Ò+Ã^ò,íñŠÒ¥Õ@ÔÌÕ×ä – û9Ã'À

Á+ÂÓ9ØÝ@ÂÓ9ØÒUÃfþÑ,ÕÀÉ+̃Ó9À׃ÓÓ9ÍÉHÑҀÓ9á̉ɀ̃ÀÝ̃ÀÁ+ÂÕÁUÒ+Ã'ɀÑ,Ã_ÖPÁ_ÊÂÓß Ù4ÕɀÁ1ÕÀÔãߊÂÃ'Ò+Ããÿ ÌwÙ$Õ5ÀÚ9æ

ߊÂÃ'Ҁ×ÕÁ$ÖPÓ9Àû9Ã'ҀÝ9Ã'ɖ̉É3ÀÓ@Á$Öf׃Ã_Õ5Ò_䖿ÀÓ@Á+ÂÃ'Ò3ßÓ9ÒfÔÉ_Ê/Õ@ÔỖÁ+̃Ó@À,Õ×|Á+Ã'ҀáÉ3̃À¨Á+ÂÃUÃfþÑ,Õ5ÀÉ+̃Ó9À

á̃Ý@ÂNÁ|Ü,Ã*ÀÃ'Ã_ÔRÃ_ÔJä)¿ÁŠÕÑÑ,Ã_Õ5Ò+ÉÁ+Â,Õ5ÁDÁ€ÂÃ`ҀÃ'É+Ó@׃ØÁ+̃Ó9À^Ó5Ù/Á+ÂÕÙØ׃×ɀÚNɀÁ+Ã'á ÿ4Ïä>Æ\²RÏäƒÄ@Ä#Jߊ̃׃×ɀÂÃ_Ô

É+Ó@áÃ׃̉Ý@ÂÁÓ@À^Á+ẪÉ)ÑÓ9̃ÀÁ`΃ÄfÐ+ä|̃À,Õ5׉׃ÚÊÁ+ÂÊÑҀÃ'É+ÃTÀNÁ`ÖPÒ+̃Á+Ã'Ҁ̃Ó9À^Ù Ó9Ò̃ÀÉ+Ã'ҀÁ7ÔRÃ'É+̃Ý9ÀÖTÕÀÜÃ9ÊÕÀ,Ô

Â,Õ5ɊÜ,Ã'ÃTÀ/ÊÑØÁŠÌ‰À.Û@ØÃ'É+Á€ÌƒÓ9À΃Ä_ÇÐ+äJ¿ÀÔÃ'Ã_ÔJỄÁD̃É_Ê@Ù Ó9Ò̉ÀÉ+Á¥Õ5À,ÖfÃ9ÊÒ+Ã'á.ÕҀÍ9ÕÜ׃Ã`Á€Â,ÕÁ̝ÙÁ€ÂÃ3É¥ÕáÃ

ÕÀÕ׃ÚÉ+̃ÉH̃ɑÖTÕÒ+Ҁ̃Ã_Ô Ó9ØÁUߊ̃Á+ š# Pë’í

 

êñcŸâրÂ,Õ5Ò¥Õ9ÖPÁ+Ã'Ҁ̉ɀÁ+ÌÖfÉ^̃ÀɀÁ+Ã_Õ@Ô Ó5Ù`É+Á€Ò+Ã'ɀɓրÂ,ÕÒfÕ9ÖfÁ€Ã'Ò+̃ɀÁ+ÌÖfÉ_Ê

á^Ø,ր¨Ü̃Ý@Ý9Ã'Ò3̃ÀÉ+ÃTÒ+Á+É^ÕҀÃHÙ Ó9ØÀ,ԙÁ+Ó.ÜÃ^Ò+Ã_Û@Ø̃ҀÃ_Ô ÿ„Ù4Õ9ÖfÁ€Ó9ÒD{.Á+ÓÄ_ÇH'äUåŠÂÃ^ҀÃ'É+Ø׃Á€ÉHÓ9ÜÁfÕ̃ÀÃ_Ô

Á+ẨɊߊÕÚÔÓ^ÀÓ@Á`ÕÑÑÃ_Õ5ҊÁ+ÓÕÝ@Ò+Ã'Ã3̃À¨ÕÀÚ^ߊÕÚ^ߊ̉Á€Â.Á+ÂÃ3ÃfþÑÃ'Ò+̃áÃTÀNÁfÕ×Jû9Õ5׉ØÃ'É_ä

˜ ½

"3,) )(' ú(

½DtÃDÂ,Õû@Ã)̃ÀÁ+Ò+ÓÔØÖfÃ_ÔUÕ`ÀÃ'ß áÃ'Á+ÂÓÔ*Ù Ó9Ò/Á€ÂÃÀNØáÃ'Ҁ̒ÖTÕ×9ҀÃ'É+Ó@׃ØÁ+̃Ó9À

ÓÙÝ9Ò¥Õ5ÀØ×ÕÒ|Þ,ÓߊÉ)ÕҀÓ9ØÀ,ԖÓ9ÜÉ+Á¥Õ@Öf׃Ã'ÉØÀ,ÔÃTÒ)É+Á€Ò+Ó9ÀÝHÝ9Ã'Ó@áÃ'Á€Ò+ÌÖ'Õ5×9Ò+ÃTÉ+Á+ҀÌÖfÁ+̃Ó9ÀÉ_ÊÀ,Õ5áÃ'׃Ú`̃ÀUÁ+ÂÃ

Ö'Õ5É+Ã3ÓÙÖfÓ@ÀÌÖ'Õ×ÂÓ@ÑÑ,ÃTÒ+Ɋߊ̃Á+ẨÀû@Ã'Ò+Á€Ã_ÔÖfÓ@ÀÌÖ'Õ×̃ÀÉ+ÃTÒ+Á+Éä)åŠÂÃ*áÃ'Á€ÂÓÔUÉ+Á€Ã'áɐÙÓ9ÒÕÀÃÕÒ+׃̃Ã'Ò

ÖfÓ@ÀÉ+Á€Ò+Ø,ÖfÁ€ÌƒÓ9À/Ê)ÔØÃ^Á+Ó.Ë9Ã'À̉Í@èÎ>ÏÐ+ÊÓيҥÕ9ÔR̒Õ5×)É+̃á̉×Õ5Ò+̃ÁÚ^É+Ó@׉ØÁ+̃Ó9ÀÉäUåŠÂÃ^ÑÒ+ÃTÉ+Ã'ÀÁ^ÕÑÑҀÓNÕ@Ö+Â

Ô̝óJÃ'Ò+ɕÙÒ+Ó@á ̃ÁŠÜÚÕ׃׃Óߊ̃ÀÝ3ÙÓ@Ò7ՖáÓ@Ò+Ã*Ý9Ã'ÀÃTÒ¥Õ×|É+Á€Ò+Ø,ÖfÁ€ØÒ+ÃUÓÙÁ+ÂÃ3ɀÓ9׃ØÁ+̃Ó@ÀÉ_ÊߊÂÌր¨ÔÓUÀÓ9Á

Â,Õû@ÊÁ+ÓHÜÃ`ÒfÕ9ÔÌÕ×ä<ØÒ+Á+ÂÃ'Ò_Êɀ̉ÀÖfÃ`̃Á)׃Ã_Õ@ÔÉDÁ€Ó1Õ3ɀÚNɀÁ+Ã'áùÓÙ/Ó9ÒfỖÀ,ÕҀڑÔRÌwóJÃ'ҀÃ'ÀÁ+ÌÕ×Ã_Û@Ø,ÕÁ€ÌƒÓ9ÀÉ

ߊ̃Á+Â^ÜÓ9ØÀÔÕҀڑÖfÓ@À,ỖÁ+̃Ó@ÀÉ_ỄÁ)̃É)ɀÁ+̃׃×á^Ø,րÂUÉ+̃áÑ׃Ã'ÒÁ€Â,ÕÀ^Á€ÂÃ`ÀØáÃ'Ò+ÌÖ'Õ5×NҀÃ'É+Ó@׃ØÁ+̃Ó9À^Ó5Ù/Á+ÂÃ

ÙØ׃×JɀÚNɀÁ+Ã'á ÓÙ)Ñ,Õ5Ò+Á€Ì’Õ5×øÔRÌwóJÃ'ҀÃ'ÀÁ+ÌÕ×|Ã_Û@Ø,ÕÁ€Ì‰Ó@ÀÉ`ÖfÓ@Ò+Ò+ÃTÉ+ÑÓ9À,ỖÀÝÁ+Ó^Á€ÂÃ3ÑÒ+Ó@Ü׃Ã'á ÎҀÃfÙÝ9á Ð+ä

¿Á|Ì‰É ÙÓ9ØÀ,Ô*Á+Â,Õ5ÁJÙÓ@ÒJÉ+á“Õ5׃×û9Õ׃ØÃ'ÉJÓ5Ù,Á+ÂÐÑÂÚNɀÌÖ'Õ×@Ñ,ÕÒfÕáÃTÁ+Ã'ҀÉ)ÿÓ@Ñ,ÃTÀ̃ÀÝ$Õ5ÀÝ9׃Ã9ỄÀÁ+Ã'ҀÀ,Õ×

ÕÀÔUß7Õ5׉×@ÙҀÌÖfÁ+̃Ó9ÀÉ'Ê5Á+ÂÃ*ÑÒ+Ã'ɀÃ'ÀÁDáÃ'Á+ÂÓRԖ׃Ã_Õ9ÔRÉ)Á+Ó3Ò+ÃTÉ+Ø׃Á+ɊÛ@Ø̃Á+Ã`ÖfÓ@áÑ,Õ5Ò¥Õ5Ü׃Ã)Á+ÓHÁ€ÂÊÑØҀÃ'׃Ú

Ò¥Õ@ÔÌÕ×3ÕÑÑҀÓNÕ@Ö+ ÓÙHË9Ã'À̉Í@Ã9äßK*ØÒ¨ÖfÓ@Ò+Ò+ÃÖfÁ+̃Ó9ÀɓÜÃ_ÖfÓ@áè̃áÑ,Ó@Ò+Á¥Õ5ÀÁHÙÓ@Ò^×ÕÒ+Ý@Ã'Òû9Õ5׃ØÃ'ÉÓ5Ù

Á+ÂÓ9É+Ã.Ñ,Õ5Ò¥Õ5áÃ'Á€Ã'Ò+ÉÊ)ÌäÃ9äƒÊ)ߊÂÃ'À Á€ÂÃ'Ò+Ù̉É^ՙÉ+Ã'Àɀ̃Á+̃û9èÔÃ'ÑÕÒ+Á€ØÒ+ÃüÙÒ+Ó@á Õ¨ÒfÕ9ÔÌÕ5×DɀÁ+Ò+ØÖfÁ+ØҀÃ9ä

åŠÂÃỖÉfÖfÒ+Ã'ÑÕÀ,ÖfÚãÜÃ'ÁßDÃTÃ'ÀÁ+ÂÓ@É+Ã^ÁßÓ.áÃ'Á€ÂÓÔÉ`Â,Õ5É3Ü,Ã'ÃTÀ ̃׃׉ØÉ+Á+ÒfÕÁ€Ã_Ô¨ÂÃ'Ò+Ã^ÜÚ¨Ó@ØÒ3É+Á+ØÔÚ

ÓÙ+Ó@ÑÁ+̃á“Õ5×)É+Ì'Ãԙ̃ÀÉ+Ã'ҀÁ+ÉäšåŠÂèÖfҀ̉Á€Ã'Ò+̃Ó@ÀâØÉ+Ã_Ô Ù Ó9ÒUÁ+ÂèÔÃ'Á€Ã'Ò+á̃À,ÕÁ€Ì‰Ó@À Ó5Ù$Á+ÂÓ̃ÀɀÃ'Ò+Á€É

̃ÉHÜ,Õ5É+Ã_ÔãÓ@ÀÁ€ÂÃ^É+Á€Ò+Ã'ɀÉÖ+ÂÕÒ¥Õ@ÖfÁ+ÃTÒ+̃É+Á€Ì’ÖPɑÕ5À,ÔJÊ|Á+Ó¨Á€ÂÃÕØÁ€ÂÓ9ҀÉ_ÈJÍÀÓߊ׃Ã_ÔRÝ9Ã9Ê|ß7Õ5ÉHÓ9Ҁ̃Ý9̃À,Õ׃׃Ú

ÑҀÓ9ÑÓ9É+ÃÔHÜÚ3Ë9Ó@Â,ÕÀɀÓ9ÀÎOm\Ð~äwtÃ)ÀÓ9Á+ÃÁ+ÂÕÁ/Á€ÂÃ'ҀÃ7ÔÓÃ'ÉÀÓ@Á/ɀÃ'Ã'á Á€Ó`ÜÃ)Ó9Á€ÂÃ'ÒÁ+ÂÕÀHÃ'áÑ̃Ò+ÌÖ'Õ5×

fØɀÁ+̝ýøÖ'Õ5Á+̃Ó9ÀÉ^ÓÙ$Á€Â,ÕÁÖPÒ+̃Á+Ã'Ҁ̃Ó9À ߊÂÌրÂ/Ê)ÀÃTû9Ã'ҀÁ+ÂÃ'׃Ã'ɀÉ_Ê3ÕÑÑÃ_Õ5Ò+ÉÁ€ÓÜÃÛ@Ø̃Á+ÃØÉ+ÃPÙØ×HÿÕÀ,Ô

ØɀÃ_Ô<—ÕÀ¨ÑÒfÕ9ÖfÁ€ÌÖfèÎ>ôÐ+ä?yRÓ9áÃUÕØÁ€ÂÓ9Ҁɑ΃ÄÇÐÂÕû9ÃUÒ+ÃEfÃÖfÁ+Ã_ÔãÑÕÒ+Á3Ó5Ù7Á€ÂÃ1Ý@ÓÓRÔüÜ,Ã'ÂÕûÑÓ@Ò$Ó5Ù

Ë9Ó@Â,ÕÀÉ+Ó9À|ÈÉ`ÖPÒ+̃Á+Ã'Ҁ̃Ó9À¨ÕɊÜÃ'̃ÀÝ^ÑØҀÃ'׃Ú̃À,ÖfÌÔÃTÀNÁfÕ×ä

K*ØÒ.áÃTÁ+ÂÓÔ ÌƒÀ ÖPÓ9À#fØÀ,ÖfÁ+̃Ó@ÀšßŠÌƒÁ+šË@Ó9Â,Õ5ÀÉ+Ó@À/ÈɓÖfҀ̉Á€Ã'Ò+̃Ó@Àš×ƒÃ_Õ9ÔÉÁ+Ó áÓ9ҀÃ.É+Á+Ҁ̃ÀÝ9Ã'ÀÁ

ÖfÓ@À,ỖÁ+̃Ó9ÀÉHÓ9À Á+ÂÃ̉ÀÉ+Ã'ҀÁ+É^Á+ÂÕÀ ՙÑØÒ+ÃT׉ÚãÒ¥Õ@ÔÌÕ׊ÕÑÑÒ+ÓNÕ@րÂ/äJtÃ^ߊ̃׃×DÕ9ÔÔÒ+Ã'ɀÉ^̃ÀÙØÁ€ØÒ+Ã

ßÓ9Ò+ÍJÊÁ+ÂÒ+Ó9ØÝ9ÂãÉ+̃á^Ø×ÕÁ€Ì‰Ó@ÀÓ5ÙúÁ€ÂÃUÙØ׃×|É+ÚÉ+Á€Ã'áÊÁ+ÂÑÛ@ØÃ'ɀÁ+̃Ó9ÀãÓÙߊÂÃ'Á+ÂÃ'ÒHÁ+ẨÉ3ҀÃfÞ,Ã_ÖfÁ€ÉHÓ9À

Á+ÂÃ$û9Õ5׃̒ÔR̉ÁÚÊÓ@ҊÁ+ÂÃH×Õ@Ö+Í^Á€ÂÃ'ҀÃ'ÓÙ¥ÊÓÙÃ'̃Á+ÂÃ'Ò*Ó9ØҊÃPþRÑÕÀɀ̉Ó@À.Ó9ҊË9Ó@Â,ÕÀÉ+Ó9À|ÈÉ`ÖPÒ+̃Á+Ã'Ҁ̃Ó9À

References

Related documents

The importance of foot care knowledge in preventing foot ulcers in diabetic patients is a widely accepted fact; however, over half of the diabetic patients in this study reported

In a study, 55.5% of HBsAg and HBeAb positive blood donors had an active virus in - fection that was due to mutation of pre core and core region of virus genome that causes

If distances are measured from the body to i&#34; then only certain values of () guarantee that bodies are well separated from unopened cells. As this value is even

This has also held true for LVR induced via treatment using an alternate bronchoscopic method (endobronchial valves), where larger heterogen- eity showed correlation with

Unique biocompatibility, flexible methods of synthesis and tailor able physical properties have made the hydro gels to be used as a drug delivery device to tissue engineering

To understand the impact of psychographics on e commerce on Indian Internet users to avail different categories of services (High, Medium and Low) for

In E - NQCA (Node Quality based Clustered Algorithm), we propose four new models in clustering algorithms: Node priority and range zone aggregation models, Mobility Prediction