Elastografia em imagens de ultrassom utilizando elementos de contorno

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ANDERSON GABRIEL SANTIAGO CRAVO

ELASTOGRAFIA EM IMAGENS DE ULTRASSOM UTILIZANDO ELEMENTOS DE

CONTORNO

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E

LASTOGRAFIA EM

I

MAGENS DE

U

LTRASSOM

U

TILIZANDO

E

LEMENTOS DE

C

ONTORNO

Tese apresentada à Escola Politécnica da Universidade de São Paulo para obtenção do título de Doutor em Engenharia

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E

LASTOGRAFIA EM

I

MAGENS DE

U

LTRASSOM

U

TILIZANDO

E

LEMENTOS DE

C

ONTORNO

Tese apresentada à Escola Politécnica da Universidade de São Paulo para obtenção do título de Doutor em Engenharia

Área de Concentração:

Engenharia de Sistemas Eletrônicos

Orientador: Professor Doutor Luiz Cezar Trintinalia

SÃO PAULO

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Catalogação-na-publicação

Cravo, Anderson Gabriel Santiago

Elastografia em imagens de ultrassom utilizando o método dos elementos de contorno / A.G. Santiago. -- São Paulo, 2015.

110 p.

Tese (Doutorado) - Escola Politécnica da Universidade de São Paulo. Departamento de Engenharia de Telecomunicações e Controle.

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❆♦s ♠❡✉s ❛✈ós✱

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✏❚❤❡s❡ t✇♦ ♣❡♦♣❧❡ ❛r❡ ❤❛r❞ t♦ ✜♥❞ ✐♥ t❤❡ ✇♦r❧❞✳ ❲❤✐❝❤ t✇♦❄ ❚❤❡ ♦♥❡ ✇❤♦ ✐s ✜rst t♦ ❞♦ ❛ ❦✐♥❞♥❡ss✱ ❛♥❞ t❤❡ ♦♥❡ ✇❤♦ ✐s ❣r❛t❡❢✉❧ ❛♥❞ t❤❛♥❦❢✉❧ ❢♦r ❛ ❦✐♥❞♥❡ss ❞♦♥❡✳✧ ✑ ✲ ❚❤❡ ❇✉❞❞❤❛ ✲ ❆◆ ✷✳✶✶✾

✏❆s ❧♦♥❣ ❛s ■ ❧✐✈❡✱ s♦ ❧♦♥❣ ❞♦ ■ ❧❡❛r♥✳✑ ✲ ❘❛♠❛❦r✐s❤♥❛

✏❙♦♠❡ ♣❛rt ♦❢ ♦✉r ❜❡✐♥❣ ❦♥♦✇s t❤✐s ✲ t❤❡ ❯♥✐✈❡rs❡ ✲ ✐s ✇❤❡r❡ ✇❡ ❝❛♠❡ ❢r♦♠✳

❲❡ ❧♦♥❣ t♦ r❡t✉r♥✳ ❆♥❞ ✇❡ ❝❛♥✳ ❇❡❝❛✉s❡ t❤❡ ❝♦s♠♦s ✐s ❛❧s♦ ✇✐t❤✐♥ ✉s✳

❲❡✬r❡ ♠❛❞❡ ♦❢ st❛r✲st✉✛✳

❲❡ ❛r❡ ❛ ✇❛② ❢♦r t❤❡ ❝♦s♠♦s t♦ ❦♥♦✇ ✐ts❡❧❢✳✑

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❆❣r❛❞❡❝✐♠❡♥t♦s

❆❣r❛❞❡ç♦ ✐♠❡♥s❛♠❡♥t❡ à ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦s ♠❡✉s ❛✈ós ❍❛♠✐❧t♦♥ ❙❛♥t✐❛❣♦ ✭✐♥ ♠❡♠♦✲ r✐❛♥✮ ❡ ❉✐✈❛ ▼❛r✐❛ ❞❡ ❖❧✐✈❡✐r❛ ❙❛♥t✐❛❣♦ ✭✐♥ ♠❡♠♦r✐❛♥✮✱ à ♠✐♥❤❛ ♠ã❡ ❙❛♥❞r❛✱ ♠✐♥❤❛ ✏✐r♠ã❡✑ ▲✐❛ ❡ ♠❡✉s t✐♦s✱ ❘❡♥❛t♦ ❡ ❖tá✈✐♦ ❙❛♥t✐❛❣♦✳

❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ♣r♦❢❡ss♦r ▲✉✐③ ❈❡③❛r ❚r✐♥t✐♥á❧✐❛✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡ ✐♥❝rí✈❡❧ ♣❛❝✐✲ ê♥❝✐❛ ❝♦♠✐❣♦✳

❆♦ ♠❡✉ ❝❤❡❢❡ ❡ ❝♦✲♦r✐❡♥t❛❞♦r✱ ♣r♦❢❡ss♦r ▼❛r❝♦ ❆♥t♦♥✐♦ ●✉t✐❡rr❡③✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ♣❛❝✐ê♥❝✐❛✱ ❛♠✐③❛❞❡ ❡ ♣♦r ♠❡ ❛♣♦✐❛r ♥❡st❡ tr❛❜❛❧❤♦✳

❆♦ ♠❡✉ q✉❡r✐❞♦ ❛♠✐❣♦✱ ❋❡r♥❛♥❞♦ ❆♥tô♥✐♦ ❚❡♥ór✐♦ ❋✐r❡♠❛♥ ♣❡❧❛s ❧♦♥❣❛s ❝♦♥✈❡rs❛s ❡ ❛♣♦✐♦✳ ❆❣r❛❞❡ç♦ ❛♦ ♣❡sq✉✐s❛❞♦r ❋❡r♥❛♥❞♦ ▼✐st✉②❛♠❛ ❈❛r❞♦s♦✱ ♣❡❧❛ ✐♥❡st✐♠á✈❡❧ ❛❥✉❞❛✱ s❡♠ ❛ q✉❛❧ ♣❛rt❡ ❞❡st❡ tr❛❜❛❧❤♦ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧✳

❚❛♠❜é♠ ❛❣r❛❞❡ç♦ ✐♠❡♥s❛♠❡♥t❡ à ♣❡sq✉✐s❛❞♦r❛ ▼❛②s❛ ▼❛❧✜③❛ ▼❛❝❡❞♦✱ ♣❡❧❛ ✐♥❡st✐♠á✈❡❧ ❛❥✉❞❛ ❡ ❛♠✐③❛❞❡ ❡ ♣♦r t♦❞♦s ♦s ❞✐❛s ❞❡ ♣❛❝✐ê♥❝✐❛ ❡ ❧♦♥❣❛s ❝♦♥✈❡rs❛s✳

❆♦ s❡r✈✐ç♦ ❞❡ ✐♥❢♦r♠át✐❝❛ ❞♦ ■♥st✐t✉t♦ ❞♦ ❈♦r❛çã♦✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ ✏●r✉♣♦ ❞♦ ■♥s✉♣♦rtá✈❡❧✑✱ ❆❞r✐❛♥❛ P❛❧❤❛r❡s✱ ❆❞í❧✐♦ ❇❡r♥❛r❞❡s✱ ❑át✐❛ ❋❧á✈✐❛ ❈â♥❞✐❞❛ ▼❛t❤❡✉s✱ ▼❛r② ❘♦s❡ ❑❡♥❝❤✐❛♥ ❡ Pr✐s❝✐❧❛ ▼❛t♦s✳

❆♦s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞❡ ❧❛❜♦r❛tór✐♦ ❞❡ P✫❉ ❞♦ ■♥st✐t✉t♦ ❞♦ ❈♦r❛çã♦✱ ❆❧✐❝❡ ❙❤✐♠❛❞❛ ❇❛❝✐❝✱ ❏♦❤♥ ❆♥❞r❡✇ ❙✐♠s ❡ ▼❛r✐❛ ❚❡r❡③❛ ❆❜r❛❤ã♦ ♣❡❧♦s ❞✐✈❡rt✐❞♦s ❝❛❢és ❞❛ t❛r❞❡✱ ❆❞♠❛r ▲♦♥❣♦✱ ▼❛r✐♥❛ ❘❡❜❡❧♦ ❡ ❘❛♠♦♥ ▼♦r❡♥♦✳

➚s ♠✐♥❤❛s q✉❡r✐❞❛s ❛♠✐❣❛s q✉❡ ♠❡s♠♦ ❧♦♥❣❡✱ sã♦ ♣❛rt❡ ✐♠♣♦rt❛♥t❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛✱ ❈❛r♦❧✐♥❛ ❞❡ ❖❧✐✈❡✐r❛ ●♦♥ç❛❧✈❡s ❡ ❙❛♥❞r❛ ❈❛rt❛①♦✳

❆♦ ❑✐❦♦✱ ▼✐✱ ❋✉♠❛ç❛ ❡ ▼❛♥✉✱ ♣❡❧❛s ❤♦r❛s ❞❡ ❞✐✈❡rt✐♠❡♥t♦ ❡ ❝❛r✐♥❤♦ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛♠✳ ❆❣r❛❞❡ç♦ ❛♦ ❈◆Pq ❡ ❛♦ ♣r♦❥❡t♦ ❯❧tr❛ss♦♠✴❋✐♥❡♣ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳

❊♥✜♠✱ ❛❣r❛❞❡ç♦ à t♦❞♦s ❛q✉❡❧❡s q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞❛ ♠✐♥❤❛ ❥♦r♥❛❞❛✳ ❈❡rt❛ ✈❡③ ❧✐ q✉❡ ♠❡s♠♦ ✉♠ ♠❡♥❞✐❣♦ ❛ q✉❡♠ ♥❡❣❛♠♦s ❡s♠♦❧❛ é ♣❛rt❡ ✐♥❞✐s♦❧ú✈❡❧ ❞❡ ♥♦ss❛ ❢♦r♠❛çã♦✳✳✳ ◆ã♦ ❤á ✈❡r❞❛❞❡ ♠❛✐♦r✳ ❆❧❣✉♠❛s ♣❡ss♦❛s ✐♥✢✉❡♥❝✐❛r❛♠ ♠✐♥❤❛ ✈✐❞❛ ❞❡ ❢♦r♠❛ q✉❡ s❡q✉❡r ✐♠❛❣✐♥❛♠✱ ❝♦♠ ❝♦♠❡♥tár✐♦s ♦✉ ❛t✐t✉❞❡s ♥❡♠ s❡♠♣r❡ ✐♥t❡♥❝✐♦♥❛✐s✳

❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛ t♦❞♦s q✉❡ s❡ ❞❡t✐✈❡r❛♠ ❛❧❣✉♥s ♠✐♥✉t♦s ♣❛r❛ ❧❡r ❡st❡ t❡①t♦✳✳✳ ■ ❣✉❡ss t❤❡ ✇♦r❞ ✏t❤❛♥❦s✑ ✐s ♥♦t ❜✐❣ ❡♥♦✉❣❤✦

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▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶✳✶ ❉✐❛❣r❛♠❛ ♣❛r❛ ❡❧❛st♦❣r❛✜❛ ✈✐rt✉❛❧ ❡♠ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠✱ r❛str❡❛♠❡♥t♦ ❞❡ r✉í❞♦ s♣❡❝❦❧❡ ❡ ❛♥á❧✐s❡ ✐♥✈❡rs❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✷✳✵✳✶ ❉✐❛❣r❛♠❛ ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ❝❛♠♣♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❡ ❞❡❢♦r♠❛çõ❡s ✉s❛♥❞♦ ▲✉❝❛s✲❑❛♥❛❞❡✱ s❡❣✉♥❞♦ ❩❛❦❛r✐❛ ❡t ❛❧✳ ❬✼✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✸✳✷✳✶ ❈♦r♣♦ s✉❥❡✐t♦ à r❡str✐çõ❡s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❡ s♦❧✐❝✐t❛çõ❡s ❡①t❡r♥❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷✳✷ ❈♦rt❡ ❡♠ ✉♠ ♣❧❛♥♦ Π❡ ❛s ❢♦rç❛s ✐♥t❡r♥❛s r❡s✉❧t❛♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

✸✳✷✳✸ ❉❡✜♥✐çã♦ ❞❡ t❡♥sã♦ ♥♦r♠❛❧ ❡ ❞❡ ❝✐s❛❧❤❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷✳✹ ❈❛♠♣♦ ❞❡ t❡♥sõ❡s ❡♠ ✉♠ ❡❧❡♠❡♥t♦ ✐♥✜♥✐t❡s✐♠❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷✳✺ ❱❡t♦r ❞❡ ❢♦rç❛ ❞❡ s✉♣❡r❢í❝✐❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✷✳✻ ▼♦❞❡❧♦ ❞❡ ✉♠❛ ✜❜r❛ ❞❡❢♦r♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷✳✼ ❱❛r✐❛çã♦ ❛♥❣✉❧❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✷✳✽ ❈♦r♣♦ ❞❡ ♣r♦✈❛ ❡ ❞❡❢♦r♠❛çõ❡s ❛ss♦❝✐❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✷✳✾ ❊st❛❞♦ ♣❧❛♥♦ ❞❡ t❡♥sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✷✳✶✵❊st❛❞♦ ♣❧❛♥♦ ❞❡ ❞❡❢♦r♠❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✹✳✶✳✶ ▼❛❧❤❛ ♣❛r❛ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✶✳✷ ▼❛❧❤❛ ♣❛r❛ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✷✳✶ ❋✉♥çõ❡s ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣❛r❛ tr✐â♥❣✉❧♦s ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✷✳✷ ❊①❡♠♣❧♦ ❞❡ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❝♦♠ ❞♦✐s ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✳ ✹✵ ✹✳✷✳✸ Pr♦❣r❛♠❛ ♣❛r❛ ♠♦♥t❛❣❡♠ ❞❛ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③ ❣❧♦❜❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✸✳✶ ❉♦♠í♥✐♦ ❞❛ ❊q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❡ s❡✉ ❝♦♥t♦r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✸✳✷ ◆♦r♠❛❧ ❛♦ ❝♦♥t♦r♥♦ Γ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✹✳✸✳✸ ➶♥❣✉❧♦ ✐♥t❡r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✸✳✹ ❈♦♥t♦r♥♦ ❞✐s❝r❡t✐③❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✸✳✺ ❉❡s❝♦♥t✐♥✉✐❞❛❞❡ ❡♥tr❡ ❞♦✐s ❡❧❡♠❡♥t♦s ❛❞❥❛❝❡♥t❡s ❝❛✉s❛❞❛ ♣❡❧♦ ✉s♦ ❞❡ ❢✉♥çõ❡s ❝♦♥st❛♥t❡s✳ ✹✻ ✹✳✸✳✻ P❛r❛♠❡tr✐③❛çã♦ ❞❛ ❣❡♦♠❡tr✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✸✳✼ ❈♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ❜❡♠ ♣♦s✐❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸✳✽ ▼♦❞❡❧♦ ❝♦♠ três s✉❜✲r❡❣✐õ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✾ ▼❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ♣❛r❛ ♦ ❡①❡♠♣❧♦ ❞❛ ❋✐❣✉r❛ ✹✳✸✳✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸✳✶✵❊q✉✐❧í❜r✐♦ ❞❡ ❢♦rç❛s ❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ♥❛ ✐♥t❡r❢❛❝❡ ❞❡ ❞✉❛s s✉❜✲r❡❣✐õ❡s✳ ✺✷

(9)

✹✳✹✳✶ ▼❛❧❤❛ ♣❛r❛ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ❝♦♥s✐❞❡r❛♥❞♦ ❜❛❝❦❣r♦✉♥❞ ❡ três ❧❡sõ❡s✿ ✭❛✮ ▼❛❧❤❛ ♣❛r❛ ♦ ❜❛❝❦❣r♦✉♥❞❀ ✭❜✮ ▼❛❧❤❛ ♣❛r❛ ❛s ❧❡sõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✹✳✷ ▼❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ ❜❛❝❦❣r♦✉♥❞ ❡ três ❧❡sõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✹✳✸ ❉❡t❛❧❤❡ ❞❛ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❣❡r❛❞❛ ❛ ♣❛rt✐r ❞❛ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦✳ ✺✺ ✹✳✹✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛rq✉✐t❡t✉r❛s ❞❡ ✉♠❛ ❈P❯ ❡ ❞❡ ✉♠❛ ●P❯ ❬❝✉❞❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✹✳✺ ❉✐str✐❜✉✐çã♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ t❤r❡❛❞s ❡♠ ❜❧♦❝♦s✳ ❬✻✻❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✹✳✻ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❈P❯s ❡ ●P❯s ❡♠ t❡r♠♦s ❞❡ ●✐❣❛ ❋▲❖P❙ ❬❝✉❞❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✹✳✼ ❊①❡♠♣❧♦ ❞❡ ❝ó❞✐❣♦ ❡♠ ❈❯❉❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✹✳✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❈P❯ ❡ ●P❯ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ❝♦♥st❛♥t❡s

❬✹✺❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✺✳✶✳✶ ❉✐❛❣r❛♠❛ ♣❛r❛ ❛♥á❧✐s❡ ✐♥✈❡rs❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✹✳✶ ▼♦❞❡❧❛❣❡♠ ❞♦ ♣r♦❜❧❡♠❛ ❝♦♠ ♣❤❛♥t♦♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✹✳✷ ●rá✜❝♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ ❛♥á❧✐s❡ ✐♥✈❡rs❛ ✉t✐❧✐③❛♥❞♦ ✉♠❛ s✐♠✉❧❛çã♦ ✐❞❡❛❧✱ s❡♠ r✉í❞♦✳ ✳ ✻✾ ✺✳✹✳✸ ❉✐❛❣r❛♠❛ ✈❛❧✐❞❛çã♦ ❞❛ ❛♥á❧✐s❡ ✐♥✈❡rs❛ ✉t✐❧✐③❛♥❞♦ ❡♥tr❛❞❛ ✐❞❡❛❧ ✭s❡♠ r✉í❞♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✹✳✹ ❉✐❛❣r❛♠❛ ✈❛❧✐❞❛çã♦ ❞❛ ❛♥á❧✐s❡ ✐♥✈❡rs❛ ✉t✐❧✐③❛♥❞♦ ❡♥tr❛❞❛ ❝♦♠ r✉í❞♦✿ ✭❛✮ ❘✉í❞♦ ❛❞✐❝✐♦♥❛❞♦

❛♦ ✈❡t♦r ❞❡ ♣r❡ssã♦❀ ✭❜✮ ❘✉í❞♦ ❛❞✐❝✐♦♥❛❞♦ ❛♦ ✈❡t♦r ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s❀ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✹✳✺ ❈✉r✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❛♦ ✈❡t♦r ❞❡

♣r❡ssã♦ ✭SN RdB = 30dB✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✹✳✻ ❈✉r✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❛♦ ✈❡t♦r ❞❡ ♣r❡ssã♦ ✭SN RdB = 50dB✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✹✳✼ ❈✉r✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❛♦ ✈❡t♦r ❞❡ ♣r❡ssã♦ ✭SN RdB = 100dB✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

✺✳✹✳✽ ❈✉r✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❛♦ ✈❡t♦r ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ✭SN RdB = 30dB✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

✺✳✹✳✾ ❈✉r✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❛♦ ✈❡t♦r ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ✭SN RdB = 50dB✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✺✳✹✳✶✵❈✉r✈❛ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛ ♣❛r❛ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❛♦ ✈❡t♦r ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ✭SN RdB = 100dB✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

✻✳✶✳✶ ■♠❛❣❡♠ ❞❡ ✉❧tr❛ss♦♠ ❡ ✉♠ ❝♦♥❥✉♥t♦ χ1 ❞❡ ❡s♣❛❧❤❛❞♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺

✻✳✶✳✷ ▼❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❞❡❢♦r♠❛❞❛ ❡ ❞❡s❧♦❝❛♠❡♥t♦ ❞♦s ❡s♣❛❧❤❛❞♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✻✳✶✳✸ ❊❧❡♠❡♥t♦ ✜♥✐t♦ ❞❡❢♦r♠❛❞♦ ❡ ❞✐stâ♥❝✐❛s ❡♥tr❡ ♦ ❡s♣❛❧❤❛❞♦r ❡ ♦s ✈ért✐❝❡s ❞♦ ❡❧❡♠❡♥t♦✳ ✳ ✳ ✳ ✼✻ ✻✳✶✳✹ ♣❤❛♥t♦♠ ♠❛t❡♠át✐❝♦ r= 5.5mm✿ ✭❛✮ ■♠❛❣❡♠ ♣ré✲❞❡❢♦r♠❛çã♦❀ ✭❜✮ ■♠❛❣❡♠ ♣ós✲❞❡❢♦r♠❛çã♦✳ ✽✵

✼✳✷✳✶ P❤❛♥t♦♠s tr❛♥s❝✉tâ♥❡♦s ❝♦♠ ❧❡sã♦✱ s❡♥❞♦ ❛ ✜❣✉r❛ à ❡sq✉❡r❞❛ ❛ ✐♠❛❣❡♠ ♣ré✲❞❡❢♦r♠❛çã♦ ❡ ❛ ✐♠❛❣❡♠ ❛ ❞✐r❡✐t❛ ♣ós✲❞❡❢♦r♠❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✼✳✷✳✷ ❙✐♠✉❧❛çõ❡s ❝♦♠ ▲✉❝❛s✲❑❛♥❛❞❡ ✈❛r✐❛♥❞♦ ♦ t❛♠❛♥❤♦ ❞❛ ❥❛♥❡❧❛ ❞❡ ❛♠♦str❛❣❡♠✿ ✭❛✮ ❏❛♥❡❧❛

20_×20pixels❀ ✭❜✮ ❏❛♥❡❧❛ 40_×40pixels❀ ✭❝✮ ❏❛♥❡❧❛60_×60pixels❀ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

✼✳✹✳✶ ♣❤❛♥t♦♠ ❝♦♠ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡ ❞❡s❧♦❝❛♠❡♥t♦s ❝❛❧❝✉❧❛❞♦s ♣♦r ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✭♠❛rr♦♠✮ ❡ ✢✉①♦ ó♣t✐❝♦ ✭✈❡r♠❡❧❤♦✮ ✉t✐❧✐③❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ▲✉❝❛s✲❑❛♥❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼

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✼✳✹✳✷ ❉❡t❛❧❤❡ ♣❛r❛ ❝♦♠♣r❛çã♦ q✉❛❧✐t❛t✐✈❛ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢✉①♦ ó♣t✐❝♦ ♣♦r ▲✉❝❛s✲❑❛♥❛❞❡ ❡ ❡❧❡✲ ♠❡♥t♦s ✜♥✐t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✼✳✹✳✸ ♣❤❛♥t♦♠ ❝♦♠ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡ ❞❡s❧♦❝❛♠❡♥t♦s ❝❛❧❝✉❧❛❞♦s ♣♦r ❡❧❡♠❡♥t♦s ✜♥✐t♦s

✭♠❛rr♦♠✮ ❡ ✢✉①♦ ó♣t✐❝♦ ✭✈❡r♠❡❧❤♦✮ ✉t✐❧✐③❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❇r♦①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✼✳✹✳✹ ❉❡t❛❧❤❡ ♣❛r❛ ❝♦♠♣❛r❛çã♦ q✉❛❧✐t❛t✐✈❛ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ✢✉①♦ ó♣t✐❝♦ ♣♦r ❇r♦① ❡ ❡❧❡♠❡♥t♦s

✜♥✐t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✽✳✶✳✶ ❊rr♦ ǫ(%)♣❛r❛ ♦ ❜❛❝❦❣r♦✉♥❞ ❡♠ ❢✉♥çã♦ ❞❛ ♣r❡ssã♦ ❛♣❧✐❝❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸

✽✳✶✳✷ ❊rr♦ ǫ(%)♣❛r❛ ❛ ❧❡sã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣r❡ssã♦ ❛♣❧✐❝❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹

✽✳✷✳✶ ❊rr♦ ǫ(%)♣❛r❛ ♦ ❜❛❝❦❣r♦✉♥❞ ❡♠ ❢✉♥çã♦ ❞❛ ♣r❡ssã♦ ❛♣❧✐❝❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻

✽✳✷✳✷ ❊rr♦ ǫ(%)♣❛r❛ ❛ ❧❡sã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣r❡ssã♦ ❛♣❧✐❝❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼

✽✳✷✳✸ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❡♠ ❢✉♥çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ♣❛r❛ ❛ r❡❣✐ã♦ ❞❛ ❧❡sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✽✳✷✳✹ ❈♦♥✈❡r❣ê♥❝✐❛ ❞♦ ♠ét♦❞♦ ❡♠ ❢✉♥çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ✜♥✐t♦s ♣❛r❛ ❛ r❡❣✐ã♦ ❞❛

❧❡sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽

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▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✺✳✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ▼❱❈ ❡ ❞✐❢❡r❡♥ç❛s ✜♥✐t❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✷ P❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ s✐♠✉❧❛çã♦ ❞♦ ♣❤❛♥t♦♠ ❝♦♠ ❞✉❛s ❧❡sõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

✼✳✶ ▼❡❞✐❞❛s ❞❡ ❡rr♦ ♣❛r❛ ♦ ♣❤❛♥t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✼✳✷ ▼❡❞✐❞❛s ❞❡ ❡rr♦ ♣❛r❛ ♦ ♣❤❛♥t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✽✳✶ Pr♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡ ♠❛t❡r✐❛✐s ♣❛r❛ ♦ ♣❤❛♥t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✽✳✷ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❈ ❡ ▲✉❝❛s✲❑❛♥❛❞❡ ♣❛r❛

♦ ♣❤❛♥t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✽✳✸ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❈ ❡ ❇r♦① ♣❛r❛ ♦ ♣❤❛♥✲

t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✽✳✹ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❋ ❡ ▲✉❝❛s✲❑❛♥❛❞❡ ♣❛r❛

♦ ♣❤❛♥t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✽✳✺ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❋ ❡ ❇r♦① ♣❛r❛ ♦ ♣❤❛♥✲

t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✽✳✻ ❊rr♦ ♠é❞✐♦ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣❛r❛ ❝❛❞❛ ❛ss♦❝✐❛çã♦ ❞❡ ♠ét♦❞♦s ♣❛r❛ ♦ ♣❤❛♥t♦♠ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✽✳✼ ▼❛t❡r✐❛❧ ❛♥❞ ❣❡♦♠❡tr✐❝ ♣r♦♣❡rt✐❡s ❢♦r ♣❤❛♥t♦♠ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✽✳✽ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❈ ❡ ▲✉❝❛s✲❑❛♥❛❞❡ ♣❛r❛

♦ ♣❤❛♥t♦♠✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✽✳✾ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❈ ❡ ❇r♦① ♣❛r❛ ♦ ♣❤❛♥✲

t♦♠✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✽✳✶✵ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❋ ❡ ▲✉❝❛s✲❑❛♥❛❞❡ ♣❛r❛

♦ ♣❤❛♥t♦♠✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✽✳✶✶ ❘❡s✉❧t❛❞♦s ♣❛r❛ ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦s ✉t✐❧✐③❛♥❞♦ ▼❊❋ ❡ ❇r♦① ♣❛r❛ ♦ ♣❤❛♥✲

t♦♠✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✽✳✶✷ ❊rr♦ ♠é❞✐♦ ❡ ❞❡s✈✐♦ ♣❛❞rã♦ ♣❛r❛ ❝❛❞❛ ❛ss♦❝✐❛çã♦ ❞❡ ♠ét♦❞♦s ♣❛r❛ ♦ ♣❤❛♥t♦♠✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✽✳✶✸ ◗✉❛♥t✐❞❛❞❡ ❞❡ ✐t❡r❛çõ❡s ♣❛r❛ ❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❡ ♦ t❡♠♣♦ ♠á①✐♠♦ ♣❛r❛ ❝❛❞❛ ❝♦♠❜✐♥❛çã♦ ❞❡

♠ét♦❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽

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◆♦t❛çõ❡s ❡ ❉❡✜♥✐çõ❡s

• ▼❊❈ ✲ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦

• ▼❊❋ ✲ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s

• ▼❱❈ ✲ ▼ét♦❞♦ ❞❡ ❱❛r✐á✈❡❧ ❈♦♠♣❧❡①❛

• ❊■❈ ✲ ❊q✉❛çã♦ ■♥t❡❣r❛❧ ❞❡ ❈♦♥t♦r♥♦

• ❖❋ ✲ ❋❧✉①♦ Ó♣t✐❝♦

• ❈❆❉ ✲ ❈♦♠♣✉t❡r ❆✐❞❡❞ ❉❡t❡❝t✐♦♥

• hi(η) ✲ ❋✉♥çã♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣♦❧✐♥♦♠✐❛❧ ♣❛r❛ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦

• [H]✲ ▼❛tr✐③ ❞❡ ✐♥✢✉ê♥❝✐❛ ♣❛r❛ ❢♦rç❛s ❞❡ s✉♣❡r❢í❝✐❡

• [G]✲ ▼❛tr✐③ ❞❡ ✐♥✢✉ê♥❝✐❛ ♣❛r❛ ❞❡s❧♦❝❛♠❡♥t♦s

• ωi ✲ ❋✉♥çã♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦ ♣♦❧✐♥♦♠✐❛❧ ♣❛r❛ ❡❧❡♠❡♥t♦s ✜♥✐t♦s

• [K] ✲ ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s

• [K]e ✲ ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❡❧❡♠❡♥t❛r ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s

• η ✲ ❱❛r✐á✈❡❧ ♣❛r❛♠étr✐❝❛

• Ω✲ ❉♦♠í♥✐♦ ❞♦ ♣r♦❜❧❡♠❛

• ∂Ω ✲ ❈♦♥t♦r♥♦ ❞♦ ❞♦♠í♥✐♦ Ω

• Γ ✲ ❈♦♥t♦r♥♦ ❞♦ ❞♦♠í♥✐♦✱ Γ =∂Ω

• Ne ✲ ◆ú♠❡r♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦

• NR✲ ◗✉❛♥t✐❞❛❞❡ ❞❡ s✉❜✲r❡❣✐õ❡s ♥♦ ♣r♦❜❧❡♠❛

• NE ✲ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♠❛t❡r✐❛✐s ❝♦♠ ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❞✐st✐♥t♦s

• σ ✲ ❚❡♥sã♦ [P a] = [N/m]

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• ε ✲ ❉❡❢♦r♠❛çã♦ [m/m]

• Ei ✲ ▼ó❞✉❧♦ ❞❡ ❨♦✉♥❣ ❞♦ ✐✲és✐♠♦ ♠❛t❡r✐❛❧

• ν ✲ ❈♦❡✜❝✐❡♥t❡ ❞❡ P♦✐ss♦♥

• Cijkl ✲ ❚❡♥s♦r ❞❡ ♣r♦♣r✐❡❞❛❞❡s ♠❛t❡r✐❛✐s

• [C]✲ ▼❛tr✐③ ❞❡ ♣r♦♣r✐❡❞❛❞❡s ♠❛t❡r✐❛✐s❈♦♠♦ ✉♠❛ ❞❛s ❧✐♠✐t❛çõ❡s ❞♦ ▼❊❈ ❡ ▼❊❋

• ωi ✲ ✐✲és✐♠❛ ❢✉♥çã♦ ❞❡ ♣♦♥❞❡r❛çã♦

• u∗

ij ✲ ❋✉♥çã♦ ❞❡ ●r❡❡♥ ♣❛r❛ ❞❡s❧♦❝❛♠❡♥t♦s

• t∗

ij ✲ ❋✉♥çã♦ ❞❡ ●r❡❡♥ ♣❛r❛ ❢♦rç❛s ❞❡ s✉♣❡r❢í❝✐❡

• ~ξ✲ P♦♥t♦ ❢♦♥t❡

• j ✲ ❯♥✐❞❛❞❡ ❝♦♠♣❧❡①❛ j =√₋1

• σ¯ ✲ ❉❡s✈✐♦ ♣❛❞rã♦

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❙✉♠ár✐♦

✶ ■♥tr♦❞✉çã♦ ✶✹

✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✷ ❊str✉t✉r❛ ❞❛ ❚❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✶✾

✸ ❊❧❡♠❡♥t♦s ❞❛ ▼❡❝â♥✐❝❛ ❞♦s ❙ó❧✐❞♦s ❉❡❢♦r♠á✈❡✐s ✷✸

✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✷ ❘❡❧❛çõ❡s ❞❡ ❚❡♥sã♦✱ ❉❡❢♦r♠❛çã♦ ❡ ▲❡✐ ❞❡ ❍♦♦❦❡ ♣❛r❛ ❊❧❛st✐❝✐❞❛❞❡ ■s♦tró♣✐❝❛ ▲✐♥❡❛r ✷✸

✹ ❖ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ❡ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ✸✸ ✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✷ ❖ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✷✳✶ ❋♦r♠✉❧❛çã♦ ❞❛s ❊q✉❛çõ❡s ❞❡ ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✸ ❖ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✸✳✶ ❋♦r♠✉❧❛çã♦ ❞❛ ❊q✉❛çã♦ ■♥t❡❣r❛❧ ❞❡ ❈♦♥t♦r♥♦ ♣❛r❛ ❊❧❛st♦stát✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✸✳✷ ❉✐s❝r❡t✐③❛çã♦ ❡♠ ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✸✳✸ ▼ét♦❞♦ ❞❡ ❙✉❜✲r❡❣✐õ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✹ ▼❛❧❤❛s ♣❛r❛ ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ❡ ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✺ ❆♥á❧✐s❡ ■♥✈❡rs❛ ✻✷

✺✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✺✳✷ ❋♦r♠✉❧❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✺✳✸ ▼ét♦❞♦ ❞❡ ❱❛r✐á✈❡✐s ❈♦♠♣❧❡①❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✺✳✹ ❱❛❧✐❞❛çã♦ ❞❛ ❆♥á❧✐s❡ ■♥✈❡rs❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼

✻ ❈r✐❛çã♦ ❞❡ P❤❛♥t♦♠s ▼❛t❡♠át✐❝♦s ✼✹

✻✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✻✳✶✳✶ ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ❡ ▼♦r✜s♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✻✳✶✳✷ ❖ s♦❢t✇❛r❡ ❯❙s✐♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻

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✼ ❋❧✉①♦ Ó♣t✐❝♦ ♣❛r❛ ❘❛str❡❛♠❡♥t♦ ❞❡ ❘✉í❞♦ ❙♣❡❝❦❧❡ ✽✶ ✼✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✼✳✷ ❋❧✉①♦ Ó♣t✐❝♦ ♣♦r ▲✉❝❛s✲❑❛♥❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✼✳✸ ❋❧✉①♦ Ó♣t✐❝♦ ♣♦r ❇r♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✼✳✹ ❱❛❧✐❞❛çã♦ ❞♦s ▼ét♦❞♦s ♣❛r❛ r❛str❡❛♠❡♥t♦ ❞❡ r✉í❞♦ s♣❡❝❦❧❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✼✳✹✳✶ ❆♥á❧✐s❡ ❞❡ ❊rr♦ ♣❛r❛ ♦ ❆❧❣♦r✐t♠♦ ❞❡ ▲✉❝❛s✲❑❛♥❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✼✳✹✳✷ ❆♥á❧✐s❡ ❞❡ ❊rr♦ ♣❛r❛ ♦ ❆❧❣♦r✐t♠♦ ❞❡ ❇r♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾

✽ ❘❡s✉❧t❛❞♦s ✾✶

✽✳✶ P❤❛♥t♦♠ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✽✳✷ P❤❛♥t♦♠ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹

✾ ❉✐s❝✉ssã♦ ❞♦s ❘❡s✉❧t❛❞♦s✱ ❈♦♥❝❧✉sõ❡s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✾✾

✾✳✶ ❉✐s❝✉ssã♦ ❞♦s ❘❡s✉❧t❛❞♦s ❡ ❈♦♥❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✾✳✷ ❙✉❣❡stõ❡s ♣❛r❛ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✵✵

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❘❡s✉♠♦

❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ ♥♦✈❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❡❧❛st♦❣r❛✜❛ ✈✐rt✉❛❧ ❡♠ ✐♠❛❣❡♥s s✐♠✉❧❛❞❛s ❞❡ ✉❧tr❛ss♦♠ ✉t✐❧✐③❛♥❞♦ ♠ét♦❞♦s ♥✉♠ér✐❝♦s ❡ ♠ét♦❞♦s ❞❡ ✈✐sã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❖ ♦❜❥❡t✐✈♦ é ❡st✐✲ ♠❛r ♦ ♠ó❞✉❧♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❞❡ ❞✐❢❡r❡♥t❡s t❡❝✐❞♦s t❡♥❞♦ ❝♦♠♦ ❡♥tr❛❞❛ ❞✉❛s ✐♠❛❣❡♥s ❞❛ ♠❡s♠❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ♦❜t✐❞❛s ❡♠ ✐♥st❛♥t❡s ❞❡ t❡♠♣♦ ❡ ♣r❡ssõ❡s ❛♣❧✐❝❛❞❛s ❞✐❢❡r❡♥t❡s✳ ❊st❛ ♠❡t♦❞♦❧♦❣✐❛ ❝♦♥s✐st❡ ❡♠ ❝❛❧❝✉❧❛r ✉♠ ❝❛♠♣♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛s ✐♠❛❣❡♥s ❝♦♠ ✉♠ ♠ét♦❞♦ ❞❡ ✢✉①♦ ó♣t✐❝♦ ❡ ❛♣❧✐❝❛r ✉♠ ♠ét♦❞♦ ✐t❡r❛t✐✈♦ ♣❛r❛ ❡st✐♠❛r ♦s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ✭❛♥á❧✐s❡ ✐♥✈❡rs❛✮ ✉t✐❧✐③❛♥❞♦ ♠ét♦❞♦s ♥✉♠ér✐❝♦s✳ P❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦s ❞❡s❧♦❝❛♠❡♥t♦s✱ ❞✉❛s ❢♦r♠✉❧❛çõ❡s sã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ✢✉①♦ ó♣t✐❝♦✿ ▲✉❝❛s✲❑❛♥❛❞❡ ❡ ❇r♦①✳ ❆ ❛♥á❧✐s❡ ✐♥✈❡rs❛ é r❡❛❧✐③❛❞❛ ✉t✐❧✐③❛♥❞♦ ❞✉❛s té❝♥✐❝❛s ♥✉♠ér✐❝❛s ❞✐st✐♥t❛s✿ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✭▼❊❋✮ ❡ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ✭▼❊❈✮✱ s❡♥❞♦ ❛♠❜♦s ✐♠♣❧❡♠❡♥t❛❞♦s ❡♠ ❯♥✐❞❛❞❡s ❞❡ Pr♦❝❡ss❛♠❡♥t♦ ●rá✜❝♦ ❞❡ ✉s♦ ❣❡r❛❧✱ ●♣●P❯s ✭✏●❡✲ ♥❡r❛❧ P✉r♣♦s❡ ●r❛♣❤✐❝s ❯♥✐ts✑✮✳ ❈♦♥s✐❞❡r❛♥❞♦ ✉♠❛ q✉❛♥t✐❞❛❞❡ q✉❛❧q✉❡r ❞❡ ♠❛t❡r✐❛✐s ❛ s❡r❡♠ ❞❡t❡r♠✐♥❛❞♦s✱ ♣❛r❛ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ é ❡♠♣r❡❣❛❞❛ ❛ té❝✲ ♥✐❝❛ ❞❡ s✉❜✲r❡❣✐õ❡s ♣❛r❛ ❛❝♦♣❧❛r ❛s ♠❛tr✐③❡s ❞❡ ❞✐❢❡r❡♥t❡s ❡str✉t✉r❛s ✐❞❡♥t✐✜❝❛❞❛s ♥❛ ✐♠❛❣❡♠✳ ❖ ♣r♦❝❡ss♦ ❞❡ ♦t✐♠✐③❛çã♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛s ❝♦♥st❛♥t❡s ❡❧ást✐❝❛s é r❡❛❧✐③❛❞♦ ❞❡ ❢♦r♠❛ s❡♠✐✲❛♥❛❧ít✐❝❛ ✉t✐❧✐③❛♥❞♦ ❝á❧❝✉❧♦ ♣♦r ✈❛r✐á✈❡✐s ❝♦♠♣❧❡①❛s✳ ❆ ♠❡t♦❞♦❧♦❣✐❛ é t❡st❛❞❛ ❡♠ três ❡t❛♣❛s ❞✐st✐♥t❛s✱ ❝♦♠ s✐♠✉❧❛çõ❡s s❡♠ r✉í❞♦✱ s✐♠✉❧❛çõ❡s ❝♦♠ ❛❞✐çã♦ ❞❡ r✉í❞♦ ❜r❛♥❝♦ ❣❛✉ss✐❛♥♦ ❡ ♣❤❛♥t♦♠s ♠❛t❡♠át✐❝♦s ✉t✐❧✐③❛♥❞♦ r❛str❡❛♠❡♥t♦ ❞❡ r✉í❞♦ s♣❡❝❦❧❡✳ ❖s r❡s✉❧t❛❞♦s ❞❛s s✐♠✉❧❛çõ❡s ❛♣♦♥t❛♠ ♦ ✉s♦ ❞♦ ▼❊❋ ❝♦♠♦ ♠❛✐s ♣r❡❝✐s♦✱ ♣♦ré♠ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ♠❛✐s ❝❛r♦✱ ❡♥q✉❛♥t♦ ♦ ▼❊❈ ❛♣r❡s❡♥t❛ ❡rr♦s t♦❧❡rá✈❡✐s ❡ ♠❛✐♦r ✈❡❧♦❝✐❞❛❞❡ ♥♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳

(17)

❆❜str❛❝t

❚❤✐s t❤❡s✐s ♣r❡s❡♥ts ❛ ♥❡✇ ♠❡t❤♦❞♦❧♦❣② ❢♦r ❝♦♠♣✉t❛t✐♦♥❛❧ ❡❧❛st♦❣r❛♣❤② ❛♣♣❧✐❡❞ t♦ s✐♠✉❧❛t❡❞ ✉❧tr❛s♦✉♥❞ ✐♠❛❣❡s✱ ✉s✐♥❣ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞s ❛♥❞ ❝♦♠♣t✉t❡r ✈✐s✐♦♥ ♠❡t❤♦❞s✳ ❚❤❡ ❛✐♠ ✐s t♦ ❡st✐♠❛t❡ t❤❡ ❡❧❛st✐❝ ♠♦❞✉❧✐ ♦❢ ❞✐✛❡r❡♥t t✐ss✉❡s ✉s✐♥❣ t✇♦ ❞✐✛❡r❡♥t ✐♠❛❣❡s ♦❢ t❤❡ s❛♠❡ ❝r♦ss s❡❝t✐♦♥ ❛❝q✉✐r❡❞ ✐♥ ❞✐✛❡r❡♥t t✐♠❡s ❛♥❞ ♣r❡ss✉r❡ ❝♦♥❞✐t✐♦♥s✳ ❚❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞♦❧♦❣② ❝♦♥s✐sts ✐♥ ❡✈❛❧✉❛t❡ t❤❡ ❞✐s♣❧❛❝❡♠❡♥t ✜❡❧❞ ✉s✐♥❣ ♦♣t✐❝❛❧ ✢♦✇ t❡❝❤♥✐q✉❡s ❛♥❞ t❤❡♥ ❛♣♣❧② ❛♥ ✐♥✈❡rs❡ ❛♥❛❧②s✐s ✉s✐♥❣ ❛ ♥✉♠❡r✐✲ ❝❛❧ ♠❡t❤♦❞✳ ■♥ ♦r❞❡r t♦ ❡✈❛❧✉❛t❡ t❤❡ ❞✐s♣❧❛❝❡♠❡♥t ✜❡❧❞✱ t✇♦ ❞✐st✐♥❝t ❢♦r♠✉❧❛t✐♦♥s ❢♦r ♦♣t✐❝❛❧ ✢♦✇ ❛r❡ ✉s❡❞✿ ▲✉❝❛s✲❑❛♥❛❞❡ ❛♥❞ ❇r♦①✳ ❋♦r t❤❡ ✐♥✈❡rs❡ ❛♥❛❧②s✐s ♣r♦❜❧❡♠✱ t❤❡ ❋✐♥✐t❡ ❊❧❡♠❡♥t ▼❡t❤♦❞ ❛♥❞ t❤❡ ❇♦✉♥❞❛r② ❊❧❡♠❡♥t ▼❡t❤♦❞ ❛r❡ ✉s❡❞✱ ❜♦t❤ ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ❣❡♥❡r❛❧ ♣✉r♣♦s❡ ❣r❛♣❤✐❝ ✉♥✐ts✱ ●♣●P❯s✳ ❈♦♥s✐❞❡r✐♥❣ ❛ ♥✉♠❜❡r ♦❢ ♠❛t❡r✐❛❧s t❤❛t ♠❛② ❜❡ ♣r❡s❡♥t ✐♥ t❤❡ ✐♠❛❣❡s✱ t❤❡ ♠✉❧t✐r❡s❣✐♦♥s ❜♦✉♥❞❛r② ❡❧❡♠❡♥t ♠❡t❤♦❞ ✐s ✉s❡❞ ✐♥ ♦r❞❡r t♦ ❝♦✉♣❧❡ ❞✐✛❡r❡♥t ♠❛tr✐❝❡s ❢♦r ❞✐✛❡r❡♥t ♠❛t❡r✐❛❧s✳ ❚❤❡ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❝❡ss ✐s ❡✈❛❧✉❛t❡❞ ✉s✐♥❣ ❝♦♠♣❧❡① ✈❛r✐❛❜❧❡ ♠❡t❤♦❞✳ ❚❤❡ ♠❡t❤♦❞♦❧♦❣② ✐s ✈❛❧✐❞❛t❡❞ ✐♥ t❤r❡❡ ❞✐✛❡r❡♥t st❡♣s✿ ♥♦✐s❡❧❡ss s✐♠✉❧❛t✐♦♥s❀ ❛❞❞✐t✐✈❡ ✇❤✐t❡ ❣❛✉ss✐❛♥ ♥♦✐s❡ s✐♠✉❧❛t✐♦♥s❀ ❛♥❞ ✉❧✲ tr❛s♦✉♥❞ ♠❛t❤❡♠❛t✐❝❛❧ ♣❤❛♥t♦♠ ✇✐t❤ s♣❡❝❦❧❡ tr❛❝❦✐♥❣✳ ❚❤❡ r❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ❋✐♥✐t❡ ❊❧❡♠❡♥t ▼❡t❤♦❞ ♣r❡s❡♥ts ♠♦r❡ ❛❝❝✉r❛t❡ ❡st✐♠❛t✐✈❡s ❜✉t ❛ ❤✐❣❤ ❝♦♠♣✉t❛t✐♦♥❛❧ ❝♦st✱ ✇❤✐❧❡ t❤❡ ❇♦✉♥❞❛r② ❊❧❡♠❡♥t ▼❡t❤♦❞ ♣r❡s❡♥ts t♦❧❡r❛❜❧❡ ❡rr♦rs ❜✉t ❛ ❜❡tt❡r ♣r♦❝❡ss✐♥❣ t✐♠❡✳

(18)

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

◆❛s ú❧t✐♠❛s ❞é❝❛❞❛s✱ ♦❝♦rr❡✉ ✉♠ ❛✉♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❛ ❡①♣❡❝t❛t✐✈❛ ❞❡ ✈✐❞❛ ❣r❛ç❛s ❛♦ ❞❡s❡♥✈♦❧✲ ✈✐♠❡♥t♦ ❞❡ ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s ❡♠ ❞✐✈❡rs❛s ár❡❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❙❛ú❞❡✳ ❙❡❣✉♥❞♦ ❛ ❖r❣❛♥✐③❛çã♦ ▼✉♥❞✐❛❧ ❞❡ ❙❛ú❞❡✶ _{✭❖▼❙ ✲ ✏❲♦r❧❞ ❍❡❛❧t❤ ❖r❣❛♥✐③❛t✐♦♥✑✮✱ ❛♣❡♥❛s ♥♦ ❇r❛s✐❧✱ ❛ ❡①✲}

♣❡❝t❛t✐✈❛ ❞❡ ✈✐❞❛ ♠é❞✐❛ ❡♠ ✶✾✾✵ ❡r❛ ❞❡ ❛té ✻✻ ❛♥♦s✱ ❥á ❡♠ ✷✵✶✹ ❡r❛ ❞❡ ✼✹ ❛♥♦s✳ ●r❛♥❞❡ ♣❛rt❡ ❞❡st❛ ❡✈♦❧✉çã♦✱ s❡ ❞❡✈❡ ❛♦ ✐♥✈❡st✐♠❡♥t♦ ❡♠ ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s ❞❡ ♣r❡✈❡♥çã♦ ❞❡ ❞♦❡♥ç❛s✳ ❊♥tr❡ ❛s té❝♥✐❝❛s ♣r❡✈❡♥t✐✈❛s✱ ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s q✉❡ ♣♦❞❡♠ s❡r ❝✐t❛❞❛s é ❛ ❛q✉✐s✐çã♦ ❞❡ ✐♠❛❣❡♥s ❡ ❡♥tr❡ ❛s ♠❛✐s ✉t✐❧✐③❛❞❛s✱ ♦ ✉❧tr❛ss♦♠✳

❚é❝♥✐❝❛s ❞❡ ✉❧tr❛ss♦♠ sã♦ ✉t✐❧✐③❛❞❛s ♥♦ ❞✐❛❣♥óst✐❝♦ ❞❡ ✉♠❛ ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❞♦❡♥ç❛s✱ ❞❡s❞❡ ❞❡t❡❝çã♦ ❞❡ t✉♠♦r❡s ❡♠ ♠❛♠❛ ♦✉ t✐r❡ó✐❞❡ à ❛♣❧✐❝❛çõ❡s ✐♥tr❛✈❛s❝✉❧❛r❡s ✭✏■♥tr❛✈❛s❝✉❧❛r ❯❧tr❛s♦✉♥❞✑ ✲ ■❱❯❙✮✱ ♣❛r❛ ✈❡r✐✜❝❛çã♦ ❞❡ ❧❡sõ❡s ❡ ♣♦ssí✈❡✐s ♦❜str✉çõ❡s ✈❛s❝✉❧❛r❡s✳

❚♦♠❛♥❞♦ ❝♦♠♦ ❡①❡♠♣❧♦ ❡①❛♠❡s ❞❡ ♠❛♠♦❣r❛✜❛✱ ❛ ❞❡t❡❝çã♦ ❞❡ ♥ó❞✉❧♦s é r❡❛❧✐③❛❞❛ ❞❡ ❢♦r♠❛ s✉❜❥❡t✐✈❛ ♣❡❧♦ té❝♥✐❝♦ r❡s♣♦♥sá✈❡❧✱ q✉❡ ✈❡r✐✜❝❛ ❛ ✉♥✐❢♦r♠✐❞❛❞❡ ❞❛ ✐♠❛❣❡♠ ❡♠ r❡❧❛çã♦ ❛ ♣❛❞rõ❡s ♣r❡✲ ✈✐❛♠❡♥t❡ ❡st❛❜❡❧❡❝✐❞♦s✱ ✐st♦ é✱ ❜✉s❝❛ ♣♦r ♣♦ssí✈❡✐s ✐♥❝❧✉sõ❡s ♣r❡s❡♥t❡s ♥❛ ✐♠❛❣❡♠✳ ❆ss✐♠✱ ♦ ❧❛✉❞♦ ❞❡♣❡♥❞❡✱ ❡♥tr❡ ♦✉tr♦s ❢❛t♦r❡s✱ ❞❛ ❡①♣❡r✐ê♥❝✐❛ ❞♦ ♦♣❡r❛❞♦r ❡ t♦r♥❛ ♦ ❡①❛♠❡ ❛❧t❛♠❡♥t❡ ♦♣❡r❛❞♦r✲ ❞❡♣❡♥❞❡♥t❡✳ ❏✉❧✐❛ ❡t ❛❧✳ ❬✸✻❪ ❛♣♦♥t❛ q✉❡ ❝❡r❝❛ ❞❡10❛30%❞❛s ❧❡sõ❡s ♥ã♦ sã♦ ❝♦♥s✐❞❡r❛❞❛s✱ ❞❡✈✐❞♦

❛ ❧✐♠✐t❛çõ❡s ❞♦s té❝♥✐❝♦s r❡s♣♦♥sá✈❡✐s ❡ ♥♦ ♠❡s♠♦ ❡st✉❞♦✱ ❛♣♦♥t❛ q✉❡ ♦ ✉s♦ ❞❡ ❈❆❉ ✭✏❈♦♠♣✉t❡r ❆✐❞❡❞ ❉❡t❡❝t✐♦♥✑ ✲ ❉❡t❡❝çã♦ ♣♦r ❆✉①í❧✐♦ ❞❡ ❈♦♠♣✉t❛❞♦r✮ ❛✉♠❡♥t❛ ❡♠ ✷✶✪ ❛ s❡♥s✐❜✐❧✐❞❛❞❡ ♥❛ ❞❡t❡❝çã♦ ❞❡ ✉♠ ❝â♥❝❡r ❞❡ ♠❛♠❛ ♣❡❧♦ ❡s♣❡❝✐❛❧✐st❛✳

◆❡st❡ s❡♥t✐❞♦✱ ❡♥tr❡ ♦s ✈ár✐♦s ♠ét♦❞♦s ♣❛r❛ ❛✉①✐❧✐❛r ♦ ❡s♣❡❝✐❛❧✐st❛ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❛✈❛❧✐❛çã♦ ❞❡ ✐♠❛❣❡♥s✱ ❡stá ❛ ❊❧❛st♦❣r❛✜❛✳ ❈♦♠♦ ❞❡s❝r❡✈❡ ❉♦②❧❡② ❛♥❞ P❛r❦❡r ❬✷✸❪✱ ❛ ❡❧❛st♦❣r❛✜❛ ❝♦♥s✐st❡ ❡♠ ✭✐✮ ❛♣❧✐❝❛r ✉♠❛ ♣❡rt✉r❜❛çã♦ s♦❜r❡ ♦ t❡❝✐❞♦✱ ✉s❛♥❞♦ ✉♠❛ ❢♦♥t❡ ❞❡ ❡①❝✐t❛çã♦ ♠❡❝â♥✐❝❛ q✉❛s✐✲ ❡stát✐❝❛✱ ❤❛r♠ô♥✐❝❛ ♦✉ tr❛♥s✐❡♥t❡✳ ❚❛✐s ❢♦♥t❡s ♣♦❞❡♠ s❡r ❞❡ ♦r✐❣❡♥s ❡①t❡r♥❛s ♦✉ ✐♥t❡r♥❛s✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ♣r❡ssã♦ s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ ✐♠❛❣❡❛❞❛ ♣❡❧♦ tr❛♥s❞✉t♦r ❞❡ ✉❧tr❛ss♦♠ ♦✉ ♣♦r ❛❧❣✉♠ ❢❡♥ô♠❡♥♦ ❜✐♦❧ó❣✐❝♦✱ ❝♦♠♦ r❡s♣✐r❛çã♦ ♦✉ ❛ ♣ró♣r✐❛ ♣r❡ssã♦ ❛rt❡r✐❛❧❀ ✭✐✐✮ ♠❡❞✐r ❛ r❡s♣♦st❛ ❡♠ t❡r♠♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s✱ ❞❡❢♦r♠❛çõ❡s ♦✉ ❢❛s❡ ❡ ❛♠♣❧✐t✉❞❡ ❞❛s ✈✐❜r❛çõ❡s❀ ✭✐✐✐✮ ❡st✐♠❛r ❛s

✶_{❤tt♣✿✴✴❣❛♠❛♣s❡r✈❡r✳✇❤♦✳✐♥t✴❣❤♦✴✐♥t❡r❛❝t✐✈❡❴❝❤❛rts✴♠❜❞✴❧✐❢❡❴❡①♣❡❝t❛♥❝②✴❛t❧❛s✳❤t♠❧ ✲ ❆❝❡ss❛❞♦ ❡♠} ✶✹✴✵✽✴✷✵✶✹✳

(19)

♣r♦♣r✐❡❞❛❞❡s ♠❡❝â♥✐❝❛s ❞♦s t❡❝✐❞♦s ✐♠❛❣❡❛❞♦s✳ ❊♠❜♦r❛ ♦s tr❛❜❛❧❤♦s ♣✐♦♥❡✐r♦s ❡♠ ❊❧❛st♦❣r❛✜❛ t❡♥❤❛♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠✱ ❡st✉❞♦s ❡q✉✐✈❛❧❡♥t❡s ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞♦s ❡♠ ✈ár✐❛s ♠♦❞❛❧✐❞❛❞❡s ❞❡ ✐♠❛❣❡♥s ♠é❞✐❝❛s✱ ❝♦♠♦ t♦♠♦❣r❛✜❛ ♣♦r ❝♦❡rê♥❝✐❛ ó♣t✐❝❛ ✭✏♦♣t✐❝❛❧ ❝♦❤❡r❡♥❝❡ t♦♠♦❣r❛♣❤②✑ ✲ ❖❈❚✮ ❡ r❡ss♦♥â♥❝✐❛ ♠❛❣♥ét✐❝❛✳ ❉❡✈❡✲s❡ r❡ss❛❧t❛r q✉❡✱ s❛❧✈♦ ❛♣❧✐❝❛çõ❡s ❡♠ ✐♠❛❣❡♥s ✐♥tr❛✈❛s❝✉❧❛r❡s✱ ♦♥❞❡ é ♥❡❝❡ssár✐♦ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❝❛tét❡r❡s ♣❛r❛ ❛q✉✐s✐çã♦ ❞❛s ✐♠❛❣❡♥s ❞♦s ✈❛s♦s s❛♥❣✉í♥❡♦s✱ ♠ét♦❞♦s ❞❡ ❊❧❛st♦❣r❛✜❛ ❣❛r❛♥t❡♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♥ã♦ ✐♥✈❛s✐✈❛✱ ♣r❡s❡r✈❛♥❞♦ ❛ ✐♥t❡❣r✐❞❛❞❡ ❞♦ t❡❝✐❞♦ ✐♠❛❣❡❛❞♦ ❡ ♠✐♥✐♠✐③❛♥❞♦ ♦ ❞❡s❝♦♥❢♦rt♦ ❞♦ ♣❛❝✐❡♥t❡✳

❆ ❛♥á❧✐s❡ ❞♦s t❡❝✐❞♦s ✐♠❛❣❡❛❞♦s é ❜❛s❡❛❞❛ ♥❛ ♣r❡♠✐ss❛ q✉❡ t❡❝✐❞♦s s❛✉❞á✈❡✐s ♣♦ss✉❡♠ ❝♦♠♣♦r✲ t❛♠❡♥t♦ ♠❡❝â♥✐❝♦ ❞✐❢❡r❡♥t❡ ❞❡ t❡❝✐❞♦s ❧❡s✐♦♥❛❞♦s✱ ♦✉ q✉❡ ❛♣r❡s❡♥t❡♠ ❛❧❣✉♠ t✐♣♦ ❞❡ ❛♥♦r♠❛❧✐❞❛❞❡✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ❑r♦✉s❦♦♣ ❛♥❞ ❲❤❡❡❧❡r ❬✹✸❪ ♠♦str❛ q✉❡ t✉♠♦r❡s ❜❡♥✐❣♥♦s ❛♣r❡s❡♥t❛♠ ❝♦♠♣♦rt❛✲ ♠❡♥t♦s ♣ró①✐♠♦s ❞❛ ❧✐♥❡❛r✐❞❛❞❡ ♠❛t❡r✐❛❧✱ ❡♥q✉❛♥t♦ t✉♠♦r❡s ♠❛❧✐❣♥♦s ❛♣r❡s❡♥t❛♠ ♥ã♦✲❧✐♥❡❛r✐❞❛❞❡ ♠❛t❡r✐❛❧✱ ♦✉ s❡❥❛✱ ❛ r❡❧❛çã♦ ❡♥tr❡ t❡♥sã♦ ❡ ❞❡❢♦r♠❛çã♦ ♣♦ss✉✐ ✈❛r✐❛çã♦ ❞✐❢❡r❡t❡ ❞❡ ✉♠ ♠♦❞❡❧♦ ❧✐♥❡❛r✳ ❆ ❧✐t❡r❛t✉r❛ ❛♣r❡s❡♥t❛ ♠♦❞❡❧♦s ❝♦♠♣❧❡①♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡❧ást✐❝♦ ❞♦ t❡❝✐❞♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❝❛r❛❝t❡ríst✐❝❛s ❛♥✐s♦tró♣✐❝❛s ❬✸✵✱ ✻✽❪✱ ✈✐s❝♦❡❧ást✐❝❛s ❬✻✾✱ ✻✸❪ ❡ ❛té ♠❡s♠♦ ♣♦r♦❡❧ást✐❝❛s ❬✻✶✱ ✻✵❪✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ♠♦❞❡❧❛❣❡♠ ❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦ é ❜❡♠ s✐♠♣❧✐✜❝❛❞❛✱ s❡❣✉♥❞♦ ❉♦②❧❡② ❬✷✷❪✱ ❛❧❣✉♥s ♠♦❞❡❧♦s ❛ss✉♠❡♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❡❝â♥✐❝♦ ❞♦ ♣❤❛♥t♦♠ ❢ís✐❝♦ ❝♦♠♦ ✉♠❛ ❛ss♦❝✐❛çã♦ ❞❡ ♠♦❧❛s ❡♠ ♣❛r❛❧❡❧♦✱ ❧✐♠✐t❛♥❞♦ ❛ ❛♣❧✐❝❛çã♦ ❞❛s té❝♥✐❝❛s ❞❡s❡♥✈♦❧✈✐❞❛s ❡♠ ♠♦❞❡❧♦s ♠❛✐s r❡❛❧✐st❛s ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝❧í♥✐❝♦✳

❈♦♠♦ s❡rá ❞✐s❝✉t✐❞♦ ♥♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦✱ ❛❧❣✉♥s tr❛❜❛❧❤♦s ♣♦ss✉❡♠ ♠♦❞❡❧♦s ♠❛✐s s✐♠♣❧✐✜❝❛❞♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡❧ást✐❝♦ ❞♦s t❡❝✐❞♦s✱ ❝♦♥s✐❞❡r❛♥❞♦✲♦s ❝♦♠♦ ✐s♦tró♣✐❝♦s✱ ♣♦ré♠ ❝♦♠ ✉♠❛ ♠♦❞❡❧❛❣❡♠ ♠❛✐s r❡❛❧íst✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ❢ís✐❝♦✳ ❊st❡s tr❛❜❛❧❤♦s ❝♦♥s✐❞❡r❛♠ ♠❛♣❛s ❞❡ ❞❡❢♦r✲ ♠❛çã♦ ❝♦♠♦ ♣❛râ♠❡tr♦s ♣❛r❛ ✐❞❡♥t✐✜❝❛r ♦s t❡❝✐❞♦s ❧❡s✐♦♥❛❞♦s ❡ ❞♦✐s ♣♦♥t♦s ✐♠♣♦rt❛♥t❡s ❞❡✈❡♠ s❡r ♦❜s❡r✈❛❞♦s ❡♠ r❡❧❛çã♦ às ♠❡t♦❞♦❧♦❣✐❛s ❛♣r❡s❡♥t❛❞❛s✿ ✭✐✮ ❡♠ s✉❛ ♠❛✐♦r✐❛✱ sã♦ ✉t✐❧✐③❛❞♦s s✐♥❛✐s ❞❡ rá❞✐♦ ❢r❡q✉ê♥❝✐❛ ✭❘❋✮ ♣❛r❛ ❡st✐♠❛r ♦s ❝❛♠♣♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❡ ♦s ♠❛♣❛s ❞❡ ❞❡❢♦r♠❛çõ❡s ❞♦s t❡❝✐❞♦s ✐♠❛❣❡❛❞♦s✳ ❊♠❜♦r❛ s✐♥❛✐s ❞❡ ❘❋ ❛♣r❡s❡♥t❡♠ ♠❛✐♦r q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦✱ ♦ q✉❡ ♣❡r♠✐t❡ ❝á❧❝✉❧♦s ♠❛✐s ♣r❡❝✐s♦s ❞♦s ❝❛♠♣♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s✱ ♦ ✉s♦ ❞❡st❡ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦ é ✉♠ ❧✐♠✐t❛♥t❡ ♣❛r❛ ❛ ❛♣❧✐❝❛çã♦ ❞❛ té❝♥✐❝❛✱ ♣♦✐s ❡st❛ ✐♥❢♦r♠❛çã♦ ♥ã♦ é ❞✐s♣♦♥✐❜✐❧✐③❛❞❛ ♣❡❧♦ ❢❛❜r✐❝❛♥t❡ ❞♦ ❡q✉✐♣❛♠❡♥t♦ ❡✱ ❡♠ ♠✉✐t♦s ❝❛s♦s✱ é tr❛t❛❞❛ ❝♦♠♦ ♣r♦♣r✐❡tár✐❛ ❡ ❝♦♥✜❞❡♥❝✐❛❧✳ ❆ss✐♠✱ é ❞❡s❡❥á✈❡❧ q✉❡ ♦ ❡st✉❞♦ s❡❥❛ ❜❛s❡❛❞♦ ❡♠ ✐♠❛❣❡♥s ❝♦♠♦ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ❡ ❞❡❢♦r♠❛çõ❡s✱ ❝♦♥st✐t✉✐♥❞♦ ❛ss✐♠ ✉♠ ♠ét♦❞♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ ❢❛❜r✐❝❛♥t❡ ❞♦ ❡q✉✐♣❛♠❡♥t♦ ❞❡ ✐♠❛✲ ❣❡♥s ♠é❞✐❝❛s❀ ✭✐✐✮ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❞❡❢♦r♠❛çã♦✱ s❡♠ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r❡ssã♦ ❛♣❧✐❝❛❞❛✱ ♥ã♦ ♣♦ss✐❜✐❧✐t❛ ✉♠❛ ❡st✐♠❛t✐✈❛ ♣r❡❝✐s❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❡❧ást✐❝❛s ❞♦s t❡❝✐❞♦s ✐♠❛❣❡❛✲ ❞♦s✱ ❧❡✈❛♥❞♦ ❛ ✉♠❛ ❛♥á❧✐s❡ s✉❜❥❡t✐✈❛ ❞♦s r❡s✉❧t❛❞♦s ❞❛ ❊❧❛st♦❣r❛✜❛✳ ❈♦♠♦ r❡ss❛❧t❛ ●✉♦ ❡t ❛❧✳ ❬✸✷❪✱ ♥❡♥❤✉♠❛ ❞❛s té❝♥✐❝❛s q✉❡ ✉t✐❧✐③❛♠ ❛♣❡♥❛s ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s sã♦ ❝❛♣❛③❡s ❞❡ ❡st✐♠❛r ❞✐r❡t❛♠❡♥t❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛t❡r✐❛✐s❀ ❛♦ ✐♥✈és ❞✐st♦✱ ♣❡r♠✐t❡♠ q✉❡ ♦ ♣ró♣r✐♦ r❛❞✐♦❧♦❣✐st❛ ❛♥❛❧✐s❡ ♦ ❝❛♠♣♦ ❞❡ ❞❡❢♦r♠❛çã♦✱ t♦r♥❛♥❞♦ ♦ r❡s✉❧t❛❞♦ ❞♦ ❡st✉❞♦ ♦♣❡r❛❞♦r✲❞❡♣❡♥❞❡♥t❡✳

◆❡st❡ ❝♦♥t❡①t♦✱ ❡st❛ t❡s❡ ❛♣r❡s❡♥t❛ ✉♠❛ ♥♦✈❛ ♠❡t♦❞♦❧♦❣✐❛✱ q✉❡ ✐♥t❡❣r❛ ♠ét♦❞♦s ❞❡ ✈✐sã♦ ❝♦♠♣✉✲ t❛❝✐♦♥❛❧ ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ❡♠ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠ ❡ ♠ét♦❞♦s ❞❡ ❛♥á❧✐s❡ ❡str✉t✉r❛❧ ❡

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♦t✐♠✐③❛çã♦ ♠❛t❡r✐❛❧ ♣❛r❛ ❡st✐♠❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧ást✐❝❛s ❡ ❢♦r♥❡❝❡r ♣❛râ♠❡tr♦s ❝♦♥s✐st❡♥t❡s ♣❛r❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ t❡❝✐❞♦s ❜❛s❡❛❞♦s ❡♠ s❡✉s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡✳ ❙ã♦ ❡♠♣r❡❣❛❞♦s ♠ét♦❞♦s ❞❡ ❋❧✉①♦ Ó♣t✐❝♦ ✭❋❖✮ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s r❡❧❛t✐✈♦s ❡♥tr❡ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠✱ ♦❜t✐❞❛s ❡♠ ✐♥st❛♥t❡s ❞❡ t❡♠♣♦ ❡ ♣r❡ssõ❡s ❞✐❢❡r❡♥t❡s✳ ❖ ♠ét♦❞♦ ❞❡ ❇r♦① ❬✶✷❪ ❡ ♦ ♠ét♦❞♦ ❞❡ ▲✉❝❛s✲❑❛♥❛❞❡ ❬✺✵❪ sã♦ ✉t✐❧✐③❛❞♦s ♥❡st❛ t❡s❡✿ ❡♥q✉❛♥t♦ ♦ ♠ét♦❞♦ ❞❡ ❇r♦① ♠♦str❛✲s❡ ❡✜❝✐❡♥t❡ ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ ❣r❛♥❞❡s ❞❡s❧♦❝❛♠❡♥t♦s✱ ♦ ♠ét♦❞♦ ❞❡ ▲✉❝❛s✲❑❛♥❛❞❡ ♣♦ss✉✐ ✉♠❛ ❢♦r♠✉❧❛çã♦ ♠❛✐s s✐♠♣❧❡s ❡ ♠❡❧❤♦r ❞❡s❡♠♣❡♥❤♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❊♠ s❡❣✉✐❞❛✱ ♣❛r❛ ❛♥á❧✐s❡ ✐♥✈❡rs❛ sã♦ ❡♠♣r❡❣❛❞♦s ♠ét♦❞♦s ♥✉♠ér✐❝♦s ♣❛r❛ ❡❧❛st♦stát✐❝❛ ❜❛s❡❛❞♦s ❡♠ ❢♦r♠✉❧❛çõ❡s ✐♥t❡❣r❛✐s✱ q✉❡ ♣♦ss✐❜✐❧✐t❛♠ ✢❡①✐❜✐❧✐❞❛❞❡ ♣❛r❛ ❞❡s❝r✐çã♦ ❞❛ ❣❡♦♠❡tr✐❛ ❞♦s t❡❝✐❞♦s✳ ❉♦✐s ♠ét♦❞♦s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❞✐st✐♥t❛s sã♦ ❝♦♠♣❛r❛❞♦s✿ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✭▼❊❋✮ ❬❩✐❡♥❦✐❡✇✐❝③ ❛♥❞ ❊♠❡r✐t✉s❪ ❡ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ❬✼❪ ✭▼❊❈✮✳ P❛r❛ q✉❡ ❡st❛s ❛♥á❧✐s❡s s❡❥❛♠ r❡❛❧✐③❛❞❛s ♥♦ ♠❡♥♦r t❡♠♣♦ ♣♦ssí✈❡❧✱ ♦s ♠ét♦❞♦s ❞❡ ❛♥á❧✐s❡ ❡str✉t✉r❛❧ sã♦ ✐♠♣❧❡♠❡♥t❛❞♦s ❡♠ ❯♥✐❞❛❞❡s ❞❡ Pr♦❝❡ss❛♠❡♥t♦ ●rá✜❝♦ ✭✏●r❛♣❤✐❝❛❧ Pr♦❝❡ss ❯♥✐ts✑ ✲ ●P❯s✮✳

✶✳✶ ❖❜❥❡t✐✈♦s

❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❛ t❡s❡ é ❞❡s❡♥✈♦❧✈❡r ✉♠ ♠ét♦❞♦ ♣❛r❛ r❡❛❧✐③❛r ❡❧❛st♦❣r❛✜❛ ✈✐rt✉❛❧ ✉t✐❧✐③❛♥❞♦ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠✱ ❛❧❣♦r✐t♠♦s ❞❡ ✢✉①♦ ó♣t✐❝♦✱ ♠ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ❡ té❝♥✐❝❛s ❞❡ ❛♥á❧✐s❡ ✐♥✈❡rs❛ ♣❛r❛ ♦t✐♠✐③❛çã♦ ♠❛t❡r✐❛❧✳ ❊st❡ ♠ét♦❞♦ é ❡♥tã♦ ✈❛❧✐❞❛❞♦ ✉t✐❧✐③❛♥❞♦ s✐♠✉❧❛çõ❡s ♥✉♠ér✐❝❛s ❡ ♣♦r ✜♠✱ ❛♣❧✐❝❛❞❛ ❛ ♣❤❛♥t♦♠s ♠❛t❡♠át✐❝♦s✳

P❛r❛ q✉❡ ♦ ♦❜❥❡t✐✈♦ ❞❡st❛ t❡s❡ ❢♦ss❡ ❛t✐♥❣✐❞♦✱ ❢♦r❛♠ ♥❡❝❡ssár✐❛s ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛s s❡❣✉✐♥t❡s ❡t❛♣❛s✿

• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ❛❧❣♦r✐t♠♦ ❞❡ ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ♣❛r❛ ✐♠❛❣❡♥s ✷❉ q✉❡ s❡❥❛ ❝❛♣❛③ ❞❡ tr❛t❛r ♠ú❧t✐♣❧♦s ♠❛t❡r✐❛✐s❀

• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ✈❛❧✐❞❛çã♦ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ ✐♠❛❣❡♥s ✷❉❀

• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ✈❛❧✐❞❛çã♦ ❞♦s ♠ét♦❞♦s ♥✉♠ér✐❝♦s ❝✐t❛❞♦s ❛❝✐♠❛ ❡♠ ❯♥✐❞❛❞❡s ❞❡ Pr♦❝❡s✲ s❛♠❡♥t♦ ●rá✜❝♦ ✭●P❯s✮❀

• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ✈❛❧✐❞❛çã♦ ❞❡ ✉♠ ❛❧❣♦r✐t♠♦ ♣❛r❛ ✢✉①♦ ó♣t✐❝♦ ❝❛♣❛③ ❞❡ r❡❛❧✐③❛r ♦ r❛str❡❛✲ ♠❡♥t♦ ❞❡ r✉í❞♦ s♣❡❝❦❧❡ ❡♠ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠✱ ❛ s❛❜❡r✱ ▲✉❝❛s✲❑❛♥❛❞❡ ❡ ❇r♦①❀

• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ✈❛❧✐❞❛çã♦ ❞❡ ✉♠ ♠ét♦❞♦ ❞❡ ❛♥á❧✐s❡ ✐♥✈❡rs❛ ✉t✐❧✐③❛♥❞♦ ▼❊❈ ❡ ▼❊❋❀

• ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ♠ó❞✉❧♦s ❞❡ ✢✉①♦ ó♣t✐❝♦ ❡ ❛♥á❧✐s❡ ✐♥✈❡rs❛❀

• ❱❛❧✐❞❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ✉t✐❧✐③❛♥❞♦ ♣❤❛♥t♦♠s ♠❛t❡♠át✐❝♦s✳

❆ ❋✐❣✉r❛ ✶✳✶✳✶ ♠♦str❛ ♦ ❞✐❛❣r❛♠❛ ❞❛ ♠❡t♦❞♦❧♦❣✐❛✳ ◆♦ ❞✐❛❣r❛♠❛✱t0 ❡t1 r❡♣r❡s❡♥t❛♠ ♦s ✐♥st❛♥t❡s ♣ré ❡ ♣ós✲❞❡❢♦r♠❛çã♦ ❡ u ❡ v ♦s ❝❛♠♣♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ❤♦r✐③♦♥t❛❧ ❡ ✈❡rt✐❝❛❧ r❡s♣❡❝t✐❝❛♠❡♥t❡✱

(21)

♣r❡ssã♦ ❛♣❧✐❝❛❞❛ é ♦ ❝❛♠♣♦ ❞❡ ♣r❡ssõ❡s ❛♣❧✐❝❛❞♦ ♣❛r❛ ❞❡❢♦r♠❛r ♦ t❡❝✐❞♦ ✐♠❛❣❡❛❞♦✱ E0 é ✉♠❛ ❡st✐♠❛t✐✈❛ ✐♥✐❝✐❛❧ ♣❛r❛ ♦ ♠ó❞✉❧♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡Eestimado é ♦ ♠ó❞✉❧♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡st✐♠❛❞♦✳

❋✐❣✉r❛ ✶✳✶✳✶✿ ❉✐❛❣r❛♠❛ ♣❛r❛ ❡❧❛st♦❣r❛✜❛ ✈✐rt✉❛❧ ❡♠ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠✱ r❛str❡❛♠❡♥t♦ ❞❡ r✉í❞♦ s♣❡❝❦❧❡ ❡ ❛♥á❧✐s❡ ✐♥✈❡rs❛✳

✶✳✷ ❊str✉t✉r❛ ❞❛ ❚❡s❡

❊st❛ t❡s❡ ❡stá ❡str✉t✉r❛❞❛ ❝♦♠♦ s❡❣✉❡✿

❈❛♣ít✉❧♦ ✸ ✲ ❖ ♦❜❥❡t✐✈♦ ❞❡st❡ ❝❛♣ít✉❧♦ é ❢♦r♥❡❝❡r ♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛ ♠❡❝â♥✐❝❛ ❞❡ só❧✐❞♦s ✐s♦tró♣✐❝♦s ❡♠ r❡❣✐♠❡ ❡❧ást✐❝♦ ❧✐♥❡❛r✳ ❆♣r❡s❡♥t❛✲s❡ ♦s ❝♦♥❝❡✐t♦s ❞❡ t❡♥s♦r ❞❡ t❡♥sõ❡s ❡ s✉❛s r❡❧❛çõ❡s ❝♦♠ s♦❧✐❝✐t❛çõ❡s ❡①t❡r♥❛s✱ ♦✉ s❡❥❛✱ ❞❛❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❢♦rç❛s ❡①t❡r♥❛s ❛♣❧✐❝❛❞❛s s♦❜r❡ ✉♠ ❝♦r♣♦✱ ❞❡❞✉③ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❡q✉✐❧í❜r✐♦ ✐♥t❡r♥♦ ❡♠ ❢✉♥çã♦ ❞❡ t❡♥sõ❡s ❞❡✜♥✐❞❛s ❡♠ ❡❧❡♠❡♥t♦s ❞❡ ✈♦❧✉♠❡ ♦✉ ár❡❛ ✐♥✜♥✐t❡s✐♠❛✐s❀ t❛♠❜é♠ ❛♣r❡s❡♥t❛ ♦s ❝♦♥❝❡✐t♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦s ❡ ❞❡❢♦r♠❛çõ❡s✱ ❡st❛❜❡❧❡❝❡♥❞♦ ❛s r❡❧❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❝✐♥❡♠át✐❝❛ ❡ ❞❡✜♥✐♥❞♦ ❧✐♥❡❛r✐❞❛❞❡ ❣❡♦♠étr✐❝❛❀ ♣♦r ✜♠✱ ✉♥❡ ♦s ❝♦♥❝❡✐t♦s ❛♣r❡s❡♥t❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ♣♦r ✉♠❛ r❡❧❛çã♦ ❧✐♥❡❛r✱ ❛ ▲❡✐ ❞❡ ❍♦♦❦❡ ♣❛r❛ ♠❛t❡r✐❛✐s ✐s♦tró♣✐❝♦s✱ ❞❡✜♥✐♥❞♦ ♠ó❞✉❧♦ ❞❡ ❊❧❛st✐❝✐❞❛❞❡✱ ♦✉ ♠ó❞✉❧♦ ❞❡ ❨♦✉♥❣ ❡ ❝♦❡✜❝✐❡♥t❡ ❞❡ P♦✐ss♦♥✳

❈❛♣ít✉❧♦ ✹ ✲ ❊st❡ ❝❛♣ít✉❧♦ ✈✐s❛ ❢♦r♥❡❝❡r ✉♠❛ ✈✐sã♦ ❣❡r❛❧ ❞❛ ❢♦r♠✉❧❛çã♦ ❞♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ❡ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❞❡ ❈♦♥t♦r♥♦ ♣❛r❛ ♣r♦❜❧❡♠❛s ❜✐❞✐♠❡♥s✐♦♥❛✐s✳ ❆♣r❡s❡♥t❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛s ❊q✉❛çõ❡s ■♥t❡❣r❛✐s ❞❡ ❈♦♥t♦r♥♦ ✭❊■❈✮✱ ❛s ❢✉♥çõ❡s ❞❡ ●r❡❡♥ ♣❛r❛ ❡❧❛st✐❝✐❞❛❞❡ ❧✐♥❡❛r ✐s♦tró♣✐❝❛✱ ❛s ❝❤❛♠❛❞❛s s♦❧✉çõ❡s ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ❢♦rç❛s ❞❡ s✉♣❡r❢í❝✐❡ ❡ ❞❡s❧♦❝❛♠❡♥t♦s✳ ❆❧é♠ ❞✐st♦✱ ❝♦♠♦ ❡st❡ tr❛❜❛❧❤♦ ❡♥✈♦❧✈❡ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ✈ár✐♦s ♠❛t❡r✐❛✐s ❞❡♥tr♦ ❞❡ ✉♠ ♠❡s♠♦ ♠❡✐♦✱ é ♥❡❝❡ssár✐♦ ♦ ✉s♦ ❞❛ té❝♥✐❝❛ ❞❡ s✉❜✲r❡❣✐õ❡s✱ t❛♠❜é♠ ❛❜♦r❞❛❞❛ ♥❡st❡ ❝❛♣ít✉❧♦✳ ➱ ❞✐s❝✉t✐❞❛ ❛ ❣❡r❛çã♦ ❞❡ ♠❛❧❤❛s ♣❛r❛ ♦s ♠ét♦❞♦s ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦ ❡ ❛ ✉t✐❧✐③❛çã♦ ❞♦ s♦❢t✇❛r❡ ●▼s❤ ♣❛r❛ ❛ ❝r✐❛çã♦ ❞❡ ♠❛❧❤❛s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ❚❛♠❜é♠ é ❛❜♦r❞❛❞❛ ❛ t❡❝♥♦❧♦❣✐❛ ❞❡ ♣❧❛❝❛s ❣rá✜❝❛s ❡ s✉❛ ❛♣❧✐❝❛çã♦ ❛ ♣r♦❜❧❡♠❛s ❞❡ ♠♦❞❡❧❛❣❡♠ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ❙ã♦ ❞✐s❝✉t✐❞♦s ♦s ❛s♣❡❝t♦s ❣❡r❛✐s✱ t❛✐s ❝♦♠♦ ❛rq✉✐t❡t✉r❛ ❜ás✐❝❛✱ ❧✐♠✐t❛çõ❡s ❡ ❛❧❣✉♠❛s ❝♦♠♣❛r❛çõ❡s ❞♦ ❞❡s❡♥♣❡♥❤♦ ❞❡ ●P❯s ❡♠ r❡❧❛çã♦

(22)

❛ ❈P❯s✱ ❛❧é♠ ❞❡ tr❛t❛r ❞❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦s ♠ét♦❞♦s ♥✉♠ér✐❝♦s ✉t✐❧✐③❛❞♦s ♥❡st❛ t❡s❡✳ P♦r ✜♠✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s r❡s✉❧t❛❞♦s ❞❛ ✈❛❧✐❞❛çã♦ ❞♦ ♣r♦❣r❛♠❛ ✐♠♣❧❡♠❡♥t❛❞♦✱ ❝♦♠♣❛r❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ❝♦♠ ♠♦❞❡❧♦s s✐♠♣❧❡s✱ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ❡ ♠♦❞❡❧♦s ❛♥❛❧ít✐❝♦s✳

❈❛♣ít✉❧♦ ✺ ✲ ❆♣r❡s❡♥t❛ ❛ té❝♥✐❝❛ ❞❡ ❞❡r✐✈❛❞❛s ♣♦r ✈❛r✐á✈❡✐s ❝♦♠♣❧❡①❛s ❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛✲ çã♦ r❡❧❛❝✐♦♥❛❞♦ à ❛♥á❧✐s❡ ✐♥✈❡rs❛✱ ♥❡❝❡ssár✐❛ ♣❛r❛ ❡st✐♠❛r ♦s ✈❛❧♦r❡s ❞❡ ♠ó❞✉❧♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❞♦s ♠❛t❡r✐❛✐s ✐♠❛❣❡❛❞♦s✳ ❆❧é♠ ❞❛ ❢♦r♠✉❧❛çã♦✱ ❛♣r❡s❡♥t❛ ✉♠ ❡①❡♠♣❧♦ ❡ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❞✐❢❡r❡♥ç❛s ✜♥✐t❛s✳

❈❛♣ít✉❧♦ ✻ ✲ ❆♣r❡s❡♥t❛✲s❡ ♦s ♣❤❛♥t♦♠s ♠❛t❡♠át✐❝♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ✈❛❧✐❞❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ♥❡st❛ t❡s❡✳ ❙ã♦ ✉t✐❧✐③❛❞♦s ♣❤❛♥t♦♠s tr❛♥s❝✉tâ♥❡♦s ❝♦♠ ❧❡sã♦ ❞❡ ❞✐â♠❡tr♦ ✈❛r✐á✈❡❧ ❧♦✲ ❝❛❧✐③❛❞❛s ♥♦ ❝❡♥tr♦ ❞❛ ✐♠❛❣❡♠✳ ❚❛♠❜é♠ sã♦ ❝♦♥s✐❞❡r❛❞♦s ♣❤❛♥t♦♠s ❝♦♠ ❞✐❢❡r❡♥t❡s ♠ó❞✉❧♦s ❞❡ ❡❧❛st✐❝✐❞❛❞❡❀

❈❛♣ít✉❧♦ ✼ ✲ ❉✐s❝✉t❡ ❞♦✐s ❛❧❣♦r✐t♠♦s ♣❛r❛ ✢✉①♦ ó♣t✐❝♦✱ ❞❡ ❇r♦① ❡ ❞❡ ▲✉❝❛s✲❑❛♥❛❞❡✳ ❆♣r❡s❡♥t❛ ❛s ❢♦r♠✉❧❛çõ❡s ❡ ❝♦♠♣❛r❛çõ❡s ❡♥tr❡ ♦s ❞♦✐s ♠ét♦❞♦s ❜❛s❡❛❞♦s ❡♠ r❡s✉❧t❛❞♦s ❞❡ ✐♠❛❣❡♥s ❞❡ ✉❧tr❛ss♦♠ ❝♦♠ s✐♠✉❧❛çõ❡s ♣♦r ❡❧❡♠❡♥t♦s ✜♥✐t♦s❀

❈❛♣ít✉❧♦ ✽ ✲ ❆♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦s ❞❛ ✐♥t❡❣r❛çã♦ ❞♦s ♠ó❞✉❧♦s ❞❡ ✢✉①♦ ó♣t✐❝♦ ❝♦♠ ♦s ♠ét♦❞♦s ♥✉♠ér✐❝♦s✳ ❖ ♠ét♦❞♦ é ✈❛❧✐❞❛❞♦ ❡♠ três ❡t❛♣❛s✿ s✐♠✉❧❛çõ❡s s❡♠ r✉í❞♦❀ s✐♠✉❧❛çõ❡s ❝♦♠ r✉í❞♦ ❣❛✉ss✐❛♥♦ ❛❞✐t✐✈♦❀ ❡ ❛ ✐♥t❡❣r❛çã♦ ❞❡ ✢✉①♦ ó♣t✐❝♦ ❝♦♠ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡ ❡❧❡♠❡♥t♦s ❞❡ ❝♦♥t♦r♥♦✳

❈❛♣ít✉❧♦ ✾ ✲ ❈♦♥❝❧✉sõ❡s ❞❛ t❡s❡ ❡ s✉❣❡stõ❡s ♣❛r❛ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳