:=Z[^jZofZgh\G=Zjjbk ]MnZHHH;ZrljZgk]Za Mnbfkdbc]hkm^Zjkl\_ggucg_nlyghcl_ogbq_kdbcmgb\_jkbl_l <EBYGB?WDKIEM:L:PBHGGH=HA:=JYA?GBYG: L?IEH<U?O:J:DL?JBKLBDB:II:J:LH< <HA>MRGH=HHOE:@>?GBY=:A: < gZklhys__ \j_fy gZ djmig_crbo ]Zahijh\h^Zo gZr_c kljZgu bkihevamxlky kbkl_fu hoeZ`^_gby ]ZaZ gZ [Za_ ZiiZjZlh\ \ha^mrgh]h hoeZ`^_gby:<HOZjZdl_jghchkh[_gghklvxbfihjlguobhl_q_kl\_gguo:<H y\ey_lky ijbf_g_gb_ ^ey h[^m\Z hj_[j_gguo ih\_joghkl_c l_iehh[f_gguo ljm[ ^\mo b [he__ \_glbeylhjh\ Fgh]h\_glbeylhjgu_ kbkl_fu m^h[gu \ wdkiemZlZpbb lZd dZd iha\heyxl iml_f baf_g_gby qbkeZ jZ[hlZxsbo \_glbeylhjh\ ih^^_j`b\Zlv lj_[m_fmx l_fi_jZlmjm ]ZaZ ijb agZqbl_evguo dhe_[Zgbyol_fi_jZlmjugZjm`gh]h\ha^moZ Bkihevah\Zgb_ kbkl_f \ha^mrgh]h hoeZ`^_gby ih kjZ\g_gbx k ljZ^bpbhggufbl_iehh[f_ggbdZfbbf__ll_ogbdhwdhghfbq_kdb_ij_bfms_kl\Z mijhsZ_lky h[kem`b\Zgb_ khdjZsZxlky wdkiemZlZpbhggu_ aZljZlu gZ hoeZ`^_gb_ ijbjh^gh]h ]ZaZ bkdexqZ_lky ihlj_[e_gb_ l_ogbq_kdhc \h^u \ [hevrbo dhebq_kl\Zo b l^ LZdZy l_ogheh]by hoeZ`^_gby ]ZaZ y\ey_lky wg_j]hk[_j_]Zxs_c H^gZdh ijbf_g_gb_ kbkl_f \ha^mrgh]h hoeZ`^_gby ihdZaZeh qlh ijb wdkiemZlZpbb :<H \hagbdZxl jZaebqgu_ ijh[e_fu h[mkeh\e_ggu_ dZd ]_h]jZnbq_kdbfjZkiheh`_gb_fiehsZ^hddhfij_kkhjguoklZgpbc]Zahijh\h^h\ lZdbdebfZlbq_kdbfbmkeh\byfb >ey k_\_jguo jZchgh\ wlh \hafh`ghklv ]b^jZlhh[jZah\Zgby \ l_iehh[f_gguo ljm[Zo :<H ijb gbadbo l_fi_jZlmjZo \ha^mrghc kj_^u < x`guo jZchgZo ± g_h[oh^bfhklv hjhr_gby l_iehh[f_gguo ljm[ \h^hc ld \ e_lgbci_jbh^l_fi_jZlmjZ\ha^moZ^hklb]Z_l°Kb\ur_ < jZchgZo kj_^gbo rbjhl kha^Zxlky [eZ]hijbylgu_ mkeh\by ^ey hkZ`^_gbyiuebgZih\_joghklbhj_[j_gguoljm[:<H<k\yabkmf_gvr_gb_f dhwnnbpb_glZ l_iehi_j_^Zqb D hl ]ZaZ \ hdjm`Zxsmx kj_^m wnn_dlb\ghklv l_iehhl^Zqb j_adh kgb`Z_lky < e_lgbc i_jbh^ jZ[hlZxl ijZdlbq_kdb \k_ \_glbeylhju k_dpbc :<H kbkl_f hoeZ`^_gby ijbjh^gh]h ]ZaZ dhfij_kkhjguo klZgpbc Wlh ijb\h^bl d i_j_jZkoh^m g_ lhevdh we_dljhwg_j]bb gZ ijb\h^ \_glbeylhjh\ gh b lhieb\gh]h ]ZaZ <hagbdZxl ijh[e_fu hqbkldb l_iehh[f_gguoljm[j_]mebjh\Zgbyb^jdhlhju_g_h[oh^bfhj_rZlv IHKL:GH<D:A:>:QBBKKE?>H<:GBY GZdhfij_kkhjguoklZgpbyokbkl_fufZ]bkljZevguo]Zahijh\h^h\F= ^ey hoeZ`^_gby ijbjh^gh]h ]ZaZ gZjy^m k hl_q_kl\_ggufb ZiiZjZlZfb \ha^mrgh]hhoeZ`^_gby:<Hrbjhdhbkihevamxlkybfihjlgu_ZiiZjZlunbjf Dj_ahEmZjOZ^khgBlZevyghGmh\hIbgvhg_b^j BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX OZjZdl_jghc hkh[_gghklvx :<H aZjm[_`gh]h ijhba\h^kl\Z y\ey_lky ijbf_g_gb_ ^ey h[^m\Z hj_[j_gguo ih\_joghkl_c ^\mo \_glbeylhjh\ mklZgh\e_gguo gZ^ ljm[gufb k_dpbyfb Z lZd`_ bkihevah\Zgb_ ljm[ k \ukhdbf dhwnnbpb_glhf hj_[j_gby ! b [hevrhc ih\_joghklvx l_iehh[f_gZ «f :<H y\eyxlky wdheh]bq_kdb qbklufb mkljhckl\Zfb Bo ijbf_g_gb_ gZ h[t_dlZoagZqbl_evghkhdjZsZ_lihlj_[e_gb_\h^uHgbg_lj_[mxl^eyjZ[hlu ij_^\Zjbl_evghc ih^]hlh\db hoeZ`^Zxs_]h Z]_glZ b ijb ghjfZevguo mkeh\byo wdkiemZlZpbbkhhl\_lkl\mxlwg_j]hk[_j_]Zxsbfl_ogheh]byf H^gZdh\ijhp_kk_wdkiemZlZpbbl_iehh[f_ggu_mklZgh\dbf_gyxlk\hb oZjZdl_jbklbdb \ke_^kl\b_ dhjh[e_gby b ijh\bkZgby hj_[j_gguo ljm[ Z lZd`_ baaZbgl_gkb\gh]haZ]jyag_gbyf_`j_[_jgh]hijhkljZgkl\Z >ey\u[hjZhilbfZevguoj_`bfh\jZ[hlu:<Hbkbkl_fu]Zahijh\h^Z\ p_ehf g_h[oh^bfh gZebqb_ ^hklh\_jguo oZjZdl_jbklbd ihkljh_gguo k mq_lhf gZa\Zgguobaf_g_gbc\hagbdZxsbo\ijhp_kk_wdkiemZlZpbb J_]mebjh\Zgb_ jZ[hlu :<H hkeh`gy_lky l_f qlh iZkihjlgu_ oZjZdl_jbklbdb g_ fh]ml [ulv bkihevah\Zgu \ kha^Z\r_cky kblmZpbb Z jZkq_l j_`bfh\ hoeZ`^_gby g_\hafh`_g ld g_ba\_klgu b g_ ih^^Zxlky hij_^_e_gbx lZdb_dhwnnbpb_gluf_lh^bdbjZkq_lZdZd < ±ihijZ\hqguc dhwnnbpb_gl mqblu\Zxsbc g_jZ\ghf_jghklv jZkij_^_e_gbydhwnnbpb_glZl_iehhl^ZqbgZih\_joghklbj_[jZ Ua\g Uag ± l_ieh\u_ khijhlb\e_gby khhl\_lkl\_ggh \gmlj_gg_]h b gZjm`gh]haZ]jyag_gbyljm[ LZdb_ nZdlhju dZd aZ]jyag_gb_ dhjh[e_gb_ b ijh\bkZgb_ l_iehh[f_gguo ljm[ \aZbfgh_ \ebygb_ jZkiheh`_gguo [ebadh ^jm] hl ^jm]Z k_dpbc:<H\ebygb_j_ev_nZf_klghklbjhau\_ljh\bl^\f_lh^bdZojZkq_lZ mq_klvijZdlbq_kdbg_\hafh`gh H[t_dlb\gh kms_kl\mxsbfb f_lh^bdZfb > b ^j@ g_ mqblu\Z_lky lZd`_ \ iheghc f_j_ \ebygb_ g_jZ\ghf_jghklb l_iehhl^Zqb ih ih\_joghklb l_ieh\h]h kt_fZ :<H JZkq_lu g_ ^Zxl lZd`_ ^he`gh]h ij_^klZ\e_gby h ^bgZfbd_ baf_g_gby iZjZf_ljh\ :<H \h \j_f_gb Ihwlhfm \hagbdeZ g_h[oh^bfhklv dhjj_dlbjh\db b ihkljh_gby ^_ckl\bl_evguo l_ieh\uo oZjZdl_jbklbd HP?GD:N:DLBQ?KDH=HKHKLHYGBYIH<?JOGHKLB L?IEHH;F?GGUOLJM; >ey hij_^_e_gby nZdlbq_kdh]h khklhygby l_iehh[f_gguo ih\_joghkl_c hj_[j_gguo ljm[ k_dpbc :<H hp_gdb wnn_dlb\ghklb l_iehh[f_gZ b \ujZ[hldb khhl\_lkl\mxsbo ijZdlbq_kdbo j_r_gbc ih kh\_jr_gkl\h\Zgbx ijhp_kkZ j_]mebjh\Zgby b klZ[bebaZpbb l_fi_jZlmju ]ZaZ ^ey ih^Zqb _]h \ ]Zahijh\h^ [uebijh\_^_gukhhl\_lkl\mxsb_wdki_jbf_glZevgu_bkke_^h\ZgbygZ:<H]ZaZ \ijhfure_gguomkeh\byoDKRZjZg]Zahijh\h^ZMj_g]hc±I_ljh\kd Bkke_^h\Zgbyijh\h^bebkvgZ:<HnbjfOZ^khgBlZevyghbDj_ah± EmZj mklZgh\e_gguo gZ iehsZ^dZo hoeZ`^_gby ]ZaZ b k]jmiibjh\Zgguo ih rl K ihfhsvx baf_jbl_ey l_ieh\uo ihl_jv BLI ± ijhba\h^bebkv aZf_ju l_ieh\uoihlhdh\k±]hjy^Zihoh^m\ha^moZl_iehh[f_gguoljm[k_dpbb:<H nbjfuOZ^khg BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX Kgylb_ aZf_jh\ ijh\h^behkv gZ k_dpbb :<H ]ZaZ ijb jZ[hl_ ^\mo \_glbeylhjh\ AZf_ju l_ieh\uo ihlhdh\ ijhba\h^bebkv \ ^g_\gh_ \j_fyq_luj_`^uaZi_jbh^kihqZkbhkj_^gyebkv Ihemq_ggu_ ^Zggu_ hnhjfe_gu \ \b^_ l_ieh\hc dZjlu kf jbk GZijZ\e_gb_ oh^Z ]ZaZ ihdZaZgh klj_edhc kijZ\Z gZe_\h ih hlghr_gbx d aZf_jghc dZjl_ <_ebqbgu l_ieh\h]h kt_fZ ijb\_^_gu \ hlghkbl_evguo _^bgbpZo qlh m^h[gh ^ey ZgZebaZ g_ lhevdh kl_i_gb aZ]jyag_gby jZaebqguo mqZkldh\ l_iehh[f_gghc ih\_joghklb gh b ^ey hp_gdb \ebygby jhau \_ljh\ \aZbfgh]hjZkiheh`_gbyk_dpbc:<Hbl^ JZkij_^_e_gb_hlghkbl_evgh]hl_ieh\h]hihlhdZihih\_joghklbi_j\h]hjy^Z hj_[j_gguol_iehh[f_gguoljm[ Ihlhd]ZaZ GZijZ\e_gb_ \_ljZ Jbk H \ukhdhc g_jZ\ghf_jghklb l_ieh\h]h kt_fZ k ih\_joghklb k\b^_l_evkl\mxlke_^mxsb_nZdlu FZdkbfZevgh_ b fbgbfZevgh_ agZq_gby l_ieh\uo ihlhdh\ ih ih\_joghklbl_ieh\h]hkt_fZhlebqZxlkyijbf_jgh\jZa FZdkbfZevgh_ agZq_gb_ l_ieh\h]h ihlhdZ \ jZaZ ij_\urZxs__ kj_^g__ agZq_gb_ ^ey ^Zggh]h :<H ihemq_gh k gZ\_lj_gghc klhjhgu Kdhjhklv \_ljZ\^_gvijh\_^_gbyaZf_jh\[ueZmf_j_gghc L_ieh\hckt_fkih\_joghklb]hjy^Zljm[hdijh^m\Z_fhci_j\uf ih oh^m ]ZaZ \_glbeylhjhf khklZ\ey_l hl h[s_]h l_ieh\h]h kt_fZ qlh k\b^_l_evkl\m_lhlhfqlh\lhjhc\_glbeylhjjZ[hlZ_lf_g__wnn_dlb\gh Gbadb_ ehdZevgu_ agZq_gby \_ebqbg l_ieh\uo ihlhdh\ k\b^_l_evkl\mxl h gZebqbb aZ]jyag_gbc gZ ih\_joghklyo l_iehh[f_gZ Ke_^m_l hlf_lblvqlhkh\j_f_gbijhfu\dbgZjm`ghcih\_joghklbljm[guoimqdh\:<H ^hfhf_glZkgylbyaZf_jh\ijhreh\k_]hf_kypZ Ijb \ukhdhf agZq_gbb dhwnnbpb_glZ hj_[j_gghklb ih\_joghklb l_ieh\h]hkt_fZjZ\ghfbgbadhci_jbh^bqghklb__hqbkldbijZdlbq_kdb jZaZ \ ]h^ khojZgy_lky klZ[bevgh_ aZ]jyag_gb_ f_`j_[_jgh]h ijhkljZgkl\Z iuevxbijhqbfbf_oZgbq_kdbfb\dexq_gbyfbkh^_j`Zsbfbky\hoeZ`^Zxs_f \ha^mo_dhlhju_hk_^ZxlgZih\_joghklyol_iehh[f_gguoljm[ BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX Kl_i_gv aZ]jyag_gby imqdZ hj_[j_gguo ljm[hd m\_ebqb\Z_lky \ f_`hqbklghci_jbh^b\kZfh_`Zjdh_\j_fy]h^ZkbxgyihZ\]mklklZgh\blky fZdkbfZevghcIjbwlhfwnn_dlb\ghklvhoeZ`^_gbykgb`Z_lky\«b[he__ jZaihkjZ\g_gbxkijh_dlgufmjh\g_f HLEBQB?N:DLBQ?KDBOO:J:DL?JBKLBD:<HHLI:KIHJLGUO LZdbf h[jZahf \ jZ[hl_ l_ieh\u_ oZjZdl_jbklbdb :<H mom^rZxlky b ih \j_f_gb ]h^Z bf_xl gZklhevdh [hevrb_ hlebqby hl i_j\hgZqZevguo qlh iZkihjlgufb oZjZdl_jbklbdZfb ihevah\Zlvky ijhklh g_\hafh`gh JZkq_l ih kms_kl\mxsbf f_lh^bdZf lZd`_ g_ ^Z_l `_eZ_fh]h j_amevlZlZ \ke_^kl\b_ g_^hklZldZbkoh^ghcbgnhjfZpbbihnZdlbq_kdhfmkhklhygbxk_dpbc:<H K p_evx ihkljh_gby ^_ckl\bl_evguo l_ieh\uo oZjZdl_jbklbd mqblu\Zxsbo kgb`_gb_ dhwnnbpb_glZ l_iehi_j_^Zqb D \ke_^kl\b_ aZ]jyag_gby b ^jm]bo wdkiemZlZpbhgguo ijbqbg [ueZ ijh\_^_gZ jZ[hlZ ih k[hjm nZdlbq_kdh]h fZl_jbZeZ b ihkljh_gu emq_\u_ oZjZdl_jbklbdb ^ey k_dpbc :<H nbjfuOZ^khg < hkgh\m ihkljh_gby emq_\uo oZjZdl_jbklbd ZiiZjZlh\ \ha^mrgh]h hoeZ`^_gby[_j_lkymjZ\g_gb_l_ieh\h]h[ZeZgkZ T = 4 ⋅ ρ ⋅ F S ⋅ L − L = . ⋅ ) ⋅ L kj − W ]^_ T ± l_ieh\hc kt_f k ih\_joghklb ) l_iehh[f_ggh]h ZiiZjZlZ 4 ρ ^_ckl\bl_evguc jZkoh^ b iehlghklv ]ZaZ ijb ghjfZevguo mkeh\byo kj ± l_ieh_fdhklv]ZaZijbkj_^g_fjZ[hq_f^Z\e_gbbjkjbkj_^g_cl_fi_jZlmj_]ZaZ 7kj L b L ± l_fi_jZlmjZ ]ZaZ gZ \oh^_ b \uoh^_ :<H D ± dhwnnbpb_gl l_iehi_j_^Zqbhl]ZaZ\hdjm`Zxsmxkj_^mkl_fi_jZlmjhcW GZ jbk ijb\_^_gZ iZkihjlgZy emq_\Zy oZjZdl_jbklbdZ :<H nbjfu OZ^khg gZ jbk nZdlbq_kdZy oZjZdl_jbklbdZ k_dpbb :<H ]ZaZ nbjfu OZ^khg ihkljh_ggZy ih wdki_jbf_glZevguf ^Zgguf ihemq_gguf \ i_jbh^ k ih KjZ\g_gb_ ihdZau\Z_l kms_kl\_ggh_ hlebqb_ nZdlbq_kdbo j_`bfh\jZ[hlu:<Hhlijh_dlguo NZdlbq_kdb ijb ijhoh`^_gbb ]Zah\h]h ihlhdZ k fZkkh\uf jZkoh^hf gZijbf_j 4 d]qZk b l_fi_jZlmjghf gZihj_ ∆L L ± W °K q_j_a k_dpbx:<H]ZahoeZ`^Z_lkygZ\_ebqbgm7±7 °KWlh\jZaZf_gvr_ \_ebqbgu7±7 °Khij_^_ey_fhciZkihjlghcoZjZdl_jbklbdhckfjbk b BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX L_iehkt_fddZeq⋅ Emq_\ZyoZjZdl_jbklbdZ:<HnbjfuOZ^khg ]Zah\ucihlhd4 d]q ∆7 7W°& °& L_iehkt_fddZeq⋅ 77°& Jbk Emq_\ZyoZjZdl_jbklbdZ:<Hihke_fgh]he_lg_cwdkiemZlZpbb ]Zah\ucihlhd4 d]q ∆7 7W°& °& 77°& Jbk BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX J?DHF?G>:PBB >ey ih\ur_gby wnn_dlb\ghklb kbkl_fu \ha^mrgh]h hoeZ`^_gby ijbjh^gh]h ]ZaZ gZ \uoh^_ ba gZ]g_lZl_e_c j_dhf_g^m_lky ihkljhblv l_ieh\u_ oZjZdl_jbklbdb:<HihnZdlbq_kdhfmkhklhygbxgZhk_ggbcabfgbc\_k_ggbc be_lgbci_jbh^uwdkiemZlZpbbZlZd`_^hbihke_hqbkldb Ihkljh_ggu_ nZdlbq_kdb_ emq_\u_ oZjZdl_jbklbdb fh`gh bkihevah\Zlv ^ey p_e_c j_]mebjh\Zgby ijhp_kkZ hoeZ`^_gby ]ZaZ b j_r_gby hilbfbaZpbhgguoaZ^Zq Djhf_ lh]h ZgZeba l_ieh\uo dZjl b khihklZ\e_gb_ ^_ckl\bl_evguo oZjZdl_jbklbdkiZkihjlgufb^Z_l\hafh`ghklv^bZ]ghklbjh\Zlvkhklhygb_:<H bijbgbfZlvj_r_gb_ih\hkklZgh\e_gbxbojZ[hqboiZjZf_ljh\ EBL?J:LMJ: FZj]hebg =: <ZckfZg <? F_lh^bdZ l_ieh\h]h b Zwjh^bgZfbq_kdh]h jZkq_lZ ZiiZjZlh\ \ha^mrgh]h hoeZ`^_gby ± F <GBBG_nl_fZrk F_lh^bq_kdb_ j_dhf_g^Zpbb ^ey jZkq_lZ kbkl_f hoeZ`^_gby ]ZaZ gZ dhfij_kkhjguoklZgpbyofZ]bkljZevguo]Zahijh\h^h\±F<GBB]Zak BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB G_nl_]Zah\h_^_ehKWWSZZZRJEXVUX