Vanessa Catarina Ramos Aleixo
Licenciada em Ciências da Engenharia Civil
Rotura de fundo em escavações devida a
percolação ascendente
Dissertação para obtenção do Grau de Mestre em Engenharia Civil
Orientador: Nuno Manuel da Costa Guerra, Professor
Associado, Universidade Nova de Lisboa
Junho, 2015
Júri:
Presidente: Prof. Doutor Válter José da Guia Lúcio
Arguente: Prof. Doutor Pedro Fernando e Mota Guedes
de Melo
✏❈♦♣②r✐❣❤t✑ ❱❛♥❡ss❛ ❈❛t❛r✐♥❛ ❘❛♠♦s ❆❧❡✐①♦✱ ❋❈❚✴❯◆▲ ❡ ❯◆▲
❆ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❡ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛ tê♠ ♦ ❞✐r❡✐t♦✱ ♣❡r✲ ♣ét✉♦ ❡ s❡♠ ❧✐♠✐t❡s ❣❡♦❣rá✜❝♦s✱ ❞❡ ❛rq✉✐✈❛r ❡ ♣✉❜❧✐❝❛r ❡st❛ ❞✐ss❡rt❛çã♦ ❛tr❛✈és ❞❡ ❡①❡♠♣❧❛r❡s ✐♠♣r❡ss♦s r❡♣r♦❞✉③✐❞♦s ❡♠ ♣❛♣❡❧ ♦✉ ❞❡ ❢♦r♠❛ ❞✐❣✐t❛❧✱ ♦✉ ♣♦r q✉❛❧q✉❡r ♦✉tr♦ ♠❡✐♦ ❝♦♥❤❡❝✐❞♦ ♦✉ q✉❡ ✈❡♥❤❛ ❛ s❡r ✐♥✈❡♥t❛❞♦✱ ❡ ❞❡ ❛ ❞✐✈✉❧❣❛r ❛tr❛✈és ❞❡ r❡♣♦s✐tór✐♦s ❝✐❡♥tí✜❝♦s ❡ ❞❡ ❛❞♠✐t✐r ❛ s✉❛ ❝ó♣✐❛ ❡ ❞✐str✐❜✉✐çã♦ ❝♦♠ ♦❜❥❡t✐✈♦s ❡❞✉❝❛❝✐♦♥❛✐s ♦✉ ❞❡ ✐♥✈❡st✐❣❛çã♦✱ ♥ã♦ ❝♦♠❡r❝✐❛✐s✱ ❞❡s❞❡ q✉❡ s❡❥❛ ❞❛❞♦ ❝ré❞✐t♦ ❛♦ ❛✉t♦r ❡ ❡❞✐t♦r✳
❆❣r❛❞❡❝✐♠❡♥t♦s
❆♣ós ❛ ❝♦♥❝❧✉sã♦ ❞❡ t♦❞♦ ♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦ ♥ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r ❛ t♦❞❛s ❛s ♣❡ss♦❛s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ♣❛r❛ ❛ s✉❛ ❝♦♥❝r❡✲ t✐③❛çã♦✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ Pr♦❢❡ss♦r ◆✉♥♦ ●✉❡rr❛✱ ♣♦r q✉❡♠ t❡♥❤♦ ❣r❛♥❞❡ ❛❞♠✐r❛çã♦✱ ♣❡❧❛ ♣❛❝✐✲ ê♥❝✐❛✱ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡✱ ❝♦❧❛❜♦r❛çã♦✱ ❝♦♥❤❡❝✐♠❡♥t♦s tr❛♥s♠✐t✐❞♦s ❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♠♦t✐✈❛çã♦ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ tr❛❜❛❧❤♦✳
❆♦ Pr♦❢❡ss♦r ❆r♠❛♥❞♦ ❆♥tã♦✱ ♣♦r t❡r s✐❞♦ ♦ ♣r✐♥❝✐♣❛❧ r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ♠✐♥❤❛ ❡s❝♦❧❤❛ ♣❡❧♦ ♣❡r✜❧ ❞❡ ●❡♦t❡❝♥✐❛✱ ❡ ♣♦r t♦❞♦ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ tr❛♥s♠✐t✐❞♦ ❛♦ ❧♦♥❣♦ ❞❛s ✉♥✐❞❛❞❡s ❝✉rr✐❝✉❧❛r❡s ♣♦r ❡❧❡ ❧❡❝✐♦♥❛❞❛s✳
➚ ♠✐♥❤❛ ♠ã❡✱ ♣♦r ♠❡ t❡r ❛♣♦✐❛❞♦ ❡♠ t♦❞❛s ❛s ❞❡❝✐sõ❡s ❡ ♠❡ ✐♥❝❡♥t✐✈❛r ❛ ❢❛③❡r s❡♠♣r❡ ♠❡❧❤♦r✳
❆♦s ♠❡✉s ♣❛❞r✐♥❤♦s✱ ♣❡❧♦s ❝♦♥s❡❧❤♦s q✉❡ ♠❡ ❞❡r❛♠ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞❛ ❛ ♠✐♥❤❛ ✈✐❞❛✱ ❡ ♣♦r ❡st❛r❡♠ s❡♠♣r❡ ♣r❡s❡♥t❡s ❛♣❡s❛r ❞❛ ❞✐stâ♥❝✐❛✳
❆♦ ❉❛✈✐❞✱ ♦ ♠❡✉ s✉♣♦rt❡✱ ♣♦r t♦❞❛ ❛ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♠♣r❡ssã♦ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s✳
➚ ❘✐t❛✱ ❝♦♠ q✉❡♠ ✈✐✈✐ ❞✉r❛♥t❡ ❡st❡s ✻ ❛♥♦s ❛❝❛❞é♠✐❝♦s ❡ ♣❛rt✐❧❤❡✐ ❛ ♠✐♥❤❛ ✈✐❞❛✳ ❈r❡s✲ ❝❡♠♦s ♠✉✐t♦ ❥✉♥t❛s✳
➚ ▲❛ís✱ ♣❡❧❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡✱ ❛♣♦✐♦ ❡ ❝♦♦♣❡r❛çã♦ ❞✉r❛♥t❡ ❛ r❡❛❧✐③❛çã♦ ❞❡ t♦❞♦ ♦ tr❛❜❛❧❤♦✳
P♦r ✜♠✱ ❡ ♥ã♦ ♠❡♥♦s ✐♠♣♦rt❛♥t❡✱ ❛♦s ❛♠✐❣♦s q✉❡ ✜③ ♥❛ ❋❛❝✉❧❞❛❞❡ ❡ ❝♦♠ q✉❡♠ ♣❛rt✐❧❤❡✐ ♦s ♠❡❧❤♦r❡s ♠♦♠❡♥t♦s ♥♦s ú❧t✐♠♦s s❡✐s ❛♥♦s✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❉✐♦❣♦ ❆♠❛r❛❧✱ ■♥ês P✐r❡s✱ ❏♦ã♦ ■❣r❡❥❛ ❡ ▲✉ís ❱✐♦tt②✳ ❆❣r❛❞❡ç♦ ❛❝✐♠❛ ❞❡ t✉❞♦ ♦ ❢❛t♦ ❞❡ ❝♦❧♦❝❛r❡♠ ❛ ❛♠✐③❛❞❡ s❡♠♣r❡ ❡♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✳
❘❡s✉♠♦
❆ r♦t✉r❛ ❞❡ ❢✉♥❞♦ ❞❡ ❡s❝❛✈❛çõ❡s ❡♠ s♦❧♦s ❛r❡♥♦s♦s✱ ❝♦♠ ♥í✈❡❧ ❢r❡át✐❝♦ ❡❧❡✈❛❞♦ ❡ ❡♠ q✉❡ s❡ ♣r♦❝❡❞❡ ❛♦ r❡❜❛✐①❛♠❡♥t♦ ❞♦ ♥í✈❡❧ ❞❡ á❣✉❛ ♥♦ ✐♥t❡r✐♦r ❞❛ ❡s❝❛✈❛çã♦✱ ❝❛✉s❛♥❞♦ ♣❡r❝♦❧❛çã♦ ❡♠ t♦r♥♦ ❞❛ ❝♦rt✐♥❛✱ é s♦❜r❡t✉❞♦ tr❛t❛❞❛ ❝♦♠♦ s❡ ❢♦ss❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦✱ ❡♠ q✉❡ ♦ ❝♦❧❛♣s♦ ♦❝♦rr❡ ♣♦r ❛♥✉❧❛çã♦ ❞❛ t❡♥sã♦ ❡❢❡t✐✈❛ ❡ é ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ r❡s✐stê♥❝✐❛ ❞♦ s♦❧♦✳ ◆♦ ❡♥t❛♥t♦✱ ❡♠ ❢❛s❡ ❛♥t❡r✐♦r à ❛♥✉❧❛çã♦ ❞❛ t❡♥sã♦ ❡❢❡t✐✈❛✱ ❡st❛ ❞❡✈❡rá ❛ss✉♠✐r ✉♠ ✈❛❧♦r ❜❛✐①♦✱ q✉❡ ♣♦❞❡rá ❝❛✉s❛r ❛ r♦t✉r❛ ❞♦ ❢✉♥❞♦✳ ❚❛❧ ♣r♦❜❧❡♠❛ ♥ã♦ é✱ ♣r❛t✐❝❛♠❡♥t❡✱ ❛❜♦r❞❛❞♦ ♥❛ ❜✐❜❧✐♦❣r❛✜❛✱ s❡♥❞♦ ♦❜❥❡t♦ ❞♦ ❡st✉❞♦ ❞❡s❡♥✈♦❧✈✐❞♦✳ ❘❡❝♦rr❡✲s❡ à ❛♥á❧✐s❡ t❡♥sã♦✲❞❡❢♦r♠❛çã♦✱ ♣♦r ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❞❡ ✉♠ ❝❛s♦ ❞❡ ❡st✉❞♦✱ s❡❣✉✐❞♦ ❞❛ ❞❡t❡r♠✐♥❛çã♦ ♥✉♠ér✐❝❛ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ s❡❣✉r❛♥ç❛ ❡✱ ♣♦rt❛♥t♦✱ ❞♦ ♣❛râ♠❡tr♦ ❞❡ r❡s✐stê♥❝✐❛ ❞♦ s♦❧♦ ♥♦ ❝♦❧❛♣s♦✳ ❆ ♣❛rt✐r ❞❡st❡ ❝❛s♦ ❞❡ ❡st✉❞♦✱ ❞❡s❡♥✈♦❧✈❡✲s❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛♥á❧✐s❡s ♣❛r❛♠étr✐❝❛s ✐♥❝✐❞✐♥❞♦ s♦❜r❡ ❛s♣❡t♦s ❡str✉t✉r❛✐s✱ ♠❡❝â♥✐❝♦s ❡ ❣❡♦♠étr✐❝♦s✳ ❙ã♦ ❛♥❛❧✐s❛❞♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❡ sã♦ t✐r❛❞❛s ❝♦♥❝❧✉sõ❡s r❡❧❛t✐✈❛♠❡♥t❡ ❛♦ ❢❡♥ó♠❡♥♦ ❞❡ r♦t✉r❛ ❞❡ ❢✉♥❞♦ ❞❡ ❡s❝❛✈❛çõ❡s ❡♠ s♦❧♦s ❛r❡♥♦s♦s✳
P❛❧❛✈r❛s ❝❤❛✈❡✿
r♦t✉r❛ ❞❡ ❢✉♥❞♦✱ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦✱ ❡s❝❛✈❛çõ❡s ❡s❝♦r❛❞❛s✱ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❛♥á❧✐s❡ à r♦t✉r❛✳
❆❜str❛❝t
❇❛s❛❧ st❛❜✐❧✐t② ♦❢ ❡①❝❛✈❛t✐♦♥s ✐♥ s❛♥❞② s♦✐❧s ✇✐t❤ ❤✐❣❤ ✇❛t❡r t❛❜❧❡ ✇❤❡r❡ t❤❡ ✇❛t❡r ❧❡✈❡❧ ✐s ❧♦✇❡r❡❞ ✐♥s✐❞❡ t❤❡ ❡①❝❛✈❛t✐♦♥ ❝❛✉s✐♥❣ s❡❡♣❛❣❡ ❛r♦✉♥❞ t❤❡ r❡t❛✐♥✐♥❣ ✇❛❧❧✱ ✐s ♠❛✐♥❧② tr❡❛t❡❞ ❛s ❛♥ ❤②❞r❛✉❧✐❝ ❤❡❛✈❡ ♣r♦❜❧❡♠✳ ❆s ❛♥ ❤②❞r❛✉❧✐❝ ❤❡❛✈❡ ♣r♦❜❧❡♠✱ ❝♦❧❧❛♣s❡ ❝❛♥ ♦❝❝✉r ✇❤❡♥ t❤❡ ❡✛❡❝t✐✈❡ str❡ss❡s ❜❡❝♦♠❡ ♥✉❧❧ ❛♥❞ ❞♦❡s ♥♦t ❞❡♣❡♥❞ ♦♥ t❤❡ s♦✐❧ str❡♥❣t❤✳ ❍♦✇❡✈❡r✱ ❜❡❢♦r❡ ❜❡❝♦♠✐♥❣ ♥✉❧❧✱ t❤❡ ❡✛❡❝t✐✈❡ str❡ss❡s s❤♦✉❧❞ r❡❛❝❤ ✈❡r② ❧♦✇ ✈❛❧✉❡s✱ t❤❡r❡❢♦r❡ ❝❛✉s✐♥❣ ❜❛s❛❧ ✐♥st❛❜✐❧✐t②✳ ❙✉❝❤ ♣r♦❜❧❡♠ ✐s ✈❡r② ❧✐tt❧❡ ❛♥❛❧②s❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡ ❛♥❞ ✐s t❤❡ ♦❜❥❡❝t ♦❢ t❤❡ ♣r❡s❡♥t st✉❞②✳ ❚❤❡ st✉❞② ✉s❡s str❡ss✲str❛✐♥ ✜♥✐t❡ ❡❧❡♠❡♥t ❛♥❛❧②s❡s ♦❢ ❛ ❝❛s❡ st✉❞②✱ ❢♦❧❧♦✇❡❞ ❜② t❤❡ ♥✉♠❡r✐❝❛❧ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ t❤❡ s❛❢❡t② ❢❛❝t♦r ❛♥❞✱ t❤❡r❡❢♦r❡✱ ♦❢ t❤❡ ❝♦❧❧❛♣s❡ s♦✐❧ str❡♥❣t❤ ♣❛r❛♠❡t❡rs✳ ❋r♦♠ t❤✐s ❝❛s❡ st✉❞②✱ ❛ ♣❛r❛♠❡tr✐❝ ❛♥❛❧②s✐s ✐s ♣r❡❢♦r♠❡❞✱ st✉❞②✐♥❣ str✉❝t✉r❛❧✱ ♠❡❝❤❛♥✐❝❛❧ ❛♥❞ ❣❡♦♠❡tr✐❝❛❧ ♣❛r❛♠❡t❡rs✳ ❈♦♥❝❧✉s✐♦♥s ❢r♦♠ t❤❡ st✉❞② ❛r❡ ❞r❛✇♥ ❛♥❞ ♣r❡s❡♥t❡❞✳
❑❡②✇♦r❞s✿
❜❛s❛❧ st❛❜✐❧✐t②✱ ❤②❞r❛✉❧✐❝ ❤❡❛✈❡✱ ❜r❛❝❡❞ ❡①❝❛✈❛t✐♦♥s✱ ✜♥✐t❡ ❡❧❡♠❡♥ts✱ ❝♦❧❧❛♣s❡ ❛♥❛❧②s✐s✳
❮♥❞✐❝❡ ❞❡ ▼❛tér✐❛s
❮♥❞✐❝❡ ❞❡ ▼❛tér✐❛s ✐①
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s ①✐✐✐
❮♥❞✐❝❡ ❞❡ ❚❛❜❡❧❛s ①✈✐✐
▲✐st❛ ❞❡ ❛❜r❡✈✐❛t✉r❛s✱ s✐❣❧❛s ❡ sí♠❜♦❧♦s ①✐①
✶ ■♥tr♦❞✉çã♦ ❡ ❡st✉❞♦ ❜✐❜❧✐♦❣rá✜❝♦ ✶
✶✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❘♦t✉r❛ ❞❡ ❢✉♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ♥ã♦ ❞r❡♥❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷✳✶ ▼ét♦❞♦s ❝❧áss✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷✳✷ ▼ét♦❞♦s q✉❡ ✉t✐❧✐③❛♠ ❝á❧❝✉❧♦ ♥✉♠ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸ ❘♦t✉r❛ ❞❡ ❢✉♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸✳✶ ❆❜♦r❞❛❣❡♠ ❡♥q✉❛♥t♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸✳✷ ❆❜♦r❞❛❣❡♠ ❡♥q✉❛♥t♦ ♣r♦❜❧❡♠❛ ❞❡ r♦t✉r❛ ❞♦ s♦❧♦ ✭▼ét♦❞♦ ❞❡ ❈♦st❡t ❡
❙❛♥❣❧❡r❛t✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷ ❈❛s♦ ❜❛s❡ ✾
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷ ▼♦❞❡❧♦ ❝♦♥st✐t✉t✐✈♦ ❛❞♦t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✸ ❘❡❞✉çã♦ ❞♦s ♣❛râ♠❡tr♦s ❝′ ❡φ′ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✷✳✹ ▼♦❞❡❧❛çã♦ ❞♦ ❝❛s♦ ❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✺ ❆♥á❧✐s❡ ❞❡ r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✺✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✺✳✷ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✺✳✸ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✺✳✹ ❉❡s❧♦❝❛♠❡♥t♦s ✈❡rt✐❝❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺✳✺ ❉❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺✳✻ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ♣❛r❡❞❡ ❡ ♥♦ t❛r❞♦③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺✳✼ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
❮♥❞✐❝❡ ❞❡ ▼❛tér✐❛s
✷✳✺✳✽ ❚❡♥sõ❡s ❞❡ ❝♦rt❡ r❡❧❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✺✳✾ P♦♥t♦s ♣❧ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✺✳✶✵ ❋♦rç❛s ♥❛s ❡s❝♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✺✳✶✶ ❊s❢♦rç♦s ♥❛ ♣❛r❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✻ ❖❜s❡r✈❛çõ❡s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸ ❊st✉❞♦ ♣❛r❛♠étr✐❝♦ r❡❢❡r❡♥t❡ ❛♦s ❛s♣❡t♦s ❡str✉t✉r❛✐s ✸✺ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷ ■♥✢✉ê♥❝✐❛ ❞❛ r✐❣✐❞❡③ à ✢❡①ã♦ ❞❛ ♣❛r❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✷✳✺ P♦♥t♦s ♣❧ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✷✳✻ ❖❜s❡r✈❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✸ ■♥✢✉ê♥❝✐❛ ❞❛ r✐❣✐❞❡③ ❞❛s ❡s❝♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✸✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞❡ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✸✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✸✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹ ❊st✉❞♦ ♣❛r❛♠étr✐❝♦ r❡❢❡r❡♥t❡ às ❝❛r❛❝t❡ríst✐❝❛s ❞♦ s♦❧♦ ✹✼ ✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❡s♦ ✈♦❧ú♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✷✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✷✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✷✳✺ P♦♥t♦s ♣❧ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✷✳✻ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸ ■♥✢✉ê♥❝✐❛ ❞❡ Rinter ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✹✳✸✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✸✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✸✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✸✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✸✳✺ P♦♥t♦s ♣❧ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✹ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✹✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✹✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✹✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✹✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✺ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✺✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✺✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✺✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✺✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✻ ■♥✢✉ê♥❝✐❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❡❝â♥✐❝❛s ❞♦ s♦❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✻✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
❮♥❞✐❝❡ ❞❡ ▼❛tér✐❛s
✹✳✻✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✻✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✺ ❊st✉❞♦ ♣❛r❛♠étr✐❝♦ r❡❢❡r❡♥t❡ à ❣❡♦♠❡tr✐❛ ✼✾ ✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷ ■♥✢✉ê♥❝✐❛ ❞❛ ✜❝❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✳✷✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✷✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✷✳✺ P♦♥t♦s ♣❧ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✷✳✻ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✷✳✼ ❆♥á❧✐s❡ ❞♦s ♠♦❞❡❧♦s ❆✱ ❇ ❡ ❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✷✳✼✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✷✳✼✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✷✳✽ ❱❛r✐❛çã♦ ❞❛ ✜❝❤❛ ♣❛r❛ ✈ár✐❛s r✐❣✐❞❡③❡s ❞❛ ♣❛r❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✷✳✽✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✷✳✽✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✷✳✾ ❱❛r✐❛çã♦ ❞❛ ✜❝❤❛ ♣❛r❛ ✈ár✐♦s â♥❣✉❧♦s ❞❡ ❞✐❧❛tâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✷✳✾✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✷✳✾✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✸ ■♥✢✉ê♥❝✐❛ ❞❛ ❧❛r❣✉r❛ ❞❡ ❡s❝❛✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✸✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✸✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✸✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✸✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✸✳✺ P♦♥t♦s ♣❧ást✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✸✳✻ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✹ ■♥✢✉ê♥❝✐❛ ❞❛ ❞✐stâ♥❝✐❛ ❛♦ ❡str❛t♦ rí❣✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✹✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✹✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✹✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✹✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✹✳✺ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✺ ■♥✢✉ê♥❝✐❛ ❞❛ ❡s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✺✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✺✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✺✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✺✳✺✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✺✳✺ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✻ ■♥✢✉ê♥❝✐❛ ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✻✳✶ ➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✻✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✺✳✻✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✺✳✻✳✹ ❉❡❢♦r♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✺✳✻✳✺ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹
✻ ❆♥á❧✐s❡ ❞❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ❢❡♥ó♠❡♥♦ ❞❡ r♦t✉r❛ ❞❡ ❢✉♥❞♦ ✶✶✾
❮♥❞✐❝❡ ❞❡ ▼❛tér✐❛s
✻✳✶ ❆♥á❧✐s❡ ❞❛ s❡❣✉r❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✻✳✷ ❱❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ à ❧✉③ ❞♦ ❊✉r♦❝ó❞✐❣♦ ✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
✼ ❈♦♥❝❧✉sõ❡s ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ❢✉t✉r♦s ✶✷✾ ✼✳✶ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ✼✳✷ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵
❇✐❜❧✐♦❣r❛✜❛ ✶✸✶
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❋❛t♦r❡s ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❡♠ ❢✉♥çã♦ ❞❛ ❣❡♦♠❡tr✐❛✱ ♣❛r❛ s♦❧♦s ❛r❣✐❧♦s♦s r❡s✲ ♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ♥ã♦ ❞r❡♥❛❞❛s ✭❙❦❡♠♣t♦♥ ✭✶✾✺✶✮❀ ❛❞❛♣t❛❞♦ ❞❡ ▼❛t♦s ❋❡r✲ ♥❛♥❞❡s ✭✶✾✽✸✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷ ❘á❝✐♦s ❞❡ ❞✐ss✐♣❛çã♦ r❡❧❛t✐✈❛ ♣❛r❛ ❍✴▲❂✵✱✷ ✭t♦♣♦✮✱ ❍✴▲❂✵✱✺ ✭❡sq✉❡r❞❛✮ ❡ ❍✴▲❂✷✼✱✺
✭❞✐r❡✐t❛✮✱ ♣❛r❛ ✉♠ rá❝✐♦ ❞❡ ♣r♦❢✉♥❞✐❞❛❞❡ ✭❢✰❉✮✴❍❂✶ ✭❝✐♥③❡♥t♦ ❝❧❛r♦ ❝♦rr❡s♣♦♥❞❡ ❛♦ rá❝✐♦ ❞❡ ❞✐ss✐♣❛çã♦ r❡❧❛t✐✈❛ ♥✉❧❛ ❡ ♣r❡t♦ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♠á①✐♠♦ ✈❛❧♦r✮ ✭❏♦s❡✜♥♦ ❡t ❛❧✳✱ ✷✵✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✸ ❇❧♦❝♦ ❞❡ s♦❧♦ ♣❛r❛ ❛♥á❧✐s❡ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✹ ❊sq✉❡♠❛ r❡♣r❡s❡♥t❛t✐✈♦ ❞♦ ♠ét♦❞♦ ❞❡ ❈♦st❡t ❡ ❙❛♥❣❧❡r❛t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✶ ❊sq✉❡♠❛ ✐❧✉str❛t✐✈♦ ❞♦ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷ ●❡♦♠❡tr✐❛ ❞♦ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✸ ▼❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✉s❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹ ❋❛s❡❛♠❡♥t♦ ❝♦♥str✉t✐✈♦ ❛❞♦t❛❞♦ ♥♦s ❝á❧❝✉❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✺ ❉❡✜♥✐çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❡st✉❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✻ ❈❛r❣❛ ❤✐❞rá✉❧✐❝❛ ✲ ❋❛s❡ ✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✼ Pr❡ssã♦ ✐♥t❡rst✐❝✐❛❧ ✲ ❋❛s❡ ✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✽ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✲ ❋❛s❡s ✷✱ ✹ ❡ ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✾ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ✲ ❋❛s❡ ✽ ❡ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✶✵ ❉❡s❧♦❝❛♠❡♥t♦s ✈❡rt✐❝❛✐s ✲ ❋❛s❡s ✷✱ ✹ ❡ ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✶✶ ❉❡s❧♦❝❛♠❡♥t♦s ✈❡rt✐❝❛✐s ✲ ❋❛s❡ ✽ ❡ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✶✷ ❉❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ✲ ❋❛s❡s ✷✱ ✹ ❡ ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✶✸ ❉❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛✐s ✲ ❋❛s❡ ✽ ❡ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✶✹ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ❡ ❞♦ s♦❧♦ ♥♦ t❛r❞♦③ ✲ ❋❛s❡s ❝♦♥str✉t✐✈❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✶✺ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ❡ ❞♦ s♦❧♦ ♥♦ t❛r❞♦③ ✲ ❈♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✶✻ ❉❡❢♦r♠❛❞❛s ♥♦ ❝♦❧❛♣s♦ ❞♦s ♠♦❞❡❧♦s ❆✱ ❇ ❡ ❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✶✼ ❊✈♦❧✉çã♦ ❞❛s t❡♥sõ❡s r❡❧❛t✐✈❛s ❞❡ ❝♦rt❡ ✲ ❋❛s❡s ✷✱ ✹ ❡ ✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✶✽ ❚❡♥sõ❡s r❡❧❛t✐✈❛s ✲ ❋❛s❡ ✽ ❡ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✶✾ P♦♥t♦s ♣❧ást✐❝♦s ✲ ❋❛s❡ ✷✱ ✹ ❡ ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✷✵ P♦♥t♦s ♣❧ást✐❝♦s ✲ ❋❛s❡ ✽ ❡ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✷✶ ❊s❢♦rç♦s ♥❛ ❝♦rt✐♥❛ ✲ ❋❛s❡s ✷✱ ✹ ❡ ✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s
✷✳✷✷ ❊s❢♦rç♦s ♥❛ ❝♦rt✐♥❛ ✲ ❋❛s❡ ✽ ❡ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶ ■♥✢✉ê♥❝✐❛ ❞❛ r✐❣✐❞❡③ ❞❛ ♣❛r❡❞❡ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✸✻ ✸✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ r✐❣✐❞❡③ ❞❛ ♣❛r❡❞❡✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✸ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✲ ❋❛s❡ ✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✹ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ r✐❣✐❞❡③ ❞❛ ♣❛r❡❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✺ P♦♥t♦s ♣❧ást✐❝♦s ♥❛ ❢❛s❡ ✽ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ r✐❣✐❞❡③ ❞❛ ♣❛r❡❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✻ ■♥✢✉ê♥❝✐❛ ❞❛ r✐❣✐❞❡③ ❞❛s ❡s❝♦r❛s ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✹✶ ✸✳✼ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ r✐❣✐❞❡③ ❞❛s ❡s❝♦r❛s ✲ ❊■cb✭❡sq✉❡r❞❛✮
❡ ✶✵✵❊■cb✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✽ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✾ ❉❡❢♦r♠❛❞❛s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ r✐❣✐❞❡③ ❞❛s ❡s❝♦r❛s ✲ ❊■cb✭❡sq✉❡r❞❛✮
❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✹✳✶ ■♥✢✉ê♥❝✐❛ ❞♦ ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✲ ♠♦❞❡❧♦s ❆✱ ❇ ❡ ❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ♣❡s♦s ✈♦❧ú♠✐❝♦s ❞♦ s♦❧♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✺✵
✹✳✸ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ♣❡s♦s ✈♦❧ú♠✐❝♦s ❞♦ s♦❧♦ ✲ ✶✵✵❊■cb✳ ✳ ✺✶
✹✳✹ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✺ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ♣❡s♦s ✈♦❧ú♠✐❝♦s ❞♦ s♦❧♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✹✳✻ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ♣❡s♦s ✈♦❧ú♠✐❝♦s ❞♦ s♦❧♦ ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✹✳✼ P♦♥t♦s ♣❧ást✐❝♦s ♣❛r❛ ✈ár✐♦s ♣❡s♦s ✈♦❧ú♠✐❝♦s ❞♦ s♦❧♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✽ P♦♥t♦s ♣❧ást✐❝♦s ♣❛r❛ ✈ár✐♦s ♣❡s♦s ✈♦❧ú♠✐❝♦s ❞♦ s♦❧♦ ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✾ ■♥✢✉ê♥❝✐❛ ❞❡ Rinter ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹✳✶✵ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ Rinter ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡
✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✶✶ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡Rinter ❝♦♠ ♣❡s♦ ❞❛ ❝♦rt✐♥❛
♥✉❧♦ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
✹✳✶✷ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹✳✶✸ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ ❘inter ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb
✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✶✹ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡ ❘inter ❝♦♠ ♣❡s♦ ❞❛ ❝♦rt✐♥❛ ♥✉❧♦ ✲ ❊■cb
✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✹✳✶✺ P♦♥t♦s ♣❧ást✐❝♦s ♣❛r❛ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮ ✲ ❈♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✹✳✶✻ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✻✼ ✹✳✶✼ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s â♥❣✉❧♦s ❞❡ ❞✐❧❛tâ♥❝✐❛ ✲ ❊■cb✭❡sq✉❡r❞❛✮
❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✹✳✶✽ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✹✳✶✾ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐♦s â♥❣✉❧♦s ❞❡ ❞✐❧❛tâ♥❝✐❛ ✲ ❊■cb✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb
✭❞✐r❡✐t❛❧✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✷✵ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ φ′ = 30♦ ❡ φ= 40♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✹✳✷✶ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ❡ ✶✵✵❊■cb ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✹✳✷✷ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ φ′ = 30♦ ✭❡sq✉❡r❞❛✮ ❡ φ= 40♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✹✳✷✸ ■♥✢✉ê♥❝✐❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❡❝â♥✐❝❛s ❞♦ s♦❧♦ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✷✹ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✹✳✷✺ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♣❛r❛ ✈ár✐♦s ❝❛s♦s ❝♦♠ ✈❛r✐❛çã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❡✲ ❝â♥✐❝❛s ❞♦ s♦❧♦ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s
✺✳✶ ■♥✢✉ê♥❝✐❛ ❞❛ ✜❝❤❛ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✳✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
✺✳✸ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✺✳✹ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✺✳✺ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✺✳✻ ❉❡❢♦r♠❛❞❛s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
✺✳✼ P♦♥t♦s ♣❧ást✐❝♦s ♥❛ ❢❛s❡ ✽ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
✺✳✽ ■♥✢✉ê♥❝✐❛ ❞❛ ✜❝❤❛ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ✲ ▼♦❞❡❧♦s ❆✱ ❇ ❡ ❈✳ ✽✾ ✺✳✾ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ❝♦♠ r✐❣✐❞❡③ ❊■cb ✲ ▼♦❞❡❧♦s ❆✱
❇ ❡ ❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✺✳✶✵ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ❝♦♠ r✐❣✐❞❡③ ✶✵✵❊■cb ✲ ▼♦❞❡❧♦s
❆✱ ❇ ❡ ❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✺✳✶✶ ■♥✢✉ê♥❝✐❛ ❞❛ r✐❣✐❞❡③ ❞❛ ♣❛r❡❞❡ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛
✈ár✐❛s ✜❝❤❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✶✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ❝♦♠ ❞✐❢❡r❡♥t❡s r✐❣✐❞❡③❡s ❞❛ ❝♦rt✐♥❛✳ ✾✸ ✺✳✶✸ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦
♣❛r❛ ✈ár✐❛s ✜❝❤❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✺✳✶✹ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ❝♦♠ ❞✐❢❡r❡♥t❡s â♥❣✉❧♦s ❞❡ ❞✐❧❛✲
tâ♥❝✐❛ ❞♦ s♦❧♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
✺✳✶✺ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ✜❝❤❛s ❝♦♠ ❞✐❢❡r❡♥t❡s â♥❣✉❧♦s ❞❡ ❞✐❧❛✲ tâ♥❝✐❛ ❞♦ s♦❧♦ ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✺✳✶✻ ■♥✢✉ê♥❝✐❛ ❞❛ ❧❛r❣✉r❛ ❞❡ ❡s❝❛✈❛çã♦ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✾✼ ✺✳✶✼ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♣❛r❛ ✈ár✐❛s ❧❛r❣✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾
✺✳✶✽ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♣❛r❛ ✈ár✐❛s ❧❛r❣✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
✺✳✶✾ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
✺✳✷✵ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ❧❛r❣✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
✺✳✷✶ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ❧❛r❣✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ✶✵✵❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
✺✳✷✷ P♦♥t♦s ♣❧ást✐❝♦s ♣❛r❛ ✈ár✐❛s ❧❛r❣✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ❊■cb✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
✺✳✷✸ ■♥✢✉ê♥❝✐❛ ❞❛ ❞✐stâ♥❝✐❛ ❛♦ ❡str❛t♦ rí❣✐❞♦ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳✶✵✻ ✺✳✷✹ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ❞✐stâ♥❝✐❛s ❛♦ ❡str❛t♦ rí❣✐❞♦ ✲ ❊■cb
✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼
✺✳✷✺ ❉❡s❧♦❝❛♠❡♥t♦s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽
✺✳✷✻ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ❞✐stâ♥❝✐❛s ❛♦ ❡str❛t♦ rí❣✐❞♦ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡
✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
✺✳✷✼ ■♥✢✉ê♥❝✐❛ ❞❛ ❛❧t✉r❛ ❞❡ ❡s❝❛✈❛çã♦ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✶✶✵ ✺✳✷✽ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ❛❧t✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ❊■cb✭❡sq✉❡r❞❛✮
❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
✺✳✷✾ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✶✶✷
✺✳✸✵ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ❛❧t✉r❛s ❞❡ ❡s❝❛✈❛çã♦ ✲ ❊■cb✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb
✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✸✶ ■♥✢✉ê♥❝✐❛ ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦
❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✺✳✸✷ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ♣r♦❢✉♥❞✐❞❛❞❡s ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦ ✲ ❊■cb
✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺
✺✳✸✸ ❉❡s❧♦❝❛♠❡♥t♦s t♦t❛✐s ❞❛ ❝♦rt✐♥❛ ♥❛ ❢❛s❡ ✽ ✲ ❊■cb ✭❡sq✉❡r❞❛✮ ❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✶✶✻
✺✳✸✹ ❉❡❢♦r♠❛❞❛ ♥♦ ❝♦❧❛♣s♦ ♣❛r❛ ✈ár✐❛s ♣r♦❢✉♥❞✐❞❛❞❡s ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦ ✲ ❊■cb✭❡sq✉❡r❞❛✮
❡ ✶✵✵❊■cb ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s
✻✳✶ ❆♥á❧✐s❡ ❞❛ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦s ♣❛râ♠❡tr♦s ❡str✉t✉r❛✐s ❡st✉❞❛❞♦s ♥♦ ❝❛♣í✲ t✉❧♦ ✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✻✳✷ ❆♥á❧✐s❡ ❞❛ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦s ♣❛râ♠❡tr♦s ❞♦ s♦❧♦ ❡st✉❞❛❞♦s ♥♦ ❝❛♣ít✉❧♦
✹ ✭❛s ❝✉r✈❛s ❛ tr❛ç♦ ✐♥t❡rr♦♠♣✐❞♦ ❝♦rr❡s♣♦♥❞❡♠ ❛♦ ♣❡s♦ ❞❛ ❝♦rt✐♥❛ ♥✉❧♦✮✳ ✳ ✳ ✳ ✳ ✶✷✶ ✻✳✸ ❆♥á❧✐s❡ ❞❛ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦s ♣❛râ♠❡tr♦s ❣❡♦♠étr✐❝♦s ❡st✉❞❛❞♦s ♥♦ ❝❛✲
♣ít✉❧♦ ✺ ✲ ❋✐❝❤❛✱ ❧❛r❣✉r❛ ❡ ❞✐stâ♥❝✐❛ ❛♦ ❡str❛t♦ rí❣✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✻✳✹ ❆♥á❧✐s❡ ❞❛ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦s ♣❛râ♠❡tr♦s ❣❡♦♠étr✐❝♦s ❡st✉❞❛❞♦s ♥♦ ❝❛✲
♣ít✉❧♦ ✺ ✲ ❊s❝❛❧❛ ❡ ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✻✳✺ ❱❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ s❡❣✉♥❞♦ ♦ ❊❈✼ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❡str✉t✉r❛✐s ❡st✉❞❛❞♦s
♥♦ ❝❛♣ít✉❧♦ ✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ✻✳✻ ❱❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ s❡❣✉♥❞♦ ♦ ❊❈✼ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞♦ s♦❧♦ ❡st✉❞❛❞♦s ♥♦
❝❛♣ít✉❧♦ ✹ ✭❛s ❝✉r✈❛s ❛ tr❛ç♦ ✐♥t❡rr♦♠♣✐❞♦ ❝♦rr❡s♣♦♥❞❡♠ ❛♦ ♣❡s♦ ❞❛ ❝♦rt✐♥❛ ♥✉❧♦✮✳ ✶✷✺ ✻✳✼ ❱❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ s❡❣✉♥❞♦ ♦ ❊❈✼ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❣❡♦♠étr✐❝♦s ❡st✉❞❛❞♦s
♥♦ ❝❛♣ít✉❧♦ ✺ ✲ ❋✐❝❤❛✱ ❧❛r❣✉r❛ ❡ ❞✐stâ♥❝✐❛ ❛♦ ❡str❛t♦ rí❣✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ✻✳✽ ❱❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ s❡❣✉♥❞♦ ♦ ❊❈✼ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❣❡♦♠étr✐❝♦s ❡st✉❞❛❞♦s
♥♦ ❝❛♣ít✉❧♦ ✺ ✲ ❊s❝❛❧❛ ❡ ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼
❮♥❞✐❝❡ ❞❡ ❚❛❜❡❧❛s
✶✳✶ ❙♦❧✉çõ❡s ❝❧áss✐❝❛s ♣❛r❛ r♦t✉r❛ ❞❡ ❢✉♥❞♦ ✭❛❞❛♣t❛❞♦ ❞❡ ❯❦r✐t❝❤♦♥ ❡t ❛❧✳ ✭✷✵✵✸✮✮✳ ✳ ✳ ✷
✷✳✶ P❛râ♠❡tr♦s ❞♦ s♦❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✷ P❛râ♠❡tr♦s ❞❛ ♣❛r❡❞❡ ♠♦❧❞❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✸ P❛râ♠❡tr♦s ❞❛s ❡s❝♦r❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✹ ❱❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ ✲ ❝❛s♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✺ ❊✈♦❧✉çã♦ ❞❛s ❢♦rç❛s ❞❛s ❡s❝♦r❛s ❬❦◆✴♠❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹✳✶ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ♣❡s♦ ✈♦❧ú✲ ♠✐❝♦ ✲ ▼♦❞❡❧♦ ❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✷ ■♥✢✉ê♥❝✐❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ φ′✱ ♥♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡
♥♦ ❝♦❧❛♣s♦✱φ′
col✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✹✳✸ ❈❛r❛❝t❡ríst✐❝❛s ♠❡❝â♥✐❝❛s ❞♦ s♦❧♦ ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✹ ■♥✢✉ê♥❝✐❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❡❝â♥✐❝❛s ❞♦ s♦❧♦ ♥♦ ❝♦❧❛♣s♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✺✳✶ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ✜❝❤❛✳ ✳ ✳ ✳ ✽✽ ✺✳✷ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❧❛r❣✉r❛ ❞❡
❡s❝❛✈❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✸ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❞✐stâ♥❝✐❛ ❛♦
❡str❛t♦ rí❣✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✹ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❡s❝❛❧❛✳ ✳ ✳ ✳ ✶✶✷ ✺✳✺ ❱❡r✐✜❝❛çã♦ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ♣♦s✐çã♦ ❞♦
♥í✈❡❧ ❢r❡át✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻
▲✐st❛ ❞❡ ❛❜r❡✈✐❛t✉r❛s✱ s✐❣❧❛s ❡ sí♠❜♦❧♦s
❆❜r❡✈✐❛t✉r❛s
❊❈✼ ❊✉r♦❝ó❞✐❣♦ ✼
❍❨❉ ❊st❛❞♦ ❧✐♠✐t❡ ú❧t✐♠♦ ❞❡ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦
❙✐❣❧❛s
❋❈❚ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❍❙▼ ❍❛r❞❡♥✐♥❣ ❙♦✐❧ ▼♦❞❡❧
❯◆▲ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛
❙í♠❜♦❧♦s
c′ ❝♦❡sã♦ ❡❢❡t✐✈❛ ❞♦ s♦❧♦
c′
r ❝♦❡sã♦ ❡❢❡t✐✈❛ ❞♦ s♦❧♦ r❡❞✉③✐❞❛
cu r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥ã♦ ❞r❡♥❛❞❛
❉ ❞✐stâ♥❝✐❛ ❡♥tr❡ ♦ ♣é ❞❛ ❝♦rt✐♥❛ ❡ ♦ ❡str❛t♦ rí❣✐❞♦ ❞ ❡s♣❡ss✉r❛ ❞❛ ♣❛r❡❞❡ ♠♦❧❞❛❞❛
❊❆ r✐❣✐❞❡③ ❛①✐❛❧ ❞❛s ❡s❝♦r❛s
❊❆cb r✐❣✐❞❡③ ❛①✐❛❧ ❞❛s ❡s❝♦r❛s ❛❞♦t❛❞❛ ♥♦ ❝❛s♦ ❜❛s❡
❊■ r✐❣✐❞❡③ ❞❡ ✢❡①ã♦ ❞❛ ❝♦rt✐♥❛
❊■cb r✐❣✐❞❡③ ❞❡ ✢❡①ã♦ ❞❛ ❝♦rt✐♥❛ ❛❞♦t❛❞❛ ♥♦ ❝❛s♦ ❜❛s❡
E50 ♠ó❞✉❧♦ ❞❡ ❞❡❢♦r♠❛❜✐❧✐❞❛❞❡ s❡❝❛♥t❡ ❡♠ ❡st❛❞♦ tr✐❛①✐❛❧✱ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛50%❞❛ t❡♥sã♦
❞❡ r♦t✉r❛
E50ref ♠ó❞✉❧♦ ❞❡ ❞❡❢♦r♠❛❜✐❧✐❞❛❞❡ s❡❝❛♥t❡ ❞❡ r❡❢❡rê♥❝✐❛✱ ❡♠ ❡st❛❞♦ tr✐❛①✐❛❧✱ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛
50% ❞❛ t❡♥sã♦ ❞❡ r♦t✉r❛
Eoed ♠ó❞✉❧♦ ❞❡ ❞❡❢♦r♠❛❜✐❧✐❞❛❞❡ t❛♥❣❡♥t❡ ♣❛r❛ ❝❛rr❡❣❛♠❡♥t♦ ❡❞♦♠étr✐❝♦ ♣r✐♠ár✐♦
Eoedref ♠ó❞✉❧♦ ❞❡ ❞❡❢♦r♠❛❜✐❧✐❞❛❞❡ t❛♥❣❡♥t❡ ❞❡ r❡❢❡rê♥❝✐❛ ♣❛r❛ ❝❛rr❡❣❛♠❡♥t♦ ❡❞♦♠étr✐❝♦ ♣r✐✲
♠ár✐♦
▲✐st❛ ❞❡ ❛❜r❡✈✐❛t✉r❛s✱ s✐❣❧❛s ❡ sí♠❜♦❧♦s
Eur ♠ó❞✉❧♦ ❞❡ ❞❡❢♦r♠❛❜✐❧✐❞❛❞❡ ❞❡ ❞❡s❝❛r❣❛✲r❡❝❛r❣❛
Eurref ♠ó❞✉❧♦ ❞❡ ❞❡❢♦r♠❛❜✐❧✐❞❛❞❡ ❞❡ ❞❡s❝❛r❣❛✲r❡❝❛r❣❛ ❞❡ r❡❢❡rê♥❝✐❛
❢ ❛❧t✉r❛ ❡♥t❡rr❛❞❛✱ t❛♠❜é♠ ❞❡s✐❣♥❛❞❛ ♣♦r ✧✜❝❤❛✧ ❋❙ ❝♦❡✜❝✐❡♥t❡ ❞❡ s❡❣✉r❛♥ç❛
❋❙lh ❝♦❡✜❝✐❡♥t❡ ❞❡ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦
❋❙rf ❝♦❡✜❝✐❡♥t❡ ❞❡ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ à r♦t✉r❛ ❞❡ ❢✉♥❞♦
❋❙CS
rf ❝♦❡✜❝✐❡♥t❡ ❞❡ s❡❣✉r❛♥ç❛ r❡❧❛t✐✈❛♠❡♥t❡ à r♦t✉r❛ ❞❡ ❢✉♥❞♦ ♦❜t✐❞♦ ❛tr❛✈és ❞♦ ♠ét♦❞♦ ❞❡
❈♦st❡t ❡ ❙❛♥❣❧❡r❛t
●✬ ♣❡s♦ ❡❢❡t✐✈♦ ❞♦ ❜❧♦❝♦ ❞❡ s♦❧♦ ♣❛r❛ ✈❡r✐✜❝❛çã♦ ❞❛ s❡❣✉r❛♥ç❛ ❛♦ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦ ❍ ❛❧t✉r❛ ❡s❝❛✈❛❞❛
K0 ❝♦❡✜❝✐❡♥t❡ ❞❡ ✐♠♣✉❧s♦ ❞❡ t❡rr❛s ❡♠ r❡♣♦✉s♦
Kx ❝♦❡✜❝✐❡♥t❡ ❞❡ ♣❡r❝♦❧❛çã♦ ❤♦r✐③♦♥t❛❧
Ky ❝♦❡✜❝✐❡♥t❡ ❞❡ ♣❡r❝♦❧❛çã♦ ✈❡rt✐❝❛❧
▲ ❧❛r❣✉r❛ ❞❛ ❡s❝❛✈❛çã♦
m ♣♦tê♥❝✐❛ ♣❛r❛ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❛ r✐❣✐❞❡③ ❞♦ s♦❧♦
◆c ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛
◆q ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛
◆qd ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ❝á❧❝✉❧♦
◆s ♥ú♠❡r♦ ❞❡ ❡st❛❜✐❧✐❞❛❞❡
p′
ref t❡♥sã♦ ❡❢❡t✐✈❛ ♠é❞✐❛ ❞❡ r❡❢❡rê♥❝✐❛
Rinter r❡❧❛çã♦ ❡♥tr❡ ❛ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❛tr✐t♦ s♦❧♦✲❡str✉t✉r❛ ❡ ❛ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡
r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦
❙ ❝♦♠♣r✐♠❡♥t♦ ❧♦♥❣✐t✉❞✐♥❛❧ ❞❛ ❡s❝❛✈❛çã♦
❯ ❢♦rç❛ r❡s✉❧t❛♥t❡ ❞❡✈✐❞❛ à ♣r❡ssã♦ ❞❡ á❣✉❛ ♥♦s ♣♦r♦s ❯perc ❢♦rç❛ ❞❡ ♣❡r❝♦❧❛çã♦ ♠é❞✐❛
✇ ♣❡s♦ ❞❛ ❝♦rt✐♥❛
Znf ♣r♦❢✉♥❞✐❞❛❞❡ ❞♦ ♥í✈❡❧ ❢r❡át✐❝♦
γ ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦
γ′ ♣❡s♦ ✈♦❧ú♠✐❝♦ s✉❜♠❡rs♦ ❞♦ s♦❧♦
▲✐st❛ ❞❡ ❛❜r❡✈✐❛t✉r❛s✱ s✐❣❧❛s ❡ sí♠❜♦❧♦s
γG ❝♦❡✜❝✐❡♥t❡ ♣❛r❝✐❛❧ ♣❛r❛ ❛s ❛çõ❡s ♣❡r♠❛♥❡♥t❡s
γG;dst ❝♦❡✜❝✐❡♥t❡ ♣❛r❝✐❛❧ ♣❛r❛ ✈❡r✐✜❝❛çã♦ ❞❡ ❡st❛❞♦s ❧✐♠✐t❡s ú❧t✐♠♦s ❞❡ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦
♣❛r❛ ❛s ❛çõ❡s ♣❡r♠❛♥❡♥t❡s ❞❡s❢❛✈♦rá✈❡✐s ✭❞❡s❡st❛❜✐❧✐③❛♥t❡s✮
γG;stb ❝♦❡✜❝✐❡♥t❡ ♣❛r❝✐❛❧ ♣❛r❛ ✈❡r✐✜❝❛çã♦ ❞❡ ❡st❛❞♦s ❧✐♠✐t❡s ú❧t✐♠♦s ❞❡ ❧❡✈❛♥t❛♠❡♥t♦ ❤✐❞rá✉❧✐❝♦
♣❛r❛ ❛s ❛çõ❡s ♣❡r♠❛♥❡♥t❡ ❢❛✈♦rá✈❡✐s ✭❡st❛❜✐❧✐③❛♥t❡s✮
γR;v ❝♦❡✜❝✐❡♥t❡ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞♦ t❡rr❡♥♦ ❛♦ ❝❛rr❡❣❛♠❡♥t♦
γsat ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦ s❛t✉r❛❞♦
γw ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞❛ á❣✉❛
γφ′ ❝♦❡✜❝✐❡♥t❡ ♣❛r❝✐❛❧ ♣❛r❛ ❛ t❛♥❣❡♥t❡ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ ✐♥t❡r♥♦ ❡♠ t❡♥sõ❡s ❡❢❡t✐✈❛s
φ′ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❡❢❡t✐✈♦
φ′
col â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♥♦ ❝♦❧❛♣s♦
φ′
d â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞❡ ❝á❧❝✉❧♦
φ′
r â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ r❡❞✉③✐❞♦
ψ â♥❣✉❧♦ ❞❡ ❞✐❧❛tâ♥❝✐❛
σ′ t❡♥sã♦ ❡❢❡t✐✈❛ ✈❡rt✐❝❛❧
σ′
n t❡♥sã♦ ❡❢❡t✐✈❛ ♥♦r♠❛❧
τ t❡♥sã♦ ❞❡ ❝♦rt❡
τr t❡♥sã♦ ❞❡ ❝♦rt❡ ♠í♥✐♠❛ ♣❛r❛ ❣❛r❛♥t✐r ♦ ❡q✉✐❧í❜r✐♦
ν ❝♦❡✜❝✐❡♥t❡ ❞❡ P♦✐ss♦♥
