❙■❉◆❊❨ ❘■❇❊■❘❖ ❉❆ ❙■▲❱❊■❘❆
❈❖◆❉❯➬➹❖ ❉❊ ❈❆▲❖❘ ❊◆❱❖▲❱❊◆❉❖ ❋❖◆❚❊
▼Ó❱❊▲
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆
❋❆❈❯▲❉❆❉❊ ❉❊ ❊◆●❊◆❍❆❘■❆ ▼❊❈➶◆■❈❆
❙■❉◆❊❨ ❘■❇❊■❘❖ ❉❆ ❙■▲❱❊■❘❆
❈❖◆❉❯➬➹❖ ❉❊ ❈❆▲❖❘ ❊◆❱❖▲❱❊◆❉❖ ❋❖◆❚❊
▼Ó❱❊▲
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲
❣r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼❡❝â♥✐❝❛ ❞❛ ❯♥✐✈❡r✲
s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✱ ❝♦♠♦ ♣❛rt❡ ❞♦s
r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❊❙✲
❚❘❊ ❊▼ ❊◆●❊◆❍❆❘■❆ ▼❊❈➶◆■❈❆✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❚r❛♥s❢❡rê♥❝✐❛ ❞❡ ❈❛❧♦r
❡ ▼❡❝â♥✐❝❛ ❞♦s ❋❧✉✐❞♦s
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ●✐❧♠❛r ●✉✐♠❛rã❡s
Dados Internacionais de Catalogação na Publicação (CIP) Sistema de Bibliotecas da UFU, MG, Brasil.
S587c 2015
Silveira, Sidney Ribeiro da, 1984-
Condução de calor envolvendo fonte móvel / Sidney Ribeiro da Silveira. - 2015.
93 f. : il.
Orientador: Gilmar Guimarães.
Dissertação (mestrado) - Universidade Federal de Uberlândia, Programa de Pós-Graduação em Engenharia Mecânica.
Inclui bibliografia.
1. Engenharia mecânica - Teses. 2. Calor - Condução - Teses. 3. Problemas inversos (Equações diferenciais) - Teses. 4. Green, Funções de - Teses. I. Guimarães, Gilmar. II. Universidade Federal de Uberlândia. Programa de Pós-Graduação em Engenharia Mecânica. III. Título.
❆❣r❛❞❡❝✐♠❡♥t♦s
➚ ●❛❜r✐❡❧❛✱ ♣❡❧❛s ❜♦❛s ✐❞❡✐❛s ❡ ❝♦♠♣❛♥❤❡r✐s♠♦✳
➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦ ❡ ✐♥❝❡♥t✐✈♦✳
❆♦s ❛♠✐❣♦s ❞♦ ▲❚❈▼✿ ●❛❜r✐❡❧❛✱ ❆♥❛ P❛✉❧❛✱ ❋❡r♥❛♥❞♦✱ ❋á❜✐♦✱ ❆❧✐ss♦♥✱ ▲✉✐s✳ P❡❧❛s ❜♦❛s ✐❞❡✐❛s ❞✉r❛♥t❡ ❛ ❝♦♥❝❡♣çã♦ ❞❡st❛ ♣❡sq✉✐s❛✳
❆♦s ❛♠✐❣♦s ❞❛ ❋❊▼❊❈✿ ♣r♦❢❡ss♦r❡s✱ té❝♥✐❝♦s✲❛❞♠✐♥✐str❛t✐✈♦s✱ ▲P▼ ❡ ❛❣r❡❣❛❞♦s✳
❆♦ ●✐❧♠❛r ♣❡❧❛ ❖r✐❡♥t❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❘✐❜❡✐r♦✱ ❙✳ ❙✳ ❈♦♥❞✉çã♦ ❞❡ ❈❛❧♦r ❊♥✈♦❧✈❡♥❞♦ ❋♦♥t❡ ▼ó✈❡❧✳ ✷✵✶✺✳ ✾✸❢✳ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✱ ❯❜❡r❧â♥❞✐❛✲▼●✳
❘❡s✉♠♦
Pr♦❜❧❡♠❛s ❡♥✈♦❧✈❡♥❞♦ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ♣♦❞❡♠ s❡r ♦❜s❡r✈❛❞♦s ❡♠ ❞✐✈❡rs♦s ❛s♣❡❝t♦s ❡ ♥❛s ♠❛✐s ✈❛r✐❛❞❛s ❢♦r♠❛s✱ ♣♦❞❡✲s❡ ❝✐t❛r✿ ❖ ❛q✉❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❝❤❛♣❛ ❡♠ ✉♠ ♣r♦❝❡ss♦ ❞❡ s♦❧✲ ❞❛❣❡♠ ♦✉ ❛ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ♣r♦✈❡♥✐❡♥t❡ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❢✉r❛çã♦ ♦✉ ❝♦rt❡✳ ❆ss✐♠✱ ♣r❡t❡♥❞❡✲s❡✱ ✉s❛♥❞♦ ❢❡rr❛♠❡♥t❛s ❞❡ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❡ ❝♦♥❝❡✐t♦s ❞❡ ❡♥❣❡♥❤❛r✐❛ ❡ ❢ís✐❝❛ ❡st❛❜❡❧❡❝❡r ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦✱ ❛tr❛✈és ❞♦ ❝á❧❝✉❧♦ ❞❡ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ✶❉✱ ✷❉ ❡ ✸❉ ✈❛r✐❛♥❞♦✲s❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❡ ❛♣❧✐❝á✲❧❛ ❛ ✉♠ ♣r♦❝❡ss♦ ❞❡ s♦❧❞❛❣❡♠✳ ❆ ♦❜t❡♥çã♦ ❞❡ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ♣❛r❛ ❡st❡ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛ r❡q✉❡r❡♠ ♣r♦❝❡❞✐♠❡♥t♦s ♠❛✐s ❡❧❛❜♦r❛❞♦s ❛♦s q✉❡ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ♣r♦❜❧❡♠❛s ✜①♦s✱ ❞❡✈✐❞♦ ❛♦s t❡r♠♦s ❛❞✐❝✐♦♥❛✐s q✉❡ s✉r❣❡♠ ♥❛ ❡q✉❛çã♦ ❣♦✈❡r♥❛♥t❡✳ ❊ ❞❡ss❡ ♠♦❞♦✱ ♣r❡t❡♥❞❡✲s❡ ❝♦♥tr✐❜✉✐r ❝♦♠ ❛ ❧✐t❡r❛t✉r❛ ♥❡st❡ ❛s♣❡❝t♦✳ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣❛r❛ r❡s♦❧✈❡r ❛s ❡q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s ♣❛r❝✐❛✐s s❡rá ♦ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥✳ ➱ t❛♠❜é♠ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈❡r ❛ ✈❡r✐✜❝❛çã♦ ❞❛s s♦❧✉çõ❡s ♦❜t✐❞❛s ❛♥❛❧✐t✐❝❛♠❡♥t❡✱ ❢❛③❡r ❝♦♠♣❛r❛çõ❡s à s♦❧✉çõ❡s ♦❜t✐❞❛s ♥✉♠❡r✐❝❛♠❡♥t❡ ❡ ❛♣❧✐❝❛çã♦ à ♣r♦❜❧❡♠❛s ✐♥✈❡rs♦s✳ ◆❡ss❡ ❝❛s♦✱ ♣r♦♣õ❡✲s❡ ❛ ❛♣❧✐❝❛çã♦ ❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ té❝♥✐❝❛ ❚❋❇●❋ ✭tr❛♥s❢❡r ❢✉♥❝t✐♦♥ ❜❛s❡❞ ●r❡❡♥✬s ❢✉♥❝t✐♦♥s✮ ♣❛r❛ ❡st✐♠t✐✈❛ ❞❡ ❛♣♦rt❡ tér♠✐❝♦✳ ❖ ✉s♦ ❞❡ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛ ♠♦♥str♦✉✲s❡✱ ❛♣ós ❝❛❧❝✉❧❛❞❛ ❡ ✈❡r✐✜❝❛✱ ✉♠❛ ❢❡rr❛♠❡♥t❛ r♦❜✉st❛✱ ❞❡ ❢á❝✐❧ ✐♠♣❧❡♠❡♥t❛çã♦✱ ❡ ❞❡ ❜❛✐①♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ q✉❛♥❞♦ ❛♣❧✐❝❛❞❛ ❛ ♣r♦❜❧❡♠❛s ❞✐r❡t♦s ♦✉ ✐♥✈❡rs♦s ❡♠ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ♣♦r ❢♦♥t❡s ♠ó✈❡✐s✳
❘✐❜❡✐r♦✱ ❙✳ ❙✳ ❍❡❛t ❈♦♥❞✉❝t✐♦♥ ■♥✈♦❧✈✐♥❣ ▼♦✈✐♥❣ ❙♦✉r❝❡✳ ✷✵✶✺✳ ✾✸♣✳ ▼❛st❡r✬s ❚❤❡s✐s✱ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✱ ❯❜❡r❧â♥❞✐❛✲▼●✳
❆❜str❛❝t
Pr♦❜❧❡♠s ✐♥✈♦❧✈✐♥❣ ❤❡❛t ❝♦♥❞✉❝t✐♦♥ ❝❛♥ ❜❡ ♦❜s❡r✈❡❞ ✐♥ ♠❛♥② ✇❛②s ❛♥❞ ✐♥ ✈❛r✐♦✉s ❢♦r♠s✱ ✇❡ ❝❛♥ ❜❡ ♠❡♥t✐♦♥❡❞✿ ❤❡❛t✐♥❣ ❛ s❧❛❜ ✐♥ ❛ ✇❡❧❞✐♥❣ ♣r♦❝❡ss ♦r ❤❡❛t ❝♦♥❞✉❝t✐♦♥ ❢r♦♠ ❛ ♣r♦❝❡ss ♦❢ ❞r✐❧❧✐♥❣ ♦r ❝✉tt✐♥❣✳ ❚❤✉s✱ ✐t ✐s ✐♥t❡♥❞❡❞✱ ✉s✐♥❣ ♠❛t❤❡♠❛t✐❝❛❧ ❛♥❛❧②s✐s t♦♦❧s ❛♥❞ ❡♥❣✐♥❡❡r✐♥❣ ❝♦♥❝❡♣ts ❛♥❞ ♣❤②s✐❝❛❧ ❡st❛❜❧✐s❤ t❤✐s t❤❡r♠❛❧ ❜❡❤❛✈✐♦r✱ ❜② ❝❛❧❝✉❧❛t✐♥❣ ✶❉✱ ✷❉ ❛♥❞ ✸❉ tr❛♥s✐❡♥t ❛♥❛❧②t✐❝❛❧ s♦❧✉t✐♦♥s ✈❛r②✐♥❣ ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥s ❛♥❞ ❛♣♣❧② ✐t t♦ ❛ ✇❡❧❞✐♥❣ ♣r♦❝❡ss✳ ❖❜t❛✐♥✐♥❣ ❛♥❛❧②t✐❝❛❧ s♦❧✉t✐♦♥s t♦ t❤✐s ♣r♦❜❧❡♠ r❡q✉✐r❡ ♠♦r❡ ❡❧❛❜♦r❛t❡ ♣r♦❝❡❞✉r❡s t♦ t❤♦s❡ ✉s❡❞ ❢♦r ✜①❡❞ ♣r♦❜❧❡♠s ❜❡❝❛✉s❡ ♦❢ t❤❡ ❛❞❞✐t✐♦♥❛❧ t❡r♠s t❤❛t ❛r✐s❡ ✐♥ t❤❡ ❣♦✈❡r♥✐♥❣ ❡q✉❛t✐♦♥✳ ❆♥❞ s♦✱ ✇❡ ✐♥t❡♥❞ t♦ ❝♦♥tr✐❜✉t❡ t♦ t❤❡ ❧✐t❡r❛t✉r❡ ✐♥ t❤✐s r❡❣❛r❞✳ ❚❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞ ❢♦r s♦❧✈✐♥❣ ♣❛rt✐❛❧ ❞✐✛❡r❡♥t✐❛❧ ❡q✉❛t✐♦♥s ✇✐❧❧ ❜❡ t❤❡ ●r❡❡♥✬s ❢✉♥❝t✐♦♥s ♠❡t❤♦❞✳ ■t ✐s ❛❧s♦ ♦❜❥❡❝t✐✈❡ ♦❢ t❤✐s ✇♦r❦ t♦ ❞❡✈❡❧♦♣ t❤❡ ✈❡r✐✜❝❛t✐♦♥ ♦❢ t❤❡ s♦❧✉t✐♦♥s ♦❜t❛✐♥❡❞ ❛♥❛❧②t✐❝❛❧❧②✱ ♠❛❦✐♥❣ ❝♦♠♣❛r✐s♦♥s t♦ t❤❡ s♦❧✉t✐♦♥s ♦❜t❛✐♥❡❞ ♥✉♠❡r✐❝❛❧❧② ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥ ✐♥ ✐♥✈❡rs❡ ♣r♦❜❧❡♠s✳ ■♥ t❤✐s ❝❛s❡✱ ✐t ✐s ♣r♦♣♦s❡❞ t♦ ❛♣♣❧✐❝❛t✐♦♥ ❛♥❞ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ❚❋❇●❋ t❡❝❤♥✐q✉❡ ❢♦r ❤❡❛t s♦✉r❝❡ ❡st✐♠❛t❡✳ ❚❤❡ ✉s❡ ♦❢ ❛♥❛❧②t✐❝❛❧ s♦❧✉t✐♦♥ s❤♦✇❡❞ ✉♣ ❛❢t❡r ❝❛❧❝✉❧❛t❡❞ ❛♥❞ ❝❤❡❝❦s✱ ❛ r♦❜✉st t♦♦❧✱ ❡❛s② t♦ ✐♠♣❧❡♠❡♥t✱ ❛♥❞ ❧♦✇ ❝♦♠♣✉t❛t✐♦♥❛❧ ❝♦st ✇❤❡♥ ❛♣♣❧✐❡❞ t♦ ❞✐r❡❝t ♦r ✐♥✈❡rs❡ ♣r♦❜❧❡♠s ♦❢ ❤❡❛t ❝♦♥❞✉❝t✐♦♥ ❜② ♠♦✈✐♥❣ s♦✉r❝❡s✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✸✳✶ Pr♦❜❧❡♠❛ ❳✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✷ Pr♦❜❧❡♠❛ ❳✶✶❨✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✸ Pr♦❜❧❡♠❛ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✹ Pr♦❜❧❡♠❛ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✶ ❙♦❧✉ç❛♦ ♣r♦❜❧❡♠❛ ❳✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✹✳✷ ❋♦♥t❡ ♠ó✈❡❧ ❞❡ ❝❛❧♦r ❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ v= 0,001m/s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✹✳✸ ❙♦❧✉ç❛♦ ♣r♦❜❧❡♠❛ ❳✶✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✹ ●rá✜❝♦ ❞♦ ♣r♦❜❧❡♠❛X13 ❝♦♠v= 0,0005m/s♥❛ ✈❛r✐á✈❡❧ x ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✹✳✺ ❙♦❧✉ç❛♦ ♣r♦❜❧❡♠❛ ❳✶✶❨✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✻ ❙♦❧✉ç❛♦ ♣r♦❜❧❡♠❛ ❳✶✶❨✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✼ ❙♦❧✉ç❛♦ ♣r♦❜❧❡♠❛ ❳✶✶❨✶✶②✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✽ ❙♦❧✉ç❛♦ ♣r♦❜❧❡♠❛ ❳✶✶❨✶✶②✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✾ ❈♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ❛ s♦❧✉çã♦ X10 ❡ X11✱v= 0,0001m/s✱t= 30s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✹✳✶✵ ❉✐❢❡r❡♥ç❛ ❡♥tr❡ ❛s s♦❧✉çõ❡s X10 ❡X11✱v= 0,0001m/s✱t= 30s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✹✳✶✶ ❆♣r♦①✐♠❛çã♦ ❞❛ s♦❧✉çã♦ ❳✶✶ s♦❜r❡ ❳✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✶✷ ❆♣r♦①✐♠❛çã♦ ❞❛ s♦❧✉çã♦ ❳✶✶ s♦❜r❡ ❳✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✸ ❈♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ❛ s♦❧✉çã♦ X10 ❡ X13✱v= 0,0001m/s✱t= 30s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✶✹ ❉✐❢❡r❡♥ç❛s ❛❜s♦❧✉t❛ ❡ r❡❧❛t✐✈❛ ❡♥tr❡ ❛s s♦❧✉çõ❡s ❳✶✵ ❡ ❳✶✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✶✺ ❊sq✉❡♠❛ ♣❛r❛ ✉t✐❧✐③❛çã♦ ❞♦ ♠ét♦❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✶✻ ❈♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ❛s s♦❧✉çõ❡s ❳✶✶ ❡ ❳✶✶❨✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✶✼ ❊sq✉❡♠❛ ♠❡t♦❞♦❧ó❣✐❝♦ ♣❛r❛ ❝♦♠♣❛r❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✶✽ ❈♦♠♣❛r❛t✐✈♦ ❡♥tr❡ ❛s s♦❧✉çõ❡s ❳✶✶ ❡ ❳✶✶❨✶✶❩✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✶✾ ❊sq✉❡♠❛ ❞❡ ❝♦♠♣❛r❛çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ tr✐❞✐♠❡♥s✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷✵ ❈♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ❞❛s s♦❧✉çõ❡s ❳✶✸ ❡ ❳✶✶❨✶✶❩✶✸ ♣❛r❛v= 0,0001m/s❡t= 30s ✻✵
✹✳✷✶ ❉✐❢❡r❡♥ç❛s ❛❜s♦❧✉t❛ ❡ r❡❧❛t✐✈❛ ❡♥tr❡ ❛s s♦❧✉çõ❡s ❳✶✸ ❡ ❳✶✶❨✶✶❩✶✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✷✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛ ❡ ♥✉♠ér✐❝❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❳✶✶✳ ✳ ✳ ✻✸ ✹✳✷✸ P❡r✜❧ ❞❡ t❡♠♣❡r❛t✉r❛ ❡♥tr❡ ❛s s♦❧✉çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✷✹ ❉✐❢❡r❡♥ç❛ ❛❜s♦❧✉t❛ ❡♥tr❡ ❛s s♦❧✉çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷✺ ❈♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ❞❛s s♦❧✉çõ❡s ❳✶✶❨✶✶ ❛♥❛❧ít✐❝❛ ❡ ♥✉♠ér✐❝❛ ♣❛r❛v= 0,0001m/s
❡ t= 30s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✹✳✷✻ ❈♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ❞❛s s♦❧✉çõ❡s ❳✶✶❨✶✶❩✶✶ ❛♥❛❧ít✐❝❛ ❡ ♥✉♠ér✐❝❛ ♣❛r❛ v = 0,0001m/s ❡ t= 30s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✺✳✶ Pr♦❜❧❡♠❛ ❞❡ s♦❧❞❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✐✐
✺✳✷ Pr♦❜❧❡♠❛ ❞❡ s♦❧❞❛❣❡♠ ❡ ♣♦♥t♦s ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ t❡♠♣❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✸ P❡r✜❧ ❞❡ t❡♠♣❡r❛t✉r❛ ♥♦s ♣♦♥t♦s ❞❡s❝r✐t♦s ♣❡❧❛ ❚❛❜✳✺✳✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✹ ❚❡♠♣❡r❛t✉r❛ ♥♦s ♣♦♥t♦s ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ y= 0,02m✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✺✳✺ ❚❡♠♣❡r❛t✉r❛ ♥♦s ♣♦♥t♦s ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ y= 0,07m✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❚✐♣♦s ❡ ♥✉♠❡r❛çã♦ ❞❛s ❈♦♥❞✐çõ❡s ❞❡ ❈♦♥t♦r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✺✳✶ P♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦s ♣♦♥t♦s ❞❡ ❝á❧❝✉❧♦ ❞❡ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✹
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✷✳✷ ❈♦♥❞✉çã♦ ❞❡ ❈❛❧♦r ♣♦r ❋♦♥t❡s ▼ó✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✸ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✶✶
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✸✳✷ ❙♦❧✉çã♦ ●❡r❛❧ 1D tr❛♥s✐❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸✳✷✳✶ ❖ ▼ét♦❞♦ ❞❡ ❋✉♥çõ❡s ❞❡ ●r❡❡♥ ✭❋●✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✸✳✸ ▼♦❞❡❧♦ ❚ér♠✐❝♦ 1D ❚r❛♥s✐❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸✳✸✳✶ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✹ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✺ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶❨✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✻ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✼ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶❨✶✶❩✶✶ s❡ ♠♦✈❡♥❞♦ ♣❡❧♦s ✸ ❡✐①♦s ✭①✱②✱③✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✽ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶❨✶✶❩✶✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✹ ❆✉t♦✈❛❧♦r❡s✱ ❘❡♣r❡s❡♥t❛çã♦ ●rá✜❝❛✱ ❱❡r✐✜❝❛çã♦ ❡ ❈♦♠♣❛r❛çõ❡s ✸✻ ✹✳✶ ❆✉t♦✈❛❧♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✷ ❘❡♣r❡s❡♥t❛çã♦ ●rá✜❝❛ ❞♦s ♣r♦❜❧❡♠❛s ❳✶✶✱ ❳✶✸✱ ❳✶✶❨✶✶ ❡ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✸✽ ✹✳✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ●rá✜❝❛ ❞♦ Pr♦❜❧❡♠❛ ❳✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ●rá✜❝❛ ❞♦ Pr♦❜❧❡♠❛ ❳✶✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✹✳✷✳✸ ❘❡♣r❡s❡♥t❛çã♦ ●rá✜❝❛ ❳✶✶❨✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✷✳✹ ❘❡♣r❡s❡♥t❛çã♦ ●rá✜❝❛ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✸ ❱❡r✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✸✳✶ ❱❡r✐✜❝❛çã♦✱ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✸✳✷ ❱❡r✐✜❝❛çã♦ ❳✶✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸✳✸ ❱❡r✐✜❝❛çã♦ ❳✶✶❨✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✸✳✹ ❱❡r✐✜❝❛çã♦ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✸✳✺ ❱❡r✐✜❝❛çã♦ ❳✶✶❨✶✶❩✶✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✹ ❈♦♠♣❛r❛çã♦ ❝♦♠ ▼ét♦❞♦ ◆✉♠ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✹✳✶ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✹✳✷ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✈
✹✳✹✳✸ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶❨✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✹✳✹ Pr♦❜❧❡♠❛ ❚ér♠✐❝♦ ❳✶✶❨✶✶❩✶✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✺ ❆♣❧✐❝❛çã♦ ❡ Pr♦❜❧❡♠❛ ■♥✈❡rs♦ ✻✽
✺✳✶ ❆♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✺✳✷ Pr♦❜❧❡♠❛ ❉✐r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✸ Pr♦❜❧❡♠❛ ■♥✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✸✳✶ ❋✉♥çã♦ ❞❡ ❚r❛♥s❢❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✸✳✷ ❊st✐♠❛t✐✈❛ ❞❡ ●❡r❛çã♦ ❞❡ ❈❛❧♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✻ ❈♦♥❝❧✉sã♦ ✾✶
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
Pr♦❜❧❡♠❛s ❡♥✈♦❧✈❡♥❞♦ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ♣♦❞❡♠ s❡r ♦❜s❡r✈❛❞♦s ❡♠ ❞✐✈❡rs♦s ❛s♣❡❝t♦s ❡ ♥❛s ♠❛✐s ✈❛r✐❛❞❛s ❢♦r♠❛s✱ ♣♦❞❡✲s❡ ❝✐t❛r ❞❡♥tr❡ ♦s ♠❛✐s ✈❛r✐❛❞♦s ❝❛s♦s✿ ❖ ❛q✉❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❝❤❛♣❛ ❡♠ ✉♠ tr❛t❛♠❡♥t♦ tér♠✐❝♦✱ ❛ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ♣r♦✈❡♥✐❡♥t❡ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ❢✉r❛çã♦ ♦✉ ❝♦rt❡✱ ❝♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ❞✉r❛♥t❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ s♦❧❞❛❣❡♠ ♦✉ ♦ ❛ ❣❡r❛çã♦ ❞❡ ❝❛❧♦r ❞❡✈✐❞♦ ❛ ♣r♦❝❡ss♦s ❞❡ ♠❡t❛❜♦❧✐s♠♦ ❝❡❧✉❧❛r✳ ◆❡st❡ ú❧t✐♠♦ ❝❛s♦✱ tr❛t❛✲s❡ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ t❡❝✐❞♦s ❜✐♦❧ó❣✐❝♦s✳
◆♦s ❝❛s♦s✱ ❛❝✐♠❛ ❝✐t❛❞♦s✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r ❛ r❡❧❡✈â♥❝✐❛ ♥♦ ❡st✉❞♦ ❞❡ t❛❧ ❢❡♥ô♠❡♥♦✱ ♣♦✐s✱ s✉❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥çã♦ ♣♦❞❡ ❧❡✈❛r ❛♦ ❡♠♣r❡❣♦ ❡ ❝r✐❛çã♦ ❞❡ ♥♦✈❛s té❝♥✐❝❛s ❞❡ ❛♣❧✐❝❛çã♦ ❡ ❛♥á❧✐s❡✳
❆ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❛tr❛✈és ❞❡ ✉♠ só❧✐❞♦ s❡ ❞á ♣♦r ♠❡✐♦ ❞❡ ❛❣✐t❛çã♦ ♠♦❧❡❝✉❧❛r✱ ❞❡✈✐❞♦ ❛ ✉♠❛ ❡①✐t❛çã♦ ✐♥t❡r♥❛ ♦✉ ❡①t❡r♥❛✳ ❉❡ss❛ ❢♦r♠❛ ♦ ❡st✉❞♦ s❡ ❞á ♣♦r ♠❡✐♦ ❞❡ ❛♥á❧✐s❡s ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ✈❛r✐❛♥❞♦✲s❡ ♠❛t❡r✐❛✐s✱ ❣❡♦♠❡tr✐❛s✱ ❡ ❢♦r♠❛s ❞❡ ❡①✐t❛çã♦ q✉❡ ♣♦❞❡♠ s❡r ♣♦r ✉♠ ✢✉①♦ ❞❡ ❝❛❧♦r ❡①t❡r♥♦✱ ❝♦♥✈❡❝çã♦ tér♠✐❝❛ ♦✉ ✉♠❛ ❣❡r❛çã♦ ✐♥t❡r♥❛ ❞❡ ❝❛❧♦r✳
❆ss✐♠✱ ♣r❡t❡♥❞❡✲s❡✱ ✉s❛♥❞♦ ❢❡rr❛♠❡♥t❛s ❞❡ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❡ ❝♦♥❝❡✐t♦s ❞❡ ❡♥❣❡♥❤❛r✐❛ ❡ ❢ís✐❝❛ ❡st❛❜❡❧❡❝❡r ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦✱ ❛tr❛✈és ❞♦ ❝á❧❝✉❧♦ ❞♦ ❝❛♠♣♦ ❞❡ t❡♠♣❡r❛t✉r❛ q✉❡ ❛♣r❡s❡♥t❛rá ✉♠ só❧✐❞♦ ❛q✉❡❝✐❞♦ ♦✉ ❡♠ ♣r♦❝❡ss♦ ❞❡ ❛q✉❡❝✐♠❡♥t♦✳ ◆❡st❡ ❝❛s♦✱ ❞✐③❡♠♦s q✉❡ ❡st❛ ❛♥á❧✐s❡ é ❢❡✐t❛ ❞❡ ❢♦r♠❛ ❞✐r❡t❛✱ ✐st♦ é✱ ❝♦♥❤❡❝❡✲s❡ ♣r❡✈✐❛♠❡♥t❡ t♦❞❛s ❛s ✈❛r✐á✈❡✐s q✉❡ ❡♥✈♦❧✈❡♠ ♦ ❢❡♥ô♠❡♥♦✱ r❡st❛♥t♦ ❛♣❡♥❛s r❡❛❧✐③❛r ♦ ❝á❧❝✉❧♦ ❞♦ ❝❛♠♣♦ ❞❡ t❡♠♣❡r❛t✉r❛✳
❖✉tr❛ ❢♦r♠❛ ❞❡ ❛♥á❧✐s❡ q✉❡ ♣♦❞❡ s❡r ❡♠♣r❡❣❛❞❛ ❛♦ ❡st✉❞♦ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r é ❞❡✜♥✐❞❛ ❝♦♠♦ ♣r♦❜❧❡♠❛ ✐♥✈❡rs♦✳ ◆❡st❡ ❝❛s♦ ♥ã♦ s❡ ❝♦♥❤❡❝❡ t♦❞❛s ❛s ✈❛r✐á✈❡✐s q✉❡ ❝❛✉s❛r❛♠ ❛ ♠✉❞❛♥ç❛ ❞❡ t❡♠♣❡r❛t✉r❛✱ ❛♣❡♥❛s s❡ ❝♦♥❤❡❝❡ ❛ ✈❛r✐❛çã♦ ❞❡ t❡♠♣❡r❛t✉r❛ ❡ ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♠❛t❡r✐❛❧✱ ❡ ❛ss✐♠ ♣r❡t❡♥❞❡✲s❡ ❡st✐♠❛r ❛ ❝❛✉s❛ ❞♦ ❢❡♥ô♠❡♥♦✳
❱❛r✐❛❞❛s sã♦ ❛s ❛❜♦r❞❛❣❡♥s q✉❡ ♣♦❞❡♠ s❡r r❡❛❧✐③❛❞❛s ♥❡st❡ ❝♦♥t❡①t♦✱ ❡♥✈♦❧✈❡♥❞♦ ♣r♦❜❧❡✲ ♠❛s ❞✐r❡t♦ ♦✉ ✐♥✈❡rs♦✿ ▼ét♦❞♦s ♥✉♠ér✐❝♦s✱ ❞❡ ♦t✐♠✐③❛çã♦✱ ❡st❛tíst✐❝♦s✱ ✐♠❛❣❡♥s tér♠✐❝❛s✱ ❡
✷
♠ét♦❞♦s ♠❛t❡♠át✐❝♦s ♣❛r❛ ❝á❧❝✉❧♦ ❞❡ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s✳
❆s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ❡♠ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❛♣r❡s❡♥t❛♠✲s❡ ❝♦♠♦ ✉♠❛ ❢♦rt❡ ❡ r♦❜✉st❛ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ t❡♠♣❡r❛t✉r❛ ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ❞✐r❡t♦ ♦✉ ✐♥✈❡rs♦✳ ❆s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s t❡♠ ❡st❛ ❢♦rç❛ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♥ã♦ ❞❡♣❡♥❞❡r❡♠ ❞❡ ❛♣r♦①✐♠❛çõ❡s✱ ❡st✐♠❛t✐✈❛s✱ ❡r✲ r♦s ❞❡ ❛rr❡♥❞♦❞❛♠❡♥t♦ ♦✉ tr✉♥❝❛♠❡♥t♦✱ ♣♦✐s sã♦ ❡①❛t❛s✱ ❞❡ ❢á❝✐❧ ✐♠♣❧❡♠❡♥t❛çã♦ ❡ ❛♣r❡s❡♥t❛♠ ❜❛✐①♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳
❆ ♦❜t❡♥çã♦ ❞❡ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ tr❛t❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦ r❡q✉❡r ♣r♦❝❡✲ ❞✐♠❡♥t♦s ♠❛✐s ❡❧❛❜♦r❛❞♦s ❛♦s q✉❡ sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ♣r♦❜❧❡♠❛s ✜①♦s✱ ❞❡✈✐❞♦ ❛♦s t❡r♠♦s ❛❞✐❝✐♦♥❛✐s q✉❡ s✉r❣❡♠ ♥❛ ❡q✉❛çã♦ ❣♦✈❡r♥❛♥t❡✳ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣❛r❛ r❡s♦❧✈❡r ❛s ❡q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s ♣❛r❝✐❛✐s q✉❡ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ♠♦❞❡❧❛♠ ♦ ♣r♦❜❧❡♠❛ s❡rá ♦ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥✳
❉❡st❛ ❢♦r♠❛ ♦ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ❛ ✐♥✈❡st✐❣❛çã♦✱ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s♦❧✉çõ❡s ❛♥❛✲ ❧ít✐❝❛s ❡ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❞❡ ♣r♦❜❧❡♠❛s ❡♥✈♦❧✈❡♥❞♦ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ ❝♦r♣♦s ❛q✉❡❝✐❞♦s ♣♦r ❢♦♥t❡s ♠ó✈❡✐s ❞❡ ❝❛❧♦r✱ ♦✉ ❢♦♥t❡s ✜①❛s ❞❡ ❝❛❧♦r ❛q✉❡❝❡♥❞♦ só❧✐❞♦s ♠ó✈❡✐s✳ ➱ t❛♠❜é♠ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈❡r ❛ ✈❡r✐✜❝❛çã♦ ❞❛s s♦❧✉çõ❡s ♦❜t✐❞❛s ❛♥❛❧✐t✐❝❛♠❡♥t❡ ✉s❛♥❞♦ s♦❧✉çõ❡s ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ❣❡♦♠❡tr✐❛s ✜♥✐t❛s ♦✉ s❡♠✐✲✐♥✜♥✐t❛s✱ ❛ ✜♠ ❞❡ ❣❛r❛♥t✐r ❛ ❝♦♥✜❛❜✐❧✐✲ ❞❛❞❡ ❡ s❡❣✉r❛♥ç❛ ❞❛s s♦❧✉çõ❡s ❝❛❧❝✉❧❛❞❛s✳
❖✉tr♦ ♦❜❥❡t✐✈♦ é ♦ ✉s♦ ❞❛s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ♥❛ ❛♣❧✐❝❛çã♦ à ♣r♦❜❧❡♠❛s ✐♥✈❡rs♦s✳ ◆❡ss❡ ❝❛s♦✱ ♣r♦♣õ❡✲s❡ ❛ ❛♣❧✐❝❛çã♦ ❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ té❝♥✐❝❛ ❚❋❇●❋ ✭tr❛♥s❢❡r ❢✉♥❝t✐♦♥ ❜❛s❡❞ ●r❡❡♥✬s ❢✉♥❝t✐♦♥s✮✳ Pr❡t❡♥❞❡✲s❡ ❡♠♣r❡❣á✲❧❛ ❛ ♣r♦❜❧❡♠❛s ❞❡ s♦❧❞❛❣❡♠✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❛♣♦rt❡ tér♠✐❝♦ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦✳
❆ ✐♠♣♦rtâ♥❝✐❛ ❞❛s ❛♥á❧✐s❡s r❡❛❧✐③❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦ r❡s✐❞❡♠ ♥❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥ç❛♦ ❞♦s ❢❡♥ô♠❡♥♦s ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ♣♦r ❢♦♥t❡s ♠ó✈❡✐s ❡ ❣❡r❛çã♦ ❞❡ ❝♦♥tr✐❜✉✐çõ❡s ❜✐❜❧✐♦❣rá✜✲ ❝❛s✱ ✈✐st♦ q✉❡ ♥ã♦ ❡①✐st❡♠ ♠✉✐t♦s tr❛❜❛❧❤♦s ♣✉❜❧✐❝❛❞♦s ❡♥✈♦❧✈❡♥❞♦ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ♥❡st❡ s❡♥t✐❞♦✳
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛✲s❡ ❡str✉t✉r❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
• ◆♦ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❡♥✈♦❧✈❡♥❞♦ ♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s q✉❡ ❛❜♦r❞❛♠ ❞❡ ❢♦r♠❛ ✈❛r✐❛❞❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ só❧✐❞♦s ♠ó✈❡✐s✳
• ❖ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❡ ❛♥á❧✐s❡ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❝á❧❝✉❧♦ ❞❛s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ❡♠ ♣r♦❜❧❡♠❛s ♠ó✈❡✐s ✈❛r✐❛♥❞♦✲s❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❡ ❣❡♦✲ ♠❡tr✐❛s✳
✸
♥✉♠ér✐❝♦s✳
❈❛♣ít✉❧♦ ✷
❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛
✷✳✶ ■♥tr♦❞✉çã♦
❆♣r❡s❡♥t❛✲s❡ ♥❡st❡ ❝❛♣ít✉❧♦ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞❡ tr❛❜❛❧❤♦s ❡♠ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♥✈♦❧✈❡♥❞♦ ❢♦♥t❡s ♠ó✈❡✐s ❝♦♠ ❞✐✈❡rs❛s ❛❜♦r❞❛❣❡♥s✿ ❛♥❛❧ít✐❝❛✱ ♥✉♠ér✐❝❛✱ ❤í❜r✐❞❛✱ ✐♥✈❡rs❛ ❡ ❝♦♥❝❡✐t♦ ❞❡ ✈❡r✐✜❝❛çã♦ ✐♥trí♥s❡❝❛✳ ❯t✐❧✐③❛♥❞♦ ❞✐❢❡r❡♥t❡s ❝♦♠❜✐♥❛çõ❡s ❞❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r✲ ♥♦s✱ ❝♦♥❞✐çõ❡s ✐♥✐❝✐❛✐s ❡ s✐st❡♠❛s ❞❡ ❝♦♦r❞❡♥❛❞❛s sã♦ ❡①❡♠♣❧✐✜❝❛❞❛s ♣♦r ✈❛r✐❛❞❛s ❛♣❧✐❝❛çõ❡s✳
✷✳✷ ❈♦♥❞✉çã♦ ❞❡ ❈❛❧♦r ♣♦r ❋♦♥t❡s ▼ó✈❡✐s
❋♦✉r✐❡r ✭✶✽✷✷✱ ♣✳✸✺✹✲✸✻✺✮ ❡♠ ❚❤é♦r✐❡ ❆♥❛❧②t✐q✉❡ ❞❡ ❧❛ ❈❤❛❧❡✉r✱ ❛♣r❡s❡♥t♦✉ ♦ ♣r✐♠❡✐r♦ t❡①t♦ ♣✉❜❧✐❝❛❞♦ ❝♦♠ ❛ ✐♥t❡♥çã♦ ❞❡ ✐♥✈❡st✐❣❛r ♦ ❢❡♥ô♠❡♥♦ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ ✉♠ só❧✐❞♦✳ ❆ ✐♠♣♦rtâ♥❝✐❛ ❞❡st❡ t❡①t♦ s❡ ❞á ♣❡❧❛ ✐♥tr♦❞✉çã♦ à ✐♥t❡r♣r❡t❛çã♦ ❡ r❡♣r❡s❡♥t❛çã♦ ♠❛t❡♠át✐❝❛ ❞♦ q✉❡ ♦ ❛✉t♦r ❝❧❛ss✐✜❝♦✉ ❝♦♠♦ ❝❛❧♦r✱ ❛tr❛✈és ❞❡ ❛♥á❧✐s❡ ❞❡ sér✐❡s tr✐❣♦♥♦♠étr✐❝❛s✱ q✉❡ ♣♦s✲ t❡r✐♦r♠❡♥t❡ ❢♦r❛♠ ❜❛t✐③❛❞❛s ❞❡ sér✐❡s ❞❡ ❋♦✉r✐❡r ❡♠ s✉❛ ❤♦♠❡♥❛❣❡♠✱ ❞❛♥❞♦ ✐♥í❝✐♦ ❞é❝❛❞❛s ❞❡♣♦✐s ❛♦ r❛♠♦ ❞❛ ♠❛t❡♠át✐❝❛ ❆♥á❧✐s❡ ❞❡ ❋♦✉r✐❡r✱ t♦r♥❛♥❞♦✲s❡ ❡♥tã♦ ♦ t❡①t♦ ❢♦♥t❡ ♣❛❞rã♦ ❞❡ ♣❡sq✉✐s❛s ❡♠ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r✳
❘♦s❡♥t❤❛❧ ✭✶✾✸✺✮ ❛♣r❡s❡♥t♦✉ ❡♠ s❡✉ t❡①t♦ ♦ ♣r♦❝❡ss♦ ❞❡ ♦❜t❡♥çã♦ ❞❡ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛ ❡♠ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♥✈♦❧✈❡♥❞♦ ♣r♦❝❡ss♦s ❞❡ s♦❧❞❛❣❡♠ ❡ ❝♦rt❡✱ ♦♥❞❡ ♦ ✢✉①♦ ❞❡ ❝❛❧♦r ❡♥✈♦❧✈✐❞♦ ♥♦ ♣r♦❝❡ss♦ s❡ ♠♦✈❡ ❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ❝♦♥st❛♥t❡ ♥❛ ❞✐r❡çã♦ ♣♦s✐t✐✈❛ ❞❡ ✉♠ ❞♦s ❡✐①♦s ❝❛rt❡s✐✲ ❛♥♦s✳ ❘♦s❡♥t❤❛❧ ✉s♦✉ ❛ ❤✐♣ót❡s❡ ♣❛r❛ ❝á❧❝✉❧♦ ❞❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❡ ❞✐❢✉sã♦ ❝♦♠♦ r❡❣✐♠❡ q✉❛s❡ ❡st❛❝✐♦♥ár✐♦✳ ❆s s♦❧✉çõ❡s sã♦ ♦❜t✐❞❛s ♣♦r ♠❡✐♦ ❞❡ ❛♣r♦①✐♠❛çõ❡s ❡♠ sér✐❡s ✉t✐❧✐③❛♥❞♦ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❣❡♦♠❡tr✐❛s ❡ ❢♦♥t❡s ❞❡ ❝❛❧♦r✳
❯♠ ♠ét♦❞♦ rá♣✐❞♦ ❡ ✐♥♦✈❛❞♦r ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ❝♦♥❞✉çã♦ ❡ ❝♦♥✈❡❝çã♦ ❡♠ ✉♠ s✐st❡♠❛ ❜✐❢ás✐❝♦ tr❛♥s✐❡♥t❡ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ✉♠❛ ❝❤❛♠❛ ❞❡ ❛❧t❛ t❡♠♣❡r❛t✉r❛ ♦✉ ❝♦rr❡♥t❡ ❞❡ ♣❧❛s♠❛
✺
❢♦✐ ♣r♦♣♦st♦ ♣♦r ❍✳❊✳▲❡❡ ✭✶✾✽✾✮✳ ❊♠ s❡✉ tr❛❜❛❧❤♦ ❍✳❊✳▲❡❡ ✭✶✾✽✾✮ ♣r♦♣ôs ❛ s♦❧✉çã♦ ♣❛r❛ ❡ss❡ ♣r♦❜❧❡♠❛ ♣♦r ✉♠ ♠ét♦❞♦ ♥✉♠ér✐❝♦✱ q✉❡ ♦ ❛✉t♦r ❝♦♥s✐❞❡r♦✉ ❝♦♠♦ rá♣✐❞♦ ❡ ✐♥♦✈❛❞♦r✳ ❖ ♠ét♦❞♦ ❝♦♥s✐t❡ ❡♠ s✐♠♣❧✐✜❝❛çõ❡s ❞❛ ❡q✉❛çã♦ ❣♦✈❡r♥❛♥t❡ ❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❞♦ ♣r♦❜❧❡♠❛ ♣♦r ❢✉♥çõ❡s ❞❡♥♦♠✐♥❛❞❛s ♣❡❧♦ ❛✉t♦r ❝♦♠♦ tr✐❛❧ ❢✉♥❝t✐♦♥s✱ ❡ ❡♥tã♦ ❢♦r❛♠ ✐♠♣❧❡♠❡♥t❛❞❛s ❛s ❡q✉❛çõ❡s ♣❛r❛ s♦❧✉çã♦ ♣❡❧♦ ♠ét♦❞♦ ❘✉♥❣❡✲❑✉tt❛ ❞❡ q✉❛rt❛ ♦r❞❡♠ ❡ ❛ss✐♠ ❞❡t❡r♠✐♥❛r ♦s ♣❡r✜s ❞❡ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ❡st❛s ❝♦♥❞✐çõ❡s✳
Ö③✐➩✐❦ ✭✶✾✾✸✮ ❛♣r❡s❡♥t♦✉ ❡♠ ❍❡❛t ❈♦♥❞✉❝t✐♦♥ ✈ár✐❛s ❢❡rr❛♠❡♥t❛s ♠❛t❡♠át✐❝❛s ♣❛r❛ ❛❜♦r✲ ❞❛❣❡♠ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r✱ q✉❡ sã♦✿ ▼ét♦❞♦s ♥✉♠ér✐❝♦s ❡ ❛❜♦r❞❛❣❡♠ ❛ ♣r♦❜❧❡♠❛s ✐♥✈❡rs♦s✱ ❝♦♠♦ ❡st✐♠❛t✐✈❛ ❞❡ ✉♠ ✢✉①♦ ❞❡ ❝❛❧♦r ❞❡s❝♦♥❤❡❝✐❞♦✳ ❉❡♥tr❡ ❡st❛s ❢❡r✲ r❛♠❡♥t❛s✱ ❞❡st❛❝❛✲s❡ ♦ ♠ét♦❞♦ q✉❡ s✉❣❡r❡ ♠✉❞❛♥ç❛s ❞❡ ✈❛r✐á✈❡✐s q✉❡ s❡rã♦ ✉t✐❧✐③❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✱ q✉❡ s❡ ♣r♦♣õ❡ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❡♠ t❡r♠♦s ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ só❧✐❞♦ s♦❜ ✉♠❛ ❣❡r❛çã♦ ♣♦♥t✉❛❧ ✐♥t❡r♥❛ ❞❡ ❝❛❧♦r✳
Pr✐♠❡✐r❛♠❡♥t❡ Ö③✐➩✐❦ ✭✶✾✾✸✮ ❛❜♦r❞♦✉ ❛ ✐♥t❡r♣r❡t❛çã♦ ❝❧áss✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ♦♥❞❡ ♦ só❧✐❞♦ s❡ ♠♦✈❡ ❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ❝♦♥st❛♥t❡ s♦❜ ♦s ❡✐①♦s ❝♦♦r❞❡♥❛❞♦s ♠❡❞✐❛♥t❡ ✉♠❛ ❣❡r❛çã♦ ✐♥t❡r♥❛ ♣♦♥t✉❛❧ ❡ ✜①❛ ❞❡ ❝❛❧♦r✱ ❡ ❡♥tã♦ ❢♦r❛♠ ♣r♦♣♦st❛s ♠✉❞❛♥ç❛s ❞❡ ✈❛r✐á✈❡✐s ❛ ✜♠ ❞❡ ❡❧✐♠✐♥❛r ♦s t❡r♠♦s r❡❢❡r❡♥t❡s à ✈❡❧♦❝✐❞❛❞❡ ❞❛ ❡q✉❛çã♦ ❣♦✈❡r♥❛♥t❡ ❡ ❧❡✈á✲❧♦s ♣❛r❛ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦✳ ❆ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❡♥tr❡t❛♥t♦ ♥ã♦ ❢♦✐ ❛♣r❡s❡♥t❛❞❛✳
❖✉tr♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ♣❛r❛ s♦❧✉çã♦ ❞❡ t❡♠♣❡r❛t✉r❛ ❡♠ ✉♠ ♣r♦❜❧❡♠❛ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡♥✈♦❧✈❡♥❞♦ ❢♦♥t❡ ♠ó✈❡❧ ❡♠ s♦❧❞❛❣❡♠✱ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ♣♦r ◆❡❤❛❞ ✭✶✾✾✺✮✳ ❖ ❛✉t♦r ❛♣r❡s❡♥✲ t♦✉ ❡♠ s❡✉ tr❛❜❛❧❤♦ ♦ ❞❡t❛❧❤❛♠❡♥t♦ ❞♦ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ s♦❧❞❛❣❡♠ ♣♦r ♣❧❛s♠❛ ❛r❝ ✇❡❧❞✐♥❣ ✭P❆❲✮ ❞♦ t✐♣♦ ❆■❙■304✱ ♦♥❞❡ ❢♦✐ ♠♦❞❡❧❛❞♦ ♦ ❢❡♥ô♠❡♥♦ ❝♦♠ ♠✉❞❛♥ç❛ ❞❡ ❢❛s❡ ❡ ♣r♦♣r✐❡❞❛✲
❞❡s t❡r♠♦❢ís✐❝❛s ✈❛r✐❛♥❞♦ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛✳ ❖ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ✉s❛❞♦ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❛s s✐♠✉❧❛çõ❡s ❢♦✐ ♦ ♠ét♦❞♦ ❞❡ ✈♦❧✉♠❡s ✜♥✐t♦s ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ✉♣✲✇✐♥❞ ♣❛r❛ ♦s t❡r♠♦s ❝♦♥✈❡❝t✐✈♦s✳ ❋♦✐ ❛♣r❡s❡♥t❛❞♦ ✉♠❛ ❛♥á❧✐s❡ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ♥❡st❛ s✐t✉❛çã♦ ✉s❛♥❞♦ ✈❛r✐❛çõ❡s ❞❡ ♣r♦♣r✐❡❞❛❞❡s tér♠✐❝❛s✱ ❡①♣❡ss✉r❛ ❞❛ r❡❣✐ã♦ ❛ s❡r s♦❧❞❛❞❛✱ ✈❡❧♦❝✐❞❛❞❡ ❡ ♣❛ss♦ ❞❡ t❡♠♣♦✳
✻
♠♦str❛❞♦ r❡s✉❧t❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ♣❛râ♠❡tr♦s ❞❡ s♦❧❞❛❣❡♠✳
❖✉tr❛ ❛♥á❧✐s❡ s❡♠❡❧❤❛♥t❡ ❢♦✐ ♠♦str❛❞❛ ♣♦r ❙♦❧❛♥❛ ❡ ❏✳▲✳❖❝❛♥❛ ✭✶✾✾✼✮ ♦♥❞❡ ❢♦✐ ❞❡t❛❧❤❛❞♦ ❡ ❝♦♥tr✉í❞♦ ✉♠ ♠♦❞❡❧♦ tr✐❞✐♠❡♥s✐♦♥❛❧ q✉❛s❡ ❡stát✐❝♦ ❞❡ s♦❧❞❛❣❡♠ ♣♦r ✉♠ ❧❛s❡r ♦♥❞❡ ♦ só❧✐❞♦ s❡ ♠♦✈✐♠❡♥t❛✈❛ ❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ❝♦♥st❛♥t❡ ❛tr❛✈és ❞♦ ❡✐①♦ ❳✳ ❖ ❜❛❧❛♥ç♦ ❡♥❡r❣ét✐❝♦ ❧❡✈♦✉ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦s ❡❢❡✐t♦s ❞❡ ❡✈❛♣♦r❛çã♦ ❡ ♣❡r❞❛ ♣♦r ❛❜❧❛çã♦✳ ❖ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♦❢❡r❡❝❡✉ ✉♠❛ ❞❡s❝r✐çã♦ ❝♦♠♣❧❡t❛ ❞♦ ❝❛♠♣♦ ❞❡ t❡♠♣❡r❛t✉r❛✱ ❞❡♥s✐❞❛❞❡ ❡❧❡❝trô♥✐❝❛✱ ♦ ❣r❛✉ ❞❡ ✐♦♥✐③❛çã♦ ❡ ❛❜s♦rçã♦✱ ❝♦❡✜❝✐❡♥t❡ ❞❡♥tr♦ ❞♦ ♣❧❛s♠❛✱ ❡ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞❡ ♣❡♥❡tr❛çã♦ ♠á①✐♠❛ ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s ❞♦ ❧❛s❡r✱ ❝♦♠♦ ❛ ❡♥❡r❣✐❛✱ ♦ r❛✐♦ ❞❡ ❢♦❝❛❣❡♠ ❡ ♦s❝✐❧❛✲ çã♦✳ ❙♦❧❛♥❛ ❡ ❏✳▲✳❖❝❛♥❛ ✭✶✾✾✼✮ ♦❜t✐✈❡r❛♠ ❡♠ s❡✉ tr❛❜❛❧❤♦ ❝♦♥❝♦r❞â♥❝✐❛ ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❛ ✉♠❛ ❛♠♣❧❛ ❣❛♠❛ ❞❡ ♣♦tê♥❝✐❛s ❞❡ ❧❛s❡r ❡ ❡s♣❡ss✉r❛s ❞❡ ❝❤❛♣❛s✳
▼♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ❞♦ ♣r♦❝❡ss♦ ❞❡ s♦❧❞❛❣❡♠ ●❛s ▼❡t❛❧ ❆r❝ ❲❡❧❞✐♥❣ ✭●▼❆❲✮ ❢♦r❛♠ ♣r♦♣♦st♦s ♣♦r ■✳❙✳❑✐♠ ❡ ❆✳❇❛s✉ ✭✶✾✾✽✮✱ q✉❡ ♣♦❞❡♠ s❡r ✉s❛❞♦s ♣❛r❛ ♣r❡✈❡r ♣❛râ♠❡tr♦s ❞♦ ♣r♦❝❡ss♦ ❞❡ s♦❧❞❛❣❡♠✳ ❋♦✐ ❝♦♥s✐❞❡r❛❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ❣❡♦♠❡tr✐❛ ❜✐❞✐♠❡♥s✐♦♥❛❧✱ s✐♠étr✐❝♦ ❡ ❞❡t❡r♠✐♥❛❞❛ ❣❡♦♠❡tr✐❛ ♣❛r❛ ♦ ❝♦r❞ã♦ ❞❡ s♦❧❞❛ ❡ ✈❡❧♦❝✐❞❛❞❡ ❞❡ s♦❧❞❛❣❡♠✳ ❖ ♠♦❞❡❧♦ ♠❛t❡♠á✲ t✐❝♦ ✉s❛❞♦ ♣❡❧♦s ❛✉t♦r❡s ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ q✉❛tr♦ ❢♦rç❛s ♠♦tr✐③❡s ♣❛r❛ ❛ ❢❡rr❛♠❡♥t❛ ❞❡ s♦❧❞❛❣❡♠✿ ❡❧❡tr♦♠❛❣♥ét✐❝❛✱ ✢✉t✉❛❜✐❧✐❞❛❞❡✱ t❡♥sã♦ s✉♣❡r✜❝✐❛❧ ❡ ❢♦rç❛s ❞❡ ❛rr❛st♦✳ ❆s ❝♦♥❞✐✲ çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❝♦♥s✐❞❡r❛❞❛s ❢♦r❛♠✿ ❈♦♥✈❡❝çã♦ tér♠✐❝❛ ♥❛s ❢❛❝❡s ❧❛t❡r❛✐s r❛❞✐❛çã♦ tér♠✐❝❛ ♥❛ ❢❛❝❡ ♦♣♦st❛ à ❡①♣♦st❛ ❛♦ ✢✉①♦ ❞❡ ❝❛❧♦r✱ t❛♠❜é♠ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ✉♠ ✢✉①♦ ❞❡ ❝❛❧♦r ♠♦❞❡✲ ❧❛❞♦ ❝♦♠♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛
❖ s♦❢t✇❛r❡ P❍❖❊◆■❈❙ ❢♦✐ ✉s❛❞♦ ♣♦r ■✳❙✳❑✐♠ ❡ ❆✳❇❛s✉ ✭✶✾✾✽✮ ♣❛r❛ r❡s♦❧✈❡r ❛s ❡q✉❛çõ❡s q✉❡ ❞❡s❝r❡✈❡♠ ♦ ♣r♦❜❧❡♠❛✱ ❝♦♠ ❝ó❞✐❣♦ ❜❛s❡❛❞♦ ♥♦ ❛❧❣♦rít♠♦ ❙❆▼P▲❊✳ ❖s r❡s✉❧t❛❞♦s ♠♦s✲ tr❛r❛♠ q✉❡ ❛s ❢♦rç❛s ❞❡ t❡♥sã♦ ♠❛❣♥ét✐❝❛ ❡ ❞❡ s✉♣❡r❢í❝✐❡✱ ❡ t❛♠❜é♠ ❛s ❣♦t❛s ❞❡ ♠❡t❛❧ ❢✉♥❞✐❞♦ ❛♣r❡s❡♥t❛r❛♠ ✐♥✢✉ê♥❝✐❛ ♥❛ ❢♦r♠❛çã♦ ❞❛ ❣❡♦♠❡tr✐❛ ❞♦ ❝♦r❞ã♦ ❞❡ s♦❧❞❛✳
▼✳❆✳❲❛❤❛❜✱ ▼✳❏✳P❛✐♥t❡r ❡ ▼✳❍✳❉❛✈✐❡s ✭✶✾✾✽✮ ❛♣r❡s❡♥t❛r❛♠ ❡♠ s❡✉ tr❛❜❛❧❤♦ ✉♠❛ ❛❜♦r✲ ❞❛❣❡♠ ♥✉♠ér✐❝❛ ❜❛s❡❛❞❛ ❡♠ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ s♦❧❞❛❣❡♠ ❝♦♥s✐❞❡r❛♥❞♦ ❣❡♦♠❡tr✐❛s ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡ tr✐❞✐♠❡♥s✐♦♥❛❧✳ ❖s ❛✉t♦r❡s ❛♣r❡s❡♥t❛r❛♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❞♦ tr❛❜❛❧❤♦ ❛ ❣❡r❛çã♦ ❞❡ ♥♦✈♦s ❝♦♥❤❡❝✐♠❡♥t♦s ❡ ♠❡❧❤♦r❛♠❡♥t♦ ❞♦s ♠ét♦❞♦s ❝♦♠♣✉✲ t❛❝✐♦♥❛✐s ♣❛r❛ ❝á❝✉❧♦ tér♠✐❝♦ ♥❛ r❡❣✐ã♦ ❞❡ s♦❧❞❛ ❡ ❡st✐♠❛t✐✈❛s ❞❡ ♣r♦❢✉♥❞✐❞❛❞❡ ❞❡ ♣❡♥❡tr❛çã♦ ❞❛ s♦❧❞❛✱ ❣❡♦♠❡tr✐❛✱ ❜❛♥❤♦ ❞❡ ❢✉sã♦✱ ✈❡❧♦❝✐❞❛❞❡ ❞❡ r❡s❢r✐❛♠❡♥t♦✳ ❙❡❣✉♥❞♦ ♦s ❛✉t♦r❡s✱ ❛ ♣r❡❝✐✲ sã♦ ❞♦s t❡♠♣♦s ❞❡ r❡❢r✐❣❡r❛çã♦ ♣r❡✈✐st♦s✱ ♣❡♥❡tr❛çõ❡s ❞❡ s♦❧❞❛ ❡ ♦ ❝♦♠♣r✐♠❡♥t♦s ❞❛s ♣♦ç❛s ❞❡ s♦❧❞❛ sã♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ✈❛❧♦r❡s ♦❜t✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ♣❛r❛ s♦❧❞❛s ❜❡❛❞✲♦♥✲♣❧❛t❡ ❡ ❛♣r❡s❡♥t♦✉ ✉♠❛ ❜♦❛ ❝♦♥❝♦r❞â♥❝✐❛ ❝♦♠ ❞♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ♣❛r❛ ✉♠❛ ❣❛♠❛ ❞❡ ❝♦❞✐çõ❡s ❞❡ s♦❧❞❛❣❡♠
✼
❝♦♥st❛♥t❡ ❞✉r❛♥t❡ ♦ ♣r♦❝❡ss♦✳ ❖ ♣r♦❜❧❡♠❛ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠ ❣❡♦♠❡tr✐❛ s❡♠✐✲✐♥✜♥✐t❛✱ ✢✉①♦ ❞❡ ❝❛❧♦r s❡♠✐✲❡❧✐♣s♦✐❞❛❧ ❝♦♠ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛✱ ❡ s❡♠ ❡❢❡✐t♦ ❞❡ ❝♦♥✈❡❝çã♦ tér♠✐❝❛ ♥❛ s✉♣❡r❢í❝✐❡ ❞❡ s♦❧❞❛❣❡♠✳ ❖ ♠ét♦❞♦ ❞❡ s♦❧✉çã♦ ✉s❛❞♦ ♣♦r ◆❣✉②❡♥ ❡t ❛❧✳ ✭✶✾✾✾✮ ❢♦✐ ✐♥t❡❣r❛r ♦ t❡r♠♦ ❞❡ ✢✉①♦ ❞❡ ❝❛❧♦r ❡♠ ✉♠❛ r❡❣✐ã♦ ♦♥❞❡ ♦ ♣♦♥t♦ ❞❡ ✢✉①♦ ❞❡ ❝❛❧♦r ❡st❛ ❛t✉❛♥❞♦ ❡♠ ✉♠ ❝❡rt♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✱ s❛t✐s❢❛③❡♥❞♦ ❛ ❡q✉❛çã♦ ❣♦✈❡r♥❛♥t❡ ❞♦ ♣r♦❜❧❡♠❛✳ ❆ ✜♠ ❞❡ ❝♦♠♣❛r❛r ❛ s♦❧✉çã♦ ♦❜t✐❞❛ ❛♥❛❧✐t✐❝❛♠❡♥t❡ ❝♦♠ ✉♠❛ s✐t✉❛çã♦ r❡❛❧✱ ❢♦✐ ♣r❡♣❛r❛❞♦ ✉♠ ❡①♣❡r✐♠❡♥t♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ tér♠✐❝♦ ✉s❛♥❞♦ ❛s ♠❡s♠❛s ❤✐♣ót❡s❡s ✉s❛❞❛s ♥♦ ♠ét♦❞♦ ❛♥❛❧ít✐❝♦✳ ❖❜s❡r✈♦✉✲s❡ ♣❡❧❛s ❝♦♠♣❛r❛çõ❡s✱ q✉❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛♥❛❧✐t✐❝❛♠❡♥t❡ ❢♦r❛♠ s❛t✐s❢❛tór✐♦s✳ ❯♠❛ ❛❜♦r❞❛❣❡♠ ♠❛t❡♠át✐❝❛ s♦❜r❡ ♦ ✉s♦ ❞♦ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥ ❢♦✐ ❞❛❞❛ ♣♦r ❉✳❈♦❧❡ ❡ ❍✳❨✳❨❡♥ ✭✷✵✵✶✮ ❡♠ s❡✉ tr❛❜❛❧❤♦✳ ❖s ❛✉t♦r❡s tr♦✉①❡r❛♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠❛t❡♠á✲ t✐❝❛ ❝♦♥❝❡✐t✉❛❧ ❡ ❞❡ ❛♥á❧✐s❡ ❡♠ ✈❛r✐❛❞❛s ❝♦♠❜✐♥❛çõ❡s ❞❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦✱ s✐st❡♠❛ ❞❡ ♥✉♠❡r❛çã♦ ♣❛r❛ ❢✉♥çõ❡s ❞❡ ●r❡❡♥✱ ♥♦r♠❛s✱ ❝á❧❝✉❧♦ ❡ ❛♥á❧✐s❡ ❞❡ ❛✉t♦✈❛❧♦r❡s ❡ ❛✉t♦❢✉♥çõ❡s ❛❧é♠ ❞❡ tr❛③❡r t❛❜❡❧❛❞♦s ♦s ❛✉t♦✈❛❧♦r❡s ❡ ❛✉t♦❢✉♥çõ❡s ❞❡ ❞✐✈❡rs♦s ❝❛s♦s ❞❡ ❝♦♠❜✐♥❛çõ❡s ❞❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦✱ ❝♦♥✈❡r❣ê♥❝✐❛ ❞❡ sér✐❡s✱ ❛❜♦r❞❛❣❡♠ s♦❜r❡ ❣❡r❛çã♦ ✈♦❧✉♠étr✐❝❛ ✐♥t❡r♥❛ ❞❡ ❝❛❧♦r ❡✱ ✢✉①♦ ❞❡ ❝❛❧♦r✳
❖✉tr❛ ❛❜♦r❞❛❣❡♠ ♥✉♠ér✐❝❛ ❢♦✐ ✉s❛❞❛ ♣♦r ❳✳❑✳❩❤✉ ❡ ❨✳❏✳❈❤❛♦ ✭✷✵✵✷✮✱ ❛ ✜♠ ❞❡ r❡❛❧✐③❛r ✉♠❛ ❛♥á❧✐s❡ tér♠✐❝❛ ❡ t❡r♠♦✲♠❡❝â♥✐❝❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ♥ã♦ ❧✐♥❡❛r ✉s❛♥❞♦ ♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ s✐♠✉❧❛r ❛ s♦❧❞❛❣❡♠ ❡♠ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛❧✉♠í♥✐♦✳ ❖s ❛✉t♦r❡s ✐♥✈❡st✐❣❛r❛♠ ♦ ❡❢❡✐t♦ ❞❡ ❝❛❞❛ ♣r♦♣r✐❡❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧✱ q✉❡ ❞❡♣❡♥❞❡ ❞❛ t❡♠♣❡r❛t✉r❛✱ s✐♠✉❧❛♥❞♦ ❛ s♦❧❞❛❣❡♠ ❞❡ ✉♠❛ ♣❧❛❝❛ ❞❡ ❛❧✉♠í♥✐♦ ✉s❛♥❞♦ três ❝♦♥❥✉♥t♦s ❞❡ ♣r♦♣r✐❡❞❛❞❡s✳ ❆♣ós ❞❡t❛❧❤❛r ♦ ♠ét♦❞♦ ❞❡ ♠♦❞❡❧❛❣❡♠ ❡ ❞✐s❝r❡t✐③❛çã♦ ❞❛s ❡q✉❛çõ❡s ❣♦✈❡r♥❛♥t❡s ❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦✱ ♦❜s❡r✈❛r❛♠ q✉❡ ❧✐♠✐t❡ ❞❡ ❡❧❛st✐❝✐❞❛❞❡ ❡ ♦ ♠ó❞✉❧♦ ❞❡ ❨♦✉♥❣ ❛♣r❡s❡♥t❛♠ ❡❢❡✐t♦s s✐❣♥✐✜❝❛t✐✈♦s ❞❡♣♦✐s ❞❛ s♦❧❞❛❣❡♠✳
✽
♠♦str❛♠ ✉♠❛ ♣❡q✉❡♥❛ ❞✐❢❡r❡♥ç❛ ♣❡r❝❡♥t✉❛❧ ❡♥tr❡ ♦s ✈❛❧♦r❡s ❡st✐♠❛❞♦s ❡ ❡①♣❡r✐♠❡♥t❛✐s✳ ❆ r❡s♣♦st❛ ❞❡ t❡♠♣❡r❛t✉r❛ ❞✉r❛♥t❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ s♦❧❞❛❣❡♠ ♣♦r ❢♦♥t❡ ♠ó✈❡❧✱ t✉♥❣st❡♥ ❣❛s ❛r❝✱ ❢♦✐ ♣r♦♣♦st❛ ♣♦r ❲✳❩❤❛♥❣ ❡t ❛❧✳ ✭✷✵✵✸✮ ❞❡ ❢♦r♠❛ ♥✉♠ér✐❝❛ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠ só❧✐❞♦ ❞❡ ❣❡♦♠❡tr✐❛ tr✐❞✐♠❡♥s✐♦♥❛❧ ❡♠ ❝♦♦r❞❡♥❛❞❛s r❡t❛♥❣✉❧❛r❡s ❡①♣♦st♦ ❛ ✉♠ ✢✉①♦ ❞❡ ❝❛❧♦r ❡ ❝♦♥✲ ✈❡❝çã♦ tér♠✐❝❛ ❡♠ s✉❛ s✉♣❡r❢í❝✐❡✱ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡ ♥❛s ❞❡♠❛✐s s✉♣❡r❢í❝✐❡s ❞❡ s♦❧❞❛❣❡♠ ❡ ✈❡❧♦❝✐❞❛❞❡ ❝♦♥st❛♥t❡✳ ❖ ❛✉t♦r ❞❡t❛❧❤♦✉ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛ ❞♦ ♣r♦❜❧❡♠❛ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦✳ ❱♦❧✉♠❡s ✜♥✐t♦s ❛tr❛✈és ❞❡ ✉♠❛ ♠❛❧❤❛ r❡t❛♥❣✉❧❛r ❢♦r❛♠ ✉s❛❞♦s✳ ❆♣ós r❡❛❧✐③❛r t♦❞♦s ♦s ❝á❧❝✉❧♦s ❞❡ ❞✐s❝r❡t✐③❛çã♦ ❞❛ ❡q✉❛çã♦ ❣♦✈❡r✲ ♥❛♥t❡ ❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ✈♦❧✉♠❡s ✜♥✐t♦s ❡ ❞❡t❛❧❤❛r ❛ ✐♠♣❧❡♠❡♥t❛çã♦✱ ❲✳❩❤❛♥❣ ❡t ❛❧✳ ✭✷✵✵✸✮ ❝♦♠♣❛r♦✉ s❡✉s ❞❛❞♦s ♦❜t✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ❡ ❝♦♥❝❧✉✐✉ ♦ q✉❡ ❛ ♠♦❞❡❧❛❣❡♠ ✉s❛❞❛ ❛♣r❡s❡♥t♦✉ ❞❛❞♦s ♠✉✐t♦ ♣ró①✐♠♦s ❛♦s r❡❛✐s✳
❯♠❛ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ❝♦♥❞✉çã♦ tér♠✐❝❛ tr❛♥s✐❡♥t❡ ❝♦♠ ♦ ♠♦✈✐♠❡♥t♦ ❞♦ ❝♦r♣♦ só❧✐❞♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❇❡❝❦ ❡ ▼❝▼❛st❡rs ✭✷✵✵✹✮ ♣❛r❛ ✉♠ ♣❛r❛❧❡❧❡♣í♣❡❞♦ ♦r✲ t♦tró♣✐❝♦✳ ❖s ❛✉t♦r❡s ♣r♦♣✉s❡r❛♠ ✉♠❛ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❡♥✈♦♥✈❡♥❞♦ tr❛♥s❢♦r♠❛çõ❡s ❞❡ ✈❛r✐á✈❡✐s ♣❛r❛ ❡❧✐♠✐♥❛r ❛s ❝♦♥❞✐çõ❡s ❞❡ ✢✉①♦ ❡ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ♦rt♦tró♣✐❝❛✳ ❯s❛♠✲s❡ ❞♦✐s t✐✲ ♣♦s ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥✿ ✉♠❛ ♣r♦✈❡♥✐❡♥t❡ ❞♦ ♠ét♦❞♦ ❞❡ tr❛♥s❢♦r♠❛❞❛ ▲❛♣❧❛❝❡ ❡ ♦✉tr♦ ❞♦ ♠ét♦❞♦ ❞❡ s❡♣❛r❛çã♦ ❞❡ ✈❛r✐á✈❡✐s✳ ❖ ♠ét♦❞♦ ❞❡ s♦❧✉çã♦ ✉s❛❞♦ é ♣♦❞❡r♦s♦ ♣♦rq✉❡ ✐♥❝♦r♣♦r❛ ✈❡r✐✜❝❛çã♦ ✐♥t❡r♥❛ ❞♦s r❡s✉❧t❛❞♦s ♥✉♠ér✐❝♦s ❛tr❛✈és ❞❛ ✈❛r✐❛çã♦ ❞♦ t❡♠♣♦ ❞❡ ♣❛rt✐çã♦ ❡♥tr❡ ♦s ❝♦♠♣♦♥❡♥t❡s ❝✉rt♦s ❡ ❧♦♥❣♦s✳ ❯♠ ❡①❡♠♣❧♦ ❢♦✐ ❞❛❞♦ ♣❛r❛ ✉♠❛ ❝❛s♦ ♠✉❧t✐✲❞✐♠❡♥s✐♦♥❛❧ q✉❡ ❡♥✈♦❧✈❡ ❛♠❜❛s ❛s ❝♦♥❞✐çõ❡s ❞❡ ✢✉①♦ ❞❡ ❝❛❧♦r ❡ ❞❡ ❝♦♥t♦r♥♦ ❞❡ t❡♠♣❡r❛t✉r❛ ♣r❡s❝r✐t♦s✳
❇❡❝❦ ❡t ❛❧✳ ✭✷✵✵✻✮ ❛♣r❡s❡♥t❛r❛♠ ❡♠ s❡✉ tr❛❜❛❧❤♦ ✉♠❛ ❛❜♦r❞❛❣❡♠ s♦❜r❡ ✈❡r✐✜❝❛çã♦ ✐♥✲ trí♥s❡❝❛✳ ❙❡❣✉♥❞♦ ♦s ❛✉t♦r❡s✱ ❛ ✈❡r✐✜❝❛çã♦ ❞❡ ❝ó❞✐❣♦s ♥✉♠ér✐❝♦s q✉❡ ❢♦r♥❡❝❡♠ s♦❧✉çõ❡s ❡♠ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❝❛❧♦r✱ ♦❜t✐❞♦s ♣♦r ❞✐✈❡rs♦s ♠ét♦❞♦s✱ é ♠✉✐t♦ ✐♠♣♦rt❛♥t❡✳ ❱❡r✐✜❝❛r ❡st❛s s♦❧✉çõ❡s ❝♦♥s✐st❡ ❡♠ ❝♦♠♣❛r❛r s❡✉s ✈❛❧♦r❡s ❝♦♠ s♦❧✉çõ❡s ❡①❛t❛s✱ ♠❛s t❛♠❜é♠ ❡①✐st❡♠ ♦✉tr❛s ❢♦r♠❛s ❞❡ ✈❡r✐✜❝❛çã♦ ✐♥trí♥s❡❝❛ q✉❡ ✉s❛♠✱ ♣❡❧♦ ♠❡♥♦s✱ ❞✉❛s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ✐♥❞❡♣❡♥❞❡♥t❡s ❡①❛t❛s ♣❛r❛ ♦❜t❡r ✈❛❧♦r❡s ♥✉♠ér✐❝♦s ♣r❡❝✐s♦s✳ ❚rês t✐♣♦s ❞✐❢❡r❡♥t❡s ❞❡ ✈❡r✐✜❝❛çã♦ ✐♥trí♥s❡❝❛ ♣❛r❛ ♣r♦❜❧❡♠❛s tr❛♥s✐❡♥t❡s ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s ❝♦♠ ❛❜♦r❞❛❣❡♠ ♠❛t❡♠át✐❝❛ ❡ ❡①❡♠♣❧♦s ❞❡ ❛♣❧✐❝❛çõ❡s
❏✳❑✐❞❛✇❛✲❑✉❦❧❛ ✭✷✵✵✽✮ ❛♣r❡s❡♥t♦✉ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ ✉♠❛ ♣❧❛❝❛ s✉❜♠❡t✐❞❛ ❛ ✉♠❛ ❢♦♥t❡ ❞❡ ❝❛❧♦r q✉❡ ❡stá ❡♠ ♠♦✈✐♠❡♥t♦✳ ❆ ❢♦♥t❡ ❞❡ ❝❛❧♦r s❡ ♠♦✈❡ s♦❜ ✉♠❛ tr❛❥❡tór✐❝❛ ❡❧✐♣t✐❝❛✱ s❡♠♣r❡ s♦❜ ❛ ♣❧❛❝❛✳ ❯♠❛ s♦❧✉çã♦ ❡①❛t❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ✉♠❛ ❢♦r♠❛ ❛♥❛❧ít✐❝❛ ❢♦✐ ♦❜t✐❞❛ ❛♣❧✐❝❛♥❞♦ ♦ ♠♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥✳ ❊①❡♠♣❧♦s ❞❡ r❡s✉❧t❛❞♦s ❞❡ ❝á❧❝✉❧♦s ♥✉♠ér✐❝♦s ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ ❞✐str✐❜✉✐çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♥❛ ♣❧❛❝❛ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s✳
✾
❞✐♠❡♥s✐♦♥❛❧ é ❛♣r❡s❡♥t❛❞❛ ♣♦r ❇❡❝❦ ❡t ❛❧✳ ✭✷✵✶✵✮ ❡♠ ❍❡❛t ❈♦♥❞✉❝t✐♦♥ ❯s✐♥❣ ●r❡❡♥✬s ❋✉♥❝✲ t✐♦♥s q✉❡ ❛❜♦r❞❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ✉♠ só❧✐❞♦ ♠ó✈❡❧ s❡ ♠♦✈❡♥❞♦ ❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ❝♦♥st❛♥t❡ s♦❜ ♦ ♣❧❛♥♦✱ ❛q✉❡❝✐❞♦ ♣♦r ✉♠ ✢✉①♦ ❞❡ ❝❛❧♦r✳ ◆❡st❡ t❡①t♦ é ♣r♦♣♦st♦ t❛♠❜é♠ ♣❡❧♦ ❛✉t♦r ♠✉❞❛♥ç❛s ❞❡ ✈❛r✐á✈❡✐s ♣❛r❛ q✉❡ ♦ t❡r♠♦ r❡❢❡r❡♥t❡ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞♦ só❧✐❞♦ s❡❥❛ ❧❡✈❛❞♦ ♣❛r❛ ♦s ❝♦♥t♦r♥♦s ❡ ♣♦ss❛ ❛♣❧✐❝❛r ♦ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥ ♣❛r❛ ❜✉s❝❛r s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s✳ ❖ t❡①t♦ ❛♣r❡s❡♥t❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ t❡ór✐❝♦ ❡ ❡①❡♠♣❧♦ ❞❡ ❛♣❧✐❝❛çã♦ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ s♦❜ ✉♠ só❧✐❞♦ s❡ ♠♦✈❡♥❞♦ ❝♦♠ ❣❡♦♠❡tr✐❛ s❡♠✐✲✐♥✜♥✐t❛✳
❖ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ ✉♠ ❝✐❧✐♥❞r♦ ❢♦✐ ❛♥❛❧✐s❛❞♦ ♣♦r ❈❤❡♥ ✭✷✵✶✵✮ ❡♠ s❡✉ tr❛❜❛❧❤♦✳ ❯s❛♥❞♦ ♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❝✐❧í♥❞r✐❝❛s ❢♦✐ ❛❜♦r❞❛❞♦ ✉♠ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥ ❤í❜r✐❞♦✳ ❖ ♠ét♦❞♦ ♣r♦♣♦st♦ ❝♦♠❜✐♥❛ ❛ tr❛♥s❢♦r♠❛❞❛ ❞❡ ▲❛♣❧❛❝❡ ❛♣❧✐❝❛❞❛ ❛ ❢✉♥çã♦ ❞❡ ●r❡❡♥ ❞♦ ♣r♦❜❧❡♠❛ ❡ ♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❡✲❛❧❣♦r✐t❤♠ ♣❛r❛ ❛❝❡❧❡r❛r ❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞❛s sér✐❡s ❞❛ s♦❧✉çã♦✳ ❖ ❛✉t♦r ❛♣r❡s❡♥t♦✉ s❡✐s ❡①❡♠♣❧♦s ❞✐✈✐❞✐❞♦s ❡♠ ✉♥✐❞✐♠❡♥s✐♦♥❛❧✱ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡ tr✐❞✐♠❡♥s✐♦♥❛❧✱ ♦♥❞❡ s❡ ❞❡s❝r❡✈❡ ♦ ♣r♦❜❧❡♠❛✱ ❛ ❢✉♥çã♦ ❞❡ ●r❡❡♥ q✉❡ ❝❛r❛❝t❡r✐③❛ ♦ ♣r♦❜❧❡♠❛✱ ❛ s♦❧✉çã♦ ♣❡❧♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ❡ ❣rá✜❝♦s ✐❧✉str❛♥❞♦ ❛ s♦❧✉çã♦ ♦❜t✐❞❛ ♣❛r❛ ❛❧❣✉♥s t❡♠♣♦s ❡ ♣♦s✐çõ❡s✳ ❈♦♥❝❧✉✐✲s❡ q✉❡ ♦ ♠ét♦❞♦ ❤í❜r✐❞♦ ❞❡♠♦str♦✉ s✉❝❡ss♦ ♥❛ ✐♥✈❡st✐❣❛çã♦ ❞❡st❡ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛✱ ♥ã♦ ❛♣r❡s❡♥t❛♥❞♦ ♦s❝✐❧❛çõ❡s ♥✉♠ér✐❝❛s✳
❑✐♠ ✭✷✵✶✶✮ ❢❡③ ✉♠❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛ ❞❡ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡①♣♦st♦s ❛ ❢♦♥t❡s ♠ó✈❡✐s✳ ❊st❡ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛✱ ❞❡♥♦♠✐♥❛❞♦ ♣❛r❛❜ó❧✐❝♦✱ é ♦❜s❡r✈❛❞♦ ❡♠ ✈ár✐♦s r❛♠♦s ❞❡ ❡♥❣❡♥❤❛r✐❛ ❡ s❡❣✉♥❞♦ ❑✐♠ ✭✷✵✶✶✮ ❡ ♣♦❞❡ s❡r ❛♥❛❧✐s❛❞♦ ❝♦♠ ê①✐t♦ ✉s❛♥❞♦ ♦ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✐♠♣❧❡♠❡♥t❛♥❞♦ ✉♠❛ ♠❛❧❤❛ ❛❞❛♣t❛t✐✈❛ ♣❛r❛ ❧✐❞❛r ❝♦♠ ♦ ♣r♦❜❧❡♠❛ ♦♥❞❡ ❛ ❢♦♥t❡ ❞❡ ❝❛❧♦r ❡stá ❡♠ ♠♦✈✐♠❡♥t♦✳ ❆ té❝♥✐❝❛ ❛♣r❡s❡♥t❛❞❛ ♣❡r♠✐t❡ ♦ ✉s♦ ❞❡ ♣❡q✉❡♥♦s ❡❧❡♠❡♥t♦s ❡♠ ár❡❛s ❞❡ ❣r❛♥❞❡s t❛①❛s ❞❡ ✈❛r✐❛çã♦ ❞❡ t❡♠♣♦ ❡ ♠✉❞❛♥ç❛ ❞❡ t❡♠♣❡r❛t✉r❛✳ ❖s ❛✉t♦r❡s ♠♦str❛♠ q✉❡ ✉♠ r❡❣✐♠❡ ❞❡ ♠❛❧❤❛ ❛❞❛♣t❛t✐✈❛ é ❡✜❝❛③ ♥❛ ❧♦❝❛❧✐③❛çã♦ ❞❡ ♦s❝✐❧❛çõ❡s ❞❡✈✐❞♦ ❛ ❣r❛❞✐❡♥t❡s ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡ ❛❣✉❞❛s ♥❛ s♦❧✉çã♦✱ ❛❧é♠ ❞♦ ♠ét♦❞♦ s✉♣❡r❛r ❡♠ q✉❛s❡ ✸✪ ♦ ♠ét♦❞♦ tr❛❞✐❝✐♦♥❛❧ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳
✶✵
❝♦♠ ❞❛❞♦s ♦❜t✐❞♦s ❞❡ ❛♥á❧✐s❡s ♥✉♠ér✐❝❛s ✉t✐❧✐③❛♥❞♦ ❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s✱ ♦s r❡s✉❧t❛❞♦s ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s✱ ♣❡❧♦s ❛✉t♦r❡s✱ s❛t✐s❢❛tór✐♦s✳
◆❡st❡ ❝♦♥t❡①t♦ ❡st❡ tr❛❜❛❧❤♦ ♣r❡t❡♥❞❡ ❝♦♥tr✐❜✉✐r ❛♣r❡s❡t❛♥❞♦ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ❡♠ ❝♦♥✲ ❞✉çã♦ ❞❡ ❝❛❧♦r ❝♦♠ ❢♦♥t❡s ♠ó✈❡✐s✱ tr❛♥s✐❡♥t❡s ❡ ♠✉❧t✐✲❞✐♠❡♥s✐♦♥❛✐s ❝♦♠ ✈❛r✐❛❞♦s t✐♣♦s ❞❡ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦✱ ❡ ✉♠❛ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ s♦❜r❡ ♦ ♠ét♦❞♦ ❞❡ s♦❧✉çã♦✳
❆s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s r❡♣r❡s❡♥t❛♠ ✉♠❛ ✐♠♣♦rt❛♥t❡ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡✲ ♠❛s ❞❡ ❡♥❣❡♥❤❛r✐❛✱ ✉♠❛ ✈❡③ q✉❡ ♣♦❞❡♠ s❡r ✉s❛❞❛s ♣❛r❛ ❛ ✈❛❧✐❞❛çã♦ ❞❡ s♦❧✉çõ❡s ❛♣r♦①✐♠❛❞❛s✱ ❢❛❝✐❧✐t❛♠ ❛ ❛♥á❧✐s❡ ❡ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❡ ♣r♦❜❧❡♠❛s ❢ís✐❝♦s ❋❡r♥❛♥❞❡s ✭✷✵✵✾✮✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❢♦r✲ ♥❡❝❡r ✐♥❢♦r♠❛çõ❡s ♣r❡❝✐s❛s s♦❜r❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛s ❞✐str✐❜✉✐çõ❡s ❞❡ t❡♠♣❡r❛t✉r❛ ❡ ✢✉①♦ ❞❡ ❝❛❧♦r q✉❡ ♣♦❞❡♠ s❡r ❞✐❢í❝❡✐s ❞❡ ♣❡r❝❡❜❡r ❛ ♣❛rt✐r ❞❛s s♦❧✉çõ❡s ♥✉♠ér✐❝❛s✳ ❈♦♥t✉❞♦ ❡①✐st❡ ✉♠❛ ❣r❛♥❞❡ ❞✐✜❝✉❧❞❛❞❡ ♠❛t❡♠át✐❝❛ ♥❛ ♦❜t❡♥çã♦ ❞❡ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ❡♥✈♦❧✈❡♥❞♦ ✐♥t❡r♣r❡✲ t❛çã♦ ❡ ❝á❧❝✉❧♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ tér♠✐❝♦✱ ❝♦♠♦ s✉❣❡r❡ ❋❡r♥❛♥❞❡s ✭✷✵✵✾✮ ✏❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ✉♠ ♠♦❞❡❧♦ tér♠✐❝♦✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❡ ♦❜t❡♥çã♦ ❞❡ s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s✱ ♥♦r♠❛❧♠❡♥t❡ ❡♥❝♦♥tr❛✲s❡ ❡♠ ♣r♦❜❧❡♠❛s ♠✉❧t✐❞✐♠❡♥s✐♦♥❛✐s tr❛♥s✐❡♥t❡s s✉❜♠❡t✐❞♦s ❛ ♥ã♦ ❤♦♠♦❣❡♥❡✐❞❛❞❡s ❝♦♠♦ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ✢✉①♦ ♣r❡s❝r✐t♦✱ ❣❡r❛çã♦ ❞❡ ❝❛❧♦r ♦✉ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❝♦♠♦ t❡♠♣❡r❛t✉r❛ ✈❛r✐❛♥❞♦ ❝♦♠ ♦ t❡♠♣♦✳✑
❈❛♣ít✉❧♦ ✸
❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛
✸✳✶ ■♥tr♦❞✉çã♦
◆❡st❛ s❡çã♦ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠❡t♦❞♦❧ó❣✐❝❛ ❞❡ ❛♥á❧✐s❡ ♠❛t❡♠át✐❝❛ ❡ ❢ís✐❝❛ ❡♥✲ ✈♦❧✈❡♥❞♦ ♣r♦❜❧❡♠❛s ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❛q✉❡❝✐❞♦s ♣♦r ❢♦♥t❡s ♠ó✈❡✐s✳ ■♥✐❝✐❛❧♠❡♥t❡ ❛♣r❡s❡♥t❛✲ s❡ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ✉♠ ♣r♦❜❧❡♠❛ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ ❡ ❡♠ s❡❣✉✐❞❛ s❡rã♦ ❛❜♦r❞❛❞♦s ♦s ♣r♦✲ ❜❧❡♠❛s ❜✐ ❡ tr✐❞✐♠❡♥s✐♦♥❛✐s✳ ❊♠ t♦❞♦s ♦s ❝❛s♦s ❛s s♦❧✉çõ❡s ❛♥❛❧ít✐❝❛s ❢♦r❛♠ ♦❜t✐❞❛s ✉s❛♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥✳
✸✳✷ ❙♦❧✉çã♦ ●❡r❛❧
1
D
tr❛♥s✐❡♥t❡
❖ ❢❡♥ô♠❡♥♦ ❢ís✐❝♦ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❝❛❧♦r ❡♠ ✉♠ só❧✐❞♦ ♠ó✈❡❧ q✉❛❧q✉❡r é ❞❡s❝r✐t♦ ♣♦r✿
k∂
2T
∂x2 =ρcp
∂T ∂t +v
∂T ∂x
, ✭✸✳✶✮
♦♥❞❡v é ❛ ✈❡❧♦❝✐❞❛❞❡ ❡♠ q✉❡ ♦ só❧✐❞♦ s❡ ♠♦✈✐♠❡♥t❛ ♣❡❧❛ ❞✐r❡çã♦ ♥❡❣❛t✐✈❛ ❛tr❛✈és ❞♦ ❡✐①♦
❝♦♦r❞❡♥❛❞♦ x✳
❉❡ ❢♦r♠❛ ❣❡r❛❧✱ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ♣r✐♠❡✐r♦ t✐♣♦ ♣♦❞❡♠ s❡r ❞❛❞❛s ♣♦r✿
T(0, t) = Tx1, ✭✸✳✷✮
T(L, t) = Tx2, ✭✸✳✸✮
✶✷
❥á ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❞❡ s❡❣✉♥❞♦ ❡ t❡r❝❡✐r♦ t✐♣♦s sã♦ ❞❛❞❛s ♣♦r✿
−k∂T ∂x
x=0 = hx1[T∞−T(0, t)] +qx1, ✭✸✳✹✮ −k∂T
∂x
x=L= hx2[T(L, t)−T
∞]−qx2, ✭✸✳✺✮
s✉❥❡✐t♦ à ✉♠❛ ❝♦♥❞✐çã♦ ✐♥✐❝✐❛❧✿
T(x,0) =F(x). ✭✸✳✻✮
P❛r❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠ét♦❞♦ ❞❡ ❢✉♥çõ❡s ❞❡ ●r❡❡♥ s✉❣❡r❡✲s❡ ✉♠❛ ♠✉❞❛♥ç❛ ❞❡ ✈❛r✐á✈❡❧ ❛❞❡✲ q✉❛❞❛ ♣❛r❛ ❛♣❧✐❝❛r ♦ ♠ét♦❞♦✱ ✐ss♦ ❞❡✈✐❞♦ ❛♦ t❡r♠♦✿
ρcpv
∂T
∂x ✭✸✳✼✮
♣r❡s❡♥t❡ ♥❛ ❊q✳✭✸✳✶✮
❉❡st❛ ❢♦r♠❛ ✉t✐❧✐③❛♥❞♦ ❛ r❡❧❛çã♦✱ ❞❛❞❛ ♣❡❧❛ ❊q✳✭✸✳✽✮✱ ❞❡✜♥✐❞❛ ♣♦r ❏✳❚✉s❡❦✱ ❏✳❚♦♠❝ ❡ ▼✳❘❛❞❦♦✈✐❝ ✭✷✵✵✷✮ ❝♦♠♦ ▲✐♦✉✈✐❧❧❡ tr❛♥s❢♦r♠❛t✐♦♥✿
exp
vx
2α − v2t
4α
, ✭✸✳✽✮
t❡r❡♠♦s ✉♠ ♥♦✈♦ ♣r♦❜❧❡♠❛✱ ♣♦ré♠ ❛❣♦r❛ ♥❛ ✈❛r✐á✈❡❧W✱ ❛ss✐♠ ❛ r❡s♣♦st❛ ❞❡ t❡♠♣❡r❛t✉r❛ ❞♦
♣r♦❜❧❡♠❛ s❡rá ❝❛❧❝✉❧❛❞❛ ❢❛③❡♥❞♦✿
T(x, t) = W(x, t)expvx
2α − v2t
4α
. ✭✸✳✾✮
▼❛s ♣❛r❛ r❡❛❧✐③❛r♠♦s ❛ ♠✉❞❛♥ç❛ ♣❛r❛ ❛ ♥♦✈❛ ✈❛r✐á✈❡❧ W ♣r✐♠❡✐r❛♠❡♥t❡✱ ❛ ♣❛rt✐r ❞❛
❊q✳✭✸✳✾✮ ❝❛❧❝✉❧❛♠♦s✿ ∂T ∂x = ∂W ∂x exp vx
2α − v2t
4α
+W v
2αexp
vx
2α − v2t
4α
∂2T
∂x2 =
∂2W
∂x2 exp
vx
2α − v2t
4α
+∂W
∂x v
2αexp
vx
2α − v2t
4α
+ ∂W
∂x v
2αexp
vx
2α − v2t
4α
+W v
2
4αexp
vx
2α − v2t
4α , ∂T ∂t = ∂W ∂t exp vx
2α − v2t
4α
−Wv
2
4αexp
vx
2α − v2t
4α
✶✸
❙✉❜st✐t✉✐♥❞♦ ♥❛ ❊q✳✭✸✳✶✮ t❡r❡♠♦s✿
exp
vx
2α − v2t
4α
∂2W
∂x2 + 2
∂W ∂x
v
2α +W v2 4α = 1 α exp vx
2α − v2t
4α
∂W
∂t −W
v2 4α + v exp vx
2α − v2t
4α
∂W
∂x +W
v
2α
✭✸✳✶✶✮
❆♣ós s✐♠♣❧✐✜❝❛çõ❡s ♦❜té♠✲s❡✿
k∂
2W
∂x2 =ρcp
∂W
∂t , ✭✸✳✶✷✮
q✉❡ é ♦ ♣r♦❜❧❡♠❛ ❛✉①✐❧✐❛r ♥❛ ✈❛r✐á✈❡❧W✳ ◆♦t❡ ❛ ❛✉sê♥❝✐❛ ❞♦ t❡r♠♦ ❞❡♣❡♥❞❡♥t❡ ❞❛ ✈❡❧♦❝✐❞❛❞❡
♥❛ ❊q✳ ✭✸✳✶✷✮✳
❆ss✐♠✱ ❞❛ ♠❡s♠❛ ❢♦r♠❛ s✉❜st✐t✉✐✲s❡ ❛s ❊qs✳ ✭✸✳✶✵✮ ♥❛s ❊qs✳✭✸✳✷ ✲ ✸✳✻✮ ❡ ♦❜té♠✲s❡ ♣❛r❛ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❞❡ ♣r✐♠❡✐r♦ t✐♣♦✿
W(0, t) = T(0, t)exp
v2t
4α
, ✭✸✳✶✸✮
W(L, t) = T(L, t)exp
−vL
2α + v2t
4α
, ✭✸✳✶✹✮
♦s ❝♦♥t♦r♥♦s ❞❡ s❡❣✉♥❞♦ ❡ t❡r❝❡✐r♦ t✐♣♦ s❡rã♦✿
−k
exp
−v2t
4α
∂W
∂x +W
v
2α
x=0+hx1W exp
−v2t
4α
=hx1T∞+qx1 ✭✸✳✶✺✮
s✐♠♣❧✐✜❝❛♥❞♦✿
−k∂W ∂x
x=0+W|x=0
−kv
2α +hx1
=exp
v2t
4α
(hx1T∞+qx1), ✭✸✳✶✻✮
❞❡ ❢♦r♠❛ ❛♥á❧♦❣❛ ♣❛r❛ ♦ ❝♦♥t♦r♥♦ ❡♠x=L✿
k∂W ∂x
x=L+W|x=L
kv
2α +hx1
=exp
−v2t
4α + v2t
4α
(hx2T∞+qx2), ✭✸✳✶✼✮
❆ ❝♦♥❞✐çã♦ ✐♥✐❝✐❛❧ é t❛♠❜é♠ ♦❜t✐❞❛ ❞❛ ❊q✳ ✭✸✳✶✵✮ ❡ t❡♠ ❛ ❢♦r♠❛✿
W(x,0) =F(x)exp−vx
2α
. ✭✸✳✶✽✮
