❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ◗✉í♠✐❝❛
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦
❡♠ ❊♥❣❡♥❤❛r✐❛ ◗✉í♠✐❝❛
●❡r❛çã♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♠♦♥♦❞✐s♣❡rs❛s ❡♠
❝♦rr❡♥t❡s ❣❛s♦s❛s
▼❛✉r✐❡❧❡♠ ●✉t❡rr❡s ❉❛❧❝✐♥
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ◗✉í♠✐❝❛
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦
❡♠ ❊♥❣❡♥❤❛r✐❛ ◗✉í♠✐❝❛
●❡r❛çã♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♠♦♥♦❞✐s♣❡rs❛s ❡♠
❝♦rr❡♥t❡s ❣❛s♦s❛s
▼❛✉r✐❡❧❡♠ ●✉t❡rr❡s ❉❛❧❝✐♥
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ◗✉í♠✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♥❡❝❡ssár✐♦s à ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❊♥❣❡♥❤❛r✐❛ ◗✉í♠✐❝❛✱ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ Pr♦❝❡ss♦s ◗✉í♠✐❝♦s✳
Dados Internacionais de Catalogação na Publicação (CIP) Sistema de Bibliotecas da UFU, MG - Brasil
G983g 2013
Guterres Dalcin, Maurielem, 1983-
Geração de nanopartículas monodispersas em correntes gasosas / Maurielem Guterres Dalcin. - 2013.
128 f. : il.
Orientador: João Jorge Ribeiro Damasceno. Coorientador: Fábio de Oliveira Arouca.
Tese (doutorado) – Universidade Federal de Uberlândia, Pro- grama de Pós-Graduação em Engenharia Química.
Inclui bibliografia.
1. Engenharia química - Teses. 2. Nanopartículas - Teses. 3. Aerossóis - Teses. I. Damasceno, João Jorge Ribeiro. II. Arou- ca, Fábio de Oliveira, 1977- III. Universidade Federal de Uber- lândia. Programa de Pós-Graduação em Engenharia Química. IV. Título.
CDU: 66.0
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
Pr✐♠❡✐r❛♠❡♥t❡ ❛❣r❛❞❡ç♦ ❛ ❉❡✉s ♣♦r t✉❞♦✱ ❡❧❡ ♠❛✐s ❞♦ q✉❡ ♥✐♥❣✉é♠ é ♦ ❣r❛♥❞❡ ❡♥❣❡♥❤❡✐r♦ ❞❡ ♥♦ss❛s ✈✐❞❛s✳ ❆✐♥❞❛ q✉❡ ❝♦✐s❛s ✐♥❡s♣❡r❛❞❛s ❛❝♦♥t❡ç❛♠✱ ♥❛❞❛ é ♣♦r ❛❝❛s♦✱ ❊❧❡ s❡♠♣r❡ s❛❜❡ ♦ ♣♦rq✉ê✳ ➱ ♣r❡❝✐s♦ ❡♥t❡♥❞✐♠❡♥t♦ ♣❛r❛ ♣❡r❝❡❜❡r ❛ ♣❡r❢❡✐çã♦ ❞❛ ✈♦♥t❛❞❡ s✉♣❡r✐♦r✳ ●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛ ♠❡✉s ♣❛✐s ▼❛✉r✐ ❡ ◆❡í q✉❡✱ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ q✉❛❧q✉❡r ❝♦✐s❛✱ s❡♠♣r❡ ❛❝r❡❞✐t❛r❛♠ ❡♠ ♠✐♠ ❡ ❡st✐✈❡r❛♠ ❛♦ ♠❡✉ ❧❛❞♦✱ ♠❡s♠♦ q✉❛♥❞♦ ♦s ✈❡♥t♦s ❡r❛♠ ❝♦♥trár✐♦s✳
❆♦s ♣r♦❢❡ss♦r❡s ❋á❜✐♦ ❡ ❉❛♠❛s❝❡♥♦ ❛❣r❛❞❡ç♦ ♣❡❧❛ ❝♦♥✜❛♥ç❛✱ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s✱ ♣❡❧♦s ❝♦♥s❡❧❤♦s ❜❛st❛♥t❡ ✈❛❧✐♦s♦s ❡ ♣♦r t♦❞♦s ♦s ❡s❢♦rç♦s ❡♠♣❡♥❤❛❞♦s ♥❡st❛ t❡s❡✱ q✉❡ ♥ã♦ ❢♦r❛♠ ♣♦✉❝♦s ❡ tã♦ ✐♠♣r❡s❝✐♥❞í✈❡✐s ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦ ♠❡✉ ❛♠✐❣♦ ❉❡✐✈✐❞ ▼❛rq✉❡s ◆✉♥❡s q✉❡ ❢♦✐ ♠❡✉ ❣r❛♥❞❡ ♣❛r❝❡✐r♦ ♥❡ss❛ ❥♦r♥❛❞❛ ❡ ♣❡ç❛✲ ❝❤❛✈❡ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ t❡s❡✳
❆♦ ♠❡✉ ♥❛♠♦r❛❞♦ ❱✐♥í❝✐♦ ❉✐❛s ❋❡rr❡✐r❛ ♣❡❧♦ ❛♠♦r✱ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ ❛♠✐③❛❞❡ ❞❡ s❡♠♣r❡✳ ➚ Pr✐s❝✐❧❛ ❇❛rr♦s ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ❡♠ ❙ã♦ ❈❛r❧♦s✱ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ❛♠✐❣❛ ◆á❞✐❛ ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ♥♦ ▲❛t❡① ❡ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ q✉❡ t❡✈❡ ❝♦♠✐❣♦✳ ➚s ♠✐♥❤❛s ❛♠✐❣❛s ❇❡tâ♥✐❛✱ ❈❛r❧❛ ❡ ❈✐❞❛ ♣❡❧❛ ❛❥✉❞❛ ❡ ❜❡❧❛s ♣❛❧❛✈r❛s ❞❡ ❛♣♦✐♦✳ ➚ ❏❛♥❛í♥❛✱ ❋r❛♥❝✐❡❧❧❡✱ ❇r✉♥♦✱ ❍é❧✐♦✱ ❆❧✐♥❡✱ ●✉st❛✈♦✱ ❲❡s❧❡②✱ ❇r✉♥❛✱ ▲❛r✐ss❛✱ ▲í❜✐❛✱ ❍❡♥✲ r✐q✉❡✱ ▼❛❣♥♦✱ ❲✐❧s♦♥✱ ❚❤❛♠❛②♥❡ ❡ t♦❞♦s ❛q✉❡❧❡s q✉❡ ♣♦r✈❡♥t✉r❛ ❡✉ t❡♥❤❛ ❡sq✉❡❝✐❞♦ ❞❡ ❝✐t❛r✱ ♣❡❧❛ ❧❡❛❧❞❛❞❡ ❡ ♣❡❧♦ ♦♠❜r♦ ❛♠✐❣♦✳ ◆ã♦ t❡♥❤♦ ❞ú✈✐❞❛s ❞❡ q✉❡ ❛♠✐❣♦s sã♦ ✐r♠ã♦s q✉❡ ♣♦❞❡♠♦s ❡s❝♦❧❤❡r✳
❆♦s ♣r♦❢❡ss♦r❡s ▼❛r❝♦s ❆♥tô♥✐♦ ❇❛rr♦③♦✱ ▲✉✐③ ●✉st❛✈♦ ❱✐❡✐r❛ ❡ ▲✉✐s ❈❧á✉❞✐♦ ▲♦♣❡s ♣♦r t♦❞❛ ❛ ❛❥✉❞❛✳
➚ ♣r♦❢❡ss♦r❛ ❘♦s❡♥❞❛ ❱❛❧❞és ❆r❡♥❝✐❜✐❛ ❞❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ▼❡❝â♥✐❝❛ ♣♦r t♦❞♦ ♦ ❛♣♦✐♦ ❡ s✉♣♦rt❡ ♥❛ ár❡❛ ❞❡ ♠❡tr♦❧♦❣✐❛✳
❆❣r❛❞❡❝✐♠❡♥t♦s ✐✐✐
♦ ❛♣♦✐♦ ❡ s✉♣♦rt❡ ❝♦♠ ❛ ❢♦♥t❡ ❞❡ ❛❧t❛ t❡♥sã♦✳
❆♦ ❏♦sé ▲✉❝❛s ▼♦❣♥♦♥ ♣❡❧♦s ❞❡s❡♥❤♦s ❞❛ ✉♥✐❞❛❞❡ ❡ ❞♦ ❉▼❆ ♥♦ s♦❢t✇❛r❡ ❙♦❧✐❞✇♦r❦s✳ ❆♦s ❛❧✉♥♦s ❞❡ ■♥✐❝✐❛çã♦ ❈✐❡♥tí✜❝❛ ❈❛r♦❧✐♥❛ ❡ ❆♠❛✉r✐ ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ❡ ❡♠♣❡♥❤♦✳ ➚ ❈❧❡✉③✐❧❡♥❡ ❙✐❧✈❛ ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ❡ ❛♠✐③❛❞❡✳
❆♦s s❡❝r❡tár✐♦s ●❛❜r✐❡❧✱ ❙✐❧✈✐♥♦ ❡ ❈❡❝í❧✐❛ ♣♦r s❡✉ ♣r♦✜ss✐♦♥❛❧✐s♠♦ ❡ ♣♦r s✉❛ ❛♠✐③❛❞❡✳ ❆♦ ❍✉♠❜❡rt♦ ❡ ❛♦ ❯❧✐ss❡s ❞❛ ❖✜❝✐♥❛ ▼❡❝â♥✐❝❛ ❞❛ ❋❊◗❯■ ♣♦r t♦❞❛ ❛ ❛❥✉❞❛ ❡ ❡♠♣❡♥❤♦ ♥♦ ❉▼❆✱ ❛♦ P❛✉❧♦ ♣❡❧❛ ❛❥✉❞❛ ♥❛ ✐♥st❛❧❛çã♦ ❞❡ s♦❢t✇❛r❡✳
✏❆ ❢é ❡ ❛ r❛③ã♦ ❝❛♠✐♥❤❛♠ ❥✉♥t❛s✱ ♠❛s ❛ ❢é ✈❛✐ ♠❛✐s ❧♦♥❣❡✑✳
❙❯▼➪❘■❖
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✈✐✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①
◆♦♠❡♥❝❧❛t✉r❛ ①✐
❘❡s✉♠♦ ①✈
❆❜str❛❝t ①✈✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✺
❙✉♠ár✐♦ ✈✐
✷✳✸✳✶ ❚❡♦r✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✸✳✷ ❆ ❢✉♥çã♦ tr❛♥s❢❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✸✳✸ ❚❡♠♣♦ ❞❡ r❡s✐❞ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✸✳✹ ❋✉♥çã♦ ❞❡ ❚r❛♥s❢❡rê♥❝✐❛ ❞♦ ❝❧❛ss✐✜❝❛❞♦r ❉▼❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✸✳✺ ❘❡s♦❧✉çã♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✹ ❊s♣❡❝trô♠❡tr♦s ❞❡ ❛❡r♦ssó✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✷✳✹✳✶ ❈❧❛ss✐✜❝❛❞♦r ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ♠♦❜✐❧✐❞❛❞❡ ❞❡ ✈❛rr❡❞✉r❛ ✭❙❝❛♥♥✐♥❣ ▼♦❜✐❧✐t② P❛rt✐❝❧❡ ❙✐③❡r✲❙▼P❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✹✳✷ ❆♥❛❧✐s❛❞♦r ❞❡ ❛❡r♦ss♦❧ ❡❧étr✐❝♦ ✭❊❧❡❝tr✐❝❛❧ ❆❡r♦s♦❧ ❆♥❛❧②s❡r✲❊❆❆✮ ✳ ✹✻ ✷✳✹✳✸ ❊s♣❡❝trô♠❡tr♦ ❞❡ ❛❡r♦ss♦❧ ❡❧étr✐❝♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❚❛rt✉ ✭❊❧❡❝✲
tr✐❝❛❧ ❆❡r♦s♦❧ ❙♣❡❝tr♦♠❡t❡r✲❊❆❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✳✹✳✹ ❈❧❛ss✐✜❝❛❞♦r ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ♠áq✉✐♥❛ ❞❡ ❡①❛✉stã♦ ✭❊♥❣✐♥❡ ❊①❤❛✉st
P❛rt✐❝❧❡ ❙✐③❡r✲❊❊P❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✹✳✺ ❊s♣❡❝trô♠❡tr♦ ❞❡ ❛❡r♦ss♦❧ rá♣✐❞♦ ✭❋❛st ❆❡r♦s♦❧ ❙♣❡❝tr♦♠❡t❡r✲❋❆❙✮ ✹✽ ✷✳✹✳✻ ❊s♣❡❝trô♠❡tr♦ ❞❡ ♠♦❜✐❧✐❞❛❞❡ ❞✐❢❡r❡♥❝✐❛❧ ✭❉✐✛❡r❡♥t✐❛❧ ▼♦❜✐❧✐t② ❙♣❡❝tr♦♠❡t❡r✲
❉▼❙✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✹✳✼ ❖✉tr♦s ✐♥str✉♠❡♥t♦s ❞❡ ❛♠♦str❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✸ ▼❡♠ór✐❛ ❞❡ ❝á❧❝✉❧♦ ✻✵
✸✳✶ ❈♦♠♣♦♥❡♥t❡s ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❛ ♣❛rtí❝✉❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✶✳✶ ❆①✐❛❧ ✭u✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✸✳✶✳✷ ❘❛❞✐❛❧ ✭v✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
✸✳✷ ❈á❧❝✉❧♦ ❞♦ ❞✐â♠❡tr♦ ❞❛s ♣❛rtí❝✉❧❛s ♥♦ ❛❡r♦ss♦❧ ♠♦♥♦❞✐s♣❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✹ ▼❛t❡r✐❛✐s ❡ ▼ét♦❞♦s ✻✻
❙✉♠ár✐♦ ✈✐✐
✹✳✼ ❋♦♥t❡ ❞❡ ❛❧t❛ t❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✽ ❆t♦♠✐③❛❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✾ ❈♦♠♣r❡ss♦r ❞❡ ❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✵ ❈♦♥t❛❞♦r ❞❡ P❛rtí❝✉❧❛s ♣♦r ❈♦♥❞❡♥s❛çã♦ ✭❈P❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✶ ●❡r❛çã♦ ❞❡ ❛❡r♦ss♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✷ ▼❡❞✐çã♦ ❞❛ ❡s♣❡ss✉r❛ ❞❛ ❢❡♥❞❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✸ ❉❡♣❡♥❞ê♥❝✐❛ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥♦ ❛❡r♦ss♦❧ ❝♦♠ ❛ ❝♦♥❝❡♥tr❛çã♦
❞❛ s♦❧✉çã♦ s❛❧✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✹ ❊st✉❞♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❣❡r❛çã♦ ❞♦ ❛t♦♠✐③❛❞♦r ❝♦♠❡r❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✺ ❊st✉❞♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦s ❉▼❆s ❡♠♣r❡❣❛♥❞♦ ♦ ❛t♦♠✐③❛❞♦r ❝♦♠❡r❝✐❛❧ ✼✼
✺ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssã♦ ✼✽
✺✳✶ ❆❥✉st❡ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✷ Pr♦❥❡t♦ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✺✳✸ ❚❡st❡s ♣r❡❧✐♠✐♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✹ ❊st✉❞♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❙▼P❙ ❡♠♣r❡❣❛♥❞♦ ♦ ❛t♦♠✐③❛❞♦r ❝♦♠❡r❝✐❛❧ ✳ ✽✹ ✺✳✺ ❊st✉❞♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❉▼❆ ❡♠♣r❡❣❛♥❞♦ ♦ ❛t♦♠✐③❛❞♦r ❝♦♠❡r❝✐❛❧ ✳ ✽✺ ✺✳✺✳✶ ❱❛③ã♦ ❞❡ ♣❛rtí❝✉❧❛s ♠♦♥♦❞✐s♣❡rs❛s ♦✉ ❛❡r♦ss♦❧ ❝❧❛ss✐✜❝❛❞♦ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✺✳✷ ❱❛③ã♦ ❞❡ ❡①❝❡ss♦ ♦✉ ✈❛③ã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥ã♦ ❝❧❛ss✐✜❝❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✺✳✻ ❆♥á❧✐s❡ ❞♦ ❜❛❧❛♥ç♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✼ ❉✐✜❝✉❧❞❛❞❡s ❞♦ ♣r♦❥❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷
✻ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✾✹
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✷✳✶ ❊sq✉❡♠❛ ❞♦ s✐st❡♠❛ r❡s♣✐r❛tór✐♦ ❬❍✐♥❞s ✭✶✾✾✾✮ ❛♣✉❞ ❙t❡✛❡♥s ✭✷✵✵✼✮❪ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷ ❆♥á❧✐s❡ ❞❛s ❢♦rç❛s q✉❡ ❛t✉❛♠ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ s✉s♣❡♥s❛ ❡♠ ✉♠ ❣ás ❡♠
r❡♣♦✉s♦✱ s♦❜ ❛ ❛çã♦ ❞❛ ❣r❛✈✐❞❛❞❡ ❬❱✐✈❛s ✭✷✵✵✼✮❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸ ❆♥á❧✐s❡ ❞❛s ❢♦rç❛s q✉❡ ❛t✉❛♠ s♦❜r❡ ✉♠❛ ♣❛rtí❝✉❧❛ s✉s♣❡♥s❛ ❡♠ ✉♠ ❣ás ❡♠
r❡♣♦✉s♦✱ s♦❜r❡ ❛ ❛çã♦ ❞❡ ✉♠❛ ❢♦rç❛ ❡❧étr✐❝❛ ❬❱✐✈❛s ✭✷✵✵✼✮❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❢✉♥çã♦ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦✳ ❈ír❝✉✲
❧♦s só❧✐❞♦s r❡♣r❡s❡♥t❛♠ ♣❛rtí❝✉❧❛s ♥❛ ❛♠♦str❛ ❞❡ ❛❡r♦ss♦❧ q✉❡ sã♦ ❝♦❧❡t❛❞❛s ♥♦ s❡♥s♦r ✭ár❡❛ ❝✐♥③❛ ♥♦ ❡❧❡tr♦❞♦ s✉♣❡r✐♦r✮ ❡♥q✉❛♥t♦ ❧✐♥❤❛s tr❛❝❡❥❛❞❛s ❞❡✲ ♥♦t❛♠ ♣❛rtí❝✉❧❛s q✉❡ ❝❤❡❣❛♠ ❛♥t❡s ♦✉ ❞❡♣♦✐s ❞♦ ♣♦♥t♦ ❞❡ ❝♦❧❡t❛ ❬❇✐s❦♦s ✭✷✵✵✹✮❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✸✳✶ ➪r❡❛ út✐❧ ❞❡♥tr♦ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✷ ❉✐str✐❜✉✐çã♦ ❞❡ ✈❛③õ❡s ❞❡♥tr♦ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✐①
✹✳✾ ❘♦tâ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✶✵ ❋♦♥t❡ ❞❡ ❛❧t❛ t❡♥sã♦ ❈❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✶✶ ❆t♦♠✐③❛❞♦r ❝♦♠❡r❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✺✳✶ ❊♠ s❡♥t✐❞♦ ❤♦rár✐♦✿ ♣❛rt❡ s✉♣❡r✐♦r ❞♦ ❉▼❆ ❝♦♠ ♦ ❡❧❡tr♦❞♦ r♦sq✉❡❛❞♦✱ ✈✐st❛ ✐♥❢❡r✐♦r ❞❛ ♣❛rt❡ s✉♣❡r✐♦r ❞♦ ❉▼❆ s❡♠ ♦ ❡❧❡tr♦❞♦ ❡ ❜♦rr❛❝❤❛ ❞❡ ✈❡❞❛çã♦✱ ❜❛s❡ ❞♦ ❉▼❆ ❡ ❡❧❡tr♦❞♦ ✐♥t❡r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✷ ❆✉♠❡♥t♦ ❞❛ ❛♠♣❧✐t✉❞❡ ❞❛ ❝♦rr❡♥t❡ ♠♦♥♦❞✐s♣❡rs❛ ❡♠ ❢✉♥çã♦ ❞❛ t❡♥sã♦ ✳ ✳ ✽✵ ✺✳✸ ❆✉♠❡♥t♦ ❞❛ ❜❛♥❞❛ ❞❡ ❞✐â♠❡tr♦s ❝♦♠♦ ❢✉♥çã♦ ❞❡ dp❂❢✭❱✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
✺✳✹ ▼♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❞❛s ♣❛rtí❝✉❧❛s ❡♠ ❢✉♥çã♦ ❞♦ ❞✐â♠❡tr♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s ❝❛r❣❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✺ ❉✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❝❛r❣❛s ❡♠ ❢✉♥çã♦ ❞♦ ❞✐â♠❡tr♦ ❞❛s ♣❛r✲
tí❝✉❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✻ ❋❛t♦r ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ ❞❡ ❈✉♥♥✐♥❣❤❛♠ ❡♠ ❢✉♥çã♦ ❞❡ dp ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✺✳✼ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥♦ ❛❡r♦ss♦❧ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ s❛❧ ♥❛ s♦❧✉çã♦ ❞♦ ❛t♦♠✐③❛❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺✳✽ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❛❧✐♠❡♥t❛çã♦ ♣❛r❛ ❛s ✺ ❝♦♥❝❡♥tr❛çõ❡s ❡st✉❞❛❞❛s ✳ ✳ ✳ ✳ ✽✸ ✺✳✾ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s ❛❥✉st❡s ♣❛r❛ ❝❛❞❛ ❝♦♥❝❡♥tr❛✲
çã♦ s❛❧✐♥❛ ✉s❛❞❛ ♥♦ ❙▼P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✶✵ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s ❛❥✉st❡s ♣❛r❛ ❝❛❞❛ ❝♦♥❝❡♥tr❛✲
çã♦ s❛❧✐♥❛ ✉s❛❞❛ ♥❛ ❝♦rr❡♥t❡ ♠♦♥♦❞✐s♣❡rs❛ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✺✳✶✶ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❝♦♠ ♦s r❡s♣❡❝t✐✈♦s ❛❥✉st❡s ♣❛r❛ ❝❛❞❛ ❝♦♥❝❡♥tr❛✲
çã♦ s❛❧✐♥❛ ✉s❛❞❛ ♥❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝❡ss♦ ❞♦ ❉▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✺✳✶✷ ❈❧❛ss✐✜❝❛çã♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♣♦r ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛✱ ♦♥❞❡ ❛s ❡s❢❡r❛s
❛③✉✐s ❝♦rr❡s♣♦♥❞❡♠ às ♥❛♥♦♣❛rtí❝✉❧❛s ❝♦♠ ❝❛r❣❛s ♣♦s✐t✐✈❛s✱ ❛s ❡s❢❡r❛s ✈❡r✲ ❞❡s às ♥❛♥♦♣❛rtí❝✉❧❛s ♥❡✉tr❛s ❡ ❛s ❡s❢❡r❛s ♣r❡t❛s às ♥❛♥♦♣❛rtí❝✉❧❛s ❝♦♠ ❝❛r❣❛s ♥❡❣❛t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✶✸ ❈♦♠♣❛r❛çã♦ ❞♦ ❇❛❧❛♥ç♦ ❞❡ ❉✐str✐❜✉✐çã♦ ❞❡ ❈❛r❣❛s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❡①♣❡✲
r✐♠❡♥t❛✐s ♣❛r❛ ❝❛❞❛ ❝♦♥❝❡♥tr❛çã♦ s❛❧✐♥❛ ✉t✐❧✐③❛❞❛ ♥❛ ❝♦rr❡♥t❡ ♠♦♥♦❞✐s♣❡rs❛ ✾✵ ✺✳✶✹ ❈♦♠♣❛r❛çã♦ ❞♦ ❇❛❧❛♥ç♦ ❞❡ ❉✐str✐❜✉✐çã♦ ❞❡ ❈❛r❣❛s ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❡①✲
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
✷✳✶ ❉✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛s ❞❡ ❡q✉✐❧í❜r✐♦ ❞❡ ❇♦❧t③♠❛♥♥ s♦❜r❡ ♣❛rtí❝✉❧❛s ❞❡ ❛❡✲ r♦ss♦❧ ❬❱✐✈❛s ✭✷✵✵✼✮❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✷ ❈♦❡✜❝✐❡♥t❡s ❞♦ ♠♦❞❡❧♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❜✐♣♦❧❛r ✭♣❛r❛ ❊q✉❛çã♦ ✷✳✼✵✮ ❬❇✐s❦♦s
✭✷✵✵✹✮❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✸ ❉✐str✐❜✉✐çã♦ ❞❡ ❝❛r❣❛s ❡♠ ♣❛rtí❝✉❧❛s ❜✐♣♦❧❛r♠❡♥t❡ ❝❛rr❡❣❛❞❛s ❬❇✐s❦♦s ✭✷✵✵✹✮❪ ✸✺
✹✳✶ ❘❡❧❛çã♦ ❡♥tr❡ ♣r❡ssã♦ ❞❡ ❡♥tr❛❞❛ ❡ t❛①❛ ❞❡ s❛í❞❛ ❞❡ ❛❡r♦ss♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
◆❖▼❊◆❈▲❆❚❯❘❆
❖s sí♠❜♦❧♦s ✉t✐❧✐③❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠✿
a r❛✐♦ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚0
ai(n) ❝♦❡✜❝✐❡♥t❡ ❞❡ ❛♣r♦①✐♠❛çã♦ ▼0▲0❚0
A ár❡❛ út✐❧ ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❞♦ ❉▼❆ ▼0▲2❚0
A2 ár❡❛ ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❞♦ ❝✐❧✐♥❞r♦ ❡①t❡r♥♦ ▼0▲2❚0
A1 ár❡❛ ❞❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❞♦ ❝✐❧✐♥❞r♦ ✐♥t❡r♥♦ ▼0▲2❚0
b ♣❛râ♠❡tr♦ ❞❡ ❝♦❧✐sã♦ ▼0▲0❚0
bm ♣❛râ♠❡tr♦ ❞❡ ❝♦❧✐sã♦ ♠í♥✐♠♦ ▼0▲0❚0
B ♠♦❜✐❧✐❞❛❞❡ ♠❡❝â♥✐❝❛ ▼−1▲0❚1
c ✈❡❧♦❝✐❞❛❞❡ ♠♦❧❡❝✉❧❛r ▼0▲1❚−1
cm ✈❡❧♦❝✐❞❛❞❡ ♠♦❧❡❝✉❧❛r ♠❛✐s ♣r♦✈á✈❡❧ ▼0▲1❚−1
crms ✈❡❧♦❝✐❞❛❞❡ r❛✐③ q✉❛❞r❛❞❛ ♠é❞✐❛ ▼0▲1❚−1
c ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞❛s ♠♦❧é❝✉❧❛s ▼0▲1❚−1
ci ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞♦s í♦♥s ▼0▲1❚−1
ci,a ✈❡❧♦❝✐❞❛❞❡ r❡❧❛t✐✈❛ ❞♦s í♦♥s ❝♦♠ ❛s ♠♦❧é❝✉❧❛s ❞❡ ❣ás ▼0▲1❚−1
cp ✈❡❧♦❝✐❞❛❞❡ tér♠✐❝❛ ♠é❞✐❛ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚−1
Cc ❢❛t♦r ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ ❞❡ ❈✉♥♥✐♥❣❤❛♠ ▼0▲0❚0
C∗ ❢❛t♦r ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ ❞❡ ❈✉♥♥✐♥❣❤❛♠ ♥❛ ❢❡♥❞❛ ▼0▲0❚0
C1 ❧✐♠✐t❡ ✐♥❢❡r✐♦r✴❢❛t♦r ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ ❞❡ ❈✉♥♥✐♥❣❤❛♠ ▼0▲0❚0
C2 ❧✐♠✐t❡ s✉♣❡r✐♦r✴❢❛t♦r ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ ❞❡ ❈✉♥♥✐♥❣❤❛♠ ▼0▲0❚0
dp ❞✐â♠❡tr♦ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚0
dqe ❞✐â♠❡tr♦ ❡q✉✐✈❛❧❡♥t❡ ❞❡ ❝❛rr❡❣❛♠❡♥t♦ ▼0▲1❚0
dxrms ❞❡s❧♦❝❛♠❡♥t♦ ❧íq✉✐❞♦ ▼0▲1❚0
D ❧❛❝✉♥❛ ❡♥tr❡ ♦s ❞♦✐s ❝✐❧✐♥❞r♦s ❞♦ ❛♥❡❧ ▼0▲1❚0
Di ❝♦❡✜❝✐❡♥t❡ ❞❡ ❞✐❢✉sã♦ ❞♦s í♦♥s ▼0▲2❚−1
D∗
p ❞✐â♠❡tr♦ ❞❛ ♣❛rtí❝✉❧❛ ♥❛ ❢❡♥❞❛ ▼0▲1❚0
Dp1 ❧✐♠✐t❡ ✐♥❢❡r✐♦r ❞♦ ❞✐â♠❡tr♦ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚0
Dp2 ❧✐♠✐t❡ s✉♣❡r✐♦r ❞♦ ❞✐â♠❡tr♦ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚0
e ❝❛r❣❛ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ ❡❧étr♦♥ ▼0▲0❚0❈1
◆♦♠❡♥❝❧❛t✉r❛ ①✐✐
E ❝❛♠♣♦ ❡❧étr✐❝♦ ▼1▲1❚−2❈−1
Er ❝♦♠♣♦♥❡♥t❡ r❛❞✐❛❧ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ▼1▲1❚−2❈−1
Ez ❝♦♠♣♦♥❡♥t❡ ❛①✐❛❧ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ▼1▲1❚−2❈−1
E0 ❝♦rr❡çã♦ ❞❡ ♦r❞❡♠ ③❡r♦ ♣❛r❛ ❛ ❊q✉❛çã♦ ✭✷✳✺✾✮ ▼0▲0❚0
E1 ❝♦rr❡çã♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ♣❛r❛ ❛ ❊q✉❛çã♦ ✭✷✳✺✾✮ ▼0▲0❚0
f(n) ❢✉♥çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❲✐❡❞❡♥s♦❤❧❡r ▼0▲0❚0
fin ❡♥tr❛❞❛ ❞❛ ❢✉♥çã♦ tr❛♥s❢❡rê♥❝✐❛ ▼0▲0❚0
ftrans ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ▼0▲0❚0
F ❢♦rç❛ ❞❡ ✐♥t❡r❛çã♦ í♦♥✲♣❛rtí❝✉❧❛ ❞❛ ❊q✉❛çã♦ ✭✷✳✺✹✮ ▼1▲1❚−2
FD ❢♦rç❛ ❞❡ ❛rr❛st❡ ▼1▲1❚−2
FE ❢♦rç❛ ❡❧étr✐❝❛ ▼1▲1❚−2
FG ❢♦rç❛ ❞❛ ❣r❛✈✐❞❛❞❡ ▼1▲1❚−2
G ❢❛t♦r ❣❡♦♠étr✐❝♦ ▼0▲0❚0
I(γ) ❢❛t♦r ❣❡♦♠étr✐❝♦ ❞♦ ❉▼❆ ❞❛ ❊q✉❛çã♦ ✭✷✳✽✸✮ ▼0▲0❚0
Jn ✢✉①♦ ❞❡ í♦♥s ♣❛r❛ ❛ ♣❛rtí❝✉❧❛ ▼0▲3❚−1
J(r) ✢✉①♦ ❞❡ í♦♥s ❡♠ ✉♠❛ s✉♣❡r❢í❝✐❡ ❡s❢ér✐❝❛ ▼0▲1❚−1
k ❝♦♥st❛♥t❡ ❞❡ ❇♦❧t③♠❛♥♥ ▼1▲2❚−2θ−1
Kn ♥ú♠❡r♦ ❞❡ ❑♥✉❞s❡♥ ▼0▲0❚0
Kne ♥ú♠❡r♦ ❞❡ ❑♥✉❞s❡♥ ❡❢❡t✐✈♦ ▼0▲0❚0
l ❝♦♠♣r✐♠❡♥t♦ ❞♦ ❛♥❡❧ ▼0▲1❚0
L r❛③ã♦ ❞♦ ❞✐â♠❡tr♦ ♣♦❧❛r s♦❜r❡ ♦ ❡q✉❛t♦r✐❛❧ ♥❛ ❊q✉❛çã♦ ✭✷✳✻✹✮ ▼0▲0❚0
L ❞✐stâ♥❝✐❛ ❞❛ ❡♥tr❛❞❛ ❞♦ ❛❡r♦ss♦❧ ❛té ❛ ❢❡♥❞❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ▼0▲1❚0
Le ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❡♥tr❛❞❛ r❡q✉❡r✐❞♦ ▼0▲1❚0
m ♠❛ss❛ ❞❛s ♠♦❧é❝✉❧❛s ▼1▲0❚0
mi ♠❛ss❛ ❞♦s í♦♥s ▼1▲0❚0
ma ♠❛ss❛ ❞❛s ♠♦❧é❝✉❧❛s ❞❡ ❣ás ▼1▲0❚0
mi,a ♠❛ss❛ r❡❞✉③✐❞❛ ❞♦ s✐st❡♠❛ ▼1▲0❚0
n ♥ú♠❡r♦ ❞❡ ❝❛r❣❛s ❡❧❡♠❡♥t❛r❡s ❞♦ í♦♥ ▼0▲0❚0❈1
N ❝♦♥❝❡♥tr❛çã♦ ♥✉♠ér✐❝❛ ❞❛s ♠♦❧é❝✉❧❛s ▼0▲−3❚0
Na ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❣ás ❞❡ ❢✉♥❞♦ ▼0▲−3❚0
Nit ♣❛râ♠❡tr♦ ❞❡ ❝❛rr❡❣❛♠❡♥t♦ ▼0▲−3❚1
Np,n ❝♦♥❝❡♥tr❛çã♦ ♥✉♠ér✐❝❛ ❞❛s ♣❛rtí❝✉❧❛s ❝♦♠ n ❝❛r❣❛s ▼0▲−3❚0
P′ ♣r❡ssã♦ ▼1▲−1❚−2
Q ✈❛③ã♦ ✈♦❧✉♠étr✐❝❛ ▼0▲3❚−1
Qm ✈❛③ã♦ ❞❡ s❛í❞❛ ♣❛r❛ ❛ ❊q✉❛çã♦ ✭✷✳✾✵✮ ▼0▲3❚−1
Qs ✈❛③ã♦ ❞❡ ❛r ✐♥✈ó❧✉❝r♦ ♣❛r❛ ❛ ❊q✉❛çã♦ ✭✷✳✾✵✮ ▼0▲3❚−1
Qt ✈❛③ã♦ t♦t❛❧ ▼0▲3❚−1
Qex ✈❛③ã♦ ❞❡ ❡①❝❡ss♦ ❞❡ s❛í❞❛ ▼0▲3❚−1
Qsh ✈❛③ã♦ ❞❡ ✐♥✈ó❧✉❝r♦ ❞❡ ❡♥tr❛❞❛ ▼0▲3❚−1
Qmono ✈❛③ã♦ ❞❡ ❛❡r♦ss♦❧ ♠♦♥♦❞✐s♣❡rs♦ ❞❡ s❛í❞❛ ▼0▲3❚−1
Qpoli ✈❛③ã♦ ❞❡ ❛❡r♦ss♦❧ ♣♦❧✐❞✐s♣❡rs♦ ❞❡ ❡♥tr❛❞❛ ▼0▲3❚−1
r2 r❛✐♦ ❞♦ ❝✐❧✐♥❞r♦ ❡①t❡r♥♦ ▼0▲1❚0
r1 r❛✐♦ ❞♦ ❝✐❧✐♥❞r♦ ✐♥t❡r♥♦ ▼0▲1❚0
R r❡s♦❧✉çã♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ▼0▲0❚0
Rnd r❡s♦❧✉çã♦ ♥ã♦ ❞✐❢✉s✐✈❛ ▼0▲0❚0
Rdif f r❡s♦❧✉çã♦ ❞✐❢✉s✐✈❛ ▼0▲0❚0
◆♦♠❡♥❝❧❛t✉r❛ ①✐✐✐
Re ♥ú♠❡r♦ ❞❡ ❘❡②♥♦❧❞s ▼0▲0❚0
S ❝♦♥st❛♥t❡ ❞❡ ❙✉t❤❡r❧❛♥❞ ▼0▲0❚0
t t❡♠♣♦ ❞❡ r❡s✐❞ê♥❝✐❛ ♣❛r❛ ❛ ❊q✉❛çã♦ ✭✷✳✾✶✮ ▼0▲0❚1
tf t❡♠♣♦ q✉❡ ❛ ♣❛rtí❝✉❧❛ ❧❡✈❛ ♣❛r❛ ♣❡r❝♦rr❡r ❛ ❞✐stâ♥❝✐❛ L ▼0▲0❚1
tr t❡♠♣♦ q✉❡ ❛ ♣❛rtí❝✉❧❛ ❧❡✈❛ ♣❛r❛ ✐r ❞❡ r2 ❛ r1 ▼0▲0❚1
u r❛③ã♦ ❞♦ ❞✐â♠❡tr♦ ❞♦ ❝✐❧✐♥❞r♦ ✐♥t❡r✐♦r✴❡①t❡r✐♦r ❞❛ ❊q✉❛çã♦ ✭✷✳✶✶✮ ▼0▲0❚0
u ✈❡❧♦❝✐❞❛❞❡ ❛①✐❛❧ ♠é❞✐❛ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚−1
ur ❝♦♠♣♦♥❡♥t❡ r❛❞✐❛❧ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❡s❝♦❛♠❡♥t♦ ▼0▲1❚−1
uz ❝♦♠♣♦♥❡♥t❡ ❛①✐❛❧ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❡s❝♦❛♠❡♥t♦ ▼0▲1❚−1
U ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❡s❝♦❛♠❡♥t♦ ✭❛①✐❛❧✮ ♠é❞✐❛ ❞❛ ❊q✉❛çã♦ ✭✷✳✶✶✮ ▼0▲1❚−1
v ✈❡❧♦❝✐❞❛❞❡ r❛❞✐❛❧ ♠é❞✐❛ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲1❚−1
v ✈❡❧♦❝✐❞❛❞❡ ❞❛s ♠♦❧é❝✉❧❛s ▼0▲1❚−1
vT ✈❡❧♦❝✐❞❛❞❡ t❡r♠✐♥❛❧ ▼0▲1❚−1
vT E ✈❡❧♦❝✐❞❛❞❡ ❡❧❡tr♦stát✐❝❛ t❡r♠✐♥❛❧ ▼0▲1❚−1
vT S ✈❡❧♦❝✐❞❛❞❡ ❞❡ s❡❞✐♠❡♥t❛çã♦ t❡r♠✐♥❛❧ ▼0▲1❚−1
V t❡♥sã♦ ♥❛ ❤❛st❡ ❝❡♥tr❛❧ ▼1▲−1❚−2
Z ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ▼1▲2❚−3❈1
Zi ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❞♦s í♦♥s ▼1▲2❚−3❈1
Z∗
p ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❞❛ ♣❛rtí❝✉❧❛ ♥❛ ❢❡♥❞❛ ▼1▲2❚−3❈1
Zp1 ❧✐♠✐t❡ ✐♥❢❡r✐♦r ❞❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❞❛ ♣❛rtí❝✉❧❛ ▼1▲2❚−3❈1
Zp2 ❧✐♠✐t❡ s✉♣❡r✐♦r ❞❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❞❛ ♣❛rtí❝✉❧❛ ▼1▲2❚−3❈1
Zp ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❛❞✐♠❡♥s✐♦♥❛❧ ▼0▲0❚0
β ♣❛râ♠❡tr♦ ❞❡ ✢✉①♦ ❛❞✐♠❡♥s✐♦♥❛❧ ▼0▲0❚0
βn ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝♦♠❜✐♥❛çã♦ ❞♦s í♦♥s ❝♦♠ ♣❛rtí❝✉❧❛s ▼0▲3❚−1
γ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ í♦♥ ❡♥tr❛r ♥❛ ❡s❢❡r❛ ❧✐♠✐t❡ ▼0▲0❚0
γ ❢❛t♦r ❣❡♦♠étr✐❝♦ ❞♦ ❉▼❆ ❞❛ ❊q✉❛çã♦ ✭✷✳✽✶✮ ▼0▲0❚0
δ r❛✐♦ ❞❛ ❡s❢❡r❛ ❧✐♠✐t❡ ▼0▲1❚0
δ ♣❛râ♠❡tr♦ ❞❡ ✢✉①♦ ❛❞✐♠❡♥s✐♦♥❛❧ ❞❛ ❊q✉❛çã♦ ✭✷✳✼✹✮ ▼0▲0❚0
δD ❢✉♥çã♦ ❞❡❧t❛ ❞❡ ❉✐r❛❝ ▼0▲0❚0
∆P ❞✐❢❡r❡♥ç❛ ❞❡ ♣r❡ssã♦ ❛♦ ❧♦♥❣♦ ❞♦ ❞✐s♣♦s✐t✐✈♦ ▼1▲−1❚−2
∆Zp ❧❛r❣✉r❛ ❞❛ ❜❛♥❞❛ ❞❡ ♠♦❜✐❧✐❞❛❞❡ ▼1▲2❚−3❈1
ǫ ❝♦♥st❛♥t❡ ❞✐❡❧étr✐❝❛ ▼0▲0❚0
ε0 ♣❡r♠✐ss✐✈✐❞❛❞❡ ❞♦ ✈á❝✉♦ ▼−1▲−3❚2❈2
εi,a ❢❛t♦r ❞❡ ❝♦rr❡çã♦ ▼0▲0❚0
ε(x) ❢✉♥çã♦ ❡rr♦ ▼0▲0❚0
η ✈✐s❝♦s✐❞❛❞❡ ❞✐♥â♠✐❝❛ ▼1▲−1❚−1
ηr ✈✐s❝♦s✐❞❛❞❡ ❞✐♥â♠✐❝❛ à t❡♠♣❡r❛t✉r❛ ❞❡ r❡❢❡rê♥❝✐❛ Tr ▼1▲−1❚−1
κ ♣❛râ♠❡tr♦ ❢♦rç❛ ✐♠❛❣❡♠ ▼0▲0❚0
κ ❢❛t♦r ❣❡♦♠étr✐❝♦ ❞♦ ❉▼❆ ❞❛ ❊q✉❛çã♦ ✭✷✳✽✷✮ ▼0▲0❚0
λ ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ▼0▲1❚0
λi ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ❞♦s í♦♥s ▼0▲1❚0
λp ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ▼0▲1❚0
λr ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ♥❛s ❝♦♥❞✐çõ❡s ❞❡ r❡❢❡rê♥❝✐❛ Pr ❡Tr ▼0▲1❚0
µ ✈✐s❝♦s✐❞❛❞❡ ❞♦ ✢✉✐❞♦ ▼1▲−1❚−1
ρ ❞❡♥s✐❞❛❞❡ ❞♦ ❣ás ▼1▲−3❚0
ρp ❞❡♥s✐❞❛❞❡ ❞❛ ♣❛rtí❝✉❧❛ ▼1▲−3❚0
◆♦♠❡♥❝❧❛t✉r❛ ①✐✈
σ ❞✐â♠❡tr♦ ❞❛ ❡s❢❡r❛ rí❣✐❞❛ ▼0▲1❚0
σi,i ❞✐â♠❡tr♦ ❞❡ ❝♦❧✐sã♦ ✐ô♥✐❝♦ ▼0▲1❚0
σi,a ❞✐â♠❡tr♦ ❞❡ ❝♦❧✐sã♦ ❜✐♥ár✐❛ ▼0▲1❚0
σ ❞❡s❧♦❝❛♠❡♥t♦ ❞✐❢✉s✐♦♥❛❧ ❛❞✐♠❡♥s✐♦♥❛❧ ▼0▲0❚0
τ t❡♠♣♦ ♠é❞✐♦ ❡♥tr❡ ❝♦❧✐sõ❡s s✉❝❡ss✐✈❛s ▼0▲0❚1
τi,a t❡♠♣♦ ♠é❞✐♦ ❡♥tr❡ ❝♦❧✐sõ❡s s✉❝❡ss✐✈❛s ❞❡ í♦♥s✴♠♦❧é❝✉❧❛s ❞❡ ❣ás ▼0▲0❚1
τp t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲0❚1
τs t❡♠♣♦ ❞❡ r❡❧❛①❛çã♦ ❞♦ s✐st❡♠❛ ▼0▲0❚1
υ ❢r❡q✉ê♥❝✐❛ ❞❡ ❝♦❧✐sã♦ ❞❛s ♠♦❧é❝✉❧❛s ▼0▲−4❚0
υi,i ❢r❡q✉ê♥❝✐❛ ❞❡ ❝♦❧✐sã♦ í♦♥✲í♦♥ ▼0▲−4❚0
υi,a ❢r❡q✉ê♥❝✐❛ ❞❡ ❝♦❧✐sã♦ í♦♥✲♠♦❧é❝✉❧❛ ❞❡ ❣ás ▼0▲−4❚0
φ ♣♦t❡♥❝✐❛❧ ❛❞✐♠❡♥s✐♦♥❛❧ ♥❛ s✉♣❡r❢í❝✐❡ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲0❚0
φ(r) ♣♦t❡♥❝✐❛❧ à ❞✐stâ♥❝✐❛ r ▼0▲1❚−1
ψin ❞✐r❡çã♦ ❞❡ ❡♥tr❛❞❛ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲0❚0
ψout ❞✐r❡çã♦ ❞❡ s❛í❞❛ ❞❛ ♣❛rtí❝✉❧❛ ▼0▲0❚0
Ω ❢✉♥çã♦ tr❛♥s❢❡rê♥❝✐❛ ▼0▲0❚0
# ♥ú♠❡r♦ ❞❡ ♣❛rtí❝✉❧❛s ▼0▲−3❚0
❆s s✐❣❧❛s ✉s❛❞❛s ♥❡st❛ t❡s❡ sã♦✿
AT OF M S ❊s♣❡❝t✳ ❞❡ ♠❛ss❛ ❞❡ ❛❡r✳ t❡♠♣♦ ❞❡ ✈♦♦ ✭❆❡r♦s♦❧ ❚✐♠❡ ♦❢ ❋❧✐❣❤t ▼❛ss ❙♣❡❝tr♦♠❡t❡r✮ CP C ❈♦♥t❛❞♦r ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ❝♦♥❞❡♥s❛çã♦ ✭❈♦♥❞❡♥s❛t✐♦♥ P❛rt✐❝❧❡ ❈♦✉♥t❡r✮
DB ❇❛t❡r✐❛ ❞❡ ❞✐❢✉sã♦ ✭❉✐✛✉s✐♦♥ ❇❛tt❡r②✮
DM A ❆♥❛❧✐s❛❞♦r ❞❡ ▼♦❜✐❧✐❞❛❞❡ ❉✐❢❡r❡♥❝✐❛❧ ✭❉✐✛❡r❡♥t✐❛❧ ▼♦❜✐❧✐t② ❆♥❛❧②③❡r✮
DM P S ❆♠♦str❛❞♦r ❞❡ P❛rt✳ ♣♦r ▼♦❜✳ ❉✐❢❡r❡♥❝✐❛❧ ✭❉✐✛❡r❡♥t✐❛❧ ▼♦❜✐❧✐t② P❛rt✐❝❧❡ ❙✐③❡r✮ DM S ❊s♣❡❝trô♠❡tr♦ ❞❡ ▼♦❜✐❧✐❞❛❞❡ ❉✐❢❡r❡♥❝✐❛❧ ✭❉✐✛❡r❡♥t✐❛❧ ▼♦❜✐❧✐t② ❙♣❡❝tr♦♠❡t❡r✮ EAA ❆♥❛❧✐s❛❞♦r ❞❡ ❆❡r♦ss♦❧ ❊❧étr✐❝♦ ✭❊❧❡❝tr✐❝❛❧ ❆❡r♦s♦❧ ❆♥❛❧②③❡r✮
EAD ❉❡t❡❝t♦r ❞❡ ❛❡r♦ss♦❧ ❡❧étr✐❝♦ ✭❊❧❡❝tr✐❝❛❧ ❆❡r♦s♦❧ ❉❡t❡❝t♦r✮
EAS ❊s♣❡❝trô♠❡tr♦ ❞❡ ❆❡r♦ss♦❧ ❊❧étr✐❝♦ ✭❊❧❡❝tr✐❝❛❧ ❆❡r♦s♦❧ ❙♣❡❝tr♦♠❡t❡r✮
EEP S ❈❧❛ss✐✜❝❛❞♦r ❞❡ ♣❛rt✳ ♣♦r ♠áq✉✐♥❛ ❞❡ ❡①❛✉stã♦ ✭❊♥❣✐♥❡ ❊①❤❛✉st P❛rt✐❝❧❡ ❙✐③❡r✮ ELP I ■♠♣❛❝t❛❞♦r ❞❡ ❜❛✐①❛ ♣r❡ssã♦ ❡❧❡tr♦stát✐❝♦ ✭❊❧❡❝tr✐❝❛❧ ▲♦✇ Pr❡ss✉r❡ ■♠♣❛❝t♦r✮ F AS ❊s♣❡❝trô♠❡tr♦ ❞❡ ❆❡r♦ss♦❧ ❘á♣✐❞♦ ✭❋❛st ❆❡r♦s♦❧ ❙♣❡❝tr♦♠❡t❡r✮
❘❊❙❯▼❖
❘❡s✉♠♦ ①✈✐
❞❡ ❛❡r♦ss♦❧ ♠♦♥♦❞✐s♣❡rs♦✳
❆❇❙❚❘❆❈❚
❆❜str❛❝t ①✈✐✐✐
❈❆P❮❚❯▲❖ ✶
■♥tr♦❞✉çã♦
❍
á ❛❧❣✉♠❛s ❞é❝❛❞❛s ♦ ♠✉♥❞♦ ✈❡♠ s♦❢r❡♥❞♦ ✉♠❛ ✐♥t❡♥s❛ ✐♥❞✉str✐❛❧✐③❛çã♦✱ ♥ã♦s❡♥❞♦ ❛♣❡♥❛s ♦r✐✉♥❞❛ ❞♦ ❛♣❡❧♦ ❝❛♣✐t❛❧✐st❛ q✉❡ ❛ ❤✉♠❛♥✐❞❛❞❡ ✈✐✈❡♥❝✐❛✱ ♠❛s ✈✐t❛❧ ♣❛r❛ s✉♣r✐r ❛ ❝r❡s❝❡♥t❡ ❞❡♠❛♥❞❛ ♠✉♥❞✐❛❧ ♣♦r ❜❡♥s ❞❡ ❝♦♥s✉♠♦✳ ❈♦♠♦ ❝♦♥✲ s❡q✉ê♥❝✐❛ ❞✐ss♦✱ ❛s ❞❡s❝❛r❣❛s ❞❡ ❣❛s❡s✱ ❣❡r❛çã♦ ❞❡ ❡✢✉❡♥t❡s ❡ r❡sí❞✉♦s só❧✐❞♦s t❛♠❜é♠ ❛✉♠❡♥t❛r❛♠ ✲ ❢r✉t♦s ❞♦s ♣r♦❝❡ss♦s ❞❡ tr❛♥s❢♦r♠❛çã♦ ❡♠ ♠❛ss❛ ✲ ❛ ♣♦♥t♦ ❞❡ ✐♥t❡r❢❡r✐r ♥❛ q✉❛❧✐❞❛❞❡ ❞❡ ✈✐❞❛ ❞♦ ❤♦♠❡♠ ❡ ♥♦ ❡q✉✐❧í❜r✐♦ ❞♦ ❡❝♦ss✐st❡♠❛✱ ❛✐♥❞❛ q✉❡ ♠❡❞✐❞❛s ♣r❡✈❡♥t✐✈❛s ❡ ❝♦rr❡t✐✈❛s ❢♦ss❡♠ t✐♠✐❞❛♠❡♥t❡ t♦♠❛❞❛s✳❈♦♥t✉❞♦✱ ♥✉♥❝❛ ❢♦✐ tã♦ ❞✐s❝✉t✐❞❛ ❡ r❛t✐✜❝❛❞❛ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ❣❡r✐r ❞❡ ♠❛♥❡✐r❛ ♠❛✐s s✉st❡♥tá✈❡❧ ♦s ♣r♦❝❡ss♦s ❞❡ tr❛♥s❢♦r♠❛çã♦ ❝♦♠♦ ✉♠ t♦❞♦✳ ❊ ✐st♦ t❡♠ ❣❛r❛♥t✐❞♦ ❛ ❞✐✲ ♠✐♥✉✐çã♦ ❞❡ ✐♠♣❛❝t♦s✱ ❜❡♠ ❝♦♠♦ ♣r♦❞✉③✐❞♦ ✉♠❛ ✈✐sã♦ ♣♦s✐t✐✈❛ ❞♦s ❝♦♥s✉♠✐❞♦r❡s ❡♠ r❡❧❛çã♦ àq✉❡❧❡s q✉❡ ♦ ❢❛③❡♠✳ ●❛r❛♥t✐r ♦s ❜❡♥s ♥❡❝❡ssár✐♦s ❞❛s ❣❡r❛çõ❡s ❛t✉❛✐s s❡♠ ❝♦♠✲ ♣r♦♠❡t❡r ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛s ❣❡r❛çõ❡s ❢✉t✉r❛s✱ q✉❡ ♥❛❞❛ ♠❛✐s é ❞♦ q✉❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ s✉st❡♥t❛❜✐❧✐❞❛❞❡ t♦r♥♦✉✲s❡ ♦ ♣r✐♥❝✐♣❛❧ ♣✐❧❛r ❞❡ t♦❞❛ ❛ ❝❛❞❡✐❛ ♣r♦❞✉t✐✈❛ ♥♦s ♠❛✐s ❞✐❢❡r❡♥t❡s s❡❣♠❡♥t♦s✳
❈❛♣ít✉❧♦ ✶ ✲ ■♥tr♦❞✉çã♦ ✷
❝♦♠♣♦s✐çã♦✱ ✐♥ú♠❡r❛s s✉❜stâ♥❝✐❛s q✉í♠✐❝❛s ❝♦♠♦ á❝✐❞♦s ✭♥✐tr❛t♦s ❡ s✉❧❢❛t♦s✮✱ ❝♦♠♣♦st♦s ♦r❣â♥✐❝♦s✱ s✐❧✐❝♦♥❡s ❡ ó①✐❞♦s ♠❡tá❧✐❝♦s✳
❉✐✈❡rs❛s ♣❡sq✉✐s❛s ♥❛ ár❡❛ ❞❛ ❡♣✐❞❡♠✐♦❧♦❣✐❛ ❡ t♦①✐❝♦❧♦❣✐❛ ❛tr✐❜✉❡♠ q✉❡✱ q✉❛♥t♦ ♠❡✲ ♥♦r ❛ ❞✐♠❡♥sã♦ ❞❛s ♣❛rtí❝✉❧❛s ❡①♣♦st❛s ♥♦ ❛r✱ ♠❛✐♦r é ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❞♦❡♥ç❛s ❝❛r❞✐♦✲ r❡s♣✐r❛tór✐❛s ❬❍✉❛♥❣ ❡t ❛❧✳ ✭✷✵✵✹✮❪✳ P❛rtí❝✉❧❛s ♠❡♥♦r❡s q✉❡ ✶✵ µm ❣❡r❛❧♠❡♥t❡ ♥ã♦ sã♦
r❡♠♦✈✐❞❛s ♣❡❧♦ s✐st❡♠❛ r❡s♣✐r❛tór✐♦ s✉♣❡r✐♦r ❡✱ ♣♦r ❝♦♥s❡q✉ê♥❝✐❛✱ ❛❝❛❜❛♠ ❛t✐♥❣✐♥❞♦ ♦s ❛❧✈é♦❧♦s ♣✉❧♠♦♥❛r❡s ❡ ❛ ❝♦rr❡♥t❡ s❛♥❣✉í♥❡❛ ✲ ❞❡st❡ ❢❛t♦ s✉r❣✐✉ ♦ ❝♦♥❝❡✐t♦ ❞❡ P▼10✱ q✉❡
sã♦ ❛s ♣❛rtí❝✉❧❛s r❡s♣✐rá✈❡✐s ❞❡ ❛❧t♦ r✐s❝♦✳ ➱ ♥♦tór✐♦ q✉❡ ❛ ❡♠✐ssã♦ ❞❡ ♠❛t❡r✐❛✐s ♣❛rt✐❝✉❧❛✲ ❞♦s ♠❡r❡❝❡ ♠✉✐t❛ ❛t❡♥çã♦✱ ♠❛✐s ❛✐♥❞❛ ❛q✉❡❧❡s q✉❡ ❛❜r❛♥❣❡♠ ❢❛✐①❛s ♥❛♥♦♠étr✐❝❛s✱ ❝♦♠♦ ♦ ❝♦♥tr♦❧❡ ❞❛s ❝❤❛♠❛❞❛s ♣❛rtí❝✉❧❛s r❡s♣✐rá✈❡✐s ❞❡ ❛❧t♦ r✐s❝♦ P▼2,5 ✲ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛
♠❛t❡r✐❛❧ ♣❛rt✐❝✉❧❛❞♦ ❝♦♠ ❞✐â♠❡tr♦ ♠❡♥♦r ♦✉ ✐❣✉❛❧ ❛ ✷✱✺ µm ✲ ♦ q✉❡ ❝❡rt❛♠❡♥t❡ ❧❡✈❛rá à
❛❝❡❧❡r❛çã♦ ❞❛ t❡❝♥♦❧♦❣✐❛ ❞❡ ♠❡❞✐❞❛ ❞❡ ♣❛rtí❝✉❧❛s ✉❧tr❛✲✜♥❛s ❬❆❧❧❡② ✭✶✾✾✽✮❪✳
❉❡st❛ ♠❛♥❡✐r❛✱ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ r❡❝❡♥t❡s ❡st✉❞♦s ✈❡♠ ❞❡♠♦♥str❛♥❞♦ ♦ r✐s❝♦ ❞❛ ❡①♣♦s✐çã♦ às ♣❛rtí❝✉❧❛s ♥❛♥♦♠étr✐❝❛s✱ ❝♦♠♦ ♦s ❞❡ ▲✐ ❡ ❈❤❡♥ ✭✷✵✶✶✮✱ ❑✉♠❛r ❡t ❛❧✳ ✭✷✵✶✵✮✱ ❘♦❞rí❣✉❡③ ❡t ❛❧✳ ✭✷✵✶✷✮ ❡ ▼✐r♠❡ ✭✷✵✶✶✮✱ q✉❡ r❡ss❛❧t❛♠ ♣r♦❜❧❡♠❛s r❡s♣✐r❛tór✐♦s✱ ❞❡ ♣✉❧♠ã♦✱ ❞❡♥tr❡ ♦✉tr♦s✱ às ♣❡ss♦❛s ❡①♣♦st❛s ❛ ❡❧❛s✳ ❊st❛s ♣❛rtí❝✉❧❛s ✲ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ó①✐❞♦s ❞❡ ♥✐tr♦❣ê♥✐♦✱ ❞❡ ❡♥①♦❢r❡ ❡ ❞❡ ❝❛r❜♦♥♦ ✲ sã♦ ❧❛♥ç❛❞❛s ♥❛ ❛t♠♦s❢❡r❛ ❞❡ ❞✐✈❡rs❛s ♠❛♥❡✐r❛s✱ ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❛ ♣♦❧✉✐çã♦ ❛t♠♦s❢ér✐❝❛✱ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ✉r❜❛♥♦✱ ✐♥❞✉str✐❛❧ ❡ ❛ ❝r❡s❝❡♥t❡ ✉t✐❧✐③❛çã♦ ❞❡ ✈❡í❝✉❧♦s ♠♦t♦r✐③❛❞♦s✱ ♦ q✉❡ s❡ r❡✢❡t❡ ❝❛❞❛ ✈❡③ ♠❛✐s ❡♠ ❡❢❡✐t♦s ♥❡❣❛t✐✈♦s ♥♦ ❡q✉✐❧í❜r✐♦ ❞♦s ❡❝♦ss✐st❡♠❛s ❬❆ss✉♠♣çã♦ ✭✷✵✵✻✮❪✳
◗✉❛♥❞♦ s❡ ❢❛❧❛ ❡♠ ♠❛t❡r✐❛❧ ♣❛rt✐❝✉❧❛❞♦ ♥♦ ❛♠❜✐❡♥t❡✱ ❧♦❣♦ s✉r❣❡ ❛ ❞❡✜♥✐çã♦ ❞❡ ❛❡✲ r♦ss♦❧✳ ❆ ❛t♠♦s❢❡r❛ t❡rr❡str❡ é ✉♠ ❛❡r♦ss♦❧✱ ✉♠❛ ♠✐st✉r❛ ❞❡ ❣❛s❡s ❡ ♣❛rtí❝✉❧❛s ❧íq✉✐❞❛s ❡ só❧✐❞❛s s✉s♣❡♥s❛s ♥❡❧❛ ❬❋✉❝❤s ✭✶✾✻✹✮❪✳ ❖ ♠❛t❡r✐❛❧ ♣❛rt✐❝✉❧❛❞♦ ❞❡ ✉♠ ❛❡r♦ss♦❧ ❛t♠♦s❢ér✐❝♦ é ❝♦♥st✐t✉í❞♦ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣♦❧✉❡♥t❡s ❢♦r♠❛❞♦ ♣♦r ♣♦❡✐r❛s✱ ❢✉♠❛ç❛s ❡ t♦❞♦ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ só❧✐❞♦ ❡ ❧íq✉✐❞♦ q✉❡ s❡ ♠❛♥té♠ s✉s♣❡♥s♦ ♥❛ ❛t♠♦s❢❡r❛ ❞❡✈✐❞♦ ❛♦ s❡✉ ♣❡q✉❡♥♦ t❛♠❛♥❤♦✳ ❖ ♠❛t❡r✐❛❧ ♣❛rt✐❝✉❧❛❞♦ ♣♦❞❡ t❛♠❜é♠ s❡ ❢♦r♠❛r ♥❛ ❛t♠♦s❢❡r❛ ❛ ♣❛rt✐r ❞❡ ❣❛s❡s ❝♦♠♦ ❞✐ó①✐❞♦ ❞❡ ❡♥①♦❢r❡ ✭SO2✮✱ ó①✐❞♦s ❞❡ ♥✐tr♦❣ê♥✐♦ ✭N Ox✮ ❡ ❝♦♠♣♦st♦s ♦r❣â♥✐❝♦s ✈♦❧át❡✐s
✭COVs✮✱ q✉❡ sã♦ ❡♠✐t✐❞♦s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♠ ❛t✐✈✐❞❛❞❡s ❞❡ ❝♦♠❜✉stã♦✱ tr❛♥s❢♦r♠❛♥❞♦✲s❡
❡♠ ♣❛rtí❝✉❧❛s ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❡ r❡❛çõ❡s q✉í♠✐❝❛s ♥♦ ❛r ❝♦♠♦ ❞❡s❝r✐t♦ ❡♠ ❬❈❡t❡s❜ ✭✷✵✵✽✮❪✳
❊♠ ❝♦♥tr❛♣❛rt✐❞❛✱ ❡①✐st❡ ✉♠❛ t❡♥❞ê♥❝✐❛ ♥❛ ✉t✐❧✐③❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ❞✐♠❡♥sõ❡s tã♦ ♣❡q✉❡♥❛s✱ ❛❞✈✐♥❞❛ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s✱ ♠❡❝â♥✐❝❛s✱ ♠❛❣♥ét✐❝❛s ❡ q✉í♠✐❝❛s q✉❡ ❡st❛s ♣❛rtí❝✉❧❛s ♣♦❞❡♠ ❛♣r❡s❡♥t❛r ❬❈❤❡♥ ❡t ❛❧✳ ✭✶✾✾✽✮❪ ✲ ♦ ❛♣r♦✈❡✐t❛♠❡♥t♦ ❞❡st❛s ♣r♦♣r✐❡❞❛❞❡s ❡♠ ❛♣❧✐❝❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s ❢♦r♠❛ ❛ ❜❛s❡ ❞❛ ♥❛♥♦t❡❝♥♦❧♦❣✐❛ ❞❡ ♠❛t❡r✐❛✐s✳ ◆♦ ✼♦ ❙❡♠✐✲
♥ár✐♦ ■♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ◆❛♥♦t❡❝♥♦❧♦❣✐❛✱ ❙♦❝✐❡❞❛❞❡ ❡ ▼❡✐♦ ❆♠❜✐❡♥t❡ q✉❡ ♦❝♦rr❡✉ ♥♦ ❘✐♦ ❞❡ ❏❛♥❡✐r♦ ❡♠ ♥♦✈❡♠❜r♦ ❞❡ ✷✵✶✶✱ ❢♦r❛♠ ❛❜♦r❞❛❞♦s t❡♠❛s ❞♦ t✐♣♦ “◆❛♥♦t❡❝♥♦❧♦❣✐❛s ❡
s❛ú❞❡ ✲ ✉s♦s ❛t✉❛✐s ❡ ♥♦s ♣ró①✐♠♦s ✶✵ ❛ ✶✺ ❛♥♦s”✱ “◆❛♥♦♠❡❞✐❝✐♥❛✿ ♥♦✈♦s s✐st❡♠❛s ❞❡
❈❛♣ít✉❧♦ ✶ ✲ ■♥tr♦❞✉çã♦ ✸
❜r❛s✐❧❡✐r❛s ❡♠ s❛ú❞❡✱ ❜❡❧❡③❛✱ ❛❧✐♠❡♥t♦s ❡ ❛❣r✐❝✉❧t✉r❛”✱“❊❢❡✐t♦s à s❛ú❞❡ ❞❡ ♥❛♥♦♠❛t❡r✐❛✐s
❝❛r❜♦♥á❝❡♦s✿ ❞♦s ♠❡❝❛♥✐s♠♦s às ❝♦♥s❡q✉ê♥❝✐❛s r❡❣✉❧❛tór✐❛s” ❡ “◆♦✈❛s t❡❝♥♦❧♦❣✐❛s✱ ét✐❝❛
❡ s♦❝✐❡❞❛❞❡”✳ ◆❛ ♣r✐♠❡✐r❛ ❛♥á❧✐s❡ ❞♦ ❛ss✉♥t♦✱ ♣♦❞❡✲s❡ ♥♦t❛r ❛ ❣❛♠❛ ❞❡ ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡
❛♣❧✐❝❛çã♦ ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s ❡ ❛ t❡♥❞ê♥❝✐❛ ❞❡ s✉❛ ❡①♣❛♥sã♦ ♣❛r❛ ❛s ♣ró①✐♠❛s ❞é❝❛❞❛s✳
❊♠ s❡ tr❛t❛♥❞♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦♠ ❞✐♠❡♥sõ❡s tã♦ í♥✜♠❛s✱ s✐t✉❛çã♦ ❛ q✉❛❧ ♥❡♠ ♠❡s♠♦ ❛ ❢ís✐❝❛ ❝❧áss✐❝❛ ❝♦♥s❡❣✉❡ ❞❡s❝r❡✈❡r ❝♦♠ ❡①❛t✐❞ã♦✱ ♣❡r❝❡❜❡✲s❡ ❛ ❡①tr❡♠❛ ❢❛❝✐❧✐❞❛❞❡ ❞❡ ♣❡✲ ♥❡tr❛çã♦ q✉❡ ❡❧❛s ♣♦ss✉❡♠✱ ❞❡✈✐❞♦ à s✉❛ ♠❛ss❛ q✉❛s❡ ❞❡s♣r❡③í✈❡❧ ❡ ❛♦ s❡✉ t❛♠❛♥❤♦ ♠✉✐t❛s ✈❡③❡s ♠❡♥♦r q✉❡ ♦s ♦❜stá❝✉❧♦s q✉❡ ❡❧❛ ✈❡♥❤❛ ❛ ❛tr❛✈❡ss❛r✳
❇❛s❡❛❞♦ ♥♦s ♠♦t✐✈♦s ❡①♣♦st♦s ❛♥t❡r✐♦r♠❡♥t❡✱ t♦r♥❛✲s❡ ❡✈✐❞❡♥t❡ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ s❡ ♣r♦❞✉③✐r ♥❛♥♦♣❛rtí❝✉❧❛s ♣♦❧✐❞✐s♣❡rs❛s✱ ♦✉ s❡❥❛✱ ❝♦♠ ❞✐❢❡r❡♥t❡s t❛♠❛♥❤♦s ❞❡ ♣❛rtí❝✉❧❛✳ ❊ t❛♠❜é♠ ✐♠♣r❡s❝✐♥❞í✈❡❧✱ ❛ ♣❛rt✐r ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♣♦❧✐❞✐s♣❡rs❛s ❡ ❛tr❛✈és ❞❡ ♠ét♦❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ♦❜t❡r ♣❛rtí❝✉❧❛s ♥❛♥♦♠étr✐❝❛s ♠♦♥♦❞✐s♣❡rs❛s ✲ q✉❡ s❡ ❡♥❝♦♥tr❛♠ ❡♠ ✉♠❛ ❡str❡✐t❛ ❢❛✐①❛ ❞❡ ❞✐â♠❡tr♦s✳ ❆ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ❞❡ ❞✐❢❡r❡♥t❡s ❡❧❡♠❡♥t♦s q✉í♠✐❝♦s ♣❛r❛ ❞✐✈❡rs♦s ✜♥s é ✐♠❡♥s❛✱ ❜❡♠ ❝♦♠♦ ♠❛♥t❡r ♦s ♥í✈❡✐s ❞❡ P▼10 ❡ P▼2,5 ❡♠
♥í✈❡✐s t♦❧❡rá✈❡✐s✳ ❏✉st✐✜❝❛✲s❡✱ ♣♦rt❛♥t♦✱ ♦ ❡s❝♦♣♦ ❞❛ ♣r❡s❡♥t❡ t❡s❡✱ ♣r♦❞✉③✐r ♥❛♥♦♣❛rtí❝✉❧❛s ♠♦♥♦❞✐s♣❡rs❛s ❛tr❛✈és ❞❛ té❝♥✐❝❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ♣♦r ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛✳
❆ ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ é ❛ ❤❛❜✐❧✐❞❛❞❡ q✉❡ ✉♠❛ ♣❛rtí❝✉❧❛ ❝❛rr❡❣❛❞❛ t❡♠ ❞❡✱ ❛♦ ❡♥tr❛r ♥♦ ❉▼❆ ✭❆♥❛❧✐s❛❞♦r ❞❡ ▼♦❜✐❧✐❞❛❞❡ ❉✐❢❡r❡♥❝✐❛❧✮✱ ❛tr❛✈❡ss❛r ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡ s❡r ❛tr❛í❞❛ ♣❡❧♦ ❡❧❡tr♦❞♦ s✉❥❡✐t♦ ❛ ✉♠❛ t❡♥sã♦✳ P♦❞❡✲s❡ ❞❡t❡r♠✐♥❛r ♦s t❛♠❛♥❤♦s ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ✐♥t❡r❡ss❡ q✉❡ s❡rã♦ ❝❛♣t✉r❛❞♦s ❛❥✉st❛♥❞♦✲s❡ ❛ t❡♥sã♦ ❛♣❧✐❝❛❞❛✱ ✈✐st♦ q✉❡ ❛♣❡♥❛s ✉♠❛ ♣❡q✉❡♥❛ ❢❛✐①❛ ❞❡ ❞✐â♠❡tr♦s ❞❡ ♣❛rtí❝✉❧❛s ❝♦♥s❡❣✉✐rã♦ ❛❧❝❛♥ç❛r ❛ ❡str❡✐t❛ ❢❡♥❞❛ ❧♦❝❛❧✐③❛❞❛ ♥♦ ✜♥❛❧ ❞♦ ❡❧❡tr♦❞♦✳ ❖ ❡st✉❞♦ ❞❡st❡ ♣r♦❝❡❞✐♠❡♥t♦ s❡rá ❛ t❡♠át✐❝❛ ♣r✐♥❝✐♣❛❧ ❞❡st❛ t❡s❡✳
❉❡♥tr❡ ♦s ♦❜❥❡t✐✈♦s ❞❛ t❡s❡✱ ❞❡st❛❝❛♠✲s❡✿
• Pr♦❥❡t❛r ✉♠ ❆♥❛❧✐s❛❞♦r ❞❡ ▼♦❜✐❧✐❞❛❞❡ ❉✐❢❡r❡♥❝✐❛❧ ✭❉▼❆✮❀
• ❈♦♥str✉✐r ✉♠ ❉▼❆✱ ❜❡♠ ❝♦♠♦ ♠♦♥t❛r ♦ ❛♣❛r❛t♦ ❡①♣❡r✐♠❡♥t❛❧ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛
❝❧❛ss✐✜❝❛çã♦ ♣♦r ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛❀
• ❆✈❛❧✐❛r ♣r❡❧✐♠✐♥❛r♠❡♥t❡ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❉▼❆✳
❈❛♣ít✉❧♦ ✶ ✲ ■♥tr♦❞✉çã♦ ✹
❈❆P❮❚❯▲❖ ✷
❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
◆
❡st❡ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ♣✉❜❧✐❝❛çõ❡s ♠❛✐s r❡♣r❡s❡♥t❛t✐✈❛s ♥♦ q✉❡ ❞✐③r❡s♣❡✐t♦ ❛♦ ❆♥❛❧✐s❛❞♦r ❞❡ ▼♦❜✐❧✐❞❛❞❡ ❉✐❢❡r❡♥❝✐❛❧ ✭❉▼❆✮✱ ❞❡s❞❡ ♦ s❡✉ ✐♥✈❡♥t♦ ❛té ❛s ú❧t✐♠❛s ✐♥♦✈❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s q✉❡ s✉r❣✐r❛♠ ❞♦ ♣r♦❝❡ss♦ ❡✈♦❧✉t✐✈♦ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s✳❆ ❤✐stór✐❛ ❞❛ ♠❡❞✐❞❛ ❞❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ❛❡r♦ssó✐s ❞❛t❛ ❞❛ ♣r✐✲ ♠❡✐r❛ ♠❡t❛❞❡ ❞♦ sé❝✉❧♦ ❳❳✳ ❖ ♠ét♦❞♦ ❞❡ ❞❡t❡r♠✐♥❛çã♦ ♣♦r ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ❢♦✐ ✐♥✐❝✐✲ ❛❧♠❡♥t❡ ✉s❛❞♦ ♣❛r❛ ♠❡❞✐r ❛ ♠♦❜✐❧✐❞❛❞❡ ❞❡ í♦♥s ❡♠ ❣❛s❡s ❬❊r✐❦s♦♥ ✭✶✾✷✷✮✱ ❩❡❧❡♥② ✭✶✾✷✾✮❪ ❡ ♥❛ ❛t♠♦s❢❡r❛ ❬❊r✐❦s♦♥ ✭✶✾✷✼✮✱ ❈❤❛♣♠❛♥ ✭✶✾✸✼✮❪✳ ❘♦❤♠❛♥♥ ✭✶✾✷✸✮ ✐♥✈❡st✐❣♦✉ ❡ ❡♠♣r❡❣♦✉ ❡st❡ ♠ét♦❞♦ ♣❛r❛ ♠❡❞✐r ♦ t❛♠❛♥❤♦ ❞❡ ♣❛rtí❝✉❧❛s ♥♦ ❛r ❛t♠♦s❢ér✐❝♦✳ ❊♥tr❡ ♦s ♣r✐♠❡✐r♦s ❡ ♠❛✐s ♥♦tá✈❡✐s ❡st✉❞♦s ❞❡st❛❝❛♠✲s❡ ❛q✉❡❧❡s r❡❛❧✐③❛❞♦s ♣♦r ❍❡✇✐tt ✭✶✾✺✼✮✱ ❲❤✐t❜② ❡ ❈❧❛r❦ ✭✶✾✻✻✮✱ ▲✐✉ ❡ P✉✐ ✭✶✾✼✹❜✮✱ ❑♥✉ts♦♥ ❡ ❲❤✐t❜② ✭✶✾✼✺✮ ❡ ▲✐✉ ❡ P✉✐ ✭✶✾✼✺✮✳ ❍❡✇✐tt ✭✶✾✺✼✮ ❢♦✐ ✉♠ ❞♦s ♣r✐♠❡✐r♦s ♣❡sq✉✐s❛❞♦r❡s ❛ ❛♣❧✐❝❛r ✉♠ ❞✐s♣♦s✐t✐✈♦ ♣❛r❛ ♠❡❞✐r ❛ ❝❛r❣❛ ❡❧étr✐❝❛ ❞❡ ♣❛rtí❝✉❧❛s ❝❛rr❡❣❛❞❛s✳
❈❛♣ít✉❧♦ ✷ ✲ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✻
❆ r❡❧❛çã♦ ❡♥tr❡ ❛ ❝♦♥❝❡♥tr❛çã♦ ♠❡❞✐❞❛ ❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ t❛♠❛♥❤♦ ❢♦✐ t❡♦r✐❝❛♠❡♥t❡ ❜❡♠ ❞❡s❝r✐t❛ ♣♦r ❍♦♣♣❡❧ ✭✶✾✼✽✮ ❡ ❋✐ss❛♥ ❡t ❛❧✳ ✭✶✾✽✸✮✳ ❲❛♥❣ ❡ ❋❧❛❣❛♥ ✭✶✾✾✵✮ ♠♦str❛r❛♠ q✉❡ ♦s t❡♠♣♦s ❞❡ ♠❡❞✐çã♦ ❞♦ ❉▼P❙ ♣♦❞❡r✐❛♠ s❡r r❡❞✉③✐❞♦s ❛✉♠❡♥t❛♥❞♦ ❛ ✈♦❧t❛❣❡♠ ❛♣❧✐❝❛❞❛ ❝♦♥t✐♥✉❛♠❡♥t❡ ❡♠ ❢♦r♠❛ ❞❡ r❛♠♣❛✳ ❉✉r❛♥t❡ ♦ ♠❡s♠♦ ♣❡rí♦❞♦✱ ✉♠❛ ♥♦✈❛ té❝♥✐❝❛ ❞❡ ♠❡❞✐çã♦ ❣❡r❛❧ ♣❛r❛ ✉♠ ❊❆❆ ❢♦✐ ♣r♦♣♦st❛ ♣♦r ▲❡❤t✐♠❛❦✐ ✭✶✾✽✼✮✳
❋♦✐ ♦❜s❡r✈❛❞♦ q✉❡ ♦ tr❛♥s♣♦rt❡ ❞❡ ♣❛rtí❝✉❧❛s ❞❡♥tr♦ ❞♦ ❉▼❆ é ❛❢❡t❛❞♦ ♣❡❧❛ ❞✐❢✉sã♦ ❜r♦✇♥✐❛♥❛✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ♣❛r❛ ♣❛rtí❝✉❧❛s ♠❡♥♦r❡s ❞♦ q✉❡ ✺✵ ♥♠✳ ■♥✈❡st✐❣❛çõ❡s q✉❛♥t✐t❛✲ t✐✈❛s ❞♦ ❡❢❡✐t♦ ❞❡ ❞✐❢✉sã♦ ❞❛s ♣❛rtí❝✉❧❛s ♥♦ ❉▼❆ ❢♦r❛♠ ♣r✐♠❡✐r♦ r❡❣✐str❛❞❛s ♣♦r ❑♦✉s❛❦❛ ❡t ❛❧✳ ✭✶✾✽✺✮✱ ❑♦✉s❛❦❛ ❡t ❛❧✳ ✭✶✾✽✻✮ ❡ ❙t♦❧③❡♥❜✉r❣ ✭✶✾✽✽✮✳ ❯♠❛ ❝♦♥✜❣✉r❛çã♦ ❝✐❧í♥❞r✐❝❛ ❛❧✲ t❡r♥❛t✐✈❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ♣❛r❛ ♦❢❡r❡❝❡r ✈❛♥t❛❣❡♥s ♥❛ ❡st❛❜✐❧✐❞❛❞❡ ❞❛ ✈❛③ã♦ ❛ ❛❧t❛s t❛①❛s ❞❡ ❡s❝♦❛♠❡♥t♦✱ ♦ q✉❡ ♣♦r s✉❛ ✈❡③ ❛❥✉❞♦✉ ❛ ♠✐♥✐♠✐③❛r ♣❡r❞❛s ♣♦r ❞✐❢✉sã♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❛♥♦♠étr✐❝❛s✳ ❊st❛ ✐❞❡✐❛ ❢♦✐ ♣r♦♣♦st❛ ♣♦r ❘❡✐s❝❤❧ ❡ ❝♦❧❛❜♦r❛❞♦r❡s✱ q✉❡ ❞❡s❡♥✈♦❧✈❡r❛♠ ✉♠ ❉▼❆ ❞♦ t✐♣♦ ❱✐❡♥♥❛ ❬❲✐♥❦❧♠❛②r ❡t ❛❧✳ ✭✶✾✾✶✮❪✳
❯♠ ❝❧❛ss✐✜❝❛❞♦r ❡❧❡tr♦stát✐❝♦ ❝♦♠ ✢✉①♦ r❛❞✐❛❧ ❡♥tr❡ ✉♠ ♣❛r ❞❡ ♣r❛t♦s ✭❞✐s❝♦s ❝✐r❝✉✲ ❧❛r❡s ♣❛r❛❧❡❧♦s✮ ❢♦✐ ✐♥tr♦❞✉③✐❞♦ ♣♦r ❩❤❛♥❣ ❡t ❛❧✳ ✭✶✾✾✺✮✳ ❯♠ ♥❛♥♦✲❉▼❆✱ ❞❡ ♠❡♥♦r ❛❧t✉r❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦✱ ❢♦✐ t❛♠❜é♠ r❡❧❛t❛❞♦ ♣♦r ❈❤❡♥ ❡t ❛❧✳ ✭✶✾✾✻✮ ♣❛r❛ ♠✐♥✐♠✐③❛r ♣❡r❞❛s ❞✐❢✉✲ s✐♦♥❛✐s ❞❡ ♣❛rtí❝✉❧❛s ❡ ❡s♣❛❧❤❛♠❡♥t♦ ❞✐❢✉s✐♦♥❛❧✳ ❈❤❡♥ ❡ P✉✐ ✭✶✾✾✼✮ ❡ ❈❤❡♥ ❡t ❛❧✳ ✭✶✾✾✽✮ ✉s❛r❛♠ ♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ♣❛r❛ ♠❡❧❤♦r❛r ♦ ♣r♦❥❡t♦ ❞♦ ❉▼❆✳ ❉❡ ▲❛ ▼♦r❛ ❡ ❝♦❧❛❜♦r❛❞♦✲ r❡s ♠♦str❛r❛♠ q✉❡ ♦s ❡❢❡✐t♦s ♣r❡❥✉❞✐❝✐❛✐s ❞❛ ❞✐❢✉sã♦ ♣♦❞❡♠ s❡r ❡❧✐♠✐♥❛❞♦s ♣❛r❛ ♦ ❉▼❆ ❞♦ t✐♣♦ ❱✐❡♥♥❛ s❡ ♣❡q✉❡♥❛s ♠♦❞✐✜❝❛çõ❡s ❞❡ ♣r♦❥❡t♦ ❢♦r❡♠ ✐♥❝♦r♣♦r❛❞❛s q✉❡ ♣❡r♠✐t❛♠ ♦♣❡r❛çã♦ ❛ ❛❧t❛s t❛①❛s ❞❡ ✈❛③ã♦ ❬❘♦s❡❧❧✲▲❧♦♠♣❛rt ❡t ❛❧✳ ✭✶✾✾✻✮✱ ❙❡t♦ ❡t ❛❧✳ ✭✶✾✾✼✮✱ ❏✉❛♥ ❡ ▼♦r❛ ✭✶✾✾✽✮✱ ❘♦ss❡r ❡ ▼♦r❛ ✭✷✵✵✺✮❪✳
❉✐❢❡r❡♥t❡s ❛rr❛♥❥♦s ❢♦r❛♠ t❡st❛❞♦s ❡ ❝♦♠♣❛r❛❞♦s ♣❛r❛ ❛✈❛❧✐❛r ♦s s❡✉s ❞❡s❡♠♣❡♥❤♦s ❬♣♦r ❡①❡♠♣❧♦ ❋✐ss❛♥ ❡t ❛❧✳ ✭✶✾✾✻✮✱ ❇r✐♠✐❧✐ ❡t ❛❧✳ ✭✶✾✾✼✮✱ ❋❧❛❣❛♥ ✭✶✾✾✾✮✱ ▼❛rt✐♥ss♦♥ ❡t ❛❧✳ ✭✷✵✵✶✮✱ ❑❛r❧ss♦♥ ❡ ▼❛rt✐♥ss♦♥ ✭✷✵✵✸✮❪ ❡ ♣❛r❛ ❡①♣❛♥❞✐r ❛ ❢❛✐①❛ ❞❡ ♠❡❞✐çã♦✳ ❯♠ ❉▼❆ ❞❡ ❝♦❧✉♥❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❛❥✉stá✈❡❧ ♣❛r❛ ♠❡❞✐çõ❡s ❞❡ ❛♠♣❧❛ ❢❛✐①❛ ❞❡ t❛♠❛♥❤♦ ❞❡ ♣❛rtí❝✉❧❛ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❙❡♦❧ ❡t ❛❧✳ ✭✷✵✵✷✮✳ ❙❤✐♠❛❞❛ ❡t ❛❧✳ ✭✷✵✵✺✮ ❞❡s❡♥✈♦❧✈❡r❛♠ ✉♠ ❧♦♥❣♦ s✐st❡♠❛ ❞❡ ❡❧❡trô♠❡tr♦s ❝❤❛♠❛❞♦ ❆♥❛❧✐s❛❞♦r ❞❡ ▼♦❜✐❧✐❞❛❞❡ ❉✐❢❡r❡♥❝✐❛❧ ❝♦♣♦ ❞❡ ❋❛r❛❞❛②✱ ❝❛♣❛③ ❞❡ ♠❡❞✐r t❛♠❛♥❤♦s ❞❡ ♣❛rtí❝✉❧❛ ♠❛✐♦r❡s ❞♦ q✉❡ ✶ µ♠✳
✷✳✶✳ ◆❛♥♦♣❛rtí❝✉❧❛s ✼
q✉❡ ♦ ❊❆❙✳ ❇✐s❦♦s ❡t ❛❧✳ ✭✷✵✵✺✮ ♠❛✐s t❛r❞❡ r❡❧❛t❛r❛♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ✐♥✈❡st✐❣❛çã♦ ❞❡ ✉♠ ❡s♣❡❝trô♠❡tr♦ ❞❡ ♠♦❜✐❧✐❞❛❞❡ ❞✐❢❡r❡♥❝✐❛❧ ✭❉▼❙✮✱ ❞❡r✐✈❛❞♦ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ●r❛s❦♦✇✳
❯♠ ❉▼❆ ❞♦ t✐♣♦ ❞✉♣❧♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❚❛❦❡✉❝❤✐ ❡t ❛❧✳ ✭✷✵✵✺✮✱ ♦ q✉❛❧ ♣♦❞❡ ❞❡t❡❝t❛r ❝♦♥❝❡♥tr❛çõ❡s tr❛♥s✐❡♥t❡s ❞♦ ♥ú♠❡r♦ ❞❡ ♥❛♥♦♣❛rtí❝✉❧❛s ♥♦ ❛r ❛t♠♦s❢ér✐❝♦✱ ❝♦♠ ❞✐â♠❡tr♦s ♥❛ ❢❛✐①❛ ❞❡ ✶✵✲✶✵✵ ♥♠✱ ❡♠ ❣❛s❡s ❞❡ ❡s❝❛♣❡ ❞❡ ❛✉t♦♠ó✈❡✐s✳ ❇❛s❡❛❞♦ ❡♠ ♣r✐♥❝í✲ ♣✐♦s s✐♠✐❧❛r❡s ❛♦s ✐♥str✉♠❡♥t♦s ♠❡♥❝✐♦♥❛❞♦s ♣r❡✈✐❛♠❡♥t❡✱ ■♥tr❛ ❡ ❚✐♣♣❛②❛✇♦♥❣ ❞❛ ❯♥✐✲ ✈❡rs✐❞❛❞❡ ▼❛✐ ❈❤✐❛♥❣ ♥❛ ❚❛✐❧â♥❞✐❛✱ ❞❡s❡♥✈♦❧✈❡r❛♠✱ ❝♦♥str✉ír❛♠ ❡ t❡st❛r❛♠ ✉♠ s❡♥s♦r ❞❡ ♠♦❜✐❧✐❞❛❞❡ ❡❧étr✐❝❛ ♠✉❧t✐✲❝❛♥❛❧ ♣❛r❛ ♠❡❞✐çõ❡s ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ t❛♠❛♥❤♦ ❞❡ ❛❡r♦ss♦❧ ♥❛ ❢❛✐①❛ ❞❡ ✶✵✲✶✵✵✵ ♥♠ ❬■♥tr❛ ✭✷✵✵✻✮✱ ■♥tr❛ ❡ ❚✐♣♣❛②❛✇♦♥❣ ✭✷✵✵✻❛✮✱ ■♥tr❛ ❡ ❚✐♣♣❛②❛✇♦♥❣ ✭✷✵✵✻ ❜✮✱ ■♥tr❛ ❡ ❚✐♣♣❛②❛✇♦♥❣ ✭✷✵✵✽✮❪✳
▼✉✐t♦ ❛✉t♦r❡s tê♠ r❡❝♦rr✐❞♦ ❛♦ ❛rr❛♥❥♦ ❞❡ ❉▼❆s ❡♠ sér✐❡ ♣❛r❛ ♠❡❧❤♦r❛r ❛ ♠♦♥♦❞✐s✲ ♣❡rs✐✈✐❞❛❞❡ ❞❡ ✉♠ ❛❡r♦ss♦❧ ❝❧❛ss✐✜❝❛❞♦✳ ▲üö♥❞ ❡ ❙❝❤❧❛tt❡r ✭✷✵✶✸✮ ✉t✐❧✐③❛r❛♠ ❡st❛ té❝♥✐❝❛ ❡ t❛♠❜é♠ ❛ s✐♠✉❧❛çã♦ ♥✉♠ér✐❝❛ ♣❛r❛ ♦t✐♠✐③❛r ♦ ❝❛rr❡❣❛♠❡♥t♦ ✉♥✐♣♦❧❛r ❞❛s ♣❛rtí❝✉❧❛s✳ ▼❡✐ ❡t ❛❧✳ ✭✷✵✶✶✮ ❞❡s❡♥✈♦❧✈❡r❛♠ ✉♠ ❉▼❆ ❞❡ ❜❛✐①♦ ❝✉st♦ ♣❛r❛ ✈ár✐❛s ❛♣❧✐❝❛çõ❡s ❡ ♦❜t✐✲ ✈❡r❛♠ r❡s✉❧t❛❞♦s ❞❡ r❡s♦❧✉çã♦ ❝♦♠♣❛rá✈❡✐s ❛♦s ❞♦ ♥❛♥♦✲❉▼❆✱ ❝♦♥s✐❞❡r❛❞♦s ♦s ♠❡❧❤♦r❡s ❡♠ ✈✐rt✉❞❡ ❞♦ ♣❡q✉❡♥♦ ❞❡s✈✐♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦✳
◆❡st❛ t❡s❡✱ ✉♠❛ r❡✈✐sã♦ ❞❛ t❡♦r✐❛ ❛ r❡s♣❡✐t♦ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❉▼❆s ❝✐❧í♥❞r✐❝♦s ❡①✐st❡♥t❡s ♣❛r❛ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ t❛♠❛♥❤♦s ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ❛❡r♦ss♦❧ ♥❛♥♦♠étr✐❝❛s✱ ❜❡♠ ❝♦♠♦ ♦s ♣r✐♥❝í♣✐♦s ❜ás✐❝♦s ❞❡ ♦♣❡r❛çã♦ ❡ ❝❛r❛❝t❡ríst✐❝❛s ❢ís✐❝❛s ❞❡t❛❧❤❛❞❛s sã♦ ❞❡s❝r✐t♦s✳
✷✳✶ ◆❛♥♦♣❛rtí❝✉❧❛s
◆♦s ú❧t✐♠♦s ❛♥♦s ❛ ♣❡sq✉✐s❛ ❝✐❡♥tí✜❝❛ ❛❝❡r❝❛ ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s t❡♠ s❡ ✐♥t❡♥s✐✜❝❛❞♦✱ q✉❡r ♣♦r s✉❛s ❝❛r❛❝t❡ríst✐❝❛s s✐♥❣✉❧❛r❡s q✉❛♥❞♦ ❢❛③❡♠ ♣❛rt❡ ❞❛ ❡str✉t✉r❛ ❞❡ ❛❧❣✉♠ ♣r♦✲ ❞✉t♦✱ q✉❡r ❡♠ ✈✐rt✉❞❡ ❞♦s ♣r♦❜❧❡♠❛s q✉❡ ❝❛✉s❛♠ q✉❛♥❞♦ ❞✐s♣❡rs❛s ♥♦ ❛r ❛t♠♦s❢ér✐❝♦✳ ❯♠❛ q✉❡stã♦ ✐♠♣♦rt❛♥t❡✱ ❛ ❢❛✐①❛ ❞❡ t❛♠❛♥❤♦ q✉❡ ❛❜r❛♥❣❡ ❛s ♥❛♥♦♣❛rtí❝✉❧❛s✱ ❛✐♥❞❛ é ♠♦t✐✈♦ ❞❡ ❞✐✈❡r❣ê♥❝✐❛s ❡♥tr❡ ❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✳
✷✳✶✳ ◆❛♥♦♣❛rtí❝✉❧❛s ✽
❛ ✉t✐❧✐③❛❞❛ ♣❡❧❛ ❯♥✐t❡❞ ❙t❛t❡s ❊♥✈✐r♦♥♠❡♥t❛❧ Pr♦t❡❝t✐♦♥ ❆❣❡♥❝② ✭❯❙ ❊P❆✮ ❛ss✐♠ ❝♦♠♦ P✉✐ ❡ ❈❤❡♥ ✭✶✾✾✼✮ ❞❡♥♦♠✐♥❛♠ ♣❛rtí❝✉❧❛s ✉❧tr❛✜♥❛s ♦✉ ❛❡r♦ssó✐s ✉❧tr❛✜♥♦s ❛q✉❡❧❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❞✐â♠❡tr♦s ♠❡♥♦r❡s q✉❡ ✶✵✵ ♥♠✳ ❩❤✐q✐❛♥❣ ❡t ❛❧✳ ✭✷✵✵✵✮ ❜❡♠ ❝♦♠♦ ❆♠❛r❛❧ ✭✷✵✶✵✮ ❡♥t❡♥❞❡♠ q✉❡ ❛s ♥❛♥♦♣❛rtí❝✉❧❛s sã♦ ❛q✉❡❧❛s ♠❡♥♦r❡s q✉❡ ✶ µ♠✱ ♦✉ ✶✵✵✵ ♥♠✳ ❊st❛
❞❡✜♥✐çã♦ ❜❛s❡✐❛✲s❡ ♥❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ q✉❡ ❡st❛s✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❛s ♠✐❝r♦♣❛rtí❝✉❧❛s✱ ♥ã♦ sã♦ ✈✐sí✈❡✐s ♣♦r ♥ã♦ ❡s♣❛❧❤❛r❡♠ ❛ ❧✉③ ❡ ❞✐✜❝✐❧♠❡♥t❡ s❡rã♦ r❡♠♦✈✐❞❛s ❞❛ ❝♦rr❡♥t❡ ❣❛s♦s❛ ♣♦r ✐♠♣❛❝t❛çã♦✱ ✉♠❛ ✈❡③ q✉❡ ❛❝♦♠♣❛♥❤❛♠ ♦ ♠♦✈✐♠❡♥t♦ ❞♦ ❣ás q✉❛♥❞♦ ❡s❝♦❛♠ ♣ró①✐♠♦ ❛ ✉♠ ♦❜stá❝✉❧♦ ❬❙t❡✛❡♥s ✭✷✵✵✼✮❪✳ P❛r❛ ✜♥s ♣rát✐❝♦s ❡ ❞❡✈✐❞♦ à ❢r❡q✉❡♥t❡ ❛♣❧✐❝❛çã♦✱ ♥❡st❛ t❡s❡ s❡rá ❛❞♦t❛❞♦ ♦ t❡r♠♦ ♥❛♥♦♣❛rtí❝✉❧❛s ♣❛r❛ ♣❛rtí❝✉❧❛s ❝♦♠ ❞✐â♠❡tr♦ ✐♥❢❡r✐♦r ❛ 1000
♥♠ ♦✉10−6♠✳
✷✳✶✳✶ ❆♣❧✐❝❛çõ❡s ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s
❊①✐st❡ ♠✉✐t♦ ❞❡❜❛t❡ ♥❛s ✐♠♣❧✐❝❛çõ❡s ❢✉t✉r❛s ❞❛ ♥❛♥♦t❡❝♥♦❧♦❣✐❛✱ ♣♦✐s ♦s ❞❡s❛✜♦s sã♦ s❡♠❡❧❤❛♥t❡s ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s✱ ✐♥❝❧✉✐♥❞♦ q✉❡stõ❡s s♦❜r❡ ❛ t♦①✐❝✐✲ ❞❛❞❡ ❡ ✐♠♣❛❝t♦s ❛♠❜✐❡♥t❛✐s ❞♦s ♥❛♥♦♠❛t❡r✐❛✐s✳ ◆♦ ❡♥t❛♥t♦✱ é ♥♦tór✐♦ ♦ ❡❢❡✐t♦ ♣♦t❡♥❝✐❛❧ q✉❡ ❡st❡ t✐♣♦ ❞❡ t❡❝♥♦❧♦❣✐❛ ♣♦❞❡ ❛❣r❡❣❛r ❛ ❡❝♦♥♦♠✐❛ ❣❧♦❜❛❧ ❡ ♦ q✉❛♥t♦ ❡stá ❝❛❞❛ ✈❡③ ♠❛✐s ♣r❡s❡♥t❡ ♥❛ ❝♦♠♣♦s✐çã♦ ❞❡ ✐♥ú♠❡r❛s s✉❜stâ♥❝✐❛s✳
◆❛ ✈✐sã♦ ❞❡ ❈❤❡♥ ❡t ❛❧✳ ✭✶✾✾✽✮ ❛♣✉❞ ❋❡✐t♦s❛ ✭✷✵✵✾✮✱ ♦s ♠❛t❡r✐❛✐s ❝♦♠♣♦st♦s ❞❡ ♣❛r✲ tí❝✉❧❛s ♥❛♥♦♠étr✐❝❛s ❛♣r❡s❡♥t❛♠ ♠❡❧❤♦r✐❛s s✐❣♥✐✜❝❛t✐✈❛s ❡♠ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s✱ ♠❡❝â♥✐❝❛s✱ ❡❧étr✐❝❛s ❡ ♠❛❣♥ét✐❝❛s✱ ❛s q✉❛✐s sã♦ ❞❡s❡❥á✈❡✐s ❡♠ ♠✉✐t❛s ❛♣❧✐❝❛çõ❡s ♥❛ ❡♥❣❡✲ ♥❤❛r✐❛✳ ❈♦♥t✉❞♦✱ ❡①✐st❡♠ ♦✉tr♦s s❡t♦r❡s q✉❡ t❛♠❜é♠ tê♠ ❛♣r❡s❡♥t❛❞♦ ✈❛st❛ ❛♣❧✐❝❛çã♦ ❞❛s ♥❛♥♦♣❛rtí❝✉❧❛s✱ ❝♦♠♦ ❛s ár❡❛s ❞❡ ❢ís✐❝❛✱ ❝♦♠✉♥✐❝❛çõ❡s✱ ❜✐♦t❡❝♥♦❧♦❣✐❛✱ ❛❣r♦♥❡❣ó❝✐♦s✱ s❛ú❞❡✱ ❞❡♥tr❡ ♦✉tr♦s✳
❆s ❛♣❧✐❝❛çõ❡s ♠❛✐s s✐♠♣❧❡s ❞❛ ♥❛♥♦t❡❝♥♦❧♦❣✐❛ ♣♦❞❡♠ s❡r ❛q✉❡❧❛s q✉❡ ✈❡♥❤❛♠ ❛ t❡r ♠❛✐♦r ❞❡st❛q✉❡✳ ◆❛ ❡♥❣❡♥❤❛r✐❛✱ ✉♠❛ ár❡❛ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ♣r♦♠✐ss♦r ❞❛ ♥❛♥♦t❡❝♥♦❧♦✲ ❣✐❛ é ❛ ❣❡r❛çã♦ ❞❡ ❡❧❡tr✐❝✐❞❛❞❡ ❡♠ t❡r♠♦♣❛r s❡♠✐❝♦♥❞✉t♦r ✭❊❢❡✐t♦ ❙❡❡❜❡❝❦✮✳ ❙❛❜❡✲s❡ q✉❡ ❥✉♥çõ❡s s❡♠✐❝♦♥❞✉t♦r❛s ♣♦❞❡♠ ❣❡r❛r ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❛tr❛✈és ❞❛ ❧✉③ r❡❝❡❜✐❞❛ ❡♠ ❝é❧✉❧❛s ❢♦t♦✈♦❧t❛✐❝❛s ❡ ♥❡ss❡ s❡♥t✐❞♦ ❡st✉❞❛✲s❡ ❝♦♥✈❡rt❡r ❝❛❧♦r ❞✐r❡t❛♠❡♥t❡ ❡♠ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❝♦♠ s❡♠✐❝♦♥❞✉t♦r❡s ♥❛ ❡s❝❛❧❛ ♥❛♥♦♠étr✐❝❛✳ ◆❛ ♠❡s♠❛ ❧✐♥❤❛ ❡st✉❞❛✲s❡ r❡❢r✐❣❡r❛r ✉♠ ❛♠❜✐❡♥t❡ ❛tr❛✈és ❞❡ t❡r♠♦♣❛r❡s ❡♠ ❡❢❡✐t♦ ❛♥á❧♦❣♦ ✭❊❢❡✐t♦ P❡❧t✐❡r✮ ❬❲✐❦✐♣❡❞✐❛ ✭✷✵✶✷✮❪✳
◆❛ ❢ís✐❝❛✱ ❛ ❝r✐❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ✉❧tr❛✲❛❜s♦r✈❡♥t❡✱ q✉❡ ❛❜s♦r✈❡ ♠❛✐s ❞❡ ✾✾✱✾✪ ❞❡ t♦❞❛ ❛ ❧✉③ q✉❡ r❡❝❡❜❡ ✭❋♦❧❤❛ ❖♥❧✐♥❡✱ ✷✵✵✽✮ ♣♦❞❡ ♣❡r♠✐t✐r ✉♠ ♥♦✈♦ ♣❛t❛♠❛r ♥♦ ❛♣r♦✈❡✐t❛♠❡♥t♦ ❞❛ r❛❞✐❛çã♦ s♦❧❛r ♣❛r❛ ❣❡r❛çã♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛✳
