◆♦✈❡♠❜r♦ ❞❡ ✷✵✶✺
▲✉ís ▼✐❣✉❡❧ ❋✐❧✐♣❡ ❱✐♦tt②
▲✐❝❡♥❝✐❛❞♦ ❡♠ ❈✐ê♥❝✐❛s ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧❆✈❛❧✐❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡
♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❡♠ ❝♦♥❞✐çõ❡s
❞r❡♥❛❞❛s
❉✐ss❡rt❛çã♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ✲ P❡r✜❧ ●❡♦t❡❝♥✐❛
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉♦✉t♦r ❆r♠❛♥❞♦ ▼❛♥✉❡❧ ◆✉♥❡s ❙❡q✉❡✐r❛ ❆♥tã♦
❏úr✐✿
Pr❡s✐❞❡♥t❡✿ Pr♦❢✳ ❉♦✉t♦r ❏♦ã♦ P❛✉❧♦ ❇✐❧é ❙❡rr❛
❆✈❛❧✐❛çã♦ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s
❈♦♣②r✐❣❤t ➞ ▲✉ís ▼✐❣✉❡❧ ❋✐❧✐♣❡ ❱✐♦tt②✱ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ Pr♦❢❡ss♦r ❉♦✉t♦r ❆r♠❛♥❞♦ ▼❛♥✉❡❧ ◆✉♥❡s ❙❡q✉❡✐r❛ ❆♥tã♦✱ ♣❡❧❛ s✉❛ s❛♣✐ê♥❝✐❛ ❡ ♣♦r t♦❞♦s ♦s ❝♦♥❤❡❝✐♠❡♥t♦s q✉❡ ♠❡ tr❛♥s♠✐t✐✉ ❛♦ ❧♦♥❣♦ ❞♦ ❝✉rs♦✱ ♣❡❧❛ ❞✐s♣♦✲ ♥✐❜✐❧✐❞❛❞❡ ❡ ❛♣♦✐♦ ♥❛ ❝♦♥❝r❡t✐③❛çã♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✳
❆❣r❛❞❡ç♦ ❛✐♥❞❛ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ❞❛ ❋❈❚✲❯◆▲ ♣♦r t♦❞♦ ♦ ❝♦♥tr✐❜✉t♦ ❛♦ ❧♦♥❣♦ ❞♦ ♠❡✉ ♣❡r❝✉rs♦ ❛❝❛❞é♠✐❝♦✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ Pr♦❢❡ss♦r ◆✉♥♦ ●✉❡rr❛ ❡ ❛♦ Pr♦❢❡ss♦r P❡❞r♦ ▼❡❧♦ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❡ ❝♦♥s❡❧❤♦s q✉❡ ♣❛rt✐❧❤❛r❛♠ ❝♦♠✐❣♦ ❡ ♣❡❧❛ ♠♦t✐✈❛çã♦ ♥❛ ❡s❝♦❧❤❛ ❞♦ ♣❡r✜❧✳ ●♦st❛r✐❛ t❛♠❜é♠ ❞❡ ❛❣r❛❞❡❝❡r ❛♦ ❝♦❧❡❣❛ ◆✉♥♦ ❉❡✉s❞❛❞♦ ♣❡❧❛ ❛❥✉❞❛ q✉❡ ♦❢❡r❡❝❡✉ ♥❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❯♠ ❡s♣❡❝✐❛❧ ❛❣r❛❞❡❝✐♠❡♥t♦ à ♠✐♥❤❛ ❢❛♠í❧✐❛ ❡ à ❈❧á✉❞✐❛ ♣♦r t♦❞♦ ♦ ❛♣♦✐♦ q✉❡ ♠❡ tr❛♥s♠✐✲ t✐r❛♠ ❛♦ ❧♦♥❣♦ ❞❡st❡ ♣❡r❝✉rs♦ ❡ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ q✉❡ s❡♠♣r❡ t✐✈❡r❛♠ ♣❛r❛ ❝♦♠✐❣♦✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞❡ ❝✉rs♦✱ ❆❧❡①❛♥❞r❛ ❆♠❛r♦✱ ❇❡r♥❛r❞♦ ❆❧❜❡r❣❛r✐❛✱ ❉✐♦❣♦ P✐♥t♦✱ ❉✐♦❣♦ ❖❧✐✈❡✐r❛✱ ❉✐♦♥❡ ●✉✐♠❛rã❡s✱ ❉❛✈✐❞ ❈♦st❛✱ ❉❛✈✐❞ ❍❡♥r✐q✉❡s✱ ❋r❛♥❝✐s❝♦ ❋r❛♥❝♦✱ ❋r❡✲ ❞❡r✐❝♦ ❖❧✐✈❡✐r❛✱ ❏♦❛♥❛ ❈❤❛✈❡s✱ ❏♦❛♥❛ ❚❡✐①❡✐r❛✱ ❘✐t❛ ❱✐❡✐r❛✱ ❚♦♠ás ❘❛♥t❛♥❡♥ ❡ ❱❛♥❡ss❛ ❆❧❡✐①♦ ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ❡ ♣❡❧♦s ❜♦♥s ♠♦♠❡♥t♦s ♣❛ss❛❞♦s ❛♦ ❧♦♥❣♦ ❞❡st❡s ❛♥♦s✳
P♦r ú❧t✐♠♦✱ ❣♦st❛r✐❛ t❛♠❜é♠ ❞❡ ❛❣r❛❞❡❝❡r ❛♦s ♠❡✉s ❣r❛♥❞❡s ❛♠✐❣♦s ❇❡r♥❛r❞♦ ❈♦st❛ ❡ ▼❛rt❛ P❡r❡✐r❛ ♣♦✐s✱ s❡ ♥ã♦ ❢♦ss❡♠ ❡❧❡s✱ ♥✉♥❝❛ t❡r✐❛ t✐❞♦ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ♠♦str❛r ❞♦ q✉❡ s♦✉ ❝❛♣❛③✳
❘❡s✉♠♦
❊st❛ ❞✐ss❡rt❛çã♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ s❡r ✉♠ ❝♦♥tr✐❜✉t♦ ♣❛r❛ ♦ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠ s♦❧♦s r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s✳ P❛r❛ t❛❧✱ r❡❝♦rr❡✲s❡ ❛ ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s q✉❡ ✐♠♣❧❡♠❡♥t❛ ♦s t❡♦r❡♠❛s ❡stát✐❝♦ ❡ ❝✐♥❡♠át✐❝♦ ❞❛ ❛♥á❧✐s❡ ❧✐♠✐t❡ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ❝❛r❣❛ ú❧t✐♠❛ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠✳ ❖ ❞♦❝✉♠❡♥t♦ ♠♦str❛ ♦ ❡st✉❞♦ ❡❢❡t✉❛❞♦ s♦❜r❡ ❛ ✐♥✢✉ê♥❝✐❛ ❞♦s ♣❛râ♠❡tr♦s✱ q✉❡r ❣❡♦♠étr✐❝♦s✱ q✉❡r ♠❡❝â♥✐❝♦s✱ t❛♥t♦ ❞♦ ♠❛❝✐ç♦ ❝♦♠♦ ❞❛ ♣❧❛❝❛✱ s♦❜r❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ r❡❣✐st❛❞❛✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❣❡♦♠étr✐❝♦ ❢♦✐ ❡st✉❞❛❞❛ ❡♠ ❝♦♥❞✐çõ❡s ❜✐❞✐♠❡♥s✐♦♥❛✐s ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ r❡❧❛t✐✈❛ ❞❛ ❝♦❧♦❝❛çã♦ ❞❛ ♣❧❛❝❛✳ ❊♠ ❝♦♥❞✐çõ❡s tr✐❞✐♠❡♥s✐♦♥❛✐s✱ ♣❛r❛ ❛❧é♠ ❞❡st❡ ❛s♣❡t♦✱ ❢♦✐ t❛♠❜é♠ ❡st✉❞❛❞❛ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❧❛r❣✉r❛ ❞❛ ♣❧❛❝❛✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ♠❡❝â♥✐❝♦ ❡st✉❞♦✉✲s❡ ❛ ✐♥✢✉ê♥❝✐❛ ♥❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❛ss✐♠ ❝♦♠♦ ❞❛ r✉❣♦s✐❞❛❞❡ ❞❛ ♣❧❛❝❛✳ ❖s r❡s✉❧t❛❞♦s ❞❡st❡ ❡st✉❞♦ sã♦ ❛♣r❡s❡♥t❛❞♦s s♦❜ ❛ ❢♦r♠❛ ❞❡ ❢❛t♦r❡s ❞❡ ❛rr❛♥❝❛♠❡♥t♦ ❡♠ ❢✉♥çã♦ ❞♦s ❞✐✈❡rs♦s ♣❛râ♠❡tr♦s ❡st✉❞❛❞♦s✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s sã♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❞❡ ❝❛rá❝t❡r ❡①♣❡r✐♠❡♥t❛❧ ❡ ♥✉♠ér✐❝♦✲ t❡ór✐❝♦ ❞❡ ♦✉tr♦s ❛✉t♦r❡s ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✳ ◆♦ ✜♥❛❧ ❞♦ tr❛❜❛❧❤♦✱ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ ♣r♦♣♦st❛ s♦❜ ❢♦r♠❛ ❣rá✜❝❛ ❞❡ ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❝❛♣❛❝✐❞❛❞❡s ❞❡ ❝❛r❣❛ ❞❡ ✉♠❛ ♣❧❛❝❛ ✜♥✐t❛ ❡ ❞❡ ✉♠❛ ♣❧❛❝❛ ❝♦rr✐❞❛✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠✱ t❡♦r❡♠❛ ❝✐♥❡♠át✐❝♦✱ t❡♦r❡♠❛ ❡stát✐❝♦✱ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❢❛t♦r ❞❡ ❛rr❛♥❝❛♠❡♥t♦✱ ❢❛t♦r ❞❡ ❢♦r♠❛
❆❜str❛❝t
❚❤✐s ♠❛st❡r t❤❡s✐s ✐♥t❡♥❞s t♦ ❜❡ ❛ ❝♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ ❞❡s✐❣♥ ♦❢ ❛♥❝❤♦r ♣❧❛t❡s ❞✐s♣♦s❡❞ ✈❡rt✐❝❛❧❧② ✐♥ ❢r✐❝t✐♦♥❛❧ s♦✐❧s✳ ❆ ✜♥✐t ❡❧❡♠❡♥t ♣r♦❣r❛♠ t❤❛t ✐♠♣❧❡♠❡♥ts t❤❡ ✉♣♣❡r ❛♥❞ ❧♦✇❡r ❜♦✉♥❞ t❤❡♦r❡♠s ♦❢ ❧✐♠✐t ❛♥❛❧②s✐s ✐s ✉s❡❞ ✐♥ ♦r❞❡r t♦ ❝❛❧❝✉❧❛t❡ t❤❡ ✉❧t✐♠❛t❡ ❧♦❛❞ ❝❛♣❛❝✐t② ♦❢ t❤❡ ❛♥❝❤♦r ♣❧❛t❡s✳ ❚❤❡ ❞♦❝✉♠❡♥t s❤♦✇s t❤❡ st✉❞② ❞♦♥❡ ♦♥ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ♣❛r❛♠❡t❡rs✱ ❡✐t❤❡r ❣❡♦♠❡tr✐❝❛❧ ♦r ♠❡❝❤❛♥✐❝❛❧✱ ✐♥ t❤❡ ♠♦❞❡❧❡❞ s♦✐❧ ❛♥❞ ♣❧❛t❡ ♦♥ t❤❡ ❝❛❧❝✉❧❛t❡❞ ❧♦❛❞ ❝❛♣❛❝✐t②✳ ❋r♦♠ ❛ ❣❡♦♠❡tr✐❝❛❧ ♣♦✐♥t ♦❢ ✈✐❡✇✱ ✐♥ t✇♦ ❞✐♠❡♥s✐♦♥❛❧ ❝♦♥❞✐t✐♦♥s✱ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ❡♠❜❡❞♠❡♥t ❞❡♣t❤ ♦❢ t❤❡ ♣❧❛t❡ ✇❛s st✉❞✐❡❞✳ ■♥ t❤r❡❡ ❞✐♠❡♥s✐♦♥❛❧ ❝♦♥❞✐t✐♦♥s✱ ❜❡s✐❞❡s t❤❛t ❛s♣❡❝t✱ ✐t ✇❛s ❛❧s♦ st✉❞✐❡❞ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ ✇✐❞t❤ ♦❢ t❤❡ ❛♥❝❤♦r ♣❧❛t❡✳ ❋r♦♠ t❤❡ ♠❡❝❤❛♥✐❝❛❧ ♣♦✐♥t ♦❢ ✈✐❡✇✱ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ s♦❧✐❞ ❢r✐❝t✐♦♥ ❛♥❣❧❡ ❛s t❤❡ r♦✉❣❤♥❡ss ♦❢ t❤❡ ♣❧❛t❡ ❛r❡ st✉❞✐❡❞ ✳ ❚❤❡ r❡s✉❧ts ♦❢ t❤✐s st✉❞② ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❜r❡❛❦✲♦✉t ❢❛❝t♦rs ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ s❡✈❡r❛❧ ♣❛r❛♠❡t❡rs ❛♥❛❧②s❡❞✳ ❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❛r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ t❤❡ r❡s✉❧ts ♦❢ ❡①♣❡r✐♠❡♥t❛❧ ❛♥❞ t❤❡♦r❡t✐❝❛❧ ✐♥✈❡st✐❣❛t✐♦♥s ❢r♦♠ ✈❛r✐♦✉s ❛✉t❤♦rs ❢♦✉♥❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳ ❆t t❤❡ ❡♥❞ ♦❢ t❤❡ ❞♦❝✉♠❡♥t✱ ❛ ♣r♦♣♦s❡❞ ❢♦r t❤❡ r❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ ❧♦❛❞ ❝❛♣❛❝✐t② ♦❢ ❛ s✐♥❣❧❡ ❛♥❝❤♦r ❛♥❞ ❛ ❝♦♥t✐♥✉♦✉s ♦r str✐♣ ❛♥❝❤♦r ✐s s❤♦✇♥✳
❑❡②✇♦r❞s✿ ♣❧❛t❡ ❛♥❝❤♦rs✱ ✉♣♣❡r ❜♦✉♥❞✱ ❧♦✇❡r ❜♦✉♥❞✱ ✜♥✐t ❡❧❡♠❡♥ts✱ ❜r❡❛❦✲♦✉t ❢❛❝t♦r✱ s❤❛♣❡ ❢❛❝t♦r
❈♦♥t❡ú❞♦
❈♦♥t❡ú❞♦ ✈✐✐✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✈
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s✱ ❙✐❣❧❛s ❡ ❙í♠❜♦❧♦s ①✈
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷
✷ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ✸
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ●❡r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✷✳✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷✳✶ ❊st✉❞♦s ❊①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷✳✷ ❊st✉❞♦s ◆✉♠ér✐❝♦✲❚❡ór✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ❊st✉❞♦s ❊①♣❡r✐♠❡♥t❛✐s ❡ ◆✉♠ér✐❝♦✲❚❡ór✐❝♦s ✳ ✳ ✶✸
✸ ▼❡t♦❞♦❧♦❣✐❛ ❞❡ ❘❡s♦❧✉çã♦ ✶✼
✸✳✶ ❉❡s❝r✐çã♦ ❞♦ Pr♦❣r❛♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✷ ❉❡s❝r✐çã♦ ❞♦ ▼♦❞❡❧♦ ❇✐❞✐♠❡♥s✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✸ ❉❡s❝r✐çã♦ ❞♦ ▼♦❞❡❧♦ ❚r✐❞✐♠❡♥s✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✹ ❘❡s✉❧t❛❞♦s ✷✼
✹✳✶ ❈❛s♦ ❇✐❞✐♠❡♥s✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✹✳✶✳✶ ■♥✢✉ê♥❝✐❛ ❞❛ ❉✐♠❡♥sã♦ ❞♦ ❊❧❡♠❡♥t♦ ❋✐♥✐t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✹✳✶✳✷ ■♥✢✉ê♥❝✐❛ ❞❛ ❊s♣❡ss✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✶✳✸ ❘❡s✉❧t❛❞♦s ❖❜t✐❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✷ ❈❛s♦ ❚r✐❞✐♠❡♥s✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✺ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❝♦♠ ❡st✉❞♦s ❡①✐st❡♥t❡s ✺✸
✺✳✹ Pr♦♣♦st❛ ❞❡ ❋❛t♦r ❞❡ ❋♦r♠❛ sγ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✻ ❈♦♥❝❧✉sõ❡s ❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦s ❋✉t✉r♦s ✻✸
❇✐❜❧✐♦❣r❛✜❛ ✻✼
❆◆❊❳❖ ❆ ❘❡s✉❧t❛❞♦s ❇✐❞✐♠❡♥s✐♦❛♥✐s ✻✾
❆◆❊❳❖ ❇ ❘❡s✉❧t❛❞♦s ❚r✐❞✐♠❡♥s✐♦♥❛✐s ✼✶
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ P❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠✿ ✭❛✮ ❤♦r✐③♦♥t❛❧ ✭❜✮ ✈❡rt✐❝❛❧ ✭❝✮ ✐♥❝❧✐♥❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s✲
♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥✲
❝♦r❛❣❡♠ ❞✐s♣♦st❛ ✈❡rt✐❝❛❧♠❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞♦s r❡s✉❧t❛❞♦s ❞❡ ❞✐❢❡r❡♥t❡s ❛✉t♦r❡s ❝♦♠ ❛s ♠❡s♠❛s
r❡❧❛çõ❡sL/B ❡ H/B ❡ ❞✐❢❡r❡♥t❡s ❞✐♠❡♥sõ❡s ❞❡B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✺ ❊♥s❛✐♦s tr✐❛①✐❛✐s ❡ ❡♥s❛✐♦s ❞❡ ❝♦♠♣r❡ssã♦ ❡♠ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛ ♥❛ ❛r❡✐❛
❞❡♥s❛ ❞❡ ❊r✐t❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✻ ▼❡❝❛♥✐s♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♣♦r ◆❡❡❧② ❡t ❛❧✳ ✭✶✾✼✸✮✿ ✭❛✮ ▼❡❝❛♥✐s♠♦ ✶ ✭❜✮
▼❡❝❛♥✐s♠♦ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✼ ▼❡❝❛♥✐s♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♣♦r ▼✉rr❛② ❡ ●❡❞❞❡s ✭✶✾✽✾✮✿ ✭❛✮ ▼❡❝❛♥✐s♠♦ ❆
✭❜✮ ▼❡❝❛♥✐s♠♦ ❇ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✽ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛tr❛✈és ❞❛ ❛♥á❧✐s❡ ❧✐♠✐t❡ ❝♦♠ r❡s✉❧t❛❞♦s
❞♦s ❡st✉❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠♦❞❡❧♦ ❛❞♦t❛❞♦ ♣❛r❛ ♦s ❝á❧❝✉❧♦s ❜✐❞✐♠❡♥s✐♦♥❛✐s ✷✵ ✸✳✷ ▼❛❧❤❛ ❜✐❞✐♠❡♥s✐♦♥❛❧ ♣❛r❛ H/B= 2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✸✳✸ ■♥t❡r❢❛❝❡ ❞❡ ❞♦✐s ❡❧❡♠❡♥t♦s ✷❉ ❢♦r♠❛❞♦ ♣♦r ❡❧❡♠❡♥t♦s ❞❡ ❥✉♥t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠♦❞❡❧♦ ❛❞♦t❛❞♦ ♣❛r❛ ♦s ❝á❧❝✉❧♦s tr✐❞✐♠❡♥s✐✲
♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✺ ▼❛❧❤❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ♣❛r❛H/B= 1 ❡ L/B= 5 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✸✳✻ ▼❛❧❤❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ♣♦r ❢♦r♠❛ ❛ s✐♠✉❧❛r ✉♠❛ ♣❧❛❝❛ ❝♦rr✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✹✳✶ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s r❡❝♦rr❡♥❞♦ ❛♦ ❚❘❙ ❡ ❚❘■ ♣❛r❛φ′
= 30➦✱δ =φ′✱
H/B= 2
❡ e= 0,1B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✷ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s r❡❝♦rr❡♥❞♦ ❛♦ ❚❘❙ ❡ ❚❘■ ♣❛r❛φ′
= 30➦✱δ =φ′
✱H/B= 6
❡ e= 0,1B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✸ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ❛s ❞✐❢❡r❡♥t❡s ❡s♣❡ss✉r❛s ♣❛r❛H/B= 2 ❡ δ=φ′
✳ ✳ ✸✵ ✹✳✹ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ❛s ❞✐❢❡r❡♥t❡s ❡s♣❡ss✉r❛s ♣❛r❛H/B= 6 ❡ δ=φ′
✳ ✳ ✸✵ ✹✳✺ ■♥✢✉ê♥❝✐❛ ❞❡ δ ♥♦s ✈❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦ ❚❘❙ ❡♠ ❢✉♥çã♦ ❞❡ φ′ ♣❛r❛
❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡H/B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✻ ▼❡❝❛♥✐s♠♦s ♦❜t✐❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ H/B♣❛r❛ φ′
= 20➦ ❡δ =φ′ ✸✷ ✹✳✼ ▼❡❝❛♥✐s♠♦s ♦❜t✐❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ H/B♣❛r❛ φ′
✹✳✶✵ ▼❡❝❛♥✐s♠♦s ♦❜t✐❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ H/B ♣❛r❛φ = 30➦ ❡ δ= 0 ✳ ✸✺
✹✳✶✶ ▼❡❝❛♥✐s♠♦s ♦❜t✐❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ H/B ♣❛r❛φ′
= 40➦ ❡ δ= 0 ✳ ✸✻
✹✳✶✷ ❆♠♣❧✐❛çã♦ ❞♦s ♠❡❝❛♥✐s♠♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s H/B ❝♦♠φ′
= 20➦ ❡ δ=φ′ ✳ ✳ ✳ ✸✼ ✹✳✶✸ ❆♠♣❧✐❛çã♦ ❞♦s ♠❡❝❛♥✐s♠♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s H/B ❝♦♠φ′
= 30➦ ❡ δ=φ′
✳ ✳ ✳ ✸✽ ✹✳✶✹ ❆♠♣❧✐❛çã♦ ❞♦s ♠❡❝❛♥✐s♠♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s H/B ❝♦♠φ′
= 40➦ ❡ δ=φ′
✳ ✳ ✳ ✸✾ ✹✳✶✺ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦s ❚❘❙ ❡ ❚❘■ ❡♠ ❢✉♥çã♦ ❞❡ φ′ ♣❛r❛ ❞✐❢❡r❡♥t❡s
r❡❧❛çõ❡s ❞❡ H/B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✶✻ ❘❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ ❚❘❙ ♣❛r❛ ❞✐❢❡r❡♥t❡s L/B ♣❛r❛φ′
= 30➦ ❡ H/B= 1 ✹✷
✹✳✶✼ ▼❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❡Nγvsr❡s✉❧t❛❞♦s ♣r♦❥❡t❛❞♦s ❞❡Nγ❡♠ ❢✉♥çã♦ ❞❡ L/B ♣❛r❛ ❞✐❢❡r❡♥t❡sφ′
✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✶✽ ▼❡❧❤♦r❡s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❡Nγvsr❡s✉❧t❛❞♦s ♣r♦❥❡t❛❞♦s ❞❡Nγ❡♠ ❢✉♥çã♦
❞❡ φ′
♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡L/B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✶✾ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B
♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 1 ❡ φ′
= 30➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹✳✷✵ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 2 ❡ φ′
= 30➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽
✹✳✷✶ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 3 ❡ φ′
= 30➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✹✳✷✷ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 4 ❡ φ′
= 30➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✺✳✶ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠ ♦✉tr♦s ❛✉t♦r❡s ♣❛r❛ ❡st✉❞♦s ♥✉♠ér✐❝♦✲ t❡ór✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✷ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥✉♠ér✐❝♦s ❝♦♠ ♦✉tr♦s r❡s✉❧t❛❞♦s ♥✉♠é✲
r✐❝♦s ❡ ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✸ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s tr✐❞✐♠❡♥s✐♦♥❛✐s ♦❜t✐❞♦s ❝♦♠ ♦✉tr♦s r❡s✉❧t❛❞♦s
❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✺✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❡ Nγ ❞♦ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ s✐♠✉✲
❧❛♥❞♦ ❝♦♥❞✐çõ❡s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛ ❝♦♠ ♦s ❞♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡♠ ❢✉♥çã♦ ❞❡ φ′
♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡sH/B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✺✳✺ ❋❛t♦r ❞❡ ❢♦r♠❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s φ′
❡♠ ❢✉♥çã♦ ❞❡ ❞✐❢❡r❡♥t❡s H/B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ❇✳✶ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B
♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 1 ❡ φ′
= 25➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
❇✳✷ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 1 ❡ φ′
= 40➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
❇✳✸ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 2 ❡ φ′
= 25➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
❇✳✹ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 2 ❡ φ′
= 40➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
❇✳✺ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡ L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡H/B= 3 ❡ φ′
❇✳✻ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ H/B= 3 ❡φ′
= 40➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
❇✳✼ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ H/B= 4 ❡φ′
= 25➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
❇✳✽ ❚❛①❛ ❞❡ ❞✐ss✐♣❛çã♦ ♥❛s ♠❛❧❤❛s ❞❡❢♦r♠❛❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡L/B ♣❛r❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ H/B= 4 ❡φ′
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❘❡s✉♠♦ ❞❡ tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ ❡st✉❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❛ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠ s♦❧♦ r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥✲ ❞✐çõ❡s ❞r❡♥❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ P❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ r❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❛ ✜❣✉r❛ ✷✳✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✸ ❱❛❧♦r❡s ♦❜t✐❞♦s ♣♦r ❖✈❡s❡♥ ✭✶✾✻✹✮ ♣❛r❛ ✐❣✉❛✐s r❡❧❛çõ❡s ❞❡ L/B ❡H/B ✳ ✳ ✳ ✾ ✷✳✹ ❘❡s✉♠♦ ❞❡ tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ ❡st✉❞♦s ♥✉♠ér✐❝♦✲t❡ór✐❝♦s
♣❛r❛ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠ s♦❧♦ r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✺ ❱❛❧♦r❡s ❞❡ ▲✴❇ ✉t✐❧✐③❛❞♦s ♣❡❧♦s ❞✐❢❡r❡♥t❡s ❛✉t♦r❡s ♥❛ ✜❣✉r❛ ✷✳✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✹✳✶ ◆ú♠❡r♦ ❞❡ ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ❞❛s ♠❛❧❤❛s ❡ ♠é❞✐❛ ❞❡ ❞✉r❛çã♦ ❞♦s ❝á❧❝✉❧♦s
♣❡❧♦ ❚❘❙ ❡ ❚❘■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✷ ❈á❧❝✉❧♦s ❝♦♥s❡❣✉✐❞♦s ♣❛r❛ ❛s ❞✐❢❡r❡♥t❡s r❡❧❛çõ❡s ❞❡H/B ❡ L/B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✸ ◆ú♠❡r♦ ❞❡ ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ❡ ❞✉r❛çã♦ ♠é❞✐❛ ❞♦s ❝á❧❝✉❧♦s ❡❢❡t✉❛❞♦s ♣❛r❛
❛s ♠❛❧❤❛s ♠❛✐s r❡✜♥❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ❆✳✶ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦s ❚❘❙ ❡ ❚❘■ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s δ ❡ H/B ♣❛r❛
φ′
= 20➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
❆✳✷ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦s ❚❘❙ ❡ ❚❘■ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s δ ❡ H/B ♣❛r❛
φ′
= 25➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
❆✳✸ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦s ❚❘❙ ❡ ❚❘■ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s δ ❡ H/B ♣❛r❛
φ′
= 30➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
❆✳✹ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦s ❚❘❙ ❡ ❚❘■ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s δ ❡ H/B ♣❛r❛
φ′
= 35➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
❆✳✺ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❡❧♦s ❚❘❙ ❡ ❚❘■ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s δ ❡ H/B ♣❛r❛
φ′
= 40➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
❇✳✶ ❱❛❧♦r❡s ❞❡Nγ ♦❜t✐❞♦s ♣❡❧♦ ❚❘❙ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡sL/B ❡ H/B ♣❛r❛φ′ = 25➦ ✼✶ ❇✳✷ ❱❛❧♦r❡s ❞❡Nγ ♦❜t✐❞♦s ♣❡❧♦ ❚❘❙ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡sL/B ❡ H/B ♣❛r❛φ′ = 30➦ ✼✶ ❇✳✸ ❱❛❧♦r❡s ❞❡Nγ ♦❜t✐❞♦s ♣❡❧♦ ❚❘❙ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡sL/B ❡ H/B ♣❛r❛φ′ = 35➦ ✼✷ ❇✳✹ ❱❛❧♦r❡s ❞❡Nγ ♦❜t✐❞♦s ♣❡❧♦ ❚❘❙ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡sL/B ❡ H/B ♣❛r❛φ′ = 40➦ ✼✷ ❈✳✶ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ s✐♠✉❧❛♥❞♦ ❝♦♥❞✐çõ❡s
❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛ ❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ♣❛r❛ ❞✐❢❡r❡♥t❡sH/B ❡ ♣❛r❛φ′
= 25➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
❈✳✸ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ s✐♠✉❧❛♥❞♦ ❝♦♥❞✐çõ❡s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛ ❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ♣❛r❛ ❞✐❢❡r❡♥t❡sH/B❡ ♣❛r❛φ′
= 35➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
❈✳✹ ❱❛❧♦r❡s ❞❡ Nγ ♦❜t✐❞♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ s✐♠✉❧❛♥❞♦ ❝♦♥❞✐çõ❡s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛ ❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ♣❛r❛ ❞✐❢❡r❡♥t❡sH/B❡ ♣❛r❛φ′
= 40➦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s✱ ❙✐❣❧❛s ❡
❙í♠❜♦❧♦s
❆❜r❡✈✐❛t✉r❛s ❞✐✈✳ ❉✐✈✐sõ❡s ♠❡❝✳ ▼❡❝❛♥✐s♠♦ ♣r♦❥✳ Pr♦❥❡t❛❞♦ ❙✐❣❧❛s
❉❊❈ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧ ❋❈❚ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ●❞▲ ●r❛✉s ❞❡ ▲✐❜❡r❞❛❞❡
t❛❡ ❚❛♠❛♥❤♦ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛❞♦ ❞♦ ❡❧❡♠❡♥t♦ ❚❘■ ❚❡♦r❡♠❛ ❞❛ ❘❡❣✐ã♦ ■♥❢❡r✐♦r
❚❘❙ ❚❡♦r❡♠❛ ❞❛ ❘❡❣✐ã♦ ❙✉♣❡r✐♦r ❯◆▲ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛ ❙í♠❜♦❧♦s
B ❆❧t✉r❛ ❞❛ ♣❧❛❝❛ c′
■♥t❡r❝❡t♦ ❞❡ ❝♦❡sã♦
d ❊s♣❡ss✉r❛ ❞♦ ❡❧❡♠❡♥t♦ ✜♥✐t♦
b,b0 ❋♦rç❛s ❞❡ ♠❛ss❛
D ❊s♣❛ç❛♠❡♥t♦ ❡♥tr❡ ♣❧❛❝❛s
D ❖♣❡r❛❞♦r ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❞✐❢❡r❡♥❝✐❛❧
e ❊s♣❡ss✉r❛ ❞❛ ♣❧❛❝❛
H/B ❘❡❧❛çã♦ ❡♥tr❡ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❡ ❛ ❛❧t✉r❛ ❞❛ ♣❧❛❝❛ L ▲❛r❣✉r❛ ❞❛ ♣❧❛❝❛
L/B ❘❡❧❛çã♦ ❡♥tr❡ ❛ ❧❛r❣✉r❛ ❡ ❛ ❛❧t✉r❛ ❞❛ ♣❧❛❝❛ m ❋❛t♦r ❞❡ ♠♦❜✐❧✐③❛çã♦
Nγ ❋❛t♦r ❞❡ ❛rr❛♥❝❛♠❡♥t♦
Qu ❋♦rç❛ ú❧t✐♠❛ ❞❛ ♣❧❛❝❛
sγ ❋❛t♦r ❞❡ ❢♦r♠❛
t,t0 ❋♦rç❛s ❞❡ s✉♣❡r❢í❝✐❡
u ❱❡t♦r ❞♦s ❝❛♠♣♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❞♦ ❝♦r♣♦ ˙
u ❱❡t♦r ❞♦s ❝❛♠♣♦s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ❝♦r♣♦
α ▼✉❧t✐♣❧✐❝❛❞♦r ❞❡ ❝❛rr❡❣❛♠❡♥t♦
Γσ ❋r♦♥t❡✐r❛ ❞❡ ◆❡✉♠❛♥♥ Γu ❋r♦♥t❡✐r❛ ❞❡ ❉✐r✐❝❤❧❡t
γ P❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦
δ ➶♥❣✉❧♦ ❞❡ ❛tr✐t♦ s♦❧♦✲❡str✉t✉r❛
˙
ε ❈♦♠♣♦♥❡♥t❡s ❞❡ ❡①t❡♥sã♦ ❡ ❞✐st♦rçã♦ ❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ σ ❱❡t♦r ❞❛s ❝♦♠♣♦♥❡♥t❡s ♥♦r♠❛✐s ❡ ❞❡ ❝♦rt❡ ❞❛s t❡♥sõ❡s ♣❧ást✐❝❛s
λ P❛râ♠❡tr♦ ♠✉❧t✐♣❧✐❝❛❞♦r
Π ❚❛①❛ ❞❡ tr❛❜❛❧❤♦ ❞❛s ❢♦rç❛s
φ′
➶♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❡❢❡t✐✈♦
Ω ❉♦♠í♥✐♦ ❞❡ ✉♠ ❝♦r♣♦
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
✶✳✶ ▼♦t✐✈❛çã♦
❈♦♠ ♦ ❝r❡s❝✐♠❡♥t♦ ♣♦♣✉❧❛❝✐♦♥❛❧ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ❝❡♥tr♦s ✉r❜❛♥♦s✱ é ♥❡❝❡ssár✐♦ ❤❛✈❡r ✉♠ ❛♣r♦✈❡✐t❛♠❡♥t♦ ❡✜❝✐❡♥t❡ ❞♦ ❡s♣❛ç♦ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ❛ ❝♦♥s✲ tr✉çã♦ ❞❡ ❡str✉t✉r❛s✳ ❉❡st❡ ♠♦❞♦✱ é ❝❛❞❛ ✈❡③ ♠❛✐s ❢r❡q✉❡♥t❡ ❛ ❡①❡❝✉çã♦ ❞❡ ❡s❝❛✈❛çõ❡s✱ q✉❡ ♣♦r ✈❡③❡s ♣♦❞❡♠ s❡r ♠✉✐t♦ ♣r♦❢✉♥❞❛s✱ ❞❡s❛✜❛♥❞♦ ♦s ❡♥❣❡♥❤❡✐r♦s ❛ ♠✐♥✐♠✐③❛r ♦s ❞❡s❧♦✲ ❝❛♠❡♥t♦s à s✉♣❡r❢í❝✐❡ ❡ ❛ ❡q✉✐❧✐❜r❛r ❡❧❡✈❛❞♦s ❡s❢♦rç♦s ❤♦r✐③♦♥t❛✐s✱ r❡❞✉③✐♥❞♦ ♦ ✐♠♣❛❝t♦ ❡♠ ❡str✉t✉r❛s ✈✐③✐♥❤❛s✳ ▼✉✐t❛s ❞❡st❛s ❡s❝❛✈❛çõ❡s ♥❡❝❡ss✐t❛♠ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❝♦♥t❡♥çã♦ ✢❡①í✈❡❧✱ ❞❡ ♠♦❞♦ ❛ s✉♣♦rt❛r ♦s ✐♠♣✉❧s♦s ♣r♦✈♦❝❛❞♦s ♣❡❧♦ t❡rr❡♥♦✳
❖ t❡♠❛ ❞❡st❛ ❞✐ss❡rt❛çã♦ ❛❞✈é♠ ♥♦ s❡❣✉✐♠❡♥t♦ ❞❛ ❞✐ss❡rt❛çã♦ ❞❡ ▲❡❛❧ ✭✷✵✶✸✮✱ ♦r✐❡♥t❛❞❛ t❛♠❜é♠ ♣❡❧♦ Pr♦❢❡ss♦r ❉♦✉t♦r ❆r♠❛♥❞♦ ❆♥tã♦✱ ❡♠ q✉❡ ❛ ❛✉t♦r❛ r❡❛❧✐③♦✉ ❝á❧❝✉❧♦s ❛tr❛✈és ❞❡ ✉♠❛ ✈❡rsã♦ ♠❛✐s ❛♥t✐❣❛ ❞♦ ♣r♦❣r❛♠❛ ✉t✐❧✐③❛❞♦ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✱ ♥♦s q✉❛✐s ♦❜t❡✈❡ ✈❛❧♦r❡s ♣❛r❛ ❛ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐❢❡r❡♥t❡s q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❞❡ ❛❧❣✉♥s ❛✉t♦r❡s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ▼❡r✐✜❡❧❞ ❡ ❙❧♦❛♥ ✭✷✵✵✻✮✳ P♦st♦ ✐st♦✱ ♣r❡t❡♥❞❡✲s❡ ❛♥❛❧✐s❛r ❡st❛ s✐t✉❛çã♦ ❡ ♣❡r❝❡❜❡r ❛ r❛③ã♦ ♣❛r❛ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ r❡s✉❧t❛❞♦s✳ ❖ ♣r♦❣r❛♠❛ ✉t✐❧✐③❛❞♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♥❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛s ❡ ✉t✐❧✐③❛ ✉♠❛ ❢♦r♠✉❧❛çã♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ❞❡ ❡str✉t✉r❛s✱ ❛tr❛✈és ❞❛ ❛♥á❧✐s❡ ❧✐♠✐t❡✳ P♦st❡r✐♦r♠❡♥t❡ s❡rá ❞❡s❝r✐t♦ ❝♦♠ ♠❛✐s ❞❡t❛❧❤❡ ❡st❡ ♣r♦❣r❛♠❛✳
✶✳✷ ❖❜❥❡t✐✈♦s
◆❡st❡ tr❛❜❛❧❤♦ ♣r❡t❡♥❞❡✲s❡ ❞❡t❡r♠✐♥❛r ❛ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠ r❡❝♦rr❡♥❞♦ ❛ ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❝á❧❝✉❧♦ ❛✉t♦♠át✐❝♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡ ❛♥❛❧✐s❛r ♦s ♠❡❝❛✲ ♥✐s♠♦s ♣r♦✈♦❝❛❞♦s✳ ➱ t❛♠❜é♠ r❡❛❧✐③❛❞♦ ✉♠ ❡st✉❞♦ s♦❜r❡ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ♠❡❝â♥✐❝❛s ❞❛ ✐♥t❡r❢❛❝❡ ❡♥tr❡ ❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠ ❡ ♦ t❡rr❡♥♦✳ ❉❡ ♠♦❞♦ ❛ ❝♦♥❝r❡t✐③❛r ❡ss❡ ❡st✉❞♦✱ ❢♦✐ ♥❡❝❡ssár✐♦ r❡❡s❝r❡✈❡r ♦ ♣r♦❣r❛♠❛ ❞❡ ❝á❧❝✉❧♦✱ ❝r✐❛♥❞♦ ♥♦✈♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡♥tr❡ ❛ ♣❧❛❝❛ ❡ ♦ s♦❧♦✱ ❞❡♥♦♠✐♥❛❞♦s ❝♦♠♦ ❡❧❡♠❡♥t♦s ❞❡ ❥✉♥t❛✳ ❯t✐❧✐③♦✉✲s❡ ❛ ❧✐♥❣✉❛❣❡♠ P ython ♥❛ ♣r♦❣r❛♠❛çã♦ ❞♦s ♥♦✈♦s ❡❧❡♠❡♥t♦s✳
➱ ❢❡✐t♦ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞❡t❛❧❤❛❞❛ ❞♦s tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ q✉❡ tr❛t❡♠ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞❡ ♠♦❞♦ ❛ ❝♦♥❤❡❝❡r ❛s ❞✐❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❡♠ ❝❛✉s❛✳
✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦
❆ ❞✐ss❡rt❛çã♦ ❞❡s❡♥✈♦❧✈❡✲s❡ ❛♦ ❧♦♥❣♦ ❞❡ s❡✐s ❝❛♣ít✉❧♦s✱ s❡♥❞♦ ♦ ♣r❡s❡♥t❡ ♦ ♣r✐♠❡✐r♦✳ ◆♦ ❈❛♣ít✉❧♦ ✷ é ❢❡✐t❛ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦ ❜❡♠ ❝♦♠♦ ✉♠❛ ❡①♣♦s✐çã♦ ❞♦s ❞✐✈❡rs♦s ❛✉t♦r❡s q✉❡ t❡♥❤❛♠ ❛❜♦r❞❛❞♦ ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ❡♠ ❛♥á❧✐s❡✳
◆♦ ❈❛♣ít✉❧♦ ✸ ❡♥❝♦♥tr❛✲s❡ ✉♠❛ ❞❡s❝r✐çã♦ ❞♦ ♣r♦❣r❛♠❛ ✉t✐❧✐③❛❞♦ ❡ ♦s ♠♦❞❡❧♦s r❡❛❧✐③❛❞♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛s ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦✳
❖ ❈❛♣ít✉❧♦ ✹ ❡①♣õ❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❛ ❛♥á❧✐s❡ ❡❢❡t✉❛❞❛ ❡ ♥♦ ❈❛♣ít✉❧♦ ✺ é ❢❡✐t❛ ✉♠❛ ❝♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠ r❡s✉❧t❛❞♦s ❡①✐st❡♥t❡s✳
❋✐♥❛❧♠❡♥t❡✱ ♦ ❈❛♣ít✉❧♦ ✻ ❞❡s❝r❡✈❡ ❛s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❧✉sõ❡s ❞♦ tr❛❜❛❧❤♦ ❡ ♦s ❞❡s❡♥✈♦❧✈✐♠❡♥✲ t♦s ❢✉t✉r♦s✳
❈❛♣ít✉❧♦ ✷
❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛
◆❡st❡ ❝❛♣ít✉❧♦ é ❞❛❞❛ ✉♠❛ ✈✐sã♦ ❝♦♥t❡①t✉❛❧✐③❛❞❛ ❞♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✳ ➱ ❢❡✐t❛ ✉♠❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❛♥❝♦r❛❣❡♥s ❡♠ ❣❡r❛❧ ❡ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞♦s tr❛❜❛✲ ❧❤♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ s♦❜r❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠ s♦❧♦s r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s✳
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ●❡r❛✐s
❆s ❛♥❝♦r❛❣❡♥s sã♦ ❡❧❡♠❡♥t♦s ❡str✉t✉r❛✐s ♣r♦❥❡t❛❞♦s ❡ ❝♦♥str✉í❞♦s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❛r❛ tr❛♥s♠✐t✐r ❛s ❝❛r❣❛s ✐♠♣♦st❛s s♦❜r❡ ✉♠❛ ❡str✉t✉r❛ ❛♦ t❡rr❡♥♦✳ ●❡r❛❧♠❡♥t❡ ♣r❡t❡♥❞❡✲s❡ q✉❡ ❡ss❡s ❡s❢♦rç♦s s❡❥❛♠ tr❛♥s♠✐t✐❞♦s ♣❛r❛ ✉♠❛ ♠❛✐♦r ♣r♦❢✉♥❞✐❞❛❞❡ ❞♦ t❡rr❡♥♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛♣❡♥❛s s❡rã♦ ❛♥❛❧✐s❛❞❛s ❛♥❝♦r❛❣❡♥s r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❡str✉t✉r❛s ❞❡ ❝♦♥t❡♥çã♦✱ ❛✐♥❞❛ q✉❡ ❡st❡s ❡❧❡♠❡♥t♦s ♣♦ss❛♠ ❡st❛r ❛ss♦❝✐❛❞♦s ❛ ♦✉tr♦ t✐♣♦ ❞❡ ❡str✉t✉r❛s✳
❆s ❛♥❝♦r❛❣❡♥s ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞❛s q✉❛♥t♦ à s✉❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ ❡♠ ❞♦✐s t✐♣♦s✿ ❛t✐✈❛s ❡ ♣❛ss✐✈❛s✳ ❆s ❛♥❝♦r❛❣❡♥s ♣❡rt❡♥❝❡♥t❡s ❛♦ ♣r✐♠❡✐r♦ t✐♣♦ sã♦ ♣ré✲t❡♥s✐♦♥❛❞❛s ❛♥t❡s ❞❛ ❡str✉t✉r❛ ❞❡ ❝♦♥t❡♥çã♦ s♦❢r❡r q✉❛❧q✉❡r ❞❡❢♦r♠❛çã♦ ❡♥q✉❛♥t♦ q✉❡ ♥♦ ❝❛s♦ ❞❛s ♣❛ss✐✈❛s✱ ❛s ❛♥❝♦r❛❣❡♥s sã♦ t❡♥s✐♦♥❛❞❛s à ♠❡❞✐❞❛ ❡♠ q✉❡ ❛ ❡str✉t✉r❛ s❡ ❞❡❢♦r♠❛✱ ❛✉♠❡♥t❛♥❞♦ ❛ s✉❛ r❡s✐stê♥❝✐❛✳
❊st❡s ❡❧❡♠❡♥t♦s ❡str✉t✉r❛✐s sã♦ ❝♦♠♣♦st♦s ✉s✉❛❧♠❡♥t❡ ♣♦r três ③♦♥❛s ❞✐st✐♥t❛s✿ ✉♠❛ ♣r✐✲ ♠❡✐r❛✱ ❞❡♥♦♠✐♥❛❞❛ ❝♦♠♦ ❝❛❜❡ç❛ ❞❛ ❛♥❝♦r❛❣❡♠✱ ❡♠ q✉❡ s❡ ❢❛③ ❛ ❧✐❣❛çã♦ ❡♥tr❡ ♦ ❡❧❡♠❡♥t♦ ❡str✉t✉r❛❧ ❡ ❛ ❡str✉t✉r❛ ❞❡ s✉♣♦rt❡❀ ❛ s❡❣✉♥❞❛ ♦♥❞❡ s❡ ❞á ❛ tr❛♥s♠✐ssã♦ ❞♦s ❡s❢♦rç♦s ♣❛r❛ ♦ t❡rr❡♥♦ ❛❞❥❛❝❡♥t❡❀ ❡ ✉♠❛ t❡r❝❡✐r❛ ③♦♥❛ ❡♠ q✉❡ s❡ ❞á ❛ ❧✐❣❛çã♦ ❡♥tr❡ ❛s ♦✉tr❛s ❞✉❛s ③♦♥❛s ❥á r❡❢❡r✐❞❛s✳
❆ tr❛♥s♠✐ssã♦ ❞♦s ❡s❢♦rç♦s ❞❡ ✉♠❛ ❛♥❝♦r❛❣❡♠ ♣❛r❛ ♦ t❡rr❡♥♦ ❛❞❥❛❝❡♥t❡ ♣♦❞❡ s❡r ❢❡✐t❛ ❝♦♠ r❡❝✉rs♦ ❛ q✉❛tr♦ ♠ét♦❞♦s ❞✐❢❡r❡♥t❡s✿ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠✱ ❛♥❝♦r❛❣❡♥s ❞❡ ❢♦r♠❛ ❤❡❧✐❝♦✐❞❛❧✱ ❛♥❝♦r❛❣❡♥s ❞❡ ✜①❛çã♦ ❞✐r❡t❛ ❡ ❛♥❝♦r❛❣❡♥s ❝♦♠ r❡❝✉rs♦ ❛ ✐♥❥❡çã♦ ❞❡ ❝❛❧❞❛s ❝✐♠❡♥tí❝✐❛s✳ ◆❡st❡ tr❛❜❛❧❤♦ ❛❜♦r❞❛✲s❡ ♦ ♣r♦❜❧❡♠❛ ❞❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠✳ ❆ s❡❝çã♦ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠ ♥❛ ③♦♥❛ ❞❡ tr❛♥s♠✐ssã♦ ❛❞♠✐t❡ ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ❣❡♦♠étr✐❝❛s✳ ❆s ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ♣♦❞❡♠ s❡r q✉❛❞r❛❞❛s✱ r❡t❛♥❣✉❧❛r❡s ♦✉ ❝✐r❝✉❧❛r❡s✳ ❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝♦♥str✉t✐✈♦✱ é ♣♦ssí✈❡❧ ♦♣t❛r ♣♦r ❞✐❢❡r❡♥t❡s ♠❛t❡r✐❛✐s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✿ ❜❡tã♦ ❛r♠❛❞♦✱ ♠❛❞❡✐r❛ ♦✉ ♠❡t❛❧ ✭❉❛s ✷✵✵✼✮✳ ◆❛ ✜❣✉r❛ ✷✳✶ ❡stá r❡♣r❡s❡♥t❛❞♦ ✉♠ ❡sq✉❡♠❛ ❞❡ ✉♠ ❝♦rt❡ ❞❛ ❞✐s♣♦s✐çã♦ ❣❡♦♠étr✐❝❛ ❞❛s ♣❧❛❝❛s✱ q✉❡ ♣♦❞❡♠ s❡r ❤♦r✐③♦♥t❛✐s✱ ✈❡rt✐❝❛✐s ♦✉ ✐♥❝❧✐♥❛❞❛s✳
✭❛✮ ✭❜✮ ✭❝✮
❋✐❣✉r❛ ✷✳✶✿ P❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠✿ ✭❛✮ ❤♦r✐③♦♥t❛❧ ✭❜✮ ✈❡rt✐❝❛❧ ✭❝✮ ✐♥❝❧✐♥❛❞❛
❆s ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♥s ❡stã♦ ♥♦r♠❛❧♠❡♥t❡ ❞✐s♣♦st❛s ❝♦♠ ✉♠ ❡s♣❛ç❛♠❡♥t♦ ❤♦r✐③♦♥t❛❧ ❡♥✲ tr❡ ❡❧❛s ❡ é ♣♦ssí✈❡❧ ❝♦❧♦❝á✲❧❛s ❡♠ ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ ♣r♦❢✉♥❞✐❞❛❞❡ q✉❛♥❞♦ ❡st❛s ♣❧❛❝❛s sã♦ ❤♦r✐③♦♥t❛✐s✳ ❆s ❛♥❝♦r❛❣❡♥s ♣♦❞❡♠ ❛✐♥❞❛ s❡r ❝♦♥s✐❞❡r❛❞❛s ❝♦♠♦ s✉♣❡r✜❝✐❛✐s ♦✉ ♣r♦❢✉♥❞❛s✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ r❡❧❛çã♦ ❍✴❇ ❡ ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣r♦❞✉③✐❞♦✳
❆ ✜❣✉r❛ ✷✳✷ ❛♣r❡s❡♥t❛ ❛ ❣❡♦♠❡tr✐❛ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡✱ s❡♥❞♦ ❍ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❛té à ❜❛s❡ ❞❛ ♣❧❛❝❛✱ ❇ ❡ ▲ ❛ s✉❛ ❛❧t✉r❛ ❡ ❧❛r❣✉r❛ r❡s♣❡t✐✈❛♠❡♥t❡✱ ❡ ❛ s✉❛ ❡s♣❡ss✉r❛ ❡ ❉ ♦ ❡s♣❛ç❛♠❡♥t♦ ❡♥tr❡ ❞✉❛s ♣❧❛❝❛s ❛❞❥❛❝❡♥t❡s✱ t♦♠❛❞♦ ❝♦♠♦ ❝♦♥st❛♥t❡✳ ❉❡ r❡❛❧ç❛r q✉❡ ♦ tr❛❜❛❧❤♦ ✐♥❝✐❞❡ ❛♣❡♥❛s ❡♠ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❝✉❥❛ ♦r✐❡♥t❛çã♦ s❡❥❛ ✈❡rt✐❝❛❧✳ ❆ ♠♦❞❡❧❛çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ r❡❛❧ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠ só ♣♦❞❡ s❡r ❝♦♥s❡❣✉✐❞♦ ❛tr❛✈és ❞❡ ❝á❧❝✉❧♦s tr✐❞✐♠❡♥s✐♦♥❛✐s ♥❛ q✉❛❧ sã♦ ❡st✐♣✉❧❛❞♦s ♣❛râ♠❡tr♦s ❞❡ r❡s✐stê♥❝✐❛ ♣❛r❛ ♦ s♦❧♦ ❡ ♣❛r❛ ❛ ♣❧❛❝❛✳ ❉❡ ❢♦r♠❛ s❡♠❡❧❤❛♥t❡ ❛♦ ♣r♦❜❧❡♠❛ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ✉♠❛ s❛♣❛t❛✱ ❡♠ q✉❡ s❡ ❡st✉❞❛ ✉♠❛ s❛♣❛t❛ ✐♥✜♥✐t❛♠❡♥t❡ ❝♦♠♣r✐❞❛✱ ❢♦✐ ❛♥❛❧✐s❛❞♦ ♣r✐♠❡✐r❛♠❡♥t❡ ✉♠ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ♦♥❞❡ s❡ ❛ss✉♠❡ q✉❡ ❛ ♣❧❛❝❛ ♣♦ss✉✐ ✉♠❛ ❧❛r❣✉r❛✱ L✱ s✉✜❝✐❡♥t❡✲ ♠❡♥t❡ ❣r❛♥❞❡✱ ❞❡ ♠♦❞♦ ❛ s❡r ♣♦ssí✈❡❧ ❛❞♠✐t✐r ❝♦♥❞✐çõ❡s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛✳ ❖ ♠♦❞❡❧♦ ❛❞♦t❛❞♦ ❡stá r❡♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✷✳✸✳ ❆ ❢♦rç❛ ú❧t✐♠❛ ❛ q✉❡ ❛ ♣❧❛❝❛ ❝♦♥s❡❣✉❡ r❡s✐st✐r é r❡♣r❡s❡♥t❛❞❛ ♣♦r Qu✳ P♦st❡r✐♦r♠❡♥t❡ é ❝♦♥❞✉③✐❞❛ ✉♠❛ ❛♥á❧✐s❡ tr✐❞✐♠❡♥s✐♦♥❛❧✱ ❡♠ q✉❡ ♦ ♠♦❞❡❧♦ é ✉♠❛ ✈❛r✐❛♥t❡ ❞❛ ✜❣✉r❛ ✷✳✷✱ ❞❛❞♦ q✉❡ ♥ã♦ ❡①✐st❡ ✉♠❛ s❡❣✉♥❞❛ ♣❧❛❝❛✱ ✐st♦ é✱ ♦ ❡s♣❛ç❛♠❡♥t♦ ❡♥tr❡ ♣❧❛❝❛s✱ ❉✱ é ✐❣✉❛❧ ❛∞✳
✷✳✶ ❈♦♥s✐❞❡r❛çõ❡s ●❡r❛✐s
L/2 D L
H
e B D
L
Plano de simetria
~
❋✐❣✉r❛ ✷✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ❣❡r❛❧ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡
❆ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❛s ♣❧❛❝❛s é ♥♦r♠❛❧♠❡♥t❡ ❛♣r❡s❡♥t❛❞❛ r❡❝♦rr❡♥❞♦ ❛ ✉♠ ❢❛t♦r Nγ✳ ❊st❡ ❢❛t♦r r❡s✉❧t❛ ❞❛ ❛❞✐♠❡♥s✐♦♥❛❧✐③❛çã♦ ❞❛ ❝❛r❣❛Qu ❛tr❛✈és ❞❛ s✉❛ ❞✐✈✐sã♦ ♣❡❧♦ ♣r♦❞✉t♦ ❞❛ ár❡❛ ❞❛ ♣❧❛❝❛✱ B×L✱ ❝♦♠ ♦ ♣❡s♦ ✈♦❧ú♠✐❝♦ ❞♦ s♦❧♦✱ γ ❡ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❛té à ❜❛s❡ ❞❛ ♣❧❛❝❛✱H✳ ❊st❡ ❢❛t♦r é ✐♥t✐t✉❧❛❞♦ ❞❡ ❢❛t♦r ❞❡ ❛rr❛♥❝❛♠❡♥t♦ ❡ ❞❡t❡r♠✐♥❛✲s❡✱ ♣♦r ❝♦♥s❡❣✉✐♥t❡✱ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
Nγ=
Qu
BLHγ ✭✷✳✶✮
❖ ❢❛t♦r ❞❡ ❛rr❛♥❝❛♠❡♥t♦ ♣❡r♠✐t❡ ✉♠❛ rá♣✐❞❛ ❝♦♠♣❛r❛çã♦ ❞❡ ✈❛❧♦r ❛❜s♦❧✉t♦ ❡♥tr❡ ♦s r❡✲ s✉❧t❛❞♦s ❞❡ ❞✐❢❡r❡♥t❡s ❛✉t♦r❡s✱ ❛❧é♠ ❞❛ s✉❛ ✉t✐❧✐③❛çã♦ ♣❡r♠✐t✐r ✉♠ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❞❛s ♣❧❛❝❛s r❡❧❛t✐✈❛♠❡♥t❡ ❢á❝✐❧✳
H
e
B Qu
❋✐❣✉r❛ ✷✳✸✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛✲ ❣❡♠ ❞✐s♣♦st❛ ✈❡rt✐❝❛❧♠❡♥t❡
✷✳✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
◆❡st❛ s❡❝çã♦ é ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞❛s ❛❜♦r❞❛❣❡♥s ❞❡ ♦✉tr♦s ❛✉t♦r❡s ❞♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✳ ❊ss❛s ❛❜♦r❞❛❣❡♥s ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞❛s ❡♠ ❞♦✐s t✐♣♦s✿ ❡st✉❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❡ ❡st✉❞♦s ♥✉♠ér✐❝♦✲t❡ór✐❝♦s✳ ❊st❛ r❡✈✐sã♦ ♣❡r♠✐t✐✉ t♦♠❛r ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ r❡s✉❧t❛❞♦s ❞✐s♣♦♥í✈❡✐s ♥❛ ❜✐❜❧✐♦❣r❛✜❛✱ q✉❡ s❡rã♦ ✉t✐❧✐③❛❞♦s ♥❛ ✈❛❧✐❞❛çã♦ ❡ ❝♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✳
✷✳✷✳✶ ❊st✉❞♦s ❊①♣❡r✐♠❡♥t❛✐s
❆ ♣❡sq✉✐s❛ ❜✐❜❧✐♦❣rá✜❝❛ ❞♦s tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ♣❡r♠✐t✐✉ ♣ôr ❡♠ ❡✈✐❞ê♥❝✐❛ q✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❡♠ ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ❢♦r❛♠ ❡♠ ♠♦❞❡❧♦ r❡❞✉③✐❞♦ ❡♠ ❧❛✲ ❜♦r❛tór✐♦✳ ❊st❡ t✐♣♦ ❞❡ ❡♥s❛✐♦ ♣❡r♠✐t❡ ✉♠❛ r❡❧❛t✐✈❛ ❢❛❝✐❧✐❞❛❞❡ ❞❡ ❝♦♥tr♦❧♦ ❞❛s ✈❛r✐á✈❡✐s ❡♥✈♦❧✈✐❞❛s✱ s❡♥❞♦ ♣♦ssí✈❡❧ ♦❜s❡r✈❛r t❡♥❞ê♥❝✐❛s ❡ ❝♦♠♣♦rt❛♠❡♥t♦s ♣❛❞rã♦✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ♣♦❞❡♠✲s❡ ❝♦♥❥✉❣❛r ♦s r❡s✉❧t❛❞♦s ♦❜s❡r✈❛❞♦s ❝♦♠ ✉♠❛ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❞❡ ❢♦r♠❛ ❛ ❞❡✲ s❡♥✈♦❧✈❡r t❡♦r✐❛s s❡♠✐✲❡♠♣ír✐❝❛s ❝♦♠ ✐♥t✉✐t♦ ❞❡ s❡r❡♠ ❛♣❧✐❝❛❞❛s ♣❛r❛ r❡s♦❧✈❡r ✉♠❛ ♠❛✐♦r ✈❛r✐❡❞❛❞❡ ❞❡ ♣r♦❜❧❡♠❛s✳
❖s ♠♦❞❡❧♦s r❡❞✉③✐❞♦s ♣♦❞❡♠ s❡r ❡♥s❛✐❛❞♦s s♦❜ ♦ ❡❢❡✐t♦ ❞❛ ❛❝❡❧❛r❛çã♦ ❞❛ ❣r❛✈✐❞❛❞❡ ♦✉ ❡♠ ❝â♠❛r❛s ❝❡♥tr✐❢✉❣❛❞♦r❛s✱ s♦❜ ❛ ❛çã♦ ❞❡ ❛❝❡❧❡r❛çõ❡s s✉♣❡r✐♦r❡s à ❞❛ ❣r❛✈✐❞❛❞❡✳ ◆❛ t❛❜❡❧❛ ✷✳✶ ❡❧❡♥❝❛♠✲s❡ ♦s ❛rt✐❣♦s q✉❡ r❡❧❛t❛♠ tr❛❜❛❧❤♦s ❡①♣❡r✐♠❡♥t❛✐s s♦❜r❡ ❛ ❝❛♣❛❝✐❞❛❞❡ r❡s✐st❡♥t❡ ❞❡ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡✱ ❛t✉❛♥❞♦ ❡♠ s♦❧♦ r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s✱ q✉❡ ❢♦r❛♠ ♣♦ssí✈❡✐s ❡♥❝♦♥tr❛r ♥❛ ❧✐t❡r❛t✉r❛✱ ❜❡♠ ❝♦♠♦ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞♦s ❡♥s❛✐♦s✳
✷✳✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
❚❛❜❡❧❛ ✷✳✶✿ ❘❡s✉♠♦ ❞❡ tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ ❡st✉❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❛ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠ s♦❧♦ r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s
❆✉t♦r ❚✐♣♦ ❞❡ ❆♥á❧✐s❡ ●❡♦♠❡tr✐❛ φ′
❬➦❪ ❍✴❇
❍✉❡❝❦❡❧ ✭✶✾✺✼✮❛ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦ ◗✉❛❞r❛❞❛❀
❘❡t❛♥❣✉❧❛r ✸✺ ✷
❙♠✐t❤ ✭✶✾✻✷✮❛ ❊s❝❛❧❛ ❘❡❛❧ ◗✉❛❞r❛❞❛❀
❘❡t❛♥❣✉❧❛r ✸✷ ✶
−✹✱✺
❖✈❡s❡♥ ✭✶✾✻✹✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦ ❈♦♥tí♥✉❛❀ ◗✉❛❞r❛❞❛❀ ❘❡t❛♥❣✉❧❛r
✸✵❀ ✸✽ ✶−✶✵
◆❡❡❧② ❡t ❛❧✳ ✭✶✾✼✸✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦ ◗✉❛❞r❛❞❛❀
❘❡t❛♥❣✉❧❛r ✸✽ ✶
−✺
❉❛s ❡ ❙❡❡❧❡② ✭✶✾✼✺✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦ ◗✉❛❞r❛❞❛❀
❘❡t❛♥❣✉❧❛r ✸✹ ✶
−✹
❆❦✐♥♠✉s✉r✉ ✭✶✾✼✽✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦❀
P✐♥♦s ❞❡ ❛ç♦ ❘❡t❛♥❣✉❧❛r◗✉❛❞r❛❞❛❀ ✸✺ ✶
−✶✵
❉✐❝❦✐♥ ❡ ▲❡✉♥❣ ✭✶✾✽✸✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦❀
❈❡♥tr✐❢✉❣❛❞♦r❛ ◗✉❛❞r❛❞❛❀❈♦♥tí♥✉❛❀ ❘❡t❛♥❣✉❧❛r
✹✶❜ ✶−✽❀
✶−✶✸
❍♦s❤✐②❛ ❡ ▼❛♥❞❛❧ ✭✶✾✽✹✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦ ◗✉❛❞r❛❞❛❀
❘❡t❛♥❣✉❧❛r ✷✾✱✺ ✶
−✻
▼✉rr❛② ❡ ●❡❞❞❡s ✭✶✾✽✾✮ ▼♦❞❡❧♦ ❘❡❞✉③✐❞♦ ◗✉❛❞r❛❞❛❀
❘❡t❛♥❣✉❧❛r ✹✸✱✻ ✶
−✶✵ ❛❱❛❧♦r❡s r❡t✐r❛❞♦s ❞❡ ❖✈❡s❡♥ ❡ ❙trø♠❛♥♥ ✭✶✾✼✷✮✳
❜➶♥❣✉❧♦ r❡s✐st❡♥t❡ ❛♦ ❝♦rt❡ ♠í♥✐♠♦ ♠♦❜✐❧✐③❛❞♦✳
❆♣ós ❧❡✐t✉r❛ ❞♦s tr❛❜❛❧❤♦s ❞♦s ❞✐❢❡r❡♥t❡s ❛✉t♦r❡s✱ ❝♦♥st❛t❛✲s❡ q✉❡ ❡①✐st❡ ✉♠❛ ❣r❛♥❞❡ ✈❛r✐❛✲ çã♦ ❞♦s r❡s✉❧t❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ❞✐♠❡♥sõ❡s ❞❛ ♣❧❛❝❛ ❞❡ ❛♥❝♦r❛❣❡♠✱ ♦ q✉❡ s❡r✐❛ ❡①♣❡❝tá✈❡❧✳ ❆♣❡s❛r ❞❡ss❛ ✈❛r✐❛çã♦ ❞❡ r❡s✉❧t❛❞♦s✱ ❝♦♥st❛t❛✲s❡ q✉❡ ♦s ✈❛❧♦r❡s ❞❡Nγ ❝r❡s❝❡♠ ❝♦♠ ♦ ❛✉✲ ♠❡♥t♦ ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❡♠ q✉❡ s❡ ❡♥❝♦♥tr❛ ❛ ♣❧❛❝❛ ❡ ❝♦♠ ♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ❞♦ s♦❧♦✳ ➱ t❛♠❜é♠ ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ✉♠❛ ❡st❛❜✐❧✐③❛çã♦ ❞♦ ✈❛❧♦r ❞♦ ❢❛t♦r ❞❡ ❛rr❛♥❝❛♠❡♥t♦ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ ❧❛r❣✉r❛ ❞❛ ♣❧❛❝❛✱ s❡♥❞♦ ♣♦ssí✈❡❧ ❝♦♠♣❛r❛r ❝♦♠ ✉♠ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡♠ ❡st❛❞♦ ♣❧❛♥♦ ❞❡ ❞❡❢♦r♠❛çã♦✳
◆ã♦ sã♦ ❝❧❛r❛s ❛s r❛③õ❡s s✉❜❥❛❝❡♥t❡s à ✈❛r✐❛❜✐❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s✳ ❆ ❞❡✜♥✐çã♦ ❞❛ ❝❛r❣❛ ú❧t✐♠❛ ❡①♣❡r✐♠❡♥t❛❧ ♣♦❞❡ s❡r ✉♠❛ ❞❡ss❛s r❛③õ❡s✱ ❛t❡♥❞❡♥❞♦ ❛ q✉❡ ✈❛r✐❛ s❡❣✉♥❞♦ ♦s ❛✉t♦✲ r❡s✱ ✈❡r✐✜❝❛♥❞♦✲s❡ q✉❡ ❛té ❡♠ ❡♥s❛✐♦s r❡❛❧✐③❛❞♦s ♣❡❧♦ ♠❡s♠♦ ❛✉t♦r✱ ❡ss❛ ❞✐ss✐♣❛çã♦ ♣♦❞❡ ❞❡♣❡♥❞❡r ❞♦ t✐♣♦ ❞❡ ❝✉r✈❛ ❢♦rç❛✲❞❡s❧♦❝❛♠❡♥t♦ ♦❜t✐❞❛ ✭❉❛s ❡ ❙❡❡❧❡② ✶✾✼✺✮✳ ❖✉tr❛ r❛③ã♦ ♣♦❞❡rá t❡r ❛ ✈❡r ❝♦♠ ♦ ❡st❛❞♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❛s ❛♠♦str❛s ❡ ❝♦♠ ♦ ♥í✈❡❧ ❞❡ t❡♥sõ❡s ❛ q✉❡ ♦s ❡♥s❛✐♦s sã♦ r❡❛❧✐③❛❞♦s✱ ♣♦❞❡♥❞♦ ❝♦♥❞✐❝✐♦♥❛r ♦ ✈❛❧♦r ❞♦ â♥❣✉❧♦ ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡
♠♦❜✐❧✐③❛❞♦✳
◆❛s ♦❜r❛s ❞❡ ❍✉❡❝❦❡❧ ✭✶✾✺✼✮✱ ❙♠✐t❤ ✭✶✾✻✷✮✱ ❉✐❝❦✐♥ ❡ ▲❡✉♥❣ ✭✶✾✽✸✮ ❡ ❍♦s❤✐②❛ ❡ ▼❛♥❞❛❧ ✭✶✾✽✹✮✱ ♦s ❛✉t♦r❡s r❡❛❧✐③❛♠ ❡♥s❛✐♦s ✉t✐❧✐③❛♥❞♦ ❞✐❢❡r❡♥t❡s ❞✐♠❡♥sõ❡s ❞❡ ♣❧❛❝❛s✱ ♦❜t❡♥❞♦ r❡s✉❧t❛❞♦s ❞✐st✐♥t♦s ♣❛r❛ ❛ ♠❡s♠❛ r❡❧❛çã♦ H/B ❡ L/B✳ ◆❛ ✜❣✉r❛ ✷✳✹ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❡❧♦s ❛✉t♦r❡s ❝♦♠ ✉♠❛ ♣❡q✉❡♥❛ ❧❡❣❡♥❞❛ ❞♦s ♣❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝❛❞❛ ❛✉t♦r ♥❛ t❛❜❡❧❛ ✷✳✷✳ ❉❡ ♥♦t❛r q✉❡ ♦s r❡s✉❧t❛❞♦s ❞❡ ❙♠✐t❤ ✭✶✾✻✷✮ sã♦ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❡♥s❛✐♦s r❡❛❧✐③❛❞♦s ❡♠ ❡s❝❛❧❛ r❡❛❧✳
❚❛❜❡❧❛ ✷✳✷✿ P❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛ r❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❛ ✜❣✉r❛ ✷✳✹
❆✉t♦r L/B H/B φ′
❬➦❪
❍✉❡❝❦❡❧ ✭✶✾✺✼✮ ✶ ✶ ✸✺
❙♠✐t❤ ✭✶✾✻✷✮ ✶✱✷✺ ✶ ✸✷
❉✐❝❦✐♥ ❡ ▲❡✉♥❣ ✭✶✾✽✸✮ ✶ ✶ ✹✶ ❍♦s❤✐②❛ ❡ ▼❛♥❞❛❧ ✭✶✾✽✹✮ ✶ ✷ ✷✾✱✺
0 5 10 15 20
0 20 40 60 80 100 120
Nγ B[cm] Hueckel (1957) Smith (1962) 0 5 10 15 20
0 20 40 60 80 100 120
Nγ
B[cm]
Dickin e Leung (1983) Hoshiya e Mandal (1984)
❋✐❣✉r❛ ✷✳✹✿ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞♦s r❡s✉❧t❛❞♦s ❞❡ ❞✐❢❡r❡♥t❡s ❛✉t♦r❡s ❝♦♠ ❛s ♠❡s♠❛s r❡❧❛çõ❡sL/B ❡ H/B ❡ ❞✐❢❡r❡♥t❡s ❞✐♠❡♥sõ❡s ❞❡B
❊①✐st❡ ✉♠❛ t❡♥❞ê♥❝✐❛ ❡♠ q✉❡✱ ♣❛r❛ ♦s ♠❡s♠♦s ✈❛❧♦r❡s ❞❡ H/B ❡ L/B✱ ❛s ♣❧❛❝❛s ❝♦♠ ♠❡♥♦r❡s ❞✐♠❡♥sõ❡s ❛♣r❡s❡♥t❛♠ ✈❛❧♦r❡s ❞❡Nγ ♠❛✐♦r❡s q✉❡ ❛s ♣❧❛❝❛s ❝♦♠ ❞✐♠❡♥sõ❡s s✉♣❡r✐✲ ♦r❡s✱ ❝♦♠♦ s❡ ✈❡r✐✜❝❛ ♥❛ ✜❣✉r❛ ✷✳✹✳ ❊st❡ ❢❡♥ó♠❡♥♦ ♣♦❞❡ ❡st❛r ❧✐❣❛❞♦ ❛♦ ❢❛❝t♦ ❞❡ q✉❡✱ ♣❛r❛ t❡♥sõ❡s ❡❢❡t✐✈❛s ❞❡ ✈❛❧♦r r❡❞✉③✐❞♦✱ ♦s â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♠♦❜✐❧✐③❛❞♦s s❡❥❛♠ s✉♣❡r✐♦r❡s ❛♦ ❞♦ ❡st❛❞♦ ❝rít✐❝♦✳
❉✐❝❦✐♥ ❡ ▲❡✉♥❣ ✭✶✾✽✸✮ ❝❤❛♠❛♠ à ❛t❡♥çã♦ ♣❛r❛ ❡st❡ ❢❡♥ó♠❡♥♦✱ ✐❧✉str❛❞♦ ♥✉♠❛ sér✐❡ ❞❡ ❡♥s❛✐♦s ❡❢❡t✉❛❞♦s ♥✉♠❛ ♠❡s♠❛ ❛r❡✐❛ ✭✜❣✉r❛ ✷✳✺✮✳ ◆❡st❛ ✜❣✉r❛✱ ❡stã♦ r❡♣r❡s❡♥t❛❞♦s ❞♦✐s t✐♣♦s ❞❡ ❡♥s❛✐♦s✿ ❡♥s❛✐♦s tr✐❛①✐❛✐s ❡ ❡♥s❛✐♦s ❡♠ ❡st❛❞♦ ♣❧❛♥♦ ❞❡ ❞❡❢♦r♠❛çã♦✳ ❖s ✈❛❧♦r❡s ❞♦s â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❡♥s❛✐♦s ❡♠ ❡st❛❞♦ ♣❧❛♥♦ ❞❡ ❞❡❢♦r♠❛çã♦ sã♦
✷✳✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
s✉♣❡r✐♦r❡s r❡❧❛t✐✈❛♠❡♥t❡ ❛♦s â♥❣✉❧♦s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❡♥s❛✐♦s tr✐❛①✐❛✐s✳ ◆❛ ✜❣✉r❛ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r q✉❡✱ ♥♦s ❡♥s❛✐♦s ❡♠ q✉❡ ❛ t❡♥sã♦ ❞❡ ❝♦♥✜♥❛♠❡♥t♦ é ♠❛✐s r❡❞✉③✐❞❛✱ ❝♦♥❞✉③❡♠ ❛ â♥❣✉❧♦s ❞❡ r❡s✐stê♥❝✐❛ ❛♦ ❝♦rt❡ ♠❛✐♦r❡s✱ s❡♥❞♦ ♠❛✐s ❡✈✐❞❡♥t❡ ♥♦s ❡♥s❛✐♦s ❡♠ ❡st❛❞♦ ♣❧❛♥♦ ❞❡❢♦r♠❛çã♦✳
❋✐❣✉r❛ ✷✳✺✿ ❊♥s❛✐♦s tr✐❛①✐❛✐s ❡ ❡♥s❛✐♦s ❞❡ ❝♦♠♣r❡ssã♦ ❡♠ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛ ♥❛ ❛r❡✐❛ ❞❡♥s❛ ❞❡ ❊r✐t❤ ✭❆❞❛♣t❛❞♦ ❞❡ ❉✐❝❦✐♥ ❡ ▲❡✉♥❣ ✶✾✽✸✮
❆ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❡st❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❡st❛r r❡❧❛❝✐♦♥❛❞❛ ❡①❝❧✉s✐✈❛♠❡♥t❡ ❝♦♠ ❞✐✜❝✉❧❞❛❞❡s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❡❝❡ r❡❧❛t✐✈❛♠❡♥t❡ ❛❢❛st❛❞❛✱ ❝♦♠♦ s❡ ✐♥❢❡r❡ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❖✈❡s❡♥ ✭✶✾✻✹✮✳ ❖ ❛✉t♦r r❡❛❧✐③♦✉ ✈ár✐♦s ❡♥s❛✐♦s ❝♦♠ ❛ ♠❡s♠❛ ♣❧❛❝❛ s❡♠♣r❡ à ♠❡s♠❛ ♣r♦❢✉♥❞✐❞❛❞❡✱ ♦❜t❡♥❞♦ r❡s✉❧t❛❞♦s ♣ró①✐♠♦s ✉♥s ❞♦s ♦✉tr♦s✳ ◆❛ t❛❜❡❧❛ ✷✳✸ ❡stã♦ r❡♣r❡s❡♥t❛❞♦s ♦s ✈❛❧♦r❡s ♦❜t✐❞♦s ❞♦ ❢❛t♦r ❞❡ ❛rr❛♥❝❛♠❡♥t♦s ♣❛r❛ ❡ss❡s ❡♥s❛✐♦s✳
❚❛❜❡❧❛ ✷✳✸✿ ❱❛❧♦r❡s ♦❜t✐❞♦s ♣♦r ❖✈❡s❡♥ ✭✶✾✻✹✮ ♣❛r❛ ✐❣✉❛✐s r❡❧❛çõ❡s ❞❡L/B ❡ H/B
❆✉t♦r H/B L/B B ❬❝♠❪ Nγ
❖✈❡s❡♥ ✭✶✾✻✹✮ ✶ ∞ ✶✺
✷✱✻✷✻ ✷✱✻✽✺ ✷✱✹✸✹ ✷✱✻✵✼
❡st❡ ❛✉t♦r r❡❛❧✐③♦✉ ❡♥s❛✐♦s s✐♠✉❧❛♥❞♦ ✉♠❛ ♣❧❛❝❛ ❝♦♠ ❧❛r❣✉r❛ ✐♥✜♥✐t❛ s❡♥❞♦ q✉❡✱ ♣♦r ❡ss❛ r❛③ã♦✱ ♦s r❡s✉❧t❛❞♦s s❡ r❡✈❡❧❛♠ ❜❛st❛♥t❡ ✐♥❢❡r✐♦r❡s ❛♦s ❞♦s ♦✉tr♦s ❛✉t♦r❡s✳
✷✳✷✳✷ ❊st✉❞♦s ◆✉♠ér✐❝♦✲❚❡ór✐❝♦s
❋♦✐ ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ♥❛ ❧✐t❡r❛t✉r❛ ❞✐✈❡rs♦s ❡st✉❞♦s ♥✉♠ér✐❝♦✲t❡ór✐❝♦s ❜❛s❡❛❞♦s s♦❜r❡t✉❞♦ ♥♦s ♠ét♦❞♦s ❞♦ ❡q✉✐❧í❜r✐♦ ❧✐♠✐t❡ ❡ ❞❛ ❛♥á❧✐s❡ ❧✐♠✐t❡✱ ❛ss✐♠ ❝♦♠♦ ✉♠ ❡st✉❞♦ ❡♠ q✉❡ ❢♦✐ r❡❛❧✐③❛❞❛ ✉♠❛ ❛♥á❧✐s❡ ❞❡ t❡♥sã♦ ❞❡❢♦r♠❛çã♦ ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ❡❧❛st♦♣❧ást✐❝❛s✱ r❡❝♦rr❡♥❞♦ ❛♦ ♠ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ◆❛ t❛❜❡❧❛ ✷✳✹ ❡❧❡♥❝❛♠✲s❡ ♦s tr❛❜❛❧❤♦s ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ r❡❛❧✐③❛❞♦s ♣♦r ❞✐❢❡r❡♥t❡s ❛✉t♦r❡s✱ ❛♣r❡s❡♥t❛❞♦✲s❡ t❛♠❜é♠ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞♦ ♠ét♦❞♦ ❡ ❞♦s ♣❛râ♠❡tr♦s ❡♥✈♦❧✈✐❞♦s ❡♠ ❝❛❞❛ ❡♥s❛✐♦✳
❚❛❜❡❧❛ ✷✳✹✿ ❘❡s✉♠♦ ❞❡ tr❛❜❛❧❤♦s ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ❞❡ ❡st✉❞♦s ♥✉♠ér✐❝♦✲t❡ór✐❝♦s ♣❛r❛ ♣❧❛❝❛s ❞❡ ❛♥❝♦r❛❣❡♠ ❞✐s♣♦st❛s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠ s♦❧♦ r❡s♣♦♥❞❡♥❞♦ ❡♠ ❝♦♥❞✐çõ❡s ❞r❡♥❛❞❛s
❆✉t♦r ❚✐♣♦ ❞❡ ❆♥á❧✐s❡ ●❡♦♠❡tr✐❛ φ′
❬➦❪ δ ❬➦❪ ❍✴❇
❚❡♥❣ ✭✶✾✻✷✮❛ ❊q✉✐❧í❜r✐♦
▲✐♠✐t❡ ❈♦rr✐❞❛ ❚♦❞♦s
− <✷
❇✐❛r❡③ ❡t ❛❧✳
✭✶✾✻✺✮❛ ❊q✉✐❧í❜r✐♦▲✐♠✐t❡ ❈♦rr✐❞❛ ❚♦❞♦s
0 ❚♦❞♦s
❖✈❡s❡♥ ❡ ❙trø♠❛♥♥
✭✶✾✼✷✮ ❊q✉✐❧í❜r✐♦▲✐♠✐t❡ ❈♦rr✐❞❛ ❚♦❞♦s
− ❚♦❞♦s
▼❡②❡r❤♦❢ ✭✶✾✼✸✮❛ ❊q✉✐❧í❜r✐♦
▲✐♠✐t❡ ❈♦rr✐❞❛ ❚♦❞♦s
− ❚♦❞♦s
◆❡❡❧② ❡t ❛❧✳ ✭✶✾✼✸✮ ❊q✉✐❧í❜r✐♦
▲✐♠✐t❡ ❈♦rr✐❞❛ ✸✵
−✹✺ φ′
❀φ′
/2 ✶−✺
❘♦✇❡ ❡ ❉❛✈✐s
✭✶✾✽✷✮ ❋✐♥✐t♦s ❊❧❛st♦✲❊❧❡♠❡♥t♦s ♣❧❛st✐❝✐❞❛❞❡
❈♦rr✐❞❛ ✵−✹✺ ✵❀φ′
✶−✽
▼✉rr❛② ❡ ●❡❞❞❡s
✭✶✾✽✾✮ ❆♥á❧✐s❡ ▲✐♠✐t❡ ❈♦rr✐❞❛ ❚♦❞♦s ✵❀
φ′
✷−✶✵
❇❛s✉❞❤❛r ❡ ❙✐♥❣❤
✭✶✾✾✹✮ ❆♥á❧✐s❡ ▲✐♠✐t❡ ❈♦rr✐❞❛ ✸✷❀ ✸✺❀✸✽ ✵❀
φ′
✶−✺
▼❡r✐✜❡❧❞ ❡ ❙❧♦❛♥
✭✷✵✵✻✮ ❆♥á❧✐s❡ ▲✐♠✐t❡ ❈♦rr✐❞❛ ✷✵
−✹✵ ✵❀φ′
✶−✶✵
❑✉♠❛r ❡ ❙❛❤♦♦
✭✷✵✶✷✮ ❆♥á❧✐s❡ ▲✐♠✐t❡ ❈♦rr✐❞❛ ❚♦❞♦s ✵
−φ′
✶−✼ ❛❱❛❧♦r❡s r❡t✐r❛❞♦s ❞❡ ❉❛s ✭✷✵✵✼✮✳
