▼❆❘❈❊▲❆ ❉❊ ▼❊▲❖ ❆◆■❈➱❩■❖
❆t❡♥✉❛çã♦ ❞❡ ❱✐❜r❛çõ❡s ❡♠ Pás ❞❡
❍❡❧✐❝ó♣t❡r♦s ✉t✐❧✐③❛♥❞♦ ❈✐r❝✉✐t♦ P✐❡③❡❧étr✐❝♦
❙❡♠✐✲P❛ss✐✈♦
AUTORIZO A REPRODUÇÃO TOTAL OU PARCIAL DESTE TRABALHO, POR QUALQUER MEIO CONVENCIONAL OU ELETRÔNICO, PARA FINS DE ESTUDO E PESQUISA, DESDE QUE CITADA A FONTE.
de Melo Anicezio, Marcela
D597a Atenuação de Vibrações em Pás de Helicópteros utilizando Circuito Piezelétrico Semi-Passivo / Marcela de Melo Anicezio; orientador Carlos De Marqui Junior. São Carlos, 2015.
Dissertação (Mestrado) - Programa de Pós-Graduação em Engenharia Mecânica e Área de Concentração em Aeronaves -- Escola de Engenharia de São Carlos da Universidade de São Paulo, 2015.
❆❣r❛❞❡❝✐♠❡♥t♦s
❖
♣❡rí♦❞♦ q✉❡ ❝♦♠♣r❡❡♥❞❡✉ ♦ ♠❡✉ ♠❡str❛❞♦ ❢♦✐ ❛ é♣♦❝❛ ❡♠ q✉❡ ♠❛✐s ❛♣r❡♥❞✐ s♦❜r❡ ♦ ✈❡r❞❛❞❡✐r♦ ✈❛❧♦r ❞❛s ♣❡ss♦❛s ❡ ♦ q✉❛♥t♦ ❡ss❛ r❡❧❛çã♦ ✐♥t❡r♣❡ss♦❛❧ ✐♥t❡r❢❡r❡ ♥❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ❡ ♥♦s r❡s✉❧t❛❞♦s ✜♥❛✐s ❞♦ tr❛❜❛❧❤♦✳ P♦r ✐ss♦✱ t❡♥❤♦ q✉❡ ❛❣r❛❞❡❝❡r ❡ ♠✉✐t♦ ❛ ✈ár✐❛s ♣❡ss♦❛s q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ❞✉r❛♥t❡ ❡ss❡ ♣❡rí♦❞♦✳❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ❈❛r❧♦s ❉❡ ▼❛rq✉✐ ❏r✳✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✱ ❜♦♠ ❤✉♠♦r ❡ s❛❜❡❞♦r✐❛ ❡♠ ♠❡ ♦r✐❡♥t❛r✱ s❡♠♣r❡ ❛ ❞✐s♣♦s✐çã♦ ♣❛r❛ ♠❡ ♠♦str❛r ♦ ♠❡❧❤♦r ❝❛♠✐♥❤♦ ❛ s❡❣✉✐r ♥❛ ♣❡sq✉✐s❛✳ ▼✉✐t♦ ♦❜r✐❣❛❞❛ ♣❡❧❛s r❡✉♥✐õ❡s✱ ❞✐s❝✉ssõ❡s✱ ❝♦♥s❡❧❤♦s ❡ ♣❡❧♦ ❛♣♦✐♦ ❡ ❝♦♠♣r❡❡♥sã♦ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s ❞❡st❛ ❝❛♠✐♥❤❛❞❛✳ ❙❡♠ ♦ s❡♥❤♦r✱ ❝❡rt❛♠❡♥t❡ ❡ss❡ tr❛❜❛❧❤♦ ♥ã♦ s❡r✐❛ ❝♦♥❝❧✉í❞♦✳
❆❣r❛❞❡ç♦ ❛ ❋✉♥❞❛çã♦ ❞❡ ❆♠♣❛r♦ ❡ P❡sq✉✐s❛ ❞♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ✭❋❆P❊❙P✮ ♣❡❧❛ ❝♦♥❝❡ssã♦ ❞❛ ❜♦❧s❛ ❞❡ ♠❡str❛❞♦ ❡ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ♣❛r❛ ❛ ♣❡sq✉✐s❛ ❞❡s❡♥✈♦❧✈✐❞❛✳
❆❣r❛❞❡ç♦ ❛♦ ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❈✐❡♥tí✜❝♦ ❡ ❚❡❝♥♦❧ó❣✐❝♦ ✭❈◆Pq✮ ♣❡❧❛ ❝♦♥❝❡ssã♦ ❞❛ ❜♦❧s❛ ❞❡ ♠❡str❛❞♦ ❞✉r❛♥t❡ ♦s ♣r✐♠❡✐r♦s ♠❡s❡s ❞❡ss❛ ❝❛♠✐♥❤❛❞❛✳
❆❣r❛❞❡ç♦ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❆❡r♦♥á✉t✐❝❛ ♣♦r s❡r ♠✐♥❤❛ s❡❣✉♥❞❛ ❝❛s❛✳ ❖ ❛♣♦✐♦ ❞✉r❛♥t❡ ❡ss❡ ♣❡rí♦❞♦ ❢♦✐ ❡ss❡♥❝✐❛❧ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♣❡sq✉✐s❛✱ ♥ã♦ s♦♠❡♥t❡ ♣❡❧♦ ❡s♣❛ç♦ ❢ís✐❝♦✱ ♠❛s t❛♠❜é♠ ♣❡❧❛s ❛♠✐③❛❞❡s ❢❡✐t❛s ❡ ❝♦♥s♦❧✐❞❛❞❛s✳ ●✐✱ ❚✐❧t✐s ✭▼❛③é✮✱ ❈❧❛✉❞✐♥❤♦ ❡ ❏♦ã♦✱ ♠✉✐t♦ ♦❜r✐❣❛❞❛ ♣♦r s❡♠♣r❡ s❡ ♣r❡♦❝✉♣❛r❡♠ ❝♦♠✐❣♦✱ ♣❡❧❛s ❝❛r♦♥❛s ✐♥✜♥✐t❛s ❡ ♣♦r t♦❞❛s ❛s ❝♦♥✈❡rs❛s ❞✉r❛♥t❡ ♦s ♥♦ss♦s ❧❛♥❝❤❡s✳ ❱♦❝ês t♦r♥❛r❛♠ ♦s ♠❡✉s ❞✐❛s ❜❡♠ ♠❛✐s ❞✐✈❡rt✐❞♦s ❂✮ ✳ Pr♦❢❡ss♦r❡s ❈❛t❛❧❛♥♦ ❡ ❇❡❧♦✱ ♠✉✐t♦ ♦❜r✐❣❛❞❛ ♣❡❧♦ ❛♣♦✐♦ ❡♠ ❝♦♥t✐♥✉❛r ❝♦♠ ❛ ♣❡sq✉✐s❛ ❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ♥♦ r❛♠♦ ❛❡r♦♥á✉t✐❝♦✳ Pr♦❢❡ss♦r ❋❧á✈✐♦✱ ♦❜r✐❣❛❞❛ ♣❡❧♦ ❛♣♦✐♦ ❡ ♣❡❧♦s ❝♦♥s❡❧❤♦s ❞✉r❛♥t❡ ❛ q✉❛❧✐✜❝❛çã♦✱ ❡❧❡s ❢♦r❛♠ ❡ss❡♥❝✐❛✐s ♣❛r❛ ♦ tér♠✐♥♦ ❞❡ss❡ tr❛❜❛❧❤♦✳ Pr♦❢❡ss♦r ❱♦❧♥❡✐✱ ♦❜r✐❣❛❞❛ ♣♦r t❡r s❡ ❞✐s♣♦♥✐❜✐❧✐③❛❞♦ ♣❛r❛ ♠❡ ❛♣❧✐❝❛r ❛ ♣r♦✈❛ ❞❡ ❛❞♠✐ssã♦ ❛♦ ▼❡str❛❞♦ ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós ●r❛❞✉❛çã♦ ❞❛ ❊♥❣❡♥❤❛r✐❛ ▼❡❝â♥✐❝❛ ❞✉r❛♥t❡ ❛ ♠✐♥❤❛ ❡st❛❞✐❛ ♥❛ ❋r❛♥ç❛✱ s❡♠ ❛ t✉❛ ❛❥✉❞❛✱ ❡✉ ♥ã♦ ❡st❛r✐❛ ❝♦♥❝❧✉✐♥❞♦ ♠❛✐s ❡ss❛ ❡t❛♣❛✳ ❏♦ã♦ P❛✉❧♦✱ ♦❜r✐❣❛❞❛ ♣❡❧❛ ❛❥✉❞❛ ❝♦♠ ❛ ♣❛rt❡ té❝♥✐❝❛ ❝♦♠♣✉t❛❝✐♦♥❛❧✱ ❢❛❝✐❧✐t♦✉ ❡ ♠✉✐t♦ ♦ ♠❡✉ tr❛❜❛❧❤♦✳
♥❤✐❛s ❞✉r❛♥t❡ ♦s ♥♦ss♦s ❛❧♠♦ç♦s✳ ❊♠ ❡s♣❡❝✐❛❧✱ ❉♦✉❣❧❛s✱ ▼❛r❝❡❧✱ ❈✐❞✱ ❍♦♠❡r✱ ❱❛❣♥❡r✱ P❛❣❛♥♥✐ ❡ ❲❛♥❞❡r✱ ♦❜r✐❣❛❞❛ ♣❡❧❛s ❞✐s❝✉ssõ❡s ❡ ❛❥✉❞❛s✱ t❛♥t♦ ♥❛ ♣❛rt❡ té❝♥✐❝❛ q✉❛♥t♦ ♥❛ ❡①♣❡r✐♠❡♥t❛❧✳ ❱♦❝ês ❢♦r❛♠ t❛♠❜é♠ ❡ss❡♥❝✐❛✐s ♣❛r❛ ❛ ✜♥❛❧✐③❛çã♦ ❞❡ss❡ tr❛❜❛❧❤♦✳
❆❣r❛❞❡ç♦ às ♠❡♥✐♥❛s ❞❛ s❡❝r❡t❛r✐❛ ❞❛ ♣ós ❣r❛❞✉❛çã♦✱ ❆♥❛ P❛✉❧❛ ❡ ■❛r❛✱ ♣❡❧❛ ❛❥✉❞❛ ❝♦♠ ❛ ♣❛rt❡ ❜✉r♦❝rát✐❝❛✳ ❱♦❝ês s❡♠♣r❡ ❢❛❝✐❧✐t❛♠ ♥♦ss❛s ✈✐❞❛s✳
❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ❢❛♠í❧✐❛✳ ▼ã❡✱ ♠✉✐t♦ ♦❜r✐❣❛❞❛ ♣♦r t❡r ♠❡ ❛♣♦✐❛❞♦ ❡ ♠❡ ❡♥s✐♥❛❞♦ ❛ s♦♥❤❛r ❡ ❧✉t❛r ♣❡❧♦ ♦ q✉❡ ❡✉ ❛❝r❡❞✐t♦✳ P❛✐✱ ♠✉✐t♦ ♦❜r✐❣❛❞❛ ♣♦r t❡r ♠❡ ✐♥s♣✐r❛❞♦ ♥❛ ❡s❝♦❧❤❛ ❞❛ ♠✐♥❤❛ ❝❛rr❡✐r❛ ❡ t❡r ♠❡ ❛♣♦✐❛❞♦ s❡♠♣r❡ ♥❛s ♠✐♥❤❛s ❞❡❝✐sõ❡s✳ ❆❣r❛❞❡ç♦ ❛ ♠❡✉s ✐r♠ã♦s✱ ●✉st❛✈♦ ❡ ❘❛❢❛❡❧✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❞✉r❛♥t❡ ❡ss❡s ❛♥♦s✳ ❆❣r❛❞❡ç♦ ❛ ♠❡✉ ♥❛♠♦r❛❞♦✱ ●✉st❛✈♦ P❡ss✐♥✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❞✉r❛♥t❡ t♦❞♦ ❡ss❡ t❡♠♣♦ ❡ ♣❡❧♦ ❛♣♦✐♦ ❡♠ ❝♦♥t✐♥✉❛r ✜r♠❡ ❡ ❢♦rt❡ ♥❡ss❛ ❝❛♠✐♥❤❛❞❛✳ ❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ ❞❡ ❝♦r❛çã♦✱ ■❛r❛✱ ❲❛❧t❡r ❡ ❈✐♥t❤✐❛✱ ♣❡❧♦ ❛♣♦✐♦ ❡ ❝❛r✐♥❤♦ ❞✉r❛♥t❡ t♦❞♦ ❡ss❡ t❡♠♣♦✳ ❉❡s❝✉❧♣❡♠✲♠❡ ♣❡❧❛ ❛✉sê♥❝✐❛✳
❆❣r❛❞❡ç♦ ❛ t♦❞♦s ♦s ♠❡✉s ❛♠✐❣♦s ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦ ❡ ❛♣♦✐♦✱ ❡♠ ❡s♣❡❝✐❛❧✱ ▲✐❛♥♥❛ ❡ ❇ár❜❛r❛✳ ❖❜r✐❣❛❞❛ ♣❡❧❛s ❝♦♥✈❡rs❛s ❡ ♣♦r t♦r♥❛r❡♠ ♠✐♥❤❛s s❡♠❛♥❛s ♠❡♥♦s ♠❛ss❛❝r❛♥t❡s ❡ ♠❛✐s ✐♥t❡r❡ss❛♥t❡s✳
❯♠ ❜❛r❝♦ ♥❛✈❡❣❛ ♣❛r❛ ♦ ❧❡st❡ ❡ ♦✉tr♦ ♣❛r❛ ♦ ♦❡st❡✱ ❧❡✈❛❞♦s ♣❡❧♦ ♠❡s♠♦ ✈❡♥t♦✳ ➱ ❛ ♣♦s✐çã♦ ❞❛s ✈❡❧❛s ❡ ♥ã♦ ❛ ✈❡♥t❛♥✐❛ q✉❡ ❞❡t❡r♠✐♥❛ ♦ ❝❛♠✐♥❤♦ q✉❡ ❡❧❡s s❡❣✉❡♠✳ ❈♦♠♦ ♦s ✈❡♥t♦s ♥♦ ♠❛r✱ ❛ss✐♠ é ♦ ❞❡st✐♥♦❀ à ♠❡❞✐❞❛ q✉❡ ♥❛✈❡❣❛♠♦s ❛♦ ❧♦♥❣♦ ❞❛ ✈✐❞❛✱ é ❛ ♣♦s✐çã♦ ❞❛ ❛❧♠❛ q✉❡ ❞❡❝✐❞❡ s❡✉ r✉♠♦✱ ♥ã♦ ❛ ❝❛❧♠❛r✐❛ ♦✉ ♦ ❝♦♥✢✐t♦✳
❘❡s✉♠♦
❆◆■❈❊❩■❖✱ ▼✳ ▼✳ ❆t❡♥✉❛çã♦ ❞❡ ❱✐❜r❛çõ❡s ❡♠ Pás ❞❡ ❍❡❧✐❝ó♣t❡r♦s ✉t✐❧✐③❛♥❞♦ ❈✐r❝✉✐t♦ P✐❡③❡❧étr✐❝♦ ❙❡♠✐✲P❛ss✐✈♦✳ ✷✵✶✹✳ ✺✼❢✳ ❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦✮ ✕ ❊s❝♦❧❛ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❙ã♦ ❈❛r❧♦s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ ❈❛r❧♦s✲❙P✱ ❇r❛s✐❧✱ ✷✵✶✺✳
❖ ✉s♦ ❞❡ ♠❛t❡r✐❛✐s ✐♥t❡❧✐❣❡♥t❡s ❡♠ ♣r♦❜❧❡♠❛s ❞❡ ❝♦♥tr♦❧❡ ❞❡ ✈✐❜r❛çã♦ t❡♠ s✐❞♦ ✐♥✈❡st✐❣❛❞♦ ❡♠ ❞✐✈❡rs❛s ♣❡sq✉✐s❛s ❛♦ ❧♦♥❣♦ ❞♦s ú❧t✐♠♦s ❛♥♦s✳ ❆♣❡s❛r ❞❡ q✉❡ ❞✐❢❡r❡♥t❡s ♠❛t❡r✐❛✐s ✐♥t❡✲ ❧✐❣❡♥t❡s ❡stã♦ ❞✐s♣♦♥í✈❡✐s✱ ♦ ♣✐❡③❡❧étr✐❝♦ t❡♠ r❡❝❡❜✐❞♦ ❣r❛♥❞❡ ❛t❡♥çã♦ ❞❡✈✐❞♦ à ❢❛❝✐❧✐❞❛❞❡ ❞❡ ✉s♦ ❝♦♠♦ s❡♥s♦r❡s✱ ❛t✉❛❞♦r❡s✱ ♦✉ ❛♠❜♦s s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ ❆s ♣r✐♥❝✐♣❛✐s té❝♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ✉s❛♥❞♦ ♠❛t❡r✐❛✐s ♣✐❡③♦❡❧étr✐❝♦s sã♦ ♦s ❛t✐✈♦s ❡ ♣❛ss✐✈♦s✳ ❈✐r❝✉✐t♦s ♣✐❡③❡❧étr✐❝♦s ♣❛ss✐✈♦s sã♦ ❛❥✉st❛❞♦s ♣❛r❛ ✉♠❛ ❢r❡q✉ê♥❝✐❛ ❡s♣❡❝í✜❝❛ ❡✱ ♣♦rt❛♥t♦✱ ❛ ❧❛r❣✉r❛ ❞❡ ❜❛♥❞❛ ❡❢❡t✐✈❛ é ♣❡q✉❡♥❛✳ ❊♠❜♦r❛ ♦s s✐st❡♠❛s ❛t✐✈♦s ♣♦ss❛♠ ❛♣r❡s❡♥t❛r ✉♠ ❜♦♠ ❞❡s❡♠♣❡♥❤♦ ♥♦ ❝♦♥tr♦❧❡ ❞❡ ✈✐❜r❛çã♦✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❡①t❡r♥❛ ❡ ❤❛r❞✇❛r❡ ❛❞✐❝✐♦♥❛❞♦ sã♦ q✉❡stõ❡s ✐♠♣♦rt❛♥t❡s✳ ❆s té❝♥✐❝❛s ❙❙❉ ✭❙②♥❝❤r♦♥✐③❡❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣✮ ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞❛s ❝♦♠♦ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ❛♦s ❝♦♥tr♦❧❛❞♦r❡s ♣❛ss✐✈♦s ❡ ❝♦♥tr♦❧❛❞♦r❡s ❛t✐✈♦s ❞❡ ✈✐❜r❛çã♦✳ ❊❧❛s ♣♦✲ ❞❡♠ s❡r té❝♥✐❝❛s s❡♠✐✲❛t✐✈❛s ♦✉ s❡♠✐✲♣❛ss✐✈❛s q✉❡ ✐♥tr♦❞✉③❡♠ ✉♠ tr❛t❛♠❡♥t♦ ♥ã♦ ❧✐♥❡❛r ♥❛ t❡♥sã♦ ❡❧étr✐❝❛ ♣r♦✈❡♥✐❡♥t❡ ❞♦ ♠❛t❡r✐❛❧ ♣✐❡③❡❧étr✐❝♦ ❡ ✐♥❞✉③ ✉♠ ❛✉♠❡♥t♦ ♥❛ ❝♦♥✈❡rsã♦ ❞❡ ❡♥❡r❣✐❛ ♠❡❝â♥✐❝❛ ♣❛r❛ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ✉♠ ❛✉♠❡♥t♦ ♥♦ ❡❢❡✐t♦ ❞❡ ❛♠♦rt❡❝✐♠❡♥t♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ❝♦♥tr♦❧❡ ♣✐❡③♦❡❧étr✐❝♦ s❡♠✐✲♣❛ss✐✈♦ ❞❡ ✉♠❛ ♣á ♣✐❡③❡✲ ❧étr✐❝❛ ❡♥❣❛st❛❞❛ é ❛♣r❡s❡♥t❛❞♦ ❡ ❝♦♠♣❛r❛❞♦ ❝♦♠ ♦✉tr♦s ❝♦♥tr♦❧❛❞♦r❡s✳ ❖ ♠♦❞❡❧♦ ♥ã♦ ❧✐♥❡❛r ❡❧❡❝tr♦♠❡❝â♥✐❝♦ ❞❡ ✉♠❛ ♣á ❝♦♠ ♣✐❡③♦❝❡râ♠✐❝❛s ✐♥❝♦r♣♦r❛❞♦s é ❞❡t❡r♠✐♥❛❞♦ ❝♦♠ ❜❛s❡ ♥♦ ♠ét♦❞♦ ✈❛r✐❛❝✐♦♥❛❧✲❛ss✐♥tót✐❝♦ ✭❱❆▼✮✳ ❖ s✐st❡♠❛ r♦t❛t✐✈♦ ❛❝♦♣❧❛❞♦ ♥ã♦ ❧✐♥❡❛r é r❡s♦❧✈✐❞♦ ♥♦ ❞♦♠í♥✐♦ ❞♦ t❡♠♣♦✱ ✉t✐❧✐③❛♥❞♦ ✉♠ ♠ét♦❞♦ ❞❡ ✐♥t❡❣r❛çã♦ ❛❧❢❛✲❣❡♥❡r❛❧✐③❛❞♦ ❛ ✜♠ ❞❡ ❣❛r❛♥t✐r ❛ ❡st❛❜✐❧✐❞❛❞❡ ♥✉♠ér✐❝❛✳ ❆s s✐♠✉❧❛çõ❡s sã♦ r❡❛❧✐③❛❞❛s ♣❛r❛ ✉♠❛ ✈❛st❛ ❣❛♠❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❞❡ r♦t❛çã♦✳ ❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r❡s✐stê♥❝✐❛s ✭✈❛r✐✲ ❛♥❞♦ ❞❡s❞❡ ❛ ❝♦♥❞✐çã♦ ❞❡ ❝✉rt♦✲❝✐r❝✉✐t♦ ♣❛r❛ ❛ ❝♦♥❞✐çã♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦✮ é ❝♦♥s✐❞❡r❛❞❛✳ ❖ ❡❢❡✐t♦ ❞❛ r❡s✐stê♥❝✐❛ ót✐♠❛ ✭q✉❡ r❡s✉❧t❛ ❡♠ ♠á①✐♠♦ ❛♠♦rt❡❝✐♠❡♥t♦✮ s♦❜r❡ ♦ ❝♦♠♣♦rt❛✲ ♠❡♥t♦ ❞♦ s✐st❡♠❛ é ✐♥✈❡st✐❣❛❞♦ ♣❛r❛ ♦ ❛✉♠❡♥t♦ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦✳ ▼❛✐s t❛r❞❡✱ ❛ té❝♥✐❝❛ ❙❙❉❙ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛♠♦rt❡❝❡r ❛s ♦s❝✐❧❛çõ❡s ❞❛ ♣á ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛♠ q✉❡ ❛ té❝♥✐❝❛ ❙❙❉❙ ♣♦❞❡ s❡r ✉♠ ♠ét♦❞♦ út✐❧ ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❞❡ ✈✐❜r❛çõ❡s ❞❡ ✈✐❣❛s r♦t❛t✐✈❛s ♥ã♦ ❧✐♥❡❛r❡s✱ t❛✐s ❝♦♠♦ ♣ás ❞❡ ❤❡❧✐❝ó♣t❡r♦✳
❆❜str❛❝t
❆◆■❈❊❩■❖✱ ▼✳ ▼✳ ❱✐❜r❛t✐♦♥ ❆tt❡♥✉❛t✐♦♥ ✐♥ ❍❡❧✐❝♦♣t❡r ❇❧❛❞❡s ✉s✐♥❣ ❙❡♠✐✲ P❛ss✐✈❡ P✐❡③♦❡❧❡❝tr✐❝ ❈✐r❝✉✐t✳ ✷✵✶✹✳ ✺✼❢✳ ❉✐ss❡rt❛t✐♦♥ ✭▼❛rt❡r✬s ❉❡❣r❡❡✮ ✕ ❙❛♦ ❈❛r❧♦s ❙❝❤♦♦❧ ♦❢ ❊♥❣✐♥❡❡r✐♥❣✱ ❯♥✐✈❡rs✐t② ♦❢ ❙❛♦ P❛✉❧♦✱ ❙❛♦ ❈❛r❧♦s✲❙P✱ ❇r❛③✐❧✱ ✷✵✶✺✳
❚❤❡ ✉s❡ ♦❢ s♠❛rt ♠❛t❡r✐❛❧s ✐♥ ✈✐❜r❛t✐♦♥ ❝♦♥tr♦❧ ♣r♦❜❧❡♠s ❤❛s ❜❡❡♥ ✐♥✈❡st✐❣❛t❡❞ ✐♥ s❡✈❡r❛❧ r❡s❡❛r❝❤❡s ♦✈❡r t❤❡ ❧❛st ②❡❛rs✳ ❆❧t❤♦✉❣❤ ❞✐✛❡r❡♥t s♠❛rt ♠❛t❡r✐❛❧s ❛r❡ ❛✈❛✐❧❛❜❧❡✱ t❤❡ ♣✐❡③♦✲ ❡❧❡❝tr✐❝ ♦♥❡ ❤❛s r❡❝❡✐✈❡❞ ❣r❡❛t ❛tt❡♥t✐♦♥ ❞✉❡ t♦ ❡❛s❡ ♦❢ ✉s❡ ❛s s❡♥s♦rs✱ ❛❝t✉❛t♦rs✱ ♦r ❜♦t❤✳ ❚❤❡ ♠❛✐♥ ❝♦♥tr♦❧ t❡❝❤♥✐q✉❡s ✉s✐♥❣ ♣✐❡③♦❡❧❡❝tr✐❝ ♠❛t❡r✐❛❧s ❛r❡ t❤❡ ❛❝t✐✈❡ ❛♥❞ ♣❛ss✐✈❡ ♦♥❡s✳ P❛ss✐✈❡ ♣✐❡③♦❡❧❡❝tr✐❝ ♥❡t✇♦r❦s ❛r❡ ❛❞❥✉st❡❞ ❢♦r s♣❡❝✐✜❝ t❛r❣❡t ❢r❡q✉❡♥❝✐❡s ❛♥❞✱ t❤❡r❡❢♦r❡✱ t❤❡ ❡✛❡❝t✐✈❡ ❜❛♥❞✇✐❞t❤ ♦❢ s✉❝❤ s②st❡♠s ✐s s♠❛❧❧✳ ❆❧t❤♦✉❣❤ ❛❝t✐✈❡ s②st❡♠s ❝❛♥ ❛❝❤✐❡✈❡ ❣♦♦❞ ✈✐❜r❛t✐♦♥ ❝♦♥tr♦❧ ♣❡r❢♦r♠❛♥❝❡✱ t❤❡ ❛♠♦✉♥t ♦❢ ❡①t❡r♥❛❧ ♣♦✇❡r ❛♥❞ ❛❞❞❡❞ ❤❛r❞✇❛r❡ ❛r❡ ✐♠♣♦rt❛♥t ✐ss✉❡s✳ ❚❤❡ s②♥❝❤r♦♥✐③❡❞ s✇✐t❝❤ ❞❛♠♣✐♥❣ ✭❙❙❉✮ t❡❝❤♥✐q✉❡ ✇❛s ❞❡✈❡❧♦♣❡❞ ✐♥ ♦r❞❡r t♦ ❛❞❞r❡ss t❤❡ ✐ss✉❡s ♦❢ ♣❛ss✐✈❡ ❞❛♠♣✐♥❣ ♠❡t❤♦❞♦❧♦❣✐❡s ❛s ✇❡❧❧ ❛s t❤❡ ✐ss✉❡s ♦❢ ❛❝t✐✈❡ ❝♦♥tr♦❧ s②st❡♠s✳ ❚❤❡ ❙❙❉ ❝❛♥ ❜❡ ❝❧❛ss✐✜❡❞ ❛s s❡♠✐✲♣❛ss✐✈❡ t❡❝❤♥✐q✉❡ ♦r s❡♠✐✲❛❝t✐✈❡ t❡❝❤✲ ♥✐q✉❡ t❤❛t ✐♥tr♦❞✉❝❡ t❤❡ ♥♦♥❧✐♥❡❛r tr❡❛t♠❡♥t ♦❢ t❤❡ ♣✐❡③♦❡❧❡❝tr✐❝ ❡❧❡♠❡♥t ✈♦❧t❛❣❡ ♦✉t♣✉t ❛♥❞ ✐♥❞✉❝❡ ❛♥ ✐♥❝r❡❛s❡ ✐♥ ♠❡❝❤❛♥✐❝❛❧ t♦ ❡❧❡❝tr✐❝❛❧ ❡♥❡r❣② ❝♦♥✈❡rs✐♦♥ ❛♥❞✱ ❝♦♥s❡q✉❡♥t❧②✱ t❤❡ s❤✉♥t ❞❛♠♣✐♥❣ ❡✛❡❝t✳ ■♥ t❤✐s ✇♦r❦✱ t❤❡ s❡♠✐✲♣❛ss✐✈❡ ♣✐❡③♦❡❧❡❝tr✐❝ ❝♦♥tr♦❧ ♦❢ ❛ r♦t❛t✐♥❣ ❝❛♥t✐❧❡✈❡r ❜❡❛♠ r❡s♣♦♥s❡ ✐s ♣r❡s❡♥t❡❞ ❛♥❞ ❝♦♠♣❛r❡❞ ✇✐t❤ ♦t❤❡r ❝♦♥tr♦❧❧❡rs✳ ❚❤❡ ♥♦♥❧✐♥❡❛r ❡❧❡❝tr♦♠❡❝❤❛♥✐❝❛❧ ♠♦❞❡❧ ♦❢ ❛ r♦t❛t✐♥❣ ❜❡❛♠ ✇✐t❤ ❡♠❜❡❞❞❡❞ ♣✐❡③♦❝❡r❛♠✐❝s ✐s ❞❡r✐✈❡❞ ❜❛✲ s❡❞ ♦♥ t❤❡ ✈❛r✐❛t✐♦♥❛❧✲❛s②♠♣t♦t✐❝ ♠❡t❤♦❞ ✭❱❆▼✮✳ ❚❤❡ ❝♦✉♣❧❡❞ ♥♦♥✲❧✐♥❡❛r r♦t❛r② s②st❡♠ ✐s s♦❧✈❡❞ ✐♥ t❤❡ t✐♠❡✲❞♦♠❛✐♥ ❜② ✉s✐♥❣ ❛ ❣❡♥❡r❛❧✐③❡❞✲❛❧♣❤❛ ✐♥t❡❣r❛t✐♦♥ ♠❡t❤♦❞ ✐♥ ♦r❞❡r t♦ ❣✉❛r❛♥t❡❡ ♥✉♠❡r✐❝❛❧ st❛❜✐❧✐t②✳ ❚❤❡ s✐♠✉❧❛t✐♦♥s ❛r❡ ♣❡r❢♦r♠❡❞ ❢♦r ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ r♦t❛t✐♥❣ s♣❡❡❞s✳ ❋✐rst✱ ❛ s❡t ♦❢ ❧♦❛❞ r❡s✐st❛♥❝❡s ✭r❛♥❣✐♥❣ ❢r♦♠ s❤♦rt ❝✐r❝✉✐t ❝♦♥❞✐t✐♦♥ t♦ ♦♣❡♥ ❝✐r❝✉✐t ❝♦♥❞✐t✐♦♥✮ ✐s ❝♦♥s✐❞❡r❡❞✳ ❚❤❡ ❡✛❡❝t ♦❢ ♦♣t✐♠✉♠ ❧♦❛❞ r❡s✐st❛♥❝❡ ✭❢♦r ♠❛①✐♠✉♠ ❞❛♠♣✐♥❣✮ ♦♥ t❤❡ ❡❧❛st✐❝ ❜❡❤❛✈✐♦r ♦❢ t❤❡ ❜❡❛♠ ✐s ✐♥✈❡st✐❣❛t❡❞ ❢♦r ✐♥❝r❡❛s✐♥❣ r♦t❛t✐♥❣ s♣❡❡❞✳ ▲❛t❡r✱ t❤❡ s②♥❝❤r♦♥✐③❡❞ s✇✐t❝❤ ❞❛♠♣✐♥❣ ♦♥ s❤♦rt ✭❙❙❉❙✮ t❡❝❤♥✐q✉❡ ✐s ❡♠♣❧♦②❡❞ t♦ ❞❛♠♣ t❤❡ ♥♦♥❧✐♥❡❛r ♦s❝✐❧❧❛t✐♦♥s ♦❢ t❤❡ r♦t❛t✐♥❣ ❜❡❛♠ ✇✐t❤ ✐♥❝r❡❛s✐♥❣ r♦t❛t✐♥❣ s♣❡❡❞✳ ❘❡s✉❧ts s❤♦✇ t❤❛t t❤❡ ❙❙❉❙ t❡❝❤♥✐q✉❡ ❝❛♥ ❜❡ ❛ ✉s❡❢✉❧ ♠❡t❤♦❞ ♦❢ ❝♦♥tr♦❧ ❢♦r ♥♦♥❧✐♥❡❛r r♦t❛t✐♥❣ ❜❡❛♠s s✉❝❤ ❛s ❤❡❧✐❝♦♣t❡r ❜❧❛❞❡s✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
❋✐❣✉r❛ ✕ ✶ ❋r❡q✉ê♥❝✐❛ ❞❡ r❡ss♦♥â♥❝✐❛ ❞♦ tr♦♥❝♦ ❞❡ ✉♠❛ ♣❡ss♦❛❧ ❡ ❢r❡q✉ê♥❝✐❛ tr❛♥s✲ ❢❡r✐❞❛ ❞♦ r♦t♦r ♣❛r❛ ❢✉s❡❧❛❣❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ❋✐❣✉r❛ ✕ ✷ ❘❡❧❛çã♦ ❡♥tr❡✿ ❛✮ t❡♥sã♦ ♠❡❝â♥✐❝❛ ❡ ❞❡❢♦r♠❛çã♦❀ ❜✮ t❡♥sã♦ ❡ ❞❡s❧♦❝❛✲
♠❡♥t♦ ❡❧étr✐❝♦❀ ❝✮ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦ ❡ ❞❡s❧♦❝❛♠❡♥t♦ ❡❧étr✐❝♦❀ ❡ ❞✮ ❞❡❢♦r♠❛çã♦ ❡ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ✭▲❡♦ ✭✷✵✵✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ❋✐❣✉r❛ ✕ ✸ ❈✉❜♦ ❞❡ ♣✐❡③♦❡❧étr✐❝♦ ✐♥❞✐❝❛♥❞♦ ❛s ❝♦♦r❞❡♥❛❞❛s ❛①✐❛✐s ❞❛ ❛♥á❧✐s❡ tr✐✲
❞✐♠❡♥s✐♦♥❛❧✳ ✭▲❡♦ ✭✷✵✵✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ❋✐❣✉r❛ ✕ ✹ ❘❡❧❛çã♦ ❡♥tr❡ t❡♥sã♦ ♠❡❝â♥✐❝❛ ❡ ❞❡❢♦r♠❛çã♦ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❡❧ást✐❝♦
❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥t♦r♥♦ ❡❧étr✐❝❛✳ ✭▲❡♦ ✭✷✵✵✼✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ❋✐❣✉r❛ ✕ ✺ ❉✐❢❡r❡♥t❡s té❝♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ♣❛ss✐✈♦✿ ❛✮ r❡s✐st✐✈♦ ♣✉r♦❀ ❜✮ ✐♥❞✉t✐✈♦
♣✉r♦❀ ❝✮ r❡s✐st✐✈♦✲✐♥❞✉t✐✈♦ ❡♠ sér✐❡❀ ❞✮ r❡s✐st✐✈♦✲✐♥❞✉t✐✈♦ ❡♠ ♣❛r❛❧❡❧♦❀ ❡ ❡✮ r❡s✐st✐✈♦✲❝❛♣❛❝✐t✐✈♦ ❡♠ sér✐❡✳ ▼♦❞✐✜❝❛❞♦ ❞❡ ❉✬❆ss✉♥çã♦ ✭✷✵✶✸✮✳ ✳ ✳ ✳ ✸✸ ❋✐❣✉r❛ ✕ ✻ Pr✐♥❝✐♣❛✐s t✐♣♦s ❞❡ ❝♦♥tr♦❧❛❞♦r❡s s❡♠✐♣❛ss✐✈♦s✿ ❛✮ ❙❙❀ ❜✮ ❙❙❉❙❀ ❡ ❝✮
❙❙❉■✳ ✭❉✬❆ss✉♥çã♦ ✭✷✵✶✸✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ❋✐❣✉r❛ ✕ ✼ ❈♦♠♣❛r❛çã♦ ❞❛s t❡♥sõ❡s ❡❧étr✐❝❛s✿ ❛✮ ❝✐r❝✉✐t♦ ❛❜❡rt♦❀ ❜✮ ❙❙❉❙❀ ❡ ❝✮
❙❙❉■✳ ✭❘✐❝❤❛r❞ ❡t ❛❧✳ ✭✷✵✵✵✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ❋✐❣✉r❛ ✕ ✽ ❛✮ ❝✐r❝✉✐t♦ ❜ás✐❝♦ ❇❙❉❙❀ ❡ ❜✮ ❋♦r♠❛s ❞❛s ♦♥❞❛s ❞♦ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳
✭▲❛❧❧❛rt ❡t ❛❧✳ ✭✷✵✵✾✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ❋✐❣✉r❛ ✕ ✾ ❈✐r❝✉✐t♦ ❡❧étr✐❝♦ ❙❙❉❱✳ ✭▲❡❢❡✉✈r❡ ❡t ❛❧✳ ✭✷✵✵✻✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ❋✐❣✉r❛ ✕ ✶✵ ❘❡s✉♠♦ ❞❡ té❝♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ❛t✐✈♦ ❡♠ ❤❡❧✐❝ó♣t❡r♦s✳ ✭P❛tt ❡t ❛❧✳
❋✐❣✉r❛ ✕ ✶✸ ❆ss♦❝✐❛çã♦ ❞❡ ✉♠ ❝♦♥tr♦❧❛❞♦r ❞♦ t✐♣♦ ❆❈❚✱ ♦✉tr♦ ❆❈❋ ❡ ✉♠ ❆P▲ r❡♣r❡s❡♥t❛♥❞♦ ♦ ❝♦♥tr♦❧❡ ❤í❜r✐❞♦✳ ✭❋r❡❞ ◆✐t③s❝❤❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ❋✐❣✉r❛ ✕ ✶✹ ❙✐st❡♠❛s ❞❡ r❡❢❡rê♥❝✐❛ ❞❡ ✉♠❛ ✈✐❣❛ r♦t❛t✐✈❛ ✭❈❤❡♥❣ ✭✷✵✵✷✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ❋✐❣✉r❛ ✕ ✶✺ ❋❧✉①♦❣r❛♠❛ ❞♦ ♣r♦❝❡ss♦ ❞❡ s♦❧✉çã♦ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❡str✉t✉r❛❧ ❞❛ ♣á
✭❈❤❡♥❣ ✭✷✵✵✷✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ❋✐❣✉r❛ ✕ ✶✻ ❋❧✉①♦❣r❛♠❛ ❞♦ ♠ét♦❞♦ ❞❡ s♦❧✉çã♦ ◆❡✇t♦♥✲❘❛♣❤s♦♥ ✭❈❤❡♥❣ ✭✷✵✵✷✮✮✳ ✺✹ ❋✐❣✉r❛ ✕ ✶✼ ▼♦❞❡❧♦ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ❋✐❣✉r❛ ✕ ✶✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡✿ ❛✮ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ❞♦ ♠♦❞❡❧♦ ♥✉✲
♠ér✐❝♦❀ ❜✮ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❈❤❡♥❣❀ ❝✮ â♥❣✉❧♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ❞♦ ♠♦❞❡❧♦ ♥✉♠ér✐❝♦❀ ❞✮ â♥❣✉❧♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❈❤❡♥❣❀ ❡ ❡✮t❡♥sã♦ ❡❧étr✐❝❛ ❞♦ ♠♦❞❡❧♦ ♥✉♠ér✐❝♦✳ ✭❈❤❡♥❣ ✭✷✵✵✷✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ❋✐❣✉r❛ ✕ ✶✾ ❋❘❋ ✭❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ✴ ❋♦rç❛ ❞❡ ❡①❝✐t❛çã♦✮ ❞❡ ✉♠❛ ♣á ♣✐❡③❡✲
❧étr✐❝❛ ❡♥❣❛st❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ (R= 106Ω)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ❋✐❣✉r❛ ✕ ✷✵ ❋❘❋ ✭❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ✴ ❋♦rç❛ ❞❡ ❡①❝✐t❛çã♦✮ ❞❡ ✉♠❛ ♣á ♣✐❡✲
③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ (R = 106Ω) ❡♠ ✵ r♣♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ❋✐❣✉r❛ ✕ ✷✶ ❋❘❋ ✭❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ✴ ❋♦rç❛ ❞❡ ❡①❝✐t❛çã♦✮ ❞❡ ✉♠❛ ♣á ♣✐❡③❡✲
❧étr✐❝❛ ❡♥❣❛st❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ (R = 106Ω) ❡♠ ✷✵✵ r♣♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ❋✐❣✉r❛ ✕ ✷✷ ❋❘❋ ✭❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ✴ ❋♦rç❛ ❞❡ ❡①❝✐t❛çã♦✮ ❞❡ ✉♠❛ ♣á ♣✐❡③❡✲
❧étr✐❝❛ ❡♥❣❛st❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ (R = 106Ω) ❡♠ ✹✵✵ r♣♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ❋✐❣✉r❛ ✕ ✷✸ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❙❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ❋✐❣✉r❛ ✕ ✷✹ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡ ❞♦ ❝✐r❝✉✐t♦ ❝❤❛✈❡❛❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ❋✐❣✉r❛ ✕ ✷✺ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❋✐❣✉r❛ ✕ ✷✻ ➶♥❣✉❧♦s ♥❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙ ✳ ✳ ✻✷ ❋✐❣✉r❛ ✕ ✷✼ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✷✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙✳ ✻✸ ❋✐❣✉r❛ ✕ ✷✽ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✷✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❙❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ❋✐❣✉r❛ ✕ ✷✾ ➶♥❣✉❧♦s ♥❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✷✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙✳ ✻✸ ❋✐❣✉r❛ ✕ ✸✵ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✹✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙✳ ✻✹ ❋✐❣✉r❛ ✕ ✸✶ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✹✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❙❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ❋✐❣✉r❛ ✕ ✸✷ ➶♥❣✉❧♦s ♥❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✹✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙✳ ✻✺ ❋✐❣✉r❛ ✕ ✸✸ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳ ✻✺ ❋✐❣✉r❛ ✕ ✸✹ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❇❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ❋✐❣✉r❛ ✕ ✸✺ ➶♥❣✉❧♦s ♥❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳ ✳ ✻✻ ❋✐❣✉r❛ ✕ ✸✻ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✷✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳ ✻✻ ❋✐❣✉r❛ ✕ ✸✼ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✷✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❇❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ❋✐❣✉r❛ ✕ ✸✽ ➶♥❣✉❧♦s ♥❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✷✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳ ✻✼ ❋✐❣✉r❛ ✕ ✸✾ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✹✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳ ✻✼ ❋✐❣✉r❛ ✕ ✹✵ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✹✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r
❇❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ❋✐❣✉r❛ ✕ ✹✶ ➶♥❣✉❧♦s ♥❛ ♣♦♥t❛ ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✹✵✵ r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❇❙❉❙✳ ✻✽ ❋✐❣✉r❛ ✕ ✹✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛ t❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛ ❡♠ ✵ r♣♠
✲ ❝♦♥tr♦❧❛❞♦r❡s ❙❙❉❙ ❡ ❇❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ❋✐❣✉r❛ ✕ ✹✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ❞❡s❧♦❝❛♠❡♥t♦s ❞❛ ♣♦♥t❛ ❞❡ ✉♠❛ ♣á ♣✐❡③❡❧étr✐❝❛
r♣♠ ✲ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙ ❡ ❇❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ❋✐❣✉r❛ ✕ ✹✺ ❆♥❛❧♦❣✐❛ ❡♥tr❡ ❛✮ s✐st❡♠❛ ♠❡❝â♥✐❝♦ ❞❡ tr❛♥s❧❛çã♦ ❡ ❜✮ s✐st❡♠❛ ❡❧étr✐❝♦✳
✭▼❡❞❡✐r♦s ✭✭❆❝❡ss❛❞♦ ❡♠ ✶✼✴✵✻✴✷✵✶✹✮✮✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ❋✐❣✉r❛ ✕ ✹✻ ❈✐r❝✉✐t♦ ❝❤❛✈❡❛❞♦r ❛✉tô♥♦♠♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ❋✐❣✉r❛ ✕ ✹✼ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦ s✐♥❛❧ ❞❡ t❡♥sã♦ ❣❡r❛❞♦ ♣❡❧♦ ✜❧tr♦ ❡ ♦ s✐♥❛❧ ❞❡ t❡♥sã♦
❣❡r❛❞♦ ♣❡❧♦ ♣✐❡③❡❧étr✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ❋✐❣✉r❛ ✕ ✹✽ ❋❧✉①♦❣r❛♠❛ ❞❛ ♠♦❞❡❧❛❣❡♠ ❞❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ♥♦ ▼❆❚▲❆❇✴❙■▼❯▲■◆❑✳ ✽✾ ❋✐❣✉r❛ ✕ ✹✾ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❋❘❋ ❞❡ t❡♥sã♦ ❡❧étr✐❝❛ ❛♣r❡s❡♥t❛❞❛ ❡♠ ❊rt✉r❦ ❡
■♥♠❛♥ ✭✷✵✵✾✮ ❡ ❛ ❋❘❋ ♦❜t✐❞❛ ♣❡❧❛ ♠♦❞❡❧❛❣❡♠ ♥✉♠ér✐❝❛ ❞❡st❡ tr❛❜❛❧❤♦✳ ✾✵ ❋✐❣✉r❛ ✕ ✺✵ ❋❘❋ ❞❡ ✉♠❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦
(R= 102Ω) ❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ (R= 106Ω)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ❋✐❣✉r❛ ✕ ✺✶ ❘❡s♣♦st❛ ❞❡ ✢❡①ã♦ ❞❡ ✉♠❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦
t❡♠♣♦ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦ (R = 102Ω) ❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ (R= 106Ω)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ❋✐❣✉r❛ ✕ ✺✷ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦
♥♦ ❝✐r❝✉✐t♦ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ❋✐❣✉r❛ ✕ ✺✸ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦
t❡♠♣♦ ♥♦ ❝✐r❝✉✐t♦ ❝♦♥tr♦❧❛❞♦r ❙❙❉❙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ❋✐❣✉r❛ ✕ ✺✹ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦
♥♦ ❝✐r❝✉✐t♦ ❝♦♥tr♦❧❛❞♦r ❙❙❉■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ❋✐❣✉r❛ ✕ ✺✺ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦
t❡♠♣♦ ♥♦ ❝✐r❝✉✐t♦ ❝♦♥tr♦❧❛❞♦r ❙❙❉■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ❋✐❣✉r❛ ✕ ✺✻ ❚❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ✉♠❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦
♥♦ ❝✐r❝✉✐t♦ ❝♦♥tr♦❧❛❞♦r ❙❙❉❱✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ❋✐❣✉r❛ ✕ ✺✼ ❉❡s❧♦❝❛♠❡♥t♦ ❞❛ ♣♦♥t❛ ❞❛ ✈✐❣❛ ♣✐❡③❡❧étr✐❝❛ ❡♥❣❛st❛❞❛ ❡♠ ❢✉♥çã♦ ❞♦
t❡♠♣♦ ♥♦ ❝✐r❝✉✐t♦ ❝♦♥tr♦❧❛❞♦r ❙❙❉❱✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ❋✐❣✉r❛ ✕ ✺✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛ t❡♥sã♦ ❡❧étr✐❝❛ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦ ❡ ❝✉rt♦ ❝✐r❝✉✐t♦
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
❚❛❜❡❧❛ ✕ ✶ Pr♦♣r✐❡❞❛❞❡s ❞♦ ♠❛t❡r✐❛❧ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❈❤❡♥❣ ✭✷✵✵✷✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ❚❛❜❡❧❛ ✕ ✷ Pr♦♣r✐❡❞❛❞❡s ❞❛ ♣á ♣✐❡③❡❧étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ❚❛❜❡❧❛ ✕ ✸ ❆♥❛❧♦❣✐❛ ❢♦rç❛✲t❡♥sã♦ ❡♥tr❡ ♦s s✐st❡♠❛s ♠❡❝â♥✐❝♦ ❞❡ tr❛♥s❧❛çã♦ ❡ ❡❧é✲
▲✐st❛ ❞❡ ❙✐❣❧❛s
❙❙❉ ❙②♥❝❤r♦♥✐③❡❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣✱ ♣✳ ✷✼ ❙❍▼ ❙tr✉❝t✉r❛❧ ❍❡❛❧t❤ ▼♦♥✐t♦r✐♥❣✱ ♣✳ ✷✽ ❝❝ ❝✉rt♦ ❝✐r❝✉✐t♦✱ ♣✳ ✸✷
❝❛ ❝✐r❝✉✐t♦ ❛❜❡rt♦✱ ♣✳ ✸✷ ❙❙ ❙t❛t❡ ❙✇✐t❝❤✐♥❣✱ ♣✳ ✸✻
❙❙❉❙ ❙②♥❝❤r♦♥✐③❡❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣ ♦♥ ❙❤♦rt✱ ♣✳ ✸✻ ❙❙❉■ ❙②♥❝❤r♦♥✐③❡❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣ ♦♥ ■♥❞✉❝t♦r✱ ♣✳ ✸✻ ❇❙❉❙ ❇❧✐♥❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣ ♦♥ ❙❤♦rt ❈✐r❝✉✐t✱ ♣✳ ✸✽ ❇❙❉❱ ❇❧✐♥❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣ ♦♥ ❱♦❧t❛❣❡ ❙♦✉r❝❡✱ ♣✳ ✸✽ ❙❙❉❱ ❙②♥❝❤r♦♥✐③❡❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣ ♦♥ ❱♦❧t❛❣❡✱ ♣✳ ✸✾ ❆❈❙❘ ❆❝t✐✈❡ ❈♦♥tr♦❧ ♦❢ ❙tr✉❝t✉r❛❧ ❘❡s♣♦♥s❡✱ ♣✳ ✹✵ ❍❍❈ ❍✐❣❤❡r ❍❛r♠♦♥✐❝ ❈♦♥tr♦❧✱ ♣✳ ✹✵
■❇❈ ■♥❞✐✈✐❞✉❛❧ ❇❧❛❞❡ ❈♦♥tr♦❧✱ ♣✳ ✹✵ ❆❈❋ ❆❝t✐✈❡ ❈♦♥tr♦❧❧❡❞ ❋❧❛♣✱ ♣✳ ✹✶ ❆❚❘ ❆❝t✐✈❡ ❚✇✐st ❘♦t♦r✱ ♣✳ ✹✶ ❆❈❚ ❆❝t✐✈❡ ❈♦♥tr♦❧❧❡❞ ❚✐♣✱ ♣✳ ✹✶ ❆P▲ ❆❝t✐✈❡ P✐t❝❤ ▲✐♥❦✱ ♣✳ ✹✶
❇❱■ ❇❧❛❞❡ ❱♦rt❡① ■♥t❡r❛❝t✐♦♥✱ ♣✳ ✹✷
❱❆▼ ❱❛r✐❛t✐♦♥❛❧✲❆s②♠♣t♦t✐❝ ▼❡t❤♦❞✱ ♣✳ ✹✸ ❱❆❇❙ ❱❛r✐❛t✐♦♥❛❧ ❆s②♠♣t♦t✐❝ ❇❡❛♠ ❙❡❝t✐♦♥✱ ♣✳ ✹✸ ❍❲P ❍❛♠✐❧t♦♥ ❲❡❛❦ Pr✐♥❝✐♣❧❡✱ ♣✳ ✹✹
▲✐st❛ ❞❡ ❙í♠❜♦❧♦s
❚ ❚❡♥sã♦ ♠❡❝â♥✐❝❛ ❬◆✴m2❪✱ ♣✳ ✷✾ ❙ ❉❡❢♦r♠❛çã♦ ♠❡❝â♥✐❝❛ ❬♠✴♠❪✱ ♣✳ ✷✾ s ❋❧❡①✐❜✐❧✐❞❛❞❡ ❬m2✴◆❪✱ ♣✳ ✷✾
❨ ▼ó❞✉❧♦ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ♦✉ ♠ó❞✉❧♦ ❞❡ ❨♦✉♥❣ ❬◆✴m2❪✱ ♣✳ ✸✵ ❞ ❈♦❡✜❝✐❡♥t❡ ❞❡ t❡♥sã♦ ♣✐❡③❡❧étr✐❝♦ ♦✉ ❝♦♥st❛♥t❡ ♣✐❡③❡❧étr✐❝❛
❬❈✴◆❪✱ ♣✳ ✸✵
❉ ❉❡s❧♦❝❛♠❡♥t♦ ❡❧étr✐❝♦ ❬❈✴m2❪✱ ♣✳ ✸✵ ❊ ❈❛♠♣♦ ❡❧étr✐❝♦ ❬❱✴♠❪✱ ♣✳ ✸✵
ǫ P❡r♠✐ss✐✈✐❞❛❞❡ ❞✐❡❧étr✐❝❛ ❬❋✴♠❪✱ ♣✳ ✸✵
k ❈♦❡✜❝✐❡♥t❡ ❞❡ ❛❝♦♣❧❛♠❡♥t♦ ♣✐❡③❡❧étr✐❝♦✱ ♣✳ ✸✷ fs ❋r❡q✉ê♥❝✐❛ ❞❡ ❝❤❛✈❡❛♠❡♥t♦ ❇❙❉❙ ❬❍③❪✱ ♣✳ ✸✽
♥ ◆ú♠❡r♦ ❞❡ ✈❡③❡s q✉❡ fs é ♠❛✐♦r q✉❡ f0✱ ♣✳ ✸✽ f0 ❋r❡q✉ê♥❝✐❛ ❞❡ r❡ss♦♥â♥❝✐❛ ❞♦ s✐st❡♠❛ ❬❍③❪✱ ♣✳ ✸✽ I ❙✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ✐♥❡r❝✐❛❧✱ ♣✳ ✹✸
a ❙✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ❛ss♦❝✐❛❞♦ ❝♦♠ ♦ ❝❡♥tr♦ ❞❡ r♦t❛çã♦ ❞♦ r♦t♦r✱ ♣✳ ✹✸
b ❙✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✜①❛❞♦ ♥❛ ✈✐❣❛ ♥ã♦ ❞❡❢♦r♠❛❞❛✱ ♣✳ ✹✹ B ❙✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ✜①❛❞♦ ♥❛ ✈✐❣❛ ❞❡❢♦r♠❛❞❛✱ ♣✳ ✹✹ t1 ❚❡♠♣♦ ❛r❜✐trár✐♦ ❬s❪✱ ♣✳ ✹✹
t2 ❚❡♠♣♦ ❛r❜✐trár✐♦ ❬s❪✱ ♣✳ ✹✹ δE ❊♥❡r❣✐❛ ■♥t❡r♥❛ ❱✐rt✉❛❧✱ ♣✳ ✹✹ δW ❚r❛❜❛❧❤♦ ❱✐rt✉❛❧✱ ♣✳ ✹✹
F∗ ❱❡t♦r ❞❡ ❢♦rç❛s ❡ ♠♦♠❡♥t♦s✱ ♣✳ ✹✹
δγ∗ ❱❡t♦r ❞❡ ❞❡❢♦r♠❛çã♦ ❡ ❝✉r✈❛t✉r❛ ✈✐rt✉❛❧ ❣❡♥❡r❛❧✐③❛❞♦✱ ♣✳ ✹✹
M∗ ❱❡t♦r ❞❡ ♠♦♠❡♥t♦s ❛♥❣✉❧❛r ❡ ❧✐♥❡❛r✱ ♣✳ ✹✹
δV∗ ❱❡t♦r ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❛♥❣✉❧❛r ❡ ❧✐♥❡❛r✱ ♣✳ ✹✹
❑ ❊♥❡r❣✐❛ ❈✐♥ét✐❝❛✱ ♣✳ ✹✹ ❯ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧✱ ♣✳ ✹✹
γ ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ❞❡❢♦r♠❛çõ❡s✱ ♣✳ ✹✹ κ ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ❝✉r✈❛t✉r❛s✱ ♣✳ ✹✹ VB ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r✱ ♣✳ ✹✹
ΩB ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r✱ ♣✳ ✹✹
FB ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ❢♦rç❛ ✐♥t❡r♥❛ ♠❡❞✐❞♦ ♥♦ s✐st❡♠❛ ❞❡ r❡❢❡rê♥✲
❝✐❛ ❇✱ ♣✳ ✹✹
MB ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ♠♦♠❡♥t♦ ✐♥t❡r♥♦ ♠❡❞✐❞♦ ♥♦ s✐st❡♠❛ ❞❡ r❡✲
❢❡rê♥❝✐❛ ❇✱ ♣✳ ✹✹
PB ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ♠♦♠❡♥t♦ ❧✐♥❡❛r ♠❡❞✐❞♦ ♥♦ s✐st❡♠❛ ❞❡ r❡❢❡✲
rê♥❝✐❛ ❇✱ ♣✳ ✹✹
HB ❱❡t♦r ❝♦❧✉♥❛ ❞❡ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ♠❡❞✐❞♦ ♥♦ s✐st❡♠❛ ❞❡ r❡✲
❢❡rê♥❝✐❛ ❇✱ ♣✳ ✹✹ F ❱❡t♦r ❞❡ ❢♦rç❛s ✱ ♣✳ ✹✺ M ❱❡t♦r ❞❡ ♠♦♠❡♥t♦s ✱ ♣✳ ✹✺
A ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ♥♦ ♣❧❛♥♦ ❞❡ r♦t❛çã♦✱ ♣✳ ✹✺
B ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❞❡ ❛❝♦♣❧❛♠❡♥t♦ ♥♦ ♣❧❛♥♦ ❞❡ r♦t❛çã♦ ❡ ❢♦r❛ ❞♦ ♣❧❛♥♦ ❞❡ r♦t❛çã♦✱ ♣✳ ✹✺
D ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❢♦r❛ ❞♦ ♣❧❛♥♦ ❞❡ r♦t❛çã♦✱ ♣✳ ✹✺ P ❱❡t♦r ❞❡ ♠♦♠❡♥t♦ ❧✐♥❡❛r✱ ♣✳ ✹✺
H ❱❡t♦r ❞❡ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r✱ ♣✳ ✹✺ m ▼❛tr✐③ ❞❡ ♠❛ss❛ ✱ ♣✳ ✹✺
I ▼❛tr✐③ ❞❡ ✐♥ér❝✐❛✱ ♣✳ ✹✺
V ❱❡t♦r ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r✱ ♣✳ ✹✺
Ω ❱❡t♦r ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r✱ ♣✳ ✹✺
ua ❉❡s❧♦❝❛♠❡♥t♦✱ ♣✳ ✹✺
ωa ❱❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r✱ ♣✳ ✹✺
θ ➶♥❣✉❧♦ ❞❡ ♦r✐❡♥t❛çã♦✱ ♣✳ ✹✺ νa ❱❡❧♦❝✐❞❛❞❡ ❧✐♥❡❛r✱ ♣✳ ✹✺
e1 ❱❡t♦r ✉♥✐tár✐♦✱ ♣✳ ✹✺
CBa ▼❛tr✐③ ❞❡ r♦t❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ❛ ♣❛r❛ ❇✱ ♣✳ ✹✺
Cba ▼❛tr✐③ ❞❡ r♦t❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ❛ ♣❛r❛ ❜✱ ♣✳ ✹✻
δqT ❱❡t♦r ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ✈✐rt✉❛❧✱ ♣✳ ✹✻
ˆ
F ❱❡t♦r ❢♦rç❛✱ ♣✳ ✹✻
δΨT ❱❡t♦r r♦t❛çã♦ ✜♥✐t❛ ✈✐rt✉❛❧✱ ♣✳ ✹✻
ˆ
M ❱❡t♦r ♠♦♠❡♥t♦✱ ♣✳ ✹✻
u ❱❡t♦r ❞❡s❧♦❝❛♠❡♥t♦✱ ♣✳ ✹✻ FT ❱❡t♦r ❢♦rç❛ ✈✐rt✉❛❧✱ ♣✳ ✹✻
δMT ❱❡t♦r ♠♦♠❡♥t♦ ✈✐rt✉❛❧✱ ♣✳ ✹✻
ˆ
θ ❱❡t♦r ❞❡ â♥❣✉❧♦s ❞❡ ♦r✐❡♥t❛çã♦✱ ♣✳ ✹✻ FS ❖♣❡r❛❞♦r ❡str✉t✉r❛❧✱ ♣✳ ✹✽
FL ❖♣❡r❛❞♦r ❞❡ ❝❛r❣❛✱ ♣✳ ✹✽
❳ ❱❡t♦r ❞❡ ✈❛r✐á✈❡✐s ❞❡ ❝❛r❣❛✱ ♣✳ ✹✽
♥ P❛ss♦ ❞❡ t❡♠♣♦✱ ♣✳ ✺✵
Q ❈❛r❣❛ ❡❧étr✐❝❛✱ ♣✳ ✺✵ δVp P♦t❡♥❝✐❛❧ ❡❧étr✐❝♦✱ ♣✳ ✺✵
▼ ▼❛ss❛✱ ♣✳ ✼✽
❇ ❆♠♦rt❡❝✐♠❡♥t♦✱ ♣✳ ✼✽
❑ ❘✐❣✐❞❡③✱ ♣✳ ✼✽
χ(t) ❉❡s❧♦❝❛♠❡♥t♦✱ ♣✳ ✼✽
❢✭t✮ ❋♦rç❛ ❛♣❧✐❝❛❞❛✱ ♣✳ ✼✽
▲ ■♥❞✉tâ♥❝✐❛✱ ♣✳ ✼✽
❘ ❘❡s✐stê♥❝✐❛✱ ♣✳ ✼✽
❈ ❈❛♣❛❝✐tâ♥❝✐❛✱ ♣✳ ✼✽
❱✭t✮ ❋♦♥t❡ ❞❡ t❡♥sã♦ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦✱ ♣✳ ✼✽ ✐✭t✮ ❈♦rr❡♥t❡ ❡❧étr✐❝❛✱ ♣✳ ✼✽
q✭t✮ ❈❛r❣❛ ❡❧étr✐❝❛✱ ♣✳ ✼✽
T∗ ❊♥❡r❣✐❛ ❝✐♥ét✐❝❛❧ t♦t❛❧✱ ♣✳ ✽✶
❯ ❊♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧✱ ♣✳ ✽✷ We ❊♥❡r❣✐❛ ❡❧étr✐❝❛✱ ♣✳ ✽✷
✉ ❞❡s❧♦❝❛♠❡♥t♦ ♠❡❝â♥✐❝♦ ❬♠❪✱ ♣✳ ✽✷
Vs ou Vp ❱♦❧✉♠❡ ❞❛ ❡str✉t✉r❛ ♦✉ ❞❛ ♣✐❡③♦❝❡râ♠✐❝❛ ❬m3❪✱ ♣✳ ✽✷
δW ❚r❛❜❛❧❤♦✱ ♣✳ ✽✷
❢ ❋♦rç❛ ♠❡❝â♥✐❝❛✱ ♣✳ ✽✷ q ❈❛r❣❛ ❡❧étr✐❝❛✱ ♣✳ ✽✷ ϕ P♦t❡♥❝✐❛❧ ❡❧étr✐❝♦✱ ♣✳ ✽✷
φ ▼♦❞♦s✱ ♣✳ ✽✸
r✭t✮ ❈♦♦r❞❡♥❛❞❛ t❡♠♣♦r❛❧ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ✉✱ ♣✳ ✽✸ ψ P♦t❡♥❝✐❛❧ ❡❧étr✐❝♦✱ ♣✳ ✽✸
tp ❡s♣❡ss✉r❛ ❞♦ ♠❛t❡r✐❛❧ ♣✐❡③❡❧étr✐❝♦✱ ♣✳ ✽✸
vp ❚❡♥sã♦ ❡❧étr✐❝❛ ❣❡r❛❞❛ ♣❡❧❛ ♣✐❡③♦❝❡râ♠✐❝❛✱ ♣✳ ✽✸
▼ ▼❛ss❛✱ ♣✳ ✽✸
❑ ❘✐❣✐❞❡③✱ ♣✳ ✽✸
θ ❆❝♦♣❧❛♠❡♥t♦ ❡❧❡tr♦♠❡❝â♥✐❝♦✱ ♣✳ ✽✸
M∗ ❱❡t♦r ❞❡ ❢♦rç❛ ❡❢❡t✐✈❛ ❞❛ ❛❝❡❧❡r❛çã♦ ❞❡ ❜❛s❡✱ ♣✳ ✽✸
¨
ug ❆❝❡❧❡r❛çã♦ ❞❡ ❜❛s❡✱ ♣✳ ✽✸
Cp ❈❛♣❛❝✐tâ♥❝✐❛ ❞❛ ♣✐❡③♦❝❡râ♠✐❝❛✱ ♣✳ ✽✸
˙
Q(t) ❈♦rr❡♥t❡ ❡❧étr✐❝❛✱ ♣✳ ✽✸
▲ ❈♦♠♣r✐♠❡♥t♦ ❞❛ ✈✐❣❛✱ ♣✳ ✽✸
¯
m ▼❛ss❛ ❞❛ ✈✐❣❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ❝♦♠♣r✐♠❡♥t♦✱ ♣✳ ✽✸ α e β ❈♦♥st❛♥t❡ ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡✱ ♣✳ ✽✸
❘ ❘❡s✐stê♥❝✐❛ ❡❧étr✐❝❛✱ ♣✳ ✽✺
βn ❈♦♥st❛♥t❡ ❞❛ ❢✉♥çã♦ ❞❡ ♠♦❞♦s✱ ♣✳ ✽✺
σn ❈♦♥st❛♥t❡ ❞❛ ❢✉♥çã♦ ❞❡ ♠♦❞♦s✱ ♣✳ ✽✺
A ▼❛tr✐③ ❞❡ ❡st❛❞♦✱ ♣✳ ✽✺ B ▼❛tr✐③ ❞❡ ❡♥tr❛❞❛✱ ♣✳ ✽✺ C ▼❛tr✐③ ❞❡ s❛í❞❛✱ ♣✳ ✽✺
D ▼❛tr✐③ ❞❡ tr❛♥s♠✐ssá♦ ❞✐r❡t❛✱ ♣✳ ✽✺ y ❱❡t♦r ❞❡ s❛í❞❛✱ ♣✳ ✽✺
u ❱❡t♦r ❞❡ ❡♥tr❛❞❛✱ ♣✳ ✽✺ x ❱❡t♦r ❞❡ ❡st❛❞♦s✱ ♣✳ ✽✺
R1 ❡ R6 ❘❡s✐stê♥❝✐❛ ❞♦ ✜❧tr♦ ♣❛ss❛✲❜❛✐①❛✱ ♣✳ ✽✻
D1 ❡ D6 ❉✐♦❞♦ ❞♦ ✜❧tr♦ ♣❛ss❛✲❜❛✐①❛✱ ♣✳ ✽✻
C1 ❡ C2 ❈❛♣❛❝✐tâ♥❝✐❛ ❞♦ ✜❧tr♦ ♣❛ss❛✲❜❛✐①❛✱ ♣✳ ✽✻
R2✱ R3✱ R4 ❡ R5 ❘❡s✐stê♥❝✐❛ ❞♦ ❝♦♠♣❛r❛❞♦r✱ ♣✳ ✽✻
D2✱ D5✱ D9 ❉✐♦❞♦s ❞♦ ❝♦♠♣❛r❛❞♦r✱ ♣✳ ✽✻
D10✱ D11✱ D12 ❉✐♦❞♦s ❞♦ ❝♦♠♣❛r❛❞♦r✱ ♣✳ ✽✻
T1 ❡ T4 ❚r❛♥s✐st♦r ❞♦ ❝♦♠♣❛r❛❞♦r✱ ♣✳ ✽✻
T2 ❡ T3 ❚r❛♥s✐st♦r ❞❛ ❝❤❛✈❡✱ ♣✳ ✽✼
ωncircuito ❢r❡q✉ê♥❝✐❛ ♥❛t✉r❛❧ ❞♦ ❝✐r❝✉✐t♦ ❡❧étr✐❝♦✱ ♣✳ ✽✽
∆ti t❡♠♣♦ ❞❡ ✐♥✈❡rsã♦✱ ♣✳ ✽✽
Qi ❋❛t♦r ❞❡ q✉❛❧✐❞❛❞❡ ❡❧étr✐❝❛✱ ♣✳ ✽✽
Ri ❘❡s✐stê♥❝✐❛ ✐♥t❡r♥❛ ❞♦ ❝✐r❝✉✐t♦ ❝❤❛✈❡❛❞♦r✱ ♣✳ ✽✽
γ ❈♦❡✜❝✐❡♥t❡ ❞❡ ✐♥✈❡rsã♦✱ ♣✳ ✽✽
vantes ❙✐♥❛❧ ❞❡ t❡♥sã♦ ♥♦ ✜♥❛❧ ❞❡ ❝❤❛✈❡❛♠❡♥t♦✱ ♣✳ ✽✽
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ❡ ❏✉st✐✜❝❛t✐✈❛ ✷✻
✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✷✾
✷✳✶ ▼❛t❡r✐❛✐s ■♥t❡❧✐❣❡♥t❡s ❡ ▼❛t❡r✐❛✐s P✐❡③❡❧étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✷ ❊str❛té❣✐❛s ❞❡ ❈♦♥tr♦❧❡ ❞❡ ❱✐❜r❛çõ❡s ✉t✐❧✐③❛♥❞♦ ▼❛t❡r✐❛✐s P✐❡③❡❧étr✐❝♦s ✳ ✳ ✳ ✸✸ ✷✳✷✳✶ ❈♦♥tr♦❧❡ P❛ss✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷✳✷ ❈♦♥tr♦❧❡ ❆t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✷✳✸ ❈♦♥tr♦❧❡s s❡♠✐♣❛ss✐✈♦s ❡ s❡♠✐❛t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✷✳✸✳✶ ❈♦♥tr♦❧❡ ❙❡♠✐♣❛ss✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✷✳✸✳✷ ❈♦♥tr♦❧❡ ❙❡♠✐❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✷✳✸ ❯t✐❧✐③❛çã♦ ❞❡ ▼❛t❡r✐❛✐s ■♥t❡❧✐❣❡♥t❡s ❡♠ ❆s❛s ❘♦t❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✸ ▼♦❞❡❧❛❣❡♠ ❊❧❡tr♦♠❡❝â♥✐❝❛ ❞❡ ✉♠❛ Pá P✐❡③❡❧étr✐❝❛ ❊♥❣❛st❛❞❛ ✹✸ ✸✳✶ ▼♦❞❡❧❛❣❡♠ ❞❡ ✉♠❛ ❱✐❣❛ ❊❧ást✐❝❛ ❘♦t❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ ▼♦❞❡❧❛❣❡♠ ❞❡ ✉♠❛ ❱✐❣❛ ❊❧ást✐❝❛ ❘♦t❛t✐✈❛ P✐❡③❡❧étr✐❝❛ ✭Pá ✰ P✐❡③♦✮ ✳ ✳ ✳ ✳ ✺✵ ✸✳✸ ❋❧✉①♦❣r❛♠❛ ❞❡ ❙♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✺ ❈♦♥❝❧✉sõ❡s ✼✵
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✼✸
❆♣ê♥❞✐❝❡ ❆ ✲ ❆♥❛❧♦❣✐❛ ❡♥tr❡ ❙✐st❡♠❛ ▼❡❝â♥✐❝♦ ❞❡ ❚r❛♥s❧❛çã♦ ❡ ❙✐st❡♠❛
❊❧étr✐❝♦ ✼✼
❆✳✶ ✲ ■♥✢✉ê♥❝✐❛ ❞♦ ❈✐r❝✉✐t♦ ❊❧étr✐❝♦ ❡♠ ✉♠ ❙✐st❡♠❛ P✐❡③❡❧étr✐❝♦ ❊❧❡tr♦♠❡❝❛♥✐❝❛✲ ♠❡♥t❡ ❆❝♦♣❧❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
❆♣ê♥❞✐❝❡ ❇ ✲ ▼♦❞❡❧❛❣❡♠ ❞❡ ✉♠❛ ❱✐❣❛ P✐❡③❡❧étr✐❝❛ ❋✐①❛ ✽✵ ❇✳✶ ✲ ▼♦❞❡❧❛❣❡♠ ❞❛ ❱✐❣❛ P✐❡③❡❧étr✐❝❛ ❊♥❣❛st❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ❇✳✷ ✲ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❈✐r❝✉✐t♦s ❊❧étr✐❝♦s ❡ ❞♦ ❈✐r❝✉✐t♦ ❈❤❛✈❡❛❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ❇✳✸ ✲ ❱❡r✐✜❝❛çã♦ ❞♦ ▼ét♦❞♦ ◆✉♠ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ❇✳✹ ✲ ❈♦♥tr♦❧❛❞♦r P❛ss✐✈♦ ❘❡s✐st✐✈♦ P✉r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ❇✳✺ ✲ ❈♦♥tr♦❧❛❞♦r ❙❡♠✐✲♣❛ss✐✈♦ ❙❙❉❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ❇✳✻ ✲ ❈♦♥tr♦❧❛❞♦r ❙❡♠✐✲♣❛ss✐✈♦ ❙❙❉■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ❇✳✼ ✲ ❈♦♥tr♦❧❛❞♦r ❙❡♠✐✲❛t✐✈♦ ❙❙❉❱ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ❇✳✽ ✲ ❘❡s✉❧t❛❞♦s ❊①♣❡r✐♠❡♥t❛✐s ❞❛ ❱✐❣❛ P✐❡③❡❧étr✐❝❛ ❊♥❣❛st❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
❆♣ê♥❞✐❝❡ ❈ ✲ ▼ét♦❞♦ ❆❧❢❛✲●❡♥❡r❛❧✐③❛❞♦ ✾✽
❈❛♣ít✉❧♦
1
■♥tr♦❞✉çã♦ ❡ ❏✉st✐✜❝❛t✐✈❛
❍
❡❧✐❝ó♣t❡r♦s sã♦ ✐♥❡r❡♥t❡♠❡♥t❡ ❛ss♦❝✐❛❞♦s ❝♦♠ ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✈✐❜r❛çõ❡s ❞❡✈✐❞♦ ❛ ❞✐✈❡rs♦s ❢❛t♦r❡s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❢♦❧❣❛s ♦✉ ❡♥✈❡❧❤❡❝✐♠❡♥t♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s✱ ❞❡s✲ ❜❛❧❛♥❝❡❛♠❡♥t♦ ❡ ❡❢❡✐t♦s ❛❡r♦❞✐♥â♠✐❝♦s ✐♥❞❡s❡❥❛❞♦s✳ ❆s ♣ás q✉❡ ❡stã♦ ❛✈❛♥ç❛♥❞♦ ♣♦❞❡♠ ❡♥tr❛r ❡♠ r❡❣✐♠❡ tr❛♥sô♥✐❝♦ ❞❡✈✐❞♦ ❛ ❛❧t❛ ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈❛ ❞♦ ❡s❝♦❛♠❡♥t♦ ❞♦ ❛r ✭✈❡❧♦✲ ❝✐❞❛❞❡ ❞♦ ❤❡❧✐❝ó♣t❡r♦ s♦♠❛❞❛ ❝♦♠ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❛ ♣á✮ ❡ ♦❝♦rr❡r ♦ s✉r❣✐♠❡♥t♦ ❞❡ ♦♥❞❛s ❞❡ ❝❤♦q✉❡✱ ❛❧é♠ ❞✐ss♦✱ ❛s ♣ás ♥♦ r❡t♦r♥♦ ✭✈❡❧♦❝✐❞❛❞❡ ❞♦ ❤❡❧✐❝ó♣t❡r♦ s✉❜tr❛í❞❛ ❞❛ ✈❡❧♦❝✐✲ ❞❛❞❡ ❞❛ ♣á✮ ♣♦❞❡♠ ❛♣r❡s❡♥t❛r ❡st♦❧ ❞✐♥â♠✐❝♦✳ ❊ss❡ ❢❡♥ô♠❡♥♦ ✐♥❞✉③ ✈✐❜r❛çõ❡s q✉❡ sã♦ tr❛♥s❢❡r✐❞❛s ♣❛r❛ ❛ ❢✉s❡❧❛❣❡♠✱ ❝❛✉s❛♥❞♦ ❞❡s❝♦♥❢♦rt♦ ❛♦s ♣❛ss❛❣❡✐r♦s ❡ ♣✐❧♦t♦s ✭❱❛❧❧❡❥♦ ❡t ❛❧✳ ✭✶✾✾✾✮✮✳ ❆ ❢r❡qüê♥❝✐❛ ❞❡ ✈✐❜r❛çã♦ tr❛♥s❢❡r✐❞❛ ♣❛r❛ ❛ ❢✉s❡❧❛❣❡♠ ❞❡♣❡♥❞❡ ❞♦ ♥ú♠❡r♦ ❞❡ ♣ás ❞♦ r♦t♦r ❡ r❡s✉❧t❛ ❡♠ ✉♠❛ ❢❛✐①❛ ❣❡r❛❧♠❡♥t❡ ❡♥tr❡ ✷ ❍③ ❡ ✽ ❍③ ✭♦✉ s❡❥❛✱ ♥❛ ❢❛✐①❛ ❡♥tr❡ ✶✴r❡✈ ❡ ◆✴r❡✈✱ ♦♥❞❡ ◆ é ♦ ♥ú♠❡r♦ ❞❡ ♣ás ❞♦ r♦t♦r✮ ❡ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ r❡ss♦♥â♥❝✐❛ ❞❛ r❡❣✐ã♦ ❞♦ tr♦♥❝♦ ❞❡ ✉♠❛ ♣❡ss♦❛ ❡stá ❡♠ t♦r♥♦ ❞❡ ✺ ❍③✳❋✐❣✉r❛ ✶ ✕ ❋r❡q✉ê♥❝✐❛ ❞❡ r❡ss♦♥â♥❝✐❛ ❞♦ tr♦♥❝♦ ❞❡ ✉♠❛ ♣❡ss♦❛❧ ❡ ❢r❡q✉ê♥❝✐❛ tr❛♥s❢❡r✐❞❛ ❞♦ r♦t♦r ♣❛r❛ ❢✉s❡❧❛❣❡♠✳
❆ ✈❡❧♦❝✐❞❛❞❡ ♠á①✐♠❛ ❡♠ ✈♦♦ ❞❡ ❝r✉③❡✐r♦ ❞❡ ✉♠ ❤❡❧✐❝ó♣t❡r♦ t❛♠❜é♠ é ❧✐♠✐t❛❞❛ ♣❡❧♦
s✉r❣✐♠❡♥t♦ ❞❡ ✈✐❜r❛çõ❡s ✭♣r♦✈❡♥✐❡♥t❡s ❞♦ r♦t♦r✮ ♥♦ s✐st❡♠❛ ❞❡ ❝♦♠❛♥❞♦✱ tr❛♥s♠✐t✐❞❛s ❛tr❛✈és ❞♦ ♣✐t❝❤ ❧✐♥❦ ✭❋❡s③t② ❡ ◆✐t③s❝❤❡ ✭✷✵✶✶✮✮✳ ❖ ♣✐t❝❤ ❧✐♥❦ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ tr❛♥s✲ ♠✐ssã♦ ❞❡ ♠♦✈✐♠❡♥t♦ ❞❛ s✇❛s❤ ♣❧❛t❡ ✭❜❛♥❞❡❥❛ ❣✐r❛tór✐❛✮ ♣❛r❛ ♦ ♣✐t❝❤ ❤♦r♥ ✭✈✐♥❝✉❧❛❞♦ ❛♦ ❜♦r❞♦ ❞❡ ❢✉❣❛ ❞❛ ♣á ♥❛ r❡❣✐ã♦ ❞❛ r❛✐③✮✱ q✉❡ ♣♦r s✉❛ ✈❡③✱ ❛❧t❡r❛ ♦ â♥❣✉❧♦ ❞❡ ♣❛ss♦ ❞❛ ♣á ✭❋✐❣✳ ✶✮✳
❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠✐♥✐♠✐③❛r ♣r♦❜❧❡♠❛s ❝♦♠♦ ♦s ❛♥t❡r✐♦r♠❡♥t❡ ❝✐t❛❞♦s✱ ♦ ❞❡s❡♥✈♦❧✈✐✲ ♠❡♥t♦ ❞❡ s✐st❡♠❛s ❞❡ ❝♦♥tr♦❧❡ ❞❡ ✈✐❜r❛çõ❡s ♣❛r❛ ❤❡❧✐❝ó♣t❡r♦s t❡♠ r❡❝❡❜✐❞♦ ❣r❛♥❞❡ ❛t❡♥çã♦ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s✳ ❖ ❝♦♥tr♦❧❡ ❞❡ ✈✐❜r❛çõ❡s ❡♠ ❤❡❧✐❝ó♣t❡r♦s ♣♦❞❡ tr❛③❡r ❜❡♥❡❢í❝✐♦s ♣❛r❛ ♣✐❧♦t♦ ❡ ♣❛ss❛❣❡✐r♦s✱ ♣❛r❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❛ ❛❡r♦♥❛✈❡ ❡ t❛♠❜é♠ ❞❡ ❡✈✐t❛r ❢❛❞✐❣❛ ❡♠ ❝♦♠♣♦♥❡♥t❡s✳ ❆❧❣✉♥s ❛✉t♦r❡s ❛♣r❡s❡♥t❛♠ s✐st❡♠❛s ♠❡❝â♥✐❝♦s ♣❛ss✐✈♦s ✭❋❡s③t② ❡ ◆✐t③s❝❤❡ ✭✷✵✶✶✮✮✱ ❡♥q✉❛♥t♦ ♦✉tr♦s ✐♥✈❡st✐❣❛♠ s✐st❡♠❛s q✉❡ ✉t✐❧✐③❛♠ ♠❛t❡r✐❛✐s ✐♥t❡❧✐❣❡♥t❡s✱ ❝♦♠♦ ❛t✉❛❞♦r❡s ♦✉ ❝♦♠♦ s❡♥s♦r❡s ✭❇❛rr❡tt ✭✶✾✾✵✮✱ ❋❛❜✉♥♠✐ ✭✶✾✾✶✮✱ ❈❡s♥✐❦ ❡ ❙❤✐♥ ✭✷✵✵✶✮✱ ◆✐t③s❝❤❡ ❡t ❛❧✳ ✭✷✵✵✺✮✱ ❲❛❧❧ ❡t ❛❧✳ ✭✷✵✵✽✮✮✳
❖s ♠❛t❡r✐❛✐s ♣✐❡③❡❧étr✐❝♦s tê♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝♦♥✈❡rt❡r ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❡♠ ❡♥❡r❣✐❛ ♠❡❝â♥✐❝❛ ❡ ✈✐❝❡✲✈❡rs❛✳ ❖ ❡❢❡✐t♦ ♣✐❡③❡❧étr✐❝♦ ❞✐r❡t♦ é ❞❡✜♥✐❞♦ ❝♦♠♦ ❛ ❝♦♥✈❡rsã♦ ❞❡ ❡♥❡r❣✐❛ ♠❡❝â♥✐❝❛ ❡♠ ❡♥❡r❣✐❛ ❡❧étr✐❝❛✳ ❏á ❛ ❝♦♥✈❡rsã♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❡♠ ❡♥❡r❣✐❛ ♠❡❝â♥✐❝❛ ❞❡✜♥❡ ♦ ❡❢❡✐t♦ ♣✐❡③❡❧étr✐❝♦ ✐♥✈❡rs♦✳ ❯♠❛ ❝❛r❛❝t❡ríst✐❝❛ ✐♥t❡r❡ss❛♥t❡ ❞❡ss❡s ♠❛t❡r✐❛✐s é ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✉s♦ s✐♠✉❧tâ♥❡♦ ❝♦♠♦ s❡♥s♦r❡s ✭❡❢❡✐t♦ ❞✐r❡t♦✮ ❡ ❛t✉❛❞♦r❡s ✭❡❢❡✐t♦ ✐♥✈❡rs♦✮✱ ♣❡r♠✐t✐♥❞♦ ♣♦r ❡①❡♠♣❧♦ ♦ ❡st✉❞♦ ❞❡ ❝♦♥tr♦❧❛❞♦r❡s s❡♠✐✲❛t✐✈♦s ✭❩❤❛♦ ✭✷✵✶✵✮✮✳
❉❡♥tr❡ ❛s ❞✐❢❡r❡♥t❡s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ ❝♦♥tr♦❧❛❞♦r❡s ♣✐❡③❡❧étr✐❝♦s ❛♣r❡s❡♥t❛❞♦s ♥❛ ❧✐✲ t❡r❛t✉r❛ ♣❛r❛ ❛t❡♥✉❛çã♦ ❞❡ ✈✐❜r❛çã♦ ✭❛t✐✈♦s✱ ♣❛ss✐✈♦s ❡ ❤í❜r✐❞♦s✮✱ ❘✐❝❤❛r❞ ❡t ❛❧✳ ✭✶✾✾✾✮ ❛♣r❡s❡♥t❛r❛♠ ❛ ❛❧t❡r♥❛t✐✈❛ ❞♦ tr❛t❛♠❡♥t♦ ♥ã♦ ❧✐♥❡❛r ❞❛ s❛í❞❛ ❡❧étr✐❝❛ ❞❡ ♠❛t❡r✐❛✐s ♣✐✲ ❡③❡❧étr✐❝♦s ❛tr❛✈és ❞❛s té❝♥✐❝❛s ❙❙❉ ✭❙②♥❝❤r♦♥✐③❡❞ ❙✇✐t❝❤ ❉❛♠♣✐♥❣✮ ♣❛r❛ ❝♦♥tr♦❧❡ ❞❡ ✈✐❜r❛çõ❡s✳ ❖ ♣r✐♥❝í♣✐♦ ❜ás✐❝♦ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ❙❙❉ ❝♦♥s✐st❡ ♥♦ ❝❤❛✈❡❛♠❡♥t♦ ❞♦ s✐✲ ♥❛❧ ❡❧étr✐❝♦ ♣r♦✈❡♥✐❡♥t❡ ❞♦ ♠❛t❡r✐❛❧ ♣✐❡③❡❧étr✐❝♦✱ ❝♦♥❡❝t❛♥❞♦✲♦ ❡ ❞❡s❝♦♥❡❝t❛♥❞♦✲♦ ❛ ✉♠ ❝✐r❝✉✐t♦ ❡①t❡r♥♦ ❞❡ ❢♦r♠❛ s✐♥❝r♦♥✐③❛❞❛ ❝♦♠ ❛s ♦s❝✐❧❛çõ❡s ♠❡❝â♥✐❝❛s✳ ❆s ❞✐✈❡rs❛s té❝♥✐❝❛s ❙❙❉ s❡rã♦ ♣♦st❡r✐♦r♠❡♥t❡ ❞✐s❝✉t✐❞❛s✳ ❊♥tr❡t❛♥t♦✱ ❞❡ ❢♦r♠❛ ❣❡r❛❧✱ ❡❧❛s ♥ã♦ ❞❡♣❡♥❞❡♠ ❞❡ ✉♠❛ ❢♦♥t❡ ❡①t❡r♥❛ ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ s❡✉ ❢✉♥❝✐♦♥❛♠❡♥t♦ ♦✉ r❡q✉❡r❡♠ ❜❛✐①❛ ❡♥❡r❣✐❛ ♣❛r❛ ♦ ♣r♦❝❡ss♦ ❞❡ ❝❤❛✈❡❛♠❡♥t♦ ✭❞❡♣❡♥❞❡♥❞♦ ❞❛ té❝♥✐❝❛ ✉t✐❧✐③❛❞❛✮✱ ❝♦♥❞✐çõ❡s q✉❡ ♣♦❞❡♠ r❡s✉❧✲ t❛r ❡♠ ❝♦♥tr♦❧❛❞♦r❡s ❛✉t♦❛❧✐♠❡♥t❛❞♦s ✭♦✉ ❛✉tô♥♦♠♦s✮ q✉❛♥❞♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ss♦❝✐❛❞❛s ❛ s✐st❡♠❛s ❞❡ ❝♦❧❡t❛ ♣✐❡③❡❧étr✐❝❛ ❞❡ ❡♥❡r❣✐❛✳
❯♠ s✐st❡♠❛ ❞❡ ❝♦♥tr♦❧❡ ❛✉t♦❛❧✐♠❡♥t❛❞♦ ✭♦✉ ❛✉tô♥♦♠♦ ❡♥❡r❣❡t✐❝❛♠❡♥t❡✮ ❡♠ ❤❡❧✐❝ó♣✲ t❡r♦s ❡✈✐t❛r✐❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❞❛ ❢✉s❡❧❛❣❡♠ ♣❛r❛ ❛ ♣❛rt❡ r♦t❛t✐✈❛✳ ❆❧é♠ ❞✐ss♦✱ s✐st❡♠❛s ❞❡ ❝♦❧❡t❛ ♣✐❡③❡❧étr✐❝❛ ❞❡ ❡♥❡r❣✐❛ ♥♦ r❡❢❡r❡♥❝✐❛❧ r♦t❛t✐✈♦
t❛♠❜é♠ ♣♦ss✐❜✐❧✐t❛r✐❛♠ ❛ ❛❧✐♠❡♥t❛çã♦ ❞❡ ♦✉tr♦s s✐st❡♠❛s ❞❡ ❜❛✐①♦ ❝♦♥s✉♠♦✱ ❝♦♠♦ s✐s✲ t❡♠❛s ❞❡ ✈❡r✐✜❝❛çã♦ ❞❡ ✐♥t❡❣r✐❞❛❞❡ ❡str✉t✉r❛❧ ✭❙❍▼ ✲ ❙tr✉❝t✉r❛❧ ❍❡❛❧t❤ ▼♦♥✐t♦r✐♥❣✱ ❞❛ s✐❣❧❛ ❡♠ ✐♥❣❧ês✮✳
❆ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛ ✉♠ ♠♦❞❡❧♦ ❡❧❡tr♦❡❧ást✐❝♦ ❞❡ ✉♠❛ ✈✐❣❛ ❡❧ást✐❝❛ r♦✲ t❛t✐✈❛ ✭♣á ❞❡ ❤❡❧✐❝ó♣t❡r♦✮ ❝♦♠ ♣✐❡③♦❝❡râ♠✐❝❛s ❡♠❜✉t✐❞❛s ✭r❡❣✐ã♦ ❞❛ r❛✐③ ❞❛ ♣á✮ ♣❛r❛ ❛ ❛t❡♥✉❛çã♦ ❞❡ ✈✐❜r❛çõ❡s ✉t✐❧✐③❛♥❞♦ ❝✐r❝✉✐t♦s s❡♠✐✲♣❛ss✐✈♦s✳ ❆ ✈❡r✐✜❝❛çã♦ ❞♦ ♠ét♦❞♦ ♥✉✲ ♠ér✐❝♦ s❡rá ❛♣r❡s❡♥t❛❞❛ ❡ ♦s ❝♦♥tr♦❧❛❞♦r❡s ♣❛ss✐✈♦ r❡s✐st✐✈♦ ♣✉r♦✱ s❡♠✐♣❛ss✐✈♦ ❙❙❉❙ ❡ s❡♠✐♣❛ss✐✈♦ ❇❙❉❙ s❡rã♦ ✐♥✈❡st✐❣❛❞♦s✳ ❆ ♣r❡s❡♥t❡ ✐♥✈❡st✐❣❛çã♦ ♥ã♦ ♣r❡✈ê ♦ ❞❡s❡♥✈♦❧✈✐✲ ♠❡♥t♦ ❞❡ s✐st❡♠❛s ❞❡ ❝♦♥tr♦❧❡ ❛✉t♦❛❧✐♠❡♥t❛❞♦s ❡ t❛♠❜é♠ ❝♦♥s✐❞❡r❛ ♦ ❝✐r❝✉✐t♦ ❝❤❛✈❡❛❞♦r ❝♦♠♦ ✉♠ ❝✐r❝✉✐t♦ ✐❞❡❛❧ ✭s❡♠ r❡s✐stê♥❝✐❛s ✐♥t❡r♥❛s✮✳ ❊♥tr❡t❛♥t♦✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ ♣r♦❥❡t♦ é ✉♠ ♣r✐♠❡✐r♦ ♣❛ss♦ ❡♠ t❛❧ ❞✐r❡çã♦✳
❈❛♣ít✉❧♦
2
❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛
✷✳✶ ▼❛t❡r✐❛✐s ■♥t❡❧✐❣❡♥t❡s ❡ ▼❛t❡r✐❛✐s P✐❡③❡❧étr✐❝♦s
❖s ♠❛t❡r✐❛✐s ✐♥t❡❧✐❣❡♥t❡s sã♦ ❞❡✜♥✐❞♦s ❝♦♠♦ ❛q✉❡❧❡s q✉❡ ❡①✐❜❡♠ ❛❝♦♣❧❛♠❡♥t♦ ❡♥tr❡ ♠ú❧t✐♣❧♦s ❞♦♠í♥✐♦s ❢ís✐❝♦s ✭♠❡❝â♥✐❝♦✱ ❡❧étr✐❝♦✱ tér♠✐❝♦✱ ♠❛❣♥ét✐❝♦✱ q✉í♠✐❝♦ ❡ ♦✉tr♦s✮✳ ❍á ❛❝♦♣❧❛♠❡♥t♦ q✉❛♥❞♦ ✉♠❛ ♠✉❞❛♥ç❛ ♥❛ ✈❛r✐á✈❡❧ ❞❡ ❡st❛❞♦ ❞❡ ✉♠ ❞♦♠í♥✐♦ ❢ís✐❝♦ ❝❛✉s❛ ♠✉❞❛♥ç❛ ❡♠ ✉♠❛ ♦✉tr❛ ✈❛r✐á✈❡❧ ❞❡ ❡st❛❞♦ ❞❡ ✉♠ ♦✉tr♦ ❞♦♠í♥✐♦ ❢ís✐❝♦✳ P♦r ❡①❡♠♣❧♦✱ ♠❛t❡r✐❛❧ ♣✐❡③❡❧étr✐❝♦ é ❛q✉❡❧❡ q✉❡ ♣♦ss✉✐ ❛❝♦♣❧❛♠❡♥t♦ ❡♥tr❡ ♦s ❞♦♠í♥✐♦s ♠❡❝â♥✐❝♦ ❡ ❡❧étr✐❝♦ ✭❛❝♦♣❧❛♠❡♥t♦ ❡❧❡tr♦♠❡❝â♥✐❝♦✮✳
◗✉❛♥❞♦ ♦ ♠❛t❡r✐❛❧ ♣✐❡③❡❧étr✐❝♦ é s✉❜♠❡t✐❞♦ ❛ ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ♠❡❝â♥✐❝♦✱ s✉r❣❡ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡♥tr❡ ♦s ❡❧❡tr♦❞♦s✱ q✉❡ ♣♦r s✉❛ ✈❡③ ♣r♦❞✉③ ❛tr❛çã♦ ❡♥tr❡ ❛ ❝❛r❣❛ ❛♣❧✐❝❛❞❛ ❡ ♦s ❞✐♣♦❧♦s ❡❧étr✐❝♦s ❞♦ ♠❛t❡r✐❛❧✱ r♦t❛❝✐♦♥❛♥❞♦ ❡ss❡s ❞✐♣♦❧♦s ❡ ✉♠❛ s❛í❞❛ ❡❧étr✐❝❛ é ❣❡r❛❞❛ ✭■❊❊❊ ✭✶✾✽✼✮✮✳ ❊ss❡ ❡❢❡✐t♦ é ❝❤❛♠❛❞♦ ❞❡ ❡❢❡✐t♦ ♣✐❡③❡❧étr✐❝♦ ❞✐r❡t♦ ❡ ❢♦✐ ❞❡♠♦♥str❛❞♦ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♣❡❧♦s ✐r♠ã♦s ❈✉r✐❡ ❡♠ ✶✽✽✵✳ ❙❡ ♦ ♠❡s♠♦ ♠❛t❡r✐❛❧ ❢♦r s✉❜♠❡t✐❞♦ ❛ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡♥tr❡ s❡✉s ❡❧❡tr♦❞♦s✱ ❡❧❡ s❡ ❞❡❢♦r♠❛rá ♠❡❝❛♥✐❝❛♠❡♥t❡✱ ❛♣r❡s❡♥t❛♥❞♦ ♦ ❡❢❡✐t♦ ♣✐❡③❡❧étr✐❝♦ ✐♥✈❡rs♦ q✉❡ ❢♦✐ ❞❡❞✉③✐❞♦ ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ♣♦r ●❛❜r✐❡❧ ▲✐♣♣♠❛♥♥ ❡♠ ✶✽✽✶✱ ❧♦❣♦ ❛♣ós ❛ ❞❡s❝♦❜❡rt❛ ❞♦ ❡❢❡✐t♦ ♣✐❡③❡❧étr✐❝♦ ❞✐r❡t♦✳
❆ ❣r❛♥❞❡ ❡①♣❛♥sã♦ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ♠❛t❡r✐❛✐s ✐♥t❡❧✐❣❡♥t❡s ✈❡✐♦ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ♠❛t❡r✐❛✐s ❢❡rr♦❡❧étr✐❝♦s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ♦ ❚✐t❛♥❛t♦ ❩✐r❝♦♥❛t♦ ❞❡ ❈❤✉♠❜♦ ✭❝❡râ♠✐❝❛ P❩❚✮✱ ❝♦♠ ❛ ❣r❛♥❞❡ ✈❛♥t❛❣❡♠ ❞❡ q✉❡ ❛ ❡✜❝✐ê♥❝✐❛ ❞❡ ❝♦♥✈❡rsã♦ ❡❧❡tr♦♠❡❝â♥✐❝❛ é ❜❡♠ ♠❛✐♦r s❡ ❝♦♠♣❛r❛❞❛ ❝♦♠ ♦ ◗✉❛rt③♦✳
❆ r❡❧❛çã♦ ❡♥tr❡ t❡♥sã♦ ♠❡❝â♥✐❝❛ ❛♣❧✐❝❛❞❛ ❛♦ ♠❛t❡r✐❛❧ ♣✐❡③❡❧étr✐❝♦ ❚ ❬◆✴m2❪ ❡ ❞❡❢♦r✲ ♠❛çã♦ ♠❡❝â♥✐❝❛ ❙ ❬♠✴♠❪ é ❝❤❛♠❛❞❛ ❞❡ ✢❡①✐❜✐❧✐❞❛❞❡ s ❬m2✴◆❪✱
S = 1
Y T =sT ✭✷✳✶✮
