Pr♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❡♠ ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s
❇ár❜❛r❛ ▲✉✐③❛ ❚❡✐①❡✐r❛ ❘♦s❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ✲ ❯❋▼● ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ✲ ■❈❊① Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
Pr♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❡♠ ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s
❇ár❜❛r❛ ▲✉✐③❛ ❚❡✐①❡✐r❛ ❘♦s❛
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ P❛✉❧♦ ❙ér❣✐♦ ❙♦❛r❡s ●✉✐♠❛rã❡s ❈♦✲♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ➶♥❣❡❧♦ ▼❛❧❛❝❤✐❛s ❞❡ ❙♦✉③❛
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✱ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞❡ ❚ít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❋ís✐❝❛✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞♦ ❊st❛❞♦ ❙ó❧✐❞♦
❆❣r❛❞❡❝✐♠❡♥t♦s
❉✐✈❡rs❛s ♣❡ss♦❛s q✉❡r✐❞❛s ♣❛ss❛r❛♠ ♣♦r ❡st❛ ❞✐ss❡rt❛çã♦ ❡ ❝❛❞❛ ✉♠❛ ❞❡s❡♠♣❡♥❤♦✉ ✉♠ ♣❛♣❡❧ ❡ss❡♥❝✐❛❧ ❡♠ ❝❛❞❛ ❝❛♣ít✉❧♦ ♣r❡s❡♥t❡ ❛q✉✐✳ P♦r ✐ss♦ ❛❣r❛❞❡ç♦✲❛s ❞❡s❞❡ ❥á ♣♦r ❡st❛r❡♠✱ ❞❛ ❢♦r♠❛ q✉❡ ♣✉❞❡r❛♠✱ ♣r❡s❡♥t❡s✳ ◆♦ ❡♥t❛♥t♦✱ ❡✉ ❞❡s❡❥♦ ❢❛③❡r ❛❧❣✉♥s ❛❣r❛❞❡❝✐♠❡♥t♦s ❡s♣❡❝✐❛✐s✳ ◆♦✈❛♠❡♥t❡✱ ❡ ❡♠ q✉❛♥t❛s ♦♣♦rt✉♥✐❞❛❞❡s ♠❡ ❢♦r❡♠ ❞❛❞❛s✱ ❡✉ ❛❣r❛❞❡ç♦ à ♠✐♥❤❛ ♠ã❡ ♣♦r ❡❧❛ s❡r ❡❧❛ ❡♠ t♦❞♦s ♦s s❡♥t✐❞♦s✳ ❚♦❞❛s ❛s ❛❧❡❣r✐❛s ❞❛ ♠✐♥❤❛ ✈✐❞❛ ❞❡❞✐❝❛r❡✐ ❛ ✈♦❝ê✳
❆♦ ♠❡✉ ♣❛✐ ❡ à ♠✐♥❤❛ ❢❛♠í❧✐❛ ♣❡❧♦ ❝❛r✐♥❤♦ ❡ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧✳ ❙♦✉ ♣❛rt❡ ✐♥t❡✐r❛ ❞❡ ✈♦❝ês ❡ s✐♥t♦✲♠❡ ❡①tr❡♠❛♠❡♥t❡ ❢❡❧✐③ ♣♦r ✐ss♦✳
❆♦ ●✉✐❧❤❡r♠❡ q✉❡ ♠❡ ❛❝♦♠♣❛♥❤♦✉ ❞❡s❞❡ ♦ ❝♦♠❡ç♦ ❡ q✉❡ ♠❡ ❛❥✉❞♦✉ ❛ ❛♣r❡♥❞❡r ❞✐✈❡rs❛s ❝♦✐s❛s ❛❧é♠ ❞♦ ▲❆❚❊❳✳ ❖❜r✐❣❛❞❛ ♣♦r t❡♥t❛r ✭s❡♠♣r❡ ❡ s❡♠♣r❡✮ s❡r ✉♠ ❝♦♠♣❛♥❤❡✐r♦ ♠❡❧❤♦r✳
➚ ♣r♦❢❡ss♦r❛ ▼❛r❣❛r✐❞❛ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥♦✉ ❛ ♠❡❧❤♦r ❢♦r♠❛çã♦ ♣♦ssí✈❡❧ q✉❡ ❡st❛✈❛ ❡♠ s✉❛s ♠ã♦s✳
❆♦ P❛✉❧♦ ❙ér❣✐♦ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✱ ♣❛❝✐ê♥❝✐❛ ❡ ♣❛❝✐ê♥❝✐❛✳ ❆❣r❛❞❡ç♦ ♣♦r ♠❡ ❞❛r ❛ ♦♣♦r✲ t✉♥✐❞❛❞❡ ❞❡ ❛♣r❡♥❞❡r ❝♦♠ ✉♠ ❡①❝❡❧❡♥t❡ ❢ís✐❝♦✱ ♣♦r s❡♠♣r❡ t♦r♥❛r t♦❞♦s ♦s ❡♥s✐♥❛♠❡♥t♦s ❞✐❞át✐❝♦s ❡ ♣❡❧♦ ❡s❢♦rç♦ ❞❡s♣❡♥❞✐❞♦ ♥❡st❡s ❞♦✐s ❛♥♦s✳ ❊ ♣♦r ❝❛❞❛ ▲✐♥❞t t❛♠❜é♠✳
❆♦ ➶♥❣❡❧♦ ❛❣r❛❞❡ç♦ ✐♠❡♥s❛♠❡♥t❡ ♣❡❧❛ s✐♥❝❡r✐❞❛❞❡✱ ♣❡❧♦ ❝❛r✐♥❤♦ ❡ ♣♦r t♦❞♦ ♦ ❝♦♥❤❡❝✐✲ ♠❡♥t♦ q✉❡ ✈♦❝ê t❡♥t♦✉ tr❛♥s♠✐t✐r ♣❛r❛ ♠✐♠ ❡♠ tã♦ ♣♦✉❝♦ t❡♠♣♦✳ ❆❧é♠✱ é ❝❧❛r♦✱ ♣♦r t❡r s✉❣❡r✐❞♦ q✉❡ ❡✉ ♠❡❞✐ss❡ ❤á t❡♠♣♦s ❛trás ♦ q✉❡ ❤♦❥❡ sã♦ ♦s r❡s✉❧t❛❞♦s ❞❡st❛ ❞✐ss❡rt❛çã♦✳
❆♦ ❈❤r✐st♦♣❤ ♣♦r t❡r ❝r❡s❝✐❞♦ ❛s ❛♠♦str❛s ❥✉♥t♦ ❛♦ ➶♥❣❡❧♦ ❡ ❛♦ ▲✉❝❛s ♣♦r ❝♦♠♣❛rt✐❧❤❛r ♦s r❡s✉❧t❛❞♦s ❞❡ ❢♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ ❝♦♠✐❣♦✳
❆♦ ▲✉✐③ ❈✉r② ♣❡❧❛ ❞✐s♣♦s✐çã♦ ❡♠ s❡♠♣r❡ ❛❥✉❞❛r✲♥♦s✳
❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❡ ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯❋▼● q✉❡ ♣❛rt✐✲ ❝✐♣❛r❛♠ ❞❡ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❡ ❞❛ ❝♦♥❝❧✉sã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❊♠ ❡s♣❡❝✐❛❧ à ❆r✐❡t❡✱ ❘❛❝❤✐❞✱ ▼♦♥❦❡♥✱ ❊♠♠❛♥✉❡❧ ❡ ❛♦ ❡t❡r♥♦ ❛♠✐❣♦✱ ▼ár✐♦✳ ➚ q✉❡r✐❞❛ ❡ ❞♦❝❡ ❙❤✐r❧❡②✳ ❊ ❛♦ ❈❧ó✈✐s ❡ t♦❞♦s
✈
❞❛ ❈r✐♦❣❡♥✐❛✱ é ❝❧❛r♦✳
❆♦s q✉❡r✐❞♦s ❛♠✐❣♦s ❞❡ ❋ís✐❝❛ q✉❡ ♣♦r ✈❡③❡s ✜③❡r❛♠ ♠❛✐s ♣❛rt❡ ❞♦ ♠❡✉ ❞✐❛ q✉❡ ❛ ♠✐♥❤❛ ♣ró♣r✐❛ ♠ã❡✳ ❆❣r❛❞❡ç♦ ♠✉✐t♦ à ❏✉❧✐❛ ♣❡❧❛ ❛❥✉❞❛ ❡ ❝♦♠♣❛♥❤✐❛ ✭❛❣♦r❛ q✉❛s❡ ❝♦♥tí♥✉❛✮✱ ❛♦ ♠❡✉ q✉❡r✐❞♦ ❙❛✉❧♦ ❡ ❛♦ ♠❡✉ ❣r❛♥❞❡ ❛♠✐❣♦ ❚✐❛❣♦✳ ➚s q✉❡r✐❞❛s ❇ár❜❛r❛✱ ❑❛r♦❧❧✐♥❡✱ ❉❛♥✐❡❧❛✱ ■♥❣r✐❞✱ ❘❡❣✐❛♥❡ ❡ ▲í❣✭❞✮✐❛✭s✮✳ ❆♦s q✉❡r✐❞♦s ❚✭❤✮✐❛❣♦✭s✮✱ ▼❛t❤❡✉s✱ ❍❡♥r✐q✉❡✱ ❚❛ss✐✉s ❡ ❉❛✈✐✳ ❆♦ ❈♦♠❛♥❞♦✳ ❊ ❛♦s q✉❡r✐❞♦s ❞❡ ❧♦♥❣❛ ❞❛t❛✿ ❍❡❧❡♥❛✱ ❘✐❝❛r❞♦✱ P❛✉❧♦✱ ●✉✐❧❤❡r♠❡✱ ❲❡s❝❧❡②✱ ❚❤✐❛❣♦✱ ❆rt✉r✱ ❍❛②ss❛✱ ❋❛❜✐❛♥❛✱ ❇ár❜❛r❛ ❡ ▼✐❝❤❡❧❧❡✳
❆♦s ❛♠✐❣♦s ❞♦ ❈❛❡t❛♥♦ ❆③❡r❡❞♦✳ ❋✐❝♦ ❡①tr❡♠❛♠❡♥t❡ ❛❧✐✈✐❛❞❛ ♣♦r s❛❜❡r q✉❡✱ ♣♦r ♠❛✐s q✉❡ ❡st❡❥❛♠♦s ❝❛♠✐♥❤❛♥❞♦ ❝❛❞❛ q✉❛❧ ❛ s✉❛ ❥♦r♥❛❞❛✱ ❛✐♥❞❛ s♦❜r❛✲♥♦s t❡♠♣♦ ♣❛r❛ s♦rr✐s♦s ❡ ❛❜r❛ç♦s✳
❆♦s ♣❛✐s✱ ♠ã❡s ❡ ✐r♠ã♦s ❞♦ ●❊❈❘✳ ❈♦♥❤❡❝✐ ✈♦❝ês q✉❛♥❞♦ ❡st❡ ♣❡rí♦❞♦ ❞❛ ♠✐♥❤❛ ✈✐❞❛ ❝♦♠❡ç♦✉✱ ♣♦ré♠ ♣r❡t❡♥❞♦ tê✲❧♦s ❝♦♠✐❣♦ ♣♦r t♦❞♦s ♦s ❝❛♠✐♥❤♦s q✉❡ ❡✉ ♣❛ss❛r✳
➚s ✐♥st✐t✉✐çõ❡s ❞❡ ❢♦♠❡♥t♦ ❈❆P❊❙✱ ❈◆Pq✱ ❋❆P❊▼■● ❡ ■◆❈❚ ❞❡ ◆❛♥♦❞✐s♣♦s✐t✐✈♦s ❙❡✲ ♠✐❝♦♥❞✉t♦r❡s ✲ ❉■❙❙❊✳
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ ❡st✉❞❛♠♦s ❝♦♠♦ ❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❝r❡s❝✐❞♦s ❞❡♥tr♦ ❞❡ ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s ❞❡ ♠❛t❡r✐❛✐s ■■■✲❱ sã♦ ❛❢❡t❛❞❛s ♣❡❧❛ ♣r♦①✐♠✐❞❛❞❡ ❞❛s ❞✉❛s s✉♣❡r❢í❝✐❡s ❞❛ ❛♠♦str❛✳ ▼❡❞✐❞❛s ❞❡ ❢♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ ♥♦s ♠♦str❛r❛♠ q✉❡ ❛ ❝r✐❛çã♦ ❞❡ ♥❛♥♦♠❡♠❜r❛♥❛s ❛✉♠❡♥t❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ r❡❝♦♠❜✐♥❛çã♦ ❡❧étr♦♥✲❜✉r❛❝♦ ❞❡ ❡st❛❞♦s ❡①❝✐t❛❞♦s ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s✱ ❡♠ r❡❧❛çã♦ à ❡♠✐ssã♦ ♦❜s❡r✈❛❞❛ ❛♥t❡s ❞❛ ❢❛❜r✐✲ ❝❛çã♦ ❞❛s ♥❛♥♦♠❡♠❜r❛♥❛s✳ ❊st❡ ❝♦♠♣♦rt❛♠❡♥t♦ é ❡①♣❧✐❝❛❞♦ ❝♦♥s✐❞❡r❛♥❞♦ ❛s r❡❣✐õ❡s ❞❡ ❞❡♣❧❡çã♦ ✐♥❞✉③✐❞❛s ♣❡❧❛s s✉♣❡r❢í❝✐❡s ❞❛ ♥❛♥♦♠❡♠❜r❛♥❛✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ♣♦♥t♦s q✉â♥t✐❝♦s✱ r❡❣✐õ❡s ❞❡ ❞❡♣❧❡çã♦✱ ❢♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛✱ ♥❛♥♦♠❡♠❜r❛♥❛s✱ ❡st❛❞♦s ❡①❝✐t❛❞♦s
❆❜str❛❝t
■♥ t❤✐s ✇♦r❦ ✇❡ st✉❞② ❤♦✇ t❤❡ ♦♣t✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ ■♥❆s q✉❛♥t✉♠ ❞♦ts ❡♠❜❡❞❞❡❞ ✐♥ ■■■✲❱ s❡♠✐❝♦♥❞✉❝t♦r ♥❛♥♦♠❡♠❜r❛♥❡s ❛r❡ ❛✛❡❝t❡❞ ❜② t❤❡ ♥❡✐❣❤❜♦r❤♦♦❞ ♦❢ t❤❡ t✇♦ s②♠♠❡tr✐❝❛❧❧② ❧♦❝❛t❡❞ s❛♠♣❧❡ s✉r❢❛❝❡s✳ P❤♦t♦❧✉♠✐♥❡s❝❡♥❝❡ ♠❡❛s✉r❡♠❡♥ts s❤♦✇ t❤❛t t❤❡ ❝r❡❛t✐♦♥ ♦❢ t❤❡ ♥❛♥♦♠❡♠❜r❛♥❡s ✐♥❝r❡❛s❡ t❤❡ ❡❧❡❝tr♦♥✲❤♦❧❡ r❡❝♦♠❜✐♥❛t✐♦♥ ♣r♦❜❛❜✐❧✐t② ♦❢ t❤❡ ❡①❝✐t❡❞ st❛t❡s ♦❢ t❤❡ q✉❛♥t✉♠ ❞♦ts✱ r❡❧❛t✐✈❡ t♦ t❤❡ ❡♠✐ss✐♦♥ ♣r✐♦r t♦ t❤❡ ❢❛❜r✐❝❛t✐♦♥ ♦❢ t❤❡ ♥❛♥♦♠❡♠❜r❛♥❡s✳ ❚❤✐s ❜❡❤❛✈✐♦r ✐s ❡①♣❧❛✐♥❡❞ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❞❡♣❧❡t✐♦♥ ❧❛②❡rs ✐♥❞✉❝❡❞ ❜② t❤❡ s✉r❢❛❝❡s ♦❢ t❤❡ ♥❛♥♦♠❡♠❜r❛♥❡✳
❑❡②✇♦r❞s✿ q✉❛♥t✉♠ ❞♦ts✱ ❞❡♣❧❡t✐♦♥ ❧❛②❡rs✳ ♣❤♦t♦❧✉♠✐♥❡s❝❡♥❝❡✱ ♥❛♥♦♠❡♠❜r❛♥❡s✱ ❡①❝✐t❡❞ st❛t❡s
❙✉♠ár✐♦
❘❡s✉♠♦ ■
❆❜str❛❝t ■■
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✹
✷✳✶ P♦♥t♦s q✉â♥t✐❝♦s s❡♠✐❝♦♥❞✉t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✶ ❈r❡s❝✐♠❡♥t♦ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❛✉t♦✲♦r❣❛♥✐③❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ❘❡❣✐õ❡s ❞❡ ❞❡♣❧❡çã♦ ❡♠ ❤❡t❡r♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✶ P✐♥♥✐♥❣ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷✳✷ P✐♥♥✐♥❣ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r ●❛❆s ✭✵✵✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✷✳✸ Pr♦❢✉♥❞✐❞❛❞❡ ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r ●❛❆s ✭✵✵✶✮
t✐♣♦ p ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✸ ◆❛♥♦♠❡♠❜r❛♥❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛s ◆❛♥♦♠❡♠❜r❛♥❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✷✵
✸✳✶ ❋♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✶✳✶ ❊s♣❡❝tr♦s ❞❡ ❋♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✷ Pr♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❛✉t♦✲♦r❣❛♥✐③❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷✳✶ ❖❝✉♣❛çã♦ ❞❡ ❡st❛❞♦s ❡①❝✐t❛❞♦s ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✷✳✷ ❊s♣❡❝tr♦ ❞❡ ❢♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❡♠ ❞✐❢❡✲
r❡♥t❡s t❡♠♣❡r❛t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✸✳✶ ❊str✉t✉r❛ ❡ ❢❛❜r✐❝❛çã♦ ❞❛s ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
❙❯▼➪❘■❖ ■❱
✸✳✸✳✷ ▼♦♥t❛❣❡♠ ❡①♣❡r✐♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹ ❉✐s❝✉ssã♦ ❞♦s r❡s✉❧t❛❞♦s ✸✸
✹✳✶ ❆♠♦str❛s✿ ❆s ❣r♦✇♥✲✼✵ ❡ ❆s✲❣r♦✇♥✲✷✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✶✳✶ ❊s♣❡❝tr♦ ❞❡ ❢♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ ❞❛ ❛♠♦str❛ ❆s✲❣r♦✇♥✲✼✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✶✳✷ ❈♦♥tr✐❜✉✐çã♦ ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ♥❛ ❡♠✐ssã♦ ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s ✳ ✸✺ ✹✳✶✳✸ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛s ❛♠♦str❛s ✜①❛s ❛♦ s✉❜str❛t♦ ❆s✲❣r♦✇♥✲✼✵
❡ ❆s✲❣r♦✇♥✲✷✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✷ ❆♠♦str❛s✿ ▲✐❢t❡❞✲✼✵ ❡ ▲✐❢t❡❞✲✷✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹✳✷✳✶ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❡♥tr❡ ❛s ❛♠♦str❛s ✜①❛s ❛♦s s✉❜str❛t♦ ✭❆s✲❣r♦✇♥✮ ❡ ♠❡♠❜r❛♥❛s ✭▲✐❢t❡❞✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✺ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ✹✶
✺✳✶ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✺✳✷ P❡rs♣❡❝t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
❆ ❈á❧❝✉❧♦ ❞❛ ❝✉r✈❛t✉r❛ ❞❡ ❜❛♥❞❛s ♥❛ s✉♣❡r❢í❝✐❡ ⑤e❱s⑤ ✹✺
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❆ ❡✈♦❧✉çã♦ ❞❛ r❡❞✉çã♦ ❞✐♠❡♥s✐♦♥❛❧ ❞❛s ❡str✉t✉r❛s ❞♦s ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s t❡♠ ❧❡✈❛❞♦ ❛♦ ❛✉♠❡♥t♦ ❞❡ ✐♥♦✈❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s✳ ❯♠❛ ❞❛s ♣❧❛t❛❢♦r♠❛s ❛✉①✐❧✐❛❞♦r❛s ❞❡st❛ ❡✈♦❧✉çã♦ é ❜❛s❡❛❞❛ ♥♦ ✉s♦ ❞❡ ❤❡t❡r♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s ✜♥❛s ❞❛ ♦r❞❡♠ ❞❡ 100♥♠ ❞❡ ❡s♣❡ss✉r❛
q✉❡ ❞✐❢❡r❡♠ ❞❡ ♦✉tr❛s ❤❡t❡r♦❡str✉t✉r❛s ♥❛♥♦♠étr✐❝❛s ♣♦r s♦❢r❡r❡♠✱ ❡♠ ❛❧❣✉♠ ❡stá❣✐♦ ❞❡ s✉❛ ❢❛❜r✐❝❛çã♦✱ ✉♠ ❞❡s✈✐♥❝✉❧❛♠❡♥t♦ ❞♦ s✉❜str❛t♦ ♥♦ q✉❛❧ ♦r✐❣✐♥❛❧♠❡♥t❡ ❢♦r❛♠ ❝r❡s❝✐❞❛s ❬✶✱ ✷❪✳ ❆ ❡ss❛s ❤❡t❡r♦❡str✉t✉r❛s ❞❛♠♦s ♦ ♥♦♠❡ ❞❡ ♥❛♥♦♠❡♠❜r❛♥❛s✱ q✉❡ ♣♦❞❡♠ s❡r ❝♦♠♣❧❡t❛♠❡♥t❡ ♦✉ ♣❛r❝✐❛❧♠❡♥t❡ ❧✐✈r❡s ❞♦ s✉❜str❛t♦✱ ♣♦❞❡♥❞♦ t❛♠❜é♠ s❡r ❡str✉t✉r❛s ♣❧❛♥❛s ♦✉ tr✐❞✐♠❡♥s✐♦♥❛✐s✳ ❉❡♥tr❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❛✐s s✐❣♥✐✜❝❛♥t❡s ❛tr✐❜✉í❞❛s às ♥❛♥♦♠❡♠❜r❛♥❛s✱ ♣♦❞❡♠♦s ❝✐t❛r ❛ ❡s♣❡ss✉r❛✱ ✢❡①✐❜✐❧✐❞❛❞❡✱ ♣r♦①✐♠✐❞❛❞❡ ❡♥tr❡ ❛s s✉♣❡r❢í❝✐❡s ♦✉ ✐♥t❡r❢❛❝❡s✱ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♦ r❡❧❛①❛♠❡♥t♦ ❞❛ t❡♥sã♦ ❡①✐st❡♥t❡ ❡♥tr❡ ♦ s✉❜str❛t♦ ❡ ❛ ❤❡t❡r♦❡str✉t✉r❛ ♥❛♥♦♠étr✐❝❛✱ q✉❡ ♣r♦♣♦r❝✐♦♥❛♠ ♠♦t✐✈❛çõ❡s ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ❡❧❡trô♥✐❝♦s ✢❡①í✈❡✐s ❡ ♦♣t♦✲❡❧❡trô♥✐❝♦s✳
◆♦ ✐♥t✉✐t♦ ❞❡ ❡♥t❡♥❞❡r ❝♦♠♣❧❡t❛♠❡♥t❡ q✉❛✐s ❡❢❡✐t♦s ❡str✉t✉r❛✐s ❡ ❡s♣❡❝tr♦s❝ó♣✐❝♦s sã♦ ❣❡r❛❞♦s ❡♠ ✉♠ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r ❛♦ ❢❛❜r✐❝❛r✲s❡ ♥❛♥♦♠❡♠❜r❛♥❛s✱ ❞✐✈❡rs♦s t✐♣♦s ❞❡ ❤❡t❡✲ r♦❡str✉t✉r❛s ♥❛♥♦♠étr✐❝❛s ❧✐✈r❡s ❞♦ s✉❜str❛t♦ ❢♦r❛♠ ❢❛❜r✐❝❛❞❛s ❝♦♥t❡♥❞♦ ❡♠✐ss♦r❡s ó♣t✐❝♦s✱ t❛✐s ❝♦♠♦ ♣♦ç♦s q✉â♥t✐❝♦s ❡ ♣♦♥t♦s q✉â♥t✐❝♦s✳ ◆❛ ♣rát✐❝❛✱ ♣♦ré♠✱ ❛ ❢❛❜r✐❝❛çã♦ ❞❡ ♥❛♥♦✲ ♠❡♠❜r❛♥❛s ❝♦♥t❡♥❞♦ ❝❛♠❛❞❛s ❛t✐✈❛s ♦✉ ♥❛♥♦❡str✉t✉r❛s ❡s❝♦❧❤✐❞❛s ♣❛r❛ ❡♠✐t✐r ♦✉ ❛❜s♦r✈❡r ❡s♣❡❝✐✜❝❛♠❡♥t❡ ❡♠ ✉♠❛ ❢❛✐①❛ ❡s♣❡❝tr❛❧ ♣♦❞❡♠ ✐♥❞✉③✐r t❡♥sõ❡s ✐♥❞❡s❡❥❛❞❛s ❝❛✉s❛❞❛s ♣❡❧❛ r❡❧❛①❛çã♦ ❞❡ t❡♥sã♦✳ ❆❞❡♠❛✐s✱ ♣♦ç♦s q✉â♥t✐❝♦s ♦✉ ♣♦♥t♦s q✉â♥t✐❝♦s ❝r❡s❝✐❞♦s ♥❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ s✉♣❡r❢í❝✐❡s s♦❢r❡♠ ♦s ❡❢❡✐t♦s ❞♦ ♣♦t❡♥❝✐❛❧ ❝r✐❛❞♦ ♥❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦✳
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✷
❊ss❡ ❢❡♥ô♠❡♥♦ é r❡s♣♦♥sá✈❡❧ ♣❡❧♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❛tr❛✈és ❞❛ ♥❛♥♦✲ ♠❡♠❜r❛♥❛✱ q✉❡ ♣♦❞❡♠ ♣r❡❡♥❝❤❡r ♦✉ s❡r❡♠ r❡♠♦✈✐❞♦s ❞♦s ❡st❛❞♦s ❝♦♥✜♥❛❞♦s ❞♦ s❡♠✐❝♦♥❞✉✲ t♦r✱ r❡❞✉③✐♥❞♦ ♦✉ ❢❛✈♦r❡❝❡♥❞♦ ❛ r❡❝♦♠❜✐♥❛çã♦ ❡❧étr♦♥✲❜✉r❛❝♦ ♥❡ss❛s ❡str✉t✉r❛s ❝r✐st❛❧✐♥❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ❢♦r♠❛çã♦ ❞❡ss❡ ♣♦t❡♥❝✐❛❧ ❡stá ❛ss♦❝✐❛❞❛ ♥ã♦ s♦♠❡♥t❡ à q✉❛♥t✐❞❛❞❡ ❞❡ ❡st❛❞♦s q✉❡ s❡ ❢♦r♠❛♠ ♥❛ s✉♣❡r❢í❝✐❡✱ ♠❛s t❛♠❜é♠ à ❧♦❝❛❧✐③❛çã♦ ❞❡ss❡s ❡st❛❞♦s ❡♠ r❡❧❛çã♦ à ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐✳ ❈♦♠ ✐ss♦✱ ❤❛✈❡rá ❛♦ ❧♦♥❣♦ ❞♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r✱ ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❝❛r❣❛s✱ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ❝❛r❣❛s ❡s♣❛❝✐❛✐s q✉❡ ❢♦r♠❛rã♦ r❡❣✐õ❡s ❞❡ ❞❡♣❧❡çã♦✱ ✐♥✈❡rsã♦ ♦✉ ❛❝✉♠✉❧❛çã♦✱ ♥♦s q✉❛✐s ♦s ♣♦ç♦s q✉â♥t✐❝♦s ♦✉ ♣♦♥t♦s q✉â♥t✐❝♦s ❡stã♦ ✐♥s❡r✐❞♦s ❬✸✱ ✹❪✳
◆❡st❛ ❞✐ss❡rt❛çã♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠ ❡st✉❞♦ s♦❜r❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❝r❡s❝✐❞♦s ❡♠ ❤❡t❡r♦❡str✉t✉r❛s ♥❛♥♦♠étr✐❝❛s ❡ ♥❛♥♦♠❡♠❜r❛♥❛s ■■■✲❱✳ ❆s ❛♠♦str❛s sã♦ ❢♦r♠❛❞❛s ♣♦r ❝❛♠❛❞❛s ❞❡ ●❛❆s✴❆❧●❛❆s ❝r❡s❝✐❞❛s s♦❜r❡ ✉♠❛ ❝❛♠❛❞❛ s❛❝r✐✜❝✐❛❧ ✭s❡♥sí✈❡❧ à ❛t❛q✉❡ q✉í♠✐❝♦✮ ❞❡ ❆❧❆s ❡♠ s✉❜str❛t♦ ❞❡ ●❛❆s ✭✵✵✶✮ ♣❡❧❛ té❝♥✐❝❛ ❞❡ ❡♣✐t❛①✐❛ ❞❡ ❢❡✐①❡ ♠♦❧❡❝✉❧❛r ✭▼♦❧❡❝✉❧❛r ❇❡❛♠ ❊♣✐t❛①② ✲ ▼❇❊✮✳ P❛r❛ ❛ ❢❛❜r✐❝❛çã♦ ❞❛s ♥❛♥♦♠❡♠❜r❛♥❛s✱ ✉s❛✲s❡ ♦ ♠ét♦❞♦ ❞❡ ❧✐t♦❣r❛✜❛ ❡ ❝♦rr♦sã♦ q✉í♠✐❝❛ ✭❡t❝❤✐♥❣✮ ♣❛r❛ r❡t✐r❛r ❛ ❝❛♠❛❞❛ s❛❝r✐✜❝✐❛❧ ❡✱ ❛♣ós ❛ r❡♠♦çã♦✱ ❛ ♥❛♥♦♠❡♠❜r❛♥❛ é tr❛♥s❢❡r✐❞❛ ♣❛r❛ ✉♠ ♥♦✈♦ s✉❜str❛t♦ ❞❡ ●❛❆s ✭✵✵✶✮✳ ❖s ♣♦♥t♦s q✉â♥t✐❝♦s ❢♦r❛♠ ❝r❡s❝✐❞♦s ♣❡❧♦ ♠♦❞♦ ❙tr❛♥s❦✐✲❑❛str❛♥♦✈ s♦❜r❡ ✉♠❛ ❝❛♠❛❞❛ ✜♥❛ ❞❡ ■♥❆s ✭✇❡tt✐♥❣ ❧❛②❡r✮ ❞❡1,8♠♦♥♦❝❛♠❛❞❛s ❛tô♠✐❝❛s ✭▼▲✮ ❞❡ ❡s♣❡ss✉r❛✳
◆♦ ❈❛♣ít✉❧♦ 2 ♥ós ❛♣r❡s❡♥t❛r❡♠♦s ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ✐♠♣♦rt❛♥t❡s s♦❜r❡ ❤❡t❡r♦❡str✉t✉r❛s
s❡♠✐❝♦♥❞✉t♦r❛s✳ ❉✐s❝✉t✐r❡♠♦s ❜r❡✈❡♠❡♥t❡ s♦❜r❡ ♦ s✉r❣✐♠❡♥t♦ ❞♦ ❡st✉❞♦ ❞❡ ♥❛♥♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s✱ ❝♦♠ ê♥❢❛s❡ ♥♦s ❡st✉❞♦s s♦❜r❡ ❢❛❜r✐❝❛çã♦ ❡ ❛♣❧✐❝❛çõ❡s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❡ ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❡s✳ ❖ ❈❛♣ít✉❧♦3é ❞❡❞✐❝❛❞♦ ❛♦ ❡st✉❞♦ ❞❡ ♠ét♦❞♦s ❞❡ ❝❛r❛❝t❡✲
r✐③❛çã♦ ó♣t✐❝❛ ❞❡ ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s✳ ❆♣r❡s❡♥t❛r❡♠♦s ✉♠ ❡st✉❞♦ ❜r❡✈❡ s♦❜r❡ ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❝♦♠ ❡♥❢♦q✉❡ ❡♠ ❡s♣❡❝tr♦s ❞❡ ❢♦t♦❧✉♠✐♥❡s✲ ❝ê♥❝✐❛✳ ❊ ❡①♣❧✐❝❛r❡♠♦s ❝♦♠♦ ❢♦✐ ♦ ♣r♦❝❡ss♦ ❞❡ ❢❛❜r✐❝❛çã♦ ❞❛s ❛♠♦str❛s ❡ ♦s ♣r♦❝❡❞✐♠❡♥t♦s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❛ ❛s ♠❡❞✐❞❛s ❞❡ ❢♦t♦❧✉♠✐♥❡s❝ê♥❝✐❛ q✉❡ s❡rã♦ ❞❡s❝r✐t❛s ❡♠ s❡❣✉✐❞❛✳ ◆♦ ❈❛♣ít✉❧♦ 4 s❡rã♦ ♠♦str❛❞♦s ♦s r❡s✉❧t❛❞♦s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❡st✉❞❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✱ q✉❡
❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✸
❈❛♣ít✉❧♦ ✷
❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s
❍❡t❡r♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s sã♦ ❡str✉t✉r❛s q✉❡ ❝♦♥s✐st❡♠ ❡♠ ❝❛♠❛❞❛s ❞❡ ✉♠ ♦✉ ♠❛✐s s❡♠✐❝♦♥❞✉t♦r❡s ❝r❡s❝✐❞♦s ❡♣✐t❛①✐❛❧♠❡♥t❡ s♦❜r❡ ✉♠❛ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❡♠ ❝♦♠✉♠✱ s❡♥❞♦ ✈✐st❛s t❛♠❜é♠ ❝♦♠♦ ✉♠ ❝r✐st❛❧ ú♥✐❝♦ ♥♦ q✉❛❧ ❛ ♦❝✉♣❛çã♦ ❞♦s sít✐♦s ❛tô♠✐❝♦s ✈❛r✐❛ ♥❛ ✐♥t❡r❢❛❝❡✱ ❛ q✉❛❧ ❝❤❛♠❛♠♦s ❞❡ ❤❡t❡r♦❥✉♥çã♦✳ ●❡r❛❧♠❡♥t❡✱ q✉❛♥❞♦ ✉♠❛ ❤❡t❡r♦❡str✉t✉r❛ é ❢♦r♠❛❞❛✱ ❡①✐st❡ ✉♠❛ ❞✐❢❡r❡♥ç❛ ♥❛ ♣♦s✐çã♦ ❡♠ ❡♥❡r❣✐❛ ❞❛s ❜❛♥❞❛s ❞❡ ❝♦♥❞✉çã♦ ❡ ✈❛❧ê♥❝✐❛ q✉❡ ❧❡✈❛ ❛♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❡st❛s ❜❛♥❞❛s ✭❜❛♥❞ ♦✛s❡ts✮ ❬✺✱ ✻✱ ✼✱ ✽❪✳ ❚❛♥t♦ ♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❛s ❜❛♥❞❛s q✉❛♥t♦ ❛ ❞♦♣❛❣❡♠ ❞❡ ✐♠♣✉r❡③❛s ♣♦❞❡♠ s❡r ❝♦♥tr♦❧❛❞♦s✱ ♦ q✉❡ t♦r♥❛ ❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s ❛s ♣r✐♥❝✐♣❛✐s ❢♦♥t❡s ❞❡ ✐♥t❡r❡ss❡ ❡♠ ❤❡t❡r♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s ♣♦rq✉❡ ♦❢❡r❡❝❡♠ ❣r❛✉s ❡①tr❛s ❞❡ ❧✐❜❡r❞❛❞❡ às ❤❡t❡r♦❥✉♥çõ❡s✳
❆ ❋✐❣✉r❛ ✷✳✶ ✐❧✉str❛ ♦s três t✐♣♦s ❞❡ ❛❧✐♥❤❛♠❡♥t♦s ❞❡ ❜❛♥❞❛s ❢♦r♠❛❞♦s ❡♠ ❤❡t❡r♦❡s✲ tr✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s✳ ◆❡st❡ tr❛❜❛❧❤♦ t♦❞❛s ❛s ❤❡t❡r♦❥✉♥çõ❡s sã♦ ❞♦ t✐♣♦ ■ ♥❛s q✉❛✐s ❛ r❡❣✐ã♦ ❞❡ ❡♥❡r❣✐❛ ♣r♦✐❜✐❞❛ ❡♥tr❡ ❛s ❜❛♥❞❛s ❞❡ ❝♦♥❞✉çã♦ ✭❣❛♣ ✲ ❊g✮ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❡stá
❝♦♠♣❧❡t❛♠❡♥t❡ ✐♥s❡r✐❞♦ ❞❡♥tr♦ ❞♦ ❣❛♣ ❞❡ ♦✉tr♦ ♠❛t❡r✐❛❧ ❞✐st✐♥t♦✳ ❈♦♠✉♠❡♥t❡ ✉s❛♠✲s❡ ❤❡t❡✲ r♦❡str✉t✉r❛s t✐♣♦ ■ ♣❛r❛ ❢❛❜r✐❝❛r ♣♦ç♦s ❞❡ ♣♦t❡♥❝✐❛✐s ❛ ♣❛rt✐r ❞♦ ❝r❡s❝✐♠❡♥t♦ ❞❡ ❝❛♠❛❞❛s ❞❡ ❤❡t❡r♦❡str✉t✉r❛s t✐♣♦ ■ ✐♥t❡r❝❛❧❛❞❛s ❡♥tr❡ ♠❛t❡r✐❛✐s ❞❡ ❣❛♣ ♠❛✐♦r ❡ ❣❛♣ ♠❡♥♦r✳ ❙❡ ❛ ❧❛r❣✉r❛ ❞❛ ❝❛♠❛❞❛ ❝❡♥tr❛❧ ❞❡ ♠❛t❡r✐❛❧ ✭❊g ♠❡♥♦r✮ é ❧✐♠✐t❛❞❛ ❛ ✉♠❛ ❡s♣❡ss✉r❛ ❞❛ ♦r❞❡♠ ❞♦ ❝♦♠♣r✐✲
♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ❞❡ ❇r♦❣❧✐❡ ✭λ✮ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❞♦ ♠❛t❡r✐❛❧✱ ♣♦❞❡r❡♠♦s ♦❜s❡r✈❛r ❡❢❡✐t♦s ❞❡ q✉❛♥t✐③❛çã♦✳ ❆ ♣❛rt✐r ❞❡st❡ ❝♦♥❝❡✐t♦✱ s✉r❣✐r❛♠ ♥❛s ❞é❝❛❞❛s ❞❡ ✼✵ ❡ ✽✵ ❞✐✈❡rs♦s tr❛❜❛❧❤♦s t❡ór✐❝♦s ❡ ❡①♣❡r✐♠❡♥t❛✐s ❬✾✱ ✶✵✱ ✶✶✱ ✶✷❪ ❡♠ q✉❡ ❢♦r❛♠ ✉s❛❞❛s ❝❛♠❛❞❛s ✉❧tr❛✲✜♥❛s
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✺
♣❛r❛ ❡st✉❞❛r ❛ r❡❧❛çã♦ ❡♥tr❡ ❛ ❞✐♠✐♥✉✐çã♦ ❞❛s ❡s♣❡ss✉r❛s ❞❛s ❝❛♠❛❞❛s✱ ♦ ❛✉♠❡♥t♦ ❞♦ ❣❛♣ ❡ ❡❢❡✐t♦s ❞❡ t✉♥❡❧❛♠❡♥t♦ ❡♠ ❤❡t❡r♦❡str✉t✉r❛s q✉❡ ✜❝❛r❛♠ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ♣♦ç♦s q✉â♥t✐❝♦s✱ ❞❡✜♥✐❞❛s ❝♦♠♦ ❤❡t❡r♦❡str✉t✉r❛s ♥❛ q✉❛❧ ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ é q✉❛♥t✐③❛❞♦ ❡♠ ❛♣❡♥❛s ✉♠❛ ❞✐r❡çã♦ ✭2❉✮✳
❋✐❣✉r❛ ✷✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦s três t✐♣♦s ❞❡ ✏❜❛♥❞ ♦✛s❡ts✑ ❡♠ ❤❡t❡r♦❥✉♥çõ❡s✱ ♦r❣❛♥✐✲ ③❛❞♦s ♣❡❧♦ ❛❧✐♥❤❛♠❡♥t♦ ❞❛s ❜❛♥❞❛s✳
◆♦ ✜♥❛❧ ❞♦s ❛♥♦s ✽✵✱ ❝♦♠ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛s ♣r✐♥❝✐♣❛✐s ♣r♦♣r✐❡❞❛❞❡s ❞♦s ♣♦ç♦s q✉â♥✲ t✐❝♦s✱ s✉r❣✐✉ ♦ ✐♥t❡r❡ss❡ ❡♠ ❡st✉❞❛r ❤❡t❡r♦❡str✉t✉r❛s ❝♦♠ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡s ❛✐♥❞❛ ♠❛✐s r❡✲ ❞✉③✐❞❛s✱ ❝♦♠♦ ✜♦s q✉â♥t✐❝♦s ❬✶✸❪ ❡ ♣♦♥t♦s q✉â♥t✐❝♦s ✭P◗s✮✱ ♥❛s q✉❛✐s ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ é r❡❞✉③✐❞♦ ❛ 1❉ ❡ 0❉✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❉✐❛❣r❛♠❛s ❡sq✉❡♠át✐❝♦s ❞❛
♠♦r❢♦❧♦❣✐❛ ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❡❧❡trô♥✐❝♦s ❉✭❊✮ ❡♠ ❢✉♥çã♦ ❞❛ ❡♥❡r❣✐❛ ❊ ❞❛s ❡str✉t✉✲ r❛s ❝r✐st❛❧✐♥❛s ✭❛✮ só❧✐❞♦ ✈♦❧✉♠étr✐❝♦✱ ✭❜✮ ✉♠ ♣♦ç♦ q✉â♥t✐❝♦✱ ✭❝✮ ✉♠ ✜♦ q✉â♥t✐❝♦ ❡ ✭❞✮ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❡stã♦ r❡♣r❡s❡♥t❛❞♦s ♣❡❧❛s ❋✐❣✉r❛ ✷✳✷✳
✷✳✶ P♦♥t♦s q✉â♥t✐❝♦s s❡♠✐❝♦♥❞✉t♦r❡s
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✻
❋✐❣✉r❛ ✷✳✷✿ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞♦ ❝♦♥✜♥❛♠❡♥t♦ q✉â♥t✐❝♦ ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❉✭❊✮ ❡♠ ❢✉♥çã♦ ❞❛ ❡♥❡r❣✐❛ ❊ ❛ss♦❝✐❛❞❛ ❛ ❡❧étr♦♥s ❝♦♥✜♥❛❞♦s ❡♠ ✉♠ ❛✮ só❧✐❞♦ ✈♦❧✉♠étr✐❝♦✱ ❜✮ ♣♦ç♦ q✉â♥t✐❝♦✱ ❝✮ ✜♦ q✉â♥t✐❝♦ ❡ ❞✮ ♣♦♥t♦ q✉â♥t✐❝♦✳
❡♥❡r❣✐❛ ❞❡ s❡♣❛r❛çã♦ ❡♥tr❡ s✉❜♥í✈❡✐s ❡♠ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦✱ é✱ ♥♦✈❛♠❡♥t❡✱ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ❞❡ ❇r♦❣❧✐❡✱ ♣♦ré♠ r❡str✐♥❣✐♥❞♦ ❛ ❣❡♦♠❡tr✐❛ ❡♠ três ❞✐♠❡♥sõ❡s✳ ❈♦♠♦ ✉♠ tí♣✐❝♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❞❡ 10 ♥♠ ♣♦ss✉✐ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 104 ♦✉ ♠❛✐s át♦♠♦s ❬✶✹❪✱ ♦ ❡st✉❞♦ ❞❡s✲
s❛s ♥❛♥♦❡str✉t✉r❛s ❡♠ ❝♦♥❥✉♥t♦s ♦✉ ✐♥❞✐✈✐❞✉❛✐s t♦r♥♦✉✲s❡ ✉♠❛ ♦♣♦rt✉♥✐❞❛❞❡ ♣❛r❛ ✉t✐❧✐③❛r ♣♦♥t♦s q✉â♥t✐❝♦s ❡♠ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s✱ ❝♦♠♦ ❢♦♥t❡ ❞❡ ❢ót♦♥s ú♥✐❝♦s✱ ❢♦t♦❞❡t❡❝t♦r❡s ❡ ❧❛s❡rs ❬✶✺❪✳
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✼
✷✳✶✳✶ ❈r❡s❝✐♠❡♥t♦ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❛✉t♦✲♦r❣❛♥✐③❛❞♦s
P❛r❛ ♦ ❝r❡s❝✐♠❡♥t♦ ❞❡ ❤❡t❡r♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s ❡①✐st❡♠ três ♣r✐♥❝✐♣❛✐s ❢♦r♠❛s ❞❡ ❝r❡s❝✐♠❡♥t♦ ❡♣✐t❛①✐❛❧✿ ❋r❛♥❦✲✈❛♥ ❞❡r ▼❡r✇❡ ✭❋✈❞▼✮✱ ❱♦❧♠❡r✲❲❡❜❡r ✭❱❲✮ ❡ ❙tr❛♥s❦✐✲❑r❛st❛♥♦✈ ✭❙❑✮ q✉❡ sã♦ ❣♦✈❡r♥❛❞♦s ❡①❝❧✉s✐✈❛♠❡♥t❡ ♣❡❧❛s ❡♥❡r❣✐❛s ❞❡ s✉♣❡r❢í❝✐❡ ❡ ✐♥t❡r❢❛❝❡ ✭❋✐❣✳ ✷✳✸✮✳
❋✐❣✉r❛ ✷✳✸✿ ❉✐❛❣r❛♠❛ ❡sq✉❡♠❛t✐③❛❞♦ ❞❡ três ♠♦❞♦s ♣♦ssí✈❡✐s ❞❡ ❝r❡s❝✐♠❡♥t♦✿ ✭❛✮ ❋r❛♥❦✲✈❛♥ ❞❡r ▼❡r✇❡ ✭❋✈❞▼✮✱ ✭❜✮ ❱♦❧♠❡r✲❲❡❜❡r ✭❱❲✮ ❡ ✭❝✮ ❙tr❛♥s❦✐✲❑r❛st❛♥♦✈ ✭❙❑✮✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❛ r❡❢❡rê♥✲ ❝✐❛ ❬✶✹❪✳
❙❡ ❛ s♦♠❛ ❞❛ ❡♥❡r❣✐❛γ2 ❞❛ ❝❛♠❛❞❛ s✉♣❡r✜❝✐❛❧ ❞❡♣♦s✐t❛❞❛ ❝♦♠ ❛ ❡♥❡r❣✐❛γ12❞❛ ✐♥t❡r❢❛❝❡ é ♠❡♥♦r q✉❡ ❛ ❡♥❡r❣✐❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ s✉❜str❛t♦✱γ2+γ12< γ1✱ ❛s ❝❛♠❛❞❛s s❡rã♦ ❞❡♣♦s✐t❛❞❛s s♦❜r❡ ♦ s✉❜str❛t♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❢♦r♠❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❋r❛♥✲✈❛♥ ❞❡r ▼❡r✇❡ ❬✷✶❪ ✭❋✐❣✳ ✷✳✸ ❛✮✳ ❖s át♦♠♦s ❞❛ s✉♣❡r❢í❝✐❡ s❡ ✜①❛♠ ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡♠ sít✐♦s s✉♣❡r✜❝✐❛✐s✱ r❡s✉❧t❛♥❞♦ ♥♦ ❝r❡s❝✐♠❡♥t♦ ❝♦❡r❡♥t❡ ✭♦ ♠❛t❡r✐❛❧ ❞❡♣♦s✐t❛❞♦ ❛❞♦t❛ ♦ ♣❛râ♠❡tr♦ ❞❡ r❡❞❡ ❞♦ s✉❜str❛t♦✮ ❞❡ ❝❛♠❛❞❛s ❝♦♠♣❧❡t❛s ❛t♦♠✐❝❛♠❡♥t❡ s✉❛✈❡s✳ ❙❡ ❤♦✉✈❡r ✉♠ ❛✉♠❡♥t♦ ♥❛ s♦♠❛ ❞❛s ❡♥❡r❣✐❛s γ2+γ12 ♦ ❝r❡s❝✐♠❡♥t♦ ❜✐✲❞✐♠❡♥s✐♦♥❛❧ ❞❛s ❝❛♠❛❞❛s ♣♦❞❡ t♦r♥❛r✲s❡ ✉♠ ❝r❡s❝✐♠❡♥t♦ ♥♦ q✉❛❧ ✐❧❤❛s sã♦ ❢♦r♠❛❞❛s✱ ❝♦♠♦ ♦❝♦rr❡ ♥♦ ❝r❡s❝✐♠❡♥t♦ ❞❛ ❢♦r♠❛ ❱♦❧♠❡r✲❲❡❜❡r ✭❋✐❣✳ ✷✳✸ ❜✮✳
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✽
❡s♣❡ss✉r❛ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❡s♣❡ss✉r❛ ❝rít✐❝❛✱ ❛ ❡♥❡r❣✐❛ ❞❡ t❡♥sã♦ ❡♥tr❡ ❛s ❝❛♠❛❞❛s ❡♣✐t❛①✐❛✐s ❞♦ ♠❛t❡r✐❛❧ t♦r♥❛✲s❡ tã♦ ❣r❛♥❞❡ q✉❡ ❛s ❧✐❣❛çõ❡s ❞♦ ♠❛t❡r✐❛❧ ❞❡ ♠❛✐♦r ❛ s❡ ❡①♣❛♥❞❡♠ ♣❛r❛ q✉❡ ♦❝♦rr❛ ✉♠❛ ♠✐♥✐♠✐③❛çã♦ ❞❛ ❡♥❡r❣✐❛✱ ♦❝❛s✐♦♥❛♥❞♦ ❛ss✐♠ ❛ ❢♦r♠❛çã♦ ❞❡ ✐❧❤❛s ✭♣♦♥t♦s q✉â♥t✐❝♦s ❛✉t♦✲♦r❣❛♥✐③❛❞♦s✮ q✉❡ ❛ss✉♠❡♠ ♦ ♣❛râ♠❡tr♦ ❞❡ r❡❞❡ ❞♦ ♠❛t❡r✐❛❧ ❞♦ q✉❛❧ ❡❧❛s sã♦ ❝♦♥st✐t✉í❞❛s ❬✶✹✱ ✷✷❪✱ ❝♦♠♦ ✐♥❞✐❝❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✹✳ ❊st❛s ✐❧❤❛s sã♦ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡✈✐❞♦ às ❞✐♠❡♥sõ❡s ♥❛♥♦♠étr✐❝❛s ❝♦♠ ❛s q✉❛✐s sã♦ ❢♦r♠❛❞❛s ❡ ❛ ❝❛♠❛❞❛ ❡♣✐t❛①✐❛❧ ❞❡♣♦s✐t❛❞❛ s♦❜r❡ ♦ s✉❜str❛t♦✱ ❛❜❛✐①♦ ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s✱ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝❛♠❛❞❛ ♠♦❧❤❛♥t❡ ♦✉ ✇❡tt✐♥❣ ❧❛②❡r✳
❋✐❣✉r❛ ✷✳✹✿ ■❧✉str❛çã♦ ❞❛ ❢♦r♠❛çã♦ ❞❡ ✐❧❤❛s ❞✉r❛♥t❡ ♦ ❝r❡s❝✐♠❡♥t♦ ❡♣✐t❛①✐❛❧ ❞❡ ❤❡t❡r♦❡str✉t✉r❛ s❡♠✐❝♦♥❞✉t♦r❛ ♣❡❧♦ ♠♦❞♦ ❙tr❛♥s❦✐✲❑❛str❛♥♦✈✳ ❋✐❣✉r❛ ♠♦❞✐✜❝❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✸❪✳
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✾
❤❡t❡r♦❡str✉t✉r❛s ❝r✐st❛❧✐♥❛s sã♦
✶✳ ▼❇❊ ✭♠♦❧❡❝✉❧❛r ❜❡❛♠ ❡♣✐t❛①②✮✱ q✉❡ ❝♦♥s✐st❡ ❡♠ ❝r❡s❝❡r ✜❧♠❡s ✜♥♦s s❡♠✐❝♦♥❞✉t♦r❡s ❛ ♣❛rt✐r ❞❡ ✉♠ ♣r♦❝❡ss♦ ❢ís✐❝♦ ♥❛ q✉❛❧ ♦❝♦rr❡ ❞❡♣♦s✐çã♦ ❝♦♥tr♦❧❛❞❛ ❞♦s ♠❛t❡r✐❛✐s ❡✈❛✲ ♣♦r❛❞♦s s♦❜r❡ ✉♠ s✉❜str❛t♦ ❝r✐st❛❧✐♥♦ ❛q✉❡❝✐❞♦ ❡♠ ✉♠ ❛♠❜✐❡♥t❡ ❞❡ ✉❧tr❛✲❛❧t♦ ✈á❝✉♦ ❬✷✺❪✳
✷✳ ▼❖❈❱❉ ✭♠❡t❛❧ ♦r❣❛♥✐❝ ❝❤❡♠✐❝❛❧ ✈❛♣♦r ❞❡♣♦s✐t✐♦♥✮ q✉❡ ❞✐❢❡r❡ ❞❛ té❝♥✐❝❛ ❞❡ ▼❇❊ ♣♦r s❡r ✉♠ ♣r♦❝❡ss♦ q✉í♠✐❝♦ ❞❡ r❡❛çã♦ ❞♦s ❣❛s❡s ❝♦♥t❡♥❞♦ ♦s ❡❧❡♠❡♥t♦s q✉í♠✐❝♦s ❛ s❡r❡♠ ❞❡♣♦s✐t❛❞♦s✳
❋✐❣✉r❛ ✷✳✺✿ ❛✮ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞♦ ❝r❡s❝✐♠❡♥t♦ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s s♦❜r❡ ♦ s✉❜str❛t♦ ❞❡ ●❛❆s ♣❡❧♦ ♠♦❞♦ ❙tr❛♥s❦✐✲❑r❛st❛♥♦✈✳ P❛r❛ ❝❛♠❛❞❛s ❞❡ ■♥❆s ❁ 1,5 ▼▲ s♦❜r❡ ●❛❆s✱ t❡♠♦s ✉♠
❝r❡s❝✐♠❡♥t♦ ✷❉✳ ❆ ♣❛rt✐r ❞❡ss❡ ✈❛❧♦r✱ ♦❝♦rr❡ ❛ ❢♦r♠❛çã♦ ❞❡ ✐❧❤❛s✳ ❜✮ ■♠❛❣❡♠ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❛✉t♦✲♦r❣❛♥✐③❛❞♦s ❞❡ ■♥❆s s♦❜r❡ ✉♠ s✉❜str❛t♦ ❞❡ ●❛❆s ♦❜t✐❞❛ ♣♦r ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❢♦rç❛ ❛tô♠✐❝❛ ✭❆❋▼✮✳ ❋✐❣✉r❛ ♠♦❞✐✜❝❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✶✺❪✳
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✵
❞✐♠❡♥s✐♦♥❛❧ s♦❜r❡ ♦ s✉❜str❛t♦ ❞❡ ●❛❆s ♦❝♦rr❡ ❛té ✉♠❛ ❡s♣❡ss✉r❛ ❝rít✐❝❛ ♠í♥✐♠❛ ❞❡1,5 ▼▲
q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 4➴ ❞❡ ♠❛t❡r✐❛❧ ❬✷✻❪✳ ❆ ♣❛rt✐r ❞❡ss❛ ❡s♣❡ss✉r❛✱ ❞❡✈✐❞♦
à ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s ♣❛râ♠❡tr♦s ❞❡ r❡❞❡ ❛ ❞♦s ♠❛t❡r✐❛✐s ■♥❆s ✭❛ ❂ 6,06 ➴✮ ❡ ●❛❆s ✭❛ ❂ 5,65➴✮ s❡r ❞❡7 %✱ ♦❝♦rr❡ ♦ ❝r❡s❝✐♠❡♥t♦ ♣♦r ❙tr❛♥s❦✐✲❑r❛st❛♥♦✈ ❞❡ ♣♦♥t♦s ❛✉t♦✲♦r❣❛♥✐③❛❞♦s
t❡♥s✐♦♥❛❞♦s ❞❡ ■♥❆s✱ ❝♦♠♦ ✐♥❞✐❝❛❞♦ ♣❡❧❛ ❋✐❣✉r❛ ✷✳✺ ❛✮✳ ❆ ❋✐❣✉r❛ ✷✳✺ ❜✮ ♠♦str❛ ✉♠❛ ✐♠❛❣❡♠ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❢♦rç❛ ❛tô♠✐❝❛ ✭❛t♦♠✐❝ ❢♦r❝❡ ♠✐❝r♦s❝♦♣② ✲ ❆❋▼✮ ❞❡ ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s s♦❜r❡ ●❛❆s✳
✷✳✷ ❘❡❣✐õ❡s ❞❡ ❞❡♣❧❡çã♦ ❡♠ ❤❡t❡r♦❡str✉t✉r❛s s❡♠✐❝♦♥❞✉t♦r❛s
❊♠ ✉♠ ❡st✉❞♦ ♠❛✐s s✐♠♣❧✐✜❝❛❞♦ ❞❡ s❡♠✐❝♦♥❞✉t♦r❡s✱ ♣♦❞❡♠♦s ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ q✉❡ ♦ s❡♠✐❝♦♥❞✉t♦r é ✉♠ ❝r✐st❛❧ ♣❡r❢❡✐t♦ ❞❡ ❞✐♠❡♥sõ❡s ✐♥✜♥✐t❛s✳ P♦ré♠✱ q✉❛♥❞♦ ❢❛❜r✐❝❛♠♦s ❡ss❛s ❤❡t❡r♦❡str✉t✉r❛s✱ s♦♠❡♥t❡ ♥♦s é ♣♦ssí✈❡❧ ♦❜t❡r ❡str✉t✉r❛s ❞❡ ❞✐♠❡♥sõ❡s ✜♥✐t❛s✱ t❛❧ ❝♦♠♦ ❛s ♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s ❡st✉❞❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦✱ ♦ q✉❡ ❛❝❛rr❡t❛ ❛ ♣r❡s❡♥ç❛ ❞❡ s✉♣❡r❢í❝✐❡s ♥♦ s❡♠✐❝♦♥❞✉t♦r q✉❡ sã♦ ❝♦♥s✐❞❡r❛❞❛s ❞❡❢❡✐t♦s ❡♠ ✉♠ ❝r✐st❛❧ ♣❡r❢❡✐t♦ ♣♦r q✉❡❜r❛r ❛ ♣❡r✐♦❞✐❝✐❞❛❞❡ ❞♦ ♣♦t❡♥❝✐❛❧ ❝r✐st❛❧✐♥♦✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ ❝r✐❛✲s❡ ✉♠❛ ❞❡❢♦r♠❛çã♦ ♥❛ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞♦ ♠❛t❡r✐❛❧ ♣♦r ♥ã♦ s❡r ♠❛✐s ♣♦ssí✈❡❧ ✐♠♣♦r ✉♠❛ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥t♦r♥♦ ❝í❝❧✐❝❛✱ ❝♦♠♦ ❛✜r♠❛ ♦ ❚❡♦r❡♠❛ ❞❡ ❇❧♦❝❤✳ ❚♦r♥❛✲s❡ ❡♥tã♦ ♣♦ssí✈❡❧ ❛ ❢♦r♠❛çã♦ ❞❡ ♦✉tr♦s ❡st❛❞♦s ❛ s❡r❡♠ ♦❝✉♣❛❞♦s ♥❛ s✉♣❡r❢í❝✐❡✱ q✉❡ s❡rã♦ ❡st✉❞❛❞♦s ❛ s❡❣✉✐r✳
❈♦♠♦ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ✭❋✐❣✳ ✷✳✻✮ ❣❡r❛ ❡st❛❞♦s ❡♠ t♦❞❛ ❛ ❡①t❡♥sã♦ ❞♦ s❡♠✐❝♦♥❞✉t♦r ❡♠ ❝♦♥t❛t♦ ❝♦♠ ♦ ❛r✱ ✐♥❝❧✉s✐✈❡ ♥♦ ❣❛♣✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦ t✐♣♦ ❞❡ ❡st❛❞♦s ❝r✐❛❞♦s ✭❡st❛❞♦s ❞♦❛❞♦r❡s ♦✉ ❛❝❡✐t❛❞♦r❡s✮ ❡ ❞❛ ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ✭❊F✮ ♥❛ s✉♣❡r❢í❝✐❡✱ ❡ss❡s
❡st❛❞♦s ♣♦❞❡♠ s❡r ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛✱ q✉❡ s❡rã♦ ❜❛❧❛♥❝❡❛❞♦s ♣♦r ✉♠❛ ❝❛r❣❛ ♦♣♦st❛ ❞❡♥tr♦ ❞♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r✳
❆ ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ♥♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r ❝♦♠ s✉♣❡r❢í❝✐❡ é ❞❡t❡r♠✐♥❛❞❛ s✐♠♣❧❡s♠❡♥t❡ ♣❡❧❛ ❝♦♥❞✐çã♦ ❞❡ ♥❡✉tr❛❧✐❞❛❞❡ ❞❛s ❝❛r❣❛s✱ ✐st♦ é✱ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞♦s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ✭◗ss✮ ❞❡✈❡ s❡r ❝♦♠♣❡♥s❛❞❛ ♣♦r ✉♠❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ♦♣♦st❛ ❞❡♥tr♦
❞♦ s❡♠✐❝♦♥❞✉t♦r ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝❛r❣❛ ❡s♣❛❝✐❛❧ ✭◗sc✮✳ ❖ q✉❡ ❧❡✈❛ à ❝♦♥❞✐çã♦ ❞❡ ♥❡✉tr❛❧✐❞❛❞❡✿
Qss=−Qsc ✭✷✳✶✮
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✶
❋✐❣✉r❛ ✷✳✻✿ ■♠❛❣❡♠ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞❡ ●❛❆s✳ ➚ ❡sq✉❡r❞❛ ✭✐❞❡❛❧✮ ❡stá ✐♥❞✐❝❛❞♦ ♦ ❛rr❛♥❥♦ ♣❡r✐ó❞✐❝♦ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ ♣❡r❢❡✐t❛ ✭✐♥✜♥✐t❛✮✳ ➚ ❞✐r❡✐t❛ ✭r❡❝♦♥str✉í❞♦✮ ❡stá ✐♥❞✐❝❛❞♦ ❛ r❡❝♦♥str✉çã♦ ❞♦ ❛rr❛♥❥♦ ❞❡ ❛tô♠✐❝♦ ♣❡r✐♦❞✐❝✐❞❛❞❡ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ é q✉❡❜r❛❞❛ ✭❡①✿ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ ❝r✐st❛❧✮✳
❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ♥❡❣❛t✐✈❛ ◗ss ❞♦s ❡st❛❞♦s t✐♣♦ ❛❝❡✐t❛❞♦r ❞❛ s✉♣❡r❢í❝✐❡ ♣ró①✐♠♦s ❛♦ ♠❡✐♦
❞♦ ❣❛♣ ❞❡ ✉♠ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r t✐♣♦ n é ❝♦♠♣❡♥s❛❞❛ ♣♦r ❡st❛❞♦s ❞♦❛❞♦r❡s ✐♦♥✐③❛❞♦s ❞♦ s❡♠✐❝♦♥❞✉t♦r ✭◗sc✮✳ ❆ ❢♦r♠❛çã♦ ❞❛ ❝❛♠❛❞❛ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s✱ ✐✳❡✳✱ ♦ ✈❛❧♦r ♠á①✐♠♦ ❞❛
❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s ❞♦ ❝r✐st❛❧ ♣ró①✐♠♦ à s✉♣❡r❢í❝✐❡ ✭e❱s✮ ♣♦❞❡ s❡r ❡♥t❡♥❞✐❞❛ ❞❛ s❡❣✉✐♥t❡
❢♦r♠❛✿ ❡♠ ✉♠❛ r❡❣✐ã♦ ❞❡♥tr♦ ❞♦ s❡♠✐❝♦♥❞✉t♦r ❞✐st❛♥t❡ ❞❛ s✉♣❡r❢í❝✐❡✱ ❛ ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ❡♠ r❡❧❛çã♦ à ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ é ❞❡t❡r♠✐♥❛❞❛ ♣❡❧❛ ❞♦♣❛❣❡♠ ❞♦ ♠❛t❡r✐❛❧✳ Pró①✐♠♦ à s✉♣❡r❢í❝✐❡ ♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ✜❝❛ ✜①♦ ♥♦ ♣♦♥t♦ ❞❡t❡r♠✐♥❛❞♦ ♣❡❧♦s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡✳ ❆ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❝❛r❣❛s ❞❛ s✉♣❡r❢í❝✐❡ ♦✉ ♣❛r❛ ❛ s✉♣❡r❢í❝✐❡ ♣❛r❛ ❡q✉✐❧✐❜r❛r ♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ❝r✐❛ ❛ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s✳
❖s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ t✐♣♦ ❛❝❡✐t❛❞♦r✱ ♥♦ ❡♥t❛♥t♦ sã♦ ✐♥❡r❡♥t❡♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦s à ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡❀ s✉❛ ♣♦s✐çã♦ ❡♥❡r❣ét✐❝❛ ❡♠ r❡❧❛çã♦ à ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ é ✜①❛ ❡ ❞❡t❡r♠✐♥❛❞❛ ♣♦r ♣♦t❡♥❝✐❛✐s ✐♥t❡r❛tô♠✐❝♦s✳ ❖ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ♥❛ s✉♣❡r❢í❝✐❡ ❞❛ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❧♦❝❛❧✐③❛✲s❡ ❡♠ ♣♦s✐çã♦ ❞✐❢❡r❡♥t❡ ❛♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ♥♦ ✐♥t❡r✐♦r ❞❛ ❡str✉t✉r❛✱ ❞❡✈✐❞♦ ❛ ❢♦r♠❛çã♦ ❞❡ ❡st❛❞♦s ❛❝❡✐t❛❞♦r❡s✳ ❊st❛ s✐t✉❛çã♦ ♣♦r s❡r ❡♥❡r❣✐❝❛♠❡♥t❡ ❞❡s❢❛✈♦rá✈❡❧✱ ♥ã♦ ♣♦❞❡ s❡r ❡stá✈❡❧✱ ❣❡r❛♥❞♦ ❡♥tã♦✱ ♣❛r❛ ❡q✉✐❧✐❜r❛r ❛ ❡♥❡r❣✐❛✱ ✉♠❛ ❝❛♠❛❞❛ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s r❡♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✼ ♣♦r ◗sc ❞❡✈✐❞♦ ❛♦s ❡❧étr♦♥s ❞❡s❧♦❝❛❞♦s ♣❛r❛ ❛ s✉♣❡r❢í❝✐❡ ♥♦
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✷
❋✐❣✉r❛ ✷✳✼✿ ❊s❜♦ç♦ ❡sq✉❡♠át✐❝♦ ♣❛r❛ ✉♠ s❡♠✐❝♦♥❞✉t♦r t✐♣♦ n✳ ◗ss r❡♣r❡s❡♥t❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡
❝❛r❣❛s ❞♦s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡✳ ◗scr❡♣r❡s❡♥t❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❢♦r♠❛❞❛s ❞❡♥tr♦ ❞♦
s❡♠✐❝♦♥❞✉t♦r✳ ❊F✱ ❊C✱ ❊V r❡♣r❡s❡♥t❛♠ ❛s ❡♥❡r❣✐❛s ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐✱ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ ❡ ❜❛♥❞❛ ❞❡
✈❛❧ê♥❝✐❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❊D r❡♣r❡s❡♥t❛ ❛ ❡♥❡r❣✐❛ ❞♦s ❞♦❛❞♦r❡s ❞♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r✳ ❋✐❣✉r❛
r❡t✐r❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✸❪✳
❞❡ s✉♣❡r❢í❝✐❡ ❛tr❛✈❡ss❛r❡♠ ♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐✱ ❞❡ss❡ ♠♦❞♦ ❞✐♠✐♥✉✐♥❞♦ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛s s✉♣❡r✜❝✐❛✐s ❬✸✱ ✹❪✳
P❡❧❛ ♠❡s♠❛ r❛③ã♦✱ ♦s ❡st❛❞♦s ❞♦❛❞♦r❡s ❞♦ s❡♠✐❝♦♥❞✉t♦r sã♦ ❡❧❡✈❛❞♦s ❛❝✐♠❛ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ❡ ❡stã♦ ✈❛③✐♦s ❞❡ ❡❧étr♦♥s✱ ♦ q✉❡ ♦s ❧❡✈❛ ❛ ❛❝✉♠✉❧❛r ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❞❛ r❡❣✐ã♦ ✜①❛ ✐♦♥✐③❛❞❛ ❞❡ ❞♦❛❞♦r❡s ✭❊D✮✳ ❆ ♣♦s✐çã♦ ❡①❛t❛ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ♥❛ s✉♣❡r❢í❝✐❡ ❞❡♥tr♦ ❞❛ ❜❛♥❞❛
❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡✱ ❡ ♣♦rt❛♥t♦ ♦ t❛♥t♦ q✉❡ ❛s ❜❛♥❞❛s ✐rã♦ s❡ ❝✉r✈❛r✱ sã♦ ❞❡t❡r♠✐♥❛❞♦s ♣❡❧❛ ❝♦♥❞✐çã♦ ❞❡ ♥❡✉tr❛❧✐❞❛❞❡ ✭❡q✳ ✷✳✶✮✳ ❖ ❡q✉✐❧í❜r✐♦ ❡♥❝♦♥tr❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✼ s✐❣♥✐✜❝❛ ❡①❛t❛♠❡♥t❡ ❛ ❝♦♠♣❡♥s❛çã♦ ❞❛s ❝❛r❣❛s ◗ss ♣❡❧❛s ❝❛r❣❛s ❡s♣❛❝✐❛✐s ◗sc ❞❡♥tr♦ ❞❡ ✉♠❛ ❝❡rt❛
♣r♦❢✉♥❞✐❞❛❞❡ ♥♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r✳
❆ ❋✐❣✉r❛ ✷✳✽ ♠♦str❛ ✉♠ ❞✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❛ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞♦s três t✐♣♦ ❞❡ r❡❣✐õ❡s ❞❡ ❝❛r❣❛s s✉♣❡r✜❝✐❛✐s ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r t✐♣♦ n✿ ❞❡♣❧❡çã♦✱ ❛❝✉♠✉❧❛çã♦ ♦✉ ✐♥✈❡rsã♦✳
❉❡✈✐❞♦ à ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s✱ ❡❧étr♦♥s ❧✐✈r❡s ❞❛ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ sã♦ ❛❢❛st❛❞♦s ❞❛ s✉♣❡r❢í❝✐❡✱ t♦r♥❛♥❞♦ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ♥❡st❛ r❡❣✐ã♦ ♠❡♥♦r q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦snb
❞❡♥tr♦ ❞♦ s❡♠✐❝♦♥❞✉t♦r ✭r❡❣✐ã♦ ❢♦r❛ ❞♦ ❛❧❝❛♥❝❡ ❞❛ ❝✉r✈❛t✉r❛ ❞❡ ❜❛♥❞❛s ♥❛ q✉❛❧ ❝❤❛♠❛r❡♠♦s ❞❡ ❜✉❧❦✮✳ ❊st❡ t✐♣♦ ♣❛rt✐❝✉❧❛r ❞❡ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦✳
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✸
❋✐❣✉r❛ ✷✳✽✿ ❊s❜♦ç♦ ❡sq✉❡♠át✐❝♦ ❞❛ ❝✉r✈❛t✉r❛ ❞❡ ❜❛♥❞❛s ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ❡♠ s❡♠✐❝♦♥❞✉t♦r t✐♣♦
n✳ ❆ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ♣♦❞❡ s❡r ❞♦ t✐♣♦ ❞❡♣❧❡çã♦✱ ✐♥✈❡rsã♦ ❡ ❛❝✉♠✉❧❛çã♦✳ ❊F✱ ❊C✱ ❊V r❡♣r❡s❡♥t❛♠
❛s ❡♥❡r❣✐❛s ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐✱ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ ❡ ❜❛♥❞❛ ❞❡ ✈❛❧ê♥❝✐❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❡ ❊i é ❛
❡♥❡r❣✐❛ ✐♥trí♥s❡❝❛ ✭❡♥❡r❣✐❛ ❧♦❝❛❧✐③❛❞❛ ♥♦ ♠❡✐♦ ❞♦ ❣❛♣✮ ❞♦ s❡♠✐❝♦♥❞✉t♦r ❬✸❪✳
❡stá r❡❧❛❝✐♦♥❛❞❛ ❛ ✉♠❛ ❞✐♠✐♥✉✐çã♦ ♥❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡❧étr♦♥s ❧✐✈r❡snb✭❝❛r❣❛ ♠❛❥♦r✐tár✐❛✮ ❡ ✉♠
❛✉♠❡♥t♦ ♥❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❜✉r❛❝♦spb ✭❝❛r❣❛ ♠✐♥♦r✐tár✐❛✮✳ ◆♦ ❝❛s♦ ❞❛ r❡❣✐ã♦ ❞❡ ✐♥✈❡rsã♦✱ ♦
♣r♦❝❡ss♦ ❞❡ ❢♦r♠❛çã♦ ❞❛ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s é s❡♠❡❧❤❛♥t❡ à r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦✱ ♣♦ré♠ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ é tã♦ ❛❧t❛ q✉❡ ♦ ♥í✈❡❧ ❞❡ ❡♥❡r❣✐❛ ✐♥trí♥s❡❝❛ ❊i ❝r✉③❛ ♦
♥í✈❡❧ ❞❡ ❋❡r♠✐ ♣ró①✐♠♦ à s✉♣❡r❢í❝✐❡✳
❏á ❛ r❡❣✐ã♦ ❞❡ ❛❝✉♠✉❧❛çã♦ s✉r❣❡ ❛♣❡♥❛s s❡ ♦s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ❢♦r❡♠ ❞♦❛❞♦r❡s✳ ❈❛s♦ ❡ss❡s ❡st❛❞♦s ❡st❡❥❛♠ ❧♦❝❛❧✐③❛❞♦s ❡♠ ❛❧t❛s ❡♥❡r❣✐❛s✱ ❡❧❡s ♣♦❞❡♠ ❡st❛r ♣❛r❝✐❛❧♠❡♥t❡ ✈❛✲ ③✐♦s ❡ ❝❛rr❡❣❛r❡♠ ✉♠❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ♣♦s✐t✐✈❛ ◗ssq✉❡ é ❝♦♠♣❡♥s❛❞❛ ♣♦r ✉♠❛ ❞❡♥s✐❞❛❞❡
❞❡ ❝❛r❣❛s s✉♣❡r✜❝✐❛✐s ♥❡❣❛t✐✈❛s ❞♦ ✐♥t❡r✐♦r ❞♦ s❡♠✐❝♦♥❞✉t♦r✳ ❊ss❡ ❛❝ú♠✉❧♦ ❞❡ ❝❛r❣❛s ♥❡❣❛t✐✲ ✈❛s ❝✉r✈❛ ❛ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s s✉♣❡r✜❝✐❛✐s ♣❛r❛ ❜❛✐①♦✳ ❊♠ ❝♦♥tr❛st❡ ❝♦♠ ❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦✱ ♦♥❞❡ ❛ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❢♦r♠❛✲s❡ ❛ ♣❛rt✐r ❞❡ ❞♦❛❞♦r❡s ✐♦♥✐③❛❞♦s ❞♦ ❜✉❧❦✱ ❛ r❡❣✐ã♦ ❞❡ ❛❝✉♠✉❧❛çã♦ é ❢♦r♠❛❞❛ ♣♦r ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛s ❧✐✈r❡s✳
❆ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s é ❡♥tã♦ r❡❧❛❝✐♦♥❛❞❛ à ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s ❡❧❡trô♥✐❝❛s✱ ✐✳❡✳✱ ♦ ♣♦t❡♥❝✐❛❧ ♥❛ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❬✹✱ ✸❪✱ ✈✐❛ ❡q✉❛çã♦ ❞❡ P♦✐ss♦♥ ✭❡q✳ ❆✳✾✮✿
d2V dz2 =
−ρ(z)
ǫǫ0
. ✭✷✳✷✮
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✹
❞❡✈✐❞♦ ❛ ❡st❛❞♦s ❛❝❡✐t❛❞♦r❡s ❞♦ ❜✉❧❦ ❊A ♦❝✉♣❛❞♦s q✉❡ sã♦ ❡♠♣✉rr❛❞♦s ❛❜❛✐①♦ ❞♦ ♥í✈❡❧ ❞❡
❋❡r♠✐ ❊F✳ ❊ss❛ ❝❛r❣❛ ❡s♣❛❝✐❛❧ ✜①❛ ♥♦ ❡s♣❛ç♦ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❛ ✉♠❛ ❝✉r✈❛t✉r❛ ♥❡❣❛t✐✈❛ ❞❛s
❜❛♥❞❛s✳ ❆s ❢ór♠✉❧❛s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈❛❧♦r ♠á①✐♠♦ ❞❛ ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s ❞♦ ❝r✐st❛❧ ♣ró①✐♠♦ à s✉♣❡r❢í❝✐❡e❱s ❡♥❝♦♥tr❛♠✲s❡ ❞❡t❛❧❤❛❞❛s ♥♦ ❛♣ê♥❞✐❝❡ ❆✳
❋✐❣✉r❛ ✷✳✾✿ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❛ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ✉♠❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r t✐♣♦p❞♦♣❛❞♦ ❡♠ ❜❛✐①❛ t❡♠♣❡r❛t✉r❛✳ ◗ss r❡♣r❡s❡♥t❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡
❝❛r❣❛s ❞♦s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡✳ ◗scr❡♣r❡s❡♥t❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❢♦r♠❛❞❛s ❞❡♥tr♦ ❞♦
s❡♠✐❝♦♥❞✉t♦r✳ e❱s é ♦ ❝✉r✈❛♠❡♥t♦ ❞❛ ❜❛♥❞❛ ♥❛ s✉♣❡r❢í❝✐❡✱ ❊i é ❛ ❡♥❡r❣✐❛ ✐♥trí♥s❡❝❛✱ ❊F ❛ ❡♥❡r❣✐❛
❞❡ ❋❡r♠✐ ❡ ❊C ❡ ❊V sã♦ ❛s ❜❛♥❞❛s ❞❡ ❝♦♥❞✉çã♦ ❡ ✈❛❧ê♥❝✐❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
✷✳✷✳✶ P✐♥♥✐♥❣ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐
❉✐s❝✉t✐♠♦s ♥❛ s❡çã♦ ♣❛ss❛❞❛ q✉❡ ❛ ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s ❞♦ ♠❛t❡r✐❛❧ s❡♠✐❝♦♥❞✉t♦r ♣ró①✐♠♦ à s✉♣❡r❢í❝✐❡ s✉♣❡r❢í❝✐❡ ❞❡♣❡♥❞❡ ❞❛ ♣♦s✐çã♦ ♥❛ q✉❛❧ ♦s ❡s♣❛ç♦s ❞❡ s✉♣❡r❢í❝✐❡ sã♦ ❝r✐❛❞♦s✳ ❆ ❡①✐stê♥❝✐❛ ❞❡st❡s ❡st❛❞♦s ❣❡r❛ ✉♠ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s ❞❡♥tr♦ ❞♦ s❡♠✐❝♦♥❞✉t♦r ♣❛r❛ t♦r♥❛r ❛ r❡❣✐ã♦ ❡♥❡r❣❡t✐❝❛♠❡♥t❡ ❡q✉✐❧✐❜r❛❞❛✳ ❈♦♠ ✐ss♦✱ ♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ♥❛ s✉♣❡r❢í❝✐❡ ❧♦❝❛❧✐③❛✲s❡ ❡♠ ♣♦s✐çã♦ ❞✐❢❡r❡♥t❡ ❡♠ r❡❧❛çã♦ à ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ à s✉❛ ♣♦s✐çã♦ ♥♦ ❜✉❧❦✳
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✺
♠❛t❡r✐❛❧ ●❛❆s ✭✶✶✵✮ t✐♣♦p❡ t✐♣♦n❡①♣♦st♦ à s✉♣❡r❢í❝✐❡ ❬✷✼❪✱ q✉❡ ❛♣r❡s❡♥t❛♠ ✈❛❧♦r❡s ❧✐♠✐t❡s ♣❛r❛ à ❝✉r✈❛t✉r❛✳
❋✐❣✉r❛ ✷✳✶✵✿ ❈✉r✈❛t✉r❛ ❞❡ ❜❛♥❞❛s ❛❜s♦❧✉t❛|e❱s|❞❡✈✐❞♦ ❛ ♥í✈❡✐s ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ❛❝❡✐t❛✲
❞♦r❡s As ❡ ❞♦❛❞♦r❡s Ds ♣❛r❛ ●❛❆s✭✶✶✵✮ t✐♣♦ n ❡ t✐♣♦p✳ | e❱s | é ♣❧♦t❛❞♦ ✈❡rs✉s ❛ ❞❡♥s✐❞❛❞❡ ❞❡
❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ Nss ✭❡♠❜❛✐①♦✮ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ♣♦r át♦♠♦s ❞❛ s✉♣❡r❢í❝✐❡
✭❛❝✐♠❛✮✳ ❋✐❣✉r❛ ♠♦❞✐✜❝❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✸❪✳
❖❜s❡r✈❛♠♦s ♥❛ ❋✐❣✉r❛ ✷✳✶✵ q✉❡ ♦ ❣rá✜❝♦ r❡♣r❡s❡♥t❛ ❛ ❝✉r✈❛t✉r❛ ❛❜s♦❧✉t❛ ❞❛s ❜❛♥❞❛s
|e❱s |❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ♣♦r át♦♠♦ ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s
❞❡ s✉♣❡r❢í❝✐❡ ◆ss✳ ❖ ✈❛❧♦r ❞❛s ❞♦♣❛❣❡♥s ❞♦ s❡♠✐❝♦♥❞✉t♦r ●❛❆s ✭✶✶✵✮ ✭n= 2×1017✴❝♠3 ❡
p= 1×1017✴❝♠3✮ s❡ ♠❛♥tê♠ ❝♦♥st❛♥t❡ ❡ ❛ s❡♣❛r❛çã♦ ❡♥tr❡ ♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ❞♦s ❡st❛❞♦s
❞❡ s✉♣❡r❢í❝✐❡ ❡ ❛ ❡♥❡r❣✐❛ ❞❛ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ é ❞❛❞❛ ♣♦r Ess✳ ❖❜s❡r✈❛♠♦s q✉❡ ♣❛r❛
Nss ♠❡♥♦r❡s 5×1011✴❝♠2 ❛ ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s é ♣❡q✉❡♥❛✱ ♠❛s ❡♠ ✉♠❛ ❞❡♥s✐❞❛❞❡ ❞❡
❛♣r♦①✐♠❛❞❛♠❡♥t❡ 1012✴❝♠2✱ ❛ ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s ✈❛r✐❛ r❛♣✐❞❛♠❡♥t❡ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❡
◆ss✳ ❆ s❛t✉r❛çã♦ ✜♥❛❧ ❞❡|e❱s|❞á✲s❡ ❡♠ ✉♠ ✈❛❧♦r ❞❡Nss❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡5×1012✴❝♠2✳
❆ ♣❛rt✐r ❞❡ss❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡✱ ♦ ❛✉♠❡♥t♦ ❞❡ ◆ss♥ã♦ ❝❛✉s❛ ✉♠❛ ✈❛r✐❛çã♦
s✐❣♥✐✜❝❛♥t❡ ♥❛ ❝✉r✈❛t✉r❛ ❞❛s ❜❛♥❞❛s✳ ❆ ❡①♣❧✐❝❛çã♦ ❞❡st❡ ❡q✉✐❧í❜r✐♦ é q✉❡ ♦s ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ❡stã♦ ❧♦❝❛❧✐③❛❞♦s ❡♥❡r❣❡t✐❝❛♠❡♥t❡ ♣ró①✐♠♦s ❞♦ ❊F✳
❈❛❞❛ ❛✉♠❡♥t♦ ♥❛ ❞❡♥s✐❞❛❞❡ Nss ❝❛✉s❛ ✉♠ ❛✉♠❡♥t♦ ✐♥✜♥✐t❡s✐♠❛❧ ❡♠ | e❱s | ❡ ✉♠❛
♥❡✉tr❛❧✐③❛çã♦ ❞♦s ❡st❛❞♦s ❧❡✈❛♥❞♦ ❛ ❡st❛❜✐❧✐③❛çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ✭♣✐♥♥✐♥❣✮ q✉❛♥❞♦ Nss
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✻
s❛t✉r❛ q✉❛♥❞♦ ♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ❝r✉③❛ ❛ ❜❛♥❞❛ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡Ess ❬✸✱ ✷✼❪✳
✷✳✷✳✷ P✐♥♥✐♥❣ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r ●❛❆s ✭✵✵✶✮
❆ ❋✐❣✉r❛ ✷✳✶✵ ♠♦str❛ ♦ ✈❛❧♦r ❞♦ ♣✐♥♥✐♥❣ ❞❡ ●❛❆s ✭✶✶✵✮ ❊ss ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡
❡st❛❞♦s ❞❛ s✉♣❡r❢í❝✐❡ ◆ss✳ ❊♥tr❡t❛♥t♦✱ ❝♦♠♦ ❛s ❛♠♦str❛s ❡st✉❞❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ ♣♦ss✉❡♠
❝❛♠❛❞❛s ❞❡ ●❛❆s ✭✵✵✶✮ ❡♠ ❝♦♥t❛t♦ ❝♦♠ ♦ ❛r✱ ❞✐s❝✉t✐r❡♠♦s ❜r❡✈❡♠❡♥t❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r P❛s❤❧❡② ❡t ❛❧✳ ❬✷✽❪ ♣❛r❛ ♦ ♣✐♥♥✐♥❣ ❞❡ ●❛❆s ✭✵✵✶✮ ❡♠ ❢✉♥çã♦ ❞❛ ❞♦♣❛❣❡♠ ❞♦ s❡♠✐❝♦♥❞✉t♦r✳ ❆ ❋✐❣✉r❛ ✷✳✶✶ ♦❜t✐❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❛ ♣❛rt✐r ❞❡ ✐♠❛❣❡♥s ❞❡ ❙❚▼ ✭❙❝❛♥♥✐♥❣ ❚✉♥♥❡❧✐♥❣ ▼✐❝r♦s❝♦♣❡✮✱ ♠♦str❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ◆ss ❡ ❛ ♣♦s✐çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐
❊F ❡♠ ❢✉♥çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❞♦♣❛❣❡♠ ♣❛r❛ ❛♠♦str❛s t✐♣♦n❡ t✐♣♦p✳ ◆♦ ●❛❆s ✭✵✵✶✮ t✐♣♦n✱ ❛
❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❛ s✉♣❡r❢í❝✐❡ ❛✉♠❡♥t❛ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ q✉❛♥❞♦ ♦ ♥í✈❡❧ ❞❡ ❞♦♣❛❣❡♠ ❛t✐♥❣❡ ✈❛❧♦r❡s ≥ 1018✴❝♠3✳ ❊ ❊F é ✜①♦ ✉♠ ♣♦✉❝♦ ❛❝✐♠❛ ❞♦ ❣❛♣ ♣❛r❛ t♦❞♦s ♦s ♥í✈❡✐s ❞❡
❞♦♣❛❣❡♠✳
❋✐❣✉r❛ ✷✳✶✶✿ ❊s❜♦ç♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ s❡♠✐❝♦♥❞✉t♦r ●❛❆s✭✵✵✶✮ t✐♣♦n❡ t✐♣♦p✳
❛✮ ❉❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡Nss ❡♠ ❢✉♥çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❞♦♣❛❣❡♠✳ ❜✮ ◆í✈❡❧ ❞❡ ❋❡r♠✐ ❡♠
❢✉♥çã♦ ❞♦ ♥í✈❡❧ ❞❡ ❞♦♣❛❣❡♠✳ ❚❛♠❜é♠ ❢♦r❛♠ ♣❧♦t❛❞♦s ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ ❞❡❢❡✐t♦s ✐♥strís❡❝♦s ✭k✮ ❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡ ♥❡❝❡ssár✐❛ ♣❛r❛ ♠❛♥t❡r ♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ♥♦ ♠❡✐♦ ❞❡ ❊g
✭i✮✳ ❋✐❣✉r❛ ♠♦❞✐✜❝❛❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✽❪✳
◆♦ ●❛❆s ✭✵✵✶✮ t✐♣♦p✱ ♦❜s❡r✈❛♠♦s q✉❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ❞❡ s✉♣❡r❢í❝✐❡Nss♠❛♥tê♠✲
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✼
♣✐♥♥✐♥❣ ❞♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐ ✈❛r✐❛ ❛❜r✉♣t❛♠❡♥t❡ ❡♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡≥ 1018✴❝♠3✳ ◆♦ ❝❛s♦ ❞❛s ❛♠♦str❛s ❡st✉❞❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ ✭p❂2×1015✴❝♠2✮✱ ♦ ✈❛❧♦r ❞♦ ♣✐♥♥✐♥❣ ❞♦ ♥í✈❡❧ ❞❡
❋❡r♠✐ ❡♥❝♦♥tr❛✲s❡ ❧♦❣♦ ❛❜❛✐①♦ ❞♦ ♠❡✐♦ ❞♦ ❣❛♣✳
✷✳✷✳✸ Pr♦❢✉♥❞✐❞❛❞❡ ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r ●❛❆s ✭✵✵✶✮ t✐♣♦ p
P♦❞❡♠♦s ❡st✐♠❛r ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ✉s❛♥❞♦ ❛ ❡q✉❛çã♦ ❞❡ P♦✐ss♦♥ ✭❡q✳ ❆✳✾✮ ❡ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❡♠ ✉♠ s❡♠✐❝♦♥❞✉t♦r t✐♣♦p❛s ❝❛r❣❛s ❡s♣❛❝✐❛✐s sã♦ ♥❡❣❛t✐✈❛s ✭NA✮✱
♦✉ s❡❥❛
Qsc=eNAd ✭✷✳✸✮
♦♥❞❡ Qsc é ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛s s✉♣❡r✜❝✐❛✐s ✭❝❛r❣❛ s✉♣❡r✜❝✐❛❧ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ár❡❛✮✱eé
❛ ❝❛r❣❛ ❞♦ ❡❧étr♦♥ ❡dé ❛ ❡s♣❡ss✉r❛ ❞❛ ❝❛♠❛❞❛ ❞❡ ❞❡♣❧❡çã♦✳ ❉❡♥tr♦ ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦✱ ♦s ❛❝❡✐t❛❞♦r❡s ❡stã♦ ❝♦♠♣❧❡t❛♠❡♥t❡ ✐♦♥✐③❛❞♦s✳
❆ ❡q✉❛çã♦ ❞❡ P♦✐ss♦♥ t♦r♥❛✲s❡ ❡♥tã♦
d2V dz2 =
−ρ(z)
ǫǫ0 = −dǫ dz = −ρ ǫǫ0 = eNA ǫǫ0 ✭✷✳✹✮
❯♠❛ ✐♥t❡❣r❛çã♦ s✐♠♣❧❡s ❧❡✈❛ ❛ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❡♥tr♦ ❞❛ r❡❣✐ã♦ ❞❡ ❝❛r❣❛s ❡s♣❛❝✐❛✐s✿
ε(z) = −ρ
ǫǫ0 = eNA
ǫǫ0 , 0≤z≤d. ✭✷✳✺✮
❋❛③✲s❡ ♠❛✐s ✉♠ ✐♥t❡❣r❛çã♦ ♣❛r❛ ♦❜t❡r ♦ ✈❛❧♦r ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡♥tr♦ ❞❛ r❡❣✐ã♦ ❞❡ ❞❡♣❧❡çã♦ ✭φ(z)✮ ✭❋✐❣✳ ✷✳✾✮✿
φ(z) =φb−
eNA
ǫǫ0
(z−d)2, 0≤z≤d ✭✷✳✻✮
❡ ♦ ✈❛❧♦r ♠á①✐♠♦ ❞♦ ♣♦t❡♥❝✐❛❧e❱s ♥❛ s✉♣❡r❢í❝✐❡ é
Vs=φs−φb=
−eNAd2
ǫǫ0 ✭✷✳✼✮
❈♦♠ ♦s ✈❛❧♦r❡s ❥á ❡st❛❜❡❧❡❝✐❞♦s ♥❛s s❡çõ❡s ❛♥t❡r✐♦r❡s ◆A≃1Ö1016✴❝♠3✱ e❱s ≃0,6 ❡❱
❈❛♣ít✉❧♦ ✷✳ ❍❡t❡r♦❡str✉t✉r❛s ❙❡♠✐❝♦♥❞✉t♦r❛s ✶✽
✷✳✸ ◆❛♥♦♠❡♠❜r❛♥❛s ❙❡♠✐❝♦♥❞✉t♦r❛s
❖s ♣♦♥t♦s q✉â♥t✐❝♦s ❞❡ ■♥❆s ❡st✉❞❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ❝r❡s❝✐❞♦s ❡♥tr❡ ❝❛♠❛❞❛s ❞❡ ✉♠❛ ❤❡t❡r♦❡str✉t✉r❛ s❡♠✐❝♦♥❞✉t♦r❛ ❞❡ ●❛❆s✴❆❧●❛❆s✳ ❆ ❡str✉t✉r❛ ❡ ❛ ❢❛❜r✐❝❛çã♦ ❞❛s ❛♠♦str❛s ❡st✉❞❛❞❛s sã♦ ❞❡s❝r✐t❛s ❡♠ ❞❡t❛❧❤❡ ♥❛ s❡çã♦ ✸✳✸✳✶✳
❯♠ ✜❧♠❡ s❡♠✐❝♦♥❞✉t♦r ❞❡ ❛té ❛❧❣✉♠❛s ❝❡♥t❡♥❛s ❞❡ ♥❛♥ô♠❡tr♦s ❝r❡s❝✐❞♦ s♦❜r❡ ✉♠ s✉❜s✲ tr❛t♦ ♣♦❞❡ s❡r ❝♦♠♣r❡❡♥❞✐❞♦ ❝♦♠♦ ✉♠❛ ♥❛♥♦❡str✉t✉r❛ ❝r✐st❛❧✐♥❛✱ ♣♦ré♠ ❛♦ ✉t✐❧✐③❛r♠♦s ♠é✲ t♦❞♦s ♣❛r❛ ❞❡s✈✐♥❝✉❧❛r ❝❛♠❛❞❛s ✜♥❛s ❜❡♠ ❞❡✜♥✐❞❛s ❞♦ s✉❜str❛t♦✱ ❢❛❜r✐❝❛♠♦s ✉♠❛ ❡str✉t✉r❛ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♥❛♥♦♠❡♠❜r❛♥❛ s❡♠✐❝♦♥❞✉t♦r❛ ✭◆▼✮✳ ❊ss❛ ❝❛r❛❝t❡ríst✐❝❛ t♦r♥❛ ❛s ♥❛♥♦♠❡♠✲ ❜r❛♥❛s ❤❡t❡r♦❡str✉t✉r❛s ❡①tr❡♠❛♠❡♥t❡ ✐♥t❡r❡ss❛♥t❡s ❞❡ ❛♥❛❧✐s❛r ❞❡✈✐❞♦ à ♠❛✐♦r ✢❡①✐❜✐❧✐❞❛❞❡✱ à ♣r♦①✐♠✐❞❛❞❡ ❡♥tr❡ ❛s s✉♣❡r❢í❝✐❡s✱ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦rq✉❡ ♦ ♣r♦❝❡ss♦ ❞❡ ❢❛❜r✐❝❛çã♦ ♣❡r✲ ♠✐t❡ às ♥❛♥♦♠❡♠❜r❛♥❛s s❡r❡♠ ❧✐✈r❡s ❞❡ q✉❛✐sq✉❡r r❡str✐çõ❡s ❝❛✉s❛❞❛s ♣❡❧♦ s✉❜str❛t♦ rí❣✐❞♦ ♥♦ q✉❛❧ ❛ ♥❛♥♦❡str✉t✉r❛ s❡♠✐❝♦♥❞✉t♦r❛ ♦r✐❣✐♥❛❧ ❢♦✐ ❝r❡s❝✐❞❛ ❬✷❪✳
❆ ❋✐❣✉r❛ ✷✳✶✷ ✐❧✉str❛ ❡①❡♠♣❧♦s ❞❡ ♣r♦♣r✐❡❞❛❞❡s ❞❡ ♥❛♥♦♠❡♠❜r❛♥❛s s❡♠✐❝♦♥❞✉t♦r❛s✳ ❖ ❡①❡♠♣❧♦ ❛✮ ✐❧✉str❛ ♥❛♥♦♠❡♠❜r❛♥❛s ❡str❡✐t❛s ❡♠ ❢♦r♠❛t♦ ❞❡ ✜t❛s✱ ❢❛❜r✐❝❛❞❛s ❛ ♣❛rt✐r ❞❡ ✇❛❢❡rs ❞❡ ❝r✐st❛✐s ú♥✐❝♦s ❝♦♠ ❛❧t♦ ❢❛t♦r ❞❡ q✉❛❧✐❞❛❞❡✳ ❊ss❛ ❡str✉t✉r❛ ❝♦♥❞✉③ ❛ r❡s✉❧t❛❞♦s ✐♥t❡r❡ss❛♥t❡s✱ ♣♦✐s s✉❛ ❢❛❜r✐❝❛çã♦ ❝♦♥s❡r✈❛ ♦ ❢❛t♦r ❞❡ q✉❛❧✐❞❛❞❡ ♣r❡s❡♥t❡ ♥♦ s❡♠✐❝♦♥❞✉t♦r ♦r✐❣✐♥❛❧✳ ❖✉tr♦ ❞✐s♣♦s✐t✐✈♦ ✐♥t❡r❡ss❛♥t❡ ♣♦❞❡ s❡r ♣r♦❞✉③✐❞♦ ❛♦ ❞❡♣♦s✐t❛r✲s❡ ✉♠❛ ♥❛♥♦♠❡♠✲ ❜r❛♥❛ s♦❜r❡ ✉♠ s✉❜str❛t♦ ❡❧ást✐❝♦ ❡st✐❝❛❞♦✳ ❆♦ ❧✐❜❡r❛r ❛ t❡♥sã♦ ❡❧ást✐❝❛ ❞❡ss❡ s✉❜str❛t♦✱ ❛ ♥❛♥♦♠❡♠❜r❛♥❛ s♦❢r❡ ✉♠❛ ❝♦♠♣r❡ssã♦ q✉❡ ❝r✐❛ r❡❣✐õ❡s r✉❣♦s❛s ❛♦ ❧♦♥❣♦ ❞❛ ❤❡t❡r♦❡str✉t✉r❛✳ ✭❋✐❣✳ ✷✳✶✷ ❜✮
❆ ❋✐❣✉r❛ ✷✳✶✷ ❝✮ ✐❧✉str❛ ✉♠ ❝✐r❝✉✐t♦ ❤❡t❡r♦❣ê♥❡♦ ❞❡ ♠✉❧t✐❝❛♠❛❞❛s tr✐❞✐♠❡♥s✐♦♥❛✐s s♦❜r❡ ✉♠ s✉❜str❛t♦ ❞❡ ♣❧ást✐❝♦ ❢❛❜r✐❝❛❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ♥❛♥♦♠❡♠❜r❛♥❛✳ ❊ss❡s ❝✐r❝✉✐t♦s ♣♦ss✉❡♠ ❡❧❡♠❡♥t♦s ❛t✐✈♦s ❡♠ ❞✐❢❡r❡♥t❡s ❝❛♠❛❞❛s q✉❡ ♣♦❞❡♠ s❡r ❝♦♥❡❝t❛❞♦s ❛tr❛✈és ❞❡ ✈✐❛s ♠❡tá✲ ❧✐❝❛s✱ ❝r✐❛♥❞♦ ❛ss✐♠ ❞✐s♣♦s✐t✐✈♦s s♦✜st✐❝❛❞♦s✳ ❖ ú❧t✐♠♦ ❡①❡♠♣❧♦ ❝✐t❛❞♦ ❜r❡✈❡♠❡♥t❡ ♥❡st❡ tr❛❜❛❧❤♦ é ❞❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✷ ❞✮✳ ◆❡st❛ ✜❣✉r❛ ✈❡♠♦s ✉♠❛ ❛♣❧✐❝❛çã♦ ❞❡ ♥❛♥♦♠❡♠❜r❛♥❛s ❡♠ ❞✐s♣♦s✐t✐✈♦s ❜✐♦✲✐♥t❡❣r❛❞♦s✳ ❯♠❛ ♠❡♠❜r❛♥❛ ❞❡ 2 ♠♠ ❢♦r♠❛❞❛ ♣♦r ✉♠ ❞✐s♣♦s✐t✐✈♦ ❝♦♠
♠✉❧t✐♣❧❡①♦✱ ❜❛s❡❛❞♦ ❡♠ ♥❛♥♦♠❡♠❜r❛♥❛s ❞❡ s✐❧✐❝♦♥❡ ✭≃ 2,5 µ♠✮ ❡♠ ❢♦r♠❛t♦ ❞❡ ✜t❛s✱ ❡stá
