❯◆■❱❊❘❙■❉❆❉❊ ❉❖ ❊❙❚❆❉❖ ❉❊ ❙❆◆❚❆ ❈❆❚❆❘■◆❆ ✲ ❯❉❊❙❈ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❚❊❈◆❖▲Ó●■❈❆❙ ✲ ❈❈❚
❈❯❘❙❖ ❉❊ ▼❊❙❚❘❆❉❖ ❊▼ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆
❉■❙❙❊❘❚❆➬➹❖ ❉❊ ▼❊❙❚❘❆❉❖
▼❖❉❊▲❆●❊▼ ❉❆ ■▼P❊❉➶◆❈■❆ ❉❊
❙❯❙P❊◆❙Õ❊❙ ❉❊ ❈➱▲❯▲❆❙ ❇■❖▲Ó●■❈❆❙ ◆❆ ❊▲❊❚❘❖P❊❘▼❊❆❇■▲■❩❆➬➹❖
❍❊❘■❈ ❉✃◆■❙ ❋❆❘■❆❙
❍❊❘■❈ ❉✃◆■❙ ❋❆❘■❆❙
▼❖❉❊▲❆●❊▼ ❉❆ ■▼P❊❉➶◆❈■❆ ❉❊ ❙❯❙P❊◆❙Õ❊❙ ❉❊ ❈➱▲❯▲❆❙ ❇■❖▲Ó●■❈❆❙ ◆❆
❊▲❊❚❘❖P❊❘▼❊❆❇■▲■❩❆➬➹❖
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥✲ ❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❊st❛❞♦ ❞❡ ❙❛♥t❛ ❈❛t❛r✐♥❛✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧é✲ tr✐❝❛✳
❖r✐❡♥t❛❞♦r✿ ❆✐rt♦♥ ❘❛♠♦s
❈♦✲♦r✐❡♥t❛❞♦r❛✿ ❉❛♥✐❡❧❛ ❖t❛ ❍✐s❛②❛s✉ ❙✉③✉❦✐
❋✷✷✹♠ ❋❛r✐❛s✱ ❍❡r✐❝ ❉ê♥✐s
▼♦❞❡❧❛❣❡♠ ❞❛ ✐♠♣❡❞â♥❝✐❛ ❞❡ s✉s♣❡♥sõ❡s ❞❡ ❝é❧✉❧❛s ❜✐♦❧ó✲ ❣✐❝❛s ♥❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✴ ❍❡r✐❝ ❉ê♥✐s ❋❛r✐❛s✳ ✕ ✷✵✶✺✳
✾✵ ♣✳ ✿ ✐❧✳ ❀ ✷✶ ❝♠
❖r✐❡♥t❛❞♦r✿ ❆✐rt♦♥ ❘❛♠♦s
❈♦♦r✐❡♥t❛❞♦r❛✿ ❉❛♥✐❡❧❛ ❖t❛ ❍✐s❛②❛s✉ ❙✉③✉❦✐ ❇✐❜❧✐♦❣r❛✜❛✿ ✽✸✲✾✵
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❊st❛❞♦ ❙❛♥t❛ ❈❛t❛r✐♥❛✱ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❚❡❝♥♦❧ó❣✐❝❛s✱ Pr♦❣r❛♠❛ ❞❡ Pós✲ ●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✱ ❏♦✐♥✈✐❧❧❡✱ ✷✵✶✺✳
✶✳ ❊❧❡tr♦♣♦r❛çã♦✳ ✷✳ ❊❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✳ ✸✳ ❊s♣❡❝tr♦s✲ ❝♦♣✐❛ ❞❡ ✐♠♣❡❞â♥❝✐❛ ❡❧étr✐❝❛✳ ✹✳ ▼ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ✺✳ ❆❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s✳ ✻✳ ▼♦❞❡❧❛❣❡♠ ♥✉♠ér✐❝❛✳ ✼✳ ❙✉s✲ ♣❡♥sõ❡s ❞❡ ❝é❧✉❧❛s ❜✐♦❧ó❣✐❝❛s✳ ■✳ ❘❛♠♦s✱ ❆✐rt♦♥✳ ■■✳ ❙✉③✉❦✐✱ ❉❛♥✐❡❧❛ ❖t❛ ❍✐s❛②❛s✉✳ ■■■✳ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❊st❛❞♦ ❙❛♥t❛ ❈❛t❛✲ r✐♥❛✳ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✳ ■❱✳ ❚ít✉❧♦
❘❊❙❯▼❖
❆ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦s ❡❧étr✐❝♦s ✐♥t❡♥s♦s ❡♠ ❝é❧✉❧❛s ❜✐♦❧ó❣✐❝❛s ♣r♦✈♦❝❛ ❛ ❢♦r♠❛çã♦ ❞❡ ♣♦r♦s ♥❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✱ ❝❛✉s❛♥❞♦ ❛ss✐♠ ♦ ❛✉♠❡♥t♦ ❞❡ s✉❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✳ ❊st❡ ❢❡♥ô♠❡♥♦✱ ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐✲ ③❛çã♦ tê♠ ❛tr❛í❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❛t❡♥çã♦ ❞❡✈✐❞♦ ❛ s✉❛ ❛♠♣❧❛ ❛♣❧✐❝❛çã♦ ❡♠ ❜✐♦t❡❝♥♦❧♦❣✐❛✳ ▼❡s♠♦ s❡♥❞♦ ❝♦♥❤❡❝✐❞♦ ❤á ✈ár✐❛s ❞é❝❛❞❛s✱ ♦ ♣r♦✲ ❝❡ss♦ ❞❡ ❛❜❡rt✉r❛ ❞❡ ♣♦r♦s ❡♠ ♠❡♠❜r❛♥❛s ❞❡ ❝é❧✉❧❛s ❜✐♦❧ó❣✐❝❛s ❛✐♥❞❛ ♥ã♦ é ♣❧❡♥❛♠❡♥t❡ ❡♥t❡♥❞✐❞♦ ❡ ♥❡♠ ❢♦✐ ❛✐♥❞❛ ❝♦rr❡t❛♠❡♥t❡ ♠♦❞❡❧❛❞♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛♣r❡s❡♥t❛✲s❡ ❞♦✐s t✐♣♦s ❞❡ ♠♦❞❡❧❛❣❡♠ q✉❡ ♣❡r♠✐t❡♠ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❡♠ s✉s♣❡♥sõ❡s ❞❡ ❝é❧✉❧❛s ❜✐♦❧ó✲ ❣✐❝❛s✳ ❯♠ ❞♦s ♠ét♦❞♦s ❜❛s❡✐❛✲s❡ ♥❛ ❛♥á❧✐s❡ ❞♦ ❡s♣❡❝tr♦ ❞❡ ✐♠♣❡❞â♥❝✐❛ ❡❧étr✐❝❛ ❞❡ s✉s♣❡♥sõ❡s ❝♦♠ ♦ ✉s♦ ❞❡ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♣❛r❛ ❞❡t❡r♠✐✲ ♥❛r ♣❛râ♠❡tr♦s ❞❡ ✉♠ ♠♦❞❡❧♦ ❣❡♥ér✐❝♦ ❞❡ ❞✐s♣❡rsã♦ ❞✐❡❧étr✐❝❛✳ ❖ ♦✉tr♦ ♠ét♦❞♦ ✉t✐❧✐③❛ ✈❛❧♦r❡s ✐♥st❛♥tâ♥❡♦s ❞❡ t❡♥sã♦ ❡ ❝♦rr❡♥t❡ ❛♣❧✐❝❛❞♦s ❡♠ ✉♠❛ s✉s♣❡♥sã♦ ❞❡ ❝é❧✉❧❛s ❞✉r❛♥t❡ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛✲ ❜✐❧✐③❛çã♦ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ ✈❛r✐❛çã♦ ❞❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦ ♠❡✐♦ ❡ ❝♦♠ ✐ss♦✱ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ ❛♥❛❧ít✐❝♦ ♣r♦♣♦st♦ ♣♦r ❘❛♠♦s ❡ ❝♦❧❛❜♦r❛❞♦r❡s ✭❘❆▼❖❙ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ❞❡t❡r♠✐♥❛r ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❛s ❝é❧✉❧❛s✳
❆tr❛✈és ❞❛ ♠♦❞❡❧❛❣❡♠ ❞♦ ❡s♣❡❝tr♦ ❞❡ ✐♠♣❡❞â♥❝✐❛✱ ❢♦✐ ♣♦ssí✈❡❧ ✈❡r✐✜❝❛r ❛ ❛❧t❡r❛çã♦ ❞❛ ❞✐s♣❡rsã♦ ❞✐❡❧étr✐❝❛ ❞❛ ❛♠♦str❛ ❞❡✈✐❞♦ ❛♦ ♣r♦❝❡ss♦ ❞❡ ❡❧❡✲ tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✱ ❛❧é♠ ❞❛ ♦❜t❡♥çã♦ ❞❛s ❝♦♥❞✉t✐✈✐❞❛❞❡s ❡ ♣❡r♠✐ss✐✈✐✲ ❞❛❞❡s ❡❧étr✐❝❛s ❞♦s ♠❡✐♦s ❡♥✈♦❧✈✐❞♦s✳ ❯t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❝é❧✉❧❛ ❡❧❡✲ tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛ ♣r♦♣♦st♦ ♣♦r ❘❛♠♦s ❡ ❝♦❧❡❣❛s ✭❘❆▼❖❙ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ❢♦✐ ♣♦ssí✈❡❧ ♦❜t❡r ❛ ✈❛r✐❛çã♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ❞✉r❛♥t❡ ❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✳ ❆ ✈❛❧✐❞❛❞❡ ❞❡st❡ ♠♦❞❡❧♦ é ❛✈❛❧✐❛❞❛ ✉t✐❧✐③❛♥❞♦ s✐♠✉❧❛çõ❡s ❡♠ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❛s q✉❛✐s ❛♣r❡s❡♥t❛r❛♠ ❣r❛♥❞❡ ❝♦♥✲ ❝♦r❞â♥❝✐❛ ❝♦♠ ♦ ♠♦❞❡❧♦ ❛♥❛❧ít✐❝♦ ✉t✐❧✐③❛❞♦✳ ❆❧❣♦r✐t♠♦s ❣❡♥ét✐❝♦s sã♦ ✉t✐❧✐③❛❞♦s ♥❛ ♦❜t❡♥çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞♦s ❞✐✈❡rs♦s ♠♦❞❡❧♦s ❛♣r❡s❡♥✲ t❛❞♦s✱ ♠♦str❛♥❞♦ ❣r❛♥❞❡ r♦❜✉st❡③ ♥❛ ♦❜t❡♥çã♦ ❞❡ ♣❛râ♠❡tr♦s ❜❛s❡❛❞❛ ♥♦ ❛❥✉st❡ ❡♥tr❡ ❝✉r✈❛s ❡①♣❡r✐♠❡♥t❛✐s ❡ t❡ór✐❝❛s✳
❆❇❙❚❘❆❈❚
❚❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❤✐❣❤ ❡❧❡❝tr✐❝ ✜❡❧❞s ♦♥ ❜✐♦❧♦❣✐❝❛❧ ❝❡❧❧s ❝❛✉s❡s t❤❡ ❢♦r✲ ♠❛t✐♦♥ ♦❢ ♣♦r❡s ✐♥ t❤❡ ❝❡❧❧ ♠❡♠❜r❛♥❡✱ t❤❡r❡❜② ❝❛✉s✐♥❣ ❛♥ ✐♥❝r❡❛s❡ ✐♥ t❤❡✐r ♣❡r♠❡❛❜✐❧✐t②✳ ❚❤✐s ♣❤❡♥♦♠❡♥♦♥✱ ❝❛❧❧❡❞ ❡❧❡❝tr♦♣❡r♠❡❛❜✐❧✐③❛✲ t✐♦♥ ❤❛✈❡ ❛ttr❛❝t❡❞ ✐♥❝r❡❛s✐♥❣ ❛tt❡♥t✐♦♥ ❞✉❡ t♦ ✐ts ✇✐❞❡ ❛♣♣❧✐❝❛t✐♦♥ ✐♥ ❜✐♦t❡❝❤♥♦❧♦❣②✳ ❊✈❡♥ ❜❡✐♥❣ ❦♥♦✇♥ ❢♦r ❞❡❝❛❞❡s✱ t❤❡ ♣♦r❡ ♦♣❡♥✐♥❣ ♣r♦✲ ❝❡ss ✐♥ ❜✐♦❧♦❣✐❝❛❧ ❝❡❧❧ ♠❡♠❜r❛♥❡s ✐s st✐❧❧ ♥♦t ❢✉❧❧② ✉♥❞❡rst♦♦❞✱ ♥♦r ✇❛s ✐t ❡✈❡♥ ♣r♦♣❡r❧② ♠♦❞❡❧❡❞✳
■♥ t❤✐s ♣❛♣❡r✱ t✇♦ t②♣❡s ♦❢ ♠♦❞❡❧✐♥❣ ❛r❡ ♣r❡s❡♥t❡❞✱ ✇❤✐❝❤ ❛❧❧♦✇ ❝❤❛r❛❝✲ t❡r✐③✐♥❣ t❤❡ ❡❧❡❝tr♦♣❡r♠❡❛❜✐❧✐③❛t✐♦♥ ✐♥ ❜✐♦❧♦❣✐❝❛❧ ❝❡❧❧ s✉s♣❡♥s✐♦♥s✳ ❖♥❡ ♦❢ t❤❡ ♠❡t❤♦❞s ✐s ❜❛s❡❞ ♦♥ t❤❡ ❛♥❛❧②s✐s ♦❢ t❤❡ ❡❧❡❝tr✐❝❛❧ ✐♠♣❡❞❛♥❝❡ s♣❡❝tr❛ ♦❢ s✉s♣❡♥s✐♦♥s ✉s✐♥❣ ❣❡♥❡t✐❝ ❛❧❣♦r✐t❤♠ t♦ ❞❡t❡r♠✐♥❡ ♣❛r❛♠❡✲ t❡rs ♦❢ ❛ ❣❡♥❡r✐❝ ♠♦❞❡❧ ❞✐❡❧❡❝tr✐❝ ❞✐s♣❡rs✐♦♥✳ ❚❤❡ ♦t❤❡r ♠❡t❤♦❞ ✉s❡s ✐♥st❛♥t❛♥❡♦✉s ✈♦❧t❛❣❡ ❛♥❞ ❝✉rr❡♥t ✈❛❧✉❡s ❛♣♣❧✐❡❞ t♦ ❛ ❝❡❧❧ s✉s♣❡♥s✐♦♥ ❞✉r✐♥❣ t❤❡ ❡❧❡❝tr♦♣♦r❛t✐♦♥ ❡①♣❡r✐♠❡♥t t♦ ❞❡t❡r♠✐♥❡ t❤❡ ✈❛r✐❛t✐♦♥ ♦❢ t❤❡ ♠❡❞✐✉♠ ❝♦♥❞✉❝t✐✈✐t② ❛♥❞ t❤✉s✱ t❤r♦✉❣❤ t❤❡ ❛♥❛❧②t✐❝❛❧ ♠♦❞❡❧ ♣r♦✲ ♣♦s❡❞ ❜② ❘❛♠♦s ❛♥❞ ❝♦❧❧❡❛❣✉❡s ✭❘❆▼❖❙ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ❞❡t❡r♠✐♥❡ t❤❡ ❝❡❧❧ ❝♦♥❞✉❝t✐✈✐t✐❡s✳
❇② ♠♦❞❡❧✐♥❣ t❤❡ ✐♠♣❡❞❛♥❝❡ s♣❡❝tr✉♠✱ ✐t ✇❛s ♦❜s❡r✈❡❞ t❤❡ ❝❤❛♥❣❡ ✐♥ t❤❡ ❞✐❡❧❡❝tr✐❝ ❞✐s♣❡rs✐♦♥ ♦❢ t❤❡ s❛♠♣❧❡ ❞✉❡ t♦ t❤❡ ❡❧❡❝tr♦♣❡r♠❡❛❜✐❧✐③❛t✐♦♥ ♣r♦❝❡ss✱ ✐♥ ❛❞❞✐t✐♦♥ t♦ ♦❜t❛✐♥✐♥❣ t❤❡ ❡❧❡❝tr✐❝❛❧ ❝♦♥❞✉❝t✐✈✐t② ❛♥❞ ♣❡r✲ ♠✐tt✐✈✐t② ♦❢ t❤❡ ✐♥✈♦❧✈❡❞ ♠❡❞✐❛✳ ❯s✐♥❣ t❤❡ ❡❧❡❝tr♦♣♦r❛t❡❞ ❝❡❧❧ ♠♦❞❡❧ ♣r♦♣♦s❡❞ ❜② ❘❛♠♦s ❛♥❞ ❝♦❧❧❡❛❣✉❡s ✭❘❆▼❖❙ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✐t ✇❛s ♣♦ss✐❜❧❡ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ❝❤❛♥❣❡ ♦❢ ♠❡♠❜r❛♥❡ ❝♦♥❞✉❝t❛♥❝❡ ❞✉r✐♥❣ t❤❡ ❡❧❡❝✲ tr♦♣❡r♠❡❛❜✐❧✐③❛t✐♦♥✳ ❚❤❡ ✈❛❧✐❞✐t② ♦❢ t❤✐s ♠♦❞❡❧ ✐s ❛ss❡ss❡❞ ✉s✐♥❣ ✜♥✐t❡ ❡❧❡♠❡♥t s✐♠✉❧❛t✐♦♥s✱ ✇❤✐❝❤ s❤♦✇❡❞ ❣♦♦❞ ❛❣r❡❡♠❡♥t ✇✐t❤ t❤❡ ❛♥❛❧②t✐❝❛❧ ♠♦❞❡❧ ✉s❡❞✳ ●❡♥❡t✐❝ ❛❧❣♦r✐t❤♠s ❛r❡ ✉s❡❞ ✐♥ ♦❜t❛✐♥✐♥❣ t❤❡ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ ✈❛r✐♦✉s ♠♦❞❡❧s ♣r❡s❡♥t❡❞✱ s❤♦✇✐♥❣ ❣r❡❛t r♦❜✉st♥❡ss ✐♥ ♦❜t❛✐♥✲ ✐♥❣ ♣❛r❛♠❡t❡rs ❜❛s❡❞ ♦♥ t❤❡ ✜t ❜❡t✇❡❡♥ ❡①♣❡r✐♠❡♥t❛❧ ❛♥❞ t❤❡♦r❡t✐❝❛❧ ❝✉r✈❡s✳
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶ ✕ ❊str✉t✉r❛ ♠♦❧❡❝✉❧❛r s✐♠♣❧✐✜❝❛❞❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ❋✐❣✉r❛ ✷ ✕ ▼♦❞❡❧♦ ❣❡♦♠étr✐❝♦ ❞❛ ❝é❧✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ❋✐❣✉r❛ ✸ ✕ ❋♦r♠❛s ❞❡ ♦♥❞❛ ♠❛✐s ✉t✐❧✐③❛❞❛s ❡♠ ❡❧❡tr♦♣♦r❛çã♦ ✸✷ ❋✐❣✉r❛ ✹ ✕ ●❡r❛❞♦r ❞❡ ▼❛r① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ❋✐❣✉r❛ ✺ ✕ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❡①♣❡r✐♠❡♥t♦ ❞❡
❡❧❡tr♦♣♦r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ❋✐❣✉r❛ ✻ ✕ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♦♣❡r❛❞♦r ❝r♦ss♦✈❡r ✹✺ ❋✐❣✉r❛ ✼ ✕ ❊s♣❡❝tr♦ ❞❡ ✐♠♣❡❞â♥❝✐❛ ❞❛ s✉s♣❡♥sã♦ ❞❡ ❧❡✈❡✲
❞✉r❛s ❛♥t❡s ❛ ❛♣ós ❛♣❧✐❝❛çã♦ ❞♦ ❝❛♠♣♦ ❞❡ ✹✵✵
kV/m ❞✉r❛♥t❡ ✶✵ ♠s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
❋✐❣✉r❛ ✽ ✕ ❈♦♥❞✉t✐✈✐❞❛❞❡ ❡♠ ❜❛✐①❛s ❢r❡q✉ê♥❝✐❛s ❞❛ s✉s✲ ♣❡♥sã♦ ❞❡ ❝é❧✉❧❛s ❝♦♠♦ ❢✉♥çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ❝❛♠♣♦ ❛♣❧✐❝❛❞♦ ❡ ❞✉r❛çã♦ ❞♦ ♣✉❧s♦ ✳ ✳ ✳ ✳ ✳ ✺✵ ❋✐❣✉r❛ ✾ ✕ ▼♦❞❡❧♦ ❞❡ ❝é❧✉❧❛ ✉t✐❧✐③❛❞♦ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❛ ❡❧❡✲
tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ❋✐❣✉r❛ ✶✵ ✕ ❉✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡ ❞❡ ♠❡♠❜r❛♥❛ ❝♦ss❡♥♦✐✲
❞❛❧ ❝♦♠ â♥❣✉❧♦ ❝rít✐❝♦ θc ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
❋✐❣✉r❛ ✶✶ ✕ ❈é❧✉❧❛s ✉♥✐tár✐❛s ♣❛r❛ ❛s ❞✐❢❡r❡♥t❡s ❣❡♦♠❡tr✐❛s✿ ❈ú❜✐❝❛ s✐♠♣❧❡s❀ ❝ú❜✐❝❛ ❞❡ ❝♦r♣♦ ❝❡♥tr❛❞♦❀ ❝ú✲ ❜✐❝❛ ❞❡ ❢❛❝❡ ❝❡♥tr❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ❋✐❣✉r❛ ✶✷ ✕ ❉✐❢❡r❡♥t❡s ❣❡♦♠❡tr✐❛s ✉t✐❧✐③❛❞❛s✿ ❈ú❜✐❝❛ s✐♠✲
♣❧❡s❀ ❝ú❜✐❝❛ ❞❡ ❝♦r♣♦ ❝❡♥tr❛❞♦❀ ❝ú❜✐❝❛ ❞❡ ❢❛❝❡ ❝❡♥tr❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ❋✐❣✉r❛ ✶✸ ✕ ▼❛❧❤❛ ❞❡ ❞✐s❝r❡t✐③❛çã♦ ♠♦str❛♥❞♦ ♦s ❡❧❡♠❡♥t♦s
♣r✐s♠át✐❝♦s ❛❧♦♥❣❛❞♦s ❝r✐❛❞♦s ♥❛ ♣❛r❡❞❡ ❝❡❧✉❧❛r ✻✺ ❋✐❣✉r❛ ✶✹ ✕ ❉✐str✐❜✉✐çõ❡s ❞❡ ♣♦t❡♥❝✐❛❧ ❞❡ ♠❡♠❜r❛♥❛✱ ❞❡♥✲
s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♥❛ ♠❡♠❜r❛♥❛ ❡ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ♣❛r❛ ✉♠❛ ❝é❧✉❧❛ ❡s❢ér✐❝❛ ✐s♦❧❛❞❛ ✳ ✼✵ ❋✐❣✉r❛ ✶✺ ✕ ❈♦♥❞✉t✐✈✐❞❛❞❡ ❞❛s ❝é❧✉❧❛s ❝♦♠♦ ❢✉♥çã♦ ❞♦ â♥✲
❣✉❧♦ ❝rít✐❝♦ ❡ ❝♦♥❞✉tâ♥❝✐❛ ❞♦ ♣♦❧♦ ❞❡ ♠❡♠❜r❛♥❛ ✼✶ ❋✐❣✉r❛ ✶✻ ✕ ❋✉♥çã♦g ❝❛❧❝✉❧❛❞❛ ♥✉♠❡r✐❝❛♠❡♥t❡ ♣❛r❛ ❛ ❣❡♦✲
♠❡tr✐❛ ❝ú❜✐❝❛ s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❋✐❣✉r❛ ✶✼ ✕ ❈♦♠♣❛r❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ tr❛♥s♠❡♠❜r❛♥❛ ♣❛r❛
✶✵
❋✐❣✉r❛ ✶✽ ✕ P❛ss❛❣❡♥s ♣♦r ③❡r♦ ❞❛s ❢✉♥çõ❡s f1 ❡f2 ✭❊q✉❛✲
çõ❡s ✹✳✹✷❛ ❡ ❜✮ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ ❝♦♥✲ ❞✉tâ♥❝✐❛ ❞❡ ♣♦❧♦ ❞❡ ♠❡♠❜r❛♥❛ ❡ â♥❣✉❧♦ ❝rít✐❝♦ ✼✻ ❋✐❣✉r❛ ✶✾ ✕ ❈✉r✈❛s ❞❡ t❡♥sã♦ ❡ ❝♦rr❡♥t❡ ❞✉r❛♥t❡ ❛ ❛♣❧✐❝❛çã♦
❞♦ ♣✉❧s♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❞❡ ❛♠♣❧✐t✉❞❡
300 kV/m ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
❋✐❣✉r❛ ✷✵ ✕ ❈♦♥❞✉t✐✈✐❞❛❞❡ ❞❛ s✉s♣❡♥sã♦ ❞✉r❛♥t❡ ❛ ❛♣❧✐❝❛✲ çã♦ ❞♦ ♣✉❧s♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ♣❛r❛ ❞✐✲ ✈❡rs❛s ✐♥t❡♥s✐❞❛❞❡s ❞❡ ❝❛♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ❋✐❣✉r❛ ✷✶ ✕ ❈♦♥❞✉t✐✈✐❞❛❞❡ ❞❛s ❝é❧✉❧❛s ❡ ❝♦♥❞✉tâ♥❝✐❛ ❞♦ ♣♦❧♦
❞❡ ♠❡♠❜r❛♥❛ ❝❛❧❝✉❧❛❞❛s ❞✉r❛♥t❡ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ♣✉❧s♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ❋✐❣✉r❛ ✷✷ ✕ ❈♦♥❞✉t✐✈✐❞❛❞❡ ❞❛s ❝é❧✉❧❛s ❡ ❝♦♥❞✉tâ♥❝✐❛ ❞♦ ♣♦❧♦
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
❚❛❜❡❧❛ ✶ ✕ ❘❡❣✐ã♦ ❞❡ ❜✉s❝❛ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ❛ ♠♦❞❡✲ ❧❛❣❡♠ ❞❛ ❞✐s♣❡rsã♦ ❞✐❡❧étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ❚❛❜❡❧❛ ✷ ✕ ❘❡❣✐ã♦ ❞❡ ❜✉s❝❛ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ❛ ♠♦❞❡✲
❧❛❣❡♠ ❞❡ ❝é❧✉❧❛s ✐♥t❛❝t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ❚❛❜❡❧❛ ✸ ✕ P❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ❞✐s♣❡rsã♦ ❛♥t❡s ❡ ❛♣ós
❛♣❧✐❝❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ❚❛❜❡❧❛ ✹ ✕ P❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ♣❛r❛ ❝é❧✉❧❛s ✐♥t❛❝t❛s ✳ ✳ ✺✶ ❚❛❜❡❧❛ ✺ ✕ P❛râ♠❡tr♦s ❡ ❢❛✐①❛s ❞❡ ✈❛r✐❛çã♦ ✉t✐❧✐③❛❞❛s ♥❛s
▲■❙❚❆ ❉❊ ❆❇❘❊❱■❆❚❯❘❆❙ ❊ ❙■●▲❆❙
❇❈❈ ❣❡♦♠❡tr✐❛ ❝ú❜✐❝❛ ❞❡ ❝♦r♣♦ ❝❡♥tr❛❞♦ ✭❜♦❞② ❝❡♥t❡r❡❞ ❝✉❜✐❝✮ ❈❆ ❝♦rr❡♥t❡ ❛❧t❡r♥❛❞❛
❈❈ ❝♦rr❡♥t❡ ❝♦♥tí♥✉❛
❊■❊ ❡s♣❡❝tr♦s❝♦♣✐❛ ❞❡ ✐♠♣❡❞â♥❝✐❛ ❡❧étr✐❝❛
❋❈❈ ❣❡♦♠❡tr✐❛ ❝ú❜✐❝❛ ❞❡ ❢❛❝❡ ❝❡♥tr❛❞❛ ✭❢❛❝❡ ❝❡♥t❡r❡❞ ❝✉❜✐❝✮ ▼❉❈▲ ♠❡♠❜r❛♥❛ ❞❡ ❞✉♣❧❛ ❝❛♠❛❞❛ ❧✐♣í❞✐❝❛
❘❋ r❛❞✐♦❢r❡q✉ê♥❝✐❛
❘▼❙ ✈❛❧♦r ❡✜❝❛③ ✭r♦♦t ♠❡❛♥ sq✉❛r❡✮
✶✺
▲■❙❚❆ ❉❊ ❙❮▼❇❖▲❖❙
β ❝♦♥st❛♥t❡ r❡❧❛❝✐♦♥❛❞❛ à ❞✐s♣❡rsã♦ ❞✐❡❧étr✐❝❛ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞♦ ❡s♣❡❝tr♦ ❞❡ ✐♠♣❡❞â♥❝✐❛
Cm ❝❛♣❛❝✐tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ár❡❛
E ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦
em ❝❛♠♣♦ ❡❧étr✐❝♦ s❡♥♦✐❞❛❧ ✉t✐❧✐③❛❞♦ ♥❛ ♠❡❞✐çã♦ ❞❡ ❝♦♥❞✉t✐✲
✈✐❞❛❞❡ ❞❛ s✉s♣❡♥sã♦
ε∞ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ❡♠ ❛❧t❛s ❢r❡q✉ê♥❝✐❛s
∆εr ❛♠♣❧✐t✉❞❡ ❞❡ ❞✐s♣❡rsã♦ ❞✐❡❧étr✐❝❛
∆σ ❛♠♣❧✐t✉❞❡ ❞❡ ❞✐s♣❡rsã♦ ❞❛ ❝♦♥❞✉t✐✈✐❞❛❞❡
g ❢✉♥çã♦ q✉❡ r❡❧❛❝✐♦♥❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♥♦ ♣♦❧♦ ❞❛ ❝é❧✉❧❛ à ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♠é❞✐❛ ♥❛ s✉s♣❡♥sã♦ Gm ❝♦♥❞✉tâ♥❝✐❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
Gmo ❝♦♥❞✉tâ♥❝✐❛ ❞❛ ♠❡♠❜r❛♥❛ ♥♦ ♣♦❧♦ ❝❡❧✉❧❛r
h ❡s♣❡ss✉r❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
jm ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♥❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
jmo ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ♥❛ ♠❡♠❜r❛♥❛ ♥♦ ♣♦❧♦ ❝❡❧✉❧❛r
jo ❞❞❡♥s✐❞❛❞❡ ❝♦rr❡♥t❡ ♠é❞✐❛ ♥❛ s✉s♣❡♥sã♦
ω ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r
φi ♣♦t❡♥❝✐❛❧ ❡❧étr✐❝♦ ❞❡♥tr♦ ❞❛ ❝é❧✉❧❛
φo ♣♦t❡♥❝✐❛❧ ❡❧étr✐❝♦ ❡①t❡r✐♦r à ❝é❧✉❧❛
R r❛✐♦ ❝❡❧✉❧❛r
Rct r❡s✐stê♥❝✐❛ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❝❛r❣❛
γc ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠♣❧❡①❛ ❞❛ ❝é❧✉❧❛
γo ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠♣❧❡①❛ ❞♦ ♠❡✐♦ ❡①t❡r✐♦r à ❝é❧✉❧❛
εo ♣❡r♠✐ss✐✈✐❞❛❞❡ ❞♦ ♠❡✐♦ ❡①t❡r✐♦r à ❝é❧✉❧❛
γi ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠♣❧❡①❛ ❞♦ ♠❡✐♦ ✐♥t❡r✐♦r ❞❛ ❝é❧✉❧❛
σi ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦ ♠❡✐♦ ✐♥t❡r✐♦r ❞❛ ❝é❧✉❧❛
εi ♣❡r♠✐ss✐✈✐❞❛❞❡ ❞♦ ♠❡✐♦ ✐♥t❡r✐♦r ❞❛ ❝é❧✉❧❛
γm ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠♣❧❡①❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
σm ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
εm ♣❡r♠✐ss✐✈✐❞❛❞❡ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
σc ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡q✉✐✈❛❧❡♥t❡ ❞❛ ❝é❧✉❧❛
σs ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡q✉✐✈❛❧❡♥t❡ ❞❛ s✉s♣❡♥sã♦
σso ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❛ s✉s♣❡♥sã♦ ♥ã♦ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛
σo ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦ ♠❡✐♦ ❡①t❡r✐♦r à ❝é❧✉❧❛
γs ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠♣❧❡①❛ ❞❛ s✉s♣❡♥sã♦ ❞❡ ❝é❧✉❧❛s
σss ❝♦♥❞✉t✐✈✐❞❛❞❡ ❈❈ ❞❛ s✉s♣❡♥sã♦
τm t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ♣❛r❛ ❛❝✉♠✉❧❛çã♦ ❞❡ ❝❛r❣❛s ♥❛ ♠❡♠✲
❜r❛♥❛ ❝❡❧✉❧❛r
τs t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ♣❛r❛ ❛ ❛❝✉♠✉❧❛çã♦ ❞❡ í♦♥s ♥❛ ✐♥t❡r❢❛❝❡
θc â♥❣✉❧♦ ❝rít✐❝♦ ♣❛r❛ ❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦
vc ✈❛❧♦r ❞❡ ♣♦t❡♥❝✐❛❧ tr❛♥s♠❡♠❜r❛♥❛ ❝rít✐❝♦ ❛❝✐♠❛ ❞♦ q✉❛❧
❙❯▼➪❘■❖
✶ ■◆❚❘❖❉❯➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✷ ❊▲❊❚❘❖P❊❘▼❊❆❇■▲■❩❆➬➹❖ ❈❊▲❯▲❆❘ ✳ ✳ ✳ ✷✶
✷✳✶ ▼❖❉❊▲❆●❊▼ ❉❆ ❊▲❊❚❘❖P❊❘▼❊❆❇■▲■❩❆➬➹❖ ❈❊✲ ▲❯▲❆❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✶✳✶ ▼❡❝❛♥✐s♠♦s ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✶✳✷ ▼♦❞❡❧❛❣❡♠ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛ ♥í✈❡❧ ♠❛✲
❝r♦s❝ó♣✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✷ ❚➱❈◆■❈❆ ❊❳P❊❘■▼❊◆❚❆▲ ❉❆ ❊▲❊❚❘❖P❊❘▼❊❆✲
❇■▲■❩❆➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✷✳✶ Pr♦t♦❝♦❧♦s ❞❡ ❊❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷✳✷ ❊❧❡tr♦♣♦r❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷✳✷✳✶ ❊❧❡tr♦❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷✳✷✳✷ ●❡r❛❞♦r❡s ❞❡ P✉❧s♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸ ❆◆➪▲■❙❊ ❉❖ ❊❙P❊❈❚❘❖ ❉❊ ■▼P❊❉➶◆❈■❆
❉❊ ❙❯❙P❊◆❙Õ❊❙ ❉❊ ❈➱▲❯▲❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶ ▼❆❚❊❘■❆■❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✷ ▼❖❉❊▲❆●❊▼ ❉❆ ❉■❙P❊❘❙➹❖ ❉■❊▲➱❚❘■❈❆ ✳ ✳ ✳ ✳ ✸✾ ✸✳✸ ▼❖❉❊▲❆●❊▼ P❆❘❆ ❈➱▲❯▲❆❙ ■◆❚❆❈❚❆❙ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✹ ❆▲●❖❘■❚▼❖❙ ●❊◆➱❚■❈❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✹✳✶ ❖♣❡r❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹✳✶✳✶ ❖♣❡r❛❞♦r ❋✐t♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹✳✶✳✷ ❖♣❡r❛❞♦r ❙❡❧❡❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹✳✶✳✸ ❖♣❡r❛❞♦r ❈r♦ss♦✈❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹✳✶✳✹ ❖♣❡r❛❞♦r ▼✉t❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✹✳✷ ❊str✉t✉r❛ ❇ás✐❝❛ ❞❡ ✉♠ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✳ ✳ ✳ ✹✺ ✸✳✺ ❘❊❙❯▲❚❆❉❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✻ ❉■❙❈❯❙❙➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✼ ❈❖◆❈▲❯❙➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹ ▼❖❉❊▲❆●❊▼ ❉❆ ❊▲❊❚❘❖P❊❘▼❊❆❇■▲■❩❆✲
➬➹❖ ❆ ◆❮❱❊▲ ❈❊▲❯▲❆❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✶ ▼❖❉❊▲❖ ❉❊ ❈❖◆❉❯❚■❱■❉❆❉❊ P❆❘❆ ❆ ❈➱▲❯▲❆
✶✽
✶✾
✶ ■◆❚❘❖❉❯➬➹❖
❊❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✱ ♦✉ ❡❧❡tr♦♣♦r❛çã♦✱ é ✉♠ ❢❡♥ô♠❡♥♦ ♥♦ q✉❛❧ ♣♦r♦s s❡ ❢♦r♠❛♠ ❡♠ ♠❡♠❜r❛♥❛s ❞❡ ❞✉♣❧❛ ❝❛♠❛❞❛ ❧✐♣í❞✐❝❛ ✭▼❉❈▲✮ s✉❥❡✐t❛s ❛ ❝❛♠♣♦s ❡❧étr✐❝♦s ✐♥t❡♥s♦s✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❛ss✐♠ ♦ tr❛♥s♣♦rt❡ ❞❡ s✉❜stâ♥❝✐❛s ❡♥tr❡ ♦s ♠❡✐♦s ♣r❡✈✐❛♠❡♥t❡ ✐s♦❧❛❞♦s✱ ❝♦♠♦ ♦s ♠❡✐♦s ✐♥tr❛ ❡ ❡①tr❛❝❡❧✉❧❛r✳ ❆ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ♣♦❞❡ s❡r ❝❧❛ss✐✜❝❛❞❛ ❡♠ r❡✈❡r✲ sí✈❡❧ ♦✉ ✐rr❡✈❡rsí✈❡❧✳ ◆♦ ❝❛s♦ ✐rr❡✈❡rsí✈❡❧✱ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦ ❞❛♥✐✜❝❛ ❛ ♠❡♠❜r❛♥❛ ❞❡ ❢♦r♠❛ ♣❡r♠❛♥❡♥t❡ ❧❡✈❛♥❞♦ à ❧✐s❡ ❝❡❧✉❧❛r✱ s❡♥❞♦ ❛ss✐♠ ❛♣❧✐❝á✈❡❧ ❡♠ s✐t✉❛çõ❡s ♦♥❞❡ s❡ ❞❡s❡❥❛ ✐♥❛t✐✈❛r ♠✐❝r♦✲♦r❣❛♥✐s♠♦s✱ ❝♦♠♦ ♥❛ ♣❛st❡✉r✐③❛çã♦ ❡ ❡st❡r✐❧✐③❛çã♦✱ ❛❧é♠ ❞❡ s❡r ❛♣❧✐❝á✈❡❧ ♥♦ tr❛t❛✲ ♠❡♥t♦ ❞❡ ❝â♥❝❡r s❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❞r♦❣❛s✳ ❆ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ r❡✈❡rsí✈❡❧ ❢♦r♥❡❝❡ ✉♠ ❛❝❡ss♦ tr❛♥s✐❡♥t❡ ❛♦ ❝✐t♦♣❧❛s♠❛ ♠❛♥t❡♥❞♦ ❛ ❢✉♥✲ ❝✐♦♥❛❧✐❞❛❞❡ ❝❡❧✉❧❛r✱ ❡st❛ é ❞❡ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ❡♠ ❜✐♦t❡❝♥♦❧♦❣✐❛✱ ✉♠❛ ✈❡③ q✉❡ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ♥❛ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ♠❛t❡r✐❛❧ ❣❡♥ét✐❝♦ ❛❧é♠ ❞❡ ♦✉tr❛s s✉❜stâ♥❝✐❛s ❝♦♠♦ í♦♥s✱ ❞r♦❣❛s✱ ❛♥t✐❝♦r♣♦s✱ ♣r♦t❡í♥❛s✱ ❡t❝✳
❆ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ t❡♠ ❣r❛♥❞❡ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❝❧í♥✐❝❛s✱ ✉♠❛ ❞❡❧❛s é ❛ ❡❧❡tr♦q✉✐♠✐♦t❡r❛♣✐❛ ✐♥✐❝✐❛❧♠❡♥t❡ ❞❡♠♦♥str❛❞❛ ♣♦r ❖❦✐♥♦ ❡ ▼♦❤r✐ ✭❖❑■◆❖❀ ▼❖❍❘■✱ ✶✾✽✼✮✱ ♥❛ q✉❛❧ t✉♠♦r❡s sã♦ ❡❧❡tr♦✲ ♣❡r♠❡❛❜✐❧✐③❛❞♦s ❢❛❝✐❧✐t❛♥❞♦ ♦ tr❛♥s♣♦rt❡ ❞❡ ❞r♦❣❛s q✉❡ ♥♦r♠❛❧♠❡♥t❡ ♥ã♦ ♣❡♥❡tr❛♠ ♥❛ ♠❡♠❜r❛♥❛ ♣❧❛s♠át✐❝❛ ❡♠ ❣r❛♥❞❡s q✉❛♥t✐❞❛❞❡s✳ ❆♣❡✲ s❛r ❞❛ ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ♣❛r❛ ❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✱ ♠✉✐t♦ s♦❜r❡ ♦s ♠❡❝❛♥✐s♠♦s ♠♦❧❡❝✉❧❛r❡s ❞♦ ♣r♦❝❡ss♦ ♣❡r♠❛♥❡❝❡ ❞❡s❝♦✲ ♥❤❡❝✐❞♦✳ ❊st❛ té❝♥✐❝❛ ♣♦ss✉✐ t❛♠❜é♠ ❛♣❧✐❝❛çõ❡s ✐♥❞✉str✐❛✐s✱ ❝♦♠♦ ♥❛ ♣❛st❡✉r✐③❛çã♦ ❛ ❢r✐♦ ❡ ♥❛ ❡①tr❛çã♦ ❞❡ s✉❜stâ♥❝✐❛s ❝♦♠♦ ♣r♦t❡í♥❛s ❡ ❡♥③✐✲ ♠❛s✳ ❯♠ ❡①❡♠♣❧♦ ❞❛ ú❧t✐♠❛ é ✉♠ ❡st✉❞♦ ❢❡✐t♦ ♣♦r ❘❛♠♦s ❡ ❙❝❤♥❡✐❞❡r ✭❘❆▼❖❙❀ ❙❈❍◆❊■❉❊❘✱ ✷✵✶✷✮ ♥♦ q✉❛❧ ❧❡✈❡❞✉r❛s ❑❧✉②✈❡r♦♠②❝❡s ♠❛r①✐❛✲ ♥✉s sã♦ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛s ♣❛r❛ ♣r♦♠♦✈❡r ❛ ❡①tr❛çã♦ ❞❡ ✉♠❛ ❡♥③✐♠❛ ✉t✐❧✐③❛❞❛ ♥❛ ✐♥❞ústr✐❛ ❛❧✐♠❡♥tí❝✐❛ ❡ ❢❛r♠❛❝ê✉t✐❝❛✱ β✲❉✲❣❛❧❛❝t♦s✐❞❛s❡✱ ❛ q✉❛❧ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ❤✐❞ró❧✐s❡ ❞❛ ❧❛❝t♦s❡✳
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❞✐✈❡rs♦s ♠♦❞❡❧♦s r❡❧❛❝✐♦♥❛❞♦s ❛ s✉s♣❡♥sõ❡s ❞❡ ❧❡✈❡❞✉r❛s ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛s ❡ ✐♥t❛❝t❛s✳ ❊st❡s ♠♦❞❡❧♦s r❡❧❛❝✐♦♥❛♠ ❛s ♠✉❞❛♥ç❛s ♠❛❝r♦s❝ó♣✐❝❛s ❞❡✲ ❝♦rr❡♥t❡s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✭❝♦♠♦ ♦ ❛✉♠❡♥t♦ ❞❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞❛ s✉s♣❡♥sã♦✮ ❝♦♠ ❛s ♠✉❞❛♥ç❛s ♠✐❝r♦s❝ó♣✐❝❛s✱ ♦✉ s❡❥❛✱ ♦ ❛✉♠❡♥t♦ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❝❡❧✉❧❛r✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❛ss✐♠ ❛ ♦❜t❡♥çã♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❞❛ s✉s♣❡♥sã♦✱ ❝♦♠♦ ❛s ❝♦♥❞✉t✐✈✐❞❛❞❡s ❡ ♣❡r♠✐ss✐✈✐❞❛❞❡s ❡❧étr✐❝❛s ❞♦s ♠❡✐♦s✱ ❛❧é♠ ❞❛ ♦❜t❡♥çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❡❧❡✲ tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛t✐♥❣✐❞♦ ♥❛s ❝é❧✉❧❛s✳
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✷✶
✷ ❊▲❊❚❘❖P❊❘▼❊❆❇■▲■❩❆➬➹❖ ❈❊▲❯▲❆❘
❖ ❢❡♥ô♠❡♥♦ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ é ❝♦♥❤❡❝✐❞♦ ❤á ✈ár✐❛s ❞é❝❛❞❛s✱ ❡ t❡♠ s✐❞♦ ❛❧✈♦ ❞❡ ✐♥✈❡st✐❣❛çã♦ ❞❡✈✐❞♦ ❛ s✉❛ ❛♠♣❧❛ ❛♣❧✐❝❛çã♦ ♥❛ ♠❛♥✐♣✉❧❛çã♦ ❞❡ ❝é❧✉❧❛s ❡ t❡❝✐❞♦s✳ ❊①♣❡r✐♠❡♥t♦s ✐♥✐❝✐❛✐s s✉❣❡r✐r❛♠ q✉❡ ❛❧❣✉♠ t✐♣♦ ❞❡ ✏r✉♣t✉r❛ ❡❧étr✐❝❛✑ ♦❝♦rr❡r✐❛ ❡♠ ♠❡♠❜r❛♥❛s ❡❧❡tr✐✲ ❝❛♠❡♥t❡ ❡st✐♠✉❧❛❞❛s ✭❙❚➘▼P❋▲■✱ ✶✾✺✽✮✳ ❈❡r❝❛ ❞❡ ❞❡③ ❛♥♦s ❞❡♣♦✐s✱ ❢♦✐ r❡♣♦rt❛❞❛ ❛ ♠♦rt❡ ♥ã♦ tér♠✐❝❛ ❞❡ ♠✐❝r♦r❣❛♥✐s♠♦s ♣♦r ♣✉❧s♦s ❡❧étr✐❝♦s ✐♥t❡♥s♦s ✭❙❆▲❊❀ ❍❆▼■▲❚❖◆✱ ✶✾✻✼✮✳ ❆♣ós ❛❧❣✉♥s ❛♥♦s✱ ❛ ❡❧❡tr♦♣❡r♠❡❛✲ ❜✐❧✐③❛çã♦ t❛♠❜é♠ ❢♦✐ ♦❜s❡r✈❛❞❛ ❡♠ ♠❡♠❜r❛♥❛s ✈❡s✐❝✉❧❛r❡s ✭◆❊❯▼❆◆◆❀ ❘❖❙❊◆❍❊❈❑✱ ✶✾✼✷✮✳ ❆ ♣❛rt✐r ❞✐st♦✱ ♦❜s❡r✈❛çõ❡s ❡①♣❡r✐♠❡♥t❛✐s ❝♦♠❡ç❛✲ r❛♠ ❛ ❛❝✉♠✉❧❛r ♠❛✐s r❛♣✐❞❛♠❡♥t❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♥❛ ❞❡s❝♦❜❡rt❛ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ tr❛♥s♣♦rt❡ ♠♦❧❡❝✉❧❛r ❡❧❡tr✐❝❛♠❡♥t❡ ❡st✐♠✉❧❛❞♦ ❡♠ ❣❧ó❜✉❧♦s ✈❡r♠❡❧❤♦s ✭❑■◆❖❙■❚❆ ❏❘✳❀ ❚❙❖◆●✱ ✶✾✼✼✱ ✶✾✼✽✮✱ ❡ ♦ ❛✉♠❡♥t♦ ❞rást✐❝♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ❛té ❝❡r❝❛ ❞❡ ✶ ❙✴❝♠✷ ❞❡♥tr♦ ❞❡ ♠✐❝r♦ s❡✲ ❣✉♥❞♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ♣✉❧s♦ ✐♥t❡♥s♦ ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ ✭❑■◆❖❙■❚❆ ❏❘✳❀ ❚❙❖◆●✱ ✶✾✼✾❀ ❇❊◆❩❀ ❇❊❈❑❊❘❙❀ ❩■▼▼❊❘▼❆◆◆✱ ✶✾✼✾❀ ❇❊◆❩❀ ❩■▼✲ ▼❊❘▼❆◆◆✱ ✶✾✽✵❛✱ ✶✾✽✵❜✱ ✶✾✽✶❀ ❈❍❊❘◆❖▼❖❘❉■❑ ❡t ❛❧✳✱ ✶✾✽✷✮✳ ❊st❡s ❡st✉❞♦s ♠♦str❛r❛♠ q✉❡ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ✐♥t❡r❛❣❡ ❝♦♠ ❛ ♣♦rçã♦ ❧✐♣í❞✐❝❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✱ ♦ q✉❡ ❝r✐♦✉ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❡ s✐s✲ t❡♠❛s ❧✐♣í❞✐❝♦s✱ ✐♥✐❝✐❛♥❞♦ ❛ss✐♠ ♦ ❡st✉❞♦ ❞♦s ♠❡❝❛♥✐s♠♦s ♠♦❧❡❝✉❧❛r❡s ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✳
❉❡ ♠♦❞♦ ❣❡r❛❧✱ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✭♦✉ ❡❧❡tr♦♣♦r❛çã♦✮ é ♦ t❡r♠♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❞❡s❝r❡✈❡r ❛ ❝r✐❛çã♦ ❞❡ ♣♦r♦s ❡♠ ♠❡♠❜r❛♥❛s ❝❡✲ ❧✉❧❛r❡s ❞❡❝♦rr❡♥t❡ ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ✐♥t❡♥s♦s ❝❛♠♣♦s ❡❧étr✐❝♦s ❞❡ ❝✉rt❛ ❞✉r❛çã♦✳ ◗✉❛♥❞♦ ✉♠❛ ❝é❧✉❧❛ ❡stá s✉❥❡✐t❛ à ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡①t❡r♥♦✱ ❡st❡ ✐♥❞✉③ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡♥tr❡ ❛s ❢❛❝❡s ✐♥t❡r✐♦r ❡ ❡①t❡r✐♦r ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✳ ❖s ♣r✐♥❝✐♣❛✐s ♣❛ss♦s ❡♥✈♦❧✈✐❞♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝r✐❛çã♦ ❞❡ ♣♦r♦s sã♦ ♦s s❡❣✉✐♥t❡s ✭❲❊❆❱❊❘✱ ✷✵✵✸✮✿
• ❆ ❛♣❧✐❝❛çã♦ ❞❡ ♣✉❧s♦s ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❡ ❞✉r❛çã♦ ♥❛ ❢❛✐①❛ ❞❡ ♠✐❝r♦ ❛ ♠✐❧✐ss❡❣✉♥❞♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ s✉✜❝✐❡♥t❡ ♣❛r❛ ✐♥❞✉③✐r ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ tr❛♥s✐❡♥t❡ ❡♥tr❡ ❛s ❢❛❝❡s ✐♥t❡r♥❛ ❡ ❡①t❡r♥❛ ❞❛ ♠❡♠❜r❛♥❛ ✭t❡♥sã♦ tr❛♥s♠❡♠❜r❛♥❛✮✱ t✐♣✐❝❛♠❡♥t❡ ❡♥tr❡ ✷✵✵ ❡ ✶✵✵✵ ♠❱✱ r❡s✉❧t❛♥❞♦ ❡♠ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❛ ♦r❞❡♠ ❞❡ ✶✵✽❱✴♠ ♥❛ ♠❡♠❜r❛♥❛ ✭t✐♣✐❝❛♠❡♥t❡ ❝♦♠ ❡s♣❡ss✉r❛ ❡♠ t♦r♥♦ ❞❡ ✺ ♥♠✮✳ • ❆❝ú♠✉❧♦ ❞❡ ❝❛r❣❛s ♥❛ ♠❡♠❜r❛♥❛ ❞❡✈✐❞♦ ❛♦ ✢✉①♦ ✐ô♥✐❝♦✳
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• ❋♦r♠❛çã♦ ❞❡ ♣♦r♦s q✉❡ ❛tr❛✈❡ss❛♠ ❛ ♠❡♠❜r❛♥❛ ❡ sã♦ ♣r❡❡♥❝❤✐❞♦s ❞❡ á❣✉❛ ✭♣♦r♦s ❤✐❞r♦❢í❧✐❝♦s✮✳
• ❯♠ ❛✉♠❡♥t♦✱ ❞❡ ✈ár✐❛s ♦r❞❡♥s ❞❡ ♠❛❣♥✐t✉❞❡✱ ♥♦ tr❛♥s♣♦rt❡ ✐ô♥✐❝♦ ❡ ♠♦❧❡❝✉❧❛r ❛tr❛✈és ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✳
◗✉❛♥❞♦ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦ t❡♠ ✐♥t❡♥s✐❞❛❞❡ ❡ ❞✉r❛çã♦ ♠♦❞❡r❛❞♦s✱ ❡st❡ ❡❢❡✐t♦ é r❡✈❡rsí✈❡❧ ❡ ♣♦ss✐❜✐❧✐t❛ ❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❝❡❧✉❧❛r✱ ♣♦r ❡st❡ ♠♦t✐✈♦✱ ❡st❡ ♣r♦❝❡ss♦ t❡♠ ✈❛st❛ ❛♣❧✐❝❛çã♦ ❡♠ ❜✐♦t❡❝♥♦❧♦❣✐❛✱ ❝♦♠♦ ♥❛ ✐♥tr♦❞✉çã♦ ❡ ❡①♣r❡ssã♦ ❞❡ ❣❡♥❡s ❡♠ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❝é✲ ❧✉❧❛s ✭❡❧❡tr♦tr❛♥s❢♦r♠❛çã♦✮ ✐♥❝❧✉✐♥❞♦ ❜❛❝tér✐❛s ✭❙❚❯❈❑❊◆ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ❧❡✈❡❞✉r❛s ✭❉❊▲❖❘▼❊✱ ✶✾✽✾✮✱ ❝é❧✉❧❛s ✈❡❣❡t❛✐s ✭❋❘❖▼▼❀ ❚❆❨▲❖❘❀ ❲❆▲✲ ❇❖❚✱ ✶✾✽✺✮✱ ❛♥✐♠❛✐s ✭P❊◆● ❡t ❛❧✳✱ ✷✵✶✷✮ ❡ ❤✉♠❛♥❛s ✭❩■▼▼❊❘▼❆◆◆ ❡t ❛❧✳✱ ✷✵✵✵✮✱ ♥♦ tr❛♥s♣♦rt❡ ❞❡ ❞r♦❣❛s ❝♦♠ ✜♥❛❧✐❞❛❞❡ t❡r❛♣ê✉t✐❝❛ ❝♦♠♦ ♥♦ tr❛t❛♠❡♥t♦ ❞❡ ❝â♥❝❡r ✭❙❯◆❉❆❘❆❘❆❏❆◆ ❡t ❛❧✳✱ ✷✵✶✶❀ ❑❖❚❯▲❙❑❆❀ ❑❯▲✲ ❇❆❈❑❆❀ ❙❆❈❩❑❖✱ ✷✵✶✸✮✱ ❛❧é♠ ❞❡ ❛♣❧✐❝❛çõ❡s ❡♠ ✐♥❞ústr✐❛ ❛❧✐♠❡♥tí❝✐❛ ✭▼❆❍◆■❷✲❑❆▲❆▼■❩❆❀ ❱❖❘❖❇■❊❱✱ ✷✵✶✹✮ ❝♦♠♦ ♥❛ ❡①tr❛çã♦ ♣r♦t❡✐❝❛✱ ❛ q✉❛❧ ♠♦str♦✉ s❡r ♠❛✐s ❡✜❝✐❡♥t❡ ❞♦ q✉❡ ♠ét♦❞♦s ❞❡ ❡①tr❛çã♦ ❜❛s❡❛❞♦s ♥❛ ❧✐s❡ ❝❡❧✉❧❛r ♠❡❝â♥✐❝❛ ❡ q✉í♠✐❝❛ ✭●❆◆❊❱❆❀ ●❆▲❯❚❩❖❱✱ ✶✾✾✾❀●❆◆❊❱❆ ❡t ❛❧✳✱ ✷✵✵✶❀❘❆▼❖❙❀ ❙❈❍◆❊■❉❊❘✱ ✷✵✶✷✮✳
P♦r ♦✉tr♦ ❧❛❞♦✱ ❝❛♠♣♦s ❡❧étr✐❝♦s ❞❡ ❛❧t❛ ✐♥t❡♥s✐❞❛❞❡ ♣♦❞❡♠ ♣r♦✈♦❝❛r ❞❛♥♦ ♣❡r♠❛♥❡♥t❡ ♥❛ ♠❡♠❜r❛♥❛ ❞❡✈✐❞♦ ❛♦ ❛✉♠❡♥t♦ ❞❡♠❛✲ s✐❛❞♦ ❞♦s ♣♦r♦s ❝r✐❛❞♦s✱ ❧❡✈❛♥❞♦ à ❧✐s❡ ❝❡❧✉❧❛r ✭❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ✐rr❡✈❡rsí✈❡❧✮✳ ❊st❛ é ✉t✐❧✐③❛❞❛ ♥❛ ✐♥❛t✐✈❛çã♦ ♠✐❝r♦❜✐❛❧✱ ❝♦♠ ❛♣❧✐❝❛çõ❡s ❛ tr❛t❛♠❡♥t♦ ❞❡ á❣✉❛ ✭❚❊■❙❙■➱ ❡t ❛❧✳✱ ✷✵✵✷✮✱ ❡♠ ✐♥❞ústr✐❛s ❛❧✐♠❡♥tí❝✐❛s ♥♦ ♣r♦❝❡ss♦ ❞❡ ♣❛st❡✉r✐③❛çã♦ ❛ ❢r✐♦ ✭❊▲✲❍❆●❀ ❏❆❨❆❘❆▼❀ ●❘■❋❋■❚❍❙✱ ✷✵✵✻✮ ❡ ❡st❡r✐❧✐③❛çã♦ s❡❧❡t✐✈❛ ✭❙❆■❚❖❀ ▼■◆❆▼■❚❆◆■✳✱ ✷✵✶✸✮✱ ❛ss✐♠ ❝♦♠♦ ♥❛ ❡①✲ tr❛çã♦ ❞❡ ♠❛t❡r✐❛❧ ❣❡♥ét✐❝♦ ✭●❊◆● ❡t ❛❧✳✱ ✷✵✶✷❀ ❍❯◆●❀ ❈❍❆◆●✱ ✷✵✶✷❀ ❇❆❍■ ❡t ❛❧✳✱ ✷✵✶✶✮✳
❆ s❡❣✉✐r✱ sã♦ ❡①♣❧♦r❛❞♦s ♦s ♠♦❞❡❧♦s ❡ ❡q✉✐♣❛♠❡♥t♦s ✉t✐❧✐③❛❞♦s ❡♠ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✳
✷✸
❋✐❣✉r❛ ✶ ✕ ❊str✉t✉r❛ ♠♦❧❡❝✉❧❛r s✐♠♣❧✐✜❝❛❞❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ✭❇▲❯▼❊✱ ✷✵✵✹✮
❢♦s❢❛t♦ ❝♦❜r❡♠ ❛♠❜❛s s✉♣❡r❢í❝✐❡s ❡ ♦s á❝✐❞♦s ❣r❛①♦s ❝♦♥st✐t✉❡♠ ♦ ✐♥t❡✲ r✐♦r ❞❛ ❞✉♣❧❛ ❝❛♠❛❞❛✳ ❊♥tr❡ ❛s ♠♦❧é❝✉❧❛s ❢♦s❢♦❧✐♣í❞✐❝❛s✱ ❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r ♣♦ss✉✐ ♦✉tr❛s ❡str✉t✉r❛s ❞❡ ❢✉♥çõ❡s ❡s♣❡❝í✜❝❛s✱ ❝♦♠♦ ♣r♦t❡í♥❛s ❡ ❝❛♥❛✐s ✐ô♥✐❝♦s ❞❡ só❞✐♦✳ ❊♥tr❡t❛♥t♦✱ ❝♦♠♦ ❢♦r♠❛ ❞❡ ❣❡♥❡r❛❧✐③❛çã♦✱ ❡st❛s ❡str✉t✉r❛s sã♦ ❞❡s♣r❡③❛❞❛s ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛✲ çã♦ ❝❡❧✉❧❛r✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❢♦r♠❛çã♦ ❞❡ ♣♦r♦s ❡stá r❡❧❛❝✐♦♥❛❞❛ à ♣♦rçã♦ ❢♦s❢♦❧✐♣í❞✐❝❛ ❞❛ ♠❡♠❜r❛♥❛ ✭❚■❊◆❀ ❖❚❚❖❱❆✱ ✷✵✵✸✮✳
❆ ▼❉❈▲ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ✉♠ ❞✐❡❧étr✐❝♦ ❝♦♠ ♣❡r❞❛s s❡♣❛r❛♥❞♦ ❞✉❛s s♦❧✉çõ❡s ❝♦♥❞✉t♦r❛s✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ▼❉❈▲ ❝♦♠♣♦rt❛✲ s❡ ❝♦♠♦ ✉♠ ❞✐❡❧étr✐❝♦ ❡♠ ✉♠ ❝❛♣❛❝✐t♦r ♥♦ q✉❛❧✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡①t❡r♥♦✱ s❡ t♦r♥❛ ♣♦❧❛r✐③❛❞♦✳ ❊♠ ❝é❧✉❧❛s ❜✐♦❧ó❣✐❝❛s✱ ❛ ❝❛♣❛❝✐tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ár❡❛ ✭Cm✮ é r❛③♦❛✈❡❧♠❡♥t❡
❝♦♥st❛♥t❡✱ q✉❛s❡ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ t✐♣♦ ❞❡ ❝é❧✉❧❛✱ ❡♥tr❡ ✺ ❡ ✶✵ mF/m2
❝♦♠ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ r❡❧❛t✐✈❛ ❡♥tr❡ ✷ ❡ ✼ ✭❚■❊◆❀ ❖❚❚❖❱❆✱ ✷✵✵✸❀ ❋❊❚❚■P▲❆❈❊❀ ❆◆❉❘❊❲❙❀ ❍❆❨❉❖◆✱ ✶✾✼✶✮✳
❖ ♣♦♥t♦ ✐♥✐❝✐❛❧ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ é ❡st✐♠❛r ❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✐♥❞✉③✐❞❛ ♥❛ ♠❡♠❜r❛♥❛✳ ❊st❛ é ❢❛✲ ❝✐❧♠❡♥t❡ ❡st✐♠❛❞❛ ♣❛r❛ ♦ ❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦ ❛♣ós ❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❝♦♥st❛♥t❡✳ ◆❡st❡ ❝❛s♦✱ ❝♦♠♦ ❛ ♠❡♠❜r❛♥❛ ❝♦♠♣♦rt❛✲s❡ ❝♦♠♦ ✉♠ ✐s♦❧❛♥t❡✱ ❛ ♣♦rçã♦ ✐♥t❡r✐♦r ❞❛ ❝é❧✉❧❛ s❡rá ❡q✉✐♣♦t❡♥❝✐❛❧✳ ❉❡st❛ ❢♦r♠❛✱ ❛ t❡♥sã♦ tr❛♥s♠❡♠❜r❛♥❛ ✭vm✮ s❡rá ❞❡♣❡♥❞❡♥t❡ s♦♠❡♥t❡ ❞♦ r❛✐♦ ❝❡❧✉❧❛r
✭R✮ ❡ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞❛ ✭E✮✿
vm=
3
✷✹
♦♥❞❡ θ é ♦ â♥❣✉❧♦ ❡♥tr❡ ♦ ✈❡t♦r ♥♦r♠❛❧ à ♠❡♠❜r❛♥❛ ♦♥❞❡ s❡ ❞❡s❡❥❛ ❝❛❧❝✉❧❛r ❛ t❡♥sã♦ ❡ ♦ ✈❡t♦r ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ❊st❛ é ✉♠❛ ❡q✉❛çã♦ ❝❧áss✐❝❛ ❞❛ t❡♦r✐❛ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❡q✉❛çã♦ ❞❡ ❙❝❤✇❛♥ ✭❙❈❍❲❆◆✱ ✶✾✺✼✮✳
❖ ❝❛s♦ ❣❡r❛❧ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ♣❡❧❛ s❡❣✉✐♥t❡ ❡q✉❛çã♦✿
vm=FsR Ecosθ ✭✷✳✷✮
♦♥❞❡ Fs é ✉♠❛ ❢✉♥çã♦ q✉❡ ❞❡s❝r❡✈❡ ❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s
❣❡♦♠étr✐❝❛s ❡ ❡❧étr✐❝❛s ❞❛ ❝é❧✉❧❛ ❡ ❛ t❡♥sã♦ tr❛♥s♠❡♠❜r❛♥❛ ✐♥❞✉③✐❞❛✳ P❛r❛ ♦ ❝❛s♦ ❡st❛❝✐♦♥ár✐♦ ❝♦♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❝♦♥st❛♥t❡✱ ♦♥❞❡ ❛ ❝♦♥✲ ❞✉t✐✈✐❞❛❞❡ ❞❛ ♠❡♠❜r❛♥❛ é ❝♦♥s✐❞❡r❛❞❛ ♥ã♦ ♥✉❧❛✱ Fs é ❞❡s❝r✐t♦ ♣❡❧❛
s❡❣✉✐♥t❡ ❡q✉❛çã♦✱ ❝♦♠♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ✭❑❖❚◆■❑❀ ❇❖❇❆◆❖❱■❶❀ ▼■✲ ❑▲❆❱❷■❷✱ ✶✾✾✼✮✳
Fs=
3σo3hR2σi+ 3h2R−h3(σm−σi)
2R3(σ
m+ 2σo)
σm+σi
2
−2 (R−h)3(σo−σm) (σi−σm)
✭✷✳✸✮
♦♥❞❡σm✱ σi ❡ σo sã♦ ❛s ❝♦♥❞✉t✐✈✐❞❛❞❡s ❞❛ ♠❡♠❜r❛♥❛ ❡ ❞♦s ♠❡✐♦s ✐♥✲
t❡r♥♦ ❡ ❡①t❡r♥♦ ❛ ❡❧❛ ❡h✱ ❛ ❡s♣❡ss✉r❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r ✭❋✐❣✉r❛ ✷✮✳ ❊♥tr❡t❛♥t♦✱ ❝❛s♦ ❛ ❝é❧✉❧❛ s❡❥❛ ❡①♣♦st❛ ❛ ❝❛♠♣♦s ❞❡ ❝♦rr❡♥t❡ ❛❧t❡r♥❛❞❛ ✭❈❆✮ ❞❡ ❜❛✐①❛ ❢r❡q✉ê♥❝✐❛✱ ❛ ❝❛♣❛❝✐tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ❞❡✈❡ t❛♠❜é♠ s❡r ❝♦♥s✐❞❡r❛❞❛✳ P❛r❛ t❛❧✱ s✉❜st✐t✉✐✲s❡ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❛ ❝é❧✉❧❛ σm
♣❡❧❛ s✉❛ ❛❞♠✐t✐✈✐❞❛❞❡✱ ♦✉ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠♣❧❡①❛ γm =σm+jωεm✱
♦♥❞❡ ω é ❛ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❞♦ ❝❛♠♣♦ ❡ εm é ❛ ♣❡r♠✐ss✐✈✐❞❛❞❡ ❞❛
♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✳ ◆❡st❡ ❝❛s♦✱ ❛ t❡♥sã♦ ✐♥❞✉③✐❞❛ é ❞❛❞❛ ♣❡❧❛ ❊q✉❛✲ çã♦ ✷✳✹✳
vm= 3
2R Ecosθ 1
1 +jωτm ✭✷✳✹❛✮
τm=RCm 1
σi +
1 2σo
✭✷✳✹❜✮ ♦♥❞❡ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ q✉❡σm≪σi, σo ❡h≪R✱ r❡✢❡t✐♥❞♦ ❛s ❝♦♥❞✐çõ❡s
♥❛t✉r❛✐s ❞❛s ❝é❧✉❧❛s✱ Cm = εm/h é ❛ ❝❛♣❛❝✐tâ♥❝✐❛ ❞❡ ♠❡♠❜r❛♥❛ ♣♦r
✉♥✐❞❛❞❡ ❞❡ ár❡❛ ❡τmé ♦ t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ♣❛r❛ ❛❝✉♠✉❧❛çã♦ ❞❡ ❝❛r❣❛s
✷✺
❋✐❣✉r❛ ✷ ✕ ▼♦❞❡❧♦ ❣❡♦♠étr✐❝♦ ❞❛ ❝é❧✉❧❛✱ γm✱ γi ❡ γo sã♦ ❛s ❝♦♥❞✉t✐✲
✈✐❞❛❞❡s ❝♦♠♣❧❡①❛s ❞❛ ♠❡♠❜r❛♥❛ ❡ ❞♦s ♠❡✐♦s ✐♥t❡r♥♦ ❡ ❡①t❡r♥♦ à ❡❧❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ σ ❡ ε ❞❡♥♦t❛♠ ❛s ❝♦♥❞✉t✐✈✐❞❛❞❡s ❡ ♣❡r♠✐ss✐✈✐❞❛❞❡s ❞❡ ❝❛❞❛ ♠❡✐♦✱ω é ❛ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦✱θé ♦ â♥❣✉❧♦ ♣♦❧❛r ♠❡❞✐❞♦ ❝♦♠ r❡❧❛çã♦ ❛♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦ E✱ R é ♦ r❛✐♦ ❝❡❧✉❧❛r ❡h✱ ❛ ❡s♣❡ss✉r❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r
❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ✭❩❖❯ ❡t ❛❧✳✱ ✷✵✶✺✮
❊♠ ❢r❡q✉ê♥❝✐❛s ♠❛✐s ❛❧t❛s✱ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞✐❡❧étr✐❝❛s ❞♦ ❝✐✲ t♦♣❧❛s♠❛ ❡ ❞♦ ♠❡✐♦ ❡①tr❛❝❡❧✉❧❛r ❞❡✈❡♠ s❡r ❧❡✈❛❞❛s ❡♠ ❝♦♥t❛✳ ❙✉❜s✲ t✐t✉✐♥❞♦ ❛s ❝♦♥❞✉t✐✈✐❞❛❞❡s σi✱ σm ❡ σo ♣❡❧❛s ❛❞♠✐t✐✈✐❞❛❞❡s γi✱ γm ❡
γo ♥❛ ❊q✉❛çã♦ ✷✳✸✱ ❛♣ós ❛❧❣✉♠❛s s✐♠♣❧✐✜❝❛çõ❡s ♦❜té♠✲s❡ ❛s ❊q✉❛çõ❡s
✷✳✺❛✱ ❜ ❡ ❝ ✭❩❖❯ ❡t ❛❧✳✱ ✷✵✶✺✮✳
vm=
3
2R Ecosθ
1 +jωτm2
1 +jωτm1 ✭✷✳✺❛✮
τm1=RCm
1
σi
+ 1 2σo
✭✷✳✺❜✮
τm2= εi+ 2εo
σi+ 2σo ✭✷✳✺❝✮
♦♥❞❡τm1é ♦ ♣r✐♠❡✐r♦ t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ❡τm2é ♦ s❡❣✉♥❞♦ t❡♠♣♦ ❞❡
r❡❧❛①❛çã♦ ❞❛ ♠❡♠❜r❛♥❛✳
✷✻
❆❧é♠ ❞♦ ♣♦t❡♥❝✐❛❧ tr❛♥s♠❡♠❜r❛♥❛ ✐♥❞✉③✐❞♦ ♣❡❧♦ ♣✉❧s♦ ❞❡ ❡❧❡✲ tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✱ ❛s ❝é❧✉❧❛s ❡♠ r❡♣♦✉s♦ ❛♣r❡s❡♥t❛♠ ✉♠ ✈❛❧♦r ❞❡ ♣♦✲ t❡♥❝✐❛❧ tr❛♥s♠❡♠❜r❛♥❛ ❞❡✈✐❞♦ à ❞✐❢❡r❡♥ç❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❡♥tr❡ í♦♥s ♣♦s✐t✐✈♦s ❡ ♥❡❣❛t✐✈♦s ♥♦ ✐♥t❡r✐♦r ❞❛ ❝é❧✉❧❛ ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❡ ♠❡❝❛♥✐s✲ ♠♦s ✜s✐♦❧ó❣✐❝♦s✳ ❊st❡ ♣♦t❡♥❝✐❛❧ é ❞❛ ♦r❞❡♠ ❞❡ −180 / vrep / −30 mV✭❚❊❑▲❊❀ ❆❙❚❯▼■❆◆❀ ❈❍❖❈❑✱ ✶✾✾✵✮✱ ♣♦❞❡♥❞♦ ❝❛✉s❛r ❛ss✐♠❡tr✐❛ ♥❛
❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❢❛❝❡ ❞❛ ❝é❧✉❧❛ ✈♦❧t❛❞❛ ❛♦ ❡❧❡tr♦❞♦ ♣♦s✐t✐✈♦ ❡①♣❡r✐♠❡♥t❛ ✉♠ ♣♦t❡♥❝✐❛❧ tr❛♥s♠❡♠❜r❛♥❛ ❛❝r❡s❝✐❞♦ ❞❡ 2vrep
❡♠ r❡❧❛çã♦ à ❢❛❝❡ ✈♦❧t❛❞❛ ❛♦ ❡❧❡tr♦❞♦ ♥❡❣❛t✐✈♦✳ ❯♠❛ ❢♦r♠❛ ❞❡ ♠✐♥✐♠✐✲ ③❛r ❡st❡ ❡❢❡✐t♦ é ❛ ✉t✐❧✐③❛çã♦ ❞❡ ♣✉❧s♦s ❜✐♣♦❧❛r❡s ❞❡ t❡♥sã♦✱ ♥♦ ❡♥t❛♥t♦✱ ❝♦♠♦ ❡st✉❞❛❞♦ ♣♦r ✭❉❊❇❘❯■◆❀ ❑❘❆❙❙❖❲❙❑❆✱ ✶✾✾✾✮✱ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ r❡✲ ♣♦✉s♦ só ❝❛✉s❛ ❛ss✐♠❡tr✐❛ ❛♣r❡❝✐á✈❡❧ q✉❛♥❞♦ s❡ ✉t✐❧✐③❛♠ ♣✉❧s♦s ♠✉✐t♦ ❝✉rt♦s ♦✉ ❞❡ ❜❛✐①❛ ✐♥t❡♥s✐❞❛❞❡✳
❆ ♣❛rt✐r ❞❡st❡s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s✱ ♦s t✐♣♦s ❞❡ ♠♦❞❡❧❛❣❡♠ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ s❡ ❞✐✈✐❞❡♠ ❡♠ ❞✉❛s ❝❛t❡❣♦r✐❛s✿ ✭■✮ ❛s q✉❡ ♣r♦✲ ❝✉r❛♠ ❞❡s❝r❡✈❡r ♦ ♣r♦❝❡ss♦ ❞❡ ❡❧❡tr♦♣♦r❛çã♦ ♠♦❞❡❧❛♥❞♦ ❛ ❢♦r♠❛çã♦ ❞❡ ♣♦r♦s ❡ ❛ t❡♥sã♦ ❞❡ r✉♣t✉r❛vm✭♠❡❝❛♥✐s♠♦s ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✮
❡ ✭■■✮ ❛s q✉❡ ❞❡s❝r❡✈❡♠ ❛s ♠✉❞❛♥ç❛s ❡❧étr✐❝❛s ❛♣ós ❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐✲ ③❛çã♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♦❜t❡r ♦ ❡st❛❞♦ ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛t✐♥❣✐❞♦ ✭♠♦❞❡❧❛❣❡♠ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛ ♥í✈❡❧ ♠❛❝r♦s❝ó♣✐❝♦✮✳
✷✳✶✳✶ ▼❡❝❛♥✐s♠♦s ❞❡ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦
❆s ♣r✐♠❡✐r❛s t❡♥t❛t✐✈❛s ❞❡ ✐♥✈❡st✐❣❛r ♦s ♠❡❝❛♥✐s♠♦s ❞❛ ❡❧❡✲ tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❝❡❧✉❧❛r ❜❛s❡❛r❛♠✲s❡ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❡❧❡tr♦♠❡❝â♥✐❝❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ❢♦✐ s✉❣❡r✐❞♦ q✉❡ ❛ ❝♦♠♣r❡ssã♦ ❞❛ ♠❡♠❜r❛♥❛ s♦❜ ❛ ❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ s❡r✐❛ r❡s♣♦♥✲ sá✈❡❧ ♣❡❧❛ r✉♣t✉r❛ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✳ ❊st❛ ❢♦✐ ♠♦❞❡❧❛❞❛ ❝♦♠♦ ✉♠ ❝❛♣❛❝✐t♦r ❡❧ást✐❝♦ ♥❛ q✉❛❧✱ ❞♦ ❡q✉✐❧í❜r✐♦ ❡♥tr❡ ❛s ❢♦rç❛s ❡❧étr✐❝❛ ❡ ❡❧ást✐❝❛ é ♣♦ssí✈❡❧ ♦❜t❡r ♦ ✈❛❧♦r ❞❡ t❡♥sã♦ ❝rít✐❝❛Vc ♥♦ q✉❛❧ ♦ s✐st❡♠❛ t♦r♥❛✲s❡
✷✼
❜❛s❡✐❛♠✲s❡ ♥❛ ❢♦r♠❛çã♦ ❞❡ ♣♦r♦s ♥❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r✳ ❊st❡s ♠♦❞❡✲ ❧❛♠ ❛ ♠❡♠❜r❛♥❛ ❝♦♠♦ ✉♠ s✐st❡♠❛ ♠❡t❛❡stá✈❡❧ ✭❢❡♥ô♠❡♥♦ ❡♠ q✉❡ ✉♠ s✐st❡♠❛ ♣❡r♠❛♥❡❝❡ ❡♠ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❞✐❢❡r❡♥t❡ ❞❛ ❞❡ ♠❡♥♦r ❡♥❡r✲ ❣✐❛✮✳ ❆ ❝❛r❛❝t❡ríst✐❝❛ ♠❡t❛❡stá✈❡❧ ❞❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r é ❡✈✐❞❡♥t❡✱ ✉♠❛ ✈❡③ q✉❡ é ♥❡❝❡ssár✐❛ ❛ r❡❛❧✐③❛çã♦ ❞❡ tr❛❜❛❧❤♦ ♣❛r❛ ❢♦r♠❛r ♠❡♠❜r❛♥❛s ❛rt✐✜❝✐❛✐s ❛ ♣❛rt✐r ❞❡ ❧✐♣í❞✐♦s ❡♠ s♦❧✉çã♦✳ ❖✉ s❡❥❛✱ ❛ t❡♥sã♦ ❞❛ ♠❡♠✲ ❜r❛♥❛ Γ✭❡♥❡r❣✐❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ár❡❛✮ é ♣♦s✐t✐✈❛✳ ■st♦ ✐♠♣❧✐❝❛ ❡♠ q✉❡
♦ ❡st❛❞♦ ❡♠ q✉❡ ♦s ❧✐♣í❞✐♦s ❞❛ ♠❡♠❜r❛♥❛ ❡stã♦ ❞❡s♦r❣❛♥✐③❛❞♦s é ♦ ❡s✲ t❛❞♦ ❞❡ ♠❡♥♦r ❡♥❡r❣✐❛ ❧✐✈r❡✳ ▲♦❣♦✱ ❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r é ✉♠ s✐st❡♠❛ ♠❡t❛❡stá✈❡❧✳ ❆ ❡❧❡tr♦♣♦r❛çã♦ é ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ✭♥✉❝❧❡❛çã♦✮ ❞❡ ✉♠❛ ♥♦✈❛ ❢❛s❡ ❛ ♣❛rt✐r ❞❛ ❢❛s❡ ✐♥t❛❝t❛✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ❊st❡ ❡st✉❞♦ ❢♦✐ ✐♥✐❝✐❛❧♠❡♥t❡ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❈❤✐③♠❛❞③❤❡✈ ❡ ❝♦❧❡❣❛s ❡♠ ✉♠❛ sér✐❡ ❞❡ s❡t❡ ❛rt✐❣♦s s♦❜r❡ ♦ ❛ss✉♥t♦ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❞❡ ♠❡♠❜r❛♥❛s ❛rt✐✜❝✐❛✐s✱ s❡♥❞♦ ✉♠ ❞❡❧❡s ❝✐t❛❞♦ ❛q✉✐ ✭❈❍■❩▼❆❉❩❍❊❱❀ ❆❘❆❑❊▲❨❆◆❀ P❆❙❚❯❙❍❊◆❑❖✱ ✶✾✼✾✮✳ ❯♠ tr❛❜❛✲ ❧❤♦ ♠❛✐s r❡❝❡♥t❡ ✭❈❍■❩▼❆❉❩❍❊❱❀ ❚❊■❙❙■➱❀ ❲❆▲❩✱ ✷✵✵✹✮ ❛♣r❡s❡♥t❛ ✉♠❛ ✈❡rsã♦ ❝♦♥t✐♥✉❛❞❛ ❡ ♠❛✐s ❝♦♠♣❛❝t❛ ❞❡st❡ tr❛❜❛❧❤♦✳
❆ ❛❜♦r❞❛❣❡♠ ❜ás✐❝❛ ♣❛r❛ ❛ ❢♦r♠❛çã♦ ❞❡ ♣♦r♦s ❝♦♥s✐❞❡r❛ ♦ ❜❛✲ ❧❛♥ç♦ ❞❡ ❡♥❡r❣✐❛ ♥❛ ♠❡♠❜r❛♥❛✱ ❛ q✉❛❧ ✐♥✐❝✐❛❧♠❡♥t❡✱ ♣♦ss✉✐ ❡♥❡r❣✐❛ Γ
♣♦r ✉♥✐❞❛❞❡ ❞❡ ár❡❛✳ ◗✉❛♥❞♦ ✉♠ ♣♦r♦ ❝✐r❝✉❧❛r é ❝r✐❛❞♦✱ ❤á ✉♠ ❣❛♥❤♦ ❞❡ ❡♥❡r❣✐❛ r❡❧❛❝✐♦♥❛❞♦ ❛ ❝r✐❛çã♦ ❞❡ ✉♠ ❛rr❛♥❥♦ ❝✐r❝✉❧❛r ❞❡ ♠♦❧é❝✉❧❛s s♦❜ t❡♥sã♦ ❞❡♥♦t❛❞♦ ♣♦rγ ✭❛ ❡♥❡r❣✐❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❛♦ ❧♦♥❣♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ♥❡❝❡ssár✐❛ ♣❛r❛ ❢♦r♠❛r ♦ ♣♦r♦✮✳ ❈♦♥t✉❞♦✱ ❤á t❛♠❜é♠ ✉♠❛ r❡❞✉çã♦ ♥❛ ❡♥❡r❣✐❛ ❞❡✈✐❞♦ à ♣❡r❞❛ ❞♦ ❢♦r♠❛t♦ ❞❡ ❞✐s❝♦ ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❞❛ ♠❡♠❜r❛♥❛✳ ❊st❛ t❡♦r✐❛ ❧❡✈❛ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❡①♣r❡ssõ❡s ❝❛♣❛③❡s ❞❡ ❡①♣❧✐❝❛r ❛ ♥❛t✉r❡③❛ ❡st♦❝ást✐❝❛ ❞❛ ❢♦r♠❛çã♦ ❞❡ ♣♦r♦s✱ ❛tr❛✈és ❞❡ ❡q✉❛çõ❡s q✉❡ r❡❧❛❝✐♦♥❛♠ ❛ ✈❛r✐❛çã♦ ❞❛ ❡♥❡r❣✐❛ ❞❛ ♠❡♠❜r❛♥❛ ❡♠ ❢✉♥çã♦ ❞♦ t❛♠❛♥❤♦ ❡ ♥ú♠❡r♦ ❞❡ ♣♦r♦s ❝r✐❛❞♦s✱ ❛❧é♠ ❞❡ ❡①♣❧✐❝❛r ♦✉tr♦s ❢❛t♦r❡s✱ ❝♦♠♦ ❛ ❝r✐❛çã♦ ❡s♣♦♥tâ♥❡❛ ❞❡ ♣♦r♦s ❤✐❞r♦❢ó❜✐✲ ❝♦s ♥❛ ♠❡♠❜r❛♥❛ ❝❡❧✉❧❛r ❞❡✈✐❞♦ à ✢✉t✉❛çõ❡s tér♠✐❝❛s ❡ ♦ ❢❡♥ô♠❡♥♦ ❞❛ r❡ss❡❧❛❣❡♠ ✭❢❡❝❤❛♠❡♥t♦✮ ❞♦s ♣♦r♦s ❛♣ós ✉♠ ❝❡rt♦ ♣❡rí♦❞♦ ❞❛ r❡♠♦çã♦ ❞♦ ❝❛♠♣♦ ✭❞❛ ♦r❞❡♠ ❞❡ ♠✐♥✉t♦s✮✳
✷✽
◆♦ ❡st✉❞♦ r❡❛❧✐③❛❞♦ ♣♦r ✭❚❆❘❊❑✱ ✷✵✵✺✮✱ ❛ ❝✐♥ét✐❝❛ ❞❛ ❢♦r♠❛✲ çã♦ ❞❡ ♣♦r♦s ♥❛ ♠❡♠❜r❛♥❛ ♠♦str♦✉ s❡r ❞❡♣❡♥❞❡♥t❡ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ❛♣❧✐❝❛❞♦✳ P❛r❛ ✉♠❛ t❡♥sã♦ tr❛♥s♠❡♠❜r❛♥❛ ❞❡ ✵✱✶ ❱✱ ♦s ♣r✐✲ ♠❡✐r♦s ❝❛♥❛✐s ❝♦♠❡ç❛r❛♠ ❛ s❡ ❢♦r♠❛r ❞❡♥tr♦ ❞❡ ✉♠ ♥❛♥♦ s❡❣✉♥❞♦✳ ❏á ♣❛r❛ ✉♠❛ t❡♥sã♦ ❞❡ ✵✱✷ ❱✱ ♦ ♣r♦❝❡ss♦ ❢♦✐ ♠❛✐s rá♣✐❞♦✱ ❧❡✈❛♥❞♦ ❝❡r❝❛ ❞❡ ✷✵✵ ♣✐❝♦ s❡❣✉♥❞♦s✳ ❆ ❢♦r♠❛çã♦ ❞♦s ♣♦r♦s ❤✐❞r♦❢í❧✐❝♦s é ♠❛✐s ❞❡♠♦r❛❞❛✱ ❝❡r❝❛ ❞❡ ✹ ♥❛♥♦ s❡❣✉♥❞♦s ♣❛r❛ ❛ t❡♥sã♦ tr❛♥s♠❡♠❜r❛♥❛ ❞❡ ✵✱✶ ❱ ❡ ✶ ♥❛♥♦ s❡❣✉♥❞♦ ♣❛r❛ ✵✱✷ ❱✳
✷✳✶✳✷ ▼♦❞❡❧❛❣❡♠ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛ ♥í✈❡❧ ♠❛❝r♦s✲ ❝ó♣✐❝♦
❖s ♠♦❞❡❧♦s ❞❡ ♠❡❝❛♥✐s♠♦s ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛♣r❡s❡♥✲ t❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ sã♦ ❜❡♠ ❛❞❡q✉❛❞♦s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❛s ♠✉❞❛♥ç❛s ❡str✉t✉r❛✐s q✉❡ ♦❝♦rr❡♠ ♥❛ ♣❛r❡❞❡ ❝❡❧✉❧❛r ❞❡✈✐❞♦ ❛♦ ♣r♦❝❡ss♦ ❞❡ ❡❧❡✲ tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦✳ ❊♥tr❡t❛♥t♦✱ ❡st❡s ♠♦❞❡❧♦s sã♦ ♠✉✐t♦ ❝♦♠♣❧❡①♦s✱ s❡♥❞♦ ❛ss✐♠✱ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ✐♥✈✐á✈❡✐s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ ❣r❛♥❞❡s ❡str✉t✉r❛s ❝♦♠♦ é ♦ ❝❛s♦ ❞❡ ✉♠❛ ❝é❧✉❧❛ ❜✐♦❧ó❣✐❝❛✳ ❊st❡s sã♦ ❛♣❧✐❝❛❞♦s à ❣❡♦♠❡tr✐❛s s✐♠♣❧✐✜❝❛❞❛s✱ ♦♥❞❡ ❝♦♥s✐❞❡r❛✲s❡ ✉♠❛ ♠❡♠❜r❛♥❛ ♣❧❛♥❛r tr✉♥❝❛❞❛✳ ➱ ♣♦rt❛♥t♦✱ ♥❡❝❡ssár✐♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠♦❞❡❧♦s ♠❛✲ ❝r♦s❝ó♣✐❝♦s ♣❛r❛ ❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❝❡❧✉❧❛r ❝❛♣❛③❡s ❞❡ ♠♦❞❡❧❛r ❝é❧✉❧❛s ✐s♦❧❛❞❛s ❡ ❝é❧✉❧❛s ❡♠ s✉s♣❡♥sã♦✳
❈♦♠♦ ❞✐s❝✉t✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❛ ❝r✐❛çã♦ ❞❡ ♣♦r♦s ♥❛ ♠❡♠✲ ❜r❛♥❛ ❝❡❧✉❧❛r ❞❡✈✐❞♦ à ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ✐♥t❡♥s♦ ❛✉♠❡♥t❛ ❛ s✉❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ ❢❛❝✐❧✐t❛♥❞♦ ❛ ♣❛ss❛❣❡♠ ❞❡ í♦♥s ❛tr❛✈és ❞❛ ♠❡♠✲ ❜r❛♥❛✳ ❊st❡ ❛✉♠❡♥t♦ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ s❡ r❡✢❡t❡ ♠❛❝r♦s❝♦♣✐❝❛♠❡♥t❡ ❝♦♠♦ ✉♠ ❛✉♠❡♥t♦ ♥❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞❛ ❛♠♦str❛✱ ♣♦✐s ❛ ❝♦r✲ r❡♥t❡ ❡❧étr✐❝❛ q✉❡ ❛♥t❡s ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❝✐r❝✉❧❛✈❛ s♦♠❡♥t❡ ♥♦ ♠❡✐♦ ❡①t❡r✐♦r às ❝é❧✉❧❛s✱ ❡♥❝♦♥tr❛ ✉♠ ❝❛♠✐♥❤♦ ❛❧t❡r♥❛t✐✈♦ ♣❡❧♦ ✐♥t❡✲ r✐♦r ❞❛s ❝é❧✉❧❛s✳ P♦r ❡st❡ ♠♦t✐✈♦✱ s✉r❣❡ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♠♦❞❡❧❛r ♦ ❢❡♥ô♠❡♥♦ ❞❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛çã♦ ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❞❛ ❝♦♥❞✉t✐✈✐✲ ❞❛❞❡ ❞❛ ❛♠♦str❛✳ ❯♠ ❡①❡♠♣❧♦ é ♦ ♠♦❞❡❧♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ✭P❆❱▲■◆ ❡t ❛❧✳✱ ✷✵✵✺✮✱ ❡st❡ ✉t✐❧✐③❛ ❞❡ ✉♠❛ ❡st✐♠❛t✐✈❛ ❞♦ ✈❛❧♦r ❞❡ t❡♥sã♦ tr❛♥s♠❡♠✲ ❜r❛♥❛ ❝rít✐❝❛vc ❛ ♣❛rt✐r ❞♦ q✉❛❧ ❝❛❧❝✉❧❛✲s❡ ♦ â♥❣✉❧♦ ❝rít✐❝♦ ✉t✐❧✐③❛♥❞♦ ❛
❡q✉❛çã♦ ❞❡ ❙❝❤✇❛♥ ✭❊q✉❛çã♦ ✷✳✶✮ ♣❛r❛ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦✳ ❆s ❝♦♥❞✉t✐✈✐❞❛❞❡s ❞❛ ❝é❧✉❧❛ ❡ ❞❛ s✉s♣❡♥sã♦ sã♦ r❡❧❛❝✐♦♥❛❞❛s ❛ ♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❞❡ ▼❛①✇❡❧❧ ✭▼❆❳❲❊▲▲✱ ✶✽✼✸✮✿
σs−σo
σs+ 2σo
=pσc−σo
σc+ 2σo ✭✷✳✻✮
✷✾
♣❛rt❡ ♥ã♦ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛ ❡ ✉t✐❧✐③❛♥❞♦ ❛ ❡q✉❛çã♦ ❞❡ P❛✉❧②✲❙❝❤✇❛♥ ✭P❆❯▲❨❀ ❙❈❍❲❆◆✱ ✶✾✺✾✮✱ q✉❡ ❞❡✜♥❡ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❡ ✉♠❛ ❡s❢❡r❛ ❝♦♠ ✉♠❛ ❝❛s❝❛ ❝♦♥❞✉t♦r❛✿
σc=σm
2 (1−ν)σm+ (1 + 2ν)σi
(2 +ν)σm+ (1−ν)σi ✭✷✳✼❛✮
ν = (1−h/R)3 ✭✷✳✼❜✮
❆❧é♠ ❞✐ss♦✱ ❛ss✉♠❡✲s❡ q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♣♦r♦s ❡ ♦ t❛♠❛✲ ♥❤♦ ❞❡st❡s ♣❡r♠❛♥❡❝❡ ❝♦♥st❛♥t❡ ♥❛ ár❡❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛✱ ✐♥❞❡♣❡♥✲ ❞❡♥t❡ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✳ ❆ss✐♠✱ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❡✜♥❡ s♦♠❡♥t❡ ❛ ár❡❛ ❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛ ✭❊q✉❛çã♦ ✷✳✽✮✳ ❊♥tr❡t❛♥t♦✱ ❡st❛ s✐♠♣❧✐✜❝❛çã♦ é ✉♠ t❛♥t♦ q✉❛♥t♦ ❣r♦ss❡✐r❛✱ ♣♦✐s ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♣♦r♦s é ❞✐r❡t❛♠❡♥t❡ ❞❡♣❡♥❞❡♥t❡ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ✭❊q✉❛çã♦ ✷✳✶✵✮✱ s❡♥❞♦ ♠á①✐♠❛ ♥♦s ♣♦❧♦s ❞❛ ❝é❧✉❧❛ ❝♦♠♦ ❞✐s❝✉t✐❞♦ ❡♠ ✭❉❊❇❘❯■◆❀ ❑❘❆❙❙❖❲❙❑❆✱ ✶✾✾✾✮✳
Sc =So(1−Ec/E) ✭✷✳✽✮
❖s r❡s✉❧t❛❞♦s ❞❡ â♥❣✉❧♦ ❝rít✐❝♦ θc ❡ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❛ ♣♦rçã♦
❡❧❡tr♦♣❡r♠❡❛❜✐❧✐③❛❞❛ ❞❛ ♠❡♠❜r❛♥❛ σm ♦❜t✐❞♦s ❛tr❛✈és ❞❡st❛ ♠♦❞❡✲
❧❛❣❡♠✱ sã♦ ✈❛❧✐❞❛❞♦s ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❛♥❛❧ít✐❝♦ ❞❡s❡♥✈♦❧✈✐❞♦ ❡♠ ✭P❆❱▲■◆❀ ▼■❑▲❆❱❷■❷✱ ✷✵✵✸✮ ❡ s✐♠✉❧❛çõ❡s ❡♠ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ◆❡s✲ t❛s s✐♠✉❧❛çõ❡s✱ é ✉t✐❧✐③❛❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ♠❡♠❜r❛♥❛ ♥ã♦✲r❡❛❧íst✐❝♦ ❞❡ ✺✵✵ nm❛♦ ✐♥✈és ❞❡ ✺ nm✳ ■st♦ é ❢❡✐t♦ ❞❡✈✐❞♦ ❛ ❧✐♠✐t❛çõ❡s ❝♦♠♣✉t❛❝✐♦✲
♥❛✐s✱ ✉♠❛ ✈❡③ q✉❡ ❛ ❡s♣❡ss✉r❛ ❞❛ ♠❡♠❜r❛♥❛ é ✷✵✵✵ ✈❡③❡s ♠❡♥♦r ❞♦ q✉❡ ♦ r❛✐♦ ❝❡❧✉❧❛r✱ t♦r♥❛♥❞♦ ❝♦♠♣❧❡①❛ ❛ ❞✐s❝r❡t✐③❛çã♦ ❡s♣❛❝✐❛❧✳ P❛r❛ q✉❡ ❛ ❝é❧✉❧❛ ❝♦♠ ♠❡♠❜r❛♥❛ ❛✉♠❡♥t❛❞❛ t❡♥❤❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡q✉✐✈❛❧❡♥t❡ à ❞❛ ❝é❧✉❧❛ ♦r✐❣✐♥❛❧✱ ❛❥✉st❛✲s❡ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❡ ♠❡♠❜r❛♥❛ ♣❛r❛ q✉❡ ❛ ❝♦♥❞✉tâ♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ s❡❥❛ ❛ ♠❡s♠❛ ❞❛ ♦r✐❣✐♥❛❧ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
σm′ =
h′
hσm ✭✷✳✾✮
♦♥❞❡σm❡hsã♦ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡ ❛ ❡s♣❡ss✉r❛ ❞❛ ♠❡♠❜r❛♥❛ ❡σ′m❡h′
