▼❛✐♦ ❞❡ ✷✵✶✽
❉✐♦❣♦ ❘♦❞r✐❣✉❡s ❆❧✈❡s
▲✐❝❡♥❝✐❛❞♦ ❡♠ ❈✐ê♥❝✐❛s ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧❉❡t❡r♠✐♥❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡
r❡s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ❞❡ ♣❡r✜s
♠❡tá❧✐❝♦s t✉❜✉❧❛r❡s ❛tr❛✈és ❞❡
❆♥á❧✐s❡ ▲✐♠✐t❡
❉✐ss❡rt❛çã♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ✲ P❡r✜❧ ❞❡ ❊str✉t✉r❛s
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉♦✉t♦r ▼ár✐♦ ❱✐❝❡♥t❡ ❞❛ ❙✐❧✈❛
❏úr✐✿
Pr❡s✐❞❡♥t❡✿ Pr♦❢✳ ❉♦✉t♦r ❈♦r♥❡❧✐✉ ❈✐s♠❛s✐✉
❉❡t❡r♠✐♥❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ❞❡ ♣❡r✜s ♠❡tá❧✐❝♦s t✉✲ ❜✉❧❛r❡s ❛tr❛✈és ❞❡ ❆♥á❧✐s❡ ▲✐♠✐t❡
❈♦♣②r✐❣❤t ➞ ❉✐♦❣♦ ❘♦❞r✐❣✉❡s ❆❧✈❡s✱ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛
❆❣r❛❞❡❝✐♠❡♥t♦s
●♦st❛r✐❛ ❞❡ ❡①♣r❡ss❛r ♦ ♠❡✉ ❛❣r❛❞❡❝✐♠❡♥t♦ ❛ ❛❧❣✉♠❛s ♣❡ss♦❛s✱ q✉❡ s❡♠ ♦ s❡✉ ❝♦♥tr✐❜✉t♦ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧ ❛ r❡❛❧✐③❛çã♦ ❞❡st❛ t❡s❡✳
❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ q✉❡r♦ ❛❣r❛❞❡❝❡r à ♣❡ss♦❛ q✉❡ ♠❛✐s ❝♦♥tr✐❜✉✐✉ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢❡ss♦r ❉♦✉t♦r ▼ár✐♦ ❱✐❝❡♥t❡ ❞❛ ❙✐❧✈❛✱ ♣♦r t♦❞♦s ♦s ❝♦♥❤❡✲ ❝✐♠❡♥t♦s q✉❡ ♠❡ tr❛♥s♠✐t✐✉✱ ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ❢❛❝✉❧t❛❞❛✱ ❡ ♣❡❧❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❢♦r♥❡❝✐❞❛✳ ❙❡♠♣r❡ ❛❞♠✐r❡✐ ♦s s❡✉s ♠ét♦❞♦s ❞❡ tr❛❜❛❧❤♦✱ ♦ s❡✉ r✐❣♦r✱ ❛ s✉❛ ♦r❣❛♥✐③❛çã♦ ❡ ❛ ❣r❛♥❞❡ q✉❛❧✐❞❛❞❡ q✉❡ t❡♠ ❡♠ s✐♠♣❧✐✜❝❛r ♣r♦❜❧❡♠❛s✳ ❖ ♠❡✉ s✐♥❝❡r♦ ♦❜r✐❣❛❞♦ ♣♦r t♦❞❛s ❛s ❝♦♠♣❡✲ tê♥❝✐❛s q✉❡ ♠❡ tr❛♥s♠✐t✐✉✱ ❥✉st✐✜❝❛♥❞♦ ❛ss✐♠✱ ♦ ♠♦t✐✈♦ ❞❛ ♠✐♥❤❛ ❡s❝♦❧❤❛✳ ❚r❛❜❛❧❤❛r ❝♦♠ ♣❡ss♦❛s ❝♦♠♣❡t❡♥t❡s✱ t♦r♥❛ ♦ ❝❛♠✐♥❤♦ ♠❛✐s ❢á❝✐❧✳
❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ q✉❡ ❞❡ ❢♦r♠❛ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛ ♠❡ ❛✉①✐❧✐❛r❛♠ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ ♠❡✉ ♣❡r❝✉rs♦ ❛❝❛❞é♠✐❝♦✳
❆♦s ♠❡✉s ♣❛✐s ♣❡❧❛ ❡①❝❡❧❡♥t❡ ❡❞✉❝❛çã♦ ❡ ♣♦r ♠❡ t❡r❡♠ ❞❛❞♦ ❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ❝♦♥❝r❡t✐③❛r ♦s ♠❡✉s ♦❜❥❡t✐✈♦s ❛❝❛❞é♠✐❝♦s✳ ❆♦ ♠❡✉ ✐r♠ã♦ ❡ ❝♦♥s❡❧❤❡✐r♦ ♥❛s ❛❧t✉r❛s ❝❡rt❛s✳ ➚ ❆♥❛ ♣❡❧♦ ❛♠♦r ❡ ♣❛❝✐ê♥❝✐❛ q✉❡ t❡✈❡ ❞❡s❞❡ ♦ ♣r✐♠❡✐r♦ ❞✐❛✱ ❡ ♣❡❧♦s ♠♦♠❡♥t♦s ♣r♦♣♦r❝✐✲ ♦♥❛❞♦s ♥❛s ❤♦r❛s ❞❡ ❞❡s❝❛♥s♦✳ ❆♦ PP✱ ▼❛♥❣✉❛❧❞❡✱ ▼❛❧❛❢❛✐❛✱ ●✐❧✱ ❱❛s❝♦ ❡ ▼✐❣✉❡❧ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦ ❡ ♣❡❧❛ ❛♠✐③❛❞❡✳
❆♦ ❆♥❞ré ❡ ❛♦ ❈♦✉t♦ ♣❡❧❛s ❧♦♥❣❛s ❤♦r❛s ❞❡ ❝♦♠♣❛♥❤✐❛ ❞❡❞✐❝❛❞❛s ❛ ❡st❡ tr❛❜❛❧❤♦✳ ❆♦s ♠❡✉s ❝♦❧❡❣❛s PP✱ ❱❛s❝♦✱ ❉✉❛rt❡✱ ◆✉♥♦ ❏♦ã♦✱ ❏♦❛♥❛✱ ❋r❡❞ ♣♦r t♦❞♦s ♦s ❜♦♥s ♠♦♠❡♥t♦s ♣❛ss❛❞♦s ♥❛ ❢❛❝✉❧❞❛❞❡✳ ➚ ❈❧á✉❞✐❛ ♣♦rq✉❡ ♠❡ ♣❡❞✐✉✳
❊ ❡♠ ❡s♣❡❝✐❛❧ à ♠✐♥❤❛ ❇♦♥❡❝❛✳
❘❡s✉♠♦
◆❡st❛ ❞✐ss❡rt❛çã♦ ♣r❡t❡♥❞❡✲s❡ ❡st✉❞❛r ❛ ❛❞❡q✉❛❜✐❧✐❞❛❞❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞♦ t❡♦r❡♠❛ ❈✐♥❡✲ ♠át✐❝♦ ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ❞❡ ♣❡r✜s ♠❡tá❧✐❝♦s t✉❜✉❧❛r❡s✳
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❛♥❛❧✐s❛ ❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ♠❡tá❧✐❝❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❝✐r❝✉❧❛r✱ ❞❛♥❞♦✲s❡ ♣❛rt✐❝✉❧❛r r❡❧❡✈♦ às ❥✉♥t❛s ❞♦ t✐♣♦ ❑✱ ◆✱ ❳ ❡ ❚ s✉❥❡✐t❛s ❛ ❝❛r❣❛s ❛①✐❛✐s✳ ❆ ❛♥á❧✐s❡ é ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦ ♦ ♣r♦❣r❛♠❛ ♠❡❝❤♣②✱ q✉❡ r❡❝♦rr❡ ❛ ✉♠❛ ❢♦r♠✉❧❛çã♦ ♥ã♦✲ ❝♦♥✈❡♥❝✐♦♥❛❧ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ❜❛s❡❛❞❛ ♥♦ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦ q✉❡ ♣❡r♠✐t❡ ♦❜t❡r ♦s ❧✐♠✐t❡s s✉♣❡r✐♦r❡s ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦✳ ❊st❡ ❡st✉❞♦ ♣r❡t❡♥❞❡ ♠♦str❛r ♦ ♣♦t❡♥❝✐❛❧ ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ♣r❡✈❡r ❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ♠❡tá❧✐❝❛s t✉❜✉❧❛r❡s✱ ❡ ♠♦str❛r ❛ ❣r❛♥❞❡ ✈❡rs❛t✐❧✐❞❛❞❡ ❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝á❧❝✉❧♦ ❞❛ ❢❡rr❛♠❡♥t❛ ♥✉♠ér✐❝❛ ✉t✐❧✐③❛❞❛✳
P❛r❛ ❛ ❛♥á❧✐s❡ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❛s ❥✉♥t❛s ♠❡tá❧✐❝❛s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ✈ár✐♦s t❡st❡s ♥✉♠ér✐❝♦s r❡♣r♦❞✉③✐♥❞♦ ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ❝♦♥❞✉③✐❞♦s ♣♦r ♦✉tr♦s ❛✉t♦r❡s✱ ❞✐s♣♦♥í✈❡✐s ♥❛ ❧✐t❡r❛t✉r❛✳ ❆s ❥✉♥t❛s sã♦ s✐♠✉❧❛❞❛s ❛tr❛✈és ❞❡ ♠♦❞❡❧♦s ✸❉ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❡ é ❢❡✐t♦ ♦ ❞❡✈✐❞♦ ❡st✉❞♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ❞❛s ❞✐❢❡r❡♥t❡s ♠❛❧❤❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❝❛❞❛ ❡♥s❛✐♦✱ ❛✉♠❡♥t❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ♥❛s ③♦♥❛s ♦♥❞❡ ❡r❛ ❡①♣❡❝tá✈❡❧ ✉♠❛ ♠❛✐♦r ❝♦♥❝❡♥tr❛çã♦ ❞❛ ❞✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ♥❛ ❢♦r♠❛çã♦ ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦✳
❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s sã♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✱ ❡ ❝♦♠ ❛s ❝❛r❣❛s ú❧t✐♠❛s ❢♦r♥❡❝✐❞❛s ♣❡❧❛s ♣r❡s❝r✐çõ❡s ❞♦ ❊✉r♦❝ó❞✐❣♦ ✸ ❡ ❝♦♠ ❛s r❡❝♦♠❡♥❞❛çõ❡s ❈■❉❊❈❚✱ ❞❡ ♠♦❞♦ ❛ ❞❡♠♦♥str❛r q✉❡ ❛ ❢❡rr❛♠❡♥t❛ ❞❡ ❝á❧❝✉❧♦ ✉t✐❧✐③❛❞❛ r❡✈❡❧❛ ✉♠❛ ❣r❛♥❞❡ ✈❡rs❛t✐❧✐❞❛❞❡✱ ♣❡r♠✐t✐♥❞♦ ♦❜t❡r ❡st✐♠❛t✐✈❛s ❞❡ ❡❧❡✈❛❞❛ q✉❛❧✐❞❛❞❡ ♣❛r❛ ♣r♦❜❧❡♠❛s ❞❡st❡ t✐♣♦✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❏✉♥t❛s ♠❡tá❧✐❝❛s✱ P❡r✜s t✉❜✉❧❛r❡s ❝✐r❝✉❧❛r❡s ✭❈❍❙✮✱ ❊❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ ❆♥á❧✐s❡ ▲✐♠✐t❡✱ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦
❆❜str❛❝t
❚❤✐s t❤❡s✐s ✐♥t❡♥❞s t♦ st✉❞② t❤❡ s✉✐t❛❜✐❧✐t② ♦❢ t❤❡ ✉s❡ ♦❢ ▲✐♠✐t ❆♥❛❧②s✐s t❤❡♦r❡♠s ♦❢ t❤❡ P❧❛st✐❝✐t② ❚❤❡♦r② ✐♥ t❤❡ ❞❡t❡r♠✐♥❛t✐♦♥ ♦❢ t❤❡ r❡s✐st❛♥t ❝❛♣❛❝✐t② ♦❢ t✉❜✉❧❛r ♠❡t❛❧ ❥♦✐♥ts✳ ❚❤❡ ♣r❡s❡♥t ✇♦r❦ ❛♥❛❧②③❡s t❤❡ r❡s✐st❛♥t ❝❛♣❛❝✐t② ♦❢ t✉❜✉❧❛r ❝✐r❝✉❧❛r ❤♦❧❧♦✇ s❡❝t✐♦♥ ✭❈❍❙✮ ♠❡t❛❧ ❥♦✐♥ts✱ ✇✐t❤ ❡♠♣❤❛s✐s ♦♥ ❑✱ ◆✱ ❳ ❛♥❞ ❚ ❥♦✐♥t t②♣❡s✱ ✉♥❞❡r ❛①✐❛❧ ❧♦❛❞s✳ ❚❤✐s ❛♥❛❧②s✐s ✐s ♠❛❞❡ ✇✐t❤ t❤❡ ♠❡❝❤♣② t♦♦❧✱ ✇❤✐❝❤ ✉s❡s ❛♥ ✉♥❝♦♥✈❡♥t✐♦♥❛❧ ❢♦r♠✉❧❛t✐♦♥ ♦❢ ✜♥✐t❡ ❡❧❡♠❡♥ts ❢♦r ▲✐♠✐t ❆♥❛❧②s✐s ❞❡r✐✈❡❞ ✇✐t❤✐♥ t❤❡ ❦✐♥❡♠❛t✐❝❛❧ t❤❡♦r❡♠ t❤❛t ❛❧❧♦✇s t♦ ♦❜t❛✐♥ t❤❡ ✉♣♣❡r ❜♦✉♥❞s ♦❢ t❤❡ ❝♦❧❧❛♣s❡ ❧♦❛❞s✳ ❚❤✐s st✉❞② ❛✐♠s t♦ ❡♠♣❤❛s✐③❡ t❤❡ ♣♦t❡♥t✐❛❧ ♦❢ ▲✐♠✐t ❆♥❛❧②s✐s ❛s t❤❡ t❤❡♦r❡t✐❝❛❧ ❜❛s✐s ❢♦r t❤❡ ♣r❡❞✐❝t✐♦♥ ♦❢ t❤❡ r❡s✐st✐♥❣ ❝❛♣❛❝✐t② ♦❢ t✉❜✉❧❛r ♠❡t❛❧ ❥♦✐♥ts ❛♥❞ t♦ s❤♦✇ t❤❡ ❣r❡❛t ✈❡rs❛t✐❧✐t② ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ❝❛♣❛❝✐t② ♦❢ t❤❡ ♥✉♠❡r✐❝❛❧ t♦♦❧ ✉s❡❞✳ ❋♦r t❤❛t ♣✉r♣♦s❡✱ s❡✈❡r❛❧ ♥✉♠❡r✐❝❛❧ t❡sts ✇❡r❡ ❝♦♥❞✉❝t❡❞ ✇✐t❤ ♠❡❝❤♣②✱ r❡♣r♦❞✉❝✐♥❣ ❡①✲ ♣❡r✐♠❡♥t❛❧ t❡sts ❝♦♥❞✉❝t❡❞ ❜② ♦t❤❡r ❛✉t❤♦rs✱ ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳ ❚❤❡ ❥♦✐♥ts ❛r❡ s✐♠✉❧❛t❡❞ t❤r♦✉❣❤ ✸❉ ♠♦❞❡❧s ♦❢ ✜♥✐t❡ ❡❧❡♠❡♥ts✱ ✐t ✐s ♣❡r❢♦r♠❡❞ ❛♥ ❡①t❡♥s✐✈❡ st✉❞② ♦❢ t❤❡ ❝♦♥✈❡r❣❡♥❝❡ ♦❢ t❤❡ ❞✐✛❡r❡♥t ♠❡s❤❡s ✉s❡❞ ✐♥ ❡❛❝❤ t❡st✱ ✐♥❝r❡❛s✐♥❣ t❤❡ ♥✉♠❜❡r ♦❢ ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠ ✐♥ t❤❡ ❛r❡❛s ✇❤❡r❡ ✐t ✐s ❡①♣❡❝t❡❞ ❛ ❤✐❣❤❡r ❝♦♥❝❡♥tr❛t✐♦♥ ♦❢ ♣❧❛st✐❝ ❞✐ss✐♣❛t✐♦♥✱ ✐♥ t❤❡ ❢♦r♠❛t✐♦♥ ♦❢ t❤❡ ❝♦❧❧❛♣s❡ ♠❡❝❤❛♥✐s♠✳
❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ✐♥ t❤❡ ♥✉♠❡r✐❝❛❧ ❛♥❛❧②s✐s ✇✐t❤ ♠❡❝❤♣②✱ ✇❡r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts✱ ❛♥❞ ✇✐t❤ t❤❡ ❝♦❧❧❛♣s❡ ❧♦❛❞s ♣r♦✈✐❞❡❞ ❜② t❤❡ ◆P ❊◆ ✶✾✾✸✲✶✲✽ ✷✵✶✵ s♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ ✇✐t❤ t❤❡ ♥❡✇ ❈■❉❊❈❚ r❡❝♦♠♠❡♥❞❛t✐♦♥s✳ ❚❤r♦✉❣❤ t❤❡s❡ ❝♦♠♣❛r✐s♦♥s✱ ✐t ✇❛s ❝♦♥❝❧✉❞❡❞ t❤❛t ❜② ✉s✐♥❣ ▲✐♠✐t ❆♥❛❧②s✐s✱ ❤✐❣❤ q✉❛❧✐t② ❡st✐♠❛t✐♦♥s ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❢♦r t❤❡ t②♣❡ ♦❢ ♣r♦❜❧❡♠s ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ✇♦r❦✳
❑❡②✇♦r❞s✿ ▼❡t❛❧ ❥♦✐♥ts✱ ❈✐r❝✉❧❛r ❍♦❧❧♦✇ ❙❡❝t✐♦♥ ✭❈❍❙✮✱ ❋✐♥✐t❡ ❡❧❡♠❡♥t ❧✐♠✐t ❛♥❛❧②s✐s✱ ❑✐♥❡♠❛t✐❝ ✭✉♣♣❡r ❜♦✉♥❞✮ ❚❤❡♦r❡♠✳
❈♦♥t❡ú❞♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✐
❘❡s✉♠♦ ✐✐✐
P❛❧❛✈r❛s ❈❤❛✈❡ ✐✐✐
❆❜str❛❝t ✈
❑❡②✇♦r❞s ✈
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✐
❙✐♠❜♦❧♦❣✐❛ ①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷
✷ ❉❡✜♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ✺
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ✐♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❘❡✈✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s ❞❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷✳✶ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷✳✷ ❊s❝♦❛♠❡♥t♦ ♣❧ást✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷✳✸ ❋✉♥çõ❡s ❞❡ ❞✐ss✐♣❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✸ ❆♥á❧✐s❡ ▲✐♠✐t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✸✳✶ ❚❡♦r❡♠❛ ❊stát✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✸✳✷ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✹ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸ ❈❛s♦s ❞❡ ❡st✉❞♦ ✶✼
✸✳✸ ❏✉♥t❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❡♠ ❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✹ ❏✉♥t❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❡♠ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✹ ▼♦❞❡❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡ ❞✐s❝✉ssã♦ ❞❡ r❡s✉❧t❛❞♦s ✷✾
✹✳✶ ❈♦♥s✐❞❡r❛çõ❡s ✐♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷ ❏✉♥t❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❡♠ ❑ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✸ ❏✉♥t❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❡♠ ◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✹ ❏✉♥t❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❡♠ ❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✺ ❏✉♥t❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❡♠ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✻ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦ ❊✉r♦❝ó❞✐❣♦ ✸ ❡ r❡❝♦♠❡♥❞❛çõ❡s ❈■❉❊❈❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵
✺ ❈♦♥❝❧✉sã♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ❢✉t✉r♦s ✽✸
❇✐❜❧✐♦❣r❛✜❛ ✽✺
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❈♦♥s❡q✉ê♥❝✐❛s ❞♦ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ❛ss♦❝✐❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❛s s✉♣❡r❢í❝✐❡s ❞❡ ❝❡❞ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❥✉♥t❛ t✉❜✉❧❛r ❡♠ ❑ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✷ ▼♦❞♦s ❞❡ r♦t✉r❛ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❥✉♥t❛ t✉❜✉❧❛r ❡♠ ◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✹ ▼♦❞♦s ❞❡ r♦t✉r❛ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✺ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❥✉♥t❛ t✉❜✉❧❛r ❡♠ ❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✻ ❘❡❧❛çã♦ ❡♥tr❡ ❛ ❝❛r❣❛ ❛①✐❛❧ ❡ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ✈❡rt✐❝❛❧ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✷✹ ✸✳✼ ▼♦❞♦s ❞❡ r♦t✉r❛ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✽ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❥✉♥t❛ t✉❜✉❧❛r ❡♠ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✾ ❘❡❧❛çã♦ ❡♥tr❡ ❛ ❝❛r❣❛ ❛①✐❛❧ ❡ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ✈❡rt✐❝❛❧ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✷✼ ✸✳✶✵ ▼♦❞♦s ❞❡ r♦t✉r❛ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶ ▼❛❧❤❛ t✐♣♦ ❞❛ ❥✉♥t❛ t✉❜✉❧❛r ❡♠ ❑ ❝♦♠ ❛❢❛st❛♠❡♥t♦ ❡♥tr❡ ❛s ❞✐❛❣♦♥❛✐s ✳ ✳ ✳ ✸✶ ✹✳✷ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭●✷❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✸ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ●✷❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✹ ▼❛❧❤❛s t✐♣♦ ❞❛s ❥✉♥t❛s t✉❜✉❧❛r❡s ❡♠ ❑ ❝♦♠ s♦❜r❡♣♦s✐çã♦ ❞❛s ❞✐❛❣♦♥❛✐s ✳ ✳ ✳ ✸✹ ✹✳✺ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭■✸❈✭✶✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✻ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭■✸❈✭✷✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✼ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ■✸❈✭✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✽ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ■✸❈✭✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✾ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭▲✸❈✭✶✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✶✵ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭▲✸❈✭✷✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✶✶ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ▲✸❈✭✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✶✷ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ▲✸❈✭✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✶✸ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ❞❛ ❏✉♥t❛ ❑ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✶✹ ▼❛❧❤❛ t✐♣♦ ❞❛ ❥✉♥t❛ t✉❜✉❧❛r ❡♠ ◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✶✺ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❋❯◆●✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✶✻ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭●❍❖✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✶✼ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ❋❯◆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✶✽ ❙♦❧✉çã♦ ❞❛ ❛♥á❧✐s❡ ❞♦ ♠♦❞❡❧♦ ●❍❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦s ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛ ❏✉♥t❛ ❑ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦s ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛ ❥✉♥t❛ ◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✸ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦s ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛ ❏✉♥t❛ ❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✹ ▼♦❞♦s ❞❡ r♦t✉r❛ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✺ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦s ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ❞❛ ❏✉♥t❛ ❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✻ ▼♦❞♦s ❞❡ r♦t✉r❛ ❞♦s ❡s♣é❝✐♠❡s ❡♥s❛✐❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭●✷❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✷ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭■✸❈✭✶✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✸ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭■✸❈✭✷✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✹ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭▲✸❈✭✶✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✺ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭▲✸❈✭✷✮✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✻ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❋❯◆●✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✼ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭●❍❖✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✽ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✽✾①✷✳✺✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✾ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✶✶✹①✸✳✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✵ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✽✾①✷✳✺❘✶✷✻✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✶✶ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✽✾①✷✳✺❘✽✹✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✶✷ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✽✾①✷✳✺❘✹✷✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✶✸ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✶✶✹①✸✳✵❘✶✷✻✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✹ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✶✶✹①✸✳✵❘✽✹✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✶✺ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❳❇✶✶✹①✸✳✵❘✹✷✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✶✻ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✽✾①✷✳✺✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✶✼ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✶✶✹①✸✳✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✶✽ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✽✾①✷✳✺❘✶✷✻✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✶✾ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✽✾①✷✳✺❘✽✹✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✷✵ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✽✾①✷✳✺❘✹✷✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✷✶ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✶✶✹①✸✳✵❘✶✷✻✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✷✷ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✶✶✹①✸✳✵❘✽✹✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✷✸ ❘❡s✉♠♦ ❞♦s ✈❛❧♦r❡s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ✭❚❇✶✶✹①✸✳✵❘✹✷✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✷✹ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✽✶ ❆✳✶ ❈❧❛ss❡s ❞♦s ♣❡r✜s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
❙✐♠❜♦❧♦❣✐❛
❆❜r❡✈✐❛t✉r❛s ❡❧❡♠✳ ❡❧❡♠❡♥t♦
❡①♣✳ ❡①♣❡r✐♠❡♥t❛❧ ♠á①✳ ♠á①✐♠❛ ♣❛râ♠✳ ♣❛râ♠❡tr♦s
r❡s✉❧t✳ r❡s✉❧t❛❞♦s ❙✐❣❧❛s
❉❊❈ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ❋❈❚ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❯◆▲ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛
❈❍❙ P❡r✜❧ ❚✉❜✉❧❛r ❞❡ ❙❡❝çã♦ ❈✐r❝✉❧❛r ❊❈✸ ❊✉r♦❝ó❞✐❣♦ ✸
❈P P❧❛st✐✜❝❛çã♦ ❞❛ ❝♦r❞❛
▲❇❋❇ ❊♥❝✉r✈❛❞✉r❛ ▲♦❝❛❧ ❞♦ ❊❧❡♠❡♥t♦ ❈❛rr❡❣❛❞♦ ▼❨❋❇ ❈❡❞ê♥❝✐❛ ❞❛ ❙❡❝çã♦ ❞♦ ❊❧❡♠❡♥t♦ ❈❛rr❡❣❛❞♦
❖❙❇ ❉❡s❧♦❝❛♠❡♥t♦ ❋♦r❛ ❞♦ P❧❛♥♦ ❞♦ ❊❧❡♠❡♥t♦ ❈❛rr❡❣❛❞♦ ❙í♠❜♦❧♦s
Ω ❉♦♠í♥✐♦ ❞❡ ✉♠ ❝♦r♣♦
u ❝❛♠♣♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s
˙
u ❝❛♠♣♦ ❞❛s ✈❡❧♦❝✐❞❛❞❡s ε ❝❛♠♣♦ ❞❛s ❞❡❢♦r♠❛çõ❡s
εe ❝❛♠♣♦ ❞❡ ❞❡❢♦r♠❛çõ❡s ❡❧ást✐❝❛s
˙
εp t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛st✐❝❛
Cc ❊s♣❛ç♦ ❢♦r♠❛❞♦ ♣♦r t♦❞♦s ♦s ❡st❛❞♦s ♣♦ssí✈❡✐s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛
σ ❡st❛❞♦ ❞❡ t❡♥sã♦
˙
σ t❡♥s♦r ❞❛s t❡♥sõ❡s
E ❊st❛❞♦ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧
s ♣❛r❝❡❧❛ ❞❡✈✐❛tór✐❝❛ ❞❛s t❡♥sõ❡s I ❚❡♥s♦r ✐❞❡♥t✐❞❛❞❡ ❞❡ ✷➟♦r❞❡♠ α ♠✉❧t✐♣❧✐❝❛❞♦r ❞❡ ❝❛rr❡❣❛♠❡♥t♦
ˆ
v ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈❛
ˆ
vn ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈❛ ♥♦r♠❛❧
ˆ
vt ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈❛ t❛❣❡♥❝✐❛❧
Cd ❊s♣❛ç♦ ❢♦r♠❛❞♦ ♣♦r t♦❞♦s ♦s ❡st❛❞♦s ♣♦ssí✈❡✐s ❞❛s ✈❡❧♦❝✐❞❛❞❡s r❡❧❛t✐✈❛s
c t❡♥sã♦ t❛♥❣❡♥❝✐❛❧ ♠á①✐♠❛ k t❡♥sã♦ ❞❡ ❝♦rt❡ ❞❡ ❝❡❞ê♥❝✐❛ kI t❡♥sã♦ ❞❡ ❝♦rt❡ ❧✐♠✐t❡
Γσ ❋r♦♥t❡✐r❛ ❡stát✐❝❛ t ❢♦rç❛s ❞❡ ❢r♦♥t❡✐r❛ b ❢♦rç❛s ❞❡ ♠❛ss❛
n ♥♦r♠❛❧ ❡①t❡r✐♦r à ❢r♦♥t❡✐r❛ Γu ❋r♦♥t❡✐r❛ ❝✐♥❡♠át✐❝❛
We P♦tê♥❝✐❛ ❞❛s ❢♦rç❛s ❡①t❡r✐♦r❡s ❛♣❧✐❝❛❞❛s
WD P♦tê♥❝✐❛ ♣❧ást✐❝❛ t♦t❛❧ ❞✐ss✐♣❛❞❛ d ❞✐â♠❡tr♦ ❞♦ ❡❧❡♠❡♥t♦
d0 ❞✐â♠❡tr♦ ❞♦ ❡❧❡♠❡♥t♦ ♣r✐♥❝✐♣❛❧
d1 ❞✐â♠❡tr♦ ❞♦ ❡❧❡♠❡♥t♦ s❡❝✉♥❞ár✐♦
t ❡s♣❡ss✉r❛ ❞♦ ❡❧❡♠❡♥t♦
t1 ❡s♣❡ss✉r❛ ❞♦ ❡❧❡♠❡♥t♦ s❡❝✉♥❞ár✐♦
L ❈♦♠♣r✐♠❡♥t♦ ❞♦ ❡❧❡♠❡♥t♦ g ❣❛♣
σy t❡♥sã♦ ❞❡ ❝❡❞ê♥❝✐❛
Θ â♥❣✉❧♦ q✉❡ ♦ ❡❧❡♠❡♥t♦ s❡❝✉♥❞ár✐♦ ❢❛③ ❝♦♠ ♦ ❡❧❡♠❡♥t♦ ♣r✐♥❝✐♣❛❧
R ❘❛✐♦ ❞❡ ❝✉r✈❛t✉r❛
1/R ❈✉r✈❛t✉r❛
fy t❡♥sã♦ ❞❡ ❝❡❞❡♥❝✐❛
R2 ❈♦❡✜❝✐❡♥t❡ ❞❡ ❞❡t❡r♠✐♥❛çã♦ Pu ❈❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ❡①♣❡r✐♠❡♥t❛❧
PALM ISES ❊st✐♠❛t✐✈❛ ❞❡ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ♣❡❧♦ ❝r✐tér✐♦ ❞❡ ✈♦♥ ▼✐s❡s PALT RESCA ❊st✐♠❛t✐✈❛ ❞❡ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ♣❡❧♦ ❝r✐tér✐♦ ❞❡ ❚r❡s❝❛
NRdEC3 ❈❛r❣❛ r❡s✐st❡♥t❡ ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞♦ ❊❈✸
NRdCIDECT ❈❛r❣❛ r❡s✐st❡♥t❡ ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞❛s r❡❝♦♠❡♥❞❛çõ❡s ❈■❉❊❈❚
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
✶✳✶ ▼♦t✐✈❛çã♦
❯♠ ❞♦s ♣r✐♥❝í♣✐♦s ❞❛ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ é ❛ ❡❧❛❜♦r❛çã♦ ❞❡ ❡str✉t✉r❛s ❡✜❝✐❡♥t❡s ❡ s❡❣✉r❛s✱ s❡♥❞♦ r❡❧❡✈❛♥t❡ s❡r✲s❡ ❝❛♣❛③ ❞❡ ❛✈❛❧✐❛r ❛ ♠á①✐♠❛ ❝❛r❣❛ s✉♣♦rt❛❞❛ ♣♦r ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❡str✉t✉r❛✱ ❞❡♥♦♠✐♥❛❞❛ ❞❡ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦✳ ❆ ❆♥á❧✐s❡ ▲✐♠✐t❡ r❡♣r❡s❡♥t❛ ✉♠❛ ❡str❛té❣✐❛ ❡✜❝✐❡♥t❡ ♥❡st❡ â♠❜✐t♦ ❝❛♣❛③ ❞❡ ❛✈❛❧✐❛r ❛ ♠á①✐♠❛ ❝❛r❣❛ s✉♣♦rt❛❞❛ ♣♦r ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❡str✉t✉r❛✳
❆ ♠♦t✐✈❛çã♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ é ❛ ❛♣❧✐❝❛çã♦ ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ♥♦ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ❥✉♥t❛s ♠❡tá❧✐❝❛s✳ ❆s ❥✉♥t❛s ♠❡tá❧✐❝❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❝✐r❝✉❧❛r sã♦ ♠✉✐t❛s ✈❡③❡s ✉t✐❧✐③❛❞❛s ❡♠ ❡str✉t✉r❛s ♠❡tá❧✐❝❛s✱ t❡♥❞♦ ❛❧❣✉♠❛s ❧✐♠✐t❛çõ❡s ♥♦ s❡✉ ❞✐✲ ♠❡♥s✐♦♥❛♠❡♥t♦✱ ❝♦♠ ❝ó❞✐❣♦s ♣♦r ✈❡③❡s ❝♦♥s❡r✈❛t✐✈♦s✳ ❆ ❆♥á❧✐s❡ ▲✐♠✐t❡ r❡✈❡❧❛ ❝♦♥❞✐çõ❡s ♣❛r❛ s❡r ✉♠❛ ❢❡rr❛♠❡♥t❛ ♠✉✐t♦ út✐❧ ♥♦ s❡✉ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦✱ ❝♦♠ ❜♦❛s ❡ rá♣✐❞❛s ❡st✐♠❛✲ t✐✈❛s ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ❡ ❛❝r❡❞✐t❛✲s❡ q✉❡✱ é ✉♠❛ ár❡❛ ❡♠ q✉❡ s❡ ♣♦❞❡ ❡①♣❧♦r❛r s♦❧✉çõ❡s ♣❡r♠✐t✐♥❞♦ ✉❧tr❛♣❛ss❛r ❛s ❧✐♠✐t❛çõ❡s ♦❜s❡r✈❛❞❛s ❛t✉❛❧♠❡♥t❡✳
❏á ❛♥t❡r✐♦r♠❡♥t❡ ♦✉tr♦s ❛✉t♦r❡s ❞❡❢❡♥❞❡r❛♠ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ♣❛r❛ ❞❡t❡r♠✐✲ ♥❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ♠❡tá❧✐❝❛s✱ r❡✜r❛✲s❡ ♦s tr❛❜❛❧❤♦s ❞❡ ▼❛❦✐♥♦ ❡t ❛❧✳ ❬✶✷❪✱ ❙♦❤ ❡t ❛❧✳ ❬✶✺❪✱ ❩❤❛♦ ❬✶✼❪ ❡ ▼❛s❤✐r✐ ❡t ❛❧✳ ❬✶✸❪✱ ❡♥tr❡ ♦✉tr♦s✳ ❈♦♥t✉❞♦✱ ❛ ❛❜♦r❞❛❣❡♠ s❡❣✉✐❞❛ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❞✐st✐♥❣✉❡✲s❡ ❞❛s ❛♥t❡r✐♦r❡s ♣❡❧♦ ❢❛❝t♦ ❞❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛s ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ♥ã♦ s❡ ❜❛s❡❛r ❡♠ ❡①♣r❡ssõ❡s ❛♥❛❧ít✐❝❛s ♦❜t✐❞❛s ❛tr❛✈és ❞❡ ♠❡❝❛♥✐s♠♦s ❞❡ r♦t✉r❛ ♣❛r❛♠❡tr✐③❛❞♦s✳
✶✳✷ ❖❜❥❡t✐✈♦
❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❡ tr❛❜❛❧❤♦ ❝♦♥s✐st❡ ❡♠ ♠♦str❛r q✉❡ ❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ❝♦♠♦ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❞❡ ❝á❧❝✉❧♦ ♣❛r❛ ♣r❡✈❡r ❜♦❛s ❡st✐♠❛t✐✈❛s ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡✲ s✐st❡♥t❡ ❞❡ ❥✉♥t❛s ♠❡tá❧✐❝❛s t✉❜✉❧❛r❡s ❝❛r❛❝t❡r✐③❛❞❛s ♣♦r ✉♠ ❝♦♠♣♦rt❛♠❡♥t❡ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦✳ P❛r❛ q✉❡ ❡st❡ ♦❜❥❡❝t✐✈♦ s❡❥❛ ❝♦♥❝r❡t✐③❛❞♦ ❝♦♠ s✉❝❡ss♦✱ é ✉s❛❞♦ ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ♠❡❝❤♣②✱ q✉❡ é s✉♣♦rt❛❞♦ t❡♦r✐❝❛♠❡♥t❡ ♣❡❧♦ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦ ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡✳ ❖ ♣r♦❣r❛♠❛ ♣❡r♠✐t❡ ♣r♦❝❡❞❡r à ❛♥á❧✐s❡ ❞❡ ✈ár✐♦s ♣r♦❜❧❡♠❛s✱ ❝✉❥♦s r❡s✉❧✲ t❛❞♦s ♣♦❞❡♠ s❡r ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ♦❜t✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳
✶✳✸ ▼❡t♦❞♦❧♦❣✐❛
P❛r❛ ❛ ❝♦♥❝r❡t✐③❛çã♦ ❞♦ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ❡♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ❢♦r❛♠ s❡❧❡❝✐♦♥❛❞♦s ❛❧❣✉♥s ❝❛s♦s ❞❡ ❡st✉❞♦ ❝♦♠ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s q✉❡ ♣❡r♠✐t✐ss❡♠ ✉♠❛ ❝♦♥❢r♦♥t❛çã♦ ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❞♦s ♠♦❞❡❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ ♣❡r♠✐t✐♥❞♦ ❛ ✈❛❧✐❞❛çã♦ ❞❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛✳ ❋♦✐ ❢❡✐t❛ ❛ ♠♦❞❡❧❛çã♦ ❞❡st❡s ❝❛s♦s ❞❡ ❡st✉❞♦✱ t❡♥❞♦ ❡♠ ❝♦♥t❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡s❝r✐t❛s ♥♦s ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s✳ P❛r❛ ❝❛❞❛ ♠♦❞❡❧♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✈ár✐♦s ♥í✈❡✐s ❞❡ r❡✜♥❛♠❡♥t♦ ❡ ❛ r❡s♣❡t✐✈❛ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦✱ ❝❛❧❝✉❧❛❞❛ ❞❡ ♠♦❞♦ ✐t❡r❛t✐✈♦ ♣❡❧♦ ♣r♦❣r❛♠❛ ♠❡❝❤♣②✱ ♣❡r♠✐t❡♠ ❢❛③❡r ✉♠❛ ❛♥á❧✐s❡ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✱ ❡ ❛ss✐♠ ❢❛③❡r ✉♠❛ ❡st✐♠❛t✐✈❛ ❞❡ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ❞❛ ❡str✉t✉r❛✳
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦
❖ ♣r❡s❡♥t❡ ❞♦❝✉♠❡♥t♦ ❡♥❝♦♥tr❛✲s❡ ♦r❣❛♥✐③❛❞♦ ❡♠ ✺ ❝❛♣ít✉❧♦s✳ ❆♣ós ❡st❡ ❝❛♣ít✉❧♦ ✐♥tr♦✲ ❞✉tór✐♦✱ ♦♥❞❡ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞❛s ❛ ♠♦t✐✈❛çã♦✱ ♦ ♦❜❥❡❝t✐✈♦ ❡ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞♦ tr❛❜❛❧❤♦✱ s❡❣✉❡♠✲s❡ ♦s ❝❛♣ít✉❧♦s ❝❡♥tr❛✐s ❞❛ t❡s❡ ❝✉❥♦ ❝♦♥t❡ú❞♦ é ❡s♣❡❝✐✜❝❛❞♦ ❡♠ s❡❣✉✐❞❛✳
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞❡✲s❡ ❛ ✉♠❛ ❞❡✜♥✐çã♦ ❞❛s ❝♦♥❞✐çõ❡s t❡ór✐❝❛s ❞♦ ♣r♦❜❧❡♠❛ ❡♠ ❛♥á❧✐s❡✳ ❉❡s❝r❡✈❡♠✲s❡ ❛❧❣✉♥s ❞♦s ❝♦♥❝❡✐t♦s ❡st❛❜❡❧❡❝✐❞♦s ♣❡❧❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ✉t✐❧✐③❛❞♦s ♥♦ ♣r♦❣r❛♠❛ ✉t✐❧✐③❛❞♦✱ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦s ♣r♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s ♥♦s ❝❛s♦s ❞❡ ❡st✉❞♦✳ ❈❛♣ít✉❧♦ ✸✳ ❉❡s❝r❡✈❡♠✲s❡ ❛s ❥✉♥t❛s ♠❡tá❧✐❝❛s t✉❜✉❧❛r❡s ❞❡ s❡❝çã♦ ❝✐r❝✉❧❛r s❡❣✉✐♥❞♦ ♦s ♣r♦♣ós✐t♦s ❞♦s ❞♦❝✉♠❡♥t♦s ❞❡ r❡❢❡rê♥❝✐❛✳ ❙ã♦ ❛♣r❡s❡♥t❛❞♦s ♦s t✐♣♦s ❞❡ ❥✉♥t❛ ✉t✐❧✐③❛❞♦s✱ ♦s ♣❛râ♠❡tr♦s ❣❡♦♠étr✐❝♦s q✉❡ ❞❡✜♥❡♠ ❛ ❥✉♥t❛✱ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦s ❡s❢♦rç♦s ❛ q✉❡ ❛ ❥✉♥t❛ ❡stá s✉❥❡✐t❛ ❡ ♦s r❡s♣❡t✐✈♦s ✈❛❧♦r❡s ❡ ♠♦❞♦s ❞❡ r♦t✉r❛ ❛t✐♥❣✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ❈❛♣ít✉❧♦ ✹✳ ❆♣r❡s❡♥t❛♠✲s❡ t♦❞♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛✱ ❝♦♠♣❧❡♠❡♥✲
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦
t❛♥❞♦ ❝♦♠ ♦s r❡s♣❡t✐✈♦s ❣rá✜❝♦s ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛✳ ➱ ❢❡✐t❛ ❛ ❝♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❛t✐♥❣✐❞♦s ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❝♦♠ ♦s ✈❛❧♦r❡s ♦❜t✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ➱ ❛✐♥❞❛ ❛♣r❡✲ s❡♥t❛❞❛ ✉♠❛ ❝♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ♦s ❝á❧❝✉❧♦s t❡ór✐❝♦s ♦❜t✐❞♦s ♣❡❧♦ ❊❈✸ ❡ ❝♦♠ ❛s r❡❝♦♠❡♥❞❛çõ❡s ❈■❉❊❈❚✳
❈❛♣ít✉❧♦ ✺✳ P♦r ✜♠✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❝♦♥❝❧✉sõ❡s r❡t✐r❛❞❛s ❞❡st❡ tr❛❜❛❧❤♦✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ s✉❣❡stõ❡s ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ❢✉t✉r♦s✳
❈❛♣ít✉❧♦ ✷
❉❡✜♥✐çã♦ ❞♦ ♣r♦❜❧❡♠❛
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ✐♥✐❝✐❛✐s
➱ ✐♥❞✐s❝✉tí✈❡❧ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ♥♦ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ✉♠❛ ❡str✉t✉r❛✳ ❆ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ♠❡❧❤♦r♦✉ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❢❡rr❛♠❡♥t❛s ♥✉♠ér✐❝❛s✱ q✉❡ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s ♠♦❞❡❧♦s ❞❡ ❛♥á❧✐s❡✱ ♣❡r♠✐t❡♠ ❛t✐♥❣✐r ✈❛❧♦r❡s ♠✉✐t♦ ♣ró①✐♠♦s ❞❛ r❡❛❧✐❞❛❞❡✳ ❖ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♦ ❝á❧❝✉❧♦ ❞♦ ❧✐♠✐t❡ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ❞❡ ❡str✉t✉r❛s ♠❡tá❧✐❝❛s t✉❜✉❧❛r❡s✱ ❛tr❛✈és ❞❡ ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ♠❡❝❤♣② ❬✻❪✱ q✉❡ ✐♠♣❧❡♠❡♥t❛ ♥✉♠❡r✐❝❛♠❡♥t❡ ♦ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦ ❡ ❊stát✐❝♦ ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡✳
◆❡st❡ ❝❛♣ít✉❧♦ ♣r❡t❡♥❞❡✲s❡ ❢❛③❡r ❛ ❞❡s❝r✐çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ♦ q✉❡ ✐♠♣❧✐❝❛ q✉❡ ♣r❡✈✐❛♠❡♥t❡ s❡ ❛♣r❡s❡♥t❡ ❛s ♥♦çõ❡s t❡ór✐❝❛s ❡ss❡♥❝✐❛✐s ✐♥❝✉t✐❞❛s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❢❡rr❛♠❡♥t❛ ❞❡ ❝á❧✲ ❝✉❧♦✳ ❈♦♥s✐❞❡r❛✲s❡ ♥❡❝❡ssár✐♦ r❡✈❡r ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❢✉♥❞❛♠❡♥t❛✐s ❡st❛❜❡❧❡❝✐❞♦s ♥❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡ ✭❬✹❪✱ ❬✶✶❪✮✱ ❝♦♠ ❡s♣❡❝✐❛❧ ✐♥t❡r❡ss❡ ♥♦s ❚❡♦r❡♠❛s ❞❡ ❆♥á❧✐s❡ ▲✐♠✐t❡✳
◆❡st❡ ❝❛♣ít✉❧♦ ❛❞♦♣t❛✲s❡ ✉♠❛ ♥♦t❛çã♦ t❡♥s♦r✐❛❧✱ ♥❛ q✉❛❧ ♦s ❝❛r❛❝t❡r❡s q✉❡ r❡♣r❡s❡♥t❛♠ ❣r❛♥❞❡③❛s t❡♥s♦r✐❛✐s sã♦ ✐❞❡♥t✐✜❝❛❞❛s ❛tr❛✈és ❞❡ ✉♠ s✉❜❧✐♥❤❛❞♦✱ ❝✉❥♦ ♥ú♠❡r♦ ❞❡ ❧✐♥❤❛s r❡♣r❡s❡♥t❛ ❛ ♦r❞❡♠ ❞♦ t❡♥s♦r✳ ◆❡st❛ ♥♦t❛çã♦✱ ♦ ♦♣❡r❛❞♦r ✏✿✑ ❞❡♥♦t❛ ♦ ♣r♦❞✉t♦ ❝♦♥tr❛í❞♦ ✭t❛♠❜é♠ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❝♦♥tr❛❝çã♦ ❞✉♣❧❛✮ ❡♥tr❡ ❞♦✐s t❡♥s♦r❡s ❞❛ ♠❡s♠❛ ♦r❞❡♠❀a:b =
aijbij✳ ❋❛③✲s❡ ❛✐♥❞❛ ♠❡♥çã♦ ❞❛ ✉t✐❧✐③❛çã♦ ❞♦ ♦♣❡r❛❞♦r✱ tr(·)✱ q✉❡ ❞❡♥♦t❛ ♦ tr❛ç♦ ❞❡ ✉♠
t❡♥s♦r ❞❡2a ♦r❞❡♠❀tr(a) =aii✳
❝♦♥s✐❞❡r❛❞❛ ✈á❧✐❞❛ ❛ ❤✐♣ót❡s❡ ❞❛s ♣❡q✉❡♥❛s ❞❡❢♦r♠❛çõ❡s✳ ❊st❛ ú❧t✐♠❛✱ ♣❡r♠✐t❡ ❡st❛❜❡❧❡❝❡r ❛ s❡❣✉✐♥t❡ r❡❧❛çã♦ ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❡♥tr❡ ♦ ❝❛♠♣♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s✱ u✱ ❡ ♦ ❝❛♠♣♦ ❞❛s
❞❡❢♦r♠❛çõ❡s✱ ε✱
εij =
1
2(ui,j+uj,i) ✭✷✳✶✮
❆❧t❡r♥❛t✐✈❛♠❡♥t❡✱ ♣♦❞❡ s❡r ❢❡✐t❛ ✉♠❛ r❡❧❛çã♦ ♠❛✐s ❝♦♥✈❡♥✐❡♥t❡ ♥♦ ♣r❡s❡♥t❡ ❝♦♥t❡①t♦✱ ❡♥tr❡ ♦ ❝❛♠♣♦ ❞❛s ✈❡❧♦❝✐❞❛❞❡s✱ u˙✱ ❡ ♦ ❝❛♠♣♦ ❞❛ t❛①❛ ❞❛s ❞❡❢♦r♠❛çõ❡s✱ε˙✱
˙
εij =
1
2( ˙ui,j+ ˙uj,i) ✭✷✳✷✮
❖ ♣r♦❜❧❡♠❛ ❛✐♥❞❛ s❡ ❜❛s❡✐❛ ♥♦s ♣r❡ss✉♣♦st♦s q✉❡ ♦s ♠❛t❡r✐❛✐s sã♦ ❝❛r❛❝t❡r✐③❛❞♦s ♣♦r ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ✐s♦tró♣✐❝♦✱ q✉❡ t♦❞❛s ❛s ❞❡❢♦r♠❛çõ❡s ✐♥❡❧ást✐❝❛s r❡s✉❧t❛♠ ❞❡ ✉♠❛ r❡s♣♦st❛ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝❛ ❞♦s ♠❛t❡r✐❛✐s✱ ❡ q✉❡ s❡ ❛♣❧✐❝❛ ♦ ❝❛rr❡❣❛♠❡♥t♦ ❡♠ ❝♦♥❞✐çõ❡s q✉❛s❡ ❡stát✐❝❛s✱ ♣❡r♠✐t✐♥❞♦ ❞❡s♣r❡③❛r q✉❛✐sq✉❡r ❡❢❡✐t♦s ✐♥❡r❝✐❛✐s✳
✷✳✷ ❘❡✈✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s ❞❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡
P❛r❛ ❛ss❡❣✉r❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❧ást✐❝♦ ❞❡ ✉♠ ♠❛t❡r✐❛❧✱ ✉♠ ❞♦s ♣r❡ss✉♣♦st♦s ❞♦ ♣r♦✲ ❜❧❡♠❛✱ r❡❝♦rr❡✲s❡ ❛♦ ❝♦♥tr♦❧♦ ❞❛ ♣❧❛st✐❝✐❞❛❞❡ ❛tr❛✈és ❞♦ ❡st❛❞♦ ❞❛s t❡♥sõ❡s✱ ✐♥tr♦❞✉③✐♥❞♦ ❛ ❞❡✜♥✐çã♦ ❞♦ ❞❡♥♦♠✐♥❛❞♦ ❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛✱
f(σ)≤0 ✭✷✳✸✮
❊st❡ ❝r✐tér✐♦ ♣r❡t❡♥❞❡ ❞❡❧✐♠✐t❛r ♦s ❡st❛❞♦s ❞❡ t❡♥sã♦ ❝♦♥s✐❞❡r❛❞♦s ❛❞♠✐ssí✈❡✐s✱ s❡♥❞♦ q✉❡ ❡st❛❜❡❧❡❝❡ t❛♠❜é♠ ❛ ❞❡♥♦♠✐♥❛❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱
f(σ) = 0 ✭✷✳✹✮
❞❡✜♥✐❞❛ ❛tr❛✈és ❞❡ ✉♠❛ ❢✉♥çã♦ ❡s❝❛❧❛r ❞♦ t❡♥s♦r ❞❛s t❡♥sõ❡s✱σ✳
P❛r❛ ♦❝♦rr❡r ✉♠ ✐♥❝r❡♠❡♥t♦ ❞❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ♥♦ ♠❛t❡r✐❛❧ é ♥❡❝❡ssár✐♦ q✉❡ ♦ ❡st❛❞♦ ❞❡ t❡♥sã♦ s❡ ❡♥❝♦♥tr❡ s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ ♦✉ s❡❥❛✱ q✉❡ s❡ ✈❡r✐✜q✉❡ ❛ ✐❣✉❛❧❞❛❞❡ ♣r❡s❡♥t❡ ❡♠ ✭✷✳✹✮✳
◆♦ ❝❛s♦ ♠❛✐s ❣❡♥ér✐❝♦ ❛❞♠✐t❡✲s❡ q✉❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ✐♥✐❝✐❛❧ ♣♦ss❛ s♦❢r❡r ❛❧t❡r❛✲ çõ❡s ❝♦♠ ♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s✳ ❖s ♠♦❞❡❧♦s ♠❛✐s ❝♦♠✉♥s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ❛ ❡✈♦❧✉çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ♣r❡✈ê❡♠ q✉❡ ❡st❛ ♣♦ss❛ s♦❢r❡r ✉♠❛
✷✳✷ ❘❡✈✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s ❞❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡
❞✐❧❛t❛çã♦✱ ♠❛♥t❡♥❞♦ ❝♦♥t✉❞♦ ❛ s✉❛ ❢♦r♠❛ ❡ ♦r✐❣❡♠ ♥♦ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s✳ ❊st❡ ❝♦♠♣♦rt❛✲ ♠❡♥t♦ ❝♦♥❞✉③ ❛ ✉♠ ❛✉♠❡♥t♦ ♥❛ r❡s✐stê♥❝✐❛ ❞♦ ♠❛t❡r✐❛❧ ❡ ❞❡♥♦♠✐♥❛✲s❡ ♣♦r ❡♥❞✉r❡❝✐♠❡♥t♦ ✭✏❤❛r❞❡♥✐♥❣✑✮ ✐s♦tró♣✐❝♦✳ ❊♠ ♦♣♦s✐çã♦✱ ♦ ❢❡♥ó♠❡♥♦ ❞❡ r❡❞✉çã♦ ❞❡ r❡s✐stê♥❝✐❛ ❞❡✈✐❞♦ ❛ ✉♠❛ ❝♦♥tr❛❝çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡♥♦♠✐♥❛✲s❡ ❞❡ ❛♠♦❧❡❝✐♠❡♥t♦ ✭✏s♦❢t❡♥✐♥❣✑✮✳ ◆♦ ❝❛s♦ ❞♦ ♠♦❞❡❧♦ ♣r❡✈❡r ❛♣❡♥❛s tr❛♥s❧❛çã♦ ❞❛ ♣♦s✐çã♦ ✐♥✐❝✐❛❧ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ♥♦ s❡♥t✐❞♦ ❞❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s✱ ♠❛♥t❡♥❞♦ ♥♦ ❡♥t❛♥t♦ ♦ s❡✉ t❛♠❛♥❤♦ ❡ ❢♦r♠❛ ✐♥✐❝✐❛❧✱ ❡stá✲s❡ ♣❡r❛♥t❡ ♦ ❞❡♥♦♠✐♥❛❞♦ ❡♥❞✉r❡❝✐♠❡♥t♦ ❝✐♥❡♠át✐❝♦ ❬✹❪✳
❆ss✐♠✱ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ♣❛ss❛ t❛♠❜é♠ ❛ s❡r ❢✉♥çã♦ ♥ã♦ só ❞♦ ❡st❛❞♦ ❞❡ t❡♥sõ❡s ♠❛s t❛♠❜é♠ ❞♦ ❡st❛❞♦ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧✱E✱
f(σ,E) = 0, ✭✷✳✺✮
s❡♥❞♦ ❛ ❡✈♦❧✉çã♦ ❞♦ ❡st❛❞♦ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ♥♦r♠❛❧♠❡♥t❡ ❝♦♥tr♦❧❛❞❛✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛ tr❛❥❡❝tór✐❛ ❞❛s ❞❡❢♦r♠❛çõ❡s✱ ❛tr❛✈és ❞❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ♦❝♦rr✐❞❛s ✭✏str❛✐♥ ❤❛r✲ ❞❡♥✐♥❣✑✮ ♦✉ ❛❧t❡r♥❛t✐✈❛♠❡♥t❡ ❛tr❛✈és ❞♦ tr❛❜❛❧❤♦ ♣❧ást✐❝♦ ❞✐ss✐♣❛❞♦ ✭✏✇♦r❦ ❤❛r❞❡♥✐♥❣✑✮✳ ❯♠❛ ❞❡✜♥✐çã♦ ♠❛✐s r❡str✐t❛ ❞❡ ✏✇♦r❦ ❤❛r❞❡♥✐♥❣✑ ❢♦✐ ❢♦r♠✉❧❛❞❛ ♣♦r ❉r✉❝❦❡r✱ s✉❣❡r❡ q✉❡ s❡ ♦ ❡♥❞✉r❡❝✐♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧ ♣♦r ❞❡❢♦r♠❛çã♦ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ❡st❛❞♦ ❞❡ t❡♥sã♦ ❡ ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ ♥❛ ❢♦r♠❛ ✐♥✜♥✐t❡s✐♠❛❧✱ é ✈á❧✐❞♦ ❝♦♥s✐❞❡r❛r ❛s s❡❣✉✐♥t❡s r❡❧❛çõ❡s ❬✶✶❪✿
˙
σ : ˙εp ⇒
≥0, endurecimento do material,
= 0, material perf eitamente pl´astico,
≤0, amolecimento do material.
✭✷✳✻✮
◆♦ ❡♥t❛♥t♦✱ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✱ ❡♠ q✉❡ ♦s ♠❛t❡r✐❛✐s ❛♣r❡s❡♥t❛♠ ✉♠ ❝♦♠♣♦rt❛✲ ♠❡♥t♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦✱ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡✈❡rá ♣❡r♠❛♥❡❝❡r ✐♥❛❧t❡r❛❞❛ ❛♦ ❧♦♥❣♦ ❞❛ ❡✈♦❧✉çã♦ ❞♦ ❝❛rr❡❣❛♠❡♥t♦ ✭E = 0✮✳ ◆❛ ♣ró①✐♠❛ s❡❝çã♦ s❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❡ ❞✐s❝✉t✐❞❛s r❡str✐çõ❡s ✐♠♣♦st❛s à ❢♦r♠❛ ❞❛ ❢✉♥çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✳
✷✳✷✳✶ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦
❈♦♥s✐❞❡r❡✲s❡ ✉♠ q✉❛❧q✉❡r ❡st❛❞♦ ❞❡ t❡♥sã♦ ❛❞♠✐ssí✈❡❧✱σ✱ ❡ ✉♠❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ás✲
t✐❝❛✱ε˙p ✱ ❣❡r❛❞❛ ♥❡ss❡ ❡st❛❞♦ ❞❡ t❡♥sã♦✳ ❖ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦ ♣♦st✉❧❛ q✉❡✱ ♣❛r❛ t♦❞♦ ♦ ❡st❛❞♦ ❞❡ t❡♥sã♦ ❛❞♠✐ssí✈❡❧✱σ∗✱ ❛r❜✐tr❛r✐❛♠❡♥t❡ ❡s❝♦❧❤✐❞♦✱ s❡ ✈❡r✐✜❝❛ ❛
s❡❣✉✐♥t❡ r❡❧❛çã♦✿
∀σ∗|f(σ∗)≤0, ∀σ|f(σ)≤0, (σ−σ∗) : ˙εp ≥0 ✭✷✳✼✮
❊st❡ ♣r✐♥❝í♣✐♦ é t❛♠❜é♠ ♠✉✐t❛s ✈❡③❡s ♦❜s❡r✈❛❞♦ ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❞♦ P♦st✉❧❛❞♦ ❞❡ ❊s✲ t❛❜✐❧✐❞❛❞❡ ❞❡ ❉r✉❝❦❡r ❬✶✶❪✳ ❉❛ ❛♣❧✐❝❛çã♦ ❞♦ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦✱ ✉♠ ♠❛t❡r✐❛❧ ♣❛r❛ s❡r ❡stá✈❡❧ ♥♦ s❡♥t✐❞♦ ❞❡ ❉r✉❝❦❡r t❡♠ ❞❡ t❡r ♠❛✐s três ♣r♦♣r✐❡❞❛❞❡s r❡❧❡✈❛♥t❡s✿
❛✮ ❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ t❡♠ ❞❡ s❡r ♦r✐❡♥t❛❞❛ s❡❣✉♥❞♦ ✉♠❛ ♥♦r♠❛❧ ❡①t❡r✐♦r à s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ✭❝♦♠ ✉♠❛ ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ❛ss♦❝✐❛❞❛✮❀
❜✮ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡✜♥❡ ♦❜r✐❣❛t♦r✐❛♠❡♥t❡ ✉♠ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s ❛❞♠✐ssí✈❡✐s ❝♦♥✈❡①♦❀
❝✮ ❛ ❞✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡✱ D✱ ❞❡✜♥✐❞❛ ♣❡❧♦ ♣r♦❞✉t♦ ✐♥t❡r♥♦ ❞❛s
t❡♥sõ❡s ♣❡❧❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛✱
D(σ,ε˙p) =σ: ˙εp ✭✷✳✽✮
♣♦❞❡ ♣❛ss❛r ❛ s❡r ❡①♣r❡ss❛ ❝♦♠♦ ❢✉♥çã♦ ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛✱D( ˙εp)✱ ❞❡s❞❡
q✉❡ s❡❥❛ ❝♦♥❤❡❝✐❞❛ ❛ ❢✉♥çã♦ ❞❡ ❝❡❞ê♥❝✐❛✱f(σ) ❬✶✹❪✳
P❛r❛ q✉❡ ♦ ♣r♦❞✉t♦ ✐♥t❡r♥♦ ♣r❡s❡♥t❡ ❡♠ ✭✷✳✼✮ ♣♦ss❛ s❡r ✈á❧✐❞♦ ♣❛r❛ ✉♠ ❡st❛❞♦ ❞❡ t❡♥sã♦ ❡❧ást✐❝♦ ✐♥✐❝✐❛❧ ❛r❜✐trár✐♦✱ ♦ ✈❡❝t♦r ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦ ✐♥❝r❡♠❡♥t♦ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛✱ ❞❡✈❡ s❡r ♥♦r♠❛❧ ❛♦ ♣❧❛♥♦ t❛♥❣❡♥t❡ à s✉♣❡r❢í❝✐❡ ❡ ❝♦♠ ♦ s❡♥t✐❞♦ ❛ ❛♣♦♥t❛r ♣❛r❛ ❢♦r❛ ❞❛ s✉♣❡r❢í❝✐❡✱ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❛ r❡❣r❛ ❞❛ ♥♦r♠❛❧✐❞❛❞❡ ❬✶✶❪✳ ❆s ❞✉❛s ♣r✐♠❡✐r❛s ♣r♦♣r✐❡❞❛❞❡s sã♦ ✐❧✉str❛❞❛s ❛tr❛✈és ❞❛ ❋✐❣✉r❛ ✷✳✶✳
✭❛✮ ◆♦r♠❛❧✐❞❛❞❡ ✭❜✮ ❈♦♥✈❡①✐❞❛❞❡
❋✐❣✉r❛ ✷✳✶✿ ❈♦♥s❡q✉ê♥❝✐❛s ❞♦ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦ ✭❘❡t✐r❛❞♦ ❞❡ ❱✐❝❡♥t❡ ❞❛ ❙✐❧✈❛❬✹❪✮
❈♦♠♦ s❡ ♣♦❞❡ ❝♦♥st❛t❛r ❛tr❛✈és ❞❛ ❛♥á❧✐s❡ ❞❛ ❋✐❣✉r❛ ✷✳✶❛✱ ❝❛s♦ ♦ ♣❧❛♥♦ ♣❡r♣❡♥❞✐❝✉❧❛r à t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ ✐♥t❡r❝❡♣t❡ ♦ ❞♦♠í♥✐♦ ❡❧ást✐❝♦ ❞❡❧✐♠✐t❛❞♦ ♣❡❧❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ é ♣♦ssí✈❡❧ ❞❡✜♥✐r ✉♠❛ s✉❜✲r❡❣✐ã♦ ♥❛ q✉❛❧ ♦s ❡st❛❞♦s ❞❡ t❡♥sã♦✱ f(σ∗)✱ ♥❡❧❛
✷✳✷ ❘❡✈✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s ❞❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡
▼á①✐♠♦✳ ❘❡♣❛r❛✲s❡ ♣♦rt❛♥t♦✱ ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❛ ♦r✐❡♥t❛çã♦ ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ s❡r ♥♦r♠❛❧ à s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ ❡ ♣♦❞❡✲s❡ t❛♠❜é♠ ❝♦♥❝❧✉✐r ❛❝❡r❝❛ ❞❛ ♦❜r✐❣❛t♦r✐❛❞❛❞❡ ❞❛ ❝♦♥✈❡①✐❞❛❞❡ ❞♦ ❞♦♠í♥✐♦ ❡❧ást✐❝♦✳ P❛r❛ t❛❧✱ ❜❛st❛ ❝♦♥st❛t❛r q✉❡ ♦ ♣❧❛♥♦ ♣❡r♣❡♥❞✐❝✉❧❛r ❛ ✉♠❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ ❛ss♦❝✐❛❞❛ ❛ ✉♠ ❡st❛❞♦ ❞❡ t❡♥sã♦✱ ❧♦❝❛❧✐③❛❞♦ ♥✉♠❛ ③♦♥❛ ❝♦♥✈❡①❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✳ ❉❡st❡ ♠♦❞♦✱ t♦❞❛ ❛ r❡❣✐ã♦ ❡❧ást✐❝❛ s❡ ❡♥❝♦♥tr❛ ❞♦ ♠❡s♠♦ ❧❛❞♦ ❞♦ ♣❧❛♥♦ t❛♥❣❡♥t❡✱ ♣❡❧♦ q✉❡ s❡ ♣♦❞❡ ❝♦♥❝❧✉✐r q✉❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ t❡♠ ❞❡ s❡r ❝♦♥✈❡①❛ ✭✷✳✶❜✮✳
❆ ú❧t✐♠❛ ♣r♦♣r✐❡❞❛❞❡ é s❛t✐s❢❡✐t❛ ❛ ♣❛rt✐r ❞❛ ♣ró♣r✐❛ ❞❡✜♥✐çã♦ ❞❛ ❞✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ✭✷✳✽✮ ❡ ❞❛ ♥♦r♠❛❧✐❞❛❞❡ ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ❢❛❝❡ à s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✳ ➱ ❞❡ s❛❧✐❡♥t❛r ♥♦ ❡♥✲ t❛♥t♦ q✉❡✱ ♠❡s♠♦ ♣❛r❛ ✉♠❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ♥ã♦ ❡str✐t❛♠❡♥t❡ ❝♦♥✈❡①❛ ❝❛r❛❝t❡r✐③❛❞❛ ♣♦r ♠ú❧t✐♣❧❛s ❤✐♣ót❡s❡s ❞❡ ❡st❛❞♦s ❞❡ t❡♥sã♦ ❛ss♦❝✐❛❞♦s ❛ ❞❡t❡r♠✐♥❛❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛✱ ❛ ❞✐ss✐♣❛çã♦ ❝♦♥s❡r✈❛✲s❡ ❛✐♥❞❛ ❝♦♠♦ ❢✉♥çã♦ ✉♥í✈♦❝❛ ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ❬✹❪✳
✷✳✷✳✷ ❊s❝♦❛♠❡♥t♦ ♣❧ást✐❝♦
P❛r❛ ❝♦♠♣❧❡t❛r ❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ❞❡✜♥✐r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧ q✉❛♥❞♦ ❡st❡ ❡♥tr❛ ❡♠ r❡❣✐♠❡ ♣❧ást✐❝♦✱ é ♥❡❝❡ssár✐♦ ❡st❛❜❡❧❡❝❡r ❝♦♠♦ s❡ ♣r♦❝❡ss❛ ♦ ❡s❝♦❛♠❡♥t♦ ♣❧ást✐❝♦✳ P❛r❛ t❛❧✱ ❝♦♥s✐❞❡r❡✲s❡ ❛ ❞❡❝♦♠♣♦s✐çã♦ ❞❛s ❞❡❢♦r♠❛çõ❡s t♦t❛✐s ♥❛s ♣❛r❝❡❧❛s ❡❧ást✐❝❛✱
εe ✱ ❡ ♣❧ást✐❝❛✱ εp ✱
ε=εe+εp ✭✷✳✾✮
s❡♥❞♦ q✉❡ ❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ❝♦♥s✐st❡♠ ❡♠ t♦❞❛s ❛s ❞❡❢♦r♠❛çõ❡s r❡s✐❞✉❛✐s r❡s✉❧t❛♥t❡s ❞❡ ✉♠ ❝❛rr❡❣❛♠❡♥t♦ q✉❡ ♣❡r♠❛♥❡❝❡♠ ♥♦ ♠❛t❡r✐❛❧ ❛♣ós s❡ r❡t✐r❛r ❛ ❝❛r❣❛✳ ❈♦♥tr❛r✐❛♠❡♥t❡ às ❞❡❢♦r♠❛çõ❡s ❡❧ást✐❝❛s✱ ❝♦♠ ❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ♥ã♦ é ♣♦ssí✈❡❧ ❡st❛❜❡❧❡❝❡r ✉♠❛ r❡❧❛çã♦ ❜✐✉♥í✈♦❝❛ ❝♦♠ ♦ ❝❛♠♣♦ ❞❛s t❡♥sõ❡s✳
P♦❞❡ ❛✜r♠❛r✲s❡ q✉❡ ❛ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ ♥✉♠ ♣♦♥t♦ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❡①✐❜✐♥❞♦ ✉♠ ❝♦♠✲ ♣♦rt❛♠❡♥t♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦ ♥ã♦ é ❧✐♠✐t❛❞❛✱ ♣♦r ✐ss♦✱ é ♠❛✐s ❛❞❡q✉❛❞♦ ❡①♣r✐♠✐r ❛ r❡❧❛çã♦ ❝♦♥st✐t✉t✐✈❛ ❡♠ t❡r♠♦s ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦✱ε˙p✳
❆ ✐♥tr♦❞✉çã♦ ❞❡ ✉♠❛ ♥♦✈❛ ❣r❛♥❞❡③❛ q✉❡ tr❛❞✉③❛ ❛ ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ♣❧ást✐❝♦✱ ♦ ♣♦t❡♥❝✐❛❧ ♣❧ást✐❝♦ Φ(σ)✱ ♣❡r♠✐t❡ ❡st❛❜❡❧❡❝❡r ❛ s❡❣✉✐♥t❡ r❡❧❛çã♦ ❝♦♠ ❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ t❛①❛ ❞❛s
❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s✿
˙
εpij =α∂Φ(σ) ∂σij
, α∈R+0 ✭✷✳✶✵✮
❉❡ ✉♠ ♣♦♥t♦ ❞❡ ✈✐st❛ ❣❡♦♠étr✐❝♦✱ ❛ ❝♦♥❞✐çã♦ ✭✷✳✶✵✮ ✐♠♣õ❡ q✉❡ ❛ ❞✐r❡❝çã♦ ❞❛ t❛①❛ ❞❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s s❡❥❛ ♥♦r♠❛❧ à s✉♣❡r❢í❝✐❡ ❞♦ ♣♦t❡♥❝✐❛❧ Φ(σ)✱ ❡ ♦ ✐♥t❡r✈❛❧♦ ❛ q✉❡ α
♦ ❡①t❡r✐♦r ❞❛ s✉♣❡r❢í❝✐❡✳ ❆ ✈❛❧✐❞❛❞❡ ❞♦ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦✱ ✐♠♣õ❡ q✉❡ ❛ ❢✉♥çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❝♦✐♥❝✐❞❛ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ ❝❡❞ê♥❝✐❛ ❛ ♠❡♥♦s ❞❡ ✉♠❛ ❝♦♥st❛♥t❡✱
Φ(σ) =f(σ) +cte ✭✷✳✶✶✮
❈♦♥s❡q✉❡♥t❡♠❡♥t❡ ❡stá✲s❡ ♣❡r❛♥t❡ ✉♠❛ ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ❛ss♦❝✐❛❞♦ ❬✶✶❪✱❬✹❪✱ ❝♦♥❢♦r♠❡ ✐❧✉s✲ tr❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✷✳ ❙❡ ♥❛ s✉♣❡r❢í❝✐❡ ❞♦ ♣♦t❡♥❝✐❛❧ ❡①✐st✐r ❡♠ ♣♦♥t♦s s✐♥❣✉❧❛r❡s ✭♥ã♦ ❞✐❢❡✲ r❡♥❝✐á✈❡✐s✮✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♥❡ss❡s ♣♦♥t♦s ❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣♦ss❛ ❛ss✉♠✐r q✉❛❧q✉❡r ❞✐r❡❝çã♦ ❝♦♥t✐❞❛ ♥♦ ❝♦♥❡ ❢♦r♠❛❞♦ ♣❡❧❛s ♥♦r♠❛✐s ❡①t❡r✐♦r❡s ♥❛ ✈✐③✐♥❤❛♥ç❛ ❞♦ ♣♦♥t♦ ✭✈❡r ♣♦♥t♦ ❇✱ ❋✐❣✉r❛ ✷✳✷✮✳ ❆ ❝♦♥✈❡①✐❞❛❞❡ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ✐♠♣♦st❛ ♣❡❧♦ Pr✐♥❝í♣✐♦ ❞♦ ❚r❛❜❛❧❤♦ P❧ást✐❝♦ ▼á①✐♠♦ é r❡q✉✐s✐t♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❣❛r❛♥t✐r ❛ ❡①✐stê♥❝✐❛ ❞❡st❡ ❝♦♥❡✳ P♦❞❡ ❛ss✐♠✱ s❡r ❢❡✐t❛ ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡ ✭✷✳✶✵✮✱ ❞❡✈✐❞♦ à ❝♦♥✈❡①✐❞❛❞❡ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ r❡❝♦rr❡♥❞♦ ❛♦ ❝♦♥❝❡✐t♦ ❞❡ s✉❜❣r❛❞✐❡♥t❡✱
˙
ε∈α∂Φ(σ), α∈R+0 ✭✷✳✶✷✮
❋✐❣✉r❛ ✷✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ❛ss♦❝✐❛❞♦ ✭❘❡t✐r❛❞♦ ❞❡ ❱✐❝❡♥t❡ ❞❛ ❙✐❧✈❛❬✹❪✮ P❛r❛ ❝♦♥❝❧✉✐r ❛ ❞❡s❝r✐çã♦ ❞♦ ❡s❝♦❛♠❡♥t♦✱ ❢❛❧t❛ ♣♦r ú❧t✐♠♦ r❡❢❡r✐r q✉❡ ♣❛r❛ ♠❛t❡r✐❛✐s ♣❡r✲ ❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦s é ♣♦ssí✈❡❧ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❞❡s❝♦♥t✐♥✉✐❞❛❞❡s ♥♦ ❝❛♠♣♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s✱ s❡♥❞♦ q✉❡ ❡st❛s ❞❡s❝♦♥t✐♥✉✐❞❛❞❡s ❡♥❝♦♥tr❛♠✲s❡ ✐❣✉❛❧♠❡♥t❡ s✉❥❡✐t❛s à ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ✭✷✳✶✵✮✱✭✷✳✶✷✮✳ ➱ ❞❡ r❡❢❡r✐r q✉❡✱ ❡♠❜♦r❛ ❛ ❢❡rr❛♠❡♥t❛ ❞❡ ❝á❧❝✉❧♦ ✉t✐❧✐③❛❞❛ ♣❡r♠✐t❛ ❝♦♥s✐❞❡✲ r❛r ❡st❡ t✐♣♦ ❞❡ ❞❡s❝♦♥t✐♥✉✐❞❛❞❡s ♥♦ ❝❛♠♣♦ ❞❛s ✈❡❧♦❝✐❞❛❞❡s✱ ❡st❡ r❡❝✉rs♦ ♥ã♦ ❢♦✐ ✉t✐❧✐③❛❞♦ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✳
✷✳✷ ❘❡✈✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s ❞❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡
✷✳✷✳✸ ❋✉♥çõ❡s ❞❡ ❞✐ss✐♣❛çã♦
❙ã♦ ❛♣r❡s❡♥t❛❞❛s ♥❡st❛ s✉❜s❡❝çã♦ ❛s ❢✉♥çõ❡s ❞❡ ❞✐ss✐♣❛çã♦ ❛ss♦❝✐❛❞❛s ❛♦s ❝r✐tér✐♦s ❞❡ ❝❡✲ ❞ê♥❝✐❛ ❝♦♠ ✐♥t❡r❡ss❡ ♥❡st❡ tr❛❜❛❧❤♦✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♦ ❝r✐tér✐♦ ❞❡ ❚r❡s❝❛ ❡ ❞❡ ✈♦♥ ▼✐s❡s✱ q✉❡ sã♦ ♦s ❝r✐tér✐♦s ♠❛✐s ❝♦♠✉♠♠❡♥t❡ ✉t✐❧✐③❛❞♦s ♣❛r❛ s✐♠✉❧❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♠❛t❡r✐❛✐s ♠❡tá❧✐❝♦s ❬✷❪✳
❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ❞❡✜♥❡✲s❡ ♦ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s ♣r✐♥❝✐♣❛✐s ✭σI✱σII✱σIII✮ ❡ ❞❛s t❛①❛s ❞❡
❞❡❢♦r♠❛çã♦ ♣r✐♥❝✐♣❛✐s ✭ε˙I ✱ε˙II✱εIII˙ ✮✱ ♣r❡ss✉♣♦♥❞♦ ❛ s❡❣✉✐♥t❡ ♦r❞❡♥❛çã♦✿
σI > σII > σIII ✭✷✳✶✸✮
❉❡✜♥❡✲s❡ t❛♠❜é♠ ♦ ❡s♣❛ç♦ ❛✉①✐❧✐❛r✱Cc✱ ♦❜r✐❣❛♥❞♦ ❞❡ ❢♦r♠❛ ✐♠♣❧í❝✐t❛ ❛ ✐♥❝❧✉sã♦ ❞❛s ❝♦♥✲
❞✐çõ❡s ❞❡ ♥♦r♠❛❧✐❞❛❞❡ ❞♦ ❡s❝♦❛♠❡♥t♦ ♣❧ást✐❝♦ ✭✷✳✶✵✮ ❡ ✭✷✳✶✷✮✱ ❢❛❧t❛♥❞♦ ❛♣❡♥❛s r❡str✐♥❣✐r ❛s t❛①❛s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ ❛❞♠✐ssí✈❡✐s ❛♦ s❡✉ ❞♦♠í♥✐♦✳ ➱ r❡❧❡✈❛♥t❡ ♠❡♥❝✐♦♥❛r q✉❡ ♣❛r❛ ♦s ❞♦✐s ❝r✐tér✐♦s ❛♥t❡r✐♦r♠❡♥t❡ r❡❢❡r✐❞♦s ♦ ❡s❝♦❛♠❡♥t♦ ♣❧ást✐❝♦ é ✐♥❝♦♠♣r❡ssí✈❡❧✱ ✐✳❡✳✱ ♥ã♦ r❡s✉❧t❛ ♥✉♠❛ ✈❛r✐❛çã♦ ❞❡ ✈♦❧✉♠❡ ❞♦ ♠❛t❡r✐❛❧✳ ❊st❡ ❢❛❝t♦ ❡stá ❡♠ ❝♦♥s♦♥â♥❝✐❛ ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❞♦s ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s r❡❛❧✐③❛❞♦s ❝♦♠ ♠❛t❡r✐❛✐s ♠❡tá❧✐❝♦s ❬✷❪✳ ◆❛ ❋✐❣✉r❛ ✷✳✸ r❡♣r❡s❡♥t❛♠✲s❡✱ ♥♦ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s ♣r✐♥❝✐♣❛✐s✱ ❛s s✉♣❡r❢í❝✐❡s ❞❡ ❝❡❞ê♥❝✐❛ ❝♦rr❡s♣♦♥❞❡♥t❡s ❛ ❝❛❞❛ ❝r✐tér✐♦ ❝♦♥s✐❞❡r❛❞♦✳
✭❛✮ ❚r❡s❝❛ ✭❜✮ ✈♦♥ ▼✐s❡s
❋✐❣✉r❛ ✷✳✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❛s s✉♣❡r❢í❝✐❡s ❞❡ ❝❡❞ê♥❝✐❛ ✭❘❡t✐r❛❞♦ ❞❡ ❱✐❝❡♥t❡ ❞❛ ❙✐❧✈❛❬✹❪✮
❈r✐tér✐♦ ❞❡ ❚r❡s❝❛
❖ ❝r✐tér✐♦ ❞❡ ❚r❡s❝❛ r❡s✉❧t❛ ❞❛ ✐♠♣♦s✐çã♦ ❞❡ ✉♠❛ t❡♥sã♦ t❛♥❣❡♥❝✐❛❧ ♠á①✐♠❛✱ ❝✱ ❛ q✉❛❧ ♥✉♥❝❛ ♣♦❞❡ s❡r ❡①❝❡❞✐❞❛ ❬✺❪✳ ❉❡st❡ ♠♦❞♦✱ ♣❛r❛ ♦ ❝r✐tér✐♦ ❞❡ ❚r❡s❝❛ ❛ ❡①♣r❡ssã♦ ❞❛ ❢✉♥çã♦
❞❡ ❝❡❞ê♥❝✐❛ é ❞❛❞❛ ♣♦r✱
f(σ) =σI −σIII −2c ✭✷✳✶✹✮
P♦r s✉❛ ✈❡③ ❛ ❢✉♥çã♦ ❞❡ ❞✐ss✐♣❛çã♦ ❡ ♦ ❡s♣❛ç♦ Cc sã♦ ❞❡✜♥✐❞♦s ❛tr❛✈és ❞❛s ❡①♣r❡ssõ❡s✱
D( ˙εp) =c(|ε˙pI |+|ε˙IIp |+|ε˙pIII |), ∀ε˙p ∈ Cc ✭✷✳✶✺✮
˙
εp ∈ Cc ⇔tr( ˙εp) = 0 ✭✷✳✶✻✮
❈r✐tér✐♦ ❞❡ ✈♦♥ ▼✐s❡s
❖ ❝r✐tér✐♦ ❞❡ ✈♦♥ ▼✐s❡s r❡s✉❧t❛ ❞❛ ✐♠♣♦s✐çã♦ ❞❡ ✉♠❛ ❡♥❡r❣✐❛ ❞❡ ❞✐st♦rçã♦ ♠á①✐♠❛✱ r❡s✉❧✲ t❛♥❞♦ ❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦ ♣❛r❛ ❞❡✜♥✐r ❛ r❡s♣❡❝t✐✈❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✿
f(σ) =
r
1
2tr(s
2)−k ✭✷✳✶✼✮
♦♥❞❡ ❦ é ❛ t❡♥sã♦ ❞❡ ❝♦rt❡ ❞❡ ❝❡❞ê♥❝✐❛ ♦❜t✐❞❛ ♥✉♠ ❡♥s❛✐♦ ❞❡ tr❛❝çã♦ ✉♥✐❛①✐❛❧✳ ❆ ❢✉♥çã♦ ❞❡ ❞✐ss✐♣❛çã♦ ❡ ♦ ❡s♣❛ç♦ Cc sã♦ ❞❡✜♥✐❞♦s ❛tr❛✈és ❞❛s ❡①♣r❡ssõ❡s✱
D( ˙εp) =kp2tr(( ˙εp)2), ∀ε˙p
∈ Cc ✭✷✳✶✽✮
˙
εp ∈ Cc ⇔tr( ˙εp) = 0 ✭✷✳✶✾✮
❉✐ss✐♣❛çã♦ ❡♠ s✉♣❡r❢í❝✐❡s ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦
❈♦♥❢♦r♠❡ ❥á ❢♦✐ ♠❡♥❝✐♦♥❛❞♦✱ ❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡ ♥ã♦ ❡①❝❧✉✐ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❛ ♦❝♦r✲ rê♥❝✐❛ ❞❡ ❞❡s❝♦♥t✐♥✉✐❞❛❞❡s ♥♦ ❝❛♠♣♦ ❞❛s ✈❡❧♦❝✐❞❛❞❡s✱ s✉r❣✐♥❞♦✱ ❛ss✐♠✱ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ q✉❛♥t✐✜❝❛r ❛ ❞✐ss✐♣❛çã♦ ♣❧ást✐❝❛ q✉❡ ♦❝♦rr❡ ♥❡st❛ s✐t✉❛çã♦✳ ❆ ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈❛✱ ˆv✱ ♥✉♠
♣♦♥t♦ ❣❡♥ér✐❝♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ é ♦❜t✐❞❛ ❛tr❛✈és ❞❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛s ✈❡✲ ❧♦❝✐❞❛❞❡s ❞❡ ❞♦✐s s✉❜✲❞♦♠í♥✐♦s ❛❞❥❛❝❡♥t❡s✱
ˆ
v= ˙u2−u˙1 ✭✷✳✷✵✮
