❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦
❙í♥t❡s❡ ❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♠❛❣♥ét✐❝❛s ❞❡ ❈♦ ❡ ◆✐ ❝♦♠ ❛♣❧✐❝❛çã♦ ❡♠ ♠❛❣♥❡t♦ ❤✐♣❡rt❡r♠✐❛
♣♦r
◆❛❣✐❧s♦♥ ▼❡♥❞❡s ❞❡ ❙♦✉s❛
❖r✐❡♥t❛❞♦r✿ ❉r✳ ▼❛r❝♦ ❆♥t♦♥✐♦ ▼♦r❛❧❡s ❚♦rr❡s
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❙í♥t❡s❡ ❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♠❛❣♥ét✐❝❛s ❞❡ ❈♦ ❡ ◆✐ ❝♦♠ ❛♣❧✐❝❛çã♦ ❡♠ ♠❛❣♥❡t♦ ❤✐♣❡rt❡r♠✐❛
◆❛❣✐❧s♦♥ ▼❡♥❞❡s ❞❡ ❙♦✉s❛
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞♦ ❉❡♣❛rt❛✲ ♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❝♦♠♦ ♣❛rt❡ ❞♦s ♣ré✲r❡q✉✐s✐t♦s à ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❊❙❚❘❊ ❡♠ ❋❮❙■❈❆✳
❖r✐❡♥t❛❞♦r✿ ❉r✳ ▼❛r❝♦ ▼♦r❛❧❡s ❚♦rr❡s
❉❡❞✐❝❛tór✐❛
❉❡❞✐❝♦ ❡st❡ tr❛❜❛❧❤♦ ❛ t♦❞❛s ❛s ♣❡ss♦❛s q✉❡ ❛♠♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ♠✐♥❤❛ ♥♦✐✈❛ ❊❞✐❛♥❛ ▼❛r✐♥❤♦ ♣❡❧♦ ❛♣♦✐♦✱ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳
❼ ❆♦s ♠❡✉s ♣❛✐s ❋r❛♥❝✐s❝♦ ❙♦✉s❛ ❡ ❘❛✐♠✉♥❞❛ ▼❡♥❞❡s✱ ♣♦r s❡r❡♠ ❛s ♣❡s✲ s♦❛s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❞❛ ♠✐♥❤❛ ✈✐❞❛✳
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛♦ ♠❡♥t♦r ❞❡ t✉❞♦✱ ❉❡✉s✳ ❈♦♠ ❛ ❛❥✉❞❛ ❞❊❧❡ t✉❞♦ é ♣♦ssí✈❡❧✳
❊♠ ❡s♣❡❝✐❛❧ ❛❣r❛❞❡ç♦✿
❼ ❆♦ Pr♦❢✳ ❉r✳ ▼❛r❝♦ ▼♦r❛❧❡s✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡ ❣r❛♥❞❡s ❝♦♥tr✐❜✉✐çõ❡s ♥❛ ♠✐♥❤❛ ✈✐❞❛ ♣❡ss♦❛❧ ❡ ♣r♦✜ss✐♦♥❛❧✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r s❡✉ ❡♥s✐♥❛♠❡♥t♦✱ ❛♣♦✐♦✱ ❡ ✐♥❝❡♥t✐✈♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❼ ❆♦s ❝♦❧❡❣❛s ❞❛ ❙❛❧❛ ❞♦s ❊①♣❡r✐♠❡♥t❛✐s ❡ ❞♦ ▲❛❜♦r❛tór✐♦ ❡♠ ❡s♣❡❝✐❛❧ ❛♦s ❛♠✐❣♦s ❆♥❣❡❧❛✱ ❙✉③❛♥❛✱ ❙✉③❛♥❡✱ ❉❛♥②❡❧❧❡✱ ❊❧♦✐s❡✱ ❆♥❞r❡✐❛✱ ❊❞✐♠✐❧s♦♥✱ ❑❡♥♥❡❞②✱ ❈❛r❧♦s✱ ◆❛③❛r❡♥♦ ❡ ❛♦s ❞❡♠❛✐s ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ❛♣♦✐♦✳
❼ ❆ t♦❞♦s ♦s ❆♠✐❣♦s✱ ❡♠ ❡s♣❡❝✐❛❧✿ ❉❛♥②✱ ▲✉❝✐❛♥♦✱ ●✉❣✉✱ ❮❝❛r♦✱ ❆❞r✐❛♥♦✱ ❘✐❝❛r❞♦ ❡ ❛♦s ❞❡♠❛✐s ♣❡❧♦s ✐♥❝♦♥tá✈❡✐s ♠♦♠❡♥t♦s ❞❡ ✐♥❝❡t✐✈♦ ❡ ❞✐✈❡rsã♦ ❢♦✐ ❜♦♠ ❞❡♠❛✐s ❝♦♥❤❡❝ê✲❧♦s✳
❼ ❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❋❚❊✲❯❋❘◆ q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❛♦s Pr♦❢s✳ ❋r❛♥❝✐s❝♦ ❇r❛❞②✱ ❋r❛♥❝✐s❝♦ ❆❧❡①❛♥❞r❡✱ ▼❛❞r❛s ●❛♥❞❤✐ ❡ ▲✉❝✐❛♥♦ ❘♦❞r✐❣✉❡s✳
❼ ❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❋❚❊✲❯❋❘◆ ❡♠ ❡s♣❡❝✐❛❧ ❛ ❈❡❧✐♥❛ ♣❡❧❛ ❛❥✉❞❛ ♥❛s ❤♦r❛s s♦❧✐❝✐t❛❞❛s✳
❘❡s✉♠♦
◆❛♥♦♣❛rtí❝✉❧❛s ✭◆♣s✮ sã♦ ✐♠♣♦rt❛♥t❡s ♥♦ ❡st✉❞♦ ❞❡ ♥♦✈♦s ❢❡♥ô♠❡♥♦s ♥❛ ❢ís✐❝❛ ❡ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈❛s ❛♣❧✐❝❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s✳ ◆❛♥♦♣❛rtí❝✉✲ ❧❛s ♠❛❣♥ét✐❝❛s ♠❡tá❧✐❝❛s t❛✐s ❝♦♠♦ ◆íq✉❡❧ ❡ ❈♦❜❛❧t♦ s✉r❣❡♠ ❝♦♠♦ ♦❜❥❡t♦s ♣r♦♠✐ss♦r❡s ❞❡✈✐❞♦ ❛s s✉❛s ❛♣❧✐❝❛❜✐❧✐❞❛❞❡s ❡♠ ✈ár✐❛s ár❡❛s ❞❛ ❝✐ê♥❝✐❛ ❡ t❡❝✲ ♥♦❧♦❣✐❛✳ ◆♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛♠♦s ✉♠ ❡st✉❞♦ s♦❜r❡ ♦ ♠ét♦❞♦ ❞❡ sí♥t❡s❡✱ ❝❛r❛❝t❡r✐③❛çã♦ ❡str✉t✉r❛❧ ❡ ♠❛❣♥ét✐❝❛ ❡♠ ♥❛♥♦♣❛rtí❝✉❧❛s ❞❡ ◆✐ ❡ ❈♦✳ ❆s ❛♠♦str❛s ❢♦r❛♠ ♣r❡♣❛r❛❞❛s ♣❡❧♦ ♠ét♦❞♦ s♦❧✲❣❡❧ ♠♦❞✐✜❝❛❞♦ ❡ ❢♦r♠❛❞❛s ♥♦s ♣♦r♦s ❞♦ ♣♦❧í♠❡r♦ q✉✐t♦s❛♥❛✱ ❛ r❡❞✉çã♦ ♦❝♦rr❡✉ ❡♠ ❛✉sê♥❝✐❛ ❞❡ ✢✉①♦ ❞❡ ❍✐❞r♦❣ê♥✐♦✳ ❆ ❢❛s❡ ❝r✐st❛❧✐♥❛ ❞♦ ◆✐ ❡ ❈♦ é ❝ú❜✐❝❛ ❞❡ ❢❛❝❡ ❝❡♥tr❛❞❛ ❡ s❡✉s ❞✐â✲ ♠❡tr♦s ✈❛r✐❛r❛♠ ❞❡ ✺✾✲✼✼♥♠ ❡ ✶✾✲✺✵♥♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆s s✉♣❡r❢í❝✐❡s ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s ❢♦r❛♠ ♥❛t✉r❛❧♠❡♥t❡ ♣❛ss✐✈❛❞❛s ❝♦♠ s❡✉s ♠♦♥ó①✐❞♦s ❛♣r❡s❡♥✲ t❛♥❞♦ ❡st❛❜✐❧✐❞❛❞❡ q✉í♠✐❝❛ ♣♦r ❧♦♥❣♦s ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦✳ ❆ ❡str✉t✉r❛ ❢♦r✲ ♠❛❞❛ é ❞♦ t✐♣♦ ♥ú❝❧❡♦✴❝❛s❝❛✱ ♦ q✉❡ ❢❛✈♦r❡❝❡✉ ❛s ✐♥t❡r❛çõ❡s ❞❡ ❡①❝❤❛♥❣❡ ❜✐❛s ❡♥tr❡ ♦ ♥ú❝❧❡♦ ❢❡rr♦♠❛❣♥ét✐❝♦ ✭❋▼✮ ❡ ❛ ❝❛s❝❛ ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝❛ ✭❆❋▼✮✳ ❆s ❝♦♥❞✐çõ❡s ❞❡ sí♥t❡s❡ ❢♦r❛♠ ♦t✐♠✐③❛❞❛s ♣❛r❛ ♦❜t❡r ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ❢❛s❡ ❋▼✳ ❆♠❜❛s ◆Ps ❢♦r❛♠ s✉❜♠❡t✐❞❛s à ❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❆❈ ❡ ❤♦✉✈❡ ❛q✉❡❝✐♠❡♥t♦ rá♣✐❞♦ ❛té ❛t✐♥❣✐r t❡♠♣❡r❛t✉r❛ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✹✵➦❈ ❡♠ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ ❞❡ ❛té ✺ ♠✐♥✳ ❆s ❛♠♦str❛s ❞✐s♣❡rs❛❞❛s ❡♠ á❣✉❛✱ ❛t✐♥❣✐✲ r❛♠ t❡♠♣❡r❛t✉r❛s ❞❡ ✹✵✲ ✺✾➦❈ ❞❡ ❛q✉❡❝✐♠❡♥t♦ ❡♠ ❛té ✶✵ ♠✐♥✉t♦s✱ ♠♦str❛♥❞♦ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ❤✐♣❡rt❡r♠✐❛ ♠❛❣♥ét✐❝❛✳
P❆▲❆❱❘❆❙✲❈❍❆❱❊✿ ◆❛♥♦♣❛rtí❝✉❧❛s✱ ◆íq✉❡❧✱ ❈♦❜❛❧t♦✱ ▼♦♥ó✲ ①✐❞♦s ❡ ❍✐♣❡rt❡r♠✐❛ ♠❛❣♥ét✐❝❛
❆❜str❛❝t
◆❛♥♦♣❛rt✐❝❧❡s ❛r❡ ✐♠♣♦rt❛♥t❡ ❢♦r t❤❡ st✉❞② ♦❢ ♥❡✇ ♣❤❡♥♦♠❡♥❛ ❛♥❞ ❢♦r t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ♥❡✇ ❛♣♣❧✐❝❛t✐♦♥s✳ ▼❡t❛❧❧✐❝ ♠❛❣♥❡t✐❝ ♥❛♥♦♣❛rt✐❝❧❡s ❧✐❦❡ ❈♦❜❛❧t ❛♥❞ ◆✐❝❦❡❧ ❛r❡ ✐♠♣♦rt❛♥t ❢♦r t❤❡✐r ❛♣♣❧✐❝❛t✐♦♥s ✐♥ ♥❛♥♦s❝✐❡♥❝❡ ❛♥❞ ♥❛✲ ♥♦t❡❝❤♥♦❧♦❣②✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ r❡♣♦rt ♦♥ t❤❡ s②♥t❤❡s✐s ❛♥❞ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ ◆✐ ❛♥❞ ❈♦ ♥❛♥♦♣❛rt✐❝❧❡s✳ ❚❤❡ ♥❛♥♦♣❛rt✐❝❧❡s ✇❡r❡ ♣r❡♣❛r❡❞ ❜② t❤❡ ♠♦❞✐✲ ✜❡❞ s♦❧✲❣❡❧ ♠❡t❤♦❞ ❛♥❞ ✇❡r❡ ❢♦r♠❡❞ ✐♥ t❤❡ ♣♦r❡✲♥❡t✇♦r❦ ♦❢ t❤❡ ❜✐♦♣♦❧②♠❡r q✉✐t♦s❛♥✳ ❚❤❡ r❡❞✉❝t✐♦♥ ♦❝❝✉rr❡❞ ✐♥ ❛❜s❡♥❝❡ ♦❢ ❍2 ✢✉①✳ ❚❤❡ ♠❡t❛❧❧✐❝ ♣❛rt✐✲
❝❧❡s ❛♥❞ t❤❡✐r ♠♦♥♦①✐❞❡s ❤❛✈❡ ❛ ❢❛❝❡✲❝❡♥t❡r❡❞✲ ❝✉❜✐❝ str✉❝t✉r❡✳ ❚❤❡ ♠❡t❛❧❧✐❝ ♣❛rt✐❝❧❡s s✐③❡s r❛♥❣❡❞ ❢r♦♠ ✺✾ t♦ ✼✼ ♥♠ ❛♥❞ ❢r♦♠ ✶✾ t♦ ✺✵ ♥♠ ❢♦r ◆✐ ❛♥❞ ❈♦✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡✐r ♠♦♥♦①✐❞❡s ❝❤❡♠✐❝❛❧❧② ♣❛ss✐✈❛t❡❞ t❤❡ ♠❡t❛❧❧✐❝ ❝♦r❡s✱ ❛♥❞ ❛❢t❡r s❡✈❡r❛❧ ✇❡❡❦s ✇❡ ❤❛✈❡ ♥♦t ♦❜s❡r✈❡❞ ❢✉rt❤❡r ✐♥❝r❡❛s❡ ✐♥ ♦①✐❞❛t✐♦♥✳ ❚❤❡ s②♥t❤❡s✐s ♠❡t❤♦❞ ✇❛s t✉♥❡❞ t♦ ♦❜t❛✐♥ ♠❛✐♥❧② t❤❡ ❢❡rr♦♠❛❣♥❡t✐❝ ♣❤❛s❡✳ ❚❤❡ s②st❡♠ ❜❡❤❛✈❡s ❧✐❦❡ ❛ ❝♦r❡✴s❤❡❧❧ str✉❝t✉r❡ ✇✐t❤ ❛ ❢❡rr♦♠❛❣♥❡t✐❝ ❝♦r❡ ❛♥❞ ❛♥ ❛♥t✐❢❡rr♦♠❛❣♥❡t✐❝ s❤❡❧❧✳ ❊①❝❤❛♥❣❡ ❜✐❛s ❡✛❡❝t ✇❛s ♦❜s❡r✈❡❞ ❛t t❡♠♣❡r❛t✉r❡s ❜❡❧♦✇ t❤❡ ◆é❡❧ t❡♠♣❡r❛t✉r❡✳ ❇♦t❤ s②st❡♠s ✇❡r❡ s✉❜♠✐tt❡❞ t♦ ❛♥ ❛❧t❡r♥❛t❡❞ ♠❛❣♥❡t✐❝ ✜❡❧❞ ❛♥❞ t❤❡ ❤❡❛t r❡❧❡❛s❡❞ ❜② t❤❡ ♣❛rt✐❝❧❡s ✐♥❝r❡❛s❡❞ t❤❡ t❡♠♣❡r❛✲ t✉r❡ t♦ ✶✹✵➦❈ ✐♥ ❛♥ ✐♥t❡r✈❛❧ ♦❢ ✺ ♠✐♥✳ ❙✐♠✐❧❛r st✉❞✐❡s ✐♥ s❛♠♣❧❡s ❞✐s♣❡rs❡❞ ✐♥ ✇❛t❡r ✐♥❝r❡❛s❡❞ t❤❡ t❡♠♣❡r❛t✉r❡s t♦ ✹✵✲✺✾➦❈✱ t❤❡s❡ r❡s✉❧ts s✉❣❣❡st t❤❛t t❤❡s❡ ♠❛t❡r✐❛❧s ❛r❡ ❝❛♥❞✐❞❛t❡s ❢♦r ♠❛❣♥❡t✐❝ ❤②♣❡rt❤❡r♠✐❛✳
❑❊❨❲❖❘❉❙✿ ◆❛♥♦♣❛rt✐❝❧❡s✱ ◆✐❝❦❡❧✱ ❈♦❜❛❧t✱ ▼♦♥♦①✐❞❡s ❡ ♠❛❣✲ ♥❡t✐❝ ❍②♣❡rt❤❡r♠✐❛
❮◆❉■❈❊
▲✐st❛ ❞❡ ✜❣✉r❛s ✈✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✹
✷✳✶ ■♥tr♦❞✉çã♦ ❛♦ ▼❛❣♥❡t✐s♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷ ◆❛♥♦♠❛❣♥❡t✐s♠♦ ❡ ♥❛♥♦♠❛t❡r✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷✳✶ ❋❡rr♦♠❛❣♥❡t✐s♠♦ ❡ ❆♥t✐❢❡rr♦♠❛❣♥❡t✐s♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷✳✷ ■♥t❡r❛çõ❡s ♠❛❣♥ét✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷✳✸ ■♥t❡r❛çã♦ ❞❡ tr♦❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✹ ■♥t❡r❛çã♦ ❞✐♣♦❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸ P❛rtí❝✉❧❛s ♠♦♥♦❞♦♠í♥✐♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✸✳✶ ❙✉♣❡r♣❛r❛♠❛❣♥❡t✐s♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✹ ❊①❝❤❛♥❣❡ ❇✐❛s ❡♠ ◆❛♥♦♣❛rtí❝✉❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✹✳✶ ❈✉r✈❛s ❞❡ ❤✐st❡r❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✹✳✷ ❊①❝❤❛♥❣❡ ❜✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺ ◆❛♥♦♣❛rtí❝✉❧❛s ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❜✐♦♠é❞✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✺✳✶ ❍✐♣❡rt❡r♠✐❛ ♠❛❣♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✷✳✺✳✷ ▼❡❝❛♥✐s♠♦s ❢ís✐❝♦s q✉❡ ✐♥✢✉❡♥❝✐❛♠ ♥❛ ❣❡r❛çã♦ ❞❡ ❝❛❧♦r
❞❡ ◆Ps ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✻ ❆ t❛①❛ ❞❡ ❛❜s♦rçã♦ ❡s♣❡❝í✜❝❛ ✭❙❆❘✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✼ Pr♦♣r✐❡❞❛❞❡s ❡str✉t✉r❛✐s ❡ ♠❛❣♥ét✐❝❛s ❞❡ ❈♦✱ ◆✐ ❡ s❡✉s r❡s✲
♣❡❝t✐✈♦s ó①✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✼✳✶ ❈♦✱ ❈♦❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✼✳✷ ◆✐ ❡ ◆✐❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✽ Pr♦♣r✐❡❞❛❞❡s ❢ís✐❝♦✲q✉í♠✐❝♦ ❞❛ ◗✉✐t♦s❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✽✳✶ ▼ét♦❞♦ s♦❧✲❣❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸ Pr♦❝❡❞✐♠❡♥t♦s ❊①♣❡r✐♠❡♥t❛✐s ✸✸
✸✳✶ Pr♦❞✉çã♦ ❞❛s ❛♠♦str❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✶✳✶ ❙í♥t❡s❡ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ❞❡ ❈♦❜❛❧t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✶✳✷ ❙í♥t❡s❡ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ❞❡ ♥íq✉❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷ ❈❛r❛❝t❡r✐③❛çã♦ ❞❛s ❛♠♦str❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✷✳✶ ❆♥á❧✐s❡ ❡str✉t✉r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✷✳✷ ▼✐❝r♦s❝♦♣✐❛ ❊❧❡trô♥✐❝❛ ❞❡ ❱❛rr❡❞✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷✳✸ ❊s♣❡❝tr♦s❝♦♣✐❛ ♥❛ r❡❣✐ã♦ ❞♦ ■♥❢r❛✈❡r♠❡❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷✳✹ ❙✐st❡♠❛ ❞❡ ♠❡❞✐❞❛ ♣❛r❛ ▼❛❣♥❡t♦ ❍✐♣❡rt❡r♠✐❛ ✳ ✳ ✳ ✳ ✳ ✹✹
✹ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✹✻
✹✳✶ ✶➟ ♣❛rt❡✿ ❛♠♦str❛s ❞❡ ❈♦❜❛❧t♦ tr❛t❛❞❛s t❡r♠✐❝❛♠❡♥t❡ à ✈á❝✉♦ ✹✻ ✹✳✶✳✶ ❈❛r❛❝t❡r✐③❛çã♦ ❡str✉t✉r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✶✳✷ ❆♥á❧✐s❡ ♠♦r❢♦❧ó❣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✶✳✸ ▼❡❞✐❞❛s ❞❡ ■♥❢r❛✈❡r♠❡❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✶✳✹ ▼❡❞✐❞❛s ▼❛❣♥ét✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✷ ✷➟ P❛rt❡✿ ❆♠♦str❛s ❞❡ ◆íq✉❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✹✳✷✳✶ ❈❛r❛t❡r✐③❛çã♦ ❊str✉t✉r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✷✳✷ ❈❛r❛❝t❡r✐③❛çã♦ ♠♦r❢♦❧ó❣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✷✳✸ ❈❛r❛❝t❡r✐③❛çã♦ ▼❛❣♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✷✳✹ ❍✐♣❡rt❡r♠✐❛ ♠❛❣♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✺ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ✼✽
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✷✳✶ ▼♦✈✐♠❡♥t♦ ❞♦ ❡❧étr♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷ P❛rtí❝✉❧❛s ❝♦♠ ❡st❛❞♦ ♠♦♥❞♦♠í♥✐♦ (D < Dc) ❡ ❡st❛❞♦ ♠✉❧t✐✲
❞♦♠í♥✐♦ (D > Dc) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✸ ❝♦❡r❝✐✈✐❞❛❞❡ ✈❡rs✉s ❞✐â♠❡tr♦ ❞❛ ♣❛rtí❝✉❧❛ ❡ s✉❛ ✐♥✢✉ê♥❝✐❛ ♥♦s
r❡❣✐♠❡s ♠❛❣♥ét✐❝♦s ❞❛s ♣❛rtí❝✉❧❛s ❬✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✹ ✭❛✮ ❊✐①♦ ✉♥✐❛①✐❛❧ ❞❡ ❢á❝✐❧ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✉♠❛ ♥❛♣❛rtí❝✉❧❛ ❡
✭❜✮ ❞❡♣❡♥❞ê♥❝✐❛ ❞❛ ❜❛rr❡✐r❛ ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ❝❛♠♣♦ ♥✉❧♦ ✭❧✐♥❤❛
❝♦♥t✐♥✉❛✮ ❡ ❝❛♠♣♦ ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦ ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮ ❬✸❪✳ ✳ ✳ ✶✹ ✷✳✺ ❈✉r✈❛s ❞❡ ❤✐st❡r❡s❡ ❡♠ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✻ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ r❡❧❛①❛çã♦ ❞❡ ◆é❡❧ ❡ ❇r♦✇♥ ❬✷✾❪✳ ✷✸ ✷✳✼ Pr✐♥❝✐♣❛✐s ❡str✉t✉r❛s ❝r✐st❛❧✐♥❛s ♣r❡s❡♥t❡s ♥♦s ♠❡t❛✐s ❬✸✾❪✳ ✳ ✳ ✷✺ ✷✳✽ ❈✉r✈❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❡ ❞✐r❡çã♦ ❝r✐st❛❧♦❣rá✜❝❛ ❞♦ ♥íq✉❡❧ ❬✻❪✳ ✷✽ ✷✳✾ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦s ❜✐♦♣♦❧í♠❡r♦s q✉✐t♦s❛♥❛ ❡ q✉✐✲
t✐♥❛ ❬✹✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ sí♥t❡s❡ ❞❡ ◆Ps ❞❡ ❝♦❜❛❧t♦ ✳ ✳ ✳ ✸✹ ✸✳✷ ❊q✉✐♣❛♠❡♥t♦ ❉❘❳✱ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛♥á❧✐s❡ ❡str✉t✉r❛❧ ❞❛s ❛♠♦s✲
tr❛s ❞❡ ❈♦ ❡ ◆✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸✳✸ ❆♠♦str❛ ❞❡ ◆✐✶ ✐❧✉str❛♥❞♦ ♦ ❘❡✜♥❛♠❡♥t♦ ❘✐❡t✈❡❧❞✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✹ ❉❡s❡♥❤♦ ❡sq✉❡♠át✐❝♦ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❜ás✐❝♦s ❞❡ ✉♠ ♠✐❝r♦s✲
❝ó♣✐❝♦ ❡❧❡trô♥✐❝♦ ❞❡ ✈❛rr❡❞✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✺ ▼❛❣♥❡tô♠❡tr♦ ❞❡ ❆♠♦str❛ ❱✐❜r❛♥t❡ ✭❱❙▼✮ ❞♦ ▲◆▼❙✱ ❞❛
❯❋❘◆✱ ♣❛r❛ ♠❡❞✐❞❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❡♠ t❡♠♣❡r❛t✉r❛ ❛♠✲
❜✐❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✻ ❙✐st❡♠❛ ❞❡ ▼❡❞✐❞❛ ❞❡ Pr♦♣r✐❡❞❛❞❡s ❋ís✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✼ ❊sq✉❡♠❛ ❞♦ s✐st❡♠❛ ❞❡ ♠♦♥✐t♦r❛♠❡♥t♦ tér♠✐❝♦✱ ❛q✉✐s✐çã♦ ❞♦s
❞❛❞♦s ❡ r❡❢r✐❣❡r❛çã♦ ❞♦ ❡q✉✐♣❛♠❡♥t♦ ❞❡ ♠❛❣♥❡t♦ ❤✐♣❡rt❡r♠✐❛ ❞♦ ❉❋❚❊ ✭❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛❧✮✱
❯❋❘◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✶ ❉✐❢r❛t♦❣r❛♠❛ ❞❡ r❛✐♦s✲ ❳ ❞❛s ❛♠♦str❛s ❞❡ ❈♦ ❡ r❡✜♥❛♠❡♥t♦
❘✐❡t✈❡❧❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷ ✭❛✮ ❆♥á❧✐s❡ ❞❡ ▼❊❱ ♥❛ ❛♠♦str❛ ❞❡ ❈♦✽✳ ✭❜✮ ❉✐str✐❜✉✐çã♦ ❞❡
t❛♠❛♥❤♦ ❞❛s ♣❛rtí❝✉❧❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✸ ▼❡❞✐❞❛s ❞❡ ■♥❢r❛✈❡r♠❡❧❤♦ ♥❛s ❛♠♦str❛s ❞❡ ❈♦ ❡ ◆✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✹ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❡♠ ✸✵✵❑ ❞❛s ❛♠♦str❛s ❞❡ ❈♦✳ ✭❜✮ ❆♠✲
♣❧✐❛çã♦ ❞❛ ✜❣✉r❛✭❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✺ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❋✐t ♣♦❧✐♥♦♠✐❛❧ ♣❛r❛ ❛ ♠❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉✲
r❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❡q✉❛çã♦ ❞❛ ❧❡✐ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞❡ s❛t✉r❛çã♦✱
❛♠♦str❛ ❞❡ ❈♦✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✻ ❘❡❧❛çã♦ ❡♥tr❡ ❝♦❡r❝✐✈✐❞❛❞❡ ❡ ▼r✴▼s ❝♦♠ ♦ ❞✐â♠❡tr♦ ❞❛ ♣❛r✲
tí❝✉❧❛ ♥❛s ❛♠♦str❛s ❞❡ ❈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✼ ▼❡❞✐❞❛s ▼①❚ ❞❡ ❋❈ ❡ ❩❋❈ ❝♦♠ ❞✐❢❡r❡♥t❡s ❛♣❧✐❝❛çõ❡s ❞❡ ❈❛♠♣♦ ✺✹ ✹✳✽ ■♥✈❡st✐❣❛çã♦ ❞❛ ❧✐♥❡❛r✐❞❛❞❡ ❞❡ ❚irr ✈❡rs✉s ❍2/3 ♥❛ ❛♠♦str❛ ❞❡
❈♦✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✾ ▼❛❣♥❡t✐③❛çã♦ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦✱ ♠❡❞✐❞❛s ❞❡ ❡♥✈❡❧❤❡❝✐✲ ♠❡♥t♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞❛s ♥❛ ❛♠♦str❛ ❞❡ ❈♦✽ tr❛t❛❞❛s t❡r✲
♠✐❝❛♠❡♥t❡ á ✈á❝✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✶✵ ▼❛❣♥❡t✐③❛çã♦ ▼①❚ ❋❈ ❝♦♠ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡
✺✵ ❦❖❡ ♣❛r❛ ❛ ❛♠♦str❛ ❞❡ ❈♦✽✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✶✶ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❋❈ ❝♦♠ ❛♣❧✐❝❛çã♦ ❞❡ ✺✵❦❖❡ ❡ ♠❡❞✐❞❛s
▼①❍ ❩❋❈ ❡♠ t❡♠♣❡r❛t✉r❛ ❞❡ ✷❑✳ ✭❜✮❆♠♣❧✐❛çã♦ ❞❛ ✜❣✉r❛ ✭❛✮✳ ✺✾ ✹✳✶✷ ▼❡❞✐❞❛s ❞❡ ❋❈ ❡ ❩❋❈ ❞❛ ❛♠♦str❛ ❞❡ ❈♦✽❆r ❝♦♠ ❞✐❢❡r❡♥t❡s
❛♣❧✐❝❛çã♦ ❞❡ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✶✸ ▼❛❣♥❡t✐③❛çã♦ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦✱ ♠❡❞✐❞❛s ❞❡ ❡♥✈❡❧❤❡❝✐✲
♠❡♥t♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞❛s ♥❛ ❛♠♦str❛ ❞❡ ❈♦✽ tr❛t❛❞❛s t❡r✲
♠✐❝❛♠❡♥t❡ ❡♠ ❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✶✹ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❋❈ ❞❛ ❛♠♦str❛ ❞❡ ❈♦✾✳ ✭❜✮❆♠♣❧✐❛çã♦
❞❛ ✜❣✉r❛ ✭❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✶✺ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦❡r❝✐✈✐❞❛❞❡ ❝♦♠ ❛ ✈❛r✐❛çã♦ ❞❛ t❡♠♣❡r❛✲
t✉r❛ ♥✉♠ ❝❛♠♣♦ ❞❡ ✺✵❦❖❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✶✻ ✭❛✮ ▼❡❞✐❞❛s ▼❳❚ ❋❈ ❡ ❩❋❈ s♦❜ ❝❛♠♣♦ ❞❡ ✺✵❖❡ ✭❜✮ ▼①❚ ❋❈
❡ ❩❋❈ s♦❜ ✉♠ ❝❛♠♣♦ ❞❡ ✶❦❖❡ ✭❝✮ ▼①❚ ❋❈ ❡♠ ❝❛♠♣♦ ❞❡ ✸✵
❦❖❡ ❞❛ ❛♠♦str❛ ❞❡ ❈♦✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✶✼ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❋❈ ❡ ❩❋❈ ❛♠♦str❛ ❞❡ ❈♦✶✶✳ ✭❜✮❆♠♣❧✐❛çã♦
❞❛ ✜❣✉r❛ ✭❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✶✽ ❉❘❳ ❡ ❘❡✜♥❛♠❡♥t♦ ❘✐❡t✈❡❧❞ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ❞❡ ◆✐ ✳ ✳ ✳ ✳ ✻✽ ✹✳✶✾ ✭❛✮ ❆♥á❧✐s❡ ❞❡ ▼❊❱ ♥❛ ❛♠♦str❛ ❞❡ ◆✐✷✳ ✭❜✮ ❉✐str✐❜✉✐çã♦ ❞❡
t❛♠❛♥❤♦ ❞❛s ♣❛rtí❝✉❧❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✷✵ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❞❛s ❛♠♦str❛s ❞❡ ◆✐✳ ✭❜✮❆♠♣❧✐❛çã♦ ❞❛
✜❣✉r❛ ✭❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✹✳✷✶ ❈✉r✈❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❋❈ ❡ ❩❋❈ ❞❡♣❡♥❞❡♥t❡ ❞❛ t❡♠♣❡r❛✲
t✉r❛✱ ❝♦♠ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ❞❡ ✶✵✵ ❖❡ ♣❛r❛ ❛♠♦str❛ ❞❡ ◆✐✶✳ ✼✶ ✹✳✷✷ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❋❈ ❡ ❩❋❈ ❛♠♦str❛s ❞❡ ◆✐✶✳ ✭❜✮❆♠♣❧✐❛çã♦
❞❛ ✜❣✉r❛ ✭❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✷✸ ▼❡❞✐❞❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❋❈ ❡ ❩❋❈✱ r❡❛❧✐③❛❞❛s ♥❛ ❛♠♦str❛ ❞❡
◆✐✷✱ s♦❜ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦ ❞❡ ✽✻ ❖❡ ✳ ✳ ✼✸ ✹✳✷✹ ✭❛✮ ▼❡❞✐❞❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❩❋❈✲✺❑✱ ❋❈✲✺❑ ❡ ✸✵✵❑ ❞❛s
❛♠♦str❛s ❞❡ ◆✐✷✳ ✭❜✮❆♠♣❧✐❛çã♦ ❞❛ ✜❣✉r❛ ✭❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✷✺ ❆♥á❧✐s❡ ❞❡ ♠❛❣♥❡t♦ ❤✐♣❡rt❡r♠✐❛ ♥❛s ❛♠♦str❛s ❞❡ ❈♦ ❡ ◆✐ ❡♠
♣ó✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✷✻ ❆♥á❧✐s❡ ❞❡ ♠❛❣♥❡t♦ ❤✐♣❡rt❡r♠✐❛ ♥❛s ❛♠♦str❛s ❞❡ ❈♦ ❡ ◆✐ ❞✐s✲
♣❡rs❛❞❛ ❡♠ á❣✉❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✈✐✐✐
✷✳✶ Pr♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ❡ ❡str✉t✉r❛✐s ❞♦ ❈♦ ❬✻✱ ✾✱ ✶✻✱ ✶✼❪✳ ✳ ✳ ✷✼ ✷✳✷ Pr♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ❡ ❡str✉t✉r❛✐s ❞♦ ◆✐ ❬✻✱ ✾✱ ✶✻✱ ✶✼❪✳ ✳ ✳ ✷✾ ✸✳✶ ♠❛t❡r✐❛✐s ✉t✐❧✐③❛❞♦s ♥♦s ♣r♦❝❡❞✐♠❡♥t♦s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷ ❆♠♦str❛s ❞❡ ❈♦❜❛❧t♦ ♣r❡♣❛r❛❞❛s ❡♠ ✈á❝✉♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✸ ❆♠♦str❛s ❞❡ ◆íq✉❡❧ ♣r❡♣❛r❛❞❛s ❡♠ ✈á❝✉♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✶ P❛râ♠❡tr♦s ❡str✉t✉r❛✐s ♣❛r❛ sér✐❡ ❞❡ ❛♠♦str❛s ❞❡ ❈♦ ✈✐❛ r❡✜✲
♥❛♠❡♥t♦ ❘✐❡t✈❡❧❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✷ ▼❡❞✐❞❛s ❞❡ ▼①❍ ❡♠ ✸✵✵ ❑✳ ▼❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ✭▼s✮✱
▼❛❣♥❡t✐③❛çã♦ r❡♠❛♥❡♥t❡ ✭▼r✮ ❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮ ❞❛s
❛♠♦str❛s ❞❡ ❈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸ ❱❛❧♦r❡s ❞❡ ▼❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ✭▼s✮✱ ▼❛❣♥❡t✐③❛çã♦ r❡✲
♠❛♥❡♥t❡ ✭▼r✮✱ ❈❛♠♣♦ ❞❡ ❜✐❛s ❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮ ❞❛s
❛♠♦str❛s ❞❡ ❈♦✽ tr❛t❛❞❛s à ✈á❝✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✹ ❱❛❧♦r❡s ❞❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮✱ ❈❛♠♣♦s ❞❡ ❜✐❛s ✭❍❜✮✱ ▼❛❣✲ ♥❡t✐③❛çã♦ r❡♠❛♥❡♥t❡ ✭▼r✮ ❡ ▼❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ✭▼s✮
❞❛ ❛♠♦str❛ ❞❡ ❈♦✾✱ tr❛t❛❞❛s à ✈á❝✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✺ ❱❛❧♦r❡s ❞❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮✱ ❈❛♠♣♦s ❞❡ ❜✐❛s ✭❍❜✮✱ ▼❛❣✲
♥❡t✐③❛çã♦ ❘❡♠❛♥❡♥t❡ ✭▼r✮ ❡ ▼❛❣♥❡t✐③❛çã♦ ❞❡ ❙❛t✉r❛çã♦ ✭▼s✮
❞❛s ❛♠♦str❛s ❞❡ ❈♦✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✻ P❛râ♠❡tr♦s ❡str✉t✉r❛✐s ♣❛r❛ sér✐❡ ❞❡ ❛♠♦str❛s ❞❡ ◆✐ ✈✐❛ ❘❡✜✲
♥❛♠❡♥t♦ ❘✐❡t✈❡❧❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✼ ❱❛❧♦r❡s ❞❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮✱ ▼❛❣♥❡t✐③❛çã♦ r❡♠❛♥❡♥t❡
✭▼r✮ ❡ ▼❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ✭▼s✮ ❞❛s ❛♠♦str❛s ❞❡ ◆✐✱
tr❛t❛❞❛s à ✈á❝✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✽ ❱❛❧♦r❡s ❞❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮✱ ▼❛❣♥❡t✐③❛çã♦ ❘❡♠❛♥❡♥t❡
✭▼r✮ ❡ ▼❛❣♥❡t✐③❛çã♦ ❞❡ ❙❛t✉r❛çã♦ ✭▼s✮ ❞❛s ❛♠♦str❛s ❞❡ ◆✐✶✱
tr❛t❛❞❛s à ✈á❝✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✾ ❱❛❧♦r❡s ❞❡ ❈❛♠♣♦ ❝♦❡r❝✐✈♦ ✭❍❝✮✱ ▼❛❣♥❡t✐③❛çã♦ r❡♠❛♥❡♥t❡
✭▼r✮ ❡ ▼❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ✭▼s✮ ❞❛s ❛♠♦str❛s ❞❡ ◆✐✷✱
tr❛t❛❞❛s à ✈á❝✉♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
❈❆P❮❚❯▲❖
✶
■◆❚❘❖❉❯➬➹❖
◆❛s ú❧t✐♠❛s ❞é❝❛❞❛s✱ ♠❛t❡r✐❛✐s ❡♠ ❡s❝❛❧❛ ♥❛♥♦♠étr✐❝❛ ✈❡♠ s❡♥❞♦ ❛♠♣❧❛✲ ♠❡♥t❡ ❡st✉❞❛❞♦s✳ ▼❛t❡r✐❛✐s ♥❛♥♦♠étr✐❝♦s ❝♦rr❡s♣♦♥❞❡♠ ❛ ✜❧♠❡s ✜♥♦s ✭✉♠❛ ❞✐♠❡♥sã♦ ♥❛♥♦♠étr✐❝❛✮✱ ♥❛♥♦✜♦s ✭❞✉❛s ❞✐♠❡♥sõ❡s ♥❛♥♦♠étr✐❝❛s✮ ❡ ♥❛♥♦♣❛r✲ tí❝✉❧❛s ♠❛❣♥ét✐❝❛s ✭três ❞✐♠❡♥sõ❡s ♥❛♥♦♠étr✐❝❛s✮✳ ❉❡♥tr❡ ❡st❡s ♠❛t❡r✐❛✐s ❛s ♥❛♥♦♣❛rtí❝✉❧❛s ♠❛❣♥ét✐❝❛s✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛s ♠❡tá❧✐❝❛s ❝♦♠♦ ❢❡rr♦✱ ♥íq✉❡❧ ❡ ❝♦❜❛❧t♦ s✉r❣❡♠ ❝♦♠♦ ♦❜❥❡t♦s ♣r♦♠✐ss♦r❡s ❞❡✈✐❞♦ ❛s s✉❛s ❛♣❧✐❝❛❜✐❧✐❞❛❞❡s ❡♠ ✈ár✐❛s ár❡❛s ❞❛ ❝✐ê♥❝✐❛ ❡ t❡❝♥♦❧♦❣✐❛✳
❖ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ♥♦ ❡st✉❞♦ ❞❡st❡s ♠❛t❡r✐❛✐s é ❞❡✈✐❞♦ ❛s ♠✉❞❛♥ç❛s ❡♠ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡ q✉í♠✐❝❛s✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ ❝♦♠ ♠❛t❡r✐❛✐s ♠❛✲ ❝r♦s❝ó♣✐❝♦s ♦✉ ♠❛ss✐✈♦s ✭❜✉❧❦✮ ❬✶❪✳ ◗✉❛♥❞♦ ❡st❡s ♠❛t❡r✐❛✐s s♦❢r❡♠ r❡❞✉çõ❡s ❞❡ t❛♠❛♥❤♦s✱ ❤á ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ át♦♠♦s ♥❛ s✉♣❡r❢í❝✐❡✱ s✉❛s ♣r♦♣r✐❡✲ ❞❛❞❡s ♠❛❣♥ét✐❝❛s ❛❧t❡r❛♠✲s❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❡ ❛❧❣✉♥s ❡❢❡✐t♦s ♠❛❣♥ét✐❝♦s sã♦ ♦❜s❡r✈❛❞♦s✱ t❛✐s ❝♦♠♦ ❝♦❡r❝✐✈✐❞❛❞❡s ❡❧❡✈❛❞❛s✱ s✉♣❡r♣❛r❛♠❛❣♥❡t✐s♠♦✱ ❡①✲ ❝❤❛♥❣❡ ❜✐❛s✱ ✈✐❞r♦s ❞❡ s♣✐♥s✱ ❡t❝✳ ❊ss❡s ♠❛t❡r✐❛✐s ❛♣r❡s❡♥t❛♠ t❛♠❛♥❤♦ ❞❡ ❛❧❣✉♠❛s ❞❡③❡♥❛s ❞❡ ♥❛♥ô♠❡tr♦s✱ ♦s q✉❛✐s sã♦ ♠❡♥♦r❡s ♦✉ ❝♦♠♣❛rá✈❡✐s ❛♦ t❛✲
♠❛♥❤♦ ❞❡ ✉♠❛ ❝é❧✉❧❛ ✭✶✵✲✶✵✵µ♠✮✱ ❞❡ ✉♠ ✈ír✉s ✭✷✵✲✹✺ ♥♠✮✱ ❞❡ ✉♠❛ ♣r♦t❡í♥❛
✭✺✲✺✵ ♥♠✮ ♦✉ ❞❡ ✉♠ ❣❡♥❡ ✭✷ ♥♠ ❞❡ ❧❛r❣✉r❛ ❡ ✶✵✲✶✵✵ ♥♠ ❞❡ ❝♦♠♣r✐♠❡♥t♦✮❬✷❪✳ ❆s ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❞❡ ♠❛t❡r✐❛✐s ♥❛♥♦♣❛rt✐❝✉❧❛❞♦s ♣♦❞❡♠ s❡r ❛❞❛♣t❛✲ ❞♦s ♣❛r❛ ✜♥s ❡s♣❡❝í✜❝♦s ❡♠ ♣❡sq✉✐s❛ ❛❝❛❞ê♠✐❝❛ ♦✉ t❡❝♥♦❧ó❣✐❝❛✳ P♦❞❡✲s❡ ❞❡s✲ t❛❝❛r✱ ❛♣❧✐❝❛çõ❡s ✐♥❞✉str✐❛✐s ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s✱ t❛✐s ❝♦♠♦ s❡❧♦s ♠❛❣♥ét✐❝♦s ❡♠ ♠♦t♦r❡s✱ t✐♥t❛s ♠❛❣♥ét✐❝❛s ♣❛r❛ ❝❤❡q✉❡s ❡♠ ❜❛♥❝♦s✱ ♠í❞✐❛ ❞❡ ❣r❛✈❛çã♦ ♠❛❣♥ét✐❝❛ ❡ ❛♣❧✐❝❛çõ❡s ❜✐♦♠é❞✐❝❛s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✿ ♠❡✐♦ ❞❡ ❝♦♥tr❛st❡ ❞❡ r❡ss♦♥â♥❝✐❛ ♠❛❣♥ét✐❝❛ ❡ ❛❣❡♥t❡s t❡r❛♣ê✉t✐❝♦s ♣❛r❛ tr❛t❛♠❡♥t♦ ❞❡ ❝â♥❝❡r ❬✸✱ ✹❪✳
◆♦ r❛♠♦ ❞❛ ♠❡❞✐❝✐♥❛✱ ♦ tr❛t❛♠❡♥t♦ ❞❡ ♥❡♦♣❧❛s✐❛s ❛tr❛✈és ❞❛ ❣❡r❛çã♦ ❞❡ ❝❛❧♦r ♣♦r ❤✐♣❡rt❡r♠✐❛ ♠❛❣♥ét✐❝❛ t❡♠ s✐❞♦ ♦❜❥❡t♦ ❞❡ t❡st❡s ❡ ❡st✉❞♦s ❞❛ ❝♦♠✉✲ ♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✳ ❆ ♣❛❧❛✈r❛ ✏❍✐♣❡rt❡r♠✐❛✑ ❡t✐♠♦❧♦❣✐❝❛♠❡♥t❡ s✐❣♥✐✜❝❛ ❣❡r❛çã♦ ❞❡ ❝❛❧♦r✳ ▲❡✈❛♥❞♦ ♣❛r❛ ❛ t❡r❛♣✐❛ ❞♦ ❝â♥❝❡r✱ t❡♠ ❝♦♠♦ s✐❣♥✐✜❝❛❞♦ ❣❡r❛çã♦ ❞❡ ❝❛❧♦r ♥♦ t✉♠♦r✱ ♦✉ s❡❥❛✱ ❛✉♠❡♥t♦ ❞❡ t❡♠♣❡r❛t✉r❛ ♥♦ ❛♠❜✐❡♥t❡ ❧♦❝❛❧✱ ❛❧t❡r❛♥❞♦ ❛ ✜s✐♦❧♦❣✐❛ ❞❛s ❝é❧✉❧❛s t✉♠♦r❛✐s✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ❧❡✈❛♥❞♦✲❛s ❛ ♠♦rt❡ ✭❧✐s❡✮✳ ❊st✉❞♦s ♠♦str❛♠ q✉❡ ❝é❧✉❧❛s t✉♠♦r❛✐s ❝❡ss❛♠ ♦ s❡✉ ❝r❡s❝✐♠❡♥t♦ q✉❛♥❞♦ ❛t✐♥❣❡♠ t❡♠♣❡r❛t✉r❛s s✉♣❡r✐♦r❡s ❛ ✹✷➦❈ ❬✺❪✳
❱ár✐♦s ♠ét♦❞♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ s✐♥t❡t✐③❛r ♥❛♥♦♣❛rtí❝✉❧❛s ♠❛❣✲ ♥ét✐❝❛s✱ ❞❡♥tr❡ ♦s q✉❛✐s ❞❡st❛❝❛♠♦s r❡❞✉çã♦ q✉í♠✐❝❛✱ ♠ét♦❞♦ ♣♦❧✐♦❧✱ ♠❡❝❛♥♦✲ s✐♥t❡s❡ ❡ ♠ét♦❞♦ s♦❧✲❣❡❧✳ ❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❛ sí♥t❡s❡ ❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♠❛❣♥ét✐❝❛s ❞❡ ✭❈♦ ❡ ◆✐✮ ❝♦♠ ❞✐❢❡r❡♥t❡s ❞✐â♠❡tr♦s ♣❛r❛ ❛ ♣♦ssí✈❡❧ ❛♣❧✐❝❛çã♦ ❡♠ ♠❛❣♥❡t♦❤✐♣❡rt❡r♠✐❛✱ ♣r❡✲ ♣❛r❛❞❛s ♣♦r ✉♠ ♣r♦❝❡ss♦ s❡♠❡❧❤❛♥t❡ ❛♦ ♠ét♦❞♦ s♦❧✲❣❡❧✳
❖ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦ ❞❡st❛ ❞✐ss❡rt❛çã♦ ❝♦♠♣r❡❡♥❞❡ ✉♠❛ r❡✈✐sã♦ ❞♦s ❢✉♥✲ ❞❛♠❡♥t♦s t❡ór✐❝♦s ❞♦ ♠❛❣♥❡t✐s♠♦ ♥❡❝❡ssár✐♦s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❖ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦ ❛❜♦r❞❛ ♦s ♣r♦❝❡❞✐♠❡♥t♦s ❡①♣❡r✐♠❡♥t❛✐s ✉t✐✲
❧✐③❛❞♦s✱ ❛ss✐♠ ❝♦♠♦ ❛s ♣r✐♥❝✐♣❛✐s té❝♥✐❝❛s ❞❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦s ♠❛t❡r✐❛✐s ♣r♦❞✉③✐❞♦s✳ ❖ q✉❛rt♦ ❝❛♣ít✉❧♦ ♣♦r s✉❛ ✈❡③✱ r❡ú♥❡ ♦s r❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssõ❡s r❡❢❡r❡♥t❡s ❛♦s ♠❛t❡r✐❛✐s s✐♥t❡t✐③❛❞♦s ❡ ♣♦r ✜♠ ❛s ❝♦♥❝❧✉sõ❡s ❡ ♣❡rs♣❡❝t✐✈❛s sã♦ ♠♦str❛❞❛s ♥♦ q✉✐♥t♦ ❝❛♣ít✉❧♦✳
❈❆P❮❚❯▲❖
✷
❋❯◆❉❆▼❊◆❚❆➬➹❖ ❚❊Ó❘■❈❆
✷✳✶ ■♥tr♦❞✉çã♦ ❛♦ ▼❛❣♥❡t✐s♠♦
❆ ❤✐stór✐❛ ❞♦ ♠❛❣♥❡t✐s♠♦ ❡stá ♣r❡s❡♥t❡ ❞❡s❞❡ ♦ s✉r❣✐♠❡♥t♦ ❞❛ ❤✉♠❛♥✐✲ ❞❛❞❡✳ ❖s ♣r✐♠❡✐r♦s r❡❧❛t♦s s♦❜r❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ✏♠❛r❛✈✐❧❤♦s❛s✑ ❞❡ ✉♠ ❝❡rt♦ ♠✐♥ér✐♦ ❞❡ ❢❡rr♦✱ ❢♦r❛♠ ❢❡✐t♦s ♣❡❧♦s ❣r❡❣♦s ❡ ❞❛t❛♠ ❞❡ ✽✵✵ ❛✳❈✳✳ ❖ ♠✐♥é✲ r✐♦ ❢♦✐ ❝❤❛♠❛❞♦ ❞❡ ♠❛❣♥❡t✐t❛✱ ♣♦✐s ❡r❛ ❡♥❝♦♥tr❛❞♦ ♥❛ ▼❛❣♥és✐❛✱ r❡❣✐ã♦ ❞❛ ❆s✐❛ ▼❡♥♦r✳ ❉✉r❛♥t❡ sé❝✉❧♦s ♦ ❢❡♥ô♠❡♥♦ ❞❡ ❛tr❛✐r ❡ r❡♣❡❧✐r ♠✐♥ér✐♦s ✐♥tr✐❣♦✉ ❝✐❡♥t✐st❛s ❡ ✜❧ós♦❢♦s✳
❯♠❛s ❞❛s ♣r✐♠❡✐r❛s ❛♣❧✐❝❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s ❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ❢♦✐ ❛ ❜úss♦❧❛✱ ✐♥✈❡♥t❛❞❛ ♣❡❧♦s ❝❤✐♥❡s❡s ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✷✺✵✵ ❛♥♦s ❛✳❈✳✱ ❡st❛ ✐♥✈❡♥çã♦ ❢♦✐ ❞❡ ❣r❛♥❞❡ ✉t✐❧✐❞❛❞❡ ♣❛r❛ ❛ ❤✉♠❛♥✐❞❛❞❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥❛ ♥❛✲ ✈❡❣❛çã♦✳ ❖ ♣r✐♠❡✐r♦ ❡st✉❞♦ ❝✐❡♥tí✜❝♦ ❞♦ ♠❛❣♥❡t✐s♠♦ ❢♦✐ ❢❡✐t❛ ♣❡❧♦ ✐♥❣❧ês ❲✐❧❧✐❛♠ ●✐❧❜❡rt ✭✶✺✹✵✲✶✻✵✸✮✱ q✉❡ ♣✉❜❧✐❝♦✉ ✉♠ ❧✐✈r♦ s♦❜r❡ ♦ í♠ã ❡ s✉❛s ♣r♦✲ ♣r✐❡❞❛❞❡s✱ ❡♠ ✶✻✵✵ ❬✻❪✳
❱ár✐♦s ❡s❢♦rç♦s ❢♦r❛♠ ❢❡✐t♦s ♣❛r❛ ❡①♣❧✐❝❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ♣r❡✲ s❡♥t❡s ♥♦s ♠❛t❡r✐❛✐s✳ ❆♣❡s❛r ❞♦ ♠❛❣♥❡t✐s♠♦ t❡r ✉♠❛ ❤✐stór✐❛ ♠✐❧❡♥❛r ❢♦✐
s♦♠❡♥t❡ ♥♦s ❞♦✐s ú❧t✐♠♦s sé❝✉❧♦s q✉❡ ❤♦✉✈❡ ✉♠ ❣r❛♥❞❡ ❛✈❛♥ç♦ ♥❡ss❡ ❝❛♠♣♦ ❞❛ ❝✐ê♥❝✐❛✱ q✉❛♥❞♦ ♦ ♠❛❣♥❡t✐s♠♦ ❢♦✐ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ❡❧❡tr✐❝✐❞❛❞❡✱ ❢♦r♠❛♥❞♦ ❛ss✐♠✱ ♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦✳
❆ r❡❝❡♥t❡ t❡♦r✐❛ ❊❧❡tr♦♠❛❣♥ét✐❝❛ é ❢✉♥❞❛♠❡♥t❛❞❛ ♣❡❧♦ tr❛❜❛❧❤♦ ❞❡ ❝✐❡♥✲ t✐st❛s ❝♦♠ ❣r❛♥❞❡s ❤❛❜✐❧✐❞❛❞❡s t❡ór✐❝❛s ❡ ❡①♣❡r✐♠❡♥t❛✐s✳ ❖❡rst❡❞ ❡ ❆♠♣èr❡✱ ❡♠ ✶✽✷✵✱ ❞❡s❝♦❜r✐r❛♠ q✉❡ ✉♠❛ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ ♣❛ss❛♥❞♦ ♣♦r ✉♠ ✜♦ ❣❡r❛✈❛ ❡❢❡✐t♦s ♠❛❣♥ét✐❝♦s✳ ❋❛r❛❞❛② ❡ ❍❡♥r②✱ ♥❛ ❞é❝❛❞❛ ❞❡ ✶✽✸✵ ❞❡s❝♦❜r✐r❛♠ q✉❡ ✉♠ ❝❛♠♣♦ ✈❛r✐á✈❡❧ ♥♦ t❡♠♣♦ ♣♦❞✐❛ ✐♥❞✉③✐r ✉♠❛ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ ❡♠ ✉♠ ❝✐r❝✉✐t♦✱ ❝♦♠♣r♦✈❛♥❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❛ ❞❡s❝♦❜❡rt❛ ❞❡ ❖❡rst❡❞✳ ❬✼✱ ✽❪✳ ◆♦ ✜♥❛❧ ❞♦ sé❝✉❧♦ ❳■❳✱ ❏❛♠❡s ▼❛①✇❡❧❧ s✐♥t❡t✐③♦✉ ❛s ❡q✉❛çõ❡s ❞♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦✱ ❞❡s❡♥✈♦❧✈❡♥❞♦ ❛ss✐♠✱ t♦❞❛ ❛ ❜❛s❡ ❞❛ ❡❧❡tr♦❞✐♥â♠✐❝❛ ❛t✉❛❧✳
❖✉tr♦ ❢❛t♦r ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ❞❡s❡♥✈♦❧✈❡r ❛ ❚❡♦r✐❛ ❞♦ ♠❛❣✲ ♥❡t✐s♠♦ ❢♦✐ ❛ ❞❡s❝♦❜❡rt❛ ❞❛ ▼❡❝â♥✐❝❛ ◗✉â♥t✐❝❛✳ ❊st❛ t❡♦r✐❛ ♣❡r♠✐t✐✉ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❡ ❡st✉❞♦s ❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ❡♠ ❡s❝❛❧❛s ♠✐❝r♦s❝ó♣✐❝❛s ❡ ♥❛♥♦s❝ó♣✐❝❛s✱ t❛✐s ♠❛t❡r✐❛✐s ✈❡♠ s❡♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❡①♣❧♦r❛❞♦s✱ ❡ tê♠ ❡♥❝♦♥tr❛❞♦s ❛♣❧✐❝❛çõ❡s t❛♥t♦ ♥♦ r❛♠♦ ❜✐♦t❡❝♥♦❧ó❣✐❝♦ ❝♦♠♦ ✐♥❞✉str✐❛❧ ❡ sã♦ ♦❜❥❡t♦s ❞❡ ❡st✉❞♦ ❞❡ ✉♠❛ ár❡❛ ❡s♣❡❝✐✜❝❛ ❞❛ ❋ís✐❝❛ ❞❡♥♦♠✐♥❛❞❛ ❞❡ ♥❛♥♦♠❛❣✲ ♥❡t✐s♠♦ ❬✾❪✳
✷✳✷ ◆❛♥♦♠❛❣♥❡t✐s♠♦ ❡ ♥❛♥♦♠❛t❡r✐❛✐s
P❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦s ❢❡♥ô♠❡♥♦s q✉❡ ❛❝♦♥t❡❝❡♠ ❡♠ ❡s❝❛❧❛s ♥❛♥♦♠étr✐✲ ❝❛s✱ é ♥❡❝❡ssár✐♦ t❡r ♣r❡s❡♥t❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❢✉♥❞❛♠❡♥t❛✐s ❞♦ ♠❛❣♥❡t✐s♠♦ ❞♦s ♠❛t❡r✐❛✐s✳ ◗✉❛♥❞♦ ❞✐✈✐❞✐♠♦s ✉♠ ✐♠ã ♣❡r♠❛♥❡♥t❡ ❡♠ ❞✉❛s ♣❛rt❡s✱ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s sã♦ ❝♦♥s❡r✈❛❞❛s✱ ❢♦r♠❛♥❞♦ ❛ss✐♠✱ ❞♦✐s ♥♦✈♦s ✐♠ãs ❝♦♠ ♣♦❧♦s ♥♦rt❡ ❡ s✉❧❀ ❛♦ ❞✐✈✐❞✐r♠♦s s✉❝❡ss✐✈❛ ✈❡③❡s ❡ss❡s ✐♠ãs ❡♠ ♣❛rt❡s
❝❛❞❛ ✈❡③ ♠❡♥♦r❡s✱ ❡st❡s ♣❡q✉❡♥♦s ♣❡❞❛ç♦s ❝♦♥t✐♥✉❛rã♦ ❝♦♥s❡r✈❛♥❞♦ s❡✉ ♠❛❣✲ ♥❡t✐s♠♦✳ ◆♦ ❧✐♠✐t❡ ♠✐❝r♦s❝ó♣✐❝♦ ❡ss❡s ♣❡q✉❡♥♦s ✐♠ãs ❢♦r❛♠ ❞❡♥♦♠✐♥❛❞♦s ❞❡ ✐♠ãs ♠♦❧❡❝✉❧❛r❡s ♦✉ ❛tô♠✐❝♦s ❡ ♣♦st❡r✐♦r♠❡♥t❡ ❞❡ ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s✳ ❆ ♠❡♥♦r ✉♥✐❞❛❞❡ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ ♠❛❣♥❡t✐s♠♦ é ❝❤❛♠❛❞❛ ❞❡ ❞✐♣♦❧♦ ♠❛❣♥ét✐❝♦✱ ♥ã♦ ♣♦❞❡♥❞♦ ❛ss✐♠ s❡r ♠❛✐s ❞✐✈✐❞✐❞♦✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ♥ã♦ ❡①✐st✐♥❞♦ ♣♦❧♦ ❝♦♠ ❝❛r❣❛ ✐s♦❧❛❞❛❬✶✵❪✳
❖ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦✱ é ❞❡t❡r♠✐♥❛❞♦ ♣❡❧❛ ♦r✐❣❡♠ ❞❡ s❡✉s ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s ❡ ♣❡❧❛ ♥❛t✉r❡③❛ ❞❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ❡❧❡s ❬✼❪✳ ❖ ♠❛❣♥❡t✐s♠♦ é ♦r✐❣✐♥❛❞♦ ♥❛ ❡str✉t✉r❛ ❞♦ át♦♠♦✳ ❖ ❡❧étr♦♥ ❣✐r❛ t❛♥t♦ s♦❜r❡ s❡✉ ❡✐①♦ ✭s♣✐♥ ❡❧❡trô♥✐❝♦✮✱ ❛♣r❡s❡♥t❛♥❞♦ ✉♠ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ✐♥trí♥s❡❝♦✱ q✉❡ é ❛ss♦❝✐❛❞♦ ❛ ✉♠ ♠♦♠❡♥t♦ ❞❡ ❞✐♣♦❧♦ ♠❛❣♥ét✐❝♦ ❞❡ s♣✐♥✱ ❝♦♠♦ ❛♦ r❡❞♦r ❞♦ ♥ú❝❧❡♦ ❞❡ ✉♠ át♦♠♦ ✭♠♦♠❡♥t♦ ♦r❜✐t❛❧✮ ❬✶✶❪✱ ❝♦♥❢♦r♠❡ r❡♣r❡s❡♥t❛❞♦ ❛tr❛✈és ❞❛ ✜❣✉r❛ ✭✷✳✶✮✳ ❖ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ t♦t❛❧ ✭❞✐♣ó❧♦ ♠❛❣♥ét✐❝♦✮ é ❞❛❞♦ ♣❡❧❛ s♦♠❛ ✈❡t♦r✐❛❧ ❞♦s ♠♦♠❡♥t♦s ❞❡ s♣✐♥ ❡ ♦r❜✐t❛❧✳
❋✐❣✉r❛ ✷✳✶✿ ▼♦✈✐♠❡♥t♦ ❞♦ ❡❧étr♦♥
◗✉❛♥❞♦ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❍ é ❛♣❧✐❝❛❞♦ ❛ ✉♠ ♠❛t❡r✐❛❧ ♦❝♦rr❡ ✉♠❛ ♠✉❞❛♥ç❛ ❡♠ s❡✉s ❞✐♣ó❧♦s✱ ♦r✐❣✐♥❛♥❞♦ ❛ss✐♠✱ ✉♠❛ r❡s♣♦st❛ ♠❛❣♥ét✐❝❛ ♠❛✲ ❝r♦s❝ó♣✐❝❛ ❞❡♥♦♠✐♥❛❞❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ▼✱ ❡st❛ é ❞❡✜♥✐❞❛ ❝♦♠♦ ♠♦♠❡♥t♦ ❞❡ ❞✐♣♦❧♦ ♠❛❣♥ét✐❝♦ t♦t❛❧ ♣♦r ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈♦❧✉♠❡ ❬✼❪ ✳
◆❛ t❡♦r✐❛ ♠❛❝r♦s❝ó♣✐❝❛✱ ❛ ♠❛❣♥❡t✐③❛çã♦ t❡♠ ♦ ♣❛♣❡❧ ❞❡ ❧❡✈❛r ✐♥❢♦r♠❛çõ❡s ❞❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ❞♦ ♠❛t❡r✐❛❧ ❬✼❪✱ ♥♦ ❙✐st❡♠❛ ■♥t❡r♥❛❝✐♦♥❛❧ ✭❙■✮ ❞❡ ✉♥✐❞❛❞❡s✱ ❛ r❡❧❛çã♦ ❡♥tr❡ ❇✱ ❍ ❡ ▼ é ❞❛❞❛ ♣♦r✿
❇ = µ0(❍+▼) ✭✷✳✶✮
♦♥❞❡ µ0 = 4π10−7N/A2 é ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ♥♦ ✈á❝✉♦ ❡ ❇ é ❛
✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛✳
❖ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣♦❞❡ s❡r ❡①♣r❡ss♦ ❡♠ ❚❡s❧❛ ✭❚✮✱ ●❛✉ss ✭●✮ ♦✉ ❖❡rst❡❞ ✭❖❡✮✱ ♥❛ ♣r♦♣♦rçã♦ ❞❡ ✶❚❂104 ●✱ ✶●❂✶❖❡ ♦✉ ❛✐♥❞❛ ✶❖❡❂✼✾✱✻❆✴♠✳
❆ r❡s♣♦st❛ ♠❛❣♥ét✐❝❛ ❞♦s ♠❛t❡r✐❛✐s ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ♠❛❣♥❡t✐③❛çã♦ ❡♠ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ❛♣❧✐❝❛❞♦✱ é r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ s✉s✲ ❝❡♣t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛✱ ♦✉ s❡❥❛✱ ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ❞❡ ✉♠ ♠❛t❡r✐❛❧ sã♦ ❝❛r❛❝t❡r✐③❛❞❛s ♥ã♦ ❛♣❡♥❛s ♣❡❧♦ s✐♥❛❧ ❞❛ ❣r❛♥❞❡③❛ ▼✱ ♠❛s t❛♠❜é♠ ♣❡❧❛ ♠❛♥❡✐r❛ ❡♠ q✉❡ ▼ ✈❛r✐❛ ❝♦♠ ❍ ❬✻❪✳ ❆ s✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❬✼✱ ✶✶❪ é ❞❡s❝r✐t❛ ♣♦r
χ = ▼
❍ ✭✷✳✷✮
❖s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞♦s ❡♠ ❝✐♥❝♦ ❝❧❛ss❡s✿ ❞✐❛♠❛❣✲ ♥ét✐❝♦s✱ ♣❛r❛♠❛❣♥ét✐❝♦s✱ ❢❡rr♦♠❛❣♥ét✐❝♦s✱ ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦s ❡ ❢❡rr✐♠❛❣♥é✲ t✐❝♦s✳ P❛r❛ ❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ❡st✉❞❛❞❛s ❡str✉t✉r❛s ❡♥✈♦❧✈❡♥❞♦ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s✱ ❝♦❜❛❧t♦ ❡ ♥íq✉❡❧ ✭❈♦ ❡ ◆✐✮ ❡ ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦s✱ ó①✐❞♦ ❞❡ ❝♦❜❛❧t♦ ❡ ó①✐❞♦ ❞❡ ♥íq✉❡❧ ✭❈♦❖✱ ❡ ◆✐❖✮ q✉❡ s❡rã♦ ❞✐s❝✉t✐❞♦s ♣♦st❡r✐♦r♠❡♥t❡✳ ❖ t❡r♠♦ ♥❛♥♦❡str✉t✉r❛✱ ❞❡s❝r❡✈❡ ♦s ♠❛t❡r✐❛✐s ❝♦♠ ❡str✉t✉r❛s ❡♠ ❡s❝❛❧❛ q✉❡ ✈❛r✐❛ ❞❡ ✶ ❛ ✶✵✵ ♥♠✳ ❊st✉❞♦s ❞❡ ♥❛♥♦❡str✉t✉r❛s ❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♠❛❣✲ ♥ét✐❝❛s ♣♦❞❡♠ s❡r ❢❡✐t♦s ♣♦r ✉♠❛ ❛♠♣❧❛ ❣❛♠❛ ❞❡ té❝♥✐❝❛s✱ ❞❡ sí♥t❡s❡ ❡ ❞❡ ❝❛r❛❝t❡r✐③❛çã♦ ❢ís✐❝❛✱ q✉í♠✐❝❛ ❬✶✷❪✳
❖ ♥❛♥♦♠❛❣♥❡t✐s♠♦ é ♦ r❛♠♦ ❞❛ ❢ís✐❝❛ q✉❡ ❡st✉❞❛ ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥é✲ t✐❝❛s ❞♦s ♠❛t❡r✐❛✐s ❡♠ ❞✐♠❡♥sõ❡s ♥❛♥♦s❝ó♣✐❝❛s ✭✉♠ ♥❛♥ô♠❡tr♦ é ❡q✉✐✈❛❧❡♥t❡ ❛ 10−9 ♠✮ ❬✾❪✳ ❉❡✈✐❞♦ ❛s s✉❛s ❞✐♠❡♥sõ❡s r❡❞✉③✐❞❛s✱ ♦s ❡❢❡✐t♦s ♦❜s❡r✈❛❞♦s
❞✐❢❡r❡♠ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❞❡ ♠❛t❡r✐❛✐s ❡♠ ❡s❝❛❧❛ ♠✐❝r♦s❝ó♣✐❝❛ ❡ ♠❛❝r♦s❝ó♣✐❝❛✳
❊st❛ ár❡❛ ❡♥❣❧♦❜❛ ♦ ❡st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❡ ❛♣❧✐❝❛çõ❡s ❞♦ ♠❛❣♥❡t✐s♠♦ ❡♠ ♥❛♥♦♣❛rtí❝✉❧❛s✱ ♥❛♥♦✜♦s✱ ✜❧♠❡s ✜♥♦s ❡ ♠✉❧t✐❝❛♠❛❞❛s✱ ❛❧é♠ ❞❡ ❛♠♦str❛s ♠❛❝r♦s❝ó♣✐❝❛s q✉❡ ✐♥❝♦r♣♦r❛♠ ♣❛rtí❝✉❧❛s ♥❛♥♦s❝ó♣✐❝❛s✱ s❡♥❞♦ ❡st❡s ú❧t✐♠♦s ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦ ♠❛t❡r✐❛✐s ♥❛♥♦❡str✉t✉r❛❞♦s✳
❖ ♥❛♥♦♠❛❣♥❡t✐s♠♦ ♠♦str❛✲s❡ ❝♦♠♦ ✉♠ ❞♦s ❢❡♥ô♠❡♥♦s ♠❛✐s ♣r♦♠✐ss♦r❡s ❞❛ ♥❛♥♦t❡❝♥♦❧♦❣✐❛✱ ♣♦ss✉✐♥❞♦ ✉♠ ✈❛r✐❛❞♦ ❧❡q✉❡ ❞❡ ❛♣❧✐❝❛çõ❡s✳ ❊♠ ✈✐rt✉❞❡ ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s ♣♦ss✉ír❡♠ ❞✐♠❡♥sõ❡s r❡❞✉③✐❞❛s✱ ♦❝♦rr❡♠ ♥♦✈❛s ♣r♦♣r✐❡✲ ❞❛❞❡s ❢ís✐❝❛s ❬✶✷❪✳ ❯♠❛ ❞❡ss❛s ♣r♦♣r✐❡❞❛❞❡s é ♦ ❢❡♥ô♠❡♥♦ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ s✉♣❡r♣❛r❛♠❛❣♥❡t✐s♠♦✱ q✉❡ é ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❜✐♦♠é✲ ❞✐❝❛s ❬✶✸❪✳
✷✳✷✳✶ ❋❡rr♦♠❛❣♥❡t✐s♠♦ ❡ ❆♥t✐❢❡rr♦♠❛❣♥❡t✐s♠♦
❖s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✭❋▼✮ ❬✻✱ ✼❪✱ sã♦ ❛ss✐♠ ❞❡♥♦♠✐♥❛❞♦s ♣♦r ♣♦ss✉ír❡♠ ✉♠❛ ♠❛❣♥❡t✐③❛çã♦ ❡s♣♦♥tâ♥❡❛ ❡ ❛♣r❡s❡♥t❛r❡♠ r❡s♣♦st❛ ♠❛❣♥ét✐❝❛ ♠❡s♠♦ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦✳
❊❧❡♠❡♥t♦s ❞♦ ❣r✉♣♦ ❞❡ tr❛♥s✐çã♦ ❝♦♠♦ ♦ ❋❡rr♦✱ ◆íq✉❡❧ ❡ ❈♦❜❛❧t♦ ❛♦ s❡r❡♠ s✉❜♠❡t✐❞♦s ❛ ✉♠ ❝❛♠♣♦ ❡①t❡r♥♦✱ r❡s♣♦♥❞❡♠ ❛ ❡ss❡ ❝❛♠♣♦ ❛❧✐♥❤❛♥❞♦ s❡✉s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s✱ ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ s✉❛ ♠❛❣♥❡t✐③❛çã♦ ❛t✐♥❣❡ ✉♠ ✈❛❧♦r ♠á①✐♠♦✱ ❝♦♥❤❡❝✐❞♦ ♣♦r ♠❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ✭▼s✮✳
❆ ♠❛❣♥❡t✐③❛çã♦ ❞❡ss❡s ♠❛t❡r✐❛✐s ❞✐♠✐♥✉✐ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ t❡♠♣❡r❛t✉r❛
❡ t♦r♥❛✲s❡ ♥✉❧❛ ❛❝✐♠❛ ❞❡ ✉♠ ❝❡rt♦ ✈❛❧♦r TC✱ ❝❤❛♠❛❞♦ ❞❡ ❚❡♠♣❡r❛t✉r❛ ❞❡
❈✉r✐❡✳ ❊st❛ é t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ t❡♠♣❡r❛t✉r❛ ❝rít✐❝❛ ❡ s❡♣❛r❛ ♦ ❡st❛❞♦ ❢❡rr♦♠❛❣♥ét✐❝♦ ❞♦ ❡st❛❞♦ ♣❛r❛♠❛❣♥ét✐❝♦✳
▼❛t❡r✐❛✐s ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦s ✭❆❋✮✱ ♣♦r s✉❛ ✈❡③✱ ♥ã♦ t❡♠ ✉♠❛ ♠❛❣♥❡t✐③❛✲ çã♦ ❡s♣♦♥tâ♥❡❛ ❡ sã♦ ❝♦♥❤❡❝✐❞♦s ♣♦r ♣♦ss✉ír❡♠ ✉♠ ♦r❞❡♥❛♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❛♥t✐♣❛r❛❧❡❧♦✳ ❖s ❢❡♥ô♠❡♥♦s ❋▼ ❡ ❆❋ ❡♠ ✈✐rt✉❞❡ ❞❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ ❡♥tr❡ át♦♠♦s ✈✐③✐♥❤♦s q✉❡ ♦r✐❡♥t❛♠ ♦s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s ❞❡ ♠❛♥❡✐r❛ ♣❛r❛❧❡❧❛ ♦✉ ❛♥t✐♣❛r❛❧❡❧❛✳ ❖s ♠❛t❡r✐❛✐s ❆❋ ❝❛r❛❝t❡r✐③❛♠✲s❡ ♣♦r ❛♣r❡s❡♥t❛r❡♠ ❞✉❛s s✉❜ r❡❞❡s ✐❞ê♥t✐❝❛s✱ ♣♦ré♠ ❝♦♠ s❡✉s ♠♦♠❡♥t♦s ❡♠ s❡♥t✐❞♦s ♦♣♦st♦s✱ q✉❡ s❡ ✐♥✲ t❡r♣❡♥❡tr❛♠ ❡ t❡♠ ♠❛❣♥❡t✐③❛çã♦ t♦t❛❧ ✐❣✉❛❧ ❛ ③❡r♦✳ ❆ss✐♠ ❝♦♠♦ ♦s ♠❛t❡r❛✐s ❋▼✱ ♦s ❆❋ ♣♦ss✉❡♠ ✉♠❛ t❡♠♣❡r❛t✉r❛ ❝rít✐❝❛✱ ❝❤❛♠❛❞❛ ❞❡ ❚❡♠♣❡r❛t✉r❛ ❞❡ ◆é❡❧(TN)✱ ❛❝✐♠❛ ❞❡st❛ t❡♠♣❡r❛t✉r❛ ♣❡r❞❡♠ s✉❛ ♣r♦♣r✐❡❞❛❞❡s ❆❋✱ t♦r♥❛♥❞♦✲
s❡ ♣❛r❛♠❛❣♥ét✐❝♦ ❬✻❪✳
✷✳✷✳✷ ■♥t❡r❛çõ❡s ♠❛❣♥ét✐❝❛s
❖s ❢❡♥ô♠❡♥♦s ♠❛❣♥ét✐❝♦s ♦❜s❡r✈❛❞♦s ♥♦s ♠❛t❡r✐❛✐s sã♦ ❝❛✉s❛❞♦s ♣❡❧❛s ✐♥✲ t❡r❛çõ❡s ♠❛❣♥ét✐❝❛s✳ ❉❡♣❡♥❞❡♥❞♦ ❞❡ ❛❧❣✉♥s ❢❛t♦r❡s ❛s ✐♥t❡r❛çõ❡s ♠❛❣♥ét✐❝❛s ♣♦❞❡♠ s❡r ❞♦ t✐♣♦ ❞❡ tr♦❝❛ ✭✐♥t❡r❛çã♦ ♣✉r❛♠❡♥t❡ q✉â♥t✐❝❛✮✱ ❞✐♣♦❧❛r ✭❡①❝❧✉s✐✲ ✈❛♠❡♥t❡ ❡❧❡tr♦♠❛❣♥ét✐❝❛✮ ❡ ❞❡ ✐♥t❡r❛çã♦ ❘✉❞❡r♠❛♥✱ ❑✐tt❡❧✱ ❑❛s✉②❛ ❡ ❨♦s✐❞❛ ✭❘❑❑❨✮✱ q✉❡ ♦❝♦rr❡♠ ❡♠ ♣❛rtí❝✉❧❛s ✐♥s❡r✐❞❛s ❡♠ ♠❛tr✐③❡s ♠❡tá❧✐❝❛s✳ ❊st❡s t✐♣♦s ❞❡ ✐♥t❡r❛çõ❡s ♠♦❞✐✜❝❛♠ ♦ ♠❛❣♥❡t✐s♠♦ ❞♦ s✐st❡♠❛✱ ❛ss✐♠ ❝♦♠♦ s✉❛s ♣r♦♣r✐❡❞❛❞❡s✳ ◆❡st❡ tr❛❜❛❧❤♦ s❡rá ❞✐s❝✉t✐❞♦ ❛♣❡♥❛s ♦s ❞♦✐s ♣r✐♠❡✐r♦s t✐♣♦s ❞❡ ✐♥t❡r❛çõ❡s✱ tr♦❝❛ ❡ ❞✐♣♦❧❛r✱ ♣♦r s❡r❡♠ r❡❧❡✈❛♥t❡s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♠❡s♠♦✳
✷✳✷✳✸ ■♥t❡r❛çã♦ ❞❡ tr♦❝❛
❊♠ ✶✾✷✽✱ ❍❡✐s❡♥❜❡r❣ ♠♦str♦✉ q✉❡ ❝❛♠♣♦s ✐♥t❡r♥♦s ❡♠ ♠❛t❡r✐❛✐s ♠❛❣✲ ♥ét✐❝♦s t❡♠ ♦r✐❣❡♠ q✉â♥t✐❝❛✱ ❞❡✈✐❞♦ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s s♣✐♥s ❞♦s át♦♠♦s ✈✐③✐♥❤♦s✳ ❊ss❡ t✐♣♦ ❞❡ ✐♥t❡r❛çã♦ é ❝❤❛♠❛❞❛ ❞❡ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ ✭♦✉ ❡①✲ ❝❤❛♥❣❡✮✱ ❡ é r❡s♣♦♥sá✈❡❧ ♣❡❧❛ ♠❛❣♥❡t✐③❛çã♦ ❡s♣♦♥tâ♥❡❛ ♥♦s ♠❛t❡r✐❛✐s ❢❡r✲ r♦♠❛❣♥ét✐❝♦s✳ ❆ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛ é ❛ ♠❛✐♦r ✐♥t❡r❛çã♦ ♠❛❣♥ét✐❝❛ ❡♠ só✲ ❧✐❞♦s (≈ 1eV) ❡ é r❡s♣♦♥sá✈❡❧ ♣❡❧♦ ❛❧✐♥❤❛♠❡♥t♦ ♣❛r❛❧❡❧♦✲❢❡rr♦♠❛❣♥ét✐❝♦✱ ❡
❛♥t✐♣❛r❛❧❡❧♦✲❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦ ❬✶✹❪✳
❊st❛ é ✉♠❛ ✐♥t❡r❛çã♦ ❞❡ ❝✉rt♦ ❛❧❝❛♥❝❡✱ ❡ é ❝♦♥s❡q✉ê♥❝✐❛ ❞✐r❡t❛ ❞♦ ♣r✐♥❝✐♣✐♦ ❞❛ ❡①❝❧✉sã♦ ❞❡ P❛✉❧✐✱ ♦ q✉❛❧ ❡st❛❜❡❧❡❝❡ q✉❡✱ ❞♦✐s ❡❧étr♦♥s ♥ã♦ ♣♦❞❡♠ ❛ss✉♠✐r ♦ ♠❡s♠♦ ❝♦♥❥✉♥t♦ ❞❡ ♥ú♠❡r♦s q✉â♥t✐❝♦s✳
❈♦♥s✐❞❡r❛♥❞♦ ✉♠ s✐st❡♠❛ ❞❡ ❞♦✐s s♣✐♥s ❡❧❡trô♥✐❝♦s ♥♦s sít✐♦s ✐ ❡ ❥✱ ❝♦♠ ♠♦♠❡♥t♦s ❛♥❣✉❧❛r ❙ih/2π ❡ ❙jh/2π✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛
❞♦s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s ✈✐③✐♥❤♦s é ❞❛❞♦ ♣♦r ❬✶✺❪
Eex = −2❏ex❙i.❙j ✭✷✳✸✮
♦♥❞❡ Jex é ❛ ✐♥t❡❣r❛❧ ❞❡ tr♦❝❛✱ ✐ ❡ ❥ r❡♣r❡s❡♥t❛♠ sít✐♦s ❞♦s í♦♥s ♠❛❣♥ét✐❝♦s
♥❛ r❡❞❡ ❝r✐st❛❧✐♥❛✱ Si ❡ Sj sã♦ ♦s ♠♦♠❡♥t♦s ❛♥❣✉❧❛r❡s ❞❡ s♣✐♥s✳ ❖ s✐♥❛❧ ❞❡
Jex ✐♥❞✐❝❛ ♦ t✐♣♦ ♦r❞❡♥❛♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❞♦ ♠❛t❡r✐❛❧✳ ❉❡ss❡ ♠♦❞♦✱ q✉❛♥❞♦
❏❃✵ ♦ s✐st❡♠❛ t❡♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❢❡rr♦♠❛❣♥ét✐❝♦ ❡ q✉❛♥❞♦ ❏❁✵ t❡♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❛♥t✐❢❡rr♦♠❛❣♥ét✐❝♦✳
✷✳✷✳✹ ■♥t❡r❛çã♦ ❞✐♣♦❧❛r
❆ ✐♥t❡r❛çã♦ ❞♦ t✐♣♦ ❞✐♣♦❧❛r é ❝♦♥❤❡❝✐❞❛ ♣♦r s❡r ✉♠❛ ✐♥t❡r❛çã♦ ❞❡ ❧♦♥❣♦
❛❧❝❛♥❝❡✳ ❊♠ ♣❛rtí❝✉❧❛s ❡st❛ ✐♥t❡r❛çã♦ ❡①✐❜❡ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❛❣♥ét✐❝♦ s✐❣♥✐✲ ✜❝❛t✐✈♦❀ ❡ é ❞❡✈✐❞❛ ❛♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞♦s ❞í♣♦❧♦s ❞♦ ♠❛t❡r✐❛❧✳ ❆ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❞♦✐s ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s✱ ❡♠❜♦r❛ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❞❛ ♦r❞❡♠ ❞❡ ❛té 103 ✈❡③❡s ♠❡♥♦r q✉❡ ❛ ✐♥t❡r❛çã♦ ❞❡ tr♦❝❛✱ é r❡s♣♦♥sá✈❡❧ ♣♦r ♠✉✐t❛s
♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ✐♥t❡r❡ss❛♥t❡s✳ ❊st❛ ✐♥t❡r❛çã♦ é ❡①❝❧✉s✐✈❛♠❡♥t❡ ❞❡ ♦r✐❣❡♠ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ❝♦♠ ✉♠❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ❞❛❞❛ ♣♦r ❬✶✻❪
U = 1
r3[♠1.♠2 −3(♠1.ˆr)(♠2.ˆr)] ✭✷✳✹✮
♦♥❞❡ ♠1 ❡ ♠2 sã♦ ♠♦♠❡♥t♦s ❞❡ ❞✐♣ó❧♦s ♠❛❣♥ét✐❝♦s ❡ r é ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡
♦s ❞✐♣ó❧♦s✳
◗✉❛♥❞♦ ♠1 ❡ ♠2 sã♦ ♣❡r♣❡♥❞✐❝✉❧❛r❡s ❛ r ❛ ❡♥❡r❣✐❛ ❞✐♣♦❧❛r é ❞❛ ❢♦r♠❛
U = 1
r3♠1.♠2 ✭✷✳✺✮
✷✳✸ P❛rtí❝✉❧❛s ♠♦♥♦❞♦♠í♥✐♦✮
❖s s✐st❡♠❛s ♥❛♥♦♠étr✐❝♦s ❝♦♠♦ ❥á ❢♦✐ ♠❡♥❝✐♦♥❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ♣♦ss✉✐ ✉♠ t❛♠❛♥❤♦ r❡❞✉③✐❞♦✱ ❡ss❛ r❡❞✉çã♦ ❞rást✐❝❛ ♥❛s ❞✐♠❡♥sõ❡s ♣r♦✈♦❝❛ ❣r❛♥❞❡s ♠✉❞❛♥ç❛s ❡♠ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s✳ ❯♠❛s ❞❡ss❛s ♠✉❞❛♥ç❛s ♦❝♦rr❡ q✉❛♥❞♦ ❛ ♣❛rtí❝✉❧❛ t❡♠ ✉♠ ❞✐â♠❡tr♦ ❝rít✐❝♦ (Dc)✱ ♥❡ss❛ ❝♦♥❞✐çã♦ ♦ s✐st❡♠❛
♣❛ss❛ ❞❡ ✉♠ ❡st❛❞♦ ♠♦♥♦❞♦♠í♥✐♦ ♣❛r❛ ♦ ❡st❛❞♦ ♠✉❧t✐❞♦♠í♥✐♦✱ ✜❣✉r❛ ✭✷✳✷✮✳ ❆s ❡str✉t✉r❛s ♠✉❧t✐❞♦♠í♥✐♦s✱ ♦✉ s❡❥❛✱ ♣❛rtí❝✉❧❛s ❝♦♠ ✉♠ ❞✐â♠❡tr♦ ✭❉✮ ♠❛✐♦r q✉❡ ♦ ❉c✱ ♣♦ss✉❡♠ r❡❣✐õ❡s s❡♣❛r❛❞❛s ♣♦r ♣❛r❡❞❡s✱ ❞❡♥♦♠✐♥❛❞❛s ❞❡ ♣❛✲
r❡❞❡s ❞❡ ❞♦♠í♥✐♦s✱ ❥á ❛s ♣❛rtí❝✉❧❛s ♠♦♥♦❞♦♠í♥✐♦✱ ✐st♦ é✱ ❝♦♠ ✉♠ ❞✐â♠❡tr♦ ♠❡♥♦r q✉❡ ♦ ❝rít✐❝♦ ♣♦ss✉❡♠ ✉♠ s✉♣❡r ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦✳ ❊✈✐❞❡♥❝✐❛s ❡①✲ ♣❡r✐♠❡♥t❛✐s ♠♦str❛♠ q✉❡ ♣❛r❛ ✈❛❧♦r❡s ♠❡♥♦r❡s q✉❡ ♦ ❉c✱ ♦ ❝♦♠♣♦rt❛♠❡♥t♦
❋✐❣✉r❛ ✷✳✷✿ P❛rtí❝✉❧❛s ❝♦♠ ❡st❛❞♦ ♠♦♥❞♦♠í♥✐♦ (D < Dc) ❡ ❡st❛❞♦ ♠✉❧t✐❞♦♠í♥✐♦(D > Dc)
✳
♥♦ ❡st❛❞♦ ♠♦♥♦❞♦♠í♥✐♦ é ♥♦tá✈❡❧ ❡ ❡ss❡ ❡st❛❞♦ é ♠❛r❝❛❞♦ ♣♦r ✉♠ ✈❛❧♦r ❝♦♥s✐❞❡rá✈❡❧ ❞❡ ❝❛♠♣♦ ❝♦❡r❝✐✈♦✱ ♠❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ❡ ♠❛❣♥❡t✐③❛çã♦ r❡♠❛♥❡♥t❡ ❬✶✼❪✳ ❖ ❝❛♠♣♦ ❝♦❡r❝✐✈♦ é ✉♠❛ ✐♠♣♦rt❛♥t❡ ❣r❛♥❞❡③❛ ♣❛r❛ ❝❛r❛❝t❡r✐✲ ③❛r ♦s ❞✐❢❡r❡♥t❡s r❡❣✐♠❡s ♠❛❣♥ét✐❝♦s ❬✾❪✳ ❱❡r✐✜❝❛✲s❡ ♥❛ ✜❣✉r❛ ✭✷✳✸✮ q✉❡ ❛❝✐♠❛ ❞♦ (Dc) ❛ ♣❛rtí❝✉❧❛ ❡♥❝♦♥tr❛✲s❡ ♥♦ r❡❣✐♠❡ ♠✉❧t✐❞♦♠í♥✐♦ ❡ ❛ ❝♦❡r❝✐✈✐❞❛❞❡ ❞✐✲
♠✐♥✉✐ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞♦ ❞✐â♠❡tr♦✳ ◆♦ ❝♦♠❡ç♦ ❞♦ r❡❣✐♠❡ ♠♦♥♦❞♦♠í♥✐♦✱ ♣♦r s✉❛ ✈❡③✱ ❛ ❝♦❡r❝✐✈✐❞❛❞❡ é ♠á①✐♠❛ ❡ ✈❛✐ ❞❡❝r❡s❝❡♥❞♦ ❛té ❛t✐♥❣✐r ✉♠ ✈❛❧♦r ♥✉❧♦✱ ♠✉❞❛♥❞♦ ♣❛r❛ ♦ r❡❣✐♠❡ s✉♣❡r♣❛r❛♠❛❣♥ét✐❝♦✱ ♥❡st❡ r❡❣✐♠❡ ❛ ♠❛❣♥❡t✐③❛çã♦ é ✐♥stá✈❡❧ ❬✻❪✳
❖ t❛♠❛♥❤♦ ❝rít✐❝♦ é ❞❛ ♦r❞❡♠ ❞❡ ❛❧❣✉♠❛s ❞❡③❡♥❛s ❞❡ ♥❛♥ô♠❡tr♦s ❡ ❞❡✲ ♣❡♥❞❡ ❞♦ ♠❛t❡r✐❛❧✳ ❖ ❞✐â♠❡tr♦ ❝rít✐❝♦ q✉❛♥❞♦ ♦ ♠❛t❡r✐❛❧ é ❡s❢ér✐❝♦ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞♦ ♣♦r ❬✶✽❪
Dc =
2A12
Ms ✭✷✳✻✮
♦♥❞❡ ❆ r❡♣r❡s❡♥t❛ ❛ ❝♦♥st❛♥t❡ ❞❡ ❡♥❡r❣✐❛ ❞❡ tr♦❝❛ ❡ ▼s ❛ ♠❛❣♥❡t✐③❛çã♦ ❞❡
s❛t✉r❛çã♦✳
❋✐❣✉r❛ ✷✳✸✿ ❝♦❡r❝✐✈✐❞❛❞❡ ✈❡rs✉s ❞✐â♠❡tr♦ ❞❛ ♣❛rtí❝✉❧❛ ❡ s✉❛ ✐♥✢✉ê♥❝✐❛ ♥♦s r❡❣✐♠❡s ♠❛❣♥ét✐❝♦s ❞❛s ♣❛rtí❝✉❧❛s ❬✻❪✳
✷✳✸✳✶ ❙✉♣❡r♣❛r❛♠❛❣♥❡t✐s♠♦
❖ ♠❛❣♥❡t✐s♠♦ ♦❜s❡r✈❛❞♦ ❡♠ ♣❛rtí❝✉❧❛s ♠♦♥♦❞♦♠í♥✐♦ é ❞❡s❝r✐t♦ ♣❡❧❛ t❡♦✲ r✐❛ s✉♣❡r♣❛r❛♠❛❣♥ét✐❝❛ ❬✶✾✱ ✷✵❪ ✐♥tr♦❞✉③✐❞❛ ♣♦r ❇❡❛♥ ❡ ▲✐✈✐♥❣st♦♥ ❡♠ ✶✾✺✾ ❬✷✵❪✳
❆ s✉♣♦s✐çã♦ ♠❛✐s s✐♠♣❧❡s ❞❡st❛ ❚❡♦r✐❛✱ é ❝♦♥s✐❞❡r❛r q✉❡ ♦s ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s ❛tô♠✐❝♦s ♥♦ ✐♥t❡r✐♦r ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ♠♦✈❡♠✲s❡ ❝♦❡r❡♥t❡♠❡♥t❡ ❡ ♦ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ t♦t❛❧ ♣❛ss❛ ❛ s❡r r❡♣r❡s❡♥t❛❞♦ ♣♦r ú♥✐❝♦ ✈❡t♦r ❝❧áss✐❝♦ ❞❡ ♠❛❣♥✐t✉❞❡ ❞❛❞♦ ♣♦r✳
µ = µatN ✭✷✳✼✮
♦♥❞❡ ◆ é ♦ ♥ú♠❡r♦ ❞❡ át♦♠♦s ♠❛❣♥ét✐❝♦s ❡ µat é ♦ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦
❛tô♠✐❝♦ ❞♦ ❡❧❡♠❡♥t♦ q✉❡ ❝♦♥st✐t✉✐ ❛ ♣❛rtí❝✉❧❛ ❬✸❪✳
❆ ❡♥❡r❣✐❛ t♦t❛❧ ❞❡st❛ ♣❛rtí❝✉❧❛ é ❝♦♥st✐t✉í❞❛ ♣❡❧❛ ❝♦♥tr✐❜✉✐çã♦ ❞❛ ❡♥❡r✲ ❣✐❛ ❛♥✐s♦tró♣✐❝❛ ✭EA✮✱ ❡ ❡♥❡r❣✐❛ ❩❡❡♠❛♥ ❞❡✈✐❞♦ à ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦
♠❛❣♥ét✐❝♦ ❡①t❡r♥♦✳ ❚❡♠✲s❡ q✉❡ ❛ ❡♥❡r❣✐❛ t♦t❛❧ é ❞❛❞❛ ♣♦r ✿
ET = KV sen2θ−µHcos(α−θ) ✭✷✳✽✮
♦♥❞❡θé ♦ â♥❣✉❧♦ ❡♥tr❡ ♦ ✈❡t♦r ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❡ ♦ ❡✐①♦ ❞❡ ❢á❝✐❧ ♠❛❣♥❡t✐③❛çã♦✱ α é ♦ â♥❣✉❧♦ ❡♥tr❡ ♦ ❡✐①♦ ❞❡ ❢á❝✐❧ ♠❛❣♥❡t✐③❛çã♦ ❡ ♦ ❝❛♠♣♦ ❡①t❡r♥♦✱ ❑❱ é ❛
❜❛rr❡✐r❛ ❞❡ ❡♥❡r❣✐❛ q✉❡ s❡♣❛r❛ ♦s ❞♦✐s ❡st❛❞♦s ❞❡ ❡q✉✐❧í❜r✐♦ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝❛♠♣♦✱ ✐st♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦ ♥❛ ✜❣✉r❛ ✭✷✳✹✮✳
❋✐❣✉r❛ ✷✳✹✿ ✭❛✮ ❊✐①♦ ✉♥✐❛①✐❛❧ ❞❡ ❢á❝✐❧ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✉♠❛ ♥❛♣❛rtí❝✉❧❛ ❡ ✭❜✮ ❞❡♣❡♥❞ê♥❝✐❛ ❞❛ ❜❛rr❡✐r❛ ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ❝❛♠♣♦ ♥✉❧♦ ✭❧✐♥❤❛ ❝♦♥t✐♥✉❛✮ ❡ ❝❛♠♣♦ ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦ ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮ ❬✸❪✳
❆ ♣❛rt✐r ❞❛ ✜❣✉r❛ ✷✳✹✭❜✮✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ ❧✐♥❤❛ ❝♦♥t✐♥✉❛ ♠♦str❛ q✉❡ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝❛♠♣♦ ✭❍❂✵✮✱ ♦ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❞❛ ♣❛rtí❝✉❧❛ ❝♦♥t❡♠ ❞♦✐s ❡st❛❞♦s ❡stá✈❡✐s ❡ ❡q✉✐✈❛❧❡♥t❡s ❝♦♠ ♠❛❣♥❡t✐③❛çã♦ ❡♠ s❡♥t✐❞♦s ♦♣♦st♦s✳ ❊st❡s ❡st❛❞♦s sã♦ s❡♣❛r❛❞♦s ♣♦r ✉♠❛ ❜❛rr❡✐r❛ ❞❡ ❡♥❡r❣✐❛✱ ❡q✉✐✈❛❧❡♥t❡ ❛ ❑❱✳ ❆ss✐♠✱ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ❝♦♥st❛♥t❡ ❞❡ ❛♥✐s♦tr♦♣✐❛ ♦✉ ✈♦❧✉♠❡✱ ♠❛✐♦r s❡rá ❛ ❜❛rr❡✐r❛ ❞❡ ❡♥❡r❣✐❛✳ P♦rt❛♥t♦✱ ♣❛r❛ ❤❛✈❡r ✉♠❛ ♠✉❞❛♥ç❛ ♥♦ s❡♥t✐❞♦ ❞♦ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❞❡ ✉♠ ❡st❛❞♦ ❡stá✈❡❧ ❛ ♦✉tr♦✱ ❛ ❡♥❡r❣✐❛ ❞❛ ♣❛rtí❝✉❧❛ t❡♠ q✉❡ s❡r ♥❡❝❡ss❛r✐❛♠❡♥t❡ s✉♣❡r✐♦r ❛ ❡st❛ ❜❛rr❡✐r❛ ❞❡ ❡♥❡r❣✐❛✳
