❆▲●❖❘■❚▼❖❙ ❉❊ ❈❖◆❚❘❖▲❊ ❉❊ ❚❘➪❋❊●❖
P❆❘❆ ❊◆❳❆▼❊❙ ❉❊ ❘❖❇Ô❙ ❈❖▼ ❆▲❱❖❙ ❊▼
❨❯❘■ ❚❆❱❆❘❊❙ ❉❖❙ P❆❙❙❖❙
❆▲●❖❘■❚▼❖❙ ❉❊ ❈❖◆❚❘❖▲❊ ❉❊ ❚❘➪❋❊●❖
P❆❘❆ ❊◆❳❆▼❊❙ ❉❊ ❘❖❇Ô❙ ❈❖▼ ❆▲❱❖❙ ❊▼
❈❖▼❯▼
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❖r✐❡♥t❛❞♦r✿ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③
❝
✷✵✶✷✱ ❨✉r✐ ❚❛✈❛r❡s ❞♦s P❛ss♦s✳ ❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳
❚❛✈❛r❡s ❞♦s P❛ss♦s✱ ❨✉r✐
❆❧❣♦r✐t♠♦s ❞❡ ❈♦♥tr♦❧❡ ❞❡ ❚rá❢❡❣♦ ♣❛r❛ ❊♥①❛♠❡s ❞❡ ❘♦❜ôs ❝♦♠ ❆❧✈♦s ❡♠ ❝♦♠✉♠ ✴ ❨✉r✐ ❚❛✈❛r❡s ❞♦s P❛ss♦s✳ ✖ ❇❡❧♦ ❍♦r✐③♦♥t❡✱ ✷✵✶✷
①✈✐✐✐✱ ✽✻ ❢✳ ✿ ✐❧✳ ❀ ✷✾❝♠
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✖ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s
❖r✐❡♥t❛❞♦r✿ ▲✉✐③ ❈❤❛✐♠♦✇✐❝③
❘❡s✉♠♦
❊♥①❛♠❡s ❞❡ r♦❜ôs sã♦ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs✱ r❡✲ ❧❛t✐✈❛♠❡♥t❡ s✐♠♣❧❡s✱ ❞✐s♣♦st♦s ♥♦ ♠❡s♠♦ ❡s♣❛ç♦ ❡ ✐♥t❡r❛❣✐♥❞♦ ❡♥tr❡ s✐ ♣❛r❛ ❛❧❝❛♥ç❛r ✉♠ ♦❜❥❡t✐✈♦ ❝♦♠✉♠✳ ❉❡♥tr❡ ♦s ♣r♦❜❧❡♠❛s ❡♥❢r❡♥t❛❞♦s ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs✱ tê♠✲s❡ ♦ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦✳ ◆❡st❡ ♣r♦❜❧❡♠❛✱ ♦s r♦❜ôs ❞❡✈❡♠ s❡ ❝♦♦r❞❡♥❛r ♣❛r❛ ❡✈✐t❛r ❝♦♥❣❡st✐✲ ♦♥❛♠❡♥t♦s✱ ❡s♣❡❝✐✜❝❛♠❡♥t❡ q✉❛♥❞♦ ♦s r♦❜ôs ❞❡✈❡♠ s❡ ♠♦✈✐♠❡♥t❛r ♣❛r❛ ♦ ♠❡s♠♦ ❧♦❝❛❧ s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ três ❛❧❣♦r✐t♠♦s ❞✐str✐❜✉í❞♦s ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs✱ ♣❡r♠✐t✐♥❞♦ ❡✈✐t❛r ❝♦♥❣❡st✐♦♥❛♠❡♥t♦s t❛♥t♦ ♥❛ ❝❤❡❣❛❞❛ ❛♦ ❛❧✈♦ ❡♠ ❝♦♠✉♠ q✉❛♥t♦ ♥❛ s❛í❞❛✳ ❖ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦ ❝♦♥s✐st❡ ❡♠ ❢♦r♠❛r r❡❣✐õ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ♣ró①✐♠♦ ❛♦ ❛❧✈♦✳ ❖ s❡❣✉♥❞♦ ❝♦♥s✐st❡ ❡♠ ❝r✐❛r ✉♠❛ ✜❧❛ ❡♠ ❢♦r♠❛ ❞❡ ❡s♣✐r❛❧ ❡♠ t♦r♥♦ ❞♦ ❛❧✈♦✳ ❖ t❡r❝❡✐r♦ ✉t✐❧✐③❛ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s ❡♥tr❡ r♦❜ôs ✈✐s❛♥❞♦ ❡①♣✉❧s❛r ❛❧❣✉♥s r♦❜ôs✱ ❧✐❜❡r❛♥❞♦ ♣❛ss❛❣❡♠ ♣❛r❛ ♦s q✉❡ ❡stã♦ ♣ró①✐♠♦s ❛♦ ❛❧✈♦✳ ➱ ❢❡✐t❛ ✉♠❛ ❛♥á❧✐s❡ ❞❡ ❝❛❞❛ ✉♠ ❞❡❧❡s ❡ ✉♠❛ ❝♦♠♣❛r❛çã♦ ❞❡ s❡✉s ❞❡s❡♠♣❡♥❤♦s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❊♥①❛♠❡s ❞❡ r♦❜ôs✱ ❘♦❜ót✐❝❛✱ ❈♦♥tr♦❧❡ ❞❡ trá❢❡❣♦✱ ❈♦♥❣❡st✐♦♥❛♠❡♥✲ t♦s✳
❆❜str❛❝t
❘♦❜♦t✐❝ ❙✇❛r♠s ❛r❡ s②st❡♠s ❢♦r♠❡❞ ❜② ❛ ❧❛r❣❡ ♥✉♠❜❡r ♦❢ r♦❜♦ts✱ r❡❧❛t✐✈❡❧② s✐♠♣❧❡✱ ♣❧❛✲ ❝❡❞ ✐♥ s❛♠❡ s♣❛❝❡ ❛♥❞ ✐♥t❡r❛❝t✐♥❣ ❛♠♦♥❣ t❤❡♠s❡❧✈❡s t♦ ❢✉❧✜❧❧ ❛ ❝♦♠♠♦♥ ❣♦❛❧✳ ❆♠♦♥❣ t❤❡ ♣r♦❜❧❡♠s ❡♥❝♦✉♥t❡r❡❞ ✐♥ s✇❛r♠s ♦❢ r♦❜♦ts✱ t❤❡r❡ ❡①✐sts tr❛✣❝ ❝♦♥tr♦❧✳ ■♥ t❤✐s ♣r♦✲ ❜❧❡♠✱ r♦❜♦ts ♠✉st ❜❡ ❝♦♦r❞✐♥❛t❡❞ t♦ ❛✈♦✐❞ ❝♦♥❣❡st✐♦♥✱ s♣❡❝✐✜❝❧② ✇❤❡♥ r♦❜♦ts ♠✉st ♠♦✈❡ t♦ s❛♠❡ ❧♦❝❛❧✱ s✐♠✉❧t❛♥❡♦✉s❧②✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ❞❡✈❡❧♦♣❡❞ t❤r❡❡ ❞✐str✐❜✉t❡❞ ❛❧✲ ❣♦r✐t❤♠s ❢♦r tr❛✣❝ ❝♦♥tr♦❧ ✐♥ r♦❜♦t✐❝ s✇❛r♠s✱ ❛❧❧♦✇✐♥❣ t♦ ❛✈♦✐❞ ❝♦♥❣❡st✐♦♥s ❜♦t❤ ♦♥ ❛rr✐✈❛❧ ❛t ❝♦♠♠♦♥ t❛r❣❡t ❛♥❞ ❧❡❛✈✐♥❣ ✐t✳ ❚❤❡ ✜rst ❛❧❣♦r✐t❤♠ ❝♦♥s✐sts ✐♥ ✉s✐♥❣ ❡♥tr② ❛♥❞ ❡①✐t✐♥❣ r❡❣✐♦♥s ♥❡①t t♦ t❤❡ ❝♦♠♠♦♥ t❛r❣❡t✳ ❚❤❡ s❡❝♦♥❞ ♦♥❡ ❝♦♥s✐sts ✐♥ ♠❛❦✐♥❣ ❛ s♣✐r❛❧✲s❤❛♣❡❞ q✉❡✉❡ ❛r♦✉♥❞ t❤❡ t❛r❣❡t✳ ❚❤❡ t❤✐r❞ ♦♥❡ ✉s❡s ♠❡ss❛❣❡ ❝♦♠✉♥✐❝❛t✐♦♥ t♦ ❞r✐✈❡ ❛✇❛② s♦♠❡ r♦❜♦ts✱ r❡❧❡❛s✐♥❣ t❤❡ ♣❛ss❛❣❡ ❢♦r t❤♦s❡ ❛r❡ ♥❡①t t♦ t❤❡ t❛r❣❡t✳ ❲❡ ♠❛❞❡ ❛♥ ❛♥❛❧②s✐s ♦❢ ❡❛❝❤ ♦♥❡ ❛♥❞ ❝♦♠♣❛r❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡s❡ ❛❧❣♦r✐t❤♠s✳
❑❡②✇♦r❞s✿ ❘♦❜♦t✐❝ s✇❛r♠✱ ❘♦❜♦t✐❝s✱ ❚r❛✣❝ ❝♦♥tr♦❧✱ ❈♦♥❣❡st✐♦♥s✳
▲✐st❛ ❞❡ sí♠❜♦❧♦s
a
▲❛r❣✉r❛ ❞❛ ❡s♣✐r❛❧✳D
❉✐stâ♥❝✐❛ ♠✐♥í♠❛ ❛té ♦ ❛❧✈♦ ♣❛r❛ ✉t✐❧✐③❛r ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♦r❞❡♥❛çã♦✳F
❱❡t♦r ❢♦rç❛ r❡s✉❧t❛♥t❡✳F
R ❱❡t♦r ❞❡ ❢♦rç❛ r❡♣✉❧s✐✈❛✳F
A ❱❡t♦r ❞❡ ❢♦rç❛ ❛tr❛t✐✈❛✳F
T ❱❡t♦r ❞❡ ❢♦rç❛ t❛♥❣❡♥❝✐❛❧ ❞♦ ❛❧❣♦r✐t♠♦ ❊s♣✐r❛❧✳F
N ❱❡t♦r ❞❡ ❢♦rç❛ ♥♦r♠❛❧ ❞♦ ❛❧❣♦r✐t♠♦ ❊s♣✐r❛❧✳F
I ❱❡t♦r ❞❡ ❢♦rç❛ t❛♥❣❡♥❝✐❛❧ ✐♥✈❡rs❛ ❞♦ ❛❧❣♦r✐t♠♦ ❊s♣✐r❛❧✳F
P ❱❡t♦r ❞❡ ❢♦rç❛ r❡♣✉❧s✐✈❛ ♣r♦❥❡t❛❞❛ ♥❛ t❛♥❣❡♥❝✐❛❧ ❞♦ ❛❧❣♦r✐t♠♦ ❊s♣✐r❛❧✳F
M ❱❡t♦r ❞❡ ❢♦rç❛ ❡♥✈✐❛❞❛ ♥❛ ♠❡♥s❛❣❡♠ ❞♦s r♦❜ôs ❡♠ ❡st❛❞♦ ❊◆❚❘❆◆❉❖ ♥♦❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳
F
E ❱❡t♦r ❞❡ ❢♦rç❛ ❞❡ ❡①♣✉❧sã♦ r❡♣❧✐❝❛❞❛ ♣❡❧♦s r♦❜ôs ♥♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳K
❈♦♥st❛♥t❡ ♠✉❧t✐♣❧✐❝❛t✐✈❛ ♣❛r❛ ❢♦rç❛ r❡s✉❧t❛♥t❡✳ρ
Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ♣❛r❛ ❡st❛❞♦ ■▼P❆❈■❊◆❚❊✳q
❱❡t♦r ♣♦s✐çã♦ ❞♦ r♦❜ô✳Raio
❘❛✐♦ ❞❛s ár❡❛s ❞❡ ♣❡r✐❣♦ ❡ ❧✐✈r❡✳T
P ■t❡r❛çõ❡s ♣❛r❛ ❡♥tr❛r ♥♦ ❡st❛❞♦ ■▼P❆❈■❊◆❚❊✳T
M ◗✉❛♥t✐❞❛❞❡ ❞❡ ✐t❡r❛çõ❡s q✉❡ ♦ r♦❜ô ❞❡✈❡ ❡s♣❡r❛r ❛té ♠❛♥❞❛r ❛ ♣ró①✐♠❛ ♠❡♥s❛✲❣❡♠✳
T
E ◆♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦✿ ◗✉❛♥t✐❞❛❞❡ ❞❡ ✐t❡r❛çõ❡s ❝♦♥s❡❝✉t✐✈❛s q✉❡ ♦ r♦❜ô ❞❡✈❡❡s♣❡r❛r ♣❛r❛ ♣❡r❝❡❜❡r s❡ ♥ã♦ ❤á ✉♠ r♦❜ô à s✉❛ ❢r❡♥t❡✳
T
E ◆♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✿ ◗✉❛♥t✐❞❛❞❡ ❞❡ ✐t❡r❛çõ❡s q✉❡ ♦ r♦❜ô ❞❡✈❡ s❡❣✉✐r ❛ ❢♦rç❛❞❡ ❡①♣✉❧sã♦✳
α
R ➶♥❣✉❧♦ ❞❡ ♣❡r❝❡♣çã♦ ♣❛r❛ ré♣❧✐❝❛ ❞❡ ♠❡♥s❛❣❡♠ ♥♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳α
A ➶♥❣✉❧♦ ❞❡ ♣❡r❝❡♣çã♦ ♣❛r❛ ✐❣♥♦r❛r ❡①♣✉❧sã♦ ♥♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳▲✐st❛ ❞❡ ❋✐❣✉r❛s
✸✳✶ Pr♦❜❧❡♠❛ ❞♦ ❛❧✈♦ ❡♠ ❝♦♠✉♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✸✳✷ ❊sq✉❡♠❛ ❣❡r❛❧ ❞♦s ❛❧❣♦r✐t♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✸✳✸ ▼áq✉✐♥❛ ❞❡ ❡st❛❞♦s ❞♦ ❛❧❣♦r✐t♠♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✸✳✹ ➪r❡❛ ❞❡ ♣❡r✐❣♦ ❡ ❧✐✈r❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✸✳✺ ❉✐✈✐sã♦ ❞❛ r❡❣✐ã♦ ❞❡ ♣❡r✐❣♦ ❡♠ ár❡❛s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✻ ❉✐stâ♥❝✐❛ ♠❛✐s ♣ró①✐♠❛ ❡♥tr❡ ✉♠ ♣♦♥t♦ ❢♦r❛ ❞❛ r❡❣✐ã♦ ❡ ❛ ❢r♦♥t❡✐r❛ ❞❛ r❡❣✐ã♦
❞❡ ❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✼ ◆♦✈❛ ♣♦s✐çã♦ ❞♦ r♦❜ô ❝❛s♦ ❡st❡❥❛ ♥❛ ár❡❛ ❧✐✈r❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✽ ◆♦✈❛ ♠áq✉✐♥❛ ❞❡ ❡st❛❞♦s ❞♦ ❛❧❣♦r✐t♠♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✾ ❘❡❞✉çã♦ ❞❛s ❢♦rç❛s r❡♣✉❧s✐✈❛s ♣❛r❛ ❡✈✐t❛r q✉❡ ♦s r♦❜ôs s❛✐❛♠ ❞❛ r❡❣✐ã♦ ❞❡
❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✶✵ ❊s♣✐r❛❧ ❞❡ ❋❡r♠❛t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✶✶ (xS, yS)✱ q✉❛♥❞♦ t >2π✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸✳✶✷ ❆❧❣✉♥s ❝❛s♦s ♣❛r❛ (xS, yS)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✸✳✶✸ ❋♦rç❛s ❛♣❧✐❝❛❞❛s ♣❛r❛ ❢♦r♠❛r ❛ ✜❧❛ ❡♠ ❡s♣✐r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✶✹ ●rá✜❝♦ ❞❡ t×θ˙✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶✺ ❊s♣❛ç❛♠❡♥t♦ ❞❛ ❡s♣✐r❛❧✱ ❞❛❞♦ ♦ r❛✐♦ ❞❡ ♣❡r❝❡♣çã♦ ❞♦ r♦❜ô✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✻ ❱❡t♦r❡s FE ❡ FM✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶✼ ❘❡❣✐ã♦✲αR✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✶✽ ▼áq✉✐♥❛ ❞❡ ❡st❛❞♦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✹✳✶ ❘♦❜ôs ❡✲♣✉❝❦ ✉t✐❧✐③❛❞♦s ♣❛r❛ t❡st❡s r❡❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✷ ❊①❡♠♣❧♦ ❞❡ ❣rá✜❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✹✳✸ ❆♥á❧✐s❡ ❞❡ Ke ♣❛r❛ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❱❡rsã♦ ✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✹ ❆♥á❧✐s❡ ❞❡ Ki ♣❛r❛ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❱❡rsã♦ ✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✺ ❆♥á❧✐s❡ ❞❡ Ki ♣❛r❛ ♦s ❛❧❣♦r✐t♠♦s ❘❡❣✐ã♦ ❱❡rsã♦ ✵ ✲ q✉❛♥t✐❞❛❞❡ ❞❡ ❝♦❧✐sõ❡s✳ ✹✹ ✹✳✻ ❘❡s✉❧t❛❞♦s ❞❛ ✈❛r✐❛çã♦ ❞❡ ρ♣❛r❛ ✻✵ ❡ ✶✵✵ r♦❜ôs ✉s❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦✳ ✹✺ ✹✳✼ ❘❡s✉❧t❛❞♦s ❞❛ ✈❛r✐❛çã♦ ❞❡ ❘❛✐♦ ♥♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹✳✽ ❘❡s✉❧t❛❞♦s ❞❛ ✈❛r✐❛çã♦ ❞❡ ❘❛✐♦ ♥♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❝♦♠ ✻✵ r♦❜ôs✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✾ ❘❡s✉❧t❛❞♦s ❞❛ ✈❛r✐❛çã♦ ❞❡ ❘❛✐♦ ♥♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❝♦♠ ✶✵✵ r♦❜ôs✳ ✳ ✳ ✳ ✹✽ ✹✳✶✵ ❘❡s✉❧t❛❞♦s ❞❛ ✈❛r✐❛çã♦ ❞❡ ❈✐❝❧♦s ♣❛r❛ ✐♠♣❛❝✐ê♥❝✐❛ ♥♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦
❝♦♠ ❘❛✐♦ ❂ ✭✸✱✺❀ ✶✱✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✶✶ ❘❡s✉❧t❛❞♦s ❞❛ ✈❛r✐❛çã♦ ❞❡ ❚❊▼P❖ ♥♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❝♦♠ ❘❆■❖ ❂ ✭✺✱✺❀
✸✱✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✶✷ ❆♥á❧✐s❡ ❈✐❝❧♦s ♣❛r❛ ♠❡♥s❛❣❡♥s ♣❛r❛ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❱❡rsã♦ ✵✭❈✐❝❧♦s ❞❡
❡s♣❡r❛ ❂ ✾✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✸ ❆♥á❧✐s❡ ❈✐❝❧♦s ♣❛r❛ ♠❡♥s❛❣❡♥s ♣❛r❛ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❱❡rsã♦ ✵ ✭❈✐❝❧♦s ❞❡
❡s♣❡r❛ ❂ ✶✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶✹ ❆♥á❧✐s❡ ❈✐❝❧♦s ❞❡ ❡s♣❡r❛ ♣❛r❛ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ❱❡rsã♦ ✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✶✺ ❆♥á❧✐s❡ ❞♦ ♣❛râ♠❡tr♦ P❡r❝❡♣çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✶✻ ■♠❛❣❡♥s ❞❛ ❡①❡❝✉çã♦ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠ ❤tt♣✿✴✴②♦✉t✉✳❜❡✴✈✸♦❞❈③❑❴❤❤✹✮✳ ✺✻ ✹✳✶✼ ❆♥á❧✐s❡ ❞❡K ♣❛r❛ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ✭a = 1,0✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹✳✶✽ ❆♥á❧✐s❡ ❞❡K ♣❛r❛ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ✭a = 2,0✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✶✾ ❋♦r♠❛ ❞❛ ❡s♣✐r❛❧ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡a✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✷✵ ❆♥á❧✐s❡ ❞❡a ♣❛r❛ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✷✶ ■♠❛❣❡♥s ❞❛ ❡①❡❝✉çã♦ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠ ❤tt♣✿✴✴②♦✉t✉✳❜❡✴✸q✺❥①q❯♣♣❯❣✮✳ ✻✸ ✹✳✷✷ ❆♥á❧✐s❡ ❞❡ ❈✐❝❧♦s ♣❛r❛ ♠❡♥s❛❣❡♥s ♣❛r❛ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷✸ ❆♥á❧✐s❡ ❞❡TE ♣❛r❛ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✹✳✷✹ ❆♥á❧✐s❡ ❞❡αR ♣❛r❛ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✹✳✷✺ ❆♥á❧✐s❡ ❞❡αA ♣❛r❛ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✹✳✷✻ ■♠❛❣❡♥s ❞❛ ❡①❡❝✉çã♦ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠ ❤tt♣✿✴✴②♦✉t✉✳❜❡✴❘◗✐✵♠✇✷♦✐t❝✮✳ ✻✾ ✹✳✷✼ ■♠❛❣❡♥s ❞❛ ❡①❡❝✉çã♦ ♣❛r❛ q✉❛tr♦ ❞✐r❡çõ❡s ❛♣ós ❛❧❝❛♥ç❛r ♦ ❛❧✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✷✽ ❈♦♠♣❛r❛çã♦ ♣❛r❛ r♦❜ôs ♥ã♦ ❤♦❧♦♥ô♠✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✷✾ ❈♦♠♣❛r❛çã♦ ♣❛r❛ r♦❜ôs ❤♦❧♦♥ô♠✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✸✵ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❡✲♣✉❝❦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❙❡♠❈♦♦r❞ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠
❤tt♣✿✴✴②♦✉t✉✳❜❡✴●✈③❣▼❤①❥q❦✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✸✶ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❡✲♣✉❝❦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❙❡♠❘❡❣✐ã♦ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠
❤tt♣✿✴✴②♦✉t✉✳❜❡✴■❦♣✹❲✉✇❢❇③✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✸✷ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❡✲♣✉❝❦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠
❤tt♣✿✴✴②♦✉t✉✳❜❡✴❲❖■①✇r♥✹✸❏✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✸✸ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❡✲♣✉❝❦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❊s♣✐r❛❧ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠
❤tt♣✿✴✴②♦✉t✉✳❜❡✴❆❲✇❥❧✷✹❛✵❧✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✸✹ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❡✲♣✉❝❦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡ ✭✈í❞❡♦ ❞✐s♣♦♥í✈❡❧ ❡♠
❤tt♣✿✴✴②♦✉t✉✳❜❡✴◗❝q♥❳✾❨✺◗◆❆✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❊st❛❞♦s ❞♦ r♦❜ô ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✹✳✶ ❱❛❧♦r❡s ♣❛❞rõ❡s ♣❛r❛ ♦s ❡①♣❡r✐♠❡♥t♦s ❝♦♠ ♦ ❆❧❣♦r✐t♠♦ ❘❡❣✐ã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✷ ❱❛❧♦r❡s ♣❛❞rõ❡s ♣❛r❛ ♦s ❡①♣❡r✐♠❡♥t♦s ❝♦♠ ♦ ❆❧❣♦r✐t♠♦ ❊s♣✐r❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✸ ❱❛❧♦r❡s ♣❛❞rõ❡s ♣❛r❛ ♦s ❡①♣❡r✐♠❡♥t♦s ❝♦♠ ♦ ❆❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✹ ❱❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❘❡❣✐ã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✺ ❱❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❊s♣✐r❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✻ ❱❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❙✐r❡♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
❙✉♠ár✐♦
❘❡s✉♠♦ ✈✐✐
❆❜str❛❝t ✐①
▲✐st❛ ❞❡ sí♠❜♦❧♦s ①✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ❡ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞❡st❡ ❞♦❝✉♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✺
✸ ❆❧❣♦r✐t♠♦s Pr♦♣♦st♦s ✾
✸✳✶ ❆❧❣♦r✐t♠♦ ✶✿ ❘❡❣✐ã♦ ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✸✳✶✳✶ ❆❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦ ♣❛r❛ ❝♦♥tr♦❧❡ ❞❡ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✶✷ ✸✳✶✳✷ ❆❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✶✳✸ ❖t✐♠✐③❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷ ❆❧❣♦r✐t♠♦ ✷✿ ❋✐❧❛ ❡♠ ❡s♣✐r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✷✳✶ ❋✉♥❞❛♠❡♥t♦s s♦❜r❡ ❡s♣✐r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✷✳✷ ❖❜t❡♥çã♦ ❞❡ ✉♠ ♣♦♥t♦ ❞❛ ❡s♣✐r❛❧ ♠❛✐s ♣ró①✐♠♦ ❞❡ ✉♠ ♣♦♥t♦
q✉❛❧q✉❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✷✳✸ ❋♦rç❛s q✉❡ ❝♦♠♣õ❡♠ ❛ ❢♦r♠❛çã♦ ❞❛ ✜❧❛ ❡♠ ❡s♣✐r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✷✳✹ ❖t✐♠✐③❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✸ ❆❧❣♦r✐t♠♦ ✸✿ ✏❙✐r❡♥❡✑ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✸✳✶ ❚r♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s ❡ ❢♦rç❛ ❞❡ ❡①♣✉❧sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✸✳✷ ▼áq✉✐♥❛ ❞❡ ❡st❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✹ ❊①♣❡r✐♠❡♥t♦s ❡ ❘❡s✉❧t❛❞♦s ✸✼ ✹✳✶ ❆❧❣♦r✐t♠♦ ✶✿ ❘❡❣✐õ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✶✳✶ ❋♦rç❛s r❡♣✉❧s✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✶✳✷ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s✐çã♦ ♣❛r❛ ■▼P❆❈■❊◆❚❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✶✳✸ ❘❛✐♦ ❞❛s r❡❣✐õ❡s ❞❡ ♣❡r✐❣♦ ❡ ❧✐✈r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✶✳✹ P❡rí♦❞♦ ❞❡ ❡s♣❡r❛ ❡♠ ❝✐❝❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✶✳✺ ❈✐❝❧♦s ♣❛r❛ ♠❡♥s❛❣❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✶✳✻ ❈✐❝❧♦s ❞❡ ❡s♣❡r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶✳✼ ➪r❡❛ ❞❡ ❛❧❝❛♥❝❡ ❞♦ s❡♥s♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✶✳✽ ❊①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✶✳✾ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✷ ❆❧❣♦r✐t♠♦ ✷✿ ❋✐❧❛ ❡♠ ❡s♣✐r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✷✳✶ ❋♦rç❛s r❡♣✉❧s✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷✳✷ ▲❛r❣✉r❛ ❞❛ ❡s♣✐r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✷✳✸ ❊①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✷✳✹ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✸ ❆❧❣♦r✐t♠♦ ✸✿ ❙✐r❡♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✸✳✶ ❈✐❝❧♦s ♣❛r❛ ♠❡♥s❛❣❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✸✳✷ ❈✐❝❧♦s ♣❛r❛ ❢♦rç❛ ❞❡ ❡①♣✉❧sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✸✳✸ ➶♥❣✉❧♦ ❞❡ ♣❡r❝❡♣çã♦ ♣❛r❛ ré♣❧✐❝❛ ❞❡ ♠❡♥s❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸✳✹ ➶♥❣✉❧♦ ❞❡ ♣❡r❝❡♣çã♦ ♣❛r❛ ✐❣♥♦r❛r ❡①♣✉❧sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✸✳✺ ❊①❡❝✉çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✸✳✻ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ❛❧❣♦r✐t♠♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✹✳✺ ❊①♣❡r✐♠❡♥t♦s r❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✺ ❈♦♥❝❧✉sõ❡s ✼✾
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✽✸
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❊♥①❛♠❡s ❞❡ r♦❜ôs sã♦ s✐st❡♠❛s ❝♦♠♣♦st♦s ♣♦r ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs s✐♠♣❧❡s q✉❡ ♥♦r♠❛❧♠❡♥t❡ ❝♦♠♣❛rt✐❧❤❛♠ ♦❜❥❡t✐✈♦s ❡♠ ❝♦♠✉♠✳ ◆❡st❡s s✐st❡♠❛s✱ ❛ ❡①❡❝✉çã♦ ❞❡ ✉♠❛ ❞❛❞❛ t❛r❡❢❛ é ♣r♦❝❡ss❛❞❛ ❞❡ ♠♦❞♦ ❞❡s❝❡♥tr❛❧✐③❛❞♦✱ ♦✉ s❡❥❛✱ ❝❛❞❛ r♦❜ô ❞❡✈❡ ♣r♦✲ ❝❡ss❛r ❛s ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s ❧♦❝❛❧♠❡♥t❡ ♣♦r s❡✉s s❡♥s♦r❡s ❡ ❡✈❡♥t✉❛❧♠❡♥t❡ ❝♦♠✉♥✐❝❛r ♦ r❡s✉❧t❛❞♦ ❛♦s ♦✉tr♦s r♦❜ôs ♥♦ ❡♥①❛♠❡✳ ❊♠ ❣❡r❛❧✱ ♦s r♦❜ôs ♣♦ss✉❡♠ ✉♠ ❧✐♠✐t❛❞♦ ♣♦❞❡r ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❞❡ ❝♦♠✉♥✐❝❛çã♦✳ ❉❡✈✐❞♦ ❛ ❡st❛ ❧✐♠✐t❛çã♦✱ ♦s ❛❧❣♦r✐t♠♦s ❞❡✲ s❡♥✈♦❧✈✐❞♦s ❞❡✈❡♠ s❡r r♦❜✉st♦s ❡ ❡s❝❛❧á✈❡✐s✱ ❣❛r❛♥t✐♥❞♦ q✉❡ ❛ ✐♥❝❧✉sã♦ ❞❡ ♠❛✐s r♦❜ôs ❛✉♠❡♥t❡♠ ❛ ❡✜❝✐ê♥❝✐❛ ❞❡st❡s s✐st❡♠❛s ❬❙❛❤✐♥✱ ✷✵✵✹❪✳
❆ ✐♥s♣✐r❛çã♦ ❞♦s ❡♥①❛♠❡s ❞❡ r♦❜ôs s✉r❣❡ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❝♦❧ô♥✐❛s ❞❡ ✐♥s❡✲ t♦s✱ ❝♦♠♦ ❢♦r♠✐❣❛s ❡ ❛❜❡❧❤❛s✳ ◆❡st❛s ❝♦❧ô♥✐❛s✱ ♦s ✐♥❞✐✈í❞✉♦s ✐♥t❡r❛❣❡♠ ❡♥tr❡ s✐ ✉s❛♥❞♦ ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛❧ ❡ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥❞✐✈✐❞✉❛❧✱ ♦✉ s❡❥❛✱ ♥ã♦ ❡①✐st❡ ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧ ❞❡ ❝♦♥tr♦❧❡ ❛❞♠✐♥✐str❛♥❞♦ ❝❛❞❛ ✉♠ ❞♦s ✐♥❞✐✈í❞✉♦s✳
❊st❡ t✐♣♦ ❞❡ ♣❛r❛❞✐❣♠❛ ♥♦ ❝♦♥tr♦❧❡ ❞❡ ♠ú❧t✐♣❧♦s r♦❜ôs ✕ ❞❡s❝❡♥tr❛❧✐③❛❞♦ ❡ ♣♦r ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛❧ ✕ t♦r♥❛ ♦ s✐st❡♠❛ ♠❛✐s r♦❜✉st♦ ❡ ❡s❝❛❧á✈❡❧✳ ❆ r♦❜✉st❡③ s❡ t♦r♥❛ ❡✈✐❞❡♥t❡ q✉❛♥❞♦ ❛❧❣✉♥s r♦❜ôs ♣❛ss❛♠ ❛ ♥ã♦ ❢✉♥❝✐♦♥❛r ❝♦rr❡t❛♠❡♥t❡✿ ❛ ♣❡r❞❛ ❞❡ r♦❜ôs ❡♠ ❡♥①❛♠❡s ♣♦❞❡ ❞✐♠✐♥✉✐r ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ s✐st❡♠❛✱ ♠❛s ♥ã♦ ✐♠♣❡❞❡ q✉❡ ❡①❡❝✉t❡ s✉❛ t❛r❡❢❛ ♥♦r♠❛❧♠❡♥t❡✳ ❆ ❡s❝❛❧❛❜✐❧✐❞❛❞❡ é ❞❡✜♥✐❞❛ ❝♦♠♦ ❛ ♥ã♦ ❞❡❣r❛❞❛çã♦ ❞♦ s✐st❡♠❛ à ♠❡❞✐❞❛ q✉❡ s❡ ❛✉♠❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ✐♥❞✐✈í❞✉♦s✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♥tr♦❧❡ ❞♦s ❡♥①❛♠❡s ❞❡ r♦❜ôs ❞❡✈❡ s❡r ♣r♦❥❡t❛❞♦ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ❛ ✐♥❝❧✉sã♦ ❞❡ ♠❛✐s r♦❜ôs ♣❛r❛ ♦ ❣r✉♣♦ t❡♥❞❛ ❛ ♠❡❧❤♦r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ s✐st❡♠❛✳ ❙❡ ♦ ❡♥①❛♠❡ ❞❡ r♦❜ôs t✐✈❡ss❡ ✉♠❛ ✉♥✐❞❛❞❡ ❞❡ ❝♦♥tr♦❧❡ ❝❡♥tr❛❧✱ ✐st♦ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧ ♣♦rq✉❡ ❛ ✐♥❝❧✉sã♦ ❞❡ ♥♦✈♦s r♦❜ôs só ❛✉♠❡♥t❛r✐❛ s✉❛ ❝❛r❣❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳
❖ ✐❞❡❛❧ é q✉❡ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs s❡❥❛ ✐♠♣❧❡♠❡♥t❛❞♦ ✈✐s❛♥❞♦ ❛ ✢❡①✐❜✐❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ♦s r♦❜ôs ❛❣✐rã♦ ❞❡ ♠♦❞♦ q✉❡ s✐t✉❛çõ❡s ❞✐❢❡r❡♥t❡s ❣❡r❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❞✐✲ ❢❡r❡♥t❡s✱ ❛✐♥❞❛ ❛ss✐♠ s❡♥❞♦ ❝❛♣❛③❡s ❞❡ ❡①❡❝✉t❛r ❛ t❛r❡❢❛ ♣r✐♥❝✐♣❛❧✳ ◆❛ ♥❛t✉r❡③❛✱ sã♦
✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❡♥❝♦♥tr❛❞♦s ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ✢❡①✐❜✐❧✐❞❛❞❡ ❝♦♠♦ ♥✉♠❛ ❝♦❧ô♥✐❛ ❞❡ ❢♦r♠✐❣❛s✳ ❙❡✉ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ é ❝♦❧❡t❛r ❛❧✐♠❡♥t♦ ♣❛r❛ ♦ ❢♦r♠✐❣✉❡✐r♦✱ ♠❛s s✉❜t❛r❡❢❛s ❞❡✈❡♠ s❡r ❝✉♠♣r✐❞❛s q✉❛♥❞♦ s✐t✉❛çõ❡s ✐♥✉s✐t❛❞❛s s✉r❣❡♠ ❞✉r❛♥t❡ ❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛ ♣r✐♥❝✐♣❛❧✿ ❢✉❣❛ ❞❡ ♣r❡❞❛❞♦r❡s✱ ❝❛rr❡❣❛♠❡♥t♦ ❞❡ ❛❧✐♠❡♥t♦s ♣❡s❛❞♦s ♦✉ ❞❡s✈✐♦ ❞❡ r♦t❛s ❜❧♦q✉❡❛❞❛s ♣♦r ❞❡rr❛♠❛♠❡♥t♦ ❞❡ ❧íq✉✐❞♦s ♦✉ ♦❜❥❡t♦s ❞❡✐①❛❞♦s ♥♦ ♠❡✐♦ ❞❛ r♦t❛✳
◆✉♠ ❛♠❜✐❡♥t❡ ❝♦♠♣❛rt✐❧❤❛❞♦ ♣♦r ✈ár✐♦s r♦❜ôs✱ ❛ t❡♥❞ê♥❝✐❛ ❞❡ ✉♠ r♦❜ô ✐♥t❡r❢❡r✐r ❝♦♠ ♦ ♦✉tr♦ é ♠❛✐♦r✳ ❊♠ ❡s♣❡❝✐❛❧✱ ✉♠ ❞♦s ♣r♦❜❧❡♠❛s ❡①✐st❡♥t❡s ♥❛ ♥❛✈❡❣❛çã♦ ❞❡ ❡♥①❛♠❡s é ♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦✱ ❡s♣❡❝✐✜❝❛♠❡♥t❡ q✉❛♥❞♦ ♦s r♦❜ôs ❞❡✈❡♠ s❡ ♠♦✈✐♠❡♥t❛r ♣❛r❛ ♦ ♠❡s♠♦ ❧♦❝❛❧ s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ ➱ ❝♦♠✉♠ q✉❡ r♦❜ôs ♣♦ss✉❛♠ ❛❧✈♦s ❞✐st✐♥t♦s q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ✉♠❛ ♠❡s♠❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦ ♦✉ ✉♠ ♠❡s♠♦ ❛❧✈♦ ❡♠ ❝♦♠✉♠✱ ❝♦♠♦ ♦❝♦rr❡ ❡♠ ♥❛✈❡❣❛çã♦ ♣♦r ♣♦♥t♦s ❞❡ ✐♥t❡r❡ss❡ ✭✇❛②♣♦✐♥t ♥❛✈✐❣❛t✐♦♥✮✳ ■st♦ t❛♠❜é♠ ♦❝♦rr❡ ♥♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦❧❡t❛ ✭❢♦r❛❣✐♥❣✮ ❬❙❛❤✐♥ ❡t ❛❧✳✱ ✷✵✵✽❪✱ q✉❛♥❞♦ ♦s r♦❜ôs ❞❡✈❡♠ s❡ ❞❡s❧♦❝❛r ♣❛r❛ ♣♦♥t♦s ❞♦ ❛♠❜✐❡♥t❡ ♣❛r❛ ❝♦❧❡t❛r ✐t❡♥s ❡ tr❛♥s♣♦rtá✲❧♦s ♣❛r❛ ✉♠ ❧♦❝❛❧ ❡s♣❡❝í✜❝♦✳ P♦❞❡✲s❡ ❝✐t❛r ❛♣❧✐❝❛çõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ❝♦❧❡t❛ ❝♦♠♦ tr❛♥s♣♦rt❡ ❞❡ ♠❛t❡r✐❛✐s tó①✐❝♦s ♦✉ ❡s❝♦♠❜r♦s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❞❡s❛❜❛♠❡♥t♦s✳
❖ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ é ✐♠♣♦rt❛♥t❡ ♣♦✐s ❛ ♣r❡s❡♥ç❛ ❞❡ ♦✉tr♦s r♦❜ôs ♥♦ ❛♠❜✐❡♥t❡ ✐rá ❛tr❛♣❛❧❤❛r ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦ ❝❛♠✐♥❤♦ ❞❡ ❝❛❞❛ r♦❜ô✳ ❊♠ ✉♠ ❝❡♥ár✐♦ ♦♥❞❡ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs ❝♦♠♣❛rt✐❧❤❛♠ ♦ ♠❡s♠♦ ❛♠❜✐❡♥t❡✱ ♦ t❡♠♣♦ ❞❡ tr❛❥❡t♦ ♣❛r❛ ❝❛❞❛ r♦❜ô ♣♦❞❡rá s❡r s✉❜st❛♥❝✐❛❧♠❡♥t❡ ❛✉♠❡♥t❛❞♦ ❞❡✈✐❞♦ ❛♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❝❛✉s❛❞♦ ♣♦r ♦✉tr♦s r♦❜ôs ♦❜str✉✐♥❞♦ s✉❛ ♣❛ss❛❣❡♠✳ ❖ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ é ♥❡❝❡ssár✐♦✱ ✈✐st♦ q✉❡ ❛ ♣r❡s❡♥ç❛ ❞❡ ♦✉tr♦s r♦❜ôs ❡♠ s✐st❡♠❛s ❝♦♦♣❡r❛t✐✈♦s s❡rá ❝♦♥st❛♥t❡ ♥❛ ♠❛✐♦r✐❛ ❞❛s t❛r❡❢❛s✳
❖ ♣r♦❜❧❡♠❛ ❞♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ♣♦❞❡r✐❛ s❡r r❡s♦❧✈✐❞♦ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ♣❛r❛ ❝♦♠♣✉t❛r ❛s ♠❡❧❤♦r❡s tr❛❥❡tór✐❛s ♣❛r❛ ❝❛❞❛ r♦❜ô✳ P♦✲ ré♠✱ ❤á ❛ ❞❡s✈❛♥t❛❣❡♠ ❞♦ s✐st❡♠❛ ✜❝❛r ❞❡♣❡♥❞❡♥t❡ ❞❡st❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧✱ ❛❧é♠ ❞❡ ♥ã♦ s❡r ✉♠❛ s♦❧✉çã♦ ❡s❝❛❧á✈❡❧ ♣❛r❛ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ r♦❜ôs✳ ◆♦ ❝♦♥t❡①t♦ ❞❡ ❡♥①❛♠❡s✱ ✉♠ ❞♦s ❞❡s❛✜♦s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡s s✐st❡♠❛s é ❛ ❣❛r❛♥t✐❛ ❞❡ q✉❡ ♦ t♦❞♦ ✐rá ❢✉♥❝✐♦♥❛r ❝♦rr❡t❛♠❡♥t❡ s❡♠ q✉❡ ❝❛❞❛ ✉♠❛ ❞❛s ♣❛rt❡s t❡♥❤❛ ❝♦♥❤❡❝✐♠❡♥t♦ ❣❧♦❜❛❧ ❞♦ ❛♠❜✐❡♥t❡✳
✶✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ❡ ❖❜❥❡t✐✈♦s
❖ ♣r♦❜❧❡♠❛ ❛ s❡r tr❛t❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦ s❡rá ♦ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs q✉❛♥❞♦ ❡①✐st❡ ✉♠ ❛❧✈♦ ❡♠ ❝♦♠✉♠ ♣❛r❛ ❡❧❡s✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❡st❡ ♣r♦❜❧❡♠❛ ♣♦❞❡ s❡r ❡♥✉♥❝✐❛❞♦ ❝♦♠♦ ❛ s❡❣✉✐r✿
✶✳✷✳ ❖r❣❛♥✐③❛çã♦ ❞❡st❡ ❞♦❝✉♠❡♥t♦ ✸
r♦❜ôs ❞❡✈❡♠ ❝♦♦♣❡r❛r ❡♥tr❡ s✐ ❞❡ ❢♦r♠❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛✱ ✉s❛♥❞♦ ❛♣❡♥❛s ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛❧✱ ❛ ✜♠ ❞❡ ♣♦ss✐❜✐❧✐t❛r q✉❡ t♦❞♦s ❛❧❝❛♥❝❡♠ ♦ ❛❧✈♦ ❡✈✐t❛♥❞♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦s ❡ s❛✐❛♠ ❞❡ss❛ r❡❣✐ã♦ ♥♦ ♠❡♥♦r t❡♠♣♦ ♣♦ssí✈❡❧✳
P♦rt❛♥t♦✱ ❞❡ ❢♦r♠❛ ❛ ❛t❛❝❛r ❡ss❡ ♣r♦❜❧❡♠❛✱ ♦ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ❞❡s❡♥✈♦❧✈❡r ❛❧❣♦r✐t♠♦s ❞❡s❝❡♥tr❛❧✐③❛❞♦s ♣❛r❛ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs q✉❛♥❞♦ ❡①✐st❡ ✉♠ ❛❧✈♦ ❡♠ ❝♦♠✉♠ ♣❛r❛ ♠✉✐t♦s ❞❡❧❡s✳ ❋♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s três ❛❧❣♦r✐t♠♦s ❞✐❢❡r❡♥t❡s ❡ ❛♥❛❧✐s❛❞♦ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❝❛❞❛ ✉♠ ❞❡❧❡s✱ ❝♦♠♣❛r❛♥❞♦✲♦s✳ ❖ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦ ❝♦♥s✐st❡ ❡♠ ❡st❡♥❞❡r ✉♠ tr❛❜❛❧❤♦ ❥á r❡❛❧✐③❛❞♦ ♣❛r❛ r❡s♦❧✈❡r ❡st❡ ♣r♦❜❧❡♠❛ ❬▼❛r❝♦❧✐♥♦ ✫ ❈❤❛✐♠♦✇✐❝③✱ ✷✵✵✾❪✱ ✐♥❝❧✉✐♥❞♦ ✉♠ ❝♦♥tr♦❧❡ ❞❡ r❡❣✐õ❡s ❞❡ ❛❝❡ss♦✱ t♦r♥❛♥❞♦ ♠❛✐s ❡✜❝✐❡♥t❡ ❛ ❝❤❡❣❛❞❛ ❡ s❛í❞❛ ❞♦ ❛❧✈♦✳ ❖ s❡❣✉♥❞♦ ❛❧❣♦r✐t♠♦ ❝♦♥s✐st❡ ❡♠ ❝♦♦r❞❡♥❛r ♦s r♦❜ôs ♣❛r❛ q✉❡ s✐❣❛♠ ✉♠❛ ✜❧❛ ❡♠ ❢♦r♠❛ ❞❡ ❡s♣✐r❛❧✱ ❝✉❥♦ ❝❡♥tr♦ é ♦♥❞❡ s❡ ❡♥❝♦♥tr❛ ♦ ❛❧✈♦✳ ❖ t❡r❝❡✐r♦ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ❝♦♥s✐st❡ ❡♠ r❡♣❡❧✐r ♦s ♦✉tr♦s r♦❜ôs q✉❛♥❞♦ ❛❧❣✉♠ r♦❜ô s❡ ❛♣r♦①✐♠❛ ❞♦ ❛❧✈♦ ❛tr❛✈és ❞❡ ♠❡♥s❛❣❡♥s ❡♠✐t✐❞❛s ♣❡❧♦s r♦❜ôs q✉❡ ❝❤❡❣❛♠ ♣ró①✐♠♦ ❛♦ ❛❧✈♦ ❡ s❛❡♠ ❞❡❧❡✳
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞❡st❡ ❞♦❝✉♠❡♥t♦
❈❛♣ít✉❧♦ ✷
❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
■♥t❡❧✐❣ê♥❝✐❛ ❞✐str✐❜✉í❞❛ s❡ r❡❢❡r❡ ❛ s✐st❡♠❛s ❞❡ ❡♥t✐❞❛❞❡s q✉❡ tr❛❜❛❧❤❛♠ ❥✉♥t♦s ♣❛r❛ ♣❧❛♥❡❥❛r✱ r❛❝✐♦❝✐♥❛r✱ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s✱ ♣❡♥s❛r ❛❜str❛t❛♠❡♥t❡✱ ❝♦♠♣r❡❡♥❞❡r ✐❞❡✐❛s ❡ ❧✐♥❣✉❛❣❡♠✱ ❡ ❛♣r❡♥❞❡r ❬P❛r❦❡r✱ ✷✵✵✽❪✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ✉♠❛ ❡♥t✐❞❛❞❡ é q✉❛❧q✉❡r t✐♣♦ ❞❡ ♣r♦❝❡ss♦ ✐♥t❡❧✐❣❡♥t❡✱ ❝♦♠♦ ❛❣❡♥t❡s ♦✉ r♦❜ôs✳ ❙❡❣✉♥❞♦ P❛r❦❡r ❬✷✵✵✽❪✱ ❛s ✐♥t❡r❛çõ❡s ❡♥tr❡ ❛s ❡♥t✐❞❛❞❡s ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞❛s ❡♠ três ❡✐①♦s✿
• ❝✐❡♥t❡ ♦✉ ♥ã♦ ❝✐❡♥t❡✿ s❡ ❝❛❞❛ ❡♥t✐❞❛❞❡ t❡♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❛s ❞❡♠❛✐s ❡♥✈♦❧✈✐❞❛s❀
• ♦❜❥❡t✐✈♦s ✐♥❞✐✈✐❞✉❛✐s ♦✉ ❝♦♠♣❛rt✐❧❤❛❞♦s✿ s❡ ❛s ❡♥t✐❞❛❞❡s ❞✐✈✐❞❡♠ ♦ ♠❡s♠♦ ♦❜❥❡✲ t✐✈♦ ♦✉ ❝❛❞❛ ✉♠❛ ♣♦ss✉✐ ✉♠ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦❀
• ✐♥✢✉ê♥❝✐❛ ❞❛s ❛çõ❡s ♥♦s ♦❜❥❡t✐✈♦s ❞❛s ♦✉tr❛s ❡♥t✐❞❛❞❡s✿ q✉❛♥❞♦ ✉♠❛ ❛çã♦ t♦♠❛❞❛ ♣♦r ✉♠❛ ❡♥t✐❞❛❞❡✱ ♣♦❞❡ ♦✉ ♥ã♦ ✐♥✢✉❡♥❝✐❛r ♦ ♦❜❥❡t✐✈♦ ❞❡ ♦✉tr❛ ❡♥t✐❞❛❞❡✳
❇❛s❡❛❞♦ ♥❡st❡s três ❡✐①♦s✱ q✉❛tr♦ t✐♣♦s ❞❡ ✐♥t❡r❛çã♦ ♣♦❞❡♠ s❡r ❞❡✜♥✐❞♦s✳ ❆ ✐♥t❡✲ r❛çã♦ é ❞♦ t✐♣♦ ❈♦❧❡t✐✈❛ q✉❛♥❞♦ ❛s ❡♥t✐❞❛❞❡s ♥ã♦ sã♦ ❝✐❡♥t❡s ❞❛s ❞❡♠❛✐s✱ ❝♦♠♣❛rt✐❧❤❛♠ ♦s ♠❡s♠♦s ♦❜❥❡t✐✈♦s ❡ s✉❛s ❛çõ❡s ✐♥✢✉❡♥❝✐❛♠ ❛s ❞❛s ❞❡♠❛✐s ❡♥t✐❞❛❞❡s✳ ❖ s❡❣✉♥❞♦ t✐♣♦ ❞❡ ✐♥t❡r❛çã♦ é ❛ ❈♦♦♣❡r❛t✐✈❛✱ ♥❛ q✉❛❧ ❛s ❡♥t✐❞❛❞❡s ❝♦♥❤❡❝❡♠ ❛s ❞❡♠❛✐s✱ ❝♦♠♣❛rt✐❧❤❛♠ ♦s ♠❡s♠♦ ♦❜❥❡t✐✈♦s ❡ s✉❛s ❛çõ❡s sã♦ ❜❡♥é✜❝❛s ♣❛r❛ ♦s ♦✉tr♦s✳ ❖ t❡r❝❡✐r♦ t✐♣♦ é ♦ ❈♦✲ ❧❛❜♦r❛t✐✈♦✱ q✉❡ ♦❝♦rr❡ q✉❛♥❞♦ ♦s ♦❜❥❡t✐✈♦s sã♦ ✐♥❞✐✈✐❞✉❛✐s✱ ❡❧❡s ♣♦ss✉❡♠ ❝♦♥❤❡❝✐♠❡♥t♦ ✉♠ ❞♦s ♦✉tr♦s ❡ s✉❛s ❛çõ❡s ✐♥✢✉❡♥❝✐❛♠ ♦s ❞❡♠❛✐s✳ P♦r ú❧t✐♠♦✱ ♦ ❈♦♦r❞❡♥❛t✐✈♦ é ❝❛✲ r❛❝t❡r✐③❛❞♦ ♣❡❧♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦s ❞❡♠❛✐s✱ ♦s ♦❜❥❡t✐✈♦s sã♦ ✐♥❞✐✈✐❞✉❛✐s✱ ♠❛s s✉❛s ❛çõ❡s ♥ã♦ ✐♥✢✉❡♥❝✐❛♠ ♦s ❞❡♠❛✐s✳
❈♦♥s✐❞❡r❛♥❞♦ ❡st❡s t✐♣♦s ❞❡ s✐st❡♠❛s ❞❡ ✐♥t❡❧✐❣ê♥❝✐❛ ❞✐str✐❜✉í❞❛ ❡ ❛ss✉♠✐♥❞♦ q✉❡ ❛s ❡♥t✐❞❛❞❡s sã♦ r♦❜ôs✱ s❡❣✉♥❞♦ P❛r❦❡r ❬✷✵✵✽❪✱ s✐st❡♠❛s ❞❡ r♦❜ôs ❝♦♦♣❡r❛t✐✈♦s sã♦ s✐st❡✲ ♠❛s ❞❡ ✐♥t❡❧✐❣ê♥❝✐❛ ❞✐str✐❜✉í❞❛✱ ❝♦♠ r♦❜ôs ❞✐s♣♦st♦s ♥♦ ♠❡s♠♦ ❛♠❜✐❡♥t❡ q✉❡ ❝♦♥❤❡❝❡♠ ♦s ❞❡♠❛✐s✱ ❝♦♠♣❛rt✐❧❤❛♠ ♦s ♠❡s♠♦s ♦❜❥❡t✐✈♦s ❡ s✉❛s ❛çõ❡s ✐♥✢✉❡♥❝✐❛♠ ♣♦s✐t✐✈❛♠❡♥t❡
✻ ❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá❢✐❝❛
❛s ❞♦s ♦✉tr♦s✳ ❊st❡s r♦❜ôs ♣♦❞❡♠ s❡r ✐❣✉❛✐s ♦✉ ❞✐❢❡r❡♥t❡s ❡♥tr❡ s✐✱ ❛ss✐♠ ❝♦♠♦ ♣♦✲ ❞❡♠ ❡st❛r ❡♠ ♣❡q✉❡♥❛ ♦✉ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡✳ ❙✐st❡♠❛s ❞❡ r♦❜ôs ❝♦♦♣❡r❛t✐✈♦s ♣♦ss✉❡♠ ❛♣❧✐❝❛çõ❡s ✐♥❞✉str✐❛✐s ❬❙✐♠♠♦♥s ❡t ❛❧✳✱ ✷✵✵✵❪✱ ♠✐❧✐t❛r❡s ❬P❛r❦❡r✱ ✷✵✵✸❪✱ ❡♠ ❡①♣❧♦r❛çã♦ ❡s♣❛❝✐❛❧ ❬●♦❧❞❜❡r❣ ❡t ❛❧✳✱ ✷✵✵✷❪ ❡ ♦♣❡r❛çõ❡s ❞❡ r❡s❣❛t❡ ❬▼✉r♣❤② ❡t ❛❧✳✱ ✷✵✵✷❪✱ ❡♥tr❡ ♦✉✲ tr❛s✳ ◗✉❛♥❞♦ ♦s r♦❜ôs sã♦ r❡❧❛t✐✈❛♠❡♥t❡ s✐♠♣❧❡s✱ ❡stã♦ ♥✉♠❛ q✉❛♥t✐❞❛❞❡ r❡❧❛t✐✈❛♠❡♥t❡ ❣r❛♥❞❡ ♥♦ ♠❡s♠♦ ❡s♣❛ç♦ ❡ ♣r❡❝✐s❛♠ ✐♥t❡r❛❣✐r ❡♥tr❡ s✐ ♣❛r❛ ❛❧❝❛♥ç❛r ✉♠ ♦❜❥❡t✐✈♦✱ ❞❡ ❢♦r♠❛ ❝♦❧❡t✐✈❛ ♦✉ ❝♦♦♣❡r❛t✐✈❛✱ ❡♥tã♦ ❡st❡ s✐st❡♠❛ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❡♥①❛♠❡ ❞❡ r♦❜ôs✳
❊♥①❛♠❡s ❞❡ r♦❜ôs é ✉♠❛ ár❡❛ r❡❧❛t✐✈❛♠❡♥t❡ ♥♦✈❛✳ ❊①✐st❡♠ ♣♦ssí✈❡✐s ❛♣❧✐❝❛çõ❡s✱ ♠❛s ❞❡✈✐❞♦ ❛♦ ❝❛rát❡r r❡❝❡♥t❡ ❞❡st❛ ár❡❛ ❞❡ ♣❡sq✉✐s❛✱ ❡❧❛s ❛✐♥❞❛ ♥ã♦ ❢♦r❛♠ ❡①❡❝✉t❛❞❛s ❡♠ s✐t✉❛çõ❡s r❡❛✐s✳ ❉❡♥tr❡ ❡❧❛s tê♠✲s❡✿ r❡s❣❛t❡ ❡♠ ❛♠❜✐❡♥t❡s ✉r❜❛♥♦s ❬▼♦♥❞❛❞❛ ❡t ❛❧✳✱ ✷✵✵✷❀ ❘❛❤♠❛♥✐✱ ✷✵✵✹❪ ❡ ♠✐♥❛s ❬❙♦♥❣❞♦♥❣ ✫ ❏✐❛♥❝❤❛♦✱ ✷✵✵✽❪✱ ❞❡t❡❝çã♦ ❞❡ ❣❛s❡s tó①✐❝♦s ❬❈✉✐ ❡t ❛❧✳✱ ✷✵✵✹❪✱ ❬❍❛②❡s✱ ✷✵✵✷❪ ❡ ❡①♣❧♦r❛çã♦ ❡s♣❛❝✐❛❧ ❬❚r✉s③❦♦✇s❦✐ ❡t ❛❧✳✱ ✷✵✵✹❪✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❚r✉s③❦♦✇s❦✐ ❡t ❛❧✳ ❞❡s❝r❡✈❡ ✉♠ s✐st❡♠❛ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ❛ s❡r ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡①♣❧♦r❛çã♦ ❞❡ ❛st❡ró✐❞❡s✱ ♣r❡✈✐st♦ ♣❛r❛ ❡♥tr❡ ✷✵✷✵ ❡ ✷✵✸✵✱ ✈✐st♦ q✉❡ r♦❜ôs ♠❛✐s ❧❡✈❡s ♣♦❞❡♠ s❡r ❛tr❛í❞♦s ♣❡❧♦ s❡✉ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧✳ ❊♠ ❣❡r❛❧✱ ♥❛ ♠❛✐♦r✐❛ ❞❡ss❛s t❛r❡❢❛s✱ é ♠❛✐s ✈❛♥t❛❥♦s♦ ♦ ✉s♦ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs ❛♦ ✐♥✈és ❞❡ ✉♠ r♦❜ô ✐♥❞✐✈✐❞✉❛❧ ❡s♣❡❝✐❛❧✐③❛❞♦ ❞❡✈✐❞♦ ❛ r❡q✉✐s✐t♦s ❝♦♠♦ ❝✉st♦✱ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦ ❡ r✐s❝♦ ❞❡ ❞❛♥♦✳
❆ ✐❞❡✐❛ ❞❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs s✉r❣✐✉ ❞❡ ✉♠❛ t❡♥t❛t✐✈❛ ❞❡ ♠♦❞❡❧❛r s✐st❡♠❛s r♦✲ ❜ót✐❝♦s ❝❡❧✉❧❛r❡s ❬❇❡♥✐ ✫ ❲❛♥❣✱ ✶✾✽✾❪✳ ◆❡st❡ ❝♦♥t❡①t♦ s✉r❣❡ ♦ t❡r♠♦ ■♥t❡❧✐❣ê♥❝✐❛ ❞❡ ❊♥①❛♠❡s ✭❙✇❛r♠ ■♥t❡❧❧✐❣❡♥❝❡✮ ❬❑❡♥♥❡❞② ❡t ❛❧✳✱ ✷✵✵✶❪✱ ✐♥✐❝✐❛♥❞♦ ♦s ❡st✉❞♦s ❞❡ s✐st❡✲ ♠❛s ❢♦r♠❛❞♦s ♣♦r ❛❣❡♥t❡s q✉❡ ♣r♦❝❡ss❛♠ ♦s ❞❛❞♦s ❞❡ ❢♦r♠❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ❛✉t♦✲ ♦r❣❛♥✐③❛❞❛✳ ❆ ✐♥s♣✐r❛çã♦ ❞❡st❛ ár❡❛ ❞❡ ♣❡sq✉✐s❛ s❡ ❞❡✈❡ ❛♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❞✐✈❡rs♦s s❡r❡s ✈✐✈♦s✱ ❞❡s❞❡ ❣r✉♣♦s ❞❡ ❝é❧✉❧❛s ❛ ✐♥s❡t♦s✳ ◆❡st❡ s✐st❡♠❛s ❜✐♦❧ó❣✐❝♦s✱ ❝❛❞❛ ✐♥❞✐✲ ✈í❞✉♦ ♣r♦❝❡ss❛ ✐♥❢♦r♠❛çõ❡s ❞❡ ❢♦r♠❛ ❞❡s❝❡♥tr❛❧✐③❛❞❛ ❡ ♣♦r ❝♦♠✉♥✐❝❛çã♦ ❧♦❝❛❧✳ ◆ã♦ ❡①✐st❡ ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❬❈❛♠❛③✐♥❡ ❡t ❛❧✳✱ ✷✵✵✶❪✱ ♠❛s ❡st❡s s✐s✲ t❡♠❛s ❝♦♥s❡❣✉❡♠ s❡r ❛✉t♦✲♦r❣❛♥✐③❛❞♦s✱ ❡①❡❝✉t❛♥❞♦ t❛r❡❢❛s ♣❛r❛ s✉❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡ ❢♦r♠❛ ❝♦♦r❞❡♥❛❞❛✳
◆❡st❡ ❝♦♥t❡①t♦✱ ♣♦❞❡✲s❡ ❞✐③❡r q✉❡ ❡♥①❛♠❡s ❞❡ r♦❜ôs sã♦ s✐st❡♠❛s q✉❡ ♣♦ss✉❡♠ ■♥✲ t❡❧✐❣ê♥❝✐❛ ❉✐str✐❜✉í❞❛✱ ♦✉ s❡❥❛✱ sã♦ ❝♦♠♣♦st♦s ♣♦r ❡♥t✐❞❛❞❡s q✉❡ tr❛❜❛❧❤❛♠ ❥✉♥t♦s ♣❛r❛ ♣❧❛♥❡❥❛r✱ r❛❝✐♦❝✐♥❛r✱ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s✱ ♣❡♥s❛r ❛❜str❛t❛♠❡♥t❡✱ ❝♦♠♣r❡❡♥❞❡r ✐❞❡✐❛s ❡ ❧✐♥❣✉❛❣❡♠✱ ❡ ❛♣r❡♥❞❡r ❬P❛r❦❡r✱ ✷✵✵✽❪✳
❊①✐st❡♠ ✈ár✐❛s t❛r❡❢❛s ❝♦♠✉♠❡♥t❡ r❡❛❧✐③❛❞❛s ♣♦r ❡♥①❛♠❡s✳ ◆❛ ❧✐t❡r❛t✉r❛ ❞❡st❛ ár❡❛✱ ❡st❛s t❛r❡❢❛s ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞❛s ♥♦s s❡❣✉✐♥t❡s ❣r✉♣♦s ❬❙❛❤✐♥ ❡t ❛❧✳✱ ✷✵✵✽❪ ❬❈❛♦ ❡t ❛❧✳✱ ✶✾✾✼❪✿
✼
✉♠❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦❀
• ❉✐s♣❡rsã♦✿ ♦s r♦❜ôs✱ ✐♥✐❝✐❛❧♠❡♥t❡ r❡✉♥✐❞♦s ♥✉♠❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦✱ ❞❡✈❡♠ s❡ ❛❢❛st❛r ♦ ♠á①✐♠♦ ♣♦ssí✈❡❧ ✉♠ ❞♦ ♦✉tr♦❀
• ❈♦❧❡t❛ ✭❞♦ ✐♥❣❧ês ❋♦r❛❣✐♥❣✮✿ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❝❛❞❛ ✉♠ ❞❡❧❡s é ❝♦❧❡t❛r ♦❜❥❡t♦s ❡s♣❡✲ ❝í✜❝♦s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ♥♦ ❛♠❜✐❡♥t❡ ❞❡ ❢♦r♠❛ ❝♦♦r❞❡♥❛❞❛ ❡ ❧❡✈❛r ❞❡ ✈♦❧t❛ ♣❛r❛ ✉♠❛ ár❡❛❀
• ❆✉t♦♠♦♥t❛❣❡♠✿ ❡❧❡s ❞❡✈❡♠ s❡ ❝♦♦r❞❡♥❛r ♣❛r❛ s❡ ❡♥❝❛✐①❛r ✉♥s ♥♦s ♦✉tr♦s✱ t♦r✲ ♥❛♥❞♦ ❣r✉♣♦s ❞❡ r♦❜ôs ❝♦♥❡❝t❛❞♦s ✜s✐❝❛♠❡♥t❡❀
• ▼♦✈✐♠❡♥t♦ ❈♦♥❡❝t❛❞♦✿ q✉❛♥❞♦ ♦s r♦❜ôs ❡stã♦ ❝♦♥❡❝t❛❞♦s ✜s✐❝❛♠❡♥t❡✱ é ♥❡❝❡ssá✲ r✐♦ q✉❡ ♦ ❣r✉♣♦ ❡st❡❥❛ ❝♦♦r❞❡♥❛❞♦ ♣❛r❛ s❡ ♠♦✈❡r ❝♦♠♦ ✉♠ t♦❞♦❀
• ❈♦♥tr♦❧❡ ❞❡ ❚rá❢❡❣♦✿ ❛ ❝♦♦r❞❡♥❛çã♦ t❡♠ ♦ ✐♥t✉✐t♦ ❞❡ ❡st❛❜❡❧❡❝❡r ✉♠ ♣❛❞rã♦ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ♥ã♦ ❤❛❥❛ ♣r♦❜❧❡♠❛s ❞❡ trá❢❡❣♦✱ ✐st♦ é✱ ✉♠ r♦❜ô ♥ã♦ ❛tr❛♣❛❧❤❛ ♥❛ ♥❛✈❡❣❛çã♦ ❞❡ ♦✉tr♦❀
• ❚r❛♥s♣♦rt❡ ❈♦♦r❞❡♥❛❞♦✿ ♦❜❥❡t♦s ♠❛✐♦r❡s ❞❡✈❡♠ s❡r tr❛♥s♣♦rt❛❞♦s ♣♦r ✈ár✐♦s r♦❜ôs ✉s❛♥❞♦ ❝♦♦r❞❡♥❛çã♦❀
• ❋♦r♠❛çã♦ ❞❡ ♣❛❞rõ❡s✿ ♦s r♦❜ôs ❞❡✈❡♠ ❢♦r♠❛r ♣❛❞rõ❡s ❣❡♦♠étr✐❝♦s ❡♥tr❡ ❡❧❡s ❝♦♠♦ ❢♦r♠❛çã♦ ❡♠ ❝♦rr❡♥t❡✱ ❢♦r♠❛çã♦ ❡♠ ❜❛♥❞♦ ♦✉ s❡ ♠♦✈✐♠❡♥t❛r ❡♠ ❢♦r♠❛ ❞❡ ✜❣✉r❛s ❣❡♦♠étr✐❝❛s❀
• ❈♦♥str✉çã♦ ❛✉t♦✲♦r❣❛♥✐③❛❞❛✿ ♦s r♦❜ôs ❞❡✈❡♠ ❧❡✈❛r ♦❜❥❡t♦s ❡s♣❛❧❤❛❞♦s ♥♦ ❛♠❜✐✲ ❡♥t❡ ❛ ❧✉❣❛r❡s ❝♦♠✉♥s✱ ❝♦♠ ✐♥t✉✐t♦ ❞❡ ♠♦♥t❛r ❛❧❣✉♠❛ ❡str✉t✉r❛✳
✽ ❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá❢✐❝❛
♦ ♣r♦❜❧❡♠❛ ❡s♣❡❝í✜❝♦ ♦♥❞❡ t♦❞♦s ❞❡s❡❥❛♠ ❝❤❡❣❛r ♥♦ ♠❡s♠♦ ♣♦♥t♦ ❬❑❛t♦ ❡t ❛❧✳✱ ✶✾✾✷❀ ❲❛♥❣✱ ✶✾✾✶❪✳
❊①✐st❡♠ tr❛❜❛❧❤♦s r❡❝❡♥t❡s q✉❡ ❧✐❞❛♠ ❝♦♠ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ ❡♠ ❣r✉♣♦s ❞❡ r♦❜ôs✳ ❊♠ ❖❧♠✐ ❡t ❛❧✳ ❬✷✵✵✾❪✱ ✉♠ ❛❧❣♦r✐t♠♦ ♣❛r❛ ❝♦♦r❞❡♥❛r ❝❛♠✐♥❤♦s ♣r❡❞❡✜♥✐❞♦s ❞❡ ✉♠ ❣r✉♣♦ ❞❡ r♦❜ôs é ❞❡s❡♥✈♦❧✈✐❞♦✱ ♠❛s ❡♠ s✉❛ ❛❜♦r❞❛❣❡♠ ❡①✐st❡ ✉♠❛ ✉♥✐❞❛❞❡ ❝❡♥tr❛❧ ❞❡ ♣r♦✲ ❝❡ss❛♠❡♥t♦ ❞❡✜♥✐♥❞♦ ❛ ❛❧t❡r❛çã♦ ❞❛s r♦t❛s ❞❡ ❝❛❞❛ r♦❜ô ❡♠ ❝❛s♦ ❞❡ ♣♦ssí✈❡❧ ❝♦❧✐sã♦✳ ❊♠ ●✉♦ ✫ P❛r❦❡r ❬✷✵✵✷❪✱ ✉♠ ❛❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦ é ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ♠♦✈✐♠❡♥t♦ ♣❛r❛ ♠ú❧t✐♣❧♦s r♦❜ôs✱ ❝♦♥t✉❞♦ s❡✉s ❡①♣❡r✐♠❡♥t♦s ♥ã♦ ❡♥✈♦❧✈❡♠ ♠✉✐t♦s r♦❜ôs✳ ❖ tr❛❜❛❧❤♦ ❞❡ P❡❛s❣♦♦❞ ❡t ❛❧✳ ❬✷✵✵✽❪ tr❛t❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦❧✐sã♦ ❞❡ tr❛❥❡tór✐❛s ♣❛r❛ ✈ár✐♦s r♦❜ôs✱ ♠❛s ♥✉♠ ❝♦♥t❡①t♦ ♦♥❞❡ ♦s ❛❧✈♦s ❞❡ ❝❛❞❛ ✉♠ ♣♦❞❡♠ s❡r ❞✐❢❡r❡♥t❡s✳ ❊♠ ❬❍♦s❤✐♥♦✱ ✷✵✶✶❪✱ é tr❛t❛❞♦ ♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ♥❛ ❢♦r♠❛ ❞❡ ❡♥❣❛rr❛❢❛♠❡♥t♦ ❞❡ ✈✐❛s✱ ♦✉ s❡❥❛✱ ❡♠ ✈✐❛s ♥❛s q✉❛✐s ♦s r♦❜ôs ♥ã♦ ♣♦❞❡♠ ✉❧tr❛♣❛ss❛r ✉♥s ❛♦s ♦✉tr♦s ❝r✐❛♥❞♦ ❛❣r✉♣❛♠❡♥t♦s ❞❡s♦r❞❡♥❛❞♦s ♥✉♠❛ r❡❣✐ã♦ ❞♦ ❡s♣❛ç♦✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❑r♦♥t✐r✐s ✫ ❇❡❦r✐s ❬✷✵✶✶❪ tr❛t❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ r❡s♦❧✉çã♦ ❞❡ ❝❤♦q✉❡s ❡♥tr❡ r♦❜ôs ❞❡ ♠♦❞♦ ❞❡s❝❡♥tr❛❧✐③❛❞♦✱ ✉s❛♥❞♦ ✉♠❛ ❡①t❡♥sã♦ ❞❡ ✉♠❛ ♣♦❧ít✐❝❛ ❞❡ ♣r❡✈❡♥çã♦ ❞❡ ♦❜stá❝✉❧♦s ❞❡♥♦♠✐♥❛❞❛ ●❡♥❡✲ r❛❧✐③❡❞ ❘♦✉♥❞❛❜♦✉t P♦❧✐❝② ❬P❛❧❧♦tt✐♥♦ ❡t ❛❧✳✱ ✷✵✵✼❪✳ ❆♣❡s❛r ❞❡ s❡r ✉♠ tr❛❜❛❧❤♦ q✉❡ ❧✐❞❛ ❝♦♠ ♦ ♣r♦❜❧❡♠❛ ❞❡ r❡s♦❧✉çã♦ ❞❡ ❝♦♥✢✐t♦s ❞❡ ♠♦❞♦ ❞❡s❝❡♥tr❛❧✐③❛❞♦ ❡ ✉s❛♥❞♦ ♣♦✉❝❛s tr♦❝❛s ❞❡ ♠❡♥s❛❣❡♥s✱ ♦s r♦❜ôs ♥ã♦ ♣♦ss✉❡♠ ✉♠ ❛❧✈♦ ❡♠ ❝♦♠✉♠✳
❈❛♣ít✉❧♦ ✸
❆❧❣♦r✐t♠♦s Pr♦♣♦st♦s
❖ ♣r♦❜❧❡♠❛ ❞♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ♥♦ ❛❝❡ss♦ à ❛❧✈♦ ❝♦♠✉♠ ♦❝♦rr❡ q✉❛♥❞♦ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ r♦❜ôs ❞❡✈❡ ❛❝❡ss❛r ♦ ♠❡s♠♦ ❛❧✈♦ ♦✉ ❛ ♠❡s♠❛ r❡❣✐ã♦ ❞❡ ❡s♣❛ç♦ ✭❋✐✲ ❣✉r❛ ✸✳✶✮✳ ❖ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ ♣❛r❛ ❡st❡ ♣r♦❜❧❡♠❛ ❝♦♥s✐st❡ ❡♠ ❡st❛❜❡❧❡❝❡r r❡❣r❛s ♦✉ ❝♦♠♣♦rt❛♠❡♥t♦s ♣❛r❛ ♦s r♦❜ôs ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ♠✐♥✐♠✐③❡ ♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ♣ró①✐♠♦ ❛♦ ❛❧✈♦✳ ❘❡❞✉③✐♥❞♦ ♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦✱ ❡s♣❡r❛✲s❡ ❞✐♠✐♥✉✐r ♦ t❡♠♣♦ ❞❡ ❝❤❡❣❛❞❛ ❡ s❛í❞❛ ♥♦ ❛❧✈♦ ❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝❤♦q✉❡s ❡♥tr❡ ❡st❡s r♦❜ôs✳
Alvo Comum
❋✐❣✉r❛ ✸✳✶✳ Pr♦❜❧❡♠❛ ❞♦ ❛❧✈♦ ❡♠ ❝♦♠✉♠✳
P❛r❛ s♦❧✉❝✐♦♥❛r ♦ ♣r♦❜❧❡♠❛ ❞♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ♣❛r❛ ❝♦♥tr♦❧❡ ❞❡ trá❢❡❣♦ ❡♠ ❡♥①❛♠❡s ❞❡ r♦❜ôs ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s três ❛❧❣♦r✐t♠♦s ❞✐st✐♥t♦s✳ ❖ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦ ❞❡s❡♥✈♦❧✈✐❞♦ ❝♦♥s✐st❡ ❡♠ ❞✐✈✐❞✐r ❛ ár❡❛ ♣ró①✐♠❛ ❛♦ ❛❧✈♦ ❡♠ r❡❣✐õ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛✳ ❖ s❡❣✉♥❞♦ ❛❧❣♦r✐t♠♦ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ❢♦r♠❛r ✉♠❛ ✜❧❛ ❡♠ ❢♦r♠❛ ❞❡ ❡s♣✐r❛❧ ❡♠ t♦r♥♦ ❞♦ ❛❧✈♦✳ ❖ t❡r❝❡✐r♦ ❛❧❣♦r✐t♠♦ ✈✐s❛ s✐♠✉❧❛r ♦ ❡❢❡✐t♦ ❞❛s s✐r❡♥❡s ✉s❛❞❛s ♥♦ trâ♥s✐t♦ ♣♦r ❛♠❜✉❧â♥❝✐❛s ❡ ✈✐❛t✉r❛s ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ❡①♣✉❧s❛r ♦s r♦❜ôs q✉❡ ❡stã♦ ♥♦ ❝❛♠✐♥❤♦ ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛ ❞♦ ❛❧✈♦✳
❚♦❞♦s ♦s três ❛❧❣♦r✐t♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s ✉t✐❧✐③❛♠ ❝❛♠♣♦s ♣♦t❡♥❝✐❛✐s ❛rt✐✜❝✐❛s ❬▲❛✲
✶✵ ❈❛♣ít✉❧♦ ✸✳ ❆❧❣♦r✐t♠♦s Pr♦♣♦st♦s
t♦♠❜❡✱ ✶✾✾✶❪ ♣❛r❛ ♥❛✈❡❣❛çã♦ ❞♦s r♦❜ôs✳ ❙❡✉ ✉s♦ ❢♦✐ ♠♦t✐✈❛❞♦ ❞❡✈✐❞♦ à s✉❛ ❢❛❝✐❧✐❞❛❞❡ ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ♣❛r❛ r♦❜ôs q✉❡ ✉t✐❧✐③❛♠ s♦♠❡♥t❡ ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s ♣❛r❛ ❧♦❝♦♠♦çã♦ ❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✳ ❊st❛s ✐♥❢♦r♠❛çõ❡s ❧♦❝❛✐s sã♦ ♦❜t✐❞❛s ♣♦r s❡♥s♦r❡s ❞❡ ❛❧❝❛♥❝❡ ❧♦❝❛❧ ❡ ❧✐♠✐t❛❞♦✳ P❛r❛ ♦s ❛❧❣♦r✐t♠♦s ♣r♦♣♦st♦s✱ s✉♣õ❡✲s❡ q✉❡ ♦ s❡♥s♦r ✉t✐❧✐③❛❞♦ ♥ã♦ ♣♦ss✉✐ ❢❛❧❤❛s✳ ❚✐♣✐❝❛♠❡♥t❡✱ ♣❛r❛ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❝❛♠✐♥❤♦s ✉s❛♥❞♦ ❝❛♠♣♦s ♣♦t❡♥❝✐❛✐s sã♦ ✉t✐❧✐③❛❞♦s ❞♦✐s t✐♣♦s ❞❡ ❝❛♠♣♦✿ ✉♠ ❝❛♠♣♦ r❡♣✉❧s✐✈♦✱ q✉❡ ♦ r❡♣❡❧❡ ❞❡ ♦✉tr♦s r♦❜ôs ❡ ✉♠ ❝❛♠♣♦ ❛tr❛t✐✈♦✱ q✉❡ ❣❡r❛ ✉♠❛ ❢♦rç❛ q✉❡ ❛tr❛✐ ♦ r♦❜ô ❛♦ ❛❧✈♦✳
❖s r♦❜ôs ✉t✐❧✐③❛♠ ✉♠ ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ r❡♣✉❧s✐✈♦ ♣❛r❛ ❡✈✐t❛r s❡ ❝❤♦❝❛r❡♠ ❝♦♠ s❡✉s ✈✐③✐♥❤♦s✳ ❊st❡ ❝❛♠♣♦ ❡stá s❡♠♣r❡ ♣r❡s❡♥t❡✱ ♥ã♦ ✐♠♣♦rt❛ q✉❛❧ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♦r❞❡♥❛çã♦ ❡stá s❡♥❞♦ ✉t✐❧✐③❛❞♦✳ ❆s ❢♦rç❛s r❡s✉❧t❛♥t❡s ❞❡st❡ ❝❛♠♣♦ sã♦ ❣❡r❛❞❛s ❧♦❝❛❧♠❡♥t❡ ❛ ♣❛rt✐r ❞♦s s❡♥s♦r❡s ❞♦ r♦❜ô✱ s❡♠ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ ♣r✐♦r✐ s♦❜r❡ ♦ ❛♠❜✐❡♥t❡ ❡ ❛ q✉❛♥t✐❞❛❞❡ t♦t❛❧ ❞❡ r♦❜ôs ♣r❡s❡♥t❡s✳ P❛r❛ ❣❡r❛r ❢♦rç❛s r❡♣✉❧s✐✈❛s é ✉s❛❞❛ ❛ s❡❣✉✐♥t❡ ❢✉♥çã♦ ❬❙✐❡❣✇❛rt ✫ ◆♦✉r❜❛❦❤s❤✱ ✷✵✵✹❪✿
FR =
−K∗
1
d −
1
I
o−q d3
s❡ d < I
0 ❝❛s♦ ❝♦♥trár✐♦
♦♥❞❡ q = [x, y]T é ❛ ♣♦s✐çã♦ ❛t✉❛❧ ❞♦ r♦❜ô✱ o = [x
o, yo]T✱ ❛ ♣♦s✐çã♦ ❞❡ ♦✉tr♦ r♦❜ô✱
d=ko−qk✱ ❛ ❞✐stâ♥❝✐❛ ❊✉❝❧✐❞✐❛♥❛ ❡♥tr❡ o ❡ q❡ I ❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ♦✉tr♦ r♦❜ô✱ ✐st♦ é✱ ❛ ❞✐stâ♥❝✐❛ ♠á①✐♠❛ ♣❛r❛ s❡ ❝♦♥s✐❞❡r❛r ❛❧❣♦ ❝♦♠♦ ♦❜stá❝✉❧♦✳
❉❡ ✉♠ ♠♦❞♦ ❣❡r❛❧✱ ♦s ❛❧❣♦r✐t♠♦s ♣r♦♣♦st♦s ✈✐s❛♠ ❛❧t❡r❛r ❛s ❢♦rç❛s ❞♦ ❝❛♠♣♦ ♣♦t❡♥❝✐❛❧ ❛tr❛t✐✈♦ ❛ ❞❡♣❡♥❞❡r ❞❛s ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s ❧♦❝❛❧♠❡♥t❡ ♣❡❧♦s r♦❜ôs✳ ❆ ♣❛rt✐r ❞❡st❛s ✐♥❢♦r♠❛çõ❡s✱ ♦s r♦❜ôs ♣♦❞❡♠✿ ✭✐✮ ❡s❝♦❧❤❡r ✉♠ ♥♦✈♦ ❛❧✈♦✱ ❞❡ ❝❛rát❡r t❡♠♣♦rár✐♦✱ tr❛t❛❞♦ ❝♦♠♦ ✉♠❛ s✉❜t❛r❡❢❛ ❛♥t❡s ❞❡ ❛❧❝❛♥ç❛r ♦ ❛❧✈♦ ♣r✐♥❝✐♣❛❧✱ ♦✉ ✭✐✐✮ s❡❣✉✐r ✉♠ s❡♥t✐❞♦ ❞✐❢❡r❡♥t❡ ❞♦ s❡♥t✐❞♦ q✉❡ ✈❛✐ ❞❡ ❡♥❝♦♥tr♦ ❛♦ ❛❧✈♦ ♣r✐♥❝✐♣❛❧✱ ✈✐s❛♥❞♦ ❡✈✐t❛r r❡❣✐õ❡s ♠✉✐t♦ ❝♦♥❣❡st✐♦♥❛❞❛s ♦✉ ❛❜r✐r ❡s♣❛ç♦ ♣❛r❛ ♦✉tr♦s r♦❜ôs✳
✶✶
♣❡❧❛ ❛t✉❛çã♦ ❞♦ r♦❜ô✳
F
Controlador
Algoritmo
proposto
Mensagens
Mensagens
Dados dos
sensores
❋✐❣✉r❛ ✸✳✷✳ ❊sq✉❡♠❛ ❣❡r❛❧ ❞♦s ❛❧❣♦r✐t♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s✳
❈❛s♦ ♦ ❛❧❣♦r✐t♠♦ ❡♥✈♦❧✈❛ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s✱ ♠❡♥s❛❣❡♥s sã♦ ❡♥✈✐❛❞❛s ❡ r❡❝❡❜✐❞❛s ♣❡❧♦s r♦❜ôs✳ ❈♦♥s✐❞❡r❛✲s❡ q✉❡ ❛s ♠❡♥s❛❣❡♥s ❡♥tr❡ r♦❜ôs ♣♦ss✉❡♠ ✉♠ r❛✐♦ ❞❡ ❛❧❝❛♥❝❡ ✐❣✉❛❧ ❛♦ ✈❛❧♦r ❞❡ I✳ ❆ss✐♠✱ ♠❡♥s❛❣❡♥s só s❡rã♦ ❡♥✈✐❛❞❛s q✉❛♥❞♦ ✉♠ r♦❜ô ♣❡r❝❡❜❡r ♦✉tr♦ ❡♠ s✉❛ ár❡❛ ❞❡ ✐♥✢✉ê♥❝✐❛✳ P❛r❛ ♦s ❛❧❣♦r✐t♠♦s ♣r♦♣♦st♦s✱ s✉♣õ❡✲s❡ q✉❡ ❛♣❡♥❛s r♦❜ôs sã♦ ♣❡r❝❡❜✐❞♦s ♣❡❧♦s s❡♥s♦r❡s✳ ❊st❛ ❝♦♥❞✐çã♦ ♣♦❞❡ s❡r r❡❧❛①❛❞❛ ❝♦♠ ♦ ✉s♦ ❞❡ ❛❧❣✉♠ ♣r♦t♦❝♦❧♦ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s q✉❡ ♣❡r♠✐t❛ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❡♥tr❡ r♦❜ôs✳
❈♦♥s✐❞❡r❛♥❞♦ ✉♠ r♦❜ô ❝♦♠♣❧❡t❛♠❡♥t❡ ❛t✉❛❞♦✱ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ✉t✐❧✐③❛❞♦ é ❞❛❞♦ ♣♦r✿
u =F−Cv,
˙
q=v,
˙
v=u.
♦♥❞❡✿ u é ❛ ❡♥tr❛❞❛ ❞❡ ❝♦♥tr♦❧❡✱ v ❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ r♦❜ô ❡ ♦ t❡r♠♦ Cv é ✉♠ ❢❛t♦r ❞❡ ❛♠♦rt❡❝✐♠❡♥t♦✳
❱✐st♦ q✉❡ ♦s ❛❧❣♦r✐t♠♦s ♣r♦♣♦st♦s ❢♦r❛♠ ♣r♦❥❡t❛❞♦s ♣❛r❛ ❡♥①❛♠❡s ❞❡ r♦❜ôs✱ ♦s r♦❜ôs ♥ã♦ ♣♦ss✉❡♠ ✐♥❢♦r♠❛çã♦ ❛ ♣r✐♦r✐ ❞❡ q✉❛♥t♦s r♦❜ôs ❡①✐st❡♠ ♥♦ ❛♠❜✐❡♥t❡✳ ❆ss✐♠✱ ♦s ❛❧❣♦r✐t♠♦s ♣r♦♣♦st♦s só ❡♥tr❛♠ ❡♠ ❢✉♥❝✐♦♥❛♠❡♥t♦ q✉❛♥❞♦ ♦ r♦❜ô ❛❧❝❛♥ç❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♠í♥✐♠❛ ❞❡ D ♠❡tr♦s ❞♦ ❛❧✈♦✳
✶✷ ❈❛♣ít✉❧♦ ✸✳ ❆❧❣♦r✐t♠♦s Pr♦♣♦st♦s
NORMAL
PRESO ESPERANDO
IMPACIENTE ρ
1-ρ
❋✐❣✉r❛ ✸✳✸✳ ▼áq✉✐♥❛ ❞❡ ❡st❛❞♦s ❞♦ ❛❧❣♦r✐t♠♦✳
♣❡❧♦ ❞✐s♣♦s✐t✐✈♦✳ ❊st❡ ❝❛♣ít✉❧♦ ❡stá ♦r❣❛♥✐③❛❞♦ ❝♦♠♦ s❡❣✉❡✿ ❛ ❙❡çã♦ ✸✳✶ ❡①♣❧✐❝❛ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ❛❧❣♦r✐t♠♦ q✉❡ ✉s❛ r❡❣✐õ❡s ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛✱ ❛ ❙❡çã♦ ✸✳✷ ❡①♣❧✐❝❛ ♦ ❛❧❣♦r✐t♠♦ q✉❡ ❝r✐❛ ✉♠❛ ✜❧❛ ❡♠ ❡s♣✐r❛❧ ❡ ❛ ❙❡çã♦ ✸✳✸✱ ♦ ❛❧❣♦r✐t♠♦ q✉❡ s✐♠✉❧❛ s✐r❡♥❡s✳
✸✳✶ ❆❧❣♦r✐t♠♦ ✶✿ ❘❡❣✐ã♦ ❞❡ ❡♥tr❛❞❛ ❡ s❛í❞❛
❆ ✐❞é✐❛ ♣r✐♥❝✐♣❛❧ ❞❡st❡ ❛❧❣♦r✐t♠♦ é ❡✈✐t❛r q✉❡ ♠✉✐t♦s r♦❜ôs ❝❤❡❣✉❡♠ s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❛♦ ♠❡s♠♦ ❛❧✈♦✳ ❚r❛t❛✲s❡ ❞❡ ✉♠❛ ❡①t❡♥sã♦ ❞♦ tr❛❜❛❧❤♦ ♣r♦♣♦st♦ ♣♦r ▼❛r❝♦❧✐♥♦ ✫ ❈❤❛✐♠♦✇✐❝③ ❬✷✵✵✾❪✱ ♦♥❞❡ é ❞❡s❝r✐t♦ ✉♠ ❛❧❣♦r✐t♠♦ q✉❡ ❝♦♥s✐st❡ ❡♠ ❝❛❞❛ r♦❜ô ✉s❛r ✉♠❛ ♠áq✉✐♥❛ ❞❡ ❡st❛❞♦s ♣r♦❜❛❜✐❧íst✐❝❛ ♣❛r❛ s❡ ❝♦♦r❞❡♥❛r ❞❡♥tr♦ ❞❡ ✉♠❛ r❡❣✐ã♦ ❡♠ ✈♦❧t❛ ❞♦ ❛❧✈♦✳ ❖ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ❝♦♥s✐st❡ ❡♠ ❡st❡♥❞❡r ❡st❡ ✐♥❝❧✉✐♥❞♦ ✉♠ ❝♦♥tr♦❧❡ ❞❡ r❡❣✐õ❡s ❞❡ ❛❝❡ss♦✱ t♦r♥❛♥❞♦ ♠❛✐s ❡✜❝✐❡♥t❡ ❛ ❝❤❡❣❛❞❛ ❡ s❛í❞❛ ❞♦ ❛❧✈♦✳ ❖ ❛❧❣♦r✐t♠♦ é ❡①❡❝✉t❛❞♦ ❞❡ ❢♦r♠❛ ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐str✐❜✉í❞❛ ❡ ♦s r♦❜ôs ✉t✐❧✐③❛♠ ❛♣❡♥❛s ❝♦♠✉♥✐❝❛çã♦ ❡ ♣❡r❝❡♣çã♦ ❧♦❝❛✐s✳
✸✳✶✳✶ ❆❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦ ♣❛r❛ ❝♦♥tr♦❧❡ ❞❡ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦
❆ ✐❞é✐❛ ♣r✐♥❝✐♣❛❧ ❞♦ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ ♣♦r ▼❛r❝♦❧✐♥♦ ✫ ❈❤❛✐♠♦✇✐❝③ ❬✷✵✵✾❪ é ❢❛③❡r ❝♦♠ q✉❡ ♦s r♦❜ôs ❡s♣❡r❡♠ s✉❛ ✈❡③ ♣❛r❛ ❛❧❝❛♥ç❛r ♦ ❛❧✈♦✱ s❡ ♣♦s✐❝✐♦♥❛♥❞♦ ♥✉♠❛ r❡❣✐ã♦ ♣ró①✐♠❛ ❛ ❡❧❡✱ ❞❡ ❢♦r♠❛ ❛ ❞✐♠✐♥✉✐r ❛ ❝❤❛♥❝❡ ❞❡ ✉♠ r♦❜ô ❛tr❛♣❛❧❤❛r ♦ ♦✉tr♦✳
