Análise não-linear física e geométrica de sistemas aporticados com elementos de rigidez variável em concreto armado

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦

❆♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❢ís✐❝❛ ❡ ❣❡♦♠étr✐❝❛ ❞❡

s✐st❡♠❛s ❛♣♦rt✐❝❛❞♦s ❝♦♠ ❡❧❡♠❡♥t♦s ❞❡

r✐❣✐❞❡③ ✈❛r✐á✈❡❧ ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦

❆✉t♦r✿

❚❛t✐❛♥❡ ▼❛❣❛ P❡r❡✐r❛ ▼❡♥❞❡s

❖r✐❡♥t❛❞♦r✿

❉r✲■♥❣ ❋r❛♥❝✐s❝♦ ❈é❧✐♦ ❞❡ ❆r❛ú❥♦

❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧

♥❛ ár❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❡♠ ❈♦♥str✉çã♦ ▼❡tá❧✐❝❛

P❘❖P❊❈

❊s❝♦❧❛ ❞❡ ▼✐♥❛s

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦

❆♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❢ís✐❝❛ ❡ ❣❡♦♠étr✐❝❛ ❞❡

s✐st❡♠❛s ❛♣♦rt✐❝❛❞♦s ❝♦♠ ❡❧❡♠❡♥t♦s ❞❡

r✐❣✐❞❡③ ✈❛r✐á✈❡❧ ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦

❆✉t♦r✿

❚❛t✐❛♥❡ ▼❛❣❛ P❡r❡✐r❛ ▼❡♥❞❡s

❖r✐❡♥t❛❞♦r✿

❉r✲■♥❣ ❋r❛♥❝✐s❝♦ ❈é❧✐♦ ❞❡ ❆r❛ú❥♦

❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ❞❛ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐✲ s✐t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ♥❛ ár❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❡♠ ❈♦♥str✉çã♦ ▼❡tá❧✐❝❛

P❘❖P❊❈ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s

❙❡t❡♠❜r♦✱ ✷✵✶✼

✏◗✉❡ ♥❛❞❛ ♥♦s ❞❡✜♥❛✱ q✉❡ ♥❛❞❛ ♥♦s s✉❥❡✐t❡✳ ◗✉❡ ❛ ❧✐❜❡r❞❛❞❡ s❡❥❛ ❛ ♥♦ss❛ ♣ró♣r✐❛ s✉❜stâ♥❝✐❛✱ ❥á q✉❡ ✈✐✈❡r é s❡r ❧✐✈r❡✳✑

❙✐♠♦♥❡ ❞❡ ❇❡❛✉✈♦✐r

❆❣r❛❞❡❝✐♠❡♥t♦s

➚ ♠✐♥❤❛ ✐r♠ã✱ ❆❞á❧✐❛ ❚á❝✐✱ ♣♦r t♦❞♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ ❛♠✐③❛❞❡ ❞✉r❛♥t❡ ❛ ✈✐❞❛✳ ❆ ❱✐♥í❝✐✉s ♣♦r t♦❞❛s ❛s ♥♦✐t❡s ❞❡ ❱✐♥❣❛❞♦r❡s✱ ❆✈❛t❛r ❡ ❍♦♠❡♠ ❆r❛♥❤❛✳

➚ ❚✐❛ ❙ô♥✐❛ ♣❡❧♦ ❛♠♦r✱ ❝❛r✐♥❤♦ ❡ ❛❝♦♥s❡❧❤❛♠❡♥t♦✳

➚ ❉é❜♦r❛ ❡ ❑❛r✐♥❡ ♣❡❧♦ ❡①❡♠♣❧♦ ❞❡ ❣✉❡rr❡✐r❛ ❛ s❡r s❡❣✉✐❞♦✳

❆♦ ●r✉♣♦ ❇✐❦❡rs ❞❛s ▼✐♥❛s✱ ❡♠ ❡s♣❡❝✐❛❧ ❛ ❆♥❛✱ ❈❧❡✐❞❡✱ ▼❛r✐✱ ❉❛♥✐ ❡ ▲✉❛♥❛✱ ♣❡❧❛ ❛ ❛♠✐③❛❞❡ ❡ ❜r✉t❛❧✐❞❛❞❡✳

➚ ▲✉í③❛ ♣❡❧♦s ❛❜r❛ç♦s ♥♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s✳

➚ ■❛r❛ ♣❡❧❛ ❛♠✐③❛❞❡✱ ❞✐s♣♦s✐çã♦ ❡♠ ❛❥✉❞❛r ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳ ❆♦ ❛♠✐❣♦ ▼❝❣❧❡♥♥♦♥ ♣❡❧❛ ❛❥✉❞❛ ❝♦♠ ♦ ▲❛t❡①

❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ❋r❛♥❝✐s❝♦ ❈é❧✐♦✱ ♣♦r t♦❞♦s ❡♥s✐♥❛♠❡♥t♦s ❡ ♣❡❧❛ ❞❡❞✐❝❛çã♦✳ ❆ t♦❞♦s ♣r♦❢❡ss♦r❡s ❞♦ P❘❖P❊❈ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s✳

❆ t♦❞♦s ♠❡✉s ❝♦❧❡❣❛s ❞❡ ♠❡str❛❞♦ ♣❡❧❛ ❝♦♠♣❛♥❤✐❛ ♥♦ ❞✐❛ ❛ ❞✐❛✳

➚s ❞✐✈❛s✱ ▼❛rí❧✐❛ ▼❡♥❞♦♥ç❛✱ ◆❛✐r❛ ❆③❡✈❡❞♦✱ ❙✐♠♦♥❡✱ ❙✐♠❛r✐❛✱ ▲✉❞✐♠✐❧❛✱ ❆❞❡❧❡✱ ❑❛t② P❡rr②✱ ❙✐❛✱ P✦♥❦ ❡ é ❝❧❛r♦ à ❘❛✐♥❤❛ ❇❡②♦♥❝é✱ ♣❡❧❛ tr✐❧❤❛ s♦♥♦r❛✳

➚ ❈❛♣❡s ♣❡❧♦ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞❡st❛ ♣❡sq✉✐s❛✳

❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❖❯❘❖ P❘❊❚❖

❘❡s✉♠♦

❊s❝♦❧❛ ❞❡ ▼✐♥❛s

P❘❖P❊❈

▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ♥❛ ár❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❡♠ ❈♦♥str✉çã♦ ▼❡tá❧✐❝❛

❆♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❢ís✐❝❛ ❡ ❣❡♦♠étr✐❝❛ ❞❡ s✐st❡♠❛s ❛♣♦rt✐❝❛❞♦s ❝♦♠ ❡❧❡♠❡♥t♦s ❞❡ r✐❣✐❞❡③ ✈❛r✐á✈❡❧ ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦

❚❛t✐❛♥❡ ▼❛❣❛ P❡r❡✐r❛ ▼❡♥❞❡s

◆❡st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛♠✲s❡ ❡str❛té❣✐❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❢ís✐❝❛ ❡ ❣❡♦♠étr✐❝❛ ❞❡ ♣órt✐❝♦s ♣❧❛♥♦s ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✳ ❆ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ❢ís✐❝❛ s❡rá ✐♥❝❧✉í❞❛ ❞❡ ❞✉❛s ❢♦r♠❛s✿ ✈✐❛ ♠♦❞❡❧♦ ❞❡ ●❤❛❧✐✲❋❛✈r❡ ❡ ✈✐❛ ♣r♦❝❡ss♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞✐r❡t♦ ❞❡ ❡s❢♦rç♦s ♥❛ s❡çã♦✳ ◆♦ ♠♦❞❡❧♦ ❞❡ ●❤❛❧✐✲❋❛✈r❡✱ ❛ r✐❣✐❞❡③ ❡♠ ✉♠❛ ❞❛❞❛ s❡çã♦ ❞❡ ✉♠ ❡❧❡♠❡♥t♦✱ ♣❛r❛ ❝❡rt♦ ♥í✈❡❧ ❞❡ s♦❧✐❝✐t❛çã♦ ♥♦ ❡stá❞✐♦ ■■✱ é ❞❡t❡r♠✐♥❛❞❛ ❛ ♣❛rt✐r ✐♥t❡r♣♦❧❛çã♦ ❞❛s ❞❡❢♦r♠❛çõ❡s ❣❡♥❡r❛❧✐③❛❞❛s ♥♦s ❡stá❞✐♦s ■ ❡ ■■ ♣✉r♦✳ ◆♦ ♠ét♦❞♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞✐r❡t♦ ❞❛ s❡çã♦✱ ❢❛③✲s❡ ✉s♦ ❞❡ ✉♠❛ ❡str❛té❣✐❛ ✐t❡r❛t✐✈❛ ❞❡ ❡q✉✐❧í❜r✐♦✱ ♦♥❞❡ ❞❡❢♦r♠❛çõ❡s ❛①✐❛✐s ❡ ✢❡①✐♦♥❛✐s sã♦ ✐t❡r❛t✐✈❛♠❡♥t❡ ✐♠♣♦st❛s ❡ ♦s ❝♦rr❡s♣♦♥❞❡♥t❡s ❡s❢♦rç♦s ✐♥t❡r♥♦s ❝❛❧❝✉❧❛❞♦s✱ ❛té q✉❡ s❡ ✈❡r✐✜q✉❡ ❡q✉✐❧í❜r✐♦ ❡♥tr❡ ❡s❢♦rç♦s r❡s✐st❡♥t❡s ❡ s♦❧✐❝✐t❛♥t❡s✳ ❆ss✐♠✱ ♣♦❞❡✲s❡ ❞❡t❡r♠✐♥❛r ❛s r✐❣✐❞❡③❡s ❛①✐❛❧ ❡ ✢❡①✐♦♥❛❧✱ ❡♠ ✉♠❛ ❞❛❞❛ s❡çã♦✱ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ ♥í✈❡❧ ❞❡ s♦❧✐❝✐t❛çã♦✳ ❉❡ ♣♦ss❡ ❡♥tã♦ ❞❛ r✐❣✐❞❡③ ✭✈❛r✐á✈❡❧✮ ❛♦ ❧♦♥❣♦ ❞♦ ❡❧❡♠❡♥t♦ ❡str✉t✉r❛❧✱ ❡♠♣r❡❣❛✲s❡ ✉♠❛ ❢♦r♠✉❧❛çã♦ ❜❛s❡❛❞❛ ♥♦ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✭▼❘❉✮ q✉❡ ♣♦ss✐❜✐❧✐t❛ ♠♦❞❡❧❛r ❡ss❛ ✈❛r✐❛çã♦ ❞❡ r✐❣✐❞❡③ s❡❣✉♥❞♦ ❧❡✐s ♠❛t❡♠át✐❝❛s q✉❛✐sq✉❡r✳ ❆❞❡♠❛✐s✱ s❡ ✐♥❝❧✉❡♠✱ ♥❛ ❢♦r♠✉❧❛çã♦✱ ♦♣çõ❡s ❞❡ ♠♦❞❡❧❛❣❡♠ ❞❡ s❡çõ❡s ❞❡ ❢♦r♠❛s ❣❡♦♠étr✐❝❛s q✉❛✐sq✉❡r✱ ❡✈❡♥t✉❛❧♠❡♥t❡ ✈❛r✐á✈❡✐s ❛♦ ❧♦♥❣♦ ❞♦ ❡❧❡♠❡♥t♦✳ P❛r❛ ❛ ❛♥á❧✐s❡ ♥ã♦✲ ❧✐♥❡❛r✱ ❛❞♦t❛✲s❡ ✉♠ ❡sq✉❡♠❛ ✐♥❝r❡♠❡♥t❛❧✲✐t❡r❛t✐✈♦ ❞❡ ◆❡✇t♦♥✲❘❛♣❤s♦♥ ♥♦ q✉❛❧ ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❣❡♦♠étr✐❝❛ é ❛t✉❛❧✐③❛❞❛✱ ❡♠ ❝❛❞❛ ✐t❡r❛çã♦ ❞♦ ♣r♦❝❡ss♦ ✐♥❝r❡♠❡♥t❛❧✲✐t❡r❛t✐✈♦✱ ❡♥q✉❛♥t♦ ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❢ís✐❝❛ é ❛t✉❛❧✐③❛❞❛ ❛♣❡♥❛s ❛ ❝❛❞❛ ♥♦✈♦ ✐♥❝r❡♠❡♥t♦ ❞❡ ❝❛r❣❛✳ ❆ss✐♠✱ t❛♥t♦ ❛ ❞❡❣r❛❞❛çã♦ ♣♦r ✜ss✉r❛çã♦ ❞♦ ❝♦♥❝r❡t♦ ❝♦♠♦ ❣r❛♥❞❡s ❞❡s❧♦❝❛♠❡♥t♦s sã♦ ❝♦♥s✐❞❡r❛❞♦s ♥❛ ❛♥á❧✐s❡✳ ◆❡ss❡ ❛❧❣♦r✐t♠♦✱ ✉♠ r❡❢❡r❡♥❝✐❛❧ ❝♦rr♦t❛❝✐♦♥❛❧ é t❛♠❜é♠ ❝♦♥s✐❞❡r❛❞♦✳ ❈♦♠♣❛r❛çõ❡s ❝♦♠ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s sã♦ ♠♦str❛❞❛s ♣❛r❛ ❛t❡st❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞❛ ❡str❛té❣✐❛✳

❋❊❉❊❘❆▲ ❯◆■❱❊❘❙■❚❨ ❖❋ ❖❯❘❖ P❘❊❚❖

❆❜str❛❝t

❊s❝♦❧❛ ❞❡ ▼✐♥❛s P❘❖P❊❈

▼❛st❡r ♦❢ ❙❝✐❡♥❝❡ ✐♥ ❈✐✈✐❧ ❊♥❣✐♥❡❡r✐♥❣

✐♥ t❤❡ ❛r❡❛ ♦❢ ❝♦♥❝❡♥tr❛t✐♦♥ ✐♥ ▼❡t❛❧❧✐❝ ❈♦♥str✉❝t✐♦♥

◆♦♥✲❧✐♥❡❛r ♣❤②s✐❝❛❧ ❛♥❞ ❣❡♦♠❡tr✐❝ ❛♥❛❧②s✐s ♦❢ ❢r❛♠❡❞ s②st❡♠s ✇✐t❤ ❡❧❡♠❡♥ts ♦❢ ✈❛r✐❛❜❧❡ st✐✛♥❡ss ✐♥ r❡✐♥❢♦r❝❡❞ ❝♦♥❝r❡t❡

❜② ❚❛t✐❛♥❡ ▼❛❣❛ P❡r❡✐r❛ ▼❡♥❞❡s

❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ str❛t❡❣② ❢♦r t❤❡ ♣❤②s✐❝❛❧ ❛♥❞ ❣❡♦♠❡tr✐❝ ♥♦♥✲❧✐♥❡❛r ❛♥❛❧②s✐s ♦❢ ♣❧❛♥❡ r❡✐♥❢♦r❝❡❞ ❝♦♥❝r❡t❡ ❢r❛♠❡s✳ ❚❤❡ ♣❤②s✐❝❛❧ ♥♦♥✲❧✐♥❡❛r✐t② ✐s ✐♥❝❧✉❞❡❞ ❜② ♠❡❛♥s ♦❢ t✇♦ ❞✐❢❡r❡♥t ♣r♦❝❡ss❡s✿ t❤❡ ●❤❛❧✐✲❋❛✈r❡ ♣r♦❝❡ss✱ ❛♥❞ t❤❡ ❞✐r❡❝t ❡q✉✐❧✐❜r✐✉♠ ♣r♦❝❡ss ♦❢ t❤❡ ❝r♦ss s❡❝t✐♦♥✳ ■♥ t❤❡ ●❤❛❧✐✲❋❛✈r❡ ♣r♦❝❡ss✱ t❤❡ r✐❣✐❞✐t② ❛t ❛ ❣✐✈❡♥ ❝r♦ss s❡❝t✐♦♥ ♦❢ ❛ ❢r❛♠❡ ❡❧❡♠❡♥t✱ ❢♦r ❛ ❣✐✈❡♥ ❧♦❛❞ ❧❡✈❡❧✱ ✐s ❞❡t❡r♠✐♥❡❞ ❜② ✐♥t❡r♣♦❧❛t✐♥❣ t❤❡ ❣❡♥❡r❛❧✐③❡❞ str❛✐♥s ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ■ ❛♥❞ ♣✉r❡ ■■ st❛t❡s ✭❢✉❧❧② ❝r❛❝❦❡❞ s❡❝t✐♦♥✮ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❣❡♥❡r❛❧✐③❡❞ str❡ss❡s✳ ■♥ t❤❡ ❞✐r❡❝t ❡q✉✐❧✐❜r✐✉♠ ♣r♦❝❡ss ♦❢ t❤❡ ❝r♦ss s❡❝t✐♦♥✱ ❛♥ ✐t❡r❛t✐✈❡ ❜❛❧❛♥❝❡ str❛t❡❣② ✐s ♣r♦♣♦s❡❞ ✐♥ ✇❤✐❝❤ ❛①✐❛❧ ❛♥❞ ✢❡①✉r❛❧ ❞❡❢♦r♠❛t✐♦♥s ❛r❡ ✐t❡r❛t✐✈❡❧② ✐♠♣♦s❡❞✱ ❛♥❞ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ✐♥t❡r♥❛❧ ❢♦r❝❡s ❡✈❛❧✉❛t❡❞✱ ✉♥t✐❧ ❜❛❧❛♥❝❡ ❜❡t✇❡❡♥ r❡s✐st✐♥❣ ❛♥❞ ❛❝t✐♥❣ ❢♦r❝❡s ✐s ❛tt❛✐♥❡❞✳ ❚❤✐s ❛❧❧♦✇s ♠❡❛s✉r✐♥❣ t❤❡ ❛①✐❛❧ ❛♥❞ ✢❡①✉r❛❧ r✐❣✐❞✐t② ❛t ❛ ❣✐✈❡♥ ❝r♦ss s❡❝t✐♦♥✳ ❚❤✉s✱ ✇✐t❤ t❤❡ ✭✈❛r✐❛❜❧❡✮ r✐❣✐❞✐t② ❛❧♦♥❣ t❤❡ ❡❧❡♠❡♥t✱ ♦♥❡ ❡♠♣❧♦②s ❛ ❢♦r♠✉❧❛t✐♦♥ ❜❛s❡❞ ♦♥ t❤❡ ❉✐r❡❝t ❙t✐✛♥❡ss ▼❡t❤♦❞ ✭❉❙▼✮✱ ✇❤✐❝❤ ❛❧❧♦✇s ❢♦r ♠♦❞❡❧✐♥❣ t❤❛t r✐❣✐❞✐t② ❛❝❝♦r❞✐♥❣ ❣❡♥❡r✐❝ ♠❛t❤❡♠❛t✐❝❛❧ ❧❛✇s✳ ■♥ ❛❞❞✐t✐♦♥✱ ♦♥❡ ❛❧s♦ ✐♠♣❧❡♠❡♥ts ♦♣t✐♦♥s ❢♦r ♠♦❞❡❧✐♥❣ ❝r♦ss s❡❝t✐♦♥s ♦❢ ❛♥② ❣❡♦♠❡tr✐❝ s❤❛♣❡s✱ ♣♦ss✐❜❧② ✈❛r✐❛❜❧❡ ❛❧♦♥❣ t❤❡ ❡❧❡♠❡♥t ❧❡♥❣t❤✳ ❚♦ ❝❛rr② ♦✉t t❤❡ ♥♦♥✲❧✐♥❡❛r ❛♥❛❧②s✐s✱ ❛♥ ✐♥❝r❡♠❡♥t❛❧✲✐t❡r❛t✐✈❡ ◆❡✇t♦♥✲❘❛♣❤s♦♥ s❝❤❡♠❡ ✐s ❡♠♣❧♦②❡❞ ✐♥ ✇❤✐❝❤ t❤❡ ❣❡♦♠❡tr✐❝ st✐✛♥❡ss ♠❛tr✐① ✐s ✉♣❞❛t❡❞ ❛t ❡✈❡r② ✐t❡r❛t✐♦♥ ♦❢ t❤❡ ✐♥❝r❡♠❡♥t❛❧✲✐t❡r❛t✐✈❡ ♣r♦❝❡ss✱ ❛♥❞ t❤❡ ♣❤②s✐❝❛❧ st✐✛♥❡ss ♠❛tr✐① ✐s ✉♣❞❛t❡❞ ♦♥❧② ❛t ❡✈❡r② ♥❡✇ ❧♦❛❞ ✐♥❝r❡♠❡♥t✳ ❚❤✉s✱ ❝♦♥❝r❡t❡ ❞❡❣r❛❞❛t✐♦♥ ❜② ❝r❛❝❦✐♥❣ ❛♥❞ ❧❛r❣❡ ❞✐s♣❧❛❝❡♠❡♥ts ❛r❡ t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t ✐♥ t❤❡ ❛♥❛❧②s✐s✳ ❇❡s✐❞❡s✱ ✐♥ t❤✐s ❛❧❣♦r✐t❤♠ ❛ ❝♦✲r♦t❛t✐♦♥❛❧ r❡❢❡r❡♥❝❡ s②st❡♠ ✐s ❝♦♥s✐❞❡r❡❞ t♦ ✐♥❝r❡❛s❡ t❤❡ r❡s♣♦♥s❡ ❛❝❝✉r❛❝②✳ ❈♦♠♣❛r✐s♦♥s ✇✐t❤ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts ❛r❡ s❤♦✇ t❤❡ ❛tt❡st t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❤❡ str❛t❡❣②✳

❙✉♠ár✐♦

▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐

▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✈

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ❊str✉t✉r❛ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✷ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✺

✷✳✶ ❋♦r♠✉❧❛çã♦ ▼❛tr✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷ ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❢ís✐❝❛ ❞❡ ❡❧❡♠❡♥t♦ ❞♦ ♣órt✐❝♦ ♣❧❛♥♦ ✭Kf✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✷✳✸ ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❣❡♦♠étr✐❝❛ ❞❡ ❡❧❡♠❡♥t♦ ❞♦ ♣órt✐❝♦ ♣❧❛♥♦ ✭Kg✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✷✳✹ ❱❛r✐❛çã♦ ❞❡ r✐❣✐❞❡③ ❡♠ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥❝r❡t♦ ❛r♠❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✸ ❆♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❢ís✐❝❛ ❞❡ ❡str✉t✉r❛s ❡♠ ❈♦♥❝r❡t♦ ❆r♠❛❞♦ ✷✶

✸✳✶ ❈♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❈❆ à ✢❡①ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✷ ❈♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❈❆ à tr❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✸ ▼♦❞❡❧♦ ❞❡ ❇r❛♥s♦♥✭✶✾✻✺✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✹ ▼♦❞❡❧♦ ❞❡ ●❤❛❧✐ ❡ ❋❛✈r❡ ✭✶✾✽✻✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹✳✶ ❚r❛çã♦ ❆①✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✹✳✷ ❋❧❡①ã♦ ❙✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✹✳✸ ❋❧❡①ã♦ ❈♦♠♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✹✳✹ ❈á❧❝✉❧♦ ❞❛ r✐❣✐❞❡③ ❞❡ s❡çõ❡s ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦ ✲ ●❤❛❧✐ ❡ ❋❛✈r❡ ✳ ✳ ✳ ✸✵ ✸✳✺ ❊q✉✐❧í❜r✐♦ ❉✐r❡t♦ ❞❛ ❙❡çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✺✳✶ ❈á❧❝✉❧♦ ❞❛ r✐❣✐❞❡③ ❞❡ s❡çõ❡s ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦ ✲ ❊q✉✐❧í❜r✐♦ ❞✐r❡t♦ ✳ ✹✵ ✸✳✺✳✷ ❊str❛té❣✐❛ ♣❛r❛ ❝✉r✈❛s M①ψ ❡N①ε ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✻ ❈♦♥s✐❞❡r❛çõ❡s ◆♦r♠❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✼ ❆♣❧✐❝❛çõ❡s Pr❡❧✐♠✐♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✹ ❆♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❣❡♦♠étr✐❝❛ ✹✻

✹✳✶ ❆♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❣❡♦♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✶✳✶ P❛râ♠❡tr♦ ❞❡ ✐♥st❛❜✐❧✐❞❛❞❡ α ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✹✳✶✳✷ ❈♦❡✜❝✐❡♥t❡ γz ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✹✳✷ ❊str❛té❣✐❛ ❞❡ s♦❧✉çã♦ ♥ã♦✲❧✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✺ ❆♣❧✐❝❛çõ❡s ✺✷

✺✳✶ ❆♣❧✐❝❛çã♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✺✳✷ ❆♣❧✐❝❛çã♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✳✸ ❆♣❧✐❝❛çã♦ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✹ ❆♣❧✐❝❛çã♦ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✻ ❈♦♥❝❧✉sõ❡s ✻✾

✻✳✶ ❙✉❣❡stõ❡s ♣❛r❛ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

❆ ❆♣ê♥❞✐❝❡ ❆ ✼✶

❆✳✶ Pr♦♣r✐❡❞❛❞❡s ♥♦s ❊stá❞✐♦s ■ ❡ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ❆✳✶✳✶ ▲✐♥❤❛ ◆❡✉tr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ▲✐♥❤❛ ◆❡✉tr❛ ✲ ❊stá❞✐♦ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ▲✐♥❤❛ ◆❡✉tr❛ ✲ ❊stá❞✐♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❆❧❣♦r✐t♠♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞❛ ❧✐♥❤❛ ♥❡✉tr❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❆✳✶✳✷ ➪r❡❛ ❡ ▼♦♠❡♥t♦ ❞❡ ■♥ér❝✐❛ ❞❛ ❙❡çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ❆✳✷ ❊s❢♦rç♦s ♥♦s ❊stá❞✐♦s ■ ❡ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ❆✳✷✳✶ ▼♦♠❡♥t♦ ❞❡ ✐♥í❝✐♦ ❞❡ ✜ss✉r❛çã♦✱ Mr ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹

❆✳✷✳✷ ▼♦♠❡♥t♦ ❞❡ ♣❧❛st✐✜❝❛çã♦ ❞❛s ❛r♠❛❞✉r❛s✱Mp ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

❆✳✷✳✸ ◆♦r♠❛❧ ❞❡ ✐♥í❝✐♦ ❞❡ ✜ss✉r❛çã♦✱ Nr ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

❇ ❆♣ê♥❞✐❝❡ ❇ ✼✻

❇✳✶ ❉❡t❡r♠✐♥❛çã♦ ❞♦ ▼♦♠❡♥t♦ Ú❧t✐♠♦ ❞❡ ✉♠❛ ❙❡çã♦ ❞❡ ❈♦♥❝r❡t♦ ❆r♠❛❞♦ ✳ ✳ ✳ ✼✻

❘❡❢❡rê♥❝✐❛s ✼✽

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ❚✇✐♥ ❚♦✇❡rs ✲ ❑✉❛❧❛ ▲✉♠♣✉r ✲ ❈♦♥❝r❡t♦ ❞❡ ✽✵▼♣❛ ❛té ♦ ✻✵♦ _{❛♥❞❛r ✳ ✳ ✳ ✳ ✳ ✷}

✷✳✶ Pórt✐❝♦ P❧❛♥♦ ✲ ❋♦♥t❡✿ ❘✐❜❡✐r♦ ✭✷✵✶✻✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❝♦♠ ♦ s❡❣✉♥❞♦ ♥ó r❡str✐♥❣✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✹ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❝♦♠ ♦ ♣r✐♠❡✐r♦ ♥ó r❡str✐♥❣✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✺ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❞❡❢♦r♠❛❞♦ ❝♦♠ ♦ s❡❣✉♥❞♦ ♥ó r❡str✐♥❣✐❞♦ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✻ ❉❡❝♦♠♣♦s✐çã♦ ❞❛s ❢♦rç❛sf1k ❡f2k ♥♦ ❡✐①♦ ❞❡❢♦r♠❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✷✳✼ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❞❡❢♦r♠❛❞♦ ❝♦♠ ♦ ♣r✐♠❡✐r♦ ♥ó r❡str✐♥❣✐❞♦ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✽ ❉❡❝♦♠♣♦s✐çã♦ ❞❛s ❢♦rç❛sf4k ❡f5k ♥♦ ❡✐①♦ ❞❡❢♦r♠❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✷✳✾ ❋✉♥çõ❡s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✸✳✶ ❈✉r✈❛ ❚❡♥sã♦✲❞❡❢♦r♠❛çã♦ ♣❛r❛ ♦ ❝♦♥❝r❡t♦✳ ❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ❉❡s❛②✐ ❡ ❑r✐s❤♥❛♥ ✭✶✾✻✹✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✷ ❆ç♦s ❡str✉t✉r❛✐s ❧❛♠✐♥❛❞♦s ❛ q✉❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✸ ❊❧❡♠❡♥t♦ ❞❡ ❈❆ ✢❡t✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✹ ❉✐❛❣r❛♠❛ ♠♦♠❡♥t♦ ❝✉r✈❛t✉r❛ ❞❛ s❡çã♦ s♦❧✐❝✐t❛❞❛ ❛ ✢❡①ã♦ s✐♠♣❧❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✺ ❈♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❈❆ à tr❛çã♦✳ ❛✲ ❋✐ss✉r❛s ❡♠ ✉♠ ❡❧❡♠❡♥t♦ s♦❧✐❝✐t❛❞♦ à

tr❛çã♦✱ ❜✲ t❡♥sã♦ ♥❛ ❜❛rr❛ ❞❡ ❛ç♦✱ ❝✲ ❛❞❡rê♥❝✐❛ ❡ ❞✲ t❡♥sã♦ ♥♦ ❝♦♥❝r❡t♦✳ ❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ●❤❛❧✐✱ ❋❛✈r❡ ❡ ❊❧❜❛❞r② ✭✷✵✵✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✻ ❉✐str✐❜✉✐çã♦ ❞❡ ✜ss✉r❛s ♥❛ ✈✐❣❛✳ ❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ●✉❛r❞❛ ✭✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✼ ❋♦rç❛ ❛①✐❛❧ ✈❡rs✉s ❞❡❢♦r♠❛çã♦ ♥♦ ❛ç♦✳ ❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ●❤❛❧✐✱ ❋❛✈r❡ ❡

❊❧❜❛❞r② ✭✷✵✵✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✽ ❊❧❡♠❡♥t♦ ❞❡ ❈❆ s✉❥❡✐t♦ à ✢❡①ã♦ ❝♦♠♣♦st❛ ✭❛✮ s❡çã♦ ♥♦ ❡stá❞✐♦ ■ ✭❜✮ s❡çã♦ ♥♦

❡stá❞✐♦ ■■✳ ❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ●❤❛❧✐✱ ❋❛✈r❡ ❡ ❊❧❜❛❞r② ✭✷✵✵✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✾ ❊❧❡♠❡♥t♦ ❡str✉t✉r❛❧ ❡ ♣♦♥t♦s ❞❡ ✐♥t❡❣r❛çã♦ ❛♦ ❧♦♥❣♦ ❞❡ s❡✉ ❡✐①♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✵ ❊❧❡♠❡♥t♦ ❡str✉t✉r❛❧ ❡ s❡çã♦ s♦❧✐❝✐t❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✶✶ ❉✐❛❣r❛♠❛ t❡sã♦✲❞❡❢♦r♠❛çã♦ ❞♦ ❝♦♥❝r❡t♦ ✭❛✮◆❇❘✻✶✶✽✱ ✷✵✶✹ ❡ ✭❜✮❊✉r♦❝♦❞❡✷✱

✶✾✾✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✶✷ ❈♦♠♣♦rt❛♠❡♥t♦ ❝♦♥❝r❡t♦ s✐♠♣❧❡s à tr❛çã♦✱ ❛❞❛♣t❛❞♦ ❞❡ ❉❡s❛②✐ ❡ ❑r✐s❤♥❛♥

✭✶✾✻✹✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✶✸ ❈♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❛ç♦ s❡❣✉♥❞♦ ◆❇❘✻✶✶✽✱ ✷✵✶✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

✸✳✶✹ ✭❛✮ ▼❛❧❤❛ ❞❡ ❝♦♥t♦r♥♦ ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❡ s✉❛ ❞✐s❝r❡t✐③❛çã♦ ❡♠ ❢❛✐①❛s ✭❜✮ ❞❡t❛❧❤❡ ❞❡ ✉♠❛ ❢❛✐①❛ ❝♦♠ s❡✉s ♣♦♥t♦s ❞❡ ✐♥t❡❣r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✶✺ Pr♦❝❡ss♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞✐r❡t♦ ❞❛ s❡çã♦ ✲ ♣r✐♠❡✐r♦ ♣❛ss♦ ❞❡ ❝❛r❣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✶✻ Pr♦❝❡ss♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞✐r❡t♦ ❞❛ s❡çã♦ ✲ ❞❡♠❛✐s ♣❛ss♦s ❞❡ ❝❛r❣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✶✼ ❙❡çõ❡s tr❛♥s✈❡rs❛✐s✭❛✮ tr❛♣❡③♦✐❞❛❧ ❝♦♠ ❢✉r♦ ✭❜✮ ❡ s❡çã♦ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✶✽ ❈✉r✈❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ♣❛r❛ s❡çã♦ tr❛♣❡③♦✐❞❛❧ ❝♦♠ ❢✉r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✶✾ ❈✉r✈❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ♣❛r❛ s❡çã♦ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹✳✶ ❈♦♥✜❣✉r❛çã♦ ❞❡❢♦r♠❛❞❛✳ ❆❞❛♣t❛❞♦ ❞❡ ❙✐❧✈❡str❡ ❡ ❈❛♠♦t✐♠ ✭✷✵✵✼✮ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷ ❊❢❡✐t♦s ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ P −∆✳ ❆❞❛♣t❛❞♦ ❞❡ ❙✐❧✈❡str❡ ❡ ❈❛♠♦t✐♠ ✭✷✵✵✼✮ ✳ ✹✼ ✹✳✸ ❊❢❡✐t♦s ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ P −δ✳ ❆❞❛♣t❛❞♦ ❞❡ ❙✐❧✈❡str❡ ❡ ❈❛♠♦t✐♠ ✭✷✵✵✼✮ ✳ ✹✽ ✹✳✹ ▼ét♦❞♦ ❞❡ ◆❡✇t♦♥✲❘❛♣❤s♦♥✳ ❆❞❛♣t❛❞♦ ❞❡ ❘✐❜❡✐r♦✱ ✷✵✶✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✺ ❋❧✉①♦❣r❛♠❛ ❞❡ s♦❧✉çã♦ ♥ã♦✲❧✐♥❡❛r✳ ❆❞❛♣t❛❞♦ ❞❡ ❘✐❜❡✐r♦✱ ✷✵✶✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✺✳✶ ❱✐❣❛ ❛♣❧✐❝❛çã♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✺✳✷ ❙❡çõ❡s tr❛♥s✈❡rs❛✐s ❛♣❧✐❝❛çã♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✳✸ ❈✉r✈❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ♣❛r❛ ❛ ✈✐❣❛ ❞❡ ✸ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✹ ❈✉r✈❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ♣❛r❛ ❛ ✈✐❣❛ ❞❡ ✺ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✺ ❈✉r✈❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ♣❛r❛ ❛ ✈✐❣❛ ❞❡ ✼ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✻ ▼♦♠❡♥t♦ ✢❡t♦r ❡♠ ❢✉♥çã♦ ❞❛ ♣♦s✐çã♦ ❞❛ ❧✐♥❤❛ ♥❡✉tr❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✼ ❘✐❣✐❞❡③ ❋❧❡①✐♦♥❛❧ ❡♠ ❢✉♥çã♦ ❞♦ ♠♦♠❡♥t♦ ✢❡t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✽ ❉❡s❧♦❝❛♠❡♥t♦ ✈❡rt✐❝❛❧ ♥♦ ♠❡✐♦ ❞❛ ✈✐❣❛ ❝♦♠ ✸ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✺✳✾ ❉❡s❧♦❝❛♠❡♥t♦ ✈❡rt✐❝❛❧ ♥♦ ♠❡✐♦ ❞❛ ✈✐❣❛ ❝♦♠ ✺ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✺✳✶✵ ❉❡s❧♦❝❛♠❡♥t♦ ✈❡rt✐❝❛❧ ♥♦ ♠❡✐♦ ❞❛ ✈✐❣❛ ❝♦♠ ✼ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✳✶✶ ❱✐❣❛ ❜✐ ❛♣♦✐❛❞❛ ❡ ❝❛rr❡❣❛♠❡♥t♦ ✲ ❆♣❧✐❝❛çã♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✶✷ ❙❡çã♦ tr❛♥s✈❡rs❛❧ ✲ ❆♣❧✐❝❛çã♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✶✸ ❈✉r✈❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ✲ ❛♣❧✐❝❛çã♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✺✳✶✹ ❘✐❣✐❞❡③ ✢❡①✐♦♥❛❧ ✈❡rs✉s ♠♦♠❡♥t♦ ✢❡t♦r ✲ ❛♣❧✐❝❛çã♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✶✺ ▼♦♠❡♥t♦ ✢❡t♦r ✈❡rs✉s ♣♦s✐çã♦ ❞❛ ❧✐♥❤❛ ♥❡✉tr❛ ✲ ❛♣❧✐❝❛çã♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✺✳✶✻ ❉❡s❧♦❝❛♠❡♥t♦ ✈❡rt✐❝❛❧ ❞♦ ♠❡✐♦ ❞♦ ✈ã♦ ❞❛ ✈✐❣❛ ❛♥❛❧✐s❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✶✼ ✭❛✮P✐❧❛r ✲ ❆♣❧✐❝❛çã♦ ✸✱ ✭❜✮ ❙❡çã♦ ❚r❛♥s✈❡rs❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✶✽ ❈❛r❣❛ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ♥♦ ❝❡♥tr♦ ❞♦ ♣✐❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✺✳✶✾ ❈❛r❣❛ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ♥♦ ❝❡♥tr♦ ❞♦ ♣✐❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✷✵ ❈❛r❣❛ ❡♠ ❢✉♥çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ♥♦ ❝❡♥tr♦ ❞♦ ♣✐❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✷✶ ✭❛✮P✐❧❛r ✲ ❆♣❧✐❝❛çã♦ ✹✱ ✭❜✮ ❉✐s❝r❡t✐③❛çã♦ ❡ ✭❝✮ ❙❡çã♦ ❚r❛♥s✈❡rs❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✷✷ ❈✉r✈❛ ♠♦♠❡♥t♦ ❝✉r✈❛t✉r❛ ♣❛r❛ ❞✐✈❡rs❛s ❢♦rç❛s ♥♦r♠❛✐s s♦❧✐❝✐t❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✷✸ ❈❛r❣❛ P ♣❡❧♦ ❞❡s❧♦❝❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ♥♦ t♦♣♦ ❞♦ ♣✐❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

❆✳✶ ❙❡çã♦ tr❛♥s✈❡rs❛❧ ✲ ❊stá❞✐♦s ■ ❡ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ❆✳✷ ▼❛❧❤❛ ❞❡ ❝♦♥t♦r♥♦ ❡ ❡❧❡♠❡♥t♦ ❣❡♥ér✐❝♦ ❞❡ ❝♦♥t♦r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

❇✳✶ ❉✐❛❣r❛♠❛ ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ❡ ❡stá❞✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✶ ❉❛❞♦s ❞♦s ♠❛t❡r✐❛✐s ✲ ❙❡çã♦ tr❛♣❡③♦✐❞❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✷ ❉❛❞♦s ❞♦s ♠❛t❡r✐❛✐s ✲ ❙❡çã♦ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

✺✳✶ ❉❛❞♦s ❞❛ s❡çã♦ ✲ ❆♣❧✐❝❛çã♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✳✷ ❉❛❞♦s ❞♦s ♠❛t❡r✐❛✐s ✲ ❆♣❧✐❝❛çã♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✳✸ ❱❛❧♦r❡s ❞❡ ♠♦♠❡♥t♦ ❞❡ ✜ss✉r❛çã♦✱ ♣❧❛st✐✜❝❛çã♦ ❡ ú❧t✐♠♦ ♣❛r❛ ❛ ✈✐❣❛ ❞❡ ✸ ϕ

❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✹ ❈✉r✈❛t✉r❛s r❡❢❡r❡♥t❡s ❛♦s ✈❛❧♦r❡s ❞❡ ♠♦♠❡♥t♦ ❞❡ ✜ss✉r❛çã♦✱ ♣❧❛st✐✜❝❛çã♦ ❡

ú❧t✐♠♦ ♣❛r❛ ❛ ✈✐❣❛ ❞❡ ✸ ϕ ❞❡ ✶✵♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✺ ❉❛❞♦s ❞❛ s❡çã♦ ✲ ❆♣❧✐❝❛çã♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✻ ❉❛❞♦s ❞♦s ♠❛t❡r✐❛✐s ✲ ❆♣❧✐❝❛çã♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✺✳✼ ❉❛❞♦s ❞♦s ♠❛t❡r✐❛✐s ✲ ❆♣❧✐❝❛çã♦ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✽ ❉❛❞♦s ❞♦s ♠❛t❡r✐❛✐s ✲ ❆♣❧✐❝❛çã♦ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

✶✳✶ ❈♦♥t❡①t♦ ❡ ▼♦t✐✈❛çã♦

❯♠ ❞♦s ❞❡s❛✜♦s ❞❛ ❡♥❣❡♥❤❛r✐❛ ❡str✉t✉r❛❧ ❡stá ❧✐❣❛❞♦ à ❝r✐❛çã♦ ❞❡ t❡❝♥♦❧♦❣✐❛s q✉❡ ♣❡r♠✐t❛♠ ✉♠❛ r❡❞✉çã♦ ❞♦ ♣❡s♦ ❞❛s ❡str✉t✉r❛s✱ ♦❜s❡r✈❛♥❞♦ ❛s♣❡❝t♦s ❜❡♠ ❞❡✜♥✐❞♦s ❞❡ s❡❣✉r❛♥ç❛ ✭●♦♥✲ ç❛❧✈❡s✱ ✷✵✵✸✮✳ ❈♦♥s❡q✉ê♥❝✐❛ ó❜✈✐❛ ❞❛ r❡❞✉çã♦ ❞❡ ♠❛t❡r✐❛❧ é t❛♠❜é♠ ❛ r❡❞✉çã♦ ❞❡ ❝✉st♦s ♥❛ ❝♦♥str✉çã♦ ❞♦s s✐st❡♠❛s ❡str✉t✉r❛✐s✳ ◆❡ss❡ ❝♦♥t❡①t♦✱ ♥ã♦ ❛♣❡♥❛s s❡ ✐♥s❡r❡♠ ❛s ♣❡sq✉✐s❛s ♥❛ ár❡❛ ❞❡ ♠❛t❡r✐❛✐s✱ s♦❜r❡t✉❞♦ ❡♠ ❝♦♠♣ós✐t♦s ❛✈❛♥ç❛❞♦s✱ ❡♠ q✉❡ s❡ ♦❜❥❡t✐✈❛♠ ♦ ❞❡s❡♥✈♦❧✲ ✈✐♠❡♥t♦ ❞❡ ♠❛t❡r✐❛✐s ❝♦♠ ❡❧❡✈❛❞❛ r❡❧❛çã♦ ❞❡ r❡s✐stê♥❝✐❛ ♠❡❝â♥✐❝❛ ♣♦r ❞❡♥s✐❞❛❞❡ ❞❡ ♠❛ss❛✱ ♠❛s t❛♠❜é♠ ❛s ♣❡sq✉✐s❛s q✉❡ ✈✐s❡♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♣r♦❝❡ss♦s ❛✈❛♥ç❛❞♦s ❞❡ s✐♠✉❧❛✲ çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ss❡s s✐st❡♠❛s ❡str✉t✉r❛✐s✳ ❖❜✈✐❛♠❡♥t❡✱ ❡str✉t✉r❛s ❛rq✉✐t❡t♦♥✐❝❛♠❡♥t❡ ❝♦♠♣❧❡①❛s✱ ♠✉✐t♦ ❛❧t❛s✱ ❡s❜❡❧t❛s✱ ❝♦♠♦ ❛s ❚✇✐♥ ❚♦✇❡rs ♠♦str❛❞❛s ♥❛ ❋✐❣✉r❛ ✶✳✶✱ t❛♠❜é♠ ❞❡♠❛♥❞❛♠ ♦ ❡♠♣r❡❣♦ ❞❡ ♣r♦❝❡ss♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❛✈❛♥ç❛❞♦s ❡♠ s❡✉ ♣r♦❥❡t♦✳

◆♦ ❝❛s♦ ❞♦ ❝♦♥❝r❡t♦✱ ♣♦❞❡✲s❡✱ ❤♦❥❡✱ ❝❤❡❣❛r ❛ r❡s✐stê♥❝✐❛s s✉♣❡r✐♦r❡s ❛ ✺✵▼P❛ ✭▼♦♥❝❛✈♦✱ ✷✵✶✶✮✱ ♦ q✉❡ ♣♦ss✐❜✐❧✐t❛ ❡❧❡♠❡♥t♦s ♠❛✐s ❡s❜❡❧t♦s ❡ ❧❡✈❡s✱ ❞❡ ♠♦❞♦ q✉❡ ❝♦♥s✐❞❡r❛çõ❡s ❞❡ ❡❢❡✐t♦s ♥ã♦✲❧✐♥❡❛r❡s ❣❡♦♠étr✐❝♦s t♦r♥❛♠✲s❡ r❡❧❡✈❛♥t❡s✳ ◆♦ ❡♥t❛♥t♦✱ ♣♦r s❡ tr❛t❛r ❞❡ ❡str✉t✉r❛s ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✱ ❤á✱ ❛❞❡♠❛✐s✱ q✉❡ s❡ ❝♦♥s✐❞❡r❛r ♦ ♣r♦❝❡ss♦ ❞❡ ✜ss✉r❛çã♦ ❡♠ s✉❛ ❛♥á❧✐s❡✳ ❚❛♠❜é♠ ❡stá ❧✐❣❛❞♦ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❡♥❣❡♥❤❛r✐❛ ❡str✉t✉r❛❧✱ ❛ ❝r✐❛çã♦ ❞❡ ❢♦r♠✉❧❛çõ❡s q✉❡ ❞❡s❝r❡✈❡♠ ♦s ❢❡♥ô♠❡♥♦s ❢ís✐❝♦s q✉❡ ♦❝♦rr❡♠ ♥❛s ❡str✉t✉r❛s✱ ♦✉ s❡❥❛✱ ❛ r❡s♣♦st❛ ❞♦ s✐st❡♠❛ ❡str✉t✉r❛❧ às ❛çõ❡s ❡①t❡r♥❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ❛♣❧✐❝❛çã♦ ❞❡ss❛s ❢♦r♠✉❧❛çõ❡s ❛ ♣r♦❜❧❡♠❛s r❡❛✐s ❡stá ❛ss♦❝✐❛❞❛ à ❣❡r❛çã♦ ❞❡ s✐st❡♠❛s ❝♦♠ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ❡q✉❛çõ❡s✱ ✐♠♣♦ssí✈❡✐s ❞❡ s❡r❡♠ r❡s♦❧✈✐❞❛s ♣♦r ♣r♦❝❡ss♦s ♠❛♥✉❛✐s✳ ❉❡ss❡ ♠♦❞♦✱ ♦ ❡♠♣r❡❣♦ ❞❡ r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ ❞✐s♣♦♥í✈❡✐s✱ ♥❛ ✈❡r❞❛❞❡✱ ❞❡s❞❡ ❛ ❞é❝❛❞❛ ❞❡ ✻✵ ✭▼❛rt❤❛✱ ✷✵✶✵✮✱ tê♠ s✐❞♦ ♦ ♠❡✐♦ ♣♦ssí✈❡❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞❡ r❡s♣♦st❛s ♣r❡❝✐s❛s✱ ♠❛✐s ♣ró①✐♠❛s ❞❛ r❡❛❧✐❞❛❞❡✱ ❞❡ss❡s s✐st❡♠❛s ❡str✉t✉r❛✐s✳ ❖ ❢❛t♦ ❞❡ ♦ ❝♦♠♣✉t❛❞♦r r❡❛❧✐③❛r ✉♠ ❡❧❡✈❛❞♦ ♥ú♠❡r♦ ❞❡ ♦♣❡r❛çõ❡s ♠❛t❡♠át✐❝❛s ❡♠ ♣♦✉❝♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ t❡♠ ♣♦ss✐❜✐❧✐t❛❞♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❢♦r♠✉❧❛çõ❡s ❡ ❢❡rr❛♠❡♥t❛s ❞❡ ♣r♦❥❡t♦s ❡str✉t✉r❛✐s ♠✉✐t♦ s♦✜st✐❝❛❞❛s✳

❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✷

❋✐❣✉r❛ ✶✳✶✿ ❚✇✐♥ ❚♦✇❡rs ✲ ❑✉❛❧❛ ▲✉♠♣✉r ✲ ❈♦♥❝r❡t♦ ❞❡ ✽✵▼♣❛ ❛té ♦ ✻✵♦ _{❛♥❞❛r}

❈á❧❝✉❧♦s ♠❛✐s r✐❣♦r♦s♦s ✐♥❝❧✉❡♠ ♦♣çõ❡s ❞❡ ❝♦♥s✐❞❡r❛çã♦ ❞❛ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ❣❡♦♠étr✐❝❛ ✭◆▲●✮✱ ❞❛ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ❢ís✐❝❛ ✭◆▲❋✮ ❡ ❞❡ ❡❢❡✐t♦s ❞✐♥â♠✐❝♦s✳ ❊♠ ❡str✉t✉r❛s ❡s❜❡❧t❛s✱ ♦s ❢❡♥ô♠❡♥♦s ❞❡ ◆▲● t♦r♥❛♠✲s❡ ❜❛st❛♥t❡ r❡❧❡✈❛♥t❡s✳ ❖ ❝♦❧❛♣s♦✱ ♥❡st❡ ❝❛s♦✱ s❡ ❞á ❛♥t❡s ❞♦ ❡s❝♦❛♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧ ❞❡✈✐❞♦ ❛ ❣r❛♥❞❡s ❞❡s❧♦❝❛♠❡♥t♦s ❧❛t❡r❛✐s✳ ❆ ◆▲❋ ❡stá ❧✐❣❛❞❛ ❛♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧✱ ❡ ♠❛♥✐❢❡st❛✲s❡ ♥❛s r❡❧❛çõ❡s t❡♥sã♦✲❞❡❢♦r♠❛çã♦✱ ♦✉ t❛♠❜é♠ ♥❛s r❡❧❛çõ❡s ❢ís✐✲ ❝❛s q✉❡ ❡♥✈♦❧✈❡♠ r❡s✉❧t❛♥t❡s ❞❡ t❡♥sã♦ ❡ ❝♦rr❡s♣♦♥❞❡♥t❡s ❞❡❢♦r♠❛çõ❡s ❣❡♥❡r❛❧✐③❛❞❛s✳ ▼❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♥♦ ❝♦♥❝r❡t♦✱ ❛ ◆▲❋ ❡stá ❧✐❣❛❞❛ à ♣❡r❞❛ ❞❡ r✐❣✐❞❡③ ❞❡✈✐❞♦ à ✜ss✉r❛çã♦✱ ❛♦ ❞❡s✲ ❧✐③❛♠❡♥t♦ ❡♥tr❡ ❛r♠❛❞✉r❛ ❡ ❝♦♥❝r❡t♦✱ à ♣❧❛st✐✜❝❛çã♦ ❞♦ ❛ç♦ ❡ à ✢✉ê♥❝✐❛ ❞♦ ❝♦♥❝r❡t♦ ✭●❡❧❛tt✐✱ ✷✵✶✷✮✳

❆ ♥♦r♠❛ ❛t✉❛❧ ❞❡ ❝♦♥❝r❡t♦ ✭◆❇❘✻✶✶✽✱ ✷✵✶✹✮ ♣r❡✈ê s✐♠♣❧✐✜❝❛çõ❡s q✉❛♥t♦ à ❝♦♥s✐❞❡r❛çã♦ ❞❛s ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡s✱ ♦ q✉❡ ❞✐♠✐♥✉✐ ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♦ t❡♠♣♦ ❞❡ ❛♥á❧✐s❡ ✭❘✐❜❡✐r♦✱ ✷✵✶✻✮✳ ◆♦ ❡♥t❛♥t♦ ♣❛r❛ ❝❡rt❛s ❡str✉t✉r❛s é ❝♦♥✈❡♥✐❡♥t❡ ❛♥❛❧✐s❛r ♦ ♣r♦❜❧❡♠❛ ❝♦♠♣❧❡t❛♠❡♥t❡✱ ❝♦♠ té❝♥✐❝❛s ♥✉♠ér✐❝❛s ❝♦♠♣❧❡①❛s✱ ❡♠♣r❡❣❛♥❞♦ r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳

✶✳✷ ❖❜❥❡t✐✈♦s

❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✸

◗✉❛♥t♦ à ◆▲❋ ✐♥❝❧✉❡♠✲s❡ r❡❧❛çõ❡s ❢ís✐❝❛s q✉❡ ❞❡s❝r❡✈❡♠ ❛ ♣❡r❞❛ ❞❡ r✐❣✐❞❡③ ❛♦ ❧♦♥❣♦ ❞♦s ❡❧❡♠❡♥t♦s ❡str✉t✉r❛✐s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ sã♦ ❝♦♥s✐❞❡r❛❞❛s✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ♣❛r❛ ❛ s✐♠✉❧❛çã♦ ❞❡ ♣❡r❞❛ ❞❡ r✐❣✐❞❡③✱ t❛♥t♦ ♠♦❞❡❧♦s ❥á ❞✐❢✉♥❞✐❞♦s ♥❛ ❧✐t❡r❛t✉r❛ té❝♥✐❝❛ ✭●❤❛❧✐✱ ❋❛✈r❡ ❡ ❊❧❜❛❞r②✱ ✷✵✵✷✮ ❝♦♠♦ ❛ ❡str❛té❣✐❛ ♣r♦♣♦st❛ ❛q✉✐ ❞❡ ❡q✉✐❧í❜r✐♦ ❞✐r❡t♦ ❞❛ s❡çã♦✳ ❘❡ss❛❧t❛✲s❡✱ q✉❡ ❡ss❛s ❢♦r♠✉❧❛çõ❡s ❢♦r❛♠ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ✐♠♣❧❡♠❡♥t❛❞❛s ♥♦ ❝ó❞✐❣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ◆❆❊❙❨✲ ✷❉❢r❛♠❡✇♦r❦✱ q✉❡ ❜❛s❡✐❛✲s❡ ♥♦ ▼ét♦❞♦ ❞❡ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✭▼❘❉✮ ❡ ❞✐s♣õ❡ ❞❡ ♦♣çõ❡s ❞❡ ❛♥á❧✐s❡ q✉❡ ♣♦ss✐❜✐❧✐t❛♠ ❛ s✐♠✉❧❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ❝♦♠ r✐❣✐❞❡③ ✈❛r✐á✈❡❧✳ ◆♦t❡✲s❡ q✉❡ ❡ss❡ t✐♣♦ ❞❡ ♦♣çã♦ ❞❡ ♠♦❞❡❧❛❣❡♠ s❡rá ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ s✐♠✉❧❛r ❛ ♣❡r❞❛ ❞❡ r✐❣✐❞❡③ ❞♦ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥❝r❡t♦ ❛r♠❛❞♦ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞♦ ♣r♦❝❡ss♦ ❞❡ ✜ss✉r❛çã♦✳ ❯♠ ❡sq✉❡♠❛ ❣❡r❛❧ ❞❡ ❛♥á❧✐s❡ ♥ã♦✲❧✐♥❡❛r ❣❡♦♠étr✐❝❛ ✈✐❛ ♠ét♦❞♦ ❞❡ ◆❡✇t♦♥✲❘❛♣❤s♦♥ ❥á s❡ ❡♥❝♦♥tr❛✈❛ ✐♠♣❧❡♠❡♥t❛❞♦ ♥♦ ♣r♦❣r❛♠❛ ◆❆❊❙❨✲✷❉❢r❛♠❡✇♦r❦✱ ♦ q✉❛❧ ❢♦✐ ❝♦♠♣❧❡♠❡♥t❛❞♦ ❝♦♠ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ♣❡❧❛ ✐♥❝❧✉sã♦ ❞♦s ❡❢❡✐t♦s ❞❛ ◆▲❋✳ ❖ ♣r♦❣r❛♠❛ ◆❆❊❙❨✲✷❉❢r❛♠❡✇♦r❦ é ✉♠❛ ❜❛s❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ q✉❡ ✈❡♠ s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❆r❛ú❥♦✱ ✶✾✾✹✱ ❡ r❡❝❡❜❡♥❞♦ ❝♦♥tr✐❜✉✐çõ❡s ❞❡ ❞✐ss❡rt❛çõ❡s ❡ tr❛❜❛❧❤♦s ❞❡ ❝♦♥❝❧✉sã♦ ❞❡ ❝✉rs♦✱ ❡♥tr❡ ♦s q✉❛✐s ❝✐t❛♠✲s❡ ♦s tr❛❜❛❧❤♦s ❞❡ P❡r❡✐r❛ ✭✷✵✶✸✮✱ ▼❛❣❛ ✭✷✵✶✺✮✱ ❘✐❜❡✐r♦ ✭✷✵✶✻✮ ❡ P❡r❡✐r❛ ✭✷✵✶✺✮✳

P❛r❛ ✈❛❧✐❞❛r ❛s ❢♦r♠✉❧❛çõ❡s ❞❡s❡♥✈♦❧✈✐❞❛s ❡ ✐♠♣❧❡♠❡♥t❛❞❛s✱ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ❡①❡♠♣❧♦s ❞❡ tr❛❜❛❧❤♦s ❡①♣❡r✐♠❡♥t❛✐s ❡ ♥✉♠ér✐❝♦s✳ ❈♦♠♦ ♠❡♥❝✐♦♥❛❞♦ ❛❝✐♠❛✱ ♦ ❢♦❝♦ ❞❛s ❛♣❧✐❝❛çõ❡s s❡rá ❡str✉t✉r❛s ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦ ✭❈❆✮✳

✶✳✸ ❊str✉t✉r❛ ❞❛ ❉✐ss❡rt❛çã♦

❊st❛ ❞✐ss❡rt❛çã♦ ❝♦♥té♠ s❡✐s ❝❛♣ít✉❧♦s ❡ ❞♦✐s ❛♣ê♥❞✐❝❡s✳ ◆♦ ❝❛♣ít✉❧♦ ✷ ❞❡s❝r❡✈❡✲s❡ ❛ ❢♦r✲ ♠✉❧❛çã♦ ❞♦ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛✳ ❊st❡ ♠ét♦❞♦ ♣♦ss✐❜✐❧✐t❛ ❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ❡❧❡♠❡♥t♦s ❡str✉t✉r❛✐s ❞❡ ♣órt✐❝♦ ♣❧❛♥♦✱ ❝♦♠ r✐❣✐❞❡③ ✈❛r✐á✈❡❧ s❡❣✉♥❞♦ ❧❡✐s q✉❛✐sq✉❡r✱ ✐♥❝❧✉sã♦ ❞❡ ❡❢❡✐t♦s ❞❡ ❞❡❢♦r♠❛çã♦ ♣♦r ❝✐s❛❧❤❛♠❡♥t♦✱ ❡ s❡çõ❡s ❞❡ ❢♦r♠❛s ❣❡♦♠étr✐❝❛s q✉❛✐sq✉❡r✳ ❚❛♠❜é♠ ♥♦ ❝❛♣ít✉❧♦ ✷ é ❢❡✐t❛ ❛ ❞❡❞✉çã♦ ❞❛s ♠❛tr✐③❡s ❞❡ r✐❣✐❞❡③ ❢ís✐❝❛ ❡ ❣❡♦♠étr✐❝❛ ❞❡ ❡❧❡♠❡♥t♦✱ ❡ sã♦ ❢❡✐t❛s ♦❜s❡r✈❛çõ❡s s♦❜r❡ ❛ ♦❜t❡♥çã♦ ❞❛s ❛çõ❡s ❞❡ ❡♥❣❛st❛♠❡♥t♦ ♣❡r❢❡✐t♦✳

◆♦ ❝❛♣ít✉❧♦ ✸✱ ❛❜♦r❞❛♠✲s❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ❢ís✐❝❛ ❞♦ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✱ ❡ ❝♦♠♦ ❡st❡ ♠❛t❡r✐❛❧ s❡ ❝♦♠♣♦rt❛ s❡❣✉♥❞♦ ❞✐✈❡rs♦s t✐♣♦s ❞❡ s♦❧✐❝✐t❛çõ❡s✳ ❊♠ s❡❣✉✐❞❛✱ ❞❡s❝r❡✈❡♠✲s❡ ♠♦❞❡❧♦s ❛♥❛❧ít✐❝♦s ❞❡s❡♥✈♦❧✈✐❞♦s ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s✱ ❡ q✉❡ s❡ ♣r♦♣õ❡♠ ❛ ❞❡s✲ ❝r❡✈❡r ❛ r✐❣✐❞❡③ ❡♠ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✳ P♦r ✜♠✱ ❞❡s❝r❡✈❡♠✲s❡ ❛s ❡str❛té❣✐❛s ❞❡s❡♥✈♦❧✈✐❞❛s ❡ ✐♠♣❧❡♠❡♥t❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦✱ q✉❡ sã♦ ♦ ♠♦❞❡❧♦ ❞❡ ●❤❛❧✐✲❋❛✈r❡ ❡ ❛ ❡s✲ tr❛té❣✐❛ ❞❡ ❡q✉✐❧í❜r✐♦ ❞✐r❡t♦ ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧✳ ❆✐♥❞❛ ❢❛③✲s❡ ♦ ❡st✉❞♦ ❞♦s ❞✐❛❣r❛♠❛s ♠♦♠❡♥t♦✲❝✉r✈❛t✉r❛ ❛tr❛✈és ❞❡ ❛♣❧✐❝❛çõ❡s ♣❛r❝✐❛✐s ❝♦♠ s❡çõ❡s ♥ã♦ ✉s✉❛✐s✳

❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✹

❝♦♥tr♦❧❡ ❞❡ ❝❛r❣❛✳ ❊st❛ ❡str❛té❣✐❛ ❝♦♥s✐❞❡r❛ s✐st❡♠❛s ❞❡ r❡❢❡rê♥❝✐❛ ❝♦rr♦t❛❝✐♦♥❛✐s ❡ ❛ ♠❡s♠❛ t❛♠❜é♠ ♣♦ss✐❜✐❧✐t❛ ❞❡s❝r✐çã♦ ❞❡ r❡s♣♦st❛s ❝♦♠ ❣r❛♥❞❡s ❞❡s❧♦❝❛♠❡♥t♦s✳

◆♦ ❝❛♣ít✉❧♦ ✺✱ sã♦ ❢❡✐t❛s ❛♣❧✐❝❛çõ❡s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ✈❛❧✐❞❛r ❛s ❢♦r♠✉❧❛çõ❡s ✐♠♣❧❡♠❡♥t❛❞❛s✳ ❊st❛s ❛♣❧✐❝❛çõ❡s sã♦ ❢♦❝❛❞❛s ❡♠ ❡str✉t✉r❛s ❞❡ ❝♦♥❝r❡t♦ ❛r♠❛❞♦ ❡ ♦s r❡s✉❧t❛❞♦s sã♦ t♦❞♦s ❝♦♠♣❛r❛❞♦s ❝♦♠ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✳

❈❛♣ít✉❧♦ ✷

▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛

◆❡st❡ tr❛❜❛❧❤♦✱ ❡ss❡♥❝✐❛❧♠❡♥t❡ ♣r♦♣õ❡♠✲s❡ ❡str❛té❣✐❛s ✈♦❧t❛❞❛s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ❡str✉✲ t✉r❛s r❡t✐❝✉❧❛❞❛s ✭❡❧❡♠❡♥t♦s ❞❡ ❜❛rr❛✮✱ q✉❡ s❡ ❝❛r❛❝t❡r✐③❛♠ ♣♦r ♣♦ss✉ír❡♠ ❡❧❡♠❡♥t♦s q✉❡ tê♠ ✉♠❛ ❞✐♠❡♥sã♦ ♣r❡♣♦♥❞❡r❛♥t❡ ❡♠ r❡❧❛çã♦ às ❞❡♠❛✐s ✭❙♦r✐❛♥♦✱ ✷✵✵✺✮✳ P❛rt✐❝✉❧❛r♠❡♥t❡ ❝♦♥s✐❞❡r❛♠✲s❡ ♣órt✐❝♦s ♣❧❛♥♦s ✭✈✐❞❡ ❋✐❣✉r❛ ✷✳✶✮✱ ♦♥❞❡ ♦ ❡✐①♦ ♣r✐♥❝✐♣❛❧ ❞❡ t♦❞❛s ❛s s❡çõ❡s é ♣❡r♣❡♥❞✐❝✉❧❛r ❛♦ ♣❧❛♥♦ ❞❛ ❡str✉t✉r❛ ❡ ❛s ❛çõ❡s ❞♦ t✐♣♦ ❢♦rç❛ ❡♥❝♦♥tr❛♠✲s❡ ♥♦ ♣❧❛♥♦ ❞❛ ❡str✉t✉r❛ ❡ ❛s ❞♦ t✐♣♦ ❝❛r❣❛s✲♠♦♠❡♥t♦ sã♦ ♣❡r♣❡♥❞✐❝✉❧❛r❡s ❛♦ ♠❡s♠♦✳

❋✐❣✉r❛ ✷✳✶✿ Pórt✐❝♦ P❧❛♥♦ ✲ ❋♦♥t❡✿ ❘✐❜❡✐r♦ ✭✷✵✶✻✮

P❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ss❛ ❝❧❛ss❡ ❞❡ s✐st❡♠❛s ❡str✉t✉r❛✐s ❡♠♣r❡❣♦✉✲s❡ ♦ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛

❈❛♣ít✉❧♦ ✷✳ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✻

✭▼❘❉✮✱ ♦ q✉❛❧ ❝♦♥s✐st❡ ♥❛ ♦❜t❡♥çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ s✐st❡♠❛ ❡str✉✲ t✉r❛❧ ❛ ♣❛rt✐r ❞♦s ✈❛❧♦r❡s ❞✐r❡t♦s ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ r✐❣✐❞❡③ ❡ ❞❛s ❝❛r❣❛s ♥♦❞❛✐s ❡q✉✐✈❛❧❡♥t❡s ✭❈❧♦✉❣❤✱ ✶✾✾✵✮✳ ❖ ▼❘❉ é ✉♠❛ ❢♦r♠✉❧❛çã♦ q✉❡ ✈❡♠ s❡♥❞♦ ❡♠♣r❡❣❛❞❛ ❞❡s❞❡ ❛ ❞é❝❛❞❛ ❞❡ ✺✵ ❡ ♥♦ q✉❛❧ s❡ ❜❛s❡✐❛ q✉❛❧q✉❡r ❢♦r♠✉❧❛çã♦ ❞❡ ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✭❆r❛ú❥♦ ❡ P❡r❡✐r❛✱ ✷✵✶✼✮✳ ❊st❡ ♠ét♦❞♦ ♣♦ss✐❜✐❧✐t❛ ❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ❡❧❡♠❡♥t♦s ❡str✉t✉r❛✐s ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❝♦♠ r✐❣✐❞❡③ ✈❛r✐á✈❡❧✱ s❡❣✉♥❞♦ ❧❡✐s q✉❛✐sq✉❡r✱ ✐♥❝❧✉sã♦ ❞❡ ❡❢❡✐t♦s ❞❡ ❞❡❢♦r♠❛çã♦ ♣♦r ❝✐s❛❧❤❛♠❡♥t♦✱ ❡ ❝♦♠ s❡çõ❡s ❞❡ ❢♦r♠❛s ❣❡♦♠étr✐❝❛s q✉❛✐sq✉❡r✳ ◆❛s s❡çõ❡s s❡❣✉✐♥t❡s ❞❡st❡ ❝❛♣ít✉❧♦✱ ❛♣r❡s❡♥t❛✲s❡ ✉♠ ♣r♦❝❡ss♦ q✉❡ ♣❡r♠✐t❡ ❛ ♦❜t❡♥çã♦ ❞❛s ❡①♣r❡ssõ❡s ❡①❛t❛s ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s ❛❧❣é❜r✐❝❛s ❞❡ss❡ ♠ét♦❞♦✳

✷✳✶ ❋♦r♠✉❧❛çã♦ ▼❛tr✐❝✐❛❧

◆❡st❡ ❝❛♣ít✉❧♦✱ ❞❡s❝r❡✈❡♠✲s❡ ❛s ❡①♣r❡ssõ❡s ❣❡♥ér✐❝❛s q✉❡ s❡ ❡♠♣r❡❣❛♠ ♥❛ ♦❜t❡♥çã♦ ❞♦ s✐s✲ t❡♠❛ ❞❡ ❡q✉❛çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✭▼❘❉✮✱ ❞❛❞♦ ♣♦r

❑t✉=❢ , ✭✷✳✶✮

♦♥❞❡ ❑t é ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ t❛♥❣❡♥t❡ ❞❛ ❡str✉t✉r❛✱ ❢ ♦ ✈❡t♦r ❞❡ ❛çõ❡s ♥♦❞❛✐s ❡q✉✐✈❛❧❡♥t❡s

❡ ✉ é ♦ ✈❡t♦r ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ♥♦❞❛✐s✱ ✐♥❝ó❣♥✐t♦s ♦✉ ♣r❡s❝r✐t♦s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❑t s❡rá ♦❜t✐❞❛ ♣❡❧❛ s♦♠❛ ❞❡ ❞✉❛s ♦✉tr❛s ♠❛tr✐③❡s✱ q✉❛✐s s❡❥❛♠✱ ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③

❡❧ást✐❝❛ ✭♦✉ ❢ís✐❝❛✮✱ ❑f✱ ❡ ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❣❡♦♠étr✐❝❛✱ ❑g✳ ◆❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❢ís✐❝❛✱

✐♥❝❧✉❡♠✲s❡ ❛s r❡❧❛çõ❡s ❝♦♥st✐t✉t✐✈❛s ❞♦ ♠❛t❡r✐❛❧✱ q✉❛✐s ❡①♣r❡ss❛♠ t❛♠❜é♠ ♦s ❡❢❡✐t♦s ❞❛ ♥ã♦✲ ❧✐♥❡❛r✐❞❛❞❡ ❢ís✐❝❛ ❝♦♠♦ ❛ ❞❡❣r❛❞❛çã♦ ❞❡ r✐❣✐❞❡③ ❝♦♥❢♦r♠❡ ♦ ♥í✈❡❧ ❞❡ t❡♥sã♦ ❡♠ ♣♦♥t♦s ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧✳ ❏á ❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❣❡♦♠étr✐❝❛✱ ❑g✱ s✉r❣❡ ❞❛ ❝♦♥s✐❞❡r❛çã♦ ❞♦ ❡q✉✐❧í❜r✐♦

❞❛ ❡str✉t✉r❛ ❡♠ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❞❡❢♦r♠❛❞❛✱ ♦✉ s❡❥❛✱ ❧❡✈❛♠✲s❡ ❡♠ ❝♦♥t❛ ♦s ❝❤❛♠❛❞♦s ❡❢❡✐t♦s ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✳ P♦❞❡✲s❡ ❡♥tã♦ ❡s❝r❡✈❡r

(❑f −λ❑g)✉=❢ , ✭✷✳✷✮

s❡♥❞♦ λ ✉♠ ♥ú♠❡r♦ ❛ss♦❝✐❛❞♦ ❛♦ ✐♥❝r❡♠❡♥t♦ ❞❡ ❝❛r❣❛s ♥❛ ❡str✉t✉r❛✳

❆s ♠❛tr✐③❡s ❑f ❡ ❑g ❞❡s❝r❡✈❡♠ ❛ ❡str✉t✉r❛ ❝♦♠♦ ✉♠ t♦❞♦✱ ❡ ♣❛r❛ ♦❜tê✲❧❛s é ♥❡❝❡ssár✐♦

❈❛♣ít✉❧♦ ✷✳ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✼

❝♦❡✜❝✐❡♥t❡s ❞♦ r❡s♣❡❝t✐✈♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s✱ ❡♠ ❝❛s♦s ♥♦s q✉❛✐s ♦s ❡❧❡♠❡♥t♦s ❡str✉t✉r❛✐s ❛♣r❡s❡♥t❡♠ ❝❛r❛❝t❡ríst✐❝❛s ❢ís✐❝❛s ❡ ❣❡♦♠étr✐❝❛ q✉❛✐sq✉❡r✳

✷✳✷ ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❢ís✐❝❛ ❞❡ ❡❧❡♠❡♥t♦ ❞♦ ♣órt✐❝♦ ♣❧❛♥♦

✭

K

✮

❆♣r❡s❡♥t❛✲s❡ ❣❡♥❡r✐❝❛♠❡♥t❡✱ ♥❡st❛ s❡çã♦✱ ❛ ❢♦r♠❛ ❞❡ ♦❜t❡♥çã♦ ❞❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❢ís✐❝❛ ✭♦✉ ❡❧ást✐❝❛✮ ❞❡ ❡❧❡♠❡♥t♦ ❞♦ ♣órt✐❝♦ ♣❧❛♥♦✳ ◆❡st❡ ♣r♦❝❡ss♦ é ♣♦ssí✈❡❧ ❝♦♥s✐❞❡r❛r ❛ ❞❡❣r❛❞❛çã♦ ❞❛ r✐❣✐❞❡③ ❞❡✈✐❞♦ ❛ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ❢ís✐❝❛ ❡♠ s✐t✉❛çõ❡s q✉❛✐sq✉❡r✱ ✐♥❝❧✉s✐✈❡ ❡♠ ❡❧❡♠❡♥t♦s ❡♠ ❝♦♥❝r❡t♦ ❛r♠❛❞♦✱ ♦♥❞❡✱ ❞❡✈✐❞♦ à ✜ss✉r❛çã♦✱ ♥ã♦ é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❛ r✐❣✐❞❡③ ♣❡❧♦ ❝á❧❝✉❧♦ ❞✐r❡t♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❣❡♦♠étr✐❝❛s ❞❛ s❡çã♦✳ P❛r❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❢♦r♠✉❧❛çã♦✱ ❝♦♥s✐❞❡r❛✲s❡ ♦ ❡❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✷✳

❋✐❣✉r❛ ✷✳✷✿ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦

❆s ❡q✉❛çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ♣❛r❛ ❡ss❡ ❡❧❡♠❡♥t♦ sã♦ ❞❛❞❛s ♣♦r

    

P

Fx1 =f1+f4+F10= 0

P

Fx2 =f2+f5+F20= 0

P

Fx3 =f3+f6−f2·l+F30 = 0

, ✭✷✳✸✮

s❡♥❞♦ fi ❛s ❛çõ❡s ❞❡ ❡①tr❡♠✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦ (i= 1, . . . ,6)✱l é ♦ ❝♦♠♣r✐♠❡♥t♦ ❞♦ ❡❧❡♠❡♥t♦✱

❈❛♣ít✉❧♦ ✷✳ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✽

❢♦rç❛s✱ r❡s✉❧t❛♠ ❛♣❡♥❛s três ❡q✉❛çõ❡s✱ ♠❛s ❤á s❡✐s ✐♥❝ó❣♥✐t❛s ❛ s❡r❡♠ ❞❡t❡r♠✐♥❛❞❛s✳ ❆♣❧✐❝❛✲ s❡ ❡♥tã♦ ♦ Pr✐♥❝í♣✐♦ ❞❛s ❋♦rç❛s ❱✐rt✉❛✐s ✭P❋❱✮ ♣❛r❛ ❝♦♠♣❧❡t❛r ♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s✱ ❡ ❡st❛❜❡❧❡❝❡♠✲s❡ ❛ss✐♠ ❛s s❡❣✉✐♥t❡s ❡q✉❛çõ❡s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦✿

fiui =

Z

l

Midθ+

Z

l

Nidδ+

Z

l

Qidλ , ✭✷✳✹✮

❡♠ q✉❡ ui sã♦ ♦s ❞❡s❧♦❝❛♠❡♥t♦s q✉❡ s❡ ❞❡s❡❥❛♠ ❝❛❧❝✉❧❛r✱dθ✱dδ ❡ dλ sã♦ r❡s♣❡❝t✐✈❛♠❡♥t❡ ♦s

❞❡s❧♦❝❛♠❡♥t♦s ✢❡①✐♦♥❛❧✱ ❛①✐❛❧ ❡ tr❛♥s✈❡rs❛❧ r❡❧❛t✐✈♦s ❡♠ ✉♠❛ s❡çã♦ ❞♦ ❡❧❡♠❡♥t♦✱ ❡ Mi✱Ni✱ ❡

Q_i sã♦ ♦s ❝♦rr❡s♣♦♥❞❡♥t❡s ❡s❢♦rç♦s ✐♥t❡r♥♦s ✭♠♦♠❡♥t♦ ✢❡t♦r✱ ❢♦rç❛ ♥♦r♠❛❧ ❡ ❢♦rç❛ ❝♦rt❛♥t❡✮ ❞❡✈✐❞♦s ❛♦ ❡st❛❞♦ ❞❡ ❝❛rr❡❣❛♠❡♥t♦ ✈✐rt✉❛❧ ❞❡✜♥✐❞♦ ♣♦r fi = 1✱ ♦✉ s❡❥❛✱

Mi =Mi(fi) , Ni =Ni(fi) , Qi =Qi(fi) . ✭✷✳✺✮

◆♦t❡ q✉❡ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞❛s ❡q✉❛çõ❡s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡✱ ❡s❝r❡✈❡✲s❡ ❛ r❡❧❛çã♦ ✷✳✹ ♣❛r❛ ♣♦♥t♦s ❡ ❞✐r❡çõ❡s ❡♠ q✉❡ ♦s ❞❡s❧♦❝❛♠❡♥t♦s s❡❥❛♠ ❝♦♥❤❡❝✐❞♦s ✭♣r❡s❝r✐t♦s✮✳

◗✉❛♥❞♦ ♦ ♠❛t❡r✐❛❧ s❡ ❝♦♠♣♦rt❛ s❡❣✉♥❞♦ ❛ ❧❡✐ ❞❡ ❍♦♦❦❡✱ ❧✐♥❡❛r♠❡♥t❡✱ ♣♦❞❡✲s❡ ❡s❝r❡✈❡r✱

dθ =ψds = M

EIds ✭✷✳✻✮

dδ =εods=

N

EAds ✭✷✳✼✮

dλ = Q

GAs

ds ✭✷✳✽✮

◆♦ ❡♥t❛♥t♦✱ ♦❜❥❡t✐✈❛✲s❡✱ ♥❡st❡ tr❛❜❛❧❤♦✱ ❝♦♥s✐❞❡r❛r ❛ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧✱ ❡ ❝♦♠♦ ❞✐t♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛ ✜ss✉r❛çã♦ q✉❡ ♦❝♦rr❡ ♥♦ ❝♦♥❝r❡t♦ ✐♠♣♦ss✐❜✐❧✐t❛ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ✉♠❛ ❣❡♦♠❡tr✐❛ ❜❡♠ ❞❡✜♥✐❞❛ ❛♦ ❧♦♥❣♦ ❞♦ ❡❧❡♠❡♥t♦✳ ❙❡♥❞♦ ❛ss✐♠✱ ♥ã♦ s❡rá ♣♦ssí✈❡❧ ❝❛❧❝✉❧❛r ❛s r✐❣✐❞❡③❡s ❡♠ ✉♠❛ ❝❡rt❛ s❡çã♦ ❞♦ ❡❧❡♠❡♥t♦ ❡♠ t❡r♠♦s ❞❡ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ❣❡♦♠étr✐❝❛s ✭A✱ As ❡ I✮✱ ❡ ♣♦rt❛♥t♦ ❡s❝r❡✈❡♠✲s❡ ❛s r❡❧❛çõ❡s ✷✳✻✱ ✷✳✼ ❡ ✷✳✽ ❝♦♠♦

dθ=ψds = M kb

ds , ✭✷✳✾✮

dδ =εods=

N ka

ds , ✭✷✳✶✵✮

dλ= Q ks

ds , ✭✷✳✶✶✮

❈❛♣ít✉❧♦ ✷✳ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✾

❯t✐❧✐③❛♥❞♦ ❛s ❊q✉❛çõ❡s ✷✳✸✱ ✷✳✹ ❡ ✷✳✺✱ ❡ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ❞♦✐s s✐st❡♠❛s ❞❡ ❛♥á❧✐s❡ ♠♦str❛❞♦s ♥❛s ❋✐❣✉r❛s ✷✳✸ ❡ ✷✳✹✱ ❞❡s✐❣♥❛❞♦s ❝♦♠♦ s✐st❡♠❛s ■ ❡ ■■✱ ♦❜tê♠✲s❡ ♦s s✐st❡♠❛s ❞❡ ❡q✉❛çõ❡s ❛❧❣é❜r✐❝❛s q✉❡ ♣♦ss✐❜✐❧✐t❛♠ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ r✐❣✐❞❡③ ❡ ❛çõ❡s ❞❡ ❡♥❣❛st❛♠❡♥t♦ ♥♦s ❝❛s♦s ♠❛✐s ❣❡r❛✐s ♣♦ssí✈❡✐s✳ P❛r❛ s❡ ❝❤❡❣❛r ♣♦ré♠ ❛ ❡ss❡s s✐st❡♠❛s✱ ❡①♣r❡ss❛♠✲s❡✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ❛s ❢✉♥çõ❡s ❞❡ ❡s❢♦rç♦s s✐♠♣❧❡s ♥♦ ❡❧❡♠❡♥t♦ ❡♠ t❡r♠♦s ❞❛s ❛çõ❡s ✐♥❝ó❣♥✐t❛s✱ fi✱ i = 1,2,3✱

❡ ❞♦ ❝❛rr❡❣❛♠❡♥t♦ ❡①t❡r♥♦ ✭❛q✉✐ ❣❡♥❡r✐❝❛♠❡♥t❡ r❡♣r❡s❡♥t❛❞♦ ♣♦r q✮✱ s✉❜st✐t✉❡♠✲s❡ ❡ss❛s ❡①♣r❡ssõ❡s ♥❛s r❡❧❛çõ❡s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ❞❛❞❛s ❡♠ ✷✳✾✱ ✷✳✶✵ ❡ ✷✳✶✶ ❡✱ ✜♥❛❧♠❡♥t❡✱ ❡s❝r❡✈❡♠✲ s❡ ❛s ❡q✉❛çõ❡s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ♣❡rt✐♥❡♥t❡s ❛ ♣❛rt✐r ❞❡ ✷✳✹✳ P❛r❛ ❝❛❞❛ ✉♠ ❞♦s s✐st❡♠❛s ❞❡ ❛♥á❧✐s❡ ■ ❡ ■■✱ ♦❜tê♠✲s❡ ❡♥tã♦ ❛s ❡①♣r❡ssõ❡s ❡①♣❧í❝✐t❛s ❞❡ss❡s s✐st❡♠❛s ❞❡ ❡q✉❛çõ❡s✱ ♠♦str❛❞❛s ❛ s❡❣✉✐r✳

❈❛s♦ ■✿ u4 = u5 =u6 = 0 ✭❡♥❣❛st❡ ♥♦ s❡❣✉♥❞♦ ♥ó✮ ◆❡st❡ ❝❛s♦✱ ♦s ❞❡s❧♦❝❛♠❡♥t♦s r❡❧❛t✐✈♦s

❋✐❣✉r❛ ✷✳✸✿ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❝♦♠ ♦ s❡❣✉♥❞♦ ♥ó r❡str✐♥❣✐❞♦

✭❊q✉❛çõ❡s ✷✳✾✕✷✳✶✶✮ ❡♠ ❞❛❞❛ s❡çã♦ ♣♦❞❡♠ s❡r ❡s❝r✐t♦s ♥❛ ❢♦r♠❛

dθ = 3 X j=1 Mj kb

ds+M

I

0

kb

ds , ✭✷✳✶✷✮

dδ = 3 X j=1 Nj ka

ds+N

I

0

ka

ds , ✭✷✳✶✸✮

dλ = 3 X j=1 Qj ks

ds+Q

I

0

ks

ds , ✭✷✳✶✹✮

q✉❡ s✉❜st✐t✉í❞❛s ♥❛ ❊q✉❛çã♦ ✷✳✹ ❢♦r♥❡❝❡♠

ui =

3

X

j=1

Z

l

MiMj

kb

ds+

Z

l

NiNj

ka

ds+

Z

l

QiQj

ks

ds

+ui0 , i= 1,2,3 ✭✷✳✶✺✮

♦♥❞❡Mi =M(fi)✱Ni =N(fi)✱Qi =Q(fi)❞❡♥♦t❛♠ ❛s ❢✉♥çõ❡s ❞❡ ❡s❢♦rç♦s s✐♠♣❧❡s ❞❡✈✐❞❛s às

❈❛♣ít✉❧♦ ✷✳ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✶✵

❞❛ ❝❛r❣❛ ❞❡ ❡❧❡♠❡♥t♦✱ q✱ ❞❛❞♦ ♣♦r

ui0 =

Z

l

MiM( I) 0 kb ds+ Z l

NiN( I) 0 ka ds+ Z l

QiQ

(I) 0

ks

ds, i= 1,2,3 ✭✷✳✶✻✮

❝♦♠ M₀(I)=M(q)✱ N₀(I) =N(q)✱ Q(₀I) =Q(q)✳

❉❡♥♦t❛♥❞♦✲s❡ ❛s ❛çõ❡s ✐♥❝ó❣♥✐t❛s ❝♦♠ ✷ í♥❞✐❝❡s✱ ♣♦r ❡①❡♠♣❧♦✱ ♥❛ ❢♦r♠❛ fik ✭✈✐❞❡ ❋✐❣✉r❛s ✷✳✸

❡ ✷✳✹✮✱ ♦♥❞❡ ♦ s❡❣✉♥❞♦ í♥❞✐❝❡ ❞❛ ✈❛r✐á✈❡❧ ❡①♣r✐♠❡ ❛ ❝❛✉s❛ q✉❡ ❣❡r❛ ❛s ❛çõ❡s ✭❞❡s❧♦❝❛♠❡♥t♦s ♣r❡s❝r✐t♦s ♦✉ ❝❛r❣❛ ❞❡ ❡❧❡♠❡♥t♦✮✱ ❛ ❡①♣r❡ssã♦ ✐♥t❡❣r❛❧ ♥❛ ❊q✉❛çã♦ ✷✳✶✺ ❛ss♦❝✐❛❞❛ ❛ ✉♠ ❝❡rt♦ í♥❞✐❝❡ j ♣♦❞❡ s❡r ❡s❝r✐t❛ ♥❛ ❢♦r♠❛

Z

l

MiMj

kb

ds+

Z

l

NiNj

ka

ds+

Z

l

QiQj

ks

ds=aikfik , ✭✷✳✶✼✮

❡♠ q✉❡ aik é ♦ ❝♦❡✜❝✐❡♥t❡ q✉❡ r❡s✉❧t❛ q✉❛♥❞♦ ❡✈✐❞❡♥❝✐❛✲s❡ ❛ ❛çã♦ fik✳ ❆ss✐♠✱ ❡♠ ❢♦r♠❛

♠❛tr✐❝✐❛❧✱ ❡①♣r❡ss❛✲s❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡q✉❛çõ❡s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ♣♦r

❆II❢Ik =✉Ik−✉I0 , k = 1,2,3, ✭✷✳✶✽✮

♦♥❞❡ ♦ s✉❜s❝r✐t♦ I ❞❡♥♦t❛ ♦ ❝❛s♦ ■ ✭❝♦♠ ❡♥❣❛st❡ ♥♦ s❡❣✉♥❞♦ ♥ó✮✳ ❊①♣❧✐❝✐t❛♠❡♥t❡✱ ❛ ♠❛tr✐③ ❆II é ❞❛❞❛ ♣♦r

❆II =

   R l 1

kadx1 0 0

0 R_lx21

kb + 1

ksdx1

R

l− x1

kadx1

0 R_l−x1

kbdx1

R

l

1

kbdx1

 

 , ✭✷✳✶✾✮

♦♥❞❡ s❡✉s ❝♦❡✜❝✐❡♥t❡ sã♦ ♦❜t✐❞♦s ❞❛ ❡①♣r❡ssã♦ ✷✳✶✼✳ ❊s❝r❡✈❡♥❞♦✲s❡✱ ♣♦r ✜♠✱ ❛s ❡q✉❛çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ✷✳✸ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ❡q✉❛çõ❡s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ✷✳✶✽✱ ♦❜té♠ ♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s ❛❧❣é❜r✐❝❛s

"

❊II ❊IF

❆II 0

# "

❢Ik

❢F k

#

=

"

❋0

✉Ik−✉I0

#

, k = 1,2,3, ✭✷✳✷✵✮

s❡♥❞♦✱

❊II =

  

1 0 0

0 1 0

0 −l 1

 

,❊IF =

  

1 0 0 0 1 0 0 0 1

  ,❢Ik =

  

f1k

f2k

f3k

 

,❢F k =

  

f4k

f5k

f6k

 

,✉Ik =

  

u1k

u2k

u3k

   .

❈❛♣ít✉❧♦ ✷✳ ▼ét♦❞♦ ❞❛ ❘✐❣✐❞❡③ ❉✐r❡t❛ ✶✶

❘❡ss❛❧t❛✲s❡ q✉❡ ❡♠ ✷✳✷✵fIk❡fF k ❝♦♥tê♠ ♦✉ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ✭s♦❧✉çã♦ ♣❛r❛

❞❡s❧♦❝❛♠❡♥t♦s ✉♥✐tár✐♦s ♣r❡s❝r✐t♦s✮ ♦✉ ❛s ❛çõ❡s ♥♦❞❛✐s ❡q✉✐✈❛❧❡♥t❡s ✭s♦❧✉çã♦ ♣❛r❛ ❝❛r❣❛s ❞❡ ♠❡♠❜r♦ ❝♦♠ ❞❡s❧♦❝❛♠❡♥t♦s ♥♦❞❛✐s ♥✉❧♦s✮✳

❈❛s♦ ■■✿ u1 =u2 =u3 = 0 ✭❡♥❣❛st❡ ♥♦ ♣r✐♠❡✐r♦ ♥ó✮

❋✐❣✉r❛ ✷✳✹✿ ❊❧❡♠❡♥t♦ ❞❡ ♣órt✐❝♦ ♣❧❛♥♦ ❝♦♠ ♦ ♣r✐♠❡✐r♦ ♥ó r❡str✐♥❣✐❞♦

P❛r❛ ♦ ❝❛s♦ ■■✱ ❞❡ ❢♦r♠❛ ❛♥á❧♦❣❛ ❛♦ ❝❛s♦ ■✱ ❡s❝r❡✈❡✲s❡

ui =

3

X

j=1

Z

l

MiMj

kb

ds+

Z

l

NiNj

ka

ds+

Z

l

QiQj

ks

ds

) +ui0 , i= 4,5,6 ✭✷✳✷✷✮

uF0 =

Z

l

MiM

(F) 0

kb

ds+

Z

l

NiN

(F) 0

ka

ds+

Z

l

QiQ

(F) 0

ks

ds , i= 4,5,6 ✭✷✳✷✸✮

❝♦♠ M₀(F) =M(q)✱ N₀(F)=N(q) ❡ Q(₀F) =Q(q)✳ ❈♦♠♦ ♥♦ ❝❛s♦ ■✱ ❡①♣r❡ss❛✲s❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡q✉❛çõ❡s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ✷✳✷✷ ❡♠ ❢♦r♠❛ ♠❛tr✐❝✐❛❧ ♣♦r

❆F F❢F k =✉F k −✉F0 , ✭✷✳✷✹✮

♦♥❞❡ s❡✉s ❝♦❡✜❝✐❡♥t❡ sã♦ ♦❜t✐❞♦s ❞❛ ❡①♣r❡ssã♦ ✷✳✷✷✱ ❛♣ós ✐s♦❧❛♠❡♥t♦ ❞♦s t❡r♠♦s ❛ss♦❝✐❛❞♦s ❛ ✉♠❛ ❝❡rt❛ ❛çã♦fik✱ ❡①❛t❛♠❡♥t❡ ❝♦♠♦ ❢❡✐t♦ ♥♦ ❝❛s♦ ■✳ ❉♦ ♠❡s♠♦ ♠♦❞♦✱ ♦❜té♠✲s❡ ♦ s✐st❡♠❛

❞❡ ❡q✉❛çõ❡s ❛❧❣é❜r✐❝❛s

"

❊II ❊IF

0 ❆F F

# "

❢Ik

❢F k

#

=

"

−❋0

✉F k −✉F0

#

, k = 4,5,6, ✭✷✳✷✺✮

❢Ik =

  

f1k

f2k

f3k

 

,❢F k =

  

f4k

f5k

f6k

 

,✉F k =

  

u4k

u5k

u6k

 