Leonardo Salas Maldonado.pdf

0
0
253
2 months ago
Preview
Full text

❯◆■❱❊❘❙■❉❆❉❊ ❉❖ ❊❙❚❆❉❖ ❉❊ ❙❆◆❚❆ ❈❆❚❆❘■◆❆ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❚❊❈◆❖▲Ó●■❈❆❙

❯◆■❱❊❘❙■❉❆❉❊ ❉❖ ❊❙❚❆❉❖ ❉❊ ❙❆◆❚❆ ❈❆❚❆❘■◆❆ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❚❊❈◆❖▲Ó●■❈❆❙❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆ P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆ ▲❊❖◆❆❘❉❖ ❏❖❙➱ ❆▼❆❉❖❘ ❙❆▲❆❙ ▼❆▲❉❖◆❆❉❖❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❊ ▼❆❚❊❘■❆■❙ ▼❆●◆➱❚■❈❖❙ ❆ ❇❆■❳❖ ❈❯❙❚❖ ❆P▲■❈❆❉❆ ➚ ❖❇❚❊◆➬➹❖ ❉❖❙P❆❘➶▼❊❚❘❖❙ ❉❊ ❯▼ ❉■❙P❖❙■❚■❱❖ ❊▲❊❚❘❖▼❆●◆➱❚■❈❖❏❖■◆❱■▲▲❊ ✷✵✶✺ ❯◆■❱❊❘❙■❉❆❉❊ ❉❖ ❊❙❚❆❉❖ ❉❊ ❙❆◆❚❆ ❈❆❚❆❘■◆❆ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❚❊❈◆❖▲Ó●■❈❆❙❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆ P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆ ▲❊❖◆❆❘❉❖ ❏❖❙➱ ❆▼❆❉❖❘ ❙❆▲❆❙ ▼❆▲❉❖◆❆❉❖❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❊ ▼❆❚❊❘■❆■❙ ▼❆●◆➱❚■❈❖❙ ❆ ❇❆■❳❖ ❈❯❙❚❖ ❆P▲■❈❆❉❆ ➚ ❖❇❚❊◆➬➹❖ ❉❖❙P❆❘➶▼❊❚❘❖❙ ❉❊ ❯▼ ❉■❙P❖❙■❚■❱❖ ❊▲❊❚❘❖▼❆●◆➱❚■❈❖ ❉✐ss❡rt❛çã♦ s✉❜♠❡t✐❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧é✲tr✐❝❛ ❞♦ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❚❡❝♥♦❧ó✲ ❣✐❝❛s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❊st❛❞♦ ❞❡❙❛♥t❛ ❈❛t❛r✐♥❛✱ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧é✲tr✐❝❛✳ ❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆♥tô♥✐♦ ❋✳ ▲✳◆♦❣✉❡✐r❛ ❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆❞❛❧❜❡rt♦❞❡ ❆✳ ❇✳ ❋✐❧❤♦ ❏❖■◆❱■▲▲❊ ✧❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❊ ▼❆❚❊❘■❆■❙ ▼❆●◆➱❚■❈❖❙ ❆❇❆■❳❖ ❈❯❙❚❖ ❆P▲■❈❆❉❆ ➚ ❖❇❚❊◆➬➹❖ ❉❖❙ P❆❘➶▼❊❚❘❖❙ ❉❊ ❯▼ ❉■❙P❖❙■❚■❱❖❊▲❊❚❘❖▼❆●◆➱❚■❈❖✧ ♣♦r▲❡♦♥❛r❞♦ ❏♦sé ❆♠❛❞♦r ❙❛❧❛s ▼❛❧❞♦♥❛❞♦ ❊st❛ ❉✐ss❡rt❛çã♦ ❢♦✐ ❥✉❧❣❛❞❛ ❛❞❡q✉❛❞❛ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❡ ❛♣r♦✈❛❞♦ ❡♠ s✉❛ ❢♦r♠❛ ✜♥❛❧ ♣❡❧♦P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆ ❉❖❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❚❊❈◆❖▲Ó●■❈❆❙ ❉❆ ❯◆■❱❊❘❙■❉❆❉❊ ❉❖ ❊❙❚❆❉❖ ❉❊ ❙❆◆❚❆ ❈❆❚❆❘❚■◆❆Pr♦❢✳ ❉r✳ ❆♥tô♥✐♦ ❋✳ ▲✳ ◆♦❣✉❡✐r❛ ❈❈❚✴❯❉❊❙❈ ✭❖r✐❡♥t❛❞♦r✴♣r❡s✐❞❡♥t❡✮❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿ Pr♦❢✳ ❉r✳ ❆❞❡♠✐r ◆✐❡❞❈❈❚✴❯❉❊❙❈ ❏♦✐♥✈✐❧❧❡✱ ✷✼ ❞❡ ❢❡✈❡r❡✐r♦ ❞❡ ✷✵✶✺✳ Pr♦❢✳ ❉r✳ ▼❛✉r✐❝✐♦ ❱✳ ❋✳ ❞❛ ▲✉③✳❯❋❙❈ Pr♦❢✳ ❉r✳ ❏♦sé ❞❡ ❖❧✐✈❡✐r❛❈❈❚✴❯❉❊❙❈ ✭❙✉♣❧❡♥t❡✮ ➚ ♠✐♥❤❛ ❡s♣♦s❛✱ ❙tt❡❧❛ ▼❛r✐s✱ ♣❡❧♦ ❛♣♦✐♦ ❡ ❝♦♠♣r❡❡♥sã♦✳❆♦s ♠❡✉s ✜❧❤♦s✱ ❆❧❡ss❛♥❞r❛✱ ❋❡r♥❛♥❞♦ ❡ ▲❡♦♥❛r❞♦ ❱✐♥✐❝✐✉s✱ ♣♦r ❛❧❡❣r❛r❡♠ ❛ ♠✐✲♥❤❛ ✈✐❞❛✳ ➚s ♠✐♥❤❛s ❢❛♠í❧✐❛s✱ ❝❤✐❧❡♥❛ ❡ ❜r❛s✐❧❡✐r❛✳❆♦s ♠❡✉s s❛✉❞♦s♦s ♣❛✐s✱ ▲✐❧✐❛♥❛ ❡ ❊✈❛✲ r✐st♦✳ ❆●❘❆❉❊❈■▼❊◆❚❖❙❆ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ♣♦ssí✈❡❧ ❣r❛ç❛s à ❝♦♦♣❡r❛çã♦ ❞❡ ✈ár✐❛s ♣❡ss♦❛s q✉❡ s❡ ❞❡❞✐❝❛r❛♠ ❛♦ ❧♦♥❣♦ ❞♦ ♣r♦❣r❡ss♦ ❞❡st❛ ❝♦♥tr✐❜✉✐✲çã♦ ❝✐❡♥tí✜❝❛✳ ●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛ t♦❞♦s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ♦❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ❡♠ ❡s♣❡❝✐❛❧✿ ✕ à ♠✐♥❤❛ ❡s♣♦s❛✱ ❙tt❡❧❛ ▼❛r✐s✱ ♣♦r s✉❛ ❛❥✉❞❛ ♥❛ ❡s❝r✐t❛ ❡ r❡✈✐sã♦♦rt♦❣rá✜❝❛ ❡ ♣♦r s❡✉ ❛♣♦✐♦ ❡ ❝❛r✐♥❤♦❀ ✕ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ♦ ❞♦✉t♦r ❆♥tô♥✐♦ ❋❧❛✈✐♦ ▲✐❝❛r✐ã♦ ◆♦❣✉❡✐r❛✱♣♦r s✉❛ ♦r✐❡♥t❛çã♦ ❡ ♠❛t❡r✐❛❧ ❞✐❞át✐❝♦✱ ♣r✐♠♦r❞✐❛✐s ♣❛r❛ ❡✈♦❧✉çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❖❜r✐❣❛❞♦ ♣♦r s✉❛ ❞❡❞✐❝❛çã♦ ❡ ♠♦t✐✈❛çã♦❀ ✕ ❛♦ ♠❡✉ ❝♦♦r✐❡♥t❛❞♦r✱ ♦ ♠❡str❡ ❆❞❛❧❜❡rt♦ ❞❡ ❆r❛ú❥♦ ❇❛rr❡t♦❋✐❧❤♦✱ ♣♦r s✉❛s ✈❛❧✐♦s❛s s✉❣❡stõ❡s ❡ ♠❛t❡r✐❛❧ ❜✐❜❧✐♦❣rá✜❝♦❀ ✕ ❛♦ ♠❡✉ ❡①✲❛❧✉♥♦✱ ●❛❜r✐❡❧ ❍❡r♠❛♥♥ ◆❡❣r✐✱ ♣❡❧♦ ❛✉①í❧✐♦ ❝♦♠ ♦s❝ó❞✐❣♦s ❡♠ ▲✉❛❀ ✕ ❛♦ ♠❡✉ ❡①✲❛❧✉♥♦✱ ❆rt❤✉r ●❛r❝✐❛ ❇❛rts❝❤✱ ♣❡❧❛ ❞✐❣✐t❛çã♦ ❡ s✉✲❣❡stõ❡s✳ ❆ ▲❡❜r❡ ❡ ❛ ❚❛rt❛r✉❣❛ ♠♦str❛ ❛ ✐♠✲ ♣♦rtâ♥❝✐❛ ❞❛ ♣❡rs❡✈❡r❛♥ç❛✱ ✉♠❛ ❤✐stór✐❛❝♦♥t❛❞❛ ♣♦r ❊s♦♣♦✱ ❢❛❜✉❧✐st❛ ❣r❡❣♦ ❞♦ sé✲ ❝✉❧♦ ❱■■ ❆❈✱ ♦✉ ❝♦♠♦ ❡r❛♠ ❝❤❛♠❛❞♦s✿✧P❡❞❛✲❣♦❣♦s✧✱ ❡s❝r❛✈♦ ❞❡ ❥♦❣♦s✳ ❖ ❡♥✲ s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧✱ ♣❛r❛ ♦s ❣r❡❣♦s✱ ❝♦♠❡✲ç❛✈❛ ♣♦r ♣r✐♥❝í♣✐♦s ♠♦r❛✐s ❡ ét✐❝♦s✳ ✧❙ó s❡✐ q✉❡ ♥❛❞❛ s❡✐✧✳ ❙ó❝r❛t❡s✳ ◆♦✐♥í❝✐♦✱ ❛❝r❡❞✐t❛✲s❡ ❡♠ ✐❞❡✐❛s ❡ ❝♦♥❝❡✐t♦s✱ ❝♦♠ ♦ t❡♠♣♦ s❡ ♣❡r❝❡❜❡ ♦ q✉ã♦ ❡rr❛❞♦♣♦❞❡✲s❡ ❡st❛r✳ ❊st❛ ❞✐ss❡rt❛çã♦ ✈❛✐ ❛♦ ❡♥❝♦♥tr♦ ❞❡ ♠✉✐✲t❛s ❞ú✈✐❞❛s ❡ ♦ r❡❛✈❡r ❞❡ ❝♦♥❝❡✐t♦s ❞✐t♦s ✏❜ás✐❝♦s✧✱ ♠❛s q✉❡ t❡r♠✐♥❛ ❛♣r❡s❡♥t❛♥❞♦♦ q✉❛♥t♦ ❛ ♥❛t✉r❡③❛ ♣♦❞❡ s❡r ❝♦♠♣❧❡①❛✳ ❋r❡♥t❡ ❛ ✐ss♦✱ só r❡st❛ ❛ ♣❡rs❡✈❡r❛♥ç❛ ❞❛❜✉s❝❛ ❞❡ ✉♠❛ r❡s♣♦st❛✱ q✉❡ ❛❧❣✉♥s ❝❤❛✲ ♠❛♠ ❞❡ ♠♦❞❡❧♦ ♦✉tr♦s ❞❡ t❡♦r✐❛✳ ❘❊❙❯▼❖❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ sí♥t❡s❡ ❞♦ ❡st❛❞♦ ❞❛ ❛rt❡ s♦❜r❡ ❛s ❝❛✲ r❛❝t❡r✐③❛çõ❡s ❡ ♣❡r❞❛s ♥♦ ❢❡rr♦ s♦❜ ♦ ❡♥❢♦q✉❡ ❞❛ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛❀♣r❡t❡♥❞❡✲s❡ ❝♦♠♣r❡❡♥❞❡r ❡ ❣❡r❛r s✉❜sí❞✐♦s ♣❛r❛ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ♠❛✲ t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ❛ ❜❛✐①♦ ❝✉st♦✱ ❛♣❧✐❝❛❞♦ ♥❛ ❛✈❛❧✐❛çã♦ ❞❡ ♣❛râ♠❡✲tr♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ❡ ❞❡ ❡✜❝✐ê♥❝✐❛ ❡♥❡r❣ét✐❝❛ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❡❧❡tr♦✲♠❛❣♥ét✐❝♦s✱ ❛tr❛✈és ❞❡ ✉♠❛ ✈✐sã♦ q✉❛❧✐t❛t✐✈❛ ❞♦s ❢❡♥ô♠❡♥♦s ❡❧❡tr♦♠❛❣✲♥ét✐❝♦s ❝♦♠♣❧❡①♦s ❛✉①✐❧✐❛♥❞♦ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❡ ❡st✉❞♦ ❞♦ ♣r♦❥❡t♦ ❞❡♠áq✉✐♥❛s ❡❧étr✐❝❛s✳P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❈♦♥t❛❝t♦r❡s❀ ■♥❞✉tâ♥❝✐❛❀ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐✲♥✐t♦s❀ P❡r❞❛s ♠❛❣♥ét✐❝❛s❀ Pr♦❣r❛♠❛s ❞❡ ❙✐♠✉❧❛çã♦❀ ❚r❛♥s❢♦r♠❛❞♦r❡s ❆❇❙❚❘❆❈❚❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ st❛t❡ ♦❢ t❤❡ ❛rt s②♥t❤❡s✐s ❛❜♦✉t t❤❡ ❝❤❛r❛❝t❡r✐③❛✲ t✐♦♥ ❛♥❞ ❧♦ss❡s ✐♥ ✐r♦♥ ✉♥❞❡r t❤❡ ❢♦❝✉s ♦❢ ❊❧❡❝tr✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣❀ ✐t ✐s✐♥t❡♥❞❡❞ t♦ ✉♥❞❡rst❛♥❞ ❛♥❞ t♦ ❣❡♥❡r❛t❡ ❛✐❞s t♦ ❢❡rr♦♠❛❣♥❡t✐❝ ♠❛t❡r✐❛❧s❝❤❛r❛❝t❡r✐③❛t✐♦♥ ❛t ❧♦✇ ❝♦st✱ ❛♣♣❧✐❡❞ ✐♥ t❤❡ ❡✈❛❧✉❛t✐♦♥ ♦❢ ❡❧❡❝tr♦♠❛❣✲♥❡t✐❝ ♣❛r❛♠❡t❡rs ❛♥❞ ❡♥❡r❣❡t✐❝❛❧ ❡✣❝✐❡♥❝② ♦❢ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ❞❡✈✐❝❡s✱✉s✐♥❣ ❛ q✉❛❧✐t❛t✐✈❡ ✈✐❡✇ ♦❢ ❝♦♠♣❧❡① ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ♣❤❡♥♦♠❡♥❛✱ ❤❡❧✲♣✐♥❣ ✐♥ t❤❡ ❝♦♠♣r❡❤❡♥s✐♦♥ ❛♥❞ ✐♥ t❤❡ st✉❞② ♦❢ t❤❡ ❡❧❡❝tr✐❝❛❧ ♠❛❝❤✐♥❡s♣r♦❥❡❝t✳❑❡②✇♦r❞s✿ ❈♦♥t❛❝t♦rs❀ ■♥❞✉❝t❛♥❝❡❀ ❋✐♥✐t❡ ❊❧❡♠❡♥t ▼❡t❤♦❞❀ ▼❛❣♥❡✲ t✐❝ ▲♦ss❡s❀ ❙✐♠✉❧❛t✐♦♥ ❙♦❢t✇❛r❡❀ ❚r❛♥s❢♦r♠❡rs ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙❋✐❣✉r❛ ✶✳✶ ▲❛ç♦s ❞❡ ❤✐st❡r❡s❡✱ ♦♣❡r❛çã♦ q✉❛s❡✲❡stát✐❝❛✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵❋✐❣✉r❛ ✶✳✷ ■♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H ❡♠ ✉♠❛ ❧❛♠✐♥❛çã♦ ❞❡ ❡s♣❡s✲ s✉r❛ d✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶❋✐❣✉r❛ ✶✳✸ ▲❛ç♦s ❞❡ ❤✐st❡r❡s❡✱ f = 50 Hz✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷❋✐❣✉r❛ ✶✳✹ ▲❛ç♦s ❞❡ ❤✐st❡r❡s❡✱ f = 250 Hz✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸❋✐❣✉r❛ ✶✳✺ ❈❛r❛❝t❡ríst✐❝❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ❧✐♥❡❛r✐③❛❞❛ ♣♦r ♣❛rt❡s✳ ✹✺❋✐❣✉r❛ ✷✳✶ ▼❛❧❤❛s ❢♦r♠❛❞❛s ♣♦r ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ♣r✐✲ ♠❡✐r❛ ♦r❞❡♠❀ ✭❛✮ ♠❛❧❤❛ ✐♥❝♦rr❡t❛❀ ✭❜✮ ♠❛❧❤❛ ❝♦rr❡t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ i (x, y)❋✐❣✉r❛ ✷✳✷ ❋✉♥çõ❡s ♣❧❛♥❛r❡s α ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸❋✐❣✉r❛ ✷✳✸ ❋✉♥çõ❡s ♣❧❛♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹❋✐❣✉r❛ ✷✳✹ ❖s ❡❧❡♠❡♥t♦s ✶✱ ✷✱ ✸ ❡ ✹ ❝♦♠♣❛rt✐❧❤❛♠ ♦ ♥ó ✏❛✑✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺❋✐❣✉r❛ ✸✳✶ ●rã♦ ♦r✐❡♥t❛❞♦ ✭●❖✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺❋✐❣✉r❛ ✸✳✷ ●rã♦ ♥ã♦✲♦r✐❡♥t❛❞♦ ✭●◆❖✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻❋✐❣✉r❛ ✸✳✸ ❖ ❞✐♣♦❧♦ ♠❛❣♥ét✐❝♦ t❡♠ ♦r✐❣❡♠ ♥♦ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ❞♦s ❡❧étr♦♥s ♥♦s í♦♥s ♦✉ át♦♠♦s q✉❡ ❢♦r♠❛♠ ❛ ♠❛tér✐❛✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼❋✐❣✉r❛ ✸✳✹ ❆tr❛✈és ❞♦ ❞✐❛❣r❛♠❛ ❞❡ ▲✐♥✉s P❛✉❧✐♥❣✱ ♦❜té♠✲s❡ ❛ ❞✐s✲ tr✐❜✉✐çã♦ ❞♦s ❡❧étr♦♥s ♥♦s ♦r❜✐t❛✐s✳ ◆♦ ❝❛s♦ ❞♦ ❢❡rr♦ sã♦ ✹ ♠♦♠❡♥✲t♦s ❛♥❣✉❧❛r❡s ❞❡ s♣✐♥ ♥ã♦ ♥✉❧♦s✱ ✐st♦ é✱ ✹ ♠❛❣♥ét♦♥s ❞❡ ❇♦❤r✳ ✳ ✳ ✳ ✻✽ ❋✐❣✉r❛ ✸✳✺ ❖ t❛♠❛♥❤♦ ❞♦s ❞♦♠í♥✐♦s ❡stá ♥❛ ❡s❝❛❧❛ ♠✐❝r♦♠étr✐❝❛❡✱ ♣❛r❛ ✉♠ ♠❛t❡r✐❛❧ ♣♦❧✐❝r✐st❛❧✐♥♦✱ ❝❛❞❛ ❣rã♦ ♣♦❞❡ ❝♦♥t❡r ♠❛✐s ❞❡✉♠ ❞♦♠í♥✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ❋✐❣✉r❛ ✸✳✻ ■❧✉str❛çã♦ ❞❛ ♣❛r❡❞❡ ❞♦ ❞♦♠í♥✐♦ ♠❛❣♥ét✐❝♦ q✉❡ s❡♣❛r❛❞♦✐s ❞♦♠í♥✐♦s ❝✉❥♦s ♠♦♠❡♥t♦s ❛tô♠✐❝♦s ♠✉❞❛♠ ❛ ♦r✐❡♥t❛çã♦ ❡♠ ◦✶✽✵ ✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ❋✐❣✉r❛ ✸✳✼ ▼❡t❛❧♦❣r❛✜❛ ❞♦ ♥ú❝❧❡♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❢❛❜r✐❝❛❞♦ ♥❛❈❤✐♥❛ ❛ç♦ ✶✵✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❋✐❣✉r❛ ✸✳✽ ❆ ❡①✐stê♥❝✐❛ ❞❡ ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s é r❡s✉❧t❛❞♦ ❞❛ ♠✐✲♥✐♠✐③❛çã♦ ❞❡ ❡♥❡r❣✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ❋✐❣✉r❛ ✸✳✾ ▼❡❝❛♥✐s♠♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♥ã♦✲❧✐♥❡❛r ❞♦ ♥ú❝❧❡♦✳ ✳ ✳ ✳ ✳ ✼✹❋✐❣✉r❛ ✸✳✶✵ ❈✉r✈❛ ❛♣r♦①✐♠❛❞❛ ❞❛ ♠❛❣♥❡t✐③❛çã♦ ❡♠ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦ ✭♥ã♦ ❧✐♥❡❛r✮ ♦❜t✐❞❛ ♣❡❧♦ ♣r♦❞✉t♦ ♣♦♥t♦ ❛ ♣♦♥t♦M = Hµ r ❞♦ ❣rá✜❝♦ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ✈❡rs✉s ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✳ ✼✺❋✐❣✉r❛ ✸✳✶✶ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦✲ ♠❛❣♥ét✐❝♦✱ ♥❛ r❡❣✐ã♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❞♦♠í♥✐♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ❋✐❣✉r❛ ✸✳✶✷ Pr♦❝❡ss♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ s♦❜ ♦ ❡♥❢♦q✉❡ ❞♦❜❛❧❛♥ç♦ ❡♥❡r❣ét✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ❋✐❣✉r❛ ✸✳✶✸ ▲â♠✐♥❛ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵❋✐❣✉r❛ ✸✳✶✹ ❋♦r♠❛s ❞❡ ♦♥❞❛ ❡st✐❧✐③❛❞❛s ❞❡ t❡♥sã♦ P❲▼ ❡ ❞❛ ❝♦r✲ r❡♥t❡ q✉❡ é ♣r♦♣♦r❝✐♦♥❛❧ à ✐♥❞✉çã♦✳ ❆ sér✐❡ ❞❡ ❋♦✉r✐❡r ♣❡r♠✐t❡r❡♣r❡s❡♥t❛r q✉❛❧q✉❡r ❢✉♥çã♦ ❝♦♠♦ ✉♠❛ s♦♠❛ ❞❡ ♦♥❞❛s s❡♥♦✐❞❛✐s❝♦♠ ❞✐❢❡r❡♥t❡s ❛♠♣❧✐t✉❞❡s ❡ ❢r❡q✉ê♥❝✐❛s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ❋✐❣✉r❛ ✸✳✶✺ ❆ té❝♥✐❝❛ P❲▼ ❣❡r❛ ✉♠❛ ♦♥❞❛ ❞❡ ❝♦rr❡♥t❡ ❞✐st♦r❝✐❞❛ q✉❡ ❛❝♦♠♣❛♥❤❛ ❛ s❡♥♦✐❞❡ ❞❡ r❡❢❡rê♥❝✐❛✱ ♣♦r ❡❢❡✐t♦ ❞❛ ✐♥t❡❣r❛çã♦❞❛ ❝♦rr❡♥t❡✱ ❝♦♠ ❜❛s❡ ♥❛ ❝♦♥st❛♥t❡ ❞❡ t❡♠♣♦ RL ❞♦ ❝✐r❝✉✐t♦✳ ❊ss❡♣r♦❝❡ss♦ ❞❡ ✐♥t❡❣r❛çã♦ ❣❡r❛ ❡①♣♦♥❡♥❝✐❛✐s ❝r❡s❝❡♥t❡s ❡ ❞❡❝r❡s❝❡♥t❡s q✉❡ ❞ã♦ ♦ ❝❛rát❡r ✧r❡❝♦rt❛❞♦✧❛♦ s✐♥❛❧ ❞❡ ❝♦rr❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ❋✐❣✉r❛ ✸✳✶✻ ❋♦r♠❛ ❞❛ ❝✉r✈❛ BH ♣❛r❛ ✉♠❛ ❢♦r♠❛ ❞❡ t❡♥sã♦ P❲▼❛s ♦♥❞❛s r❡❝♦rt❛❞❛s✱ ❛❢❡t❛♠ só ♦ ❝♦♥t♦r♥♦ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✱ s❡✉ ❡❢❡✐t♦ s♦❜r❡ ❛s ♣❡r❞❛s t♦t❛✐s é ♠í♥✐♠♦✱ ♥✉♠ ✐♥✈❡rs♦r P❲▼ ❛s♣❡r❞❛s ✜❝❛♠ ♣♦r ❝♦♥t❛ ❞♦ ❛✉♠❡♥t♦ ❞❛ ❢r❡q✉ê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ❋✐❣✉r❛ ✸✳✶✼ ❖s ❞♦✐s t✐♣♦s ❜ás✐❝♦s ❞❡ ❢♦r♠❛ ❞❡ ❞✐st♦rçã♦ ❞❛ ✐♥❞✉✲çã♦ ♠❛❣♥ét✐❝❛ ♥❛ ❢♦r♠❛çã♦ ❞❡ ❧❛ç♦s ♠❡♥♦r❡s ♥❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡♠❛❣♥ét✐❝❛✿ ✭❛✮ s❡♠ ❡①tr❡♠♦s ❧♦❝❛✐s ❡ ✭❜✮ q✉❛tr♦ ✈❛r✐❛çõ❡s ❡①tr❡✲♠❛s ♥♦ ♣❡rí♦❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ❋✐❣✉r❛ ✸✳✶✽ ❆s s✉s❝❡♣t✐❜✐❧✐❞❛❞❡s ❞✐❢❡r❡♥❝✐❛✐s sã♦ ❛s ✐♥❝❧✐♥❛çõ❡s ❞❛s r❡t❛s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐❣✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ P❡✉❣❡t ✭P❊❯●❊❚✱✶✾✾✺✮ é ❛♣❧✐❝❛❞♦ ♣❛r❛ ♦ ❡♥❝♦♥tr♦ ❞❡ ✉♠ ♣r✐♠❡✐r♦ ♣♦ssí✈❡❧ ❝♦♥❥✉♥t♦❞❡ ♣❛râ♠❡tr♦s✳ ❯t✐❧✐③❛✲s❡ ♠❡t❛❞❡ ❞❡ ✉♠ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ♣❛r❛ ❛♦❜t❡♥çã♦ ❞♦s ♥♦✈❡ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ❋✐❣✉r❛ ✸✳✶✾ P♦♥t♦s ❝❤❛✈❡s s✉❣❡r✐❞♦s ♣♦r ❏✐❧❡s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦s♥♦✈❡ ❞❛❞♦s ✭M s ✱ M m ✱ H m ✱ χ m ✱ M r ✱ χ r ✱ H c ✱ χ c ✱ ❍❝✱ χ in ✮ ♥❡❝❡ssá✲ r✐♦s ♣❛r❛ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❏❆ ❡stã♦ ✐♥❞✐❝❛❞♦s ♥❛ ✜❣✉r❛tr❛ç❛❞❛ ❛ ✶ ❍③✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ❋✐❣✉r❛ ✸✳✷✵ ❚r❛♥s❢♦r♠❛❞♦r ♠♦❞❡❧❛❞♦ ♥♦ ❋❊▼▼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾❋✐❣✉r❛ ✸✳✷✶ ❆♣❛r❡❧❤♦ ❞❡ ♠❡❞✐❞❛ ❉❲✷✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵❋✐❣✉r❛ ✸✳✷✷ ◗✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ✲ ❢♦t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶❋✐❣✉r❛ ✸✳✷✸ ◗✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ✲ ✐❧✉str❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷❋✐❣✉r❛ ✸✳✷✹ ❈✐r❝✉✐t♦ ❡sq✉❡♠át✐❝♦ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞♦ t❡st❡ ❞❡ ♣❡r❞❛s ♠❛❣♥ét✐❝❛s ❡ ❧❡✈❛♥t❛♠❡♥t♦ ❞❛ ❝✉r✈❛ BH✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷❋✐❣✉r❛ ✸✳✷✺ ❊sq✉❡♠❛ ❞♦ s❡♥s♦r ❙❙❚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸❋✐❣✉r❛ ✸✳✷✻ ❙❡♥s♦r ❞❡ ❧â♠✐♥❛ ú♥✐❝❛ ❙❙❚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹❋✐❣✉r❛ ✸✳✷✼ ❊①❡♠♣❧♦ ❞❡ ❖■▼ ❡ ❝ó❞✐❣♦ ❞❡ ❝♦r❡s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ❋✐❣✉r❛ ✸✳✷✽ ▲❛♠✐♥❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺❋✐❣✉r❛ ✸✳✷✾ ▼❛❣♥❡t✐③❛çã♦ ❡♠ r❡❧❛çã♦ ❛♦s í♥❞✐❝❡s ❞❡ ▼✐❧❧❡r ❞❡ ✉♠❛ ❡str✉t✉r❛ ❈❈❈ ✭❈ú❜✐❝❛ ❞❡ ❈♦r♣♦ ❈❡♥tr❛❞♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻❋✐❣✉r❛ ✸✳✸✵ ❈✐r❝✉✐t♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼❋✐❣✉r❛ ✸✳✸✶ ❋♦r♠❛s ❞❡ ♦♥❞❛ ❞♦s ❝❛♠♣♦s H(t) ❡ B(t)✱ ♣r♦♣♦r❝✐♦♥❛✐s ❛♦s s✐♥❛✐s ❞❡ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛ ❡ t❡♥sã♦ s❡❝✉♥❞ár✐❛✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾❋✐❣✉r❛ ✸✳✸✷ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❝♦♥str✉í❞♦ ✉t✐❧✐✲ ③❛♥❞♦ ♦s❝✐❧♦s❝ó♣✐♦ ❞✐❣✐t❛❧ ❝♦♠ ❛♠♦str❛❣❡♠ ❞❡ ✺✵✵ ♣♦♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ m = 0, 1686 m❋✐❣✉r❛ ✸✳✸✸ ❉❡✜♥✐çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ♠é❞✐♦ ❛❞♦t❛❞♦ l ✳✶✵✵❋✐❣✉r❛ ✸✳✸✹ ❖ ❡❢❡✐t♦ ❞❡ ❤✐st❡r❡s❡ é ❣❡r❛❞♦ ♣❡❧❛ r❡s✐stê♥❝✐❛ à ♠♦✈✐✲ ♠❡♥t❛çã♦ ❞❡ ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶❋✐❣✉r❛ ✸✳✸✺ ❋♦r♠❛t♦ ❞♦ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷❋✐❣✉r❛ ✸✳✸✻ ❖❜t❡♥çã♦ ♣♦♥t♦ ❛ ♣♦♥t♦ ❞❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ BH ❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸❋✐❣✉r❛ ✸✳✸✼ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❧❡✈❛♥t❛❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ✶✵✹❋✐❣✉r❛ ✸✳✸✽ ❈✉r✈❛ BH ❞❡ ❛ç♦ ❝❛r❜♦♥♦ ✶✵✶✵✳ ◆❡ss❛ ♥♦♠❡♥❝❧❛t✉r❛✱ ♦ ♥ú♠❡r♦ ✶✵✵✵ ❝♦rr❡s♣♦♥❞❡ ❢❛♠í❧✐❛ ❞❡ ❛ç♦s ❞❡ ❜❛✐①♦ ❝❛r❜♦♥♦✱ ❡♥✲ q✉❛♥t♦ ♦ ♥ú♠❡r♦ ✶✵ ❝♦rr❡s♣♦♥❞❡ ❛♦ t❡♦r ❞❡ ✵✱✶✪ ❞❡ ❝❛r❜♦♥♦✳✳ ✳ ✳ ✳ ✶✵✺❋✐❣✉r❛ ✸✳✸✾ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❡♠ r❡❧❛çã♦ à ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✱ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❧❡✈❛♥t❛❞❛ ♣❡❧♦ ❝✐r❝✉✐t♦♣r♦♣♦st♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ❋✐❣✉r❛ ✸✳✹✵ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥t❡♥✲ s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✳ ❚❡♦r✐❝❛♠❡♥t❡✱ ❡st❛ ❝✉r✈❛ ❞❡✈❡r✐❛ ♣❛rt✐r ❞♦ ③❡r♦✳✶✵✽❋✐❣✉r❛ ✸✳✹✶ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦r✲ r❡♥t❡ ❞❡ ❡①❝✐t❛çã♦ ♣r✐♠ár✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾❋✐❣✉r❛ ✸✳✹✷ ❆ ❝✉r✈❛ ❞❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ é ♦❜t✐❞❛ ♠✉❧t✐♣❧✐❝❛♥❞♦ ❛s ♦r❞❡♥❛❞❛s ❞❛ ❝❛r❛❝t❡ríst✐❝❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ✈❡rs✉s ❝♦rr❡♥t❡ ♣❡❧♦❢❛t♦r K L1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ❋✐❣✉r❛ ✸✳✹✸ ❯t✐❧✐③❛♥❞♦ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❛ ✐♥❞✉tâ♥❝✐❛❢♦✐ ❝❛❧❝✉❧❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✺✵❬♠❆❪✳ ▼❛s✱ ❡①✐st❡ ✉♠ ❡rr♦ ♥❡ss❡ ✈❛❧♦r ♣♦rq✉❡ ❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦é ❛ s♦♠❛ ❞❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✹✼ ❬♠❆❪ ❡ ✉♠❛ ♦✉tr❛❝♦rr❡♥t❡✱ ❛ss♦❝✐❛❞❛ ❛s ♣❡r❞❛s ❞♦ ❢❡rr♦✱ ❝♦♥s✐❞❡r❛♥❞♦ r❡s✐st♦r ❡q✉✐✲ n = 12665 [Ω]✈❛❧❡♥t❡ R ✱ ❝✉❥♦ ✈❛❧♦r é ✶✼ ❬♠❆❪✳ ❆ss✐♠✱ r❡❢❛③❡♥❞♦ ❛s❝♦♥t❛s ❝♦♠ ✹✼ ❬♠❆❪✱ s❡ ♦❜té♠ ❛ ❝✉r✈❛ ❝♦rr✐❣✐❞❛✱ s❡♥❞♦ ❡ss❛ ♠✉✐t♦♣ró①✐♠❛ ❞❛ ❝✉r✈❛ ❡①♣❡r✐♠❡♥t❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ❋✐❣✉r❛ ✸✳✹✹ ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ s❡❝✉♥❞ár✐❛✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ❢❛t♦r❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ K L2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ❋✐❣✉r❛ ✸✳✹✺ ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ✈✐st❛ ❞♦ s❡❝✉♥❞ár✐♦ ♣♦r ❡❢❡✐t♦ ❞❛ ❝♦r✲ r❡♥t❡ ♣r✐♠ár✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺❋✐❣✉r❛ ✸✳✹✻ ❈✉r✈❛ ❞❛ r❡❧✉tâ♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛✳ ✳ ✶✶✻❋✐❣✉r❛ ✸✳✹✼ ❈✉r✈❛ ❞❛ ♣❡r♠❡â♥❝✐❛ ❞♦ ❝✐r❝✉✐t♦ ♣r✐♠ár✐♦ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♥♦ ❡♥r♦❧❛♠❡♥t♦ ♣r✐♠ár✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼❋✐❣✉r❛ ✸✳✹✽ ❉✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡s ❡♠ ✉♠ tr❛♥s❢♦r♠❛❞♦r r❡❛❧✳✳ ✳ ✶✶✽❋✐❣✉r❛ ✸✳✹✾ ■♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ❞❡ ✽✱✷✽ ❬❍❪ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦✳ ✶✷✶❋✐❣✉r❛ ✸✳✺✵ ■♥❞✉tâ♥❝✐❛ s❡❝✉♥❞❛r✐❛ ❞❡ ✵✱✵✾✺ ❬❍❪ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛✲ çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶❋✐❣✉r❛ ✸✳✺✶ ❈✉r✈❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ♣r✐♠❛✲ r✐❛ ♥❛ ❝♦♥❞✐çã♦ s❡♠ ❝❛r❣❛ ♦ ✈❛❧♦r ♣❛r❛ ❛ ✐♥❞✉tâ♥❝✐❛ ❣r❛✜❝❛♠❡♥t❡ ❡stá ❡♠ t♦r♥♦ ❞❡ ✵✱✾✵✸ ❬❍❪ ♣❛r❛ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ♣r✐♠❛r✐❛ ❞❡ ✶✵✵❬♠❆❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ❋✐❣✉r❛ ✸✳✺✷ ▼♦❞❡❧♦ ✐❞❡❛❧ ❞❡ tr❛♥s❢♦r♠❛❞♦r ♠♦♥♦❢ás✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸❋✐❣✉r❛ ✸✳✺✸ ❈✐r❝✉✐t♦ ♣❛r❛ ❝á❧❝✉❧♦ ❞❛s ♠út✉❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹❋✐❣✉r❛ ✸✳✺✹ ❈✐r❝✉✐t♦ ♣❛r❛ ❝á❧❝✉❧♦ ❞❛s ♠út✉❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹❋✐❣✉r❛ ✸✳✺✺ ▼♦❞❡❧♦ sér✐❡ ❞♦ tr❛♥s❢♦r♠❛❞♦r ✉t✐❧✐③❛❞♦ ♣❡❧♦ ❋❊▼▼✳✳ ✶✷✼❋✐❣✉r❛ ✸✳✺✻ ❚r❛♥s❢♦r♠❛çã♦ ❝✐r❝✉✐t♦ sér✐❡ ♣❛r❛ ❝✐r❝✉✐t♦ ♣❛r❛❧❡❧♦✳ ✳ ✳ ✳ ✶✷✼❋✐❣✉r❛ ✸✳✺✼ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝✐t❛çã♦ ❡♠ ✈❛③✐♦ ♣❛r❛ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ✶✵✵♠❆✱ t♦r♥❛✲s❡ ♥❡❝❡ssár✐♦ ❛✉♠❡♥t❛r ❛ t❡♥sã♦♣❛r❛ ❛t✐♥❣✐r ❡st❡ ✈❛❧♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ❋✐❣✉r❛ ✸✳✺✽ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❡ t❡♥sã♦ ♥♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦❝✐r❝✉✐t♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✵ ❋✐❣✉r❛ ✸✳✺✾ ▼♦❞❡❧♦ ❝✐r❝✉✐t❛❧ ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷❋✐❣✉r❛ ✸✳✻✵ ▼♦❞❡❧♦ ❝✐r❝✉✐t❛❧ ❞♦ tr❛♥s❢♦r♠❛❞♦r r❡✢❡t✐❞♦ ❛♦ ♣r✐♠ár✐♦✳✶✸✷❋✐❣✉r❛ ✸✳✻✶ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❡ t❡♥sã♦ ♥♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹❋✐❣✉r❛ ✸✳✻✷ ▼♦❞❡❧♦ sér✐❡ ❞♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦ ♥♦ tr❛♥s❢♦r♠❛✲ ❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺❋✐❣✉r❛ ✸✳✻✸ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦s ❝✐❝❧♦s ❞❡ ♣❡r❞❛s ❞♦ ❢❡rr♦✿ ✭❛✮ ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡❀ ✭❜✮ ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡❋♦❝❛✉❧t❀ ✭❝✮ ♣❡r❞❛s ❡①❝❡❞❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼ ❋✐❣✉r❛ ✸✳✻✹ ❉❡r✐✈❛♥❞♦ ❛ ❝✉r✈❛ BH s❡ ♦❜té♠ ❛ ❝✉r✈❛ ❞❡ ♣❡r♠❡✲❛❜✐❧✐❞❛❞❡ ✐♥❝r❡♠❡♥t❛❧✱ ❡♠ q✉❡ ♣❡r❝❡❜❡✲s❡ q✉❡ ♦ ♣♦♥t♦ ❞❡ ♠❡♥♦r r❡❧✉tâ♥❝✐❛ ❝♦✐♥❝✐❞❡ ❝♦♠ ✉♠❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H = 100 [A/m]✳✶✹✶ ❋✐❣✉r❛ ✸✳✻✺ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ tr❛ç❛❞❛ ❛ ✶✵ ❍③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺❋✐❣✉r❛ ✸✳✻✻ ❙❡♣❛r❛çã♦ ♣❡r❞❛s ❡♠ ❢✉♥çã♦ ❞❛ ■♥❞✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻❋✐❣✉r❛ ✸✳✻✼ ❖♣❡r❛çã♦ ❡♠ r❡❣✐♠❡ q✉❛s❡ ❡stát✐❝♦✿ ❛s ♣❡r❞❛s ❞❡ ❤✐s✲ t❡r❡s❡ sã♦ ♠✉✐t♦ ♣ró①✐♠❛s ❞❛s ♣❡r❞❛s t♦t❛✐s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻❋✐❣✉r❛ ✸✳✻✽ ❙❡♣❛r❛çã♦ ❞❛s ♣❡r❞❛s ❡♠ ❢✉♥çã♦ ❞❛ ❢r❡q✉ê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼❋✐❣✉r❛ ✸✳✻✾ ❈✐r❝✉✐t♦ ♥ã♦✲❧✐♥❡❛r ♣❛r❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ tr❛♥s❢♦r✲ ♠❛❞♦r ❝♦♠ s❡❝✉♥❞ár✐♦ ❡♠ ✈❛③✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽❋✐❣✉r❛ ✸✳✼✵ ❋❧✉①♦ ❞❡ ❡♥❧❛❝❡ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ❧♦❣♦ ❛♣ós ❛ ❡♥❡r✲ ❣✐③❛çã♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✾❋✐❣✉r❛ ✸✳✼✶ ❋❧✉①♦ ❞❡ ❡♥❧❛❝❡ ❡ ❝♦rr❡♥t❡ ❞❡ ✐♥✲r✉s❤ ❡♠ ✉♠ tr❛♥s❢♦r✲ ♠❛❞♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✶❋✐❣✉r❛ ✸✳✼✷ ❈✐r❝✉✐t♦ ❝♦♥s✐❞❡r❛❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ✐♥✲ r✉s❤✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✹❋✐❣✉r❛ ✸✳✼✸ ❈✉r✈❛ BH ❞♦ ♠❛t❡r✐❛❧ ♦❜t✐❞❛ ❛tr❛✈és ❞❡ ✉♠❛ ❛♠♦str❛✲ ❣❡♠ ❞❡ ✺✵✵ ♣♦♥t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✻❋✐❣✉r❛ ✸✳✼✹ ❈♦rr❡♥t❡ tr❛♥s✐tór✐❛ ✐♥✲r✉s❤ ❞❡ ✈❛❧♦r ♠á①✐♠♦ ✶✱✸ ❬❆❪✳ ❖ tr❛♥s✐tór✐♦ s❡ ♠❛♥té♠ ♣♦r ✷✵ ❝✐❝❧♦s ❞❡ r❡❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✳ ✶✺✼❋✐❣✉r❛ ✸✳✼✺ ❚❡♥❞ê♥❝✐❛s ❞❛ ❝♦rr❡♥t❡ ❞❡ ✐♥✲r✉s❤✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✼❋✐❣✉r❛ ✸✳✼✻ ❆ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦ ♥❛ ❝♦♥❞✐çã♦ ♣❡r♠❛♥❡♥t❡ ❛t✐♥❣❡ ✉♠ ✈❛❧♦r ♠á①✐♠♦ ❞❡ ✺✺ ♠❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✽❋✐❣✉r❛ ✸✳✼✼ ▲✐♥❤❛s ❞❡ ✢✉①♦ ♥♦ tr❛♥s❢♦r♠❛❞♦r s✐♠✉❧❛❞♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✽❋✐❣✉r❛ ✸✳✼✽ ▼♦❞❡❧♦ ❞♦ ♥ú❝❧❡♦ ♥❛ ♦❜t❡♥çã♦ ❞❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛✲ çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✶❋✐❣✉r❛ ✸✳✼✾ ❈♦rr❡çã♦ ♥❛ ❝✉r✈❛ ❇❍ ❡①♣❡r✐♠❡♥t❛❧ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦r✲ r❡♥t❡ ❛ss♦❝✐❛❞❛ ❛s ♣❡r❞❛s ❞♦ ❢❡rr♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷❋✐❣✉r❛ ✸✳✽✵ ❆ ❞✐❢❡r❡♥ç❛ ♥❛s ❝✉r✈❛s ❞❡ ✐♥❞✉tâ♥❝✐❛s ♣r✐♠❛r✐❛ L 1 t❡ó✲ r✐❝❛ ❡ ❡①♣❡r✐♠❡♥t❛❧ é ♣r♦❞✉③✐❞❛ ♣❡❧❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦✳ ❊ss❛ ❝♦r✲r❡♥t❡ ❛❢❡t❛ ❛ ❝✉r✈❛ BH ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡❛❜s♦❧✉t❛ ❞♦ ♠❛t❡r✐❛❧✳ ❖✉tr♦ ❡❢❡✐t♦ ❞❡ss❛ ❝♦rr❡♥t❡ é ❛ r❡❞✉çã♦ ❞❛ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦✳ ■ss♦ ❞✐✜❝✉❧t❛ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♦ ♣r♦✲❝❡ss♦ ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ❞❡ ❞✐s♣❡rsã♦ ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷ ❋✐❣✉r❛ ✸✳✽✶ ▼♦❞❡❧♦ ❞❡ ♥ú❝❧❡♦ ❝♦♠ ❝♦rr❡♥t❡s ❞❡ ❝♦♠♣❡♥s❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✶✻✸❋✐❣✉r❛ ✸✳✽✷ ❱❛r✐❛çã♦ ♥❛ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦ ♣♦r ❡❢❡✐t♦s ❞❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦ I ✱ ♦ tr❛♥s❢♦r♠❛❞♦r ❛t✐♥❣❡ s❡✉ ✈❛❧♦r ❞❡ ♣r♦❥❡t♦✱♥❡st❡ ❝❛s♦ ❞❡ ✾✳✶✼✱ ❝♦♠ ✉♠❛ ❝♦rr❡♥t❡ ✐❣✉❛✐s ♦✉ s✉♣❡r✐♦r ❛ ♥♦♠✐♥❛❧✳❖s ✈❛❧♦r❡s ❡①♣❡r✐♠❡♥t❛✐s ❡stã♦ ✐♥❞✐❝❛❞♦s ❝♦♠ ✬①✬✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✹ ❋✐❣✉r❛ ✹✳✶ ❉✐♠❡♥sõ❡s ❞♦ ❝♦♥t❛❝t♦r ❡♠ ❡st✉❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼❋✐❣✉r❛ ✹✳✷ ❙♦♠❜r❡❛♠❡♥t♦ ❞♦s ♣♦❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✽❋✐❣✉r❛ ✹✳✸ ❈♦♥t♦r♥♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞♦s ❝á❧❝✉❧♦s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✾❋✐❣✉r❛ ✹✳✹ ❱✐st❛ ❢r♦♥t❛❧ ❞♦ ❝♦♥t❛❝t♦r ❡♠ ❡st✉❞♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✵❋✐❣✉r❛ ✹✳✺ P❛rt❡ ✜①❛ ❞♦ ❝♦♥t❛❝t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✵❋✐❣✉r❛ ✹✳✻ ❈♦♥t❛❝t♦r ✐♠♣❧❡♠❡♥t❛❞♦ ♥♦ ❋❊▼▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✶❋✐❣✉r❛ ✹✳✼ ❇♦❜✐♥❛ ❞❡ ❡s♣✐r❛s ❝♦♥❤❡❝✐❞❛s ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ t❡♥sã♦ ✐♥❞✉③✐❞❛ ♣♦r ❡s♣✐r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✷❋✐❣✉r❛ ✹✳✽ ▼♦♥t❛❣❡♠ ❞❛ ❜♦❜✐♥❛ ❞❡ ❡s♣✐r❛s ❝♦♥❤❡❝✐❞❛s q✉❡ ♣❡r♠✐t❡ ❛✈❛❧✐❛r ❛ t❡♥sã♦ ♣♦r ❡s♣✐r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✸❋✐❣✉r❛ ✹✳✾ ❉✐❛❣r❛♠❛s ❞♦s ✢✉①♦s ❣❡r❛❞♦s ♣❡❧❛ ❜♦❜✐♥❛ ♣r✐♥❝✐♣❛❧ ❡ ❛ ❡s♣✐r❛ ❞❡ s♦♠❜r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✹❋✐❣✉r❛ ✹✳✶✵ ▼❛t❡r✐❛❧ ❈❛r♣❡♥t❡r ❙✐❧✐❝♦♥ ■r♦♥ ❞❛ ❜✐❜❧✐♦t❡❝❛ ❞♦ ❋❡♠♠✳✶✼✺❋✐❣✉r❛ ✹✳✶✶ ▼❛t❡r✐❛❧ ❈❛r♣❡♥t❡r ❙✐❧✐❝♦♥ ■r♦♥ ❝♦♠ ❡♥tr❡❢❡rr♦ ❞❡ ✵✱✹♠♠✳✶✼✺❋✐❣✉r❛ ✹✳✶✷ ❈✐r❝✉✐t♦ ♣r♦♣♦st♦ ♣❛r❛ ❞✐s♣♦s✐t✐✈♦s ❝♦♠ ✉♠❛ ú♥✐❝❛ ❜♦✲ ❜✐♥❛ ❞❡ ❡①❝✐t❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻❋✐❣✉r❛ ✹✳✶✸ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ t❡♥sã♦ ❈❍✷ ✭❇✮ ❡ ❝♦rr❡♥t❡ ❝♦♠ ❜❛✐①♦ ❝♦♥t❡ú❞♦ ❤❛r♠ô♥✐❝♦ ❈❍✶✭❍✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✽❋✐❣✉r❛ ✹✳✶✹ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❞♦ ♠❛t❡r✐❛❧ ♣❛r❛ ❛ ❝♦rr❡♥t❡ ♥♦♠✐✲ ♥❛❧ ✭✼✺♠❆✮✱ s✉❛ ❛❝❡♥t✉❛❞❛ ✐♥❝❧✐♥❛çã♦ s❡ ❞❡✈❡ ❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠♠✐♥ús❝✉❧♦ ❡♥tr❡❢❡rr♦ ❞❡ ✵✱✹♠♠✱ ♥❛ tr❛✈❡ ❝❡♥tr❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✾ ❋✐❣✉r❛ ✹✳✶✺ ❈✉r✈❛ ❡①♣❡r✐♠❡♥t❛❧ ❞❡ ❍✐st❡r❡s❡ ❞♦ ♠❛t❡r✐❛❧ ✉t✐❧✐③❛❞♦♥♦ ♥ú❝❧❡♦✱ s✉❛ ❛❝❡♥t✉❛❞❛ ✐♥❝❧✐♥❛çã♦ s❡ ❞❡✈❡ ❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠♠✐♥ús❝✉❧♦ ❡♥tr❡❢❡rr♦ ❞❡ ✵✱✹♠♠✱ ♥❛ tr❛✈❡ ❝❡♥tr❛❧✱ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♥❛ ♦♣❡r❛çã♦ ♥♦♠✐♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✵ ❋✐❣✉r❛ ✹✳✶✻ ❊♠ ❛③✉❧✱ ❛ ❝✉r✈❛ BH ❞♦ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ❞♦ ♠❛t❡✲ r✐❛❧ ❈❛r♣❡♥t❡r ❝♦♠ ♦ ❡❢❡✐t♦ ❞♦ ❡♥tr❡❢❡rr♦ ❡✱ ❡♠ ✈❡r♠❡❧❤♦✱ ❛ ❝✉r✈❛❞♦ ♠❛t❡r✐❛❧ ♦❜t✐❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✶ ❋✐❣✉r❛ ✹✳✶✼ ●rá✜❝♦ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥t❡♥✲ s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷❋✐❣✉r❛ ✹✳✶✽ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ❝♦♥t❛❝t♦r ❢❡❝❤❛❞♦ ❡ ❞♦ ❝✐r❝✉✐t♦ ❡❧é✲ tr✐❝♦ s✐♠♣❧✐✜❝❛❞♦ ❡q✉✐✈❛❧❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✸❋✐❣✉r❛ ✹✳✶✾ ●rá✜❝♦ ❞❡ r❡❧✉tâ♥❝✐❛ ❞♦ ♠❛t❡r✐❛❧ ❡ ❡♠ ❢✉♥çã♦ ❞❡ ❡♥tr❡✲ ❢❡rr♦s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✹❋✐❣✉r❛ ✹✳✷✵ ❈✉r✈❛ ❛♣r♦①✐♠❛❞❛ ❞❛ ♣❡r♠❡â♥❝✐❛ ❡①♣❡r✐♠❡♥t❛❧ ❞♦ ❝♦♥✲ t❛❝t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✼❋✐❣✉r❛ ✹✳✷✶ ▲✐♥❤❛s ❞❡ ✢✉①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✽ ❋✐❣✉r❛ ✹✳✷✷ ●rá✜❝♦ ❞❛ ❝✉r✈❛ λi✱ r❡❣✐õ❡s ❞❡ ❡♥❡r❣✐❛ ❡ ❝♦❡♥❡r❣✐❛✳ ✳ ✳ ✳ ✶✾✵❋✐❣✉r❛ ✹✳✷✸ ❊♥tr❡❢❡rr♦ ❡ ❡s♣❛❧❤❛♠❡♥t♦ ❛ss♦❝✐❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✺❋✐❣✉r❛ ✹✳✷✺ ●rá✜❝♦ ❞❛ ❝✉r✈❛ ❞❡ s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛ ❇❍ ❞♦ ♠❡s♠♦ ♠❛t❡r✐❛❧ ❛♥t❡r✐♦r ❝♦♠ ✉♠ ❡♥tr❡❢❡rr♦ ❞❡ ✺♠♠✱ é ♣♦ssí✈❡❧ ♣❡r❝❡❜❡r q✉❡ ❡♠ ❢✉♥çã♦ ❞❡st❡ ❣r❛♥❞❡ ❡♥tr❡❢❡rr♦ ❛ ❝✉r✈❛ s❡ t♦r♥❛ ❧✐♥❡❛r✳ ✳ ✳ ✳ ✶✾✼❋✐❣✉r❛ ✹✳✷✻ ❊s♣❛❧❤❛♠❡♥t♦ ❞♦ ✢✉①♦ ♠❛❣♥ét✐❝♦ ♥♦ ❡♥tr❡❢❡rr♦ ❡ ❡♥❡r✲ ❣✐❛ ❛❝✉♠✉❧❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✾❋✐❣✉r❛ ✹✳✷✼ ❈♦♥t♦r♥♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❝❛♠♣♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✶❋✐❣✉r❛ ✹✳✷✽ ❋♦rç❛ ♣r♦❞✉③✐❞❛ ♥♦ ❝♦♥t❛❝t♦r ♣♦r ✉♠❛ ❝♦rr❡♥t❡ ❛❧t❡r✲ ♥❛❞❛ ✭❛③✉❧✮ ❡ ♣♦r ✉♠❛ ❝♦♥tí♥✉❛ ✭✈❡r♠❡❧❤❛✮ ❝♦♠ ✉♠ ❡♥tr❡❢❡rr♦✈❛r✐❛♥❞♦ ❞❡ ③❡r♦ ❛té ✺♠♠✳ ❊♠ ✈❡r❞❡✱ ♦ t❡♥s♦r ♣♦♥❞❡r❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✸ ❋✐❣✉r❛ ✹✳✷✾ ▼♦❞❡❧♦ ❡❧étr✐❝♦ ❞♦ ❝♦♥t❛❝t♦r ♥♦ ❋❊▼▼✱ ❛ ✐♥❞✉tâ♥❝✐❛ ❡♦ r❡s✐st♦r ❡q✉✐✈❛❧❡♥t❡ ❡stã♦ ❡♠ sér✐❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✹ ❋✐❣✉r❛ ✹✳✸✵ ▼♦❞❡❧♦ ❡❧étr✐❝♦ ❞♦ ❝♦♥t❛❝t♦r✱ ❛ ✐♥❞✉tâ♥❝✐❛ ❡ ♦ r❡s✐st♦r❡q✉✐✈❛❧❡♥t❡ ❡stã♦ ❡♠ ♣❛r❛❧❡❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✺ ❋✐❣✉r❛ ✹✳✸✶ P❡r❞❛s ♥♦ ♥ú❝❧❡♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✻❋✐❣✉r❛ ✹✳✸✷ ❋♦r♠❛t♦ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ s❡♠ ❡♥tr❡❢❡rr♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✼❋✐❣✉r❛ ✹✳✸✸ ❋♦r♠❛t♦ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❝♦♠ ❡♥tr❡❢❡rr♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✽❋✐❣✉r❛ ✹✳✸✹ ❊s♣❡❝tr♦ ❞❛ ❢♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ s❡♠ ❡♥tr❡❢❡rr♦ ✭❚❍❉ ❂ ✸✷✱✶✹✪✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✽❋✐❣✉r❛ ✹✳✸✺ ❊s♣❡❝tr♦ ❞❛ ❢♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❝♦♠ ❡♥tr❡❢❡rr♦ ✭❚❍❉ ❂ ✺✱✷✪✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✾❋✐❣✉r❛ ✹✳✸✻ ▼♦♥t❛❣❡♠ ❞❡ tr❛♥s❢♦r♠❛❞♦r ✐♥s❡r✐♥❞♦ ✉♠ ❡♥tr❡❢❡rr♦ ❞❡ ✵✱✹♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✵ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙❚❛❜❡❧❛ ✸✳✶ ▼❛t❡r✐❛✐s ❢❡rr♦❝r✐st❛❧✐♥♦s✿ ♣r♦♣r✐❡❞❛❞❡s ❡❧❡tr♦♠❛❣♥ét✐✲ = 88, 32 + j46, 9❡ I2 ♣♦r s✐♠✉❧❛çã♦✱ ♣❛r❛ ❡♥tr❡❢❡rr♦ ❞❡ ✵✱✹ ♠♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✶❚❛❜❡❧❛ ✹✳✼ ❉✐str✐❜✉✐çã♦ ❞❛ ❡♥❡r❣✐❛ ♥❛s r❡❣✐õ❡s ❞♦ s✐st❡♠❛✱ ♦❜t✐❞❛s ❞❡ ❡♥tr❡❢❡rr♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾❚❛❜❡❧❛ ✹✳✻ ❉✐str✐❜✉✐çã♦ ❞❛ ❡♥❡r❣✐❛ ♥❛s r❡❣✐õ❡s ❞♦ s✐st❡♠❛✱ ♦❜t✐❞❛s ❢❡rr♦ ❞❡ 5 mm✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✻❚❛❜❡❧❛ ✹✳✺ P❡r❞❛s ♣♦r ♠❛ss❛ ❡ ✈♦❧✉♠❡ ♣❛r❛ ❞✐❢❡r❡♥t❡s ❝♦♥❞✐çõ❡s ❢❡rr♦ ❞❡ 0, 4 mm✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✺❚❛❜❡❧❛ ✹✳✹ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡ r❡❧✉tâ♥❝✐❛✱ ❝♦♠ ❡♥tr❡✲ ❚❛❜❡❧❛ ✹✳✷ P❛râ♠❡tr♦s ❞♦ ❝✐r❝✉✐t♦ ❞❡ ❡①❝✐t❛çã♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✼❚❛❜❡❧❛ ✹✳✸ ❈♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❞❡ r❡❧✉tâ♥❝✐❛✱ ❝♦♠ ❡♥tr❡✲ ❚❛❜❡❧❛ ✹✳✶ ❉❛❞♦s ❣❡♦♠étr✐❝♦s ❞♦ ♥ú❝❧❡♦ ♠❛❣♥ét✐❝♦✱ ❝♦♥t❛❝t♦r ❢❡✲❝❤❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ = aI ′1 = 0, 5972✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✶ I ′1 = 65, 13✱ I1 ❝❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸❚❛❜❡❧❛ ✸✳✷ ❆❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✱ ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ P❛r❛ ♦s ❝á❧❝✉❧♦s✱ ❝♦♥s✐❞❡r❛r I= 23, 19+j46, 9 ❚❛❜❡❧❛ ✸✳✾ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♥♦ ❋❊▼▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✾❚❛❜❡❧❛ ✸✳✶✵ ❙í♥t❡s❡ ❞♦s ❝á❧❝✉❧♦s ❞❡ ✐♥❞✉tâ♥❝✐❛ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦ ❚❛❜❡❧❛ ✸✳✽ P❡r❝❡t✉❛❧ ❞❡ ❤❛♠ô♥✐❝♦s ❞❡ ❝♦rr❡♥t❡ ✉t✐❧✐③❛❞♦s ♣♦r r❡❧és❞✐❢❡r❡♥❝✐❛✐s ♣❛r❛ ❡✈✐t❛r ❞✐s♣❛r♦s ❞❡s♥❡❝❡ssár✐♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✷ ❆ ♣❡r❞❛ t♦t❛❧ s✐♠✉❧❛❞❛ P s ❡ ❛ ♣❡r❞❛ t♦t❛❧ ❞♦ ♠♦❞❡❧♦ P e sã♦ ❛♣r❡✲ s❡♥t❛❞❛s ❡♠ ❬❲❪✳ ❆s ♣❛r❝❡❧❛s ❞❡ ♣❡r❞❛s ❞♦s ♠♦❞❡❧♦s sã♦ ❡①♣r❡ss❛s❡♠ ❬❲❪ ❡ ❡♠ ✪✳ ◆❡ss❡ ú❧t✐♠♦ ❝❛s♦✱ r❡♣r❡s❡♥t❛ ♦ q✉❛♥t♦ ❡ss❛ ♣❛r✲❝❡❧❛ ❝♦♥tr✐❜✉✐ ♣❡r❝❡♥t✉❛❧♠❡♥t❡ ♣❛r❛ ❛s ♣❡r❞❛s ❞♦ ❞✐s♣♦s✐t✐✈♦ ❡♠✉♠❛ ❢r❡q✉ê♥❝✐❛ ❡s♣❡❝í✜❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹ ♠❛❣♥ét✐❝❛ ❡ ❛ r❡❧❛çã♦ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸❚❛❜❡❧❛ ✸✳✹ ❘❡s✉♠♦ ❞♦s ❞❛❞♦s ❝♦♥str✉t✐✈♦s ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ ✳ ✳ ✳ ✳ ✶✵✵❚❛❜❡❧❛ ✸✳✺ ❊①❡♠♣❧♦s ❞❡ ♠❛t❡r✐❛✐s ❞✉r♦s✱ ♠♦❧❡s ❡ ✐♥t❡r♠❡❞✐ár✐♦s✳ ✳ ✶✵✷❚❛❜❡❧❛ ✸✳✻ P❡r❞❛s ♣♦r ♠❛ss❛ ✉s✉❛✐s ❡♠ ♠áq✉✐♥❛s ❞❡ ❝♦rr❡♥t❡ ❛❧✲ t❡r♥❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾❚❛❜❡❧❛ ✸✳✼ P❡r❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s ❢r❡q✉ê♥❝✐❛s ❞❡ ♦♣❡r❛çã♦✱ ❡♠ ❬❍③❪✳ ✉s❛❞♦s ❡♠ ♥ú❝❧❡♦s ❞❡ tr❛♥s❢♦r♠❛❞♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼❚❛❜❡❧❛ ✸✳✸ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ♠❛t❡r✐❛✐s q✉❛♥t♦ à s✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ♣♦r s✐♠✉❧❛çã♦✱ ♣❛r❛ ❡♥tr❡❢❡rr♦ ❞❡ ✺ ♠♠✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✷ ❚❛❜❡❧❛ ✹✳✽ ❚r✐â♥❣✉❧♦ ❞❡ ♣♦tê♥❝✐❛ ❞♦ ❝♦♥t❛❝t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✸❚❛❜❡❧❛ ✹✳✾ ❊♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥♦ ❝♦♥t❛❝t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✾❚❛❜❡❧❛ ✹✳✶✵ ❙í♥t❡s❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠ ♦ ❚❡♥s♦r P♦♥❞❡r❛❞♦ ❞❡ ▼❛①✇❡❧❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✶❚❛❜❡❧❛ ✹✳✶✶ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♥♦ ❋❊▼▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✺❚❛❜❡❧❛ ✹✳✶✷ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♥♦ ❋❊▼▼✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✶ ▲■❙❚❆ ❉❊ ❆❇❘❊❱■❆❚❯❘❆❙ ❊ ❙■●▲❆❙❈❆ ❈♦rr❡♥t❡ ❆❧t❡r♥❛❞❛❈❆❉ ❈♦♠♣✉t❡r ❆✐❞❡❞ ❉❡s✐❣♥❈❈ ❈♦rr❡♥t❡ ❈♦♥tí♥✉❛❈❊❊ ❈♦♥✈❡rsã♦ ❊❧❡tr♦♠❡❝â♥✐❝❛ ❞❡ ❊♥❡r❣✐❛❋❊▼▼ ❋✐♥✐t❡ ❊❧❡♠❡♥t ▼❡t❤♦❞ ▼❛❣♥❡t✐❝s●◆❖ ●rã♦ ◆ã♦✲❖r✐❡♥t❛❞♦●❖ ●rã♦ ❖r✐❡♥t❛❞♦■❊❈ ■♥t❡r♥❛t✐♦♥❛❧ ❊❧❡❝tr♦t❡❝❤♥✐❝❛❧ ❈♦♠♠✐ss✐♦♥❏❆ ❏✐❧❡s✲❆t❤❡rt♦♥▼❊▲ ▼❛t❡r✐❛✐s ❊❧étr✐❝♦sP❲▼ P✉❧s❡ ❲✐❞t❤ ▼♦❞✉❧❛t✐♦♥ ▲■❙❚❆ ❉❊ ❙❮▼❇❖▲❖❙ a❘❡❧❛çã♦ ❞❡ ❡s♣✐r❛s ai ❈♦❡✜❝✐❡♥t❡ ❞♦ ♣♦t❡♥❝✐❛❧ ♠❛❣♥ét✐❝♦ aJA ❈♦❡✜❝✐❡♥t❡ ❞❡ ❏❆ ❉✐❢❡r❡♥❝✐❛❧ ❞❡ ❝♦♠♣r✐♠❡♥t♦ dt❉✐❢❡r❡♥❝✐❛❧ ❞❡ t❡♠♣♦ dx❉✐❢❡r❡♥❝✐❛❧ ❞❛ ❝♦♦r❞❡♥❛❞❛ ❡s♣❛❝✐❛❧ x dφ❉✐❢❡r❡♥❝✐❛❧ ❞❡ ✢✉①♦ F c❋♦rç❛ ❞♦ ❝♦♥t❛❝t♦r F CC❋♦rç❛ ❈❈ F CA❋♦rç❛ ❈❆ F❋✉♥❝✐♦♥❛❧ ❊s♣❡ss✉r❛ ❞❛ ❧â♠✐♥❛ e❊s♣❡ss✉r❛ ✐♥✐❝✐❛❧ ❞❛ ❧â♠✐♥❛ E an ❊♥❡r❣✐❛ ❞❡ ❛♥✐s♦tr♦♣✐❛ ♠❛❣♥❡t♦❝r✐st❛❧✐♥❛E ms ❊♥❡r❣✐❛ ♠❛❣♥❡t♦stát✐❝❛E mt ❊♥❡r❣✐❛ ❞❡ ♠❛❣♥❡t♦str✐❝çã♦E t ❊♥❡r❣✐❛ ❞❡ tr♦❝❛ e E❚❡♥sã♦ ✐♥❞✉③✐❞❛ ❉♦❜r♦ ❞❛ ár❡❛ ❞♦ tr✐â♥❣✉❧♦ ❞❛ ♠❛❧❤❛ d❉✐stâ♥❝✐❛ ❞❛s ❜♦r❞❛s ❞❡ ❧❛♠✐♥❛çã♦ dB❉✐❢❡r❡♥❝✐❛❧ ❞❡ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ dH❉✐❢❡r❡♥❝✐❛❧ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ dif ❉✐❢❡r❡♥❝✐❛❧ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❋♦❝❛✉❧t i f dl B❉❡♥s✐❞❛❞❡ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦ ❈❛♣❛❝✐tâ♥❝✐❛D ❉❡♥s✐❞❛❞❡ ❞❡ s❛t✉r❛çã♦C ❘❡♠❛♥ê♥❝✐❛B s ■♥❞✉çã♦ ♥♦ ♣♦♥t♦ ❞❡ s❛t✉r❛çã♦B r ■♥❞✉çã♦ ❞❡ s❛t✉r❛çã♦ ♠á①✐♠❛B sat B m ■♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ♠á①✐♠❛ ♥♦ ♠❛t❡r✐❛❧ ♥❛ ♦♣❡r❛çã♦B max B■♥❞✉çã♦ ♠á①✐♠❛ ❞❡ ✈❛③✐♦ F P❋❛t♦r ❞❡ ♣♦tê♥❝✐❛ G❈♦❡✜❝✐❡♥t❡ ❞❡ ❛tr✐t♦ g❈♦♠♣r✐♠❡♥t♦ ❞♦ ❡♥tr❡❢❡rr♦ I x ❈♦rr❡♥t❡ ♥♦ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✉r❛ ✸✳✺✸ ■♥❞✉tâ♥❝✐❛ ♠út✉❛L m ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞♦ s❡❝✉♥❞ár✐♦L M ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞♦ ♣r✐♠ár✐♦L2 ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛L1 ❈♦♥st❛♥t❡ ❞❡ ❏❆L K cont ❈♦♥st❛♥t❡ ❞❡ ❢♦rç❛ ❞♦ ❝♦♥t❛❝t♦rK exc,B ❈♦♥st❛♥t❡ ❞❡ ♣❡r❞❛s ❡①❝❡❞❡♥t❡s ❞❡ ❇❡rt♦tt✐K exc,C ❈♦♥st❛♥t❡ ❞❡ ♣❡r❞❛s ❡①❝❡❞❡♥t❡s ❞❡ ❈❛♠♣♦sK h ❈♦♥st❛♥t❡ ❞❡ ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡K L1 ❈♦♥st❛♥t❡ ❞❡ ✐♥❞✉tâ♥❝✐❛ ❞♦ ♣r✐♠ár✐♦K L2 ❈♦♥st❛♥t❡ ❞❡ ✐♥❞✉tâ♥❝✐❛ ❞♦ s❡❝✉♥❞ár✐♦ k JA K❋❛t♦r ❞❡ ❛❝♦♣❧❛♠❡♥t♦ I y ❈♦rr❡♥t❡ ♥♦ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✉r❛ ✸✳✺✹ if ❈♦rr❡♥t❡ ❞❡ ❋♦❝❛✉❧t im ❈♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ j❯♥✐❞❛❞❡ ✐♠❛❣✐♥ár✐❛ I npk ❈♦rr❡♥t❡ ♥♦♠✐♥❛❧ ❞❡ ♣✐❝♦ H■♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ I e ❈♦rr❡♥t❡ ♥❛ ❡s♣✐r❛ ❞❡ s♦♠❜r❛ I2❈♦rr❡♥t❡ ❘▼❙ ❞❡ s❡❝✉♥❞ár✐♦ I 1cc❈♦rr❡♥t❡ ❞❡ ♣r✐♠ár✐♦ ♥♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦ I1❈♦rr❡♥t❡ ❘▼❙ ❞❡ ♣r✐♠ár✐♦ I , i❈♦rr❡♥t❡ ❞❡ ✈❛③✐♦ I❈♦rr❡♥t❡ ❆❧t✉r❛ ❞❛ ❧â♠✐♥❛ h p❈♦♥st❛♥t❡ ❞❡ P❧❛♥❦ H c ❈♦❡r❝✐✈✐❞❛❞❡H m ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞♦ ♣♦♥t♦ ✜♥❛❧ ❞❛ ❝✉r✈❛ BH h H❈❛♠♣♦ ♠❛❣♥ét✐❝♦ ♠á①✐♠♦ ❞❡ ✈❛③✐♦ ■♥❞✉tâ♥❝✐❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❈❛♠♣♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦M 12 ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ❞♦ ♣r✐♠ár✐♦ ❡♠ r❡❧❛çã♦ ❛♦ s❡❝✉♥❞ár✐♦M 21 ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ❞♦ s❡❝✉♥❞ár✐♦ ❡♠ r❡❧❛çã♦ ❛♦ ♣r✐♠ár✐♦M m ▼❛❣♥❡t✐③❛çã♦ ❞♦ ♣♦♥t♦ ✜♥❛❧ ❞❛ ❝✉r✈❛ BHM r ▼❛❣♥❡t✐③❛çã♦ r❡♠❛♥❡♥t❡M s ▼❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ m B▼❛❣♥❡t♦♥ ❞❡ ❇♦❤r m e▼❛ss❛ ❞♦ ❡❧étr♦♥ m v▼❛ss❛ ❡s♣❡❝í✜❝❛ ❞♦ ♠❛t❡r✐❛❧ N◆ú♠❡r♦ ❞❡ ❡s♣✐r❛s N1◆ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❞❡ ♣r✐♠ár✐♦ N 2 ◆ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❞❡ s❡❝✉♥❞ár✐♦N e ◆ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❞♦ ❝♦♥t❛❝t♦r ne ◆ú♠❡r♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❛ ♠❛❧❤❛ PP♦t❡♥❝✐❛❧ ❡s❝❛❧❛r ♠❛❣♥ét✐❝♦ P ′❉❡r✐✈❛❞❛ ❞♦ ♣♦t❡♥❝✐❛❧ ❡s❝❛❧❛r ♠❛❣♥ét✐❝♦ P1 P♦tê♥❝✐❛ ❛t✐✈❛ ❞♦ ♣r✐♠ár✐♦P cu P❡r❞❛s ♥♦ ❝♦❜r❡P e P❡r❞❛ t♦t❛❧ ❞♦ ♠♦❞❡❧♦P exc P❡r❞❛s ❡①❝❡❞❡♥t❡sP exc,B P❡r❞❛s ❡①❝❡❞❡♥t❡s ❞❡ ❇❡rt♦tt✐P exc,C P❡r❞❛s ❡①❝❡❞❡♥t❡s ❞❡ ❈❛♠♣♦sP f P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦❝❛✉❧tP h P❡r❞❛s ♣♦r ❤✐st❡r❡s❡P s P❡r❞❛ s✐♠✉❧❛❞❛P t P❡r❞❛s t♦t❛✐s p i , q i , r i❈♦❡✜❝✐❡♥t❡s ❣❡♦♠étr✐❝♦s ❞❛ ♠❛❧❤❛ p mP❡r♠❡â♥❝✐❛ Q❱❡t♦r ❞❡ ❢♦♥t❡s ❡♥❡❣ét✐❝❛s ❞♦ s✐st❡♠❛ Q1 P♦tê♥❝✐❛ r❡❛t✐✈❛ ❞♦ ♣r✐♠ár✐♦ qe❈❛r❣❛ ❞♦ ❡❧étr♦♥ R 2 ❘❡s✐st♦r ❞❡ ♠❡❞✐çã♦ ❞♦ s❡❝✉♥❞ár✐♦R c ❘❡s✐stê♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ ❞❡ ♣❡r❞❛s ❞♦ ♥ú❝❧❡♦R eq ❘❡s✐stê♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡R f ❘❡s✐stê♥❝✐❛ ❡❧étr✐❝❛ ❞♦ ♣❡r❝✉rs♦ ♠❛❣♥ét✐❝♦R leq1 ❘❡s✐stê♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ ❞❡ ♣r✐♠ár✐♦R n ❘❡s✐stê♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ ❞♦ ♥ú❝❧❡♦R p ❘❡s✐stê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ♣❛r❛❧❡❧♦R s V ch1 ❚❡♥sã♦ ❞♦ ❝❛♥❛❧ ✶ ❞♦ ♦s❝✐❧♦s❝ó♣✐♦ W e❊♥❡r❣✐❛ ❡❧étr✐❝❛ W c❊♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥♦ ❡♥tr❡❢❡rr♦ W❊♥❡r❣✐❛ ❚❡♥sã♦ ❞♦ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✉r❛ ✸✳✺✹ v❱♦❧✉♠❡ V x ❚❡♥sã♦ ❞♦ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✉r❛ ✸✳✺✸V y V pk ❚❡♥sã♦ ❞❡ ♣✐❝♦ V o ❈❛♠♣♦ ❝♦❡r❝✐t✐✈♦ ❞♦ ♦❜❥❡t♦ ♠❛❣♥ét✐❝♦ V n ❚❡♥sã♦ ♥♦♠✐♥❛❧ ❡✜❝❛③ V ch2 ❚❡♥sã♦ ❞♦ ❝❛♥❛❧ ✷ ❞♦ ♦s❝✐❧♦s❝ó♣✐♦ V cc ❚❡♥sã♦ ❞❡ ♣r✐♠ár✐♦ ♥♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦ ❘❡s✐stê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ sér✐❡R sh V 2 ❚❡♥sã♦ ❘▼❙ ❞❡ s❡❝✉♥❞ár✐♦ V 1 ❚❡♥sã♦ ❘▼❙ ❞❡ ♣r✐♠ár✐♦ V P♦t❡♥❝✐❛❧ ❡❧étr✐❝♦ ▼❛tr✐③ ❣❧♦❜❛❧ ❞♦s ❝♦❡✜❝✐❡♥t❡sU m ❚❡♥sã♦ ♠á①✐♠❛ ❞❛ ♦♥❞❛ ▼❛tr✐③ ❞❡ r✐❣✐❞❡③ ❞♦s ❝♦❡✜❝✐❡♥t❡sSS S1 P♦tê♥❝✐❛ ❛♣❛r❡♥t❡ ❞♦ ♣r✐♠ár✐♦S f ➪r❡❛ ❡❢❡t✐✈❛ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ♦ ✢✉①♦SR S ′➪r❡❛ ❝♦rr✐❣✐❞❛ ❞❛ s❡çã♦ ❞♦ ❡♥tr❡❢❡rr♦ S❙❡çã♦ tr❛♥s✈❡rs❛❧ ❞♦ ♥ú❝❧❡♦ ❘❡s✐stê♥❝✐❛ s❤✉♥t r esp❉❡s❡♠♣❡♥❤♦ ♠❛❣♥ét✐❝♦ W m❊♥❡r❣✐❛ ♠❛❣♥ét✐❝❛ W n ❊♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥♦ ♥ú❝❧❡♦ w❉❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❋❧✉①♦ ❝♦♥❝❛t❡♥❛❞♦λ m ❋❧✉①♦ ❞❡ ♣✐❝♦λ R ❋❧✉①♦ r❡s✐❞✉❛❧µ ❉❡♥s✐❞❛❞❡ ✈♦❧✉♠étr✐❝❛ ❞❡ ❝❛r❣❛σ ❘❡s✐st✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞♦ ♠❛t❡r✐❛❧ρ v P♦t❡♥❝✐❛❧ ❞❛ ♠❛❧❤❛ρ ❋❧✉①♦ ♠á①✐♠♦φ p ❋❧✉①♦ ♠❛❣♥ét✐❝♦φ m ❘❡❧✉t✐✈✐❞❛❞❡ ♠❛❣♥ét✐❝❛φ P❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛ ❞♦ ✈á❝✉♦µ abs P❡r♠❡❛❜✐❧✐❞❛❞❡ ❛❜s♦❧✉t❛µ dif P❡r♠❡❛❜✐❧✐❞❛❞❡ ❞✐❢❡r❡♥❝✐❛❧µ max ▼á①✐♠❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛µ r P❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛ ❞♦ ♠❛t❡r✐❛❧ν P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛µ P❡r♠✐ss✐✈✐❞❛❞❡ ❡❧étr✐❝❛κ x ❈♦♥st❛♥t❡ q✉❡ ❝❛r❛❝t❡r✐③❛ ♦ ♠❡✐♦ ♠❛t❡r✐❛❧λ X leq1 ❘❡❛tâ♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ ❞❡ ♣r✐♠ár✐♦ α h ❊①♣♦❡♥t❡ ❞❡ ❤✐st❡r❡s❡α JA ❊①♣♦❡♥t❡ ❞❡ ❏❆ǫ Z y■♠♣❡❞â♥❝✐❛ ❞♦ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✉r❛ ✸✳✺✹ Z x■♠♣❡❞â♥❝✐❛ ❞♦ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✉r❛ ✸✳✺✸ Z2■♠♣❡❞â♥❝✐❛ ✈✐st❛ ❞♦ ❧❛❞♦ s❡❝✉♥❞ár✐♦ Z1■♠♣❡❞â♥❝✐❛ ✈✐st❛ ❞♦ ❧❛❞♦ ♣r✐♠ár✐♦ ❘❡❛tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ s❡❝✉♥❞❛r✐❛ y❈♦♦r❞❡♥❛❞❛ ❡s♣❛❝✐❛❧ ✈❡rt✐❝❛❧ X s ❘❡❛tâ♥❝✐❛ ✐♥❞✉t✐✈❛ ❞♦ ♠♦❞❡❧♦ sér✐❡ x❈♦♦r❞❡♥❛❞❛ ❡s♣❛❝✐❛❧ ❤♦r✐③♦♥t❛❧ x1 ❘❡❛tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ♣r✐♠❛r✐❛ x2 X m ❘❡❛tâ♥❝✐❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ X lp ❘❡❛tâ♥❝✐❛ ✐♥❞✉t✐✈❛ ❞♦ ♠♦❞❡❧♦ ♣❛r❛❧❡❧♦ ❈♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ θ❉❡❢❛s❛❣❡♠ ❞❡ ♦♥❞❛ χ c ❙✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ❝♦❡r❝✐t✐✈❛χ in ❙✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ✐♥✐❝✐❛❧χ m ❙✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ❞♦ ♣♦♥t♦ ✜♥❛❧ ❞❛ ❝✉r✈❛ BHχ r ❙✉s❝❡♣t✐❜✐❧✐❞❛❞❡ r❡♠❛♥❡♥t❡Ω ❙✉♣❡r❢í❝✐❡ ♠❛t❡♠át✐❝❛ω ❋r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛rF ❋♦rç❛ ♠❛❣♥❡t♦♠♦tr✐③ℜ ❘❡❧✉tâ♥❝✐❛∆ ❖♣❡r❛❞♦r ❞❡ ✈❛r✐❛çã♦ ❞✐s❝r❡t❛∇2 ❖♣❡r❛❞♦r ❧❛♣❧❛❝✐❛♥♦ |.| ◆♦t❛çã♦ ❞❡ ♠ó❞✉❧♦||.|| ◆♦t❛çã♦ ❞❡ t❡♥s♦r ❙❯▼➪❘■❖✶ ■◆❚❘❖❉❯➬➹❖ ✸✾ ✶✳✶ ❘❊❱■❙➹❖ ❉❊ ▲■❚❊❘❆❚❯❘❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾✶✳✶✳✶ ▼♦❞❡❧♦s ♥✉♠ér✐❝♦s ♥♦ ♣❧❛♥♦ BH ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹✶✳✶✳✷ ❈á❧❝✉❧♦ ❞❡ ♣❡r❞❛s ♠❛❣♥ét✐❝❛s ❡♠ ♣r♦❣r❛♠❛s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺✶✳✷ P❘❖P❖❙❚❆ ❉❆ ❉■❙❙❊❘❚❆➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻✶✳✸ ▼❖❚■❱❆➬➹❖ ❉❆ ❉■❙❙❊❘❚❆➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻✶✳✹ ❖❘●❆◆■❩❆➬➹❖ ❉❆ ❉■❙❙❊❘❚❆➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷ ❖ ▼➱❚❖❉❖ ❉❖❙ ❊▲❊▼❊◆❚❖❙ ❋■◆■❚❖❙ ✹✼✷✳✶ P❖❚❊◆❈■❆■❙ ❊ ▼■◆■▼❆▲■❉❆❉❊ ❊◆❊❘●➱❚■❈❆ ✳ ✳ ✹✽✷✳✷ ❖ ▼➱❚❖❉❖ ❱❆❘■❆❈■❖◆❆▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾✷✳✸ ❊▲❊▼❊◆❚❖❙ ❚❘■❆◆●❯▲❆❘❊❙ ❉❊ P❘■▼❊■❘❆ ❖❘✲ ❉❊▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵✷✳✹ ❋❯◆➬Õ❊❙ ■◆❚❊❘P❖▲❆◆❚❊❙ ❉❊ P❘■▼❊■❘❖ ●❘❆❯ ✺✷✷✳✺ ❙■❙❚❊▼❆❙ ■◆❋❖❘▼➪❚■❈❖❙ P❆❘❆ ❈➪▲❈❯▲❖ ◆❯✲ ▼➱❘■❈❖ ❉❊ ❈❆▼P❖❙ ❊▲❊❚❘❖▼❆●◆➱❚■❈❖❙ ✳ ✳ ✳ ✺✽✷✳✻ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ❉❖ ❈❆P❮❚❯▲❖ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸ ❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❊ ❯▼ ❚❘❆◆❙❋❖❘▼❆❉❖❘▼❖◆❖❋➪❙■❈❖ ✻✶✸✳✶ P❊❘❉❆❙ ❊▼ ▼❆❚❊❘■❆■❙ ❋❊❘❘❖▼❆●◆➱❚■❈❖❙ ✳ ✳ ✻✶ ✸✳✶✳✶ ❆ç♦s ❞❡ ❜❛✐①♦ ❝❛r❜♦♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷✸✳✶✳✷ ❆ç♦s ❞❡ ❣rã♦ ♦r✐❡♥t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹✸✳✶✳✸ ▼❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ❛♠♦r❢♦s ✭✈✐❞r♦s ♠❡tá✲ ❧✐❝♦s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹✸✳✶✳✹ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦✱ ♠❛❣♥❡t✐③❛çã♦ ❡ ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻✸✳✶✳✺ ❉♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s ✭♦✉✱ ❞❡ ❲❡✐ss✮✿ ✉♠❛ q✉❡s✲ tã♦ ❡♥❡r❣ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✶✳✺✳✶ P❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾✸✳✶✳✻ ▼❛❣♥❡t✐③❛çã♦ ❡ s✉s❝❡♣tâ♥❝✐❛ ♠❛❣♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✳✶✳✻✳✶ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✼✸✸✳✶✳✼ ▼♦❞❡❧♦s ❞❡ ♣❡r❞❛s ♣❛r❛ ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ✳ ✳ ✼✼ ✸✳✶✳✼✳✶ P❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡ ♣❡r❞❛s ♠❛❣♥ét✐✲ ✸✳✶✳✼✳✷ ❍✐st❡r❡s❡ ❛tr❛✈és ❞❛ ✈✐sã♦ ❞❡ ❡♥❡r❣✐❛♥♦s ❞♦♠í♥✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✸✳✶✳✼✳✸ P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ♦✉ ♣❛✲ r❛s✐t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾✸✳✶✳✼✳✹ P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ❡①❝❡✲ ❞❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶✸✳✶✳✽ ❊①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❞❛s s♦❜ r❡❣✐♠❡ ♥ã♦ s❡♥♦✐❞❛❧ ✭P❲▼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸✸✳✶✳✾ ▼♦❞❡❧♦ ❞❡ ❏✐❧❡s ❆t❤❡rt♦♥ ❞❡ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛ ❡ s❡✉s ♣❛râ♠❡tr♦s ót✐♠♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻✸✳✷ ❉■❙P❖❙■❚■❱❖ ❊▼ ❊❙❚❯❉❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽✸✳✸ ▼➱❚❖❉❖❙ ❊ ❊◗❯■P❆▼❊◆❚❖❙ P❆❘❆ ❆ ❈❆❘❆❈❚❊✲ ❘■❩❆➬➹❖ ❉❊ ▼❆❚❊❘■❆■❙ ❋❊❘❘❖▼❆●◆➱❚■❈❖❙ ✳ ✳ ✽✾✸✳✸✳✶ ▼❡❞✐❞♦r ❞❛s ♣❡r❞❛s ❞❡ ❤✐st❡r❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾✸✳✸✳✷ ❖ q✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵✸✳✸✳✸ ❈✐r❝✉✐t♦ ❡sq✉❡♠át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶✸✳✸✳✹ ❖ ❙❡♥s♦r ❞❡ ❧â♠✐♥❛ ú♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶✸✳✸✳✺ ❚é❝♥✐❝❛ ♣❛r❛ ❛ ♠❡❞✐çã♦ ❞♦s ♣r♦❝❡ss♦s ❞❡ ♦r✐❡♥✲ t❛çã♦ ❝r✐st❛❧♦❣rá✜❝❛ ✭❊❇❙❉✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸✸✳✸✳✻ ❚❡①t✉r❛ ❈r✐st❛❧♦❣rá✜❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✸✳✹ ❖❇❚❊◆➬➹❖ ❈❯❘❱❆ ❉❊ ❍■❙❚❊❘❊❙❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻✸✳✹✳✶ P♦♥t♦s ♥♦tá✈❡✐s ❞❛ ❝✉r✈❛ BH ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶✸✳✹✳✷ ❖❜t❡♥çã♦ ❞❛ ❝✉r✈❛ BH ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸✸✳✹✳✸ ■❞❡♥t✐✜❝❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✸✳✺ ❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❖ ▼❖❉❊▲❖ ❉❊ ❏■▲❊❙✲❆❚❍❊❘❚❖▼✶✵✹✸✳✻ ❈❯❘❱❆❙ ❉❊ ●❘❆◆❉❊❩❆❙ ▼❆●◆➱❚■❈❆❙ ❉❖ ❚❘❆◆❙✲ ❋❖❘▼❆❉❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻✸✳✻✳✶ ❈✉r✈❛ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❞✐❢❡r❡♥❝✐❛❧ ✳ ✶✵✻✸✳✻✳✷ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❞♦ ♥ú❝❧❡♦ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽✸✳✻✳✸ ■♥❞✉tâ♥❝✐❛s ♣ró♣r✐❛s L 1 ❡ L 2 ❡♠ ❢✉♥çã♦ ❞❛ ❝♦r✲ r❡♥t❡ ♣r✐♠ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾✸✳✻✳✹ ❖❜t❡♥çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶✸✳✻✳✺ ❈á❧❝✉❧♦ ❞❡ ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸✸✳✻✳✻ ❈✉r✈❛ ❞❡ ❘❡❧✉tâ♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹✸✳✻✳✼ ❈✉r✈❛ ❞❛ ♣❡r♠❡â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺✸✳✻✳✽ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❡ ❛ ❝✉r✈❛ BH✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✸✳✼ ❈➪▲❈❯▲❖ ❉❊ ■◆❉❯❚➶◆❈■❆❙ ❊▼ ❯▼ P❖◆❚❖ ❉❊ ✸✳✼✳✶ ❈á❧❝✉❧♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ❡ r❡❛tâ♥❝✐❛ ❞❡❞✐s♣❡rsã♦ ♣❡❧♦ ♠ét♦❞♦ ❝♦♥❝❛t❡♥❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✸✳✼✳✷ ❈á❧❝✉❧♦ ❞❡ ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ♣♦r ❡♥❡r❣✐❛ ❡♠❝♦♥❞✐çõ❡s ❞❡ ♣♦❧❛r✐❞❛❞❡ ❛❞✐t✐✈❛ ❡ s✉❜tr❛t✐✈❛ ✭❜✉❝✲❦✐♥❣ t❡st✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✸✳✼✳✸ ❈á❧❝✉❧♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ♣❡❧♦ ♠ét♦❞♦ ❣rá✜❝♦ ✳ ✳ ✳ ✶✷✵✸✳✼✳✹ ❋❛t♦r ❞❡ ❛❝♦♣❧❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✸✳✽ ❉❊❚❊❘▼■◆❆➬➹❖ ❊❳P❊❘■▼❊◆❚❆▲ ❉❆❙ ■◆❉❯❚➶◆✲❈■❆❙ ▼Ú❚❯❆❙ ◆❖ P❖◆❚❖ ❉❊ ❖P❊❘❆➬➹❖ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✸✳✾ ▼❖❉❊▲❆●❊▼ ❉❖ ❚❘❆◆❙❋❖❘▼❆❉❖❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺✸✳✾✳✶ ❈á❧❝✉❧♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦ ✭❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡✲ t✐③❛çã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺✸✳✾✳✷ ▼♦❞❡❧❛❣❡♠ ❞♦ ♥ú❝❧❡♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ✳ ✳ ✳ ✳ ✳ ✶✷✻✸✳✾✳✸ ❚r❛♥s❢♦r♠❛çã♦ ❞❡ ✐♠♣❡❞â♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻✸✳✾✳✹ ▼♦❞❡❧♦ ❛tr❛✈és ❞❡ ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✶✷✾ ✸✳✶✵ ▼❖❉❊▲❆●❊▼ ❉❆❙ P❊❘❉❆❙ ◆❖ ❚❘❆◆❙❋❖❘▼❆❉❖❘✶✸✶✸✳✶✵✳✶ ❈á❧❝✉❧♦ ❞❛s r❡s✐stê♥❝✐❛s ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛ ❞♦ ❜♦❜✐♥❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸✸✳✶✵✳✷ ❖❜t❡♥çã♦ ❡①♣❡r✐❡♠❡♥t❛❧ ❞❛s ♣❡r❞❛s r❡s✐st✐✈❛s ❡ ❛ ❞✐s♣❡rsã♦ ♠❛❣♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸✸✳✶✵✳✸ P❡r❞❛s ♥♦ ❢❡rr♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺✸✳✶✵✳✹ P❡r❞❛s ❚♦t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ✸✳✶✶ ❊◆❊❘●■❆ ❉■❙❙■P❆❉❆ ◆❆ ❈❯❘❱❆ ❉❊ ❍■❙❚❊❘❊❙❊ ✳ ✶✸✻✸✳✶✶✳✶ P❡r❞❛s ♣♦r ✉♥✐❞❛❞❡ ❞❡ ♠❛ss❛ ❡ ✈♦❧✉♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾✸✳✶✶✳✷ P♦tê♥❝✐❛ ❛t✐✈❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ♠❛ss❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾✸✳✶✶✳✸ ❘❡♥❞✐♠❡♥t♦ ♠á①✐♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵✸✳✶✶✳✹ P♦♥t♦ ót✐♠♦ ❞❡ ♦♣❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵✸✳✶✶✳✺ ❚r✐â♥❣✉❧♦ ❞❡ ♣♦tê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷ ✸✳✶✷ ❙❊P❆❘❆➬➹❖ ❉❆❙ P❊❘❉❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷✸✳✶✷✳✶ P❡r❞❛ ❞❡ ❤✐st❡r❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸✸✳✶✷✳✷ P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s ✭❋♦✉❝❛✉❧t✮ ✳ ✳ ✳ ✳ ✶✹✸✸✳✶✷✳✸ P❡r❞❛s ❡①❝❡❞❡♥t❡s ✭♠♦❞❡❧♦ ❇❡rt♦tt✐✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸✸✳✶✷✳✹ ❆♣❧✐❝❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸ ✸✳✶✸ ❈❖❘❘❊◆❚❊ ❉❊ ■◆✲❘❯❙❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼✸✳✶✸✳✶ ❈♦♠♣♦rt❛♠❡♥t♦ ❡♠ r❡❣✐♠❡ ♥ã♦✲s❛t✉r❛❞♦ ✳ ✳ ✳ ✳ ✶✹✼✸✳✶✸✳✷ ❈♦♠♣♦rt❛♠❡♥t♦ ❡♠ r❡❣✐♠❡ s❛t✉r❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵✸✳✶✸✳✸ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ✐♥✲r✉s❤ ✳ ✳ ✳ ✶✺✷✸✳✶✸✳✹ ❖s ♣r✐♥❝✐♣❛✐s ❡❢❡✐t♦s ❞❛s ❝♦rr❡♥t❡s ❞❡ ✐♥✲r✉s❤ ♥✉♠ s✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸✸✳✶✸✳✺ ❆ ✐♥t❡♥s✐❞❛❞❡ ❡ ❛ ❞✉r❛çã♦ ❞❛s ❝♦rr❡♥t❡s ❞❡ ✐♥✲r✉s❤✶✺✸ ✸✳✶✸✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❤✐st❡r❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✹✸✳✶✸✳✽ ❈✉r✈❛ BH ❞♦ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦ ❞♦ ♥ú❝❧❡♦ ✶✺✺✸✳✶✸✳✾ ❘❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✺✸✳✶✸✳✶✵ ❘❡s✉❧t❛❞♦s ❞❛s s✐♠✉❧❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✻✸✳✶✸✳✶✶ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ ♣❛r❛ ❛ ❝♦rr❡♥t❡ ❞❡ ✐♥✲r✉s❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵✸✳✶✹ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ❉❖ ❈❆P❮❚❯▲❖ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✵ ✹ ❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❊ ❯▼ ❈❖◆❚❆❈❚❖❘ ❈❆ ✶✻✺✹✳✶ ❖❇❏❊❚■❱❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✺✹✳✷ ❉❊❙❈❘■➬➹❖ ❉❖ P❘❖❇▲❊▼❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✻ ✹✳✷✳✶ ❉❡t❡r♠✐♥❛çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❞♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s❞❛ ❜♦❜✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✽ ✹✳✷✳✷ ❚❡♥sã♦ ❡ ❝♦rr❡♥t❡ ❡①♣❡r✐♠❡♥t❛✐s ♥❛ ❡s♣✐r❛ ❞❡ s♦♠✲❜r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✶ ✹✳✸ ❉❊❚❊❘▼■◆❆➬➹❖ ❉❆❙ ❈❆❘❆❈❚❊❘❮❙❚■❈❆❙ ▼❆●✲◆➱❚■❈❆❙ ❉❖ ◆Ú❈▲❊❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✹✹✳✸✳✶ ❈✐r❝✉✐t♦ ♣r♦♣♦st♦ ♣❛r❛ ❧❡✈❛♥t❛r ❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✶✼✻✹✳✸✳✷ ❋❛t♦r❡s ❞❡ ❡s❝❛❧❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✻✹✳✸✳✸ ❋♦r♠❛s ❞❡ ♦♥❞❛ ❞❛ t❡♥sã♦ ✭B✮ ❡ ❝♦rr❡♥t❡ ✭H✮ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✼✹✳✸✳✹ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✼✹✳✸✳✺ ❈✉r✈❛ ❞❡ s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛ BH ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✽ r✹✳✸✳✻ ❈✉r✈❛ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ µ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼✾✹✳✸✳✼ ❖❜t❡♥çã♦ ❣rá✜❝❛ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❛❜s♦❧✉t❛ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦ ♣❛r❛ ❛ ❝♦♥❞✐çã♦ ❡♥tr❡❢❡rr♦ ✵✱✹♠♠✶✽✶✹✳✸✳✽ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ❘❡❧✉tâ♥❝✐❛ ❞♦ ❈♦♥t❛❝t♦r ✳ ✳ ✳ ✳ ✶✽✷✹✳✸✳✾ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ❈✉r✈❛ ❞❡ P❡r♠❡â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✶✽✻ ✹✳✹ ❙■▼❯▲❆➬Õ❊❙ ❉❖ ❉■❙P❖❙■❚■❱❖ ❯❚■▲■❩❆◆❉❖ ❆ ❈❯❘❱❆BH ❊❳P❊❘■❊▼❊◆❚❆▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✻✹✳✹✳✶ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ❝♦rr❡♥t❡ ♥❛ ❡s♣✐r❛ ❞❡ s♦♠❜r❛ ✳ ✶✽✼✹✳✹✳✷ ❉❡t❡r♠✐♥❛çã♦ ❞❛ ❡♥❡r❣✐❛ ❞✐ss✐♣❛❞❛ ♥♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✽✹✳✹✳✸ P❡r❞❛s ♥♦ ❞✐s♣♦s✐t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾✹✳✹✳✹ ❆♥á❧✐s❡ ❡♥❡r❣ét✐❝❛ ❞♦ ❝♦♥t❛❝t♦r ❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ BH✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✾ ✹✳✹✳✺ ❚r✐â♥❣✉❧♦ ❞❡ ♣♦tê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✷✹✳✹✳✻ ❊♥❡r❣✐❛ ❡ ❢♦rç❛ ♥♦s ❡♥tr❡❢❡rr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✹ ✹✳✹✳✻✳✶ ▼ét♦❞♦ ❣rá✜❝♦ ❛tr❛✈és ❞❛ ❝✉r✈❛ ❇❍ ❞❛ ✹✳✹✳✻✳✷ ▼ét♦❞♦ ❣rá✜❝♦ ❛tr❛✈és ❞❛ ❝✉r✈❛ ❇❍ ❞❛❡♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥♦ ❡♥tr❡❢❡rr♦ ❞❡ 5 mm✶✾✼ ✹✳✹✳✻✳✸ ▼ét♦❞♦ ❞❛s ❡♥❡r❣✐❛s ♥♦s ❡♥tr❡❢❡rr♦s ✳ ✳ ✶✾✽✹✳✹✳✻✳✹ ▼ét♦❞♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❢♦rç❛ ✭♣r❡ssã♦ ♠❛❣♥ét✐❝❛✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✵✹✳✹✳✻✳✺ ▼ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✵✹✳✹✳✻✳✻ ❈♦♠♣❛r❛çã♦ ❞♦s ♠ét♦❞♦s ❞❡ ❝á❧❝✉❧♦ ❞❡ ❢♦rç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✶✹✳✺ ▼❖❉❊▲❆●❊▼ ❊▲➱❚❘■❈❆ ❉❖ ❉■❙P❖❙■❚■❱❖ ✳ ✳ ✳ ✳ ✷✵✹✹✳✻ ❊❋❊■❚❖❙ ❉❖ ❊◆❚❘❊❋❊❘❘❖ ◆❖ P❘❖❏❊❚❖ ❉❊ ❉■❙✲ P❖❙■❚■❱❖❙ ❊▲❊❚❘❖▼❆●◆➱❚■❈❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✼✹✳✼ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ❉❖ ❈❆P❮❚❯▲❖ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵✾ ✺ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ✷✶✸✺✳✶ P❯❇▲■❈❆➬Õ❊❙ ●❊❘❆❉❆❙ ❆❖ ▲❖◆●❖ ❉❊❙❙❊ ❚❘❆✲ ❇❆▲❍❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✹✺✳✷ P❊❘❙P❊❈❚■❱❆❙ ❉❊ ❊❱❖▲❯➬➹❖ ❉❆ ▼❊❚❖❉❖▲❖●■❆✷✶✺ ❘❊❋❊❘✃◆❈■❆❙ ❇■❇▲■❖●❘➪❋■❈❆❙ ✷✶✼❆◆❊❳❖ ❆ ✲✲ ▲❆➬❖ ❉❊ ❍■❙❚❊❘❊❙❊ ▼❆●◆➱❚■❈❆ ✕ ❋❯◆❉❆▼❊◆❚❆➬➹❖ ❚❊Ó❘■❈❆ ✷✷✸❆◆❊❳❖ ❇ ✲✲ ▼❖❉❊▲❖ ❉❊ ❏■▲❊❙ ❊ ❆❚❍❊❘❚❖▼ ✷✷✾❆◆❊❳❖ ❈ ✲✲ ▼❊❚❖❉❖▲❖●■❆ ❉❊ ❈❖◆❙❚❘❯➬➹❖ ❉❊ ❯▼ ❚❘❆◆❙❋❖❘▼❆❉❖❘ ▼❖◆❖❋➪❙■❈❖ ✷✸✺❆◆❊❳❖ ❉ ✲✲ ❋❖❘▼❆❙ ❉❊ ❖◆❉❆ ✷✹✶❆◆❊❳❖ ❊ ✲✲ ❆❘❚■●❖❙ ❉❊❙❊◆❱❖▲❱■❉❖❙ ❆❖ ▲❖◆●❖ ❉❖ ❚❘❆❇❆▲❍❖ ✷✹✺❆◆❊❳❖ ❋ ✲✲ P❘❖●❘❆▼❆➬➹❖ ❊▼ ▲❯❆ ✷✹✼❆◆❊❳❖ ● ✲✲ ▼❖❉❊▲❖❙ ❉❊ P❊❘❉❆❙ ❊❳❈❊❉❊◆❚❊❙ ❉❊ ❇❊❘❚❖❚❚■ ❊ ❈❖◆❈❊■❚❖ ❉❊ ❖❇❏❊❚❖ ▼❆●✲◆➱❚■❈❖ ✭❖▼✮ ✷✺✶ ✸✾✶ ■◆❚❘❖❉❯➬➹❖ ❖ ❡st✉❞♦ ❞❡ tr❛♥s❢♦r♠❛❞♦r❡s ❡ ♦✉tr♦s ❞✐s♣♦s✐t✐✈♦s r❡♠♦♥t❛♠ ❛♦✐♥í❝✐♦ ❞❛s ♣❡sq✉✐s❛s ❡♠ ❢❡♥ô♠❡♥♦s ♠❛❣♥ét✐❝♦s ❡✱ ❛✐♥❞❛ ❤♦❥❡✱ sã♦ ❛❧✈♦ ❞❡✐♥ú♠❡r♦s ❡st✉❞♦s✳ ❉❡ss❡ ♠♦❞♦✱ ♥❡ss❛ ✐♥tr♦❞✉çã♦✱ é r❡❛❧✐③❛❞❛ ✉♠❛ ❜r❡✈❡ r❡✈✐sã♦ ❞❡ ❧✐t❡r❛t✉r❛ ❛ r❡s♣❡✐t♦ ❞♦s ❢❡♥ô♠❡♥♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ❡♥✈♦❧✲✈❡♥❞♦ tr❛♥s❢♦r♠❛❞♦r❡s ❡ ♦✉tr♦s ❞✐s♣♦s✐t✐✈♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s✳ ❆❞✐❝✐♦✲♥❛❧♠❡♥t❡✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛ ♣r♦♣♦st❛ ❞❡ss❛ ❞✐ss❡rt❛çã♦ ❡ ❛ ♠♦t✐✈❛çã♦❞♦ tr❛❜❛❧❤♦ ❡✱ ♣♦r ✜♠✱ ❛ ♦r❣❛♥✐③❛çã♦ ❣❡r❛❧ ❞❡ t♦❞♦ ♦ ❡st✉❞♦ ❞❡s❡♥✈♦❧✲✈✐❞♦✳✶✳✶ ❘❊❱■❙➹❖ ❉❊ ▲■❚❊❘❆❚❯❘❆ ❚r❛♥s❢♦r♠❛❞♦r❡s ❡ r❡❛t♦r❡s sã♦ ❞✐s♣♦s✐t✐✈♦s ❝✉❥❛s r❡s♣♦st❛s ❛✉♠❛ ❞❛❞❛ ❡①❝✐t❛çã♦ ❞❡♣❡♥❞❡♠ ❞❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ♦♣❡r❛çã♦ ❡ ❞❡ ❢❡♥ô✲♠❡♥♦s ♥ã♦ ❧✐♥❡❛r❡s✳ ❖ ❝♦♠♣♦rt❛♠❡♥t♦ ♥ã♦ ❧✐♥❡❛r ❞♦ ♥ú❝❧❡♦ ❞❡ss❡s❞✐s♣♦s✐t✐✈♦s s❡ ❞❡✈❡ ❛ ❢❡♥ô♠❡♥♦s ❛ss♦❝✐❛❞♦s ❛♦s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥é✲ t✐❝♦s ❝♦♠♦ s❛t✉r❛çã♦ ❡ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦s ❡❢❡✐t♦s❛ss♦❝✐❛❞♦s à ❢r❡q✉ê♥❝✐❛ ❞❡ ♦♣❡r❛çã♦ sã♦ ❝❛✉s❛❞♦s ♣♦r ❝♦rr❡♥t❡s ✐♥❞✉③✐✲❞❛s ♥❛s ❧❛♠✐♥❛çõ❡s✱ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s ♦✉ ❝♦rr❡♥t❡s❞❡ ❋♦✉❝❛✉❧t✳ ❖ ♠♦❞❡❧❛♠❡♥t♦ t❡ór✐❝♦ ❝♦♠♣❧❡t♦ ❞♦ ♥ú❝❧❡♦ ❞❡✈❡ ✐♥❝❧✉✐r♦ ❡❢❡✐t♦ ❞❛s ♥ã♦ ❧✐♥❡❛r✐❞❛❞❡s ❡ ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❢r❡q✉ê♥❝✐❛✳ ❊ss❡s ♠♦✲❞❡❧♦s sã♦ ✐♠♣♦rt❛♥t❡s ♥♦ ❡st✉❞♦ ❞❡ ❢❡♥ô♠❡♥♦s ❝♦♠♦ ❢❡rr♦rr❡ss♦♥â♥❝✐❛✱❝♦rr❡♥t❡s tr❛♥s✐tór✐❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ❜❡♠ ❝♦♠♦ ♥❛ ❡st✐♠❛t✐✈❛ ❞❛s♣❡r❞❛s ✐rr❡✈❡rsí✈❡✐s ❞❡ ❡♥❡r❣✐❛ s♦❜ ❛ ❢♦r♠❛ ❞❡ ❝❛❧♦r ✭❙❆❨✱ ✶✾✽✸✮✳ ❆s té❝♥✐❝❛s ♥✉♠ér✐❝❛s ♣❛r❛ ❛♥á❧✐s❡ ❞♦s ❢❡♥ô♠❡♥♦s ♥ã♦ ❧✐♥❡❛r❡s ♣r❡s❡♥t❡s♥♦s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s sã♦✱ ❛té ❤♦❥❡✱ ♦❜❥❡t♦ ❞❡ ♠✉✐t❛s ♣❡sq✉✐s❛s❡ ♣✉❜❧✐❝❛çõ❡s q✉❡ ✐♥❝❧✉❡♠ ✉♠❛ ❞❡t❛❧❤❛❞❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❜❡♠❝♦♠♦ ✐♥ú♠❡r❛s ❛♣❧✐❝❛çõ❡s ✈♦❧t❛❞❛s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♣r♦❥❡✲ t♦s ❡ ❝♦♥str✉çã♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❡❧étr✐❝♦s ✭❙■▲❱❊❙❚❊❘❀ ❋❊❘❘❆❘■✱✶✾✾✵❀ ◆❖●❯❊■❘❆❀ P❊❘❊■❘❆ ❏❘✱ ✷✵✵✻✮✳ ❆s té❝♥✐❝❛s ♣❛r❛ ✐♥❝❧✉sã♦ ❞♦s ❡❢❡✐t♦s ❞❛s ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s sã♦❜❛s❡❛❞❛s ♥❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❞✐❢✉sã♦ ❞❡ ❝♦rr❡♥t❡s ✉t✐❧✐③❛♥❞♦ té❝✲♥✐❝❛s ♥✉♠ér✐❝❛s ❝♦♠♦ ❞✐❢❡r❡♥ç❛s ✜♥✐t❛s ♦✉ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✭❙❚❖▲▲✱✶✾✼✹✮✳ ❆ ✐♥❝❧✉sã♦ ❞❛ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ r❡q✉❡r ✉♠ tr❛t❛♠❡♥t♦ ❜❡♠ ♠❛✐s ❡❧❛❜♦r❛❞♦✳ ❖s ♠♦❞❡❧♦s ❜❛s❡❛❞♦s ♥♦ ❛❧✐♥❤❛♠❡♥t♦ ✹✵ ❞❡ ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s ❞❡s❝r❡✈❡♠ ❞❡ ❢♦r♠❛ ❝❧❛r❛ ♦ ❢❡♥ô♠❡♥♦ ❞❛ ❤✐s✲ t❡r❡s❡✱ ♠❛s ❛ ✐♥❝♦r♣♦r❛çã♦ ❞❛s ♣r❡✈✐sõ❡s t❡ór✐❝❛s ❞❡ss❡s ♠ét♦❞♦s àsté❝♥✐❝❛s ❞❡ ❛♥á❧✐s❡ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❢❡rr♦♠❛❣♥ét✐❝♦s r❡s✉❧t❛✱ q✉❛s❡ s❡♠✲♣r❡✱ ❡♠ ♣r♦❜❧❡♠❛s ♥✉♠ér✐❝♦s ❞❡ ♣r❡❝✐sã♦ ❡ ❝♦♥s✐stê♥❝✐❛ ❞❡ ❞❛❞♦s✳ P❛r❛ ❡①♣❧✐❝❛r ♦ ❢❡♥ô♠❡♥♦ ❞❛ ❤✐st❡r❡s❡ ♥❛ ❝♦♥❞✐çã♦ ❡stát✐❝❛ ♦✉ q✉❛s❡✲❡stát✐❝❛✱ ♣♦❞❡✲s❡ ❝♦♥s✐❞❡r❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ♥ú❝❧❡♦ ❢❡rr♦✲♠❛❣♥ét✐❝♦ ❞❡ ✉♠ r❡❛t♦r ♦✉ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r ♦♣❡r❛♥❞♦ ❡♠ ✈❛③✐♦✳◗✉❛♥❞♦ ♦ ❡♥r♦❧❛♠❡♥t♦ ♣r✐♠ár✐♦ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r é ❡♥❡r❣✐③❛❞♦ ♣♦r✉♠❛ ❢♦♥t❡ ❞❡ ❝♦rr❡♥t❡ ❛❥✉st❛❞❛ ❞❡ ❢♦r♠❛ q✉❡ ❛ ❝♦rr❡♥t❡ ♠❛❣♥❡t✐③❛♥t❡✈❛r✐❛ ❡♥tr❡ +i m ❡ −i m ❡ r❡t♦r♥❛ ♣❛r❛ ♦ ✈❛❧♦r +i m ✱ ❛ r❡❧❛çã♦ ❡♥tr❡♦s ❝❛♠♣♦s B ❡ H é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❝í❝❧✐❝❛ ❝♦♥❤❡✲❝✐❞❛ ❝♦♠♦ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡✳ P❛r❛ ✈❛❧♦r❡s ❞❛ ❝♦rr❡♥t❡ ♠❛❣♥❡t✐③❛♥t❡ i ms✉✜❝✐❡♥t❡♠❡♥t❡ ❡❧❡✈❛❞♦s ♣❛r❛ ❧❡✈❛r ♦ ♥ú❝❧❡♦ à s❛t✉r❛çã♦✱ ♦s ♣♦♥t♦s ❞❡ ♦♣❡r❛çã♦ ♥♦ ♣❧❛♥♦ BH s❡❣✉❡♠ ♦ ❧❛ç♦ ♠❛✐s ❡①t❡r♥♦ ❞❛ ✐❧✉str❛çã♦❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✶✳✶ q✉❡ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❞❡ss❛ ❝♦♥❞✐çã♦ ❞❡ m♦♣❡r❛çã♦✳ ◗✉❛♥❞♦ ❛ ❛♠♣❧✐t✉❞❡ ❞❛ ❝♦rr❡♥t❡ ♠❛❣♥❡t✐③❛♥t❡ ♠á①✐♠❛ i é♠❡♥♦r✱ ❧❛ç♦s ♠❡♥♦r❡s✱ t❛♠❜é♠ s✐♠étr✐❝♦s ❡♠ r❡❧❛çã♦ à ♦r✐❣❡♠ ❞♦ ♣❧❛♥♦BH ✱ sã♦ ❣❡r❛❞♦s✳ ❆ ✐❧✉str❛çã♦ ❞❛ ❋✐❣✉r❛ ✶✳✶ t❛♠❜é♠ ♠♦str❛ ❛ ❝✉r✈❛♥♦r♠❛❧ ❞❡ ♠❛❣♥❡t✐③❛çã♦ tr❛ç❛❞❛ ❛ ♣❛rt✐r ❞❛ ♦r✐❣❡♠ ❞♦ ♣❧❛♥♦ BH ❡♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ ✉♥✐ã♦ ❞♦s ✈ért✐❝❡s ❞♦s ❧❛ç♦s ❝♦♥❝ê♥tr✐❝♦s✳❋✐❣✉r❛ ✶✳✶ ✕ ▲❛ç♦s ❞❡ ❤✐st❡r❡s❡✱ ♦♣❡r❛çã♦ q✉❛s❡✲❡stát✐❝❛✳❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ✭◆❖●❯❊■❘❆❀ P❊❘❊■❘❆ ❏❘✱ ✷✵✵✻✮✳ ✹✶ ◆❛ ♦♣❡r❛çã♦ ❡♠ ✈❛③✐♦✱ q✉❛♥❞♦ s♦♠❡♥t❡ ✉♠ ❡♥r♦❧❛♠❡♥t♦ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r é ❛❧✐♠❡♥t❛❞♦ ♣♦r ✉♠❛ ❢♦♥t❡ ❛❧t❡r♥❛❞❛✱ ♦ ♣r♦❝❡ss♦ ❞❡♠❛❣♥❡t✐③❛çã♦ ❞♦ ♥ú❝❧❡♦ ♣❛ss❛ ❛ s❡r ♥ã♦ ✉♥✐❢♦r♠❡ ❞❡✈✐❞♦ à ♣r❡s❡♥ç❛❞❛s ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s✳ ❖ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❝r✐❛❞♦ ♣♦r ❡ss❛s ❝♦rr❡♥t❡s s❡ ♦♣õ❡ ❛♦ ❝❛♠♣♦ ♠❛❣♥❡t✐③❛♥t❡ ❡✱ ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ ❛ ❞✐ss✐♣❛çã♦❞❡ ❝❛❧♦r é ♠❡♥♦r ♥❛s r❡❣✐õ❡s ♠❛✐s ♣ró①✐♠❛s ❞♦ ❝❡♥tr♦ ❣❡♦♠étr✐❝♦ ❞❛s❧❛♠✐♥❛çõ❡s✳ ◆❛s r❡❣✐õ❡s ♠❛✐s ♣ró①✐♠❛s às s✉♣❡r❢í❝✐❡s ❞❛ ❧❛♠✐♥❛çã♦ ❛❞✐ss✐♣❛çã♦ ❞❡ ❝❛❧♦r é ♠❛✐♦r ❞❡✈✐❞♦ à ♠❛✐♦r ✐♥t❡♥s✐❞❛❞❡ ❡ ❝♦♥❝❡♥tr❛çã♦❞❡ ❝♦rr❡♥t❡s ✐♥❞✉③✐❞❛s✳ ❆ ❋✐❣✉r❛ ✶✳✷ ✐❧✉str❛ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❝❛✐♠❡♥t♦❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✉❧t❛♥t❡ H ❡♠ ✉♠❛ ❧❛♠✐♥❛çã♦❞❡ ❡s♣❡ss✉r❛ d ❡♠ ❢✉♥çã♦ ❞❛ ❞✐stâ♥❝✐❛ ❛té ❛s ❜♦r❞❛s ❞❛ ❧❛♠✐♥❛çã♦✳❋✐❣✉r❛ ✶✳✷ ✕ ■♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H ❡♠ ✉♠❛ ❧❛♠✐♥❛çã♦ ❞❡ ❡s♣❡ss✉r❛ d ✳❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ✭◆❖●❯❊■❘❆❀ P❊❘❊■❘❆ ❏❘✱ ✷✵✵✻✮✳ ❆ ❞✐s❝✉ssã♦ ❛❝✐♠❛ ✐❧✉str❛ ♦ ❣r❛✉ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❡♥✈♦❧✈✐❞♦ ♥♦❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ♣❛r❛ r❡♣r❡s❡♥t❛r ♦ ❢✉♥❝✐♦✲♥❛♠❡♥t♦ ♠❛❣♥❡t♦✲❞✐♥â♠✐❝♦ ❞❡ ❡str✉t✉r❛s ♠❛❣♥ét✐❝❛s ❧❛♠✐♥❛❞❛s✳ ❯♠♠♦❞❡❧♦ ♣r❡❝✐s♦ ❞❡✈❡ ❝♦♥t❡♠♣❧❛r✱ s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ♦ ❢❡♥ô♠❡♥♦ ❞❛ ❤✐s✲ t❡r❡s❡✱ q✉❡ é ♥ã♦ ❧✐♥❡❛r ❡ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ ❢r❡q✉ê♥❝✐❛ ❡ ♦ ❢❡♥ô♠❡♥♦ ✹✷ ❞❡♣❡♥❞❡♥t❡ ❞❛ ❢r❡q✉ê♥❝✐❛✳ ❖s ❣rá✜❝♦s ❛♣r❡s❡♥t❛❞♦s ♥❛s ❋✐❣✉r❛s ✶✳✸ ❡✶✳✹ ❢♦r❛♠ ♦❜t✐❞♦s ♣♦r ✭❋Ü❩■✱ ✶✾✾✾✮ ❡♠ s❡✉ tr❛❜❛❧❤♦ ❝♦♠ ❧❛♠✐♥❛çõ❡s❞❡ ❣rã♦s ♦r✐❡♥t❛❞♦s ✷✼❩❉❑❍✾✺ ❝♦♠ ❡s♣❡ss✉r❛ ❞❡ 0, 27 mm✳ ❖s ❣rá✲✜❝♦s r❡♣r❡s❡♥t❛♠ r❡s✉❧t❛❞♦s ❞❛ ♦♣❡r❛çã♦ ♥❛s ❢r❡q✉ê♥❝✐❛s ❞❡ ✺✵ ❡ ✷✺✵❤❡rt③✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❈❛❞❛ ❣rá✜❝♦ ❝♦♥té♠ q✉❛tr♦ ❞✐❢❡r❡♥t❡s ❧❛ç♦s✱❝♦♥❝ê♥tr✐❝♦s ❡♠ t♦r♥♦ ❞❛ ♦r✐❣❡♠ ❞♦ ♣❧❛♥♦ BH✳ ❈❛❞❛ ❧❛ç♦ r❡♣r❡s❡♥t❛♦s r❡s✉❧t❛❞♦s ❞❡ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❞✐❢❡r❡♥t❡✿ ♠❡❞✐çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❞♦❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ✶ ❤❡rt③✱ ♦✉ s❡❥❛✱ ♦♣❡r❛çã♦ q✉❛s❡ ❡s✲ tát✐❝❛ ✭st✳✮✱ ♠❡❞✐çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❛s ♣❡r❞❛s t♦t❛✐s ✭♠❡❛s✳✮✱ s✐♠✉❧❛çã♦❞❡ ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s ✭❡❞❞② ❝✳✮ ❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦✲♥❛❧ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞✐♥â♠✐❝♦ ✭❝♦♠♣✮✳ ❆♠❜♦s ♦s ❣rá✜❝♦s ❝♦♥tê♠♦s r❡s✉❧t❛❞♦s ❞♦s ♣r♦❝❡❞✐♠❡♥t♦s ❛ss♦❝✐❛❞♦s à ❞✐r❡çã♦ ♣r❡❢❡r❡♥❝✐❛❧ ❞❡♠❛❣♥❡t✐③❛çã♦ ❞❛ ❧❛♠✐♥❛çã♦✳❋✐❣✉r❛ ✶✳✸ ✕ ▲❛ç♦s ❞❡ ❤✐st❡r❡s❡✱ f = 50 Hz✳❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ✭❋Ü❩■✱ ✶✾✾✾✮✳ ✹✸ ❋✐❣✉r❛ ✶✳✹ ✕ ▲❛ç♦s ❞❡ ❤✐st❡r❡s❡✱ f = 250 Hz✳❋♦♥t❡✿ ❆❞❛♣t❛❞♦ ❞❡ ✭❋Ü❩■✱ ✶✾✾✾✮✳ ❉❡✈❡✲s❡ r❡ss❛❧t❛r q✉❡✱ ❡♠ ❛♠❜♦s ♦s ❣rá✜❝♦s✱ ♦ ♠❡s♠♦ ❧❛ç♦ r❡♣r❡✲ s❡♥t❛ ❛ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛ ❞❛ ♦♣❡r❛çã♦ q✉❛s❡ ❡stát✐❝❛ ✭st✳✮✱ ♥❛ ❢r❡q✉ê♥✲❝✐❛ ❞❡ ✶ ❤❡rt③✳ ❖❜s❡r✈❛r✱ ❛✐♥❞❛✱ ♦ ❛✉♠❡♥t♦ s✉❜st❛♥❝✐❛❧ ♥❛ ár❡❛ ❞♦ ❧❛ç♦❛ss♦❝✐❛❞♦ às ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s ✭❡❞❞② ❝✳✮ ❡♠ ❞❡❝♦rrê♥❝✐❛ ❞♦❛✉♠❡♥t♦ ❞❛ ❢r❡q✉ê♥❝✐❛✱ ♦ q✉❡ ❡stá ❡♠ ❝♦♥s♦♥â♥❝✐❛ ❝♦♠ ♦ ❡♥t❡♥❞✐♠❡♥t♦❢ís✐❝♦ ❞♦ ♣r♦❜❧❡♠❛✳ P❛r❛ ❛♠❜❛s ❛s ❝♦♥❞✐çõ❡s ❞❡ ♦♣❡r❛çã♦✱ ♦❜s❡r✈❛✲s❡ q✉❡ ♦ ♠♦❞❡❧♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❣❡r❛ ót✐♠❛s ❡st✐♠❛t✐✈❛s ❞♦s ✈❛❧♦r❡s ♦❜✲t✐❞♦s ❛ ♣❛rt✐r ❞❛s ♠❡❞✐çõ❡s ❡♠ ❧❛❜♦r❛tór✐♦✱ ❡ss❛s ú❧t✐♠❛s r❡❛❧✐③❛❞❛s✉t✐❧✐③❛♥❞♦✲s❡ ♦ s✐st❡♠❛ ❞❡ ♠❡❞✐❞❛s ♠❛❣♥ét✐❝❛s ❞❡s❝r✐t♦ ♣♦r ✭P❋Ü❚❩✲ ✹✹ ✶✳✶✳✶ ▼♦❞❡❧♦s ♥✉♠ér✐❝♦s ♥♦ ♣❧❛♥♦ BH❆ ❧✐t❡r❛t✉r❛ r❡❣✐str❛ ✈ár✐❛s té❝♥✐❝❛s ❞❡ ♠❡❞✐çã♦ ❞❡ ❣r❛♥❞❡③❛s ❡❧étr✐❝❛s ❡ ♠❛❣♥ét✐❝❛s q✉❡ ♣❡r♠✐t❡♠ ✉♠❛ ❛♥á❧✐s❡ rá♣✐❞❛ ❡ ♣r❡❝✐s❛ ❞❛s❝❛r❛❝t❡ríst✐❝❛s ❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ❛ ♣❛rt✐r ❞❛s ❜❛s❡s ❢ís✐❝❛s ❞❛ r❡✲❧❛çã♦ ❡♥tr❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦ B ❡ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦♠❛❣♥ét✐❝♦ H✳ P❛r❛ ❝♦♥t♦r♥❛r ❛s ❞✐✜❝✉❧❞❛❞❡s ❛ss♦❝✐❛❞❛s à ♥ã♦ ❧✐♥❡❛✲ r✐❞❛❞❡ ❞❛ r❡❧❛çã♦ ❡♥tr❡ ♦s ❝❛♠♣♦s B ❡ H✱ ✈ár✐♦s ♠♦❞❡❧♦s ♥✉♠ér✐❝♦s❛♣r♦①✐♠❛❞♦s✱ ❧✐♥❡❛r✐③❛❞♦s✱ tê♠ s✐❞♦ ♣r♦♣♦st♦s✳ ❚❛✐s ♠♦❞❡❧♦s ✉s✉❛❧✲♠❡♥t❡ ❝♦♥❞✉③❡♠ ❛ ♣r❡✈✐sõ❡s rá♣✐❞❛s ❡ út❡✐s s♦❜r❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦❞♦s ❞✐s♣♦s✐t✐✈♦s ❡♠ ❡st✉❞♦✱ ❛tr❛✈és ❞❡ ❝á❧❝✉❧♦s ♠❛✐s s✐♠♣❧❡s ❡ ❞❡ ❢á❝✐❧❡♥t❡♥❞✐♠❡♥t♦✳ ❖s ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ♠❛✐s s✐♠♣❧❡s ♣r♦❞✉③❡♠ ❝❛r❛❝✲ t❡ríst✐❝❛s ♠♦♥♦t♦♥❛♠❡♥t❡ ❝r❡s❝❡♥t❡s ❡ ✉♥✐✈❛❧❡♥t❡s✱ ❝♦♠♦ ❛ ❝❛r❛❝t❡rís✲t✐❝❛ ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✶✳✺✳ ❆❧❣✉♥s ♠♦❞❡❧♦s✱ ❢♦r♠❛❞♦s ♣♦r s❡❣♠❡♥✲ t♦s ❧✐♥❡❛r❡s✱ sã♦ ❛♣r♦①✐♠❛çõ❡s s✐♠♣❧✐✜❝❛❞❛s ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❝♦♠♦ ❛❝✉r✈❛ ✐♥✐❝✐❛❧ ❞❡ ♠❛❣♥❡t✐③❛çã♦ q✉❡ ♣♦❞❡ s❡r ♠❡❞✐❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳❖ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ♠❡❞✐çã♦ ❞❛s ❝✉r✈❛s ✐♥✐❝✐❛✐s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞❡♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s é ❞❡s❝r✐t♦ ♥❛ ♥♦r♠❛ té❝♥✐❝❛ ■❊❈ ✻✵✹✵✹✲✹✳❊①✐st❡♠ t❛♠❜é♠ ♦s ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s✱ ❧✐♥❡❛r✐③❛❞♦s ♦✉ ♥ã♦✱ q✉❡♣r❡s❡r✈❛♠ ♦ ❡❢❡✐t♦ ❞❛ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛✳ ❚❛✐s ♠♦❞❡❧♦s sã♦ ❡ss❡♥❝✐✲❛✐s ♥♦ ❡st✉❞♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❝♦♠♦ ♠áq✉✐♥❛s ❞❡ í♠ã ♣❡r♠❛♥❡♥t❡ ❡❛♠♣❧✐✜❝❛❞♦r❡s ♠❛❣♥ét✐❝♦s ✭❖❙❙❆❘❚❀ ▼❊❯◆■❊❘✱ ✶✾✾✵✮✳ ❉✐❢❡r❡♥t❡s ♠♦❞❡❧♦s ♥✉♠ér✐❝♦s ♣❛r❛ ♦ ❢❡♥ô♠❡♥♦ ❞❛ ❤✐st❡r❡s❡ ♠❛❣✲♥ét✐❝❛ tê♠ s✐❞♦ ♣r♦♣♦st♦s✳ ❚❛✐s ♠♦❞❡❧♦s r❡✢❡t❡♠✱ ♥♦ ♣❧❛♥♦ BH✱ ❞❡❢♦r♠❛ ❛♣r♦①✐♠❛❞❛✱ ❢❡♥ô♠❡♥♦s ❢ís✐❝♦s ❞❡ ❛❧t❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♠♦ ♠❛❣✲♥❡t✐③❛çã♦ r❡✈❡rsí✈❡❧✱ ♠❛❣♥❡t✐③❛çã♦ ✐rr❡✈❡rsí✈❡❧✱ ❧❛ç♦s ♠❡♥♦r❡s✱ ❡❢❡✐t♦s❞✐♥â♠✐❝♦s ❡ ❡❢❡✐t♦s ❞❛ t❡♠♣❡r❛t✉r❛ ✭▼❆❩❆❯❘■❈ ❡t ❛❧✳✱ ✷✵✵✺❀ ❏■▲❊❙ ❉✳❈✳❀ ❆❚❍❊❘❚❖◆✱ ✶✾✽✸✮✳ ❯♠ ❞♦s ♣r✐♠❡✐r♦s ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ♣❛r❛♦ ❢❡♥ô♠❡♥♦ ❞❡ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛ ❢♦✐ ♣r♦♣♦st♦✱ ❥á ❡♠ ✶✾✸✺✱ ♣♦r Pr❡✐✲ s❛❝❤ ✭P❘❊■❙❆❈❍✱ ✶✾✸✺✮✳ ❆s ❝❛r❛❝t❡ríst✐❝❛s ❡ ❛♣❧✐❝❛çõ❡s ❞♦s ♠♦❞❡❧♦s♣❛r❛ ❛ ❤✐st❡r❡s❡ q✉❛s❡ ❡stát✐❝❛ ♣r♦♣♦st♦s ♣♦r Pr❡✐s❛❝❤✱ ●❧♦❜✉s✱ ❙t♦♥❡r✲❲♦❧❤❢❛rt❤ ❡ ❏✐❧❡s✲❆t❤❡rt♦♥ ❢♦r❛♠ ❝♦♠♣❛r❛❞❛s ♣♦r ▲✐♦r③♦✉✱ P❤❡❧♣s ❡❆t❤❡rt♦♥ ✭✷✵✵✵✮✱ ❧❡✈❛♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ✈ár✐♦s ❛s♣❡❝t♦s✱ t❛✐s ❝♦♠♦✿♠❡❝❛♥✐s♠♦s ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ❞❛s ♣❛r❡❞❡s ❞♦s ❞♦♠í♥✐♦s✱ ❛♥✐s♦tr♦♣✐❛✱ t❡①t✉r❛✱ r❡✈❡rs✐❜✐❧✐❞❛❞❡✱ ❞❡s♠❛❣♥❡t✐③❛çã♦✱ ♣❛râ♠❡tr♦s ♠❡♥s✉rá✈❡✐s✱ ❞♦✲♠í♥✐♦s ❞♦s ❣rã♦s✱ ❜❡♠ ❝♦♠♦ ♦ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ ❞❛ ❛♠♦str❛✿ ♠❛❣♥❡t✐✲❝❛♠❡♥t❡ ❞✉r♦✱ ♠♦❧❡ ♦✉ ✐♥t❡r♠❡❞✐ár✐♦ ✭▲■❖❘❩❖❯❀ P❍❊▲P❙❀ ❆❚❍❊❘✲❚❖◆✱ ✷✵✵✵✮✳ ✹✺ ❋✐❣✉r❛ ✶✳✺ ✕ ❈❛r❛❝t❡ríst✐❝❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ❧✐♥❡❛r✐③❛❞❛ ♣♦r ♣❛rt❡s✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳✶✳✶✳✷ ❈á❧❝✉❧♦ ❞❡ ♣❡r❞❛s ♠❛❣♥ét✐❝❛s ❡♠ ♣r♦❣r❛♠❛s ❞❡ ❡❧❡♠❡♥✲ t♦s ✜♥✐t♦s ❯♠❛ ✐♠♣♦rt❛♥t❡ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ♦ ❡st❛❞♦ ❞❛ ❛rt❡ é ❛ ✐♥❝♦r♣♦✲ r❛çã♦ ❞❛ ♠♦❞❡❧❛❣❡♠ ❞♦s ❢❡♥ô♠❡♥♦s ❞❡ ❤✐st❡r❡s❡ ❡ ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s❡♠ ♣r♦❣r❛♠❛s ❞❡ s✐♠✉❧❛çã♦ ❜❛s❡❛❞♦s ♥❛ té❝♥✐❝❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳➱ ♦ q✉❡ ♦❝♦rr❡✉ ❝♦♠ ❛ s✉ít❡ ❞❡ ♣r♦❣r❛♠❛s ❣r❛t✉✐t♦s ❝♦♥❤❡❝✐❞❛ ♣♦♣✉❧❛r✲♠❡♥t❡ ❝♦♠♦ ❋❊▼▼ ✭▼❊❊❑❊❘✱ ✷✵✶✺✮ ❡ ❝♦♠ ♦ ♠ó❞✉❧♦ ♣❛r❛ ❛♥á❧✐s❡ ❞❡♣r♦❜❧❡♠❛s ❤❛r♠ô♥✐❝♦s ❞❛ s✉ít❡ ❞❡ ♣r♦❣r❛♠❛s ❞❛ ■♥❢♦❧②t✐❝❛ ❈♦r♣♦r❛t✐♦♥ ✹✻ ❯♠ tr❛❜❛❧❤♦ ❞❡ ♣❡sq✉✐s❛ ❡❧❡♠❡♥t❛r ✈♦❧t❛❞♦ ♣❛r❛ ❛ ❡s❝♦❧❤❛ ❡ ✐♠✲♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❡①♣❡r✐♠❡♥t❛❧ ♣❛r❛ ❛q✉✐s✐çã♦ ❡ ❛♥á❧✐s❡❞♦ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ❞♦ ♥ú❝❧❡♦ ❞❡ ❝♦♥t❛❝t♦r❡s ❡ tr❛♥s❢♦r♠❛❞♦r❡s ❞❡ ❜❛✐①❛♣♦tê♥❝✐❛ é ❞❡s❝r✐t♦ ♥❛s s❡çõ❡s q✉❡ s❡ s❡❣✉❡♠✳✶✳✷ P❘❖P❖❙❚❆ ❉❆ ❉■❙❙❊❘❚❆➬➹❖ ❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ s✐♠♣❧❡s ♣❛r❛ ❛✈❛❧✐❛r ❛s❝❛r❛❝t❡ríst✐❝❛s ♠❛❣♥ét✐❝❛s ❞♦s ♠❛t❡r✐❛✐s✱ ✉t✐❧✐③❛♥❞♦ ✉♠ ❝✐r❝✉✐t♦ RC ❡❡q✉✐♣❛♠❡♥t♦s ✉s✉❛✐s ❞❡ ✉♠ ❧❛❜♦r❛tór✐♦ ❞❡ ♠áq✉✐♥❛s ❡❧étr✐❝❛s✳ ❈♦♠ ❡s✲ s❡s ❡q✉✐♣❛♠❡♥t♦s é ♣♦ssí✈❡❧ ♦❜t❡r ❛s ❝✉r✈❛s ❞❡ ❤✐st❡r❡s❡ ❡ ❞❡ s❛t✉r❛çã♦♠❛❣♥ét✐❝❛ BH✳ ❆ ♣❛rt✐r ❞❡st❛s ❝✉r✈❛s ❡ ❝♦♠ ❛ t❡♦r✐❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛✱é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ♦s ♣❛râ♠❡tr♦s ❡❧étr✐❝♦s ❞❡ ✉♠ ❞✐s♣♦s✐t✐✈♦✱ ❝♦♠♦♣❡r❞❛s ❡ ❡✜❝✐ê♥❝✐❛ ❡♥❡r❣ét✐❝❛✱ ❢♦r♥❡❝❡♥❞♦ ✉♠❛ ✈✐sã♦ q✉❛❧✐t❛t✐✈❛ ❡ ❛✉①✐✲❧✐❛♥❞♦ ❛ ❝♦♠♣r❡❡♥sã♦ ❝♦♠♣r❡❡♥sã♦ ❞❡ ❢❡♥ô♠❡♥♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ♥♦♣r♦❥❡t♦ ❞❡ ♠áq✉✐♥❛s ❡❧étr✐❝❛s ❡ tr❛♥s❢♦r♠❛❞♦r❡s✳✶✳✸ ▼❖❚■❱❆➬➹❖ ❉❆ ❉■❙❙❊❘❚❆➬➹❖ ❆ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❛♣r❡s❡♥t❛r ✉♠❛ ✈✐sã♦ q✉❛❧✐t❛t✐✈❛ ❡ ♣rát✐❝❛ ❞❡❞✐s♣♦s✐t✐✈♦s ❛❜♦r❞❛❞♦s ♥♦s ❧❛❜♦r❛tór✐♦s ❞❛s ❞✐s❝✐♣❧✐♥❛s ❞❡ ❝♦♥✈❡rsã♦ ❡❧❡✲ tr♦♠❡❝â♥✐❝❛ ❞❡ ❡♥❡r❣✐❛ ✭❈❊❊✮ ❡ ❞❡ ♠❛t❡r✐❛✐s ❡❧étr✐❝♦s ✭▼❊▲✮✱ s❡r✈✐♥❞♦❞❡ ❛♣♦✐♦ ♥❛s ♣rát✐❝❛s ♣❡❞❛❣ó❣✐❝❛s ❞❡st❛s ❞✐s❝✐♣❧✐♥❛s✳✶✳✹ ❖❘●❆◆■❩❆➬➹❖ ❉❆ ❉■❙❙❊❘❚❆➬➹❖ ◆♦ ❈❛♣ít✉❧♦ ✷✱ sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ❢✉♥❞❛♠❡♥t♦s t❡ór✐❝♦s ❞♦ ♠é✲ t♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ q✉❡ ❢♦✐ ❛ ♣r✐♥❝✐♣❛❧ ❢❡rr❛♠❡♥t❛ ❞❡ s✐♠✉❧❛çã♦✉t✐❧✐③❛❞❛ ❡♠ t♦❞♦ ♦ tr❛❜❛❧❤♦✳ ◆♦ ❈❛♣ít✉❧♦ ✸✱ ❛♣r❡s❡♥t❛✲s❡ ✉♠ ❡st✉❞♦❞❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r ♠♦♥♦❢ás✐❝♦✱ ❞❡t❡r♠✐♥❛♥❞♦✲s❡❝❛r❛❝t❡ríst✐❝❛s ❞❡ s❡✉ ♠❛t❡r✐❛❧ ❡ s❡✉s ♣❛râ♠❡tr♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s✱ ❛♣❛rt✐r ❞❡ s✉❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳ ◆♦ ❈❛♣ít✉❧♦ ✹✱ é ❛♣r❡s❡♥t❛❞❛ ❛ ❝❛r❛❝✲ t❡r✐③❛çã♦ ❞❡ ✉♠ ❞✐s♣♦s✐t✐✈♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❝♦♠ ❡♥tr❡❢❡rr♦ ✈❛r✐á✈❡❧✱ ♦❝♦♥t❛❝t♦r✱ ❛♣❧✐❝❛♥❞♦✲s❡ ❛s ♠❡s♠❛s té❝♥✐❝❛s ❞❡s❡♥✈♦❧✈✐❞❛s ♥♦ ❈❛♣ít✉❧♦✸✳ P♦r ✜♠✱ ♥♦ ❈❛♣ít✉❧♦ ✺ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❝♦♥❝❧✉sõ❡s ❡ ❛s ❝♦♥s✐❞❡r❛✲çõ❡s ✜♥❛✐s ❞❡ss❡ tr❛❜❛❧❤♦ ❞✐ss❡rt❛t✐✈♦✱ ❛❧é♠ ❞❡ ♣r♦♣♦st❛s ♣❛r❛ ♣♦ssí✈❡✐s tr❛❜❛❧❤♦s ❢✉t✉r♦s✳ ✹✼✷ ❖ ▼➱❚❖❉❖ ❉❖❙ ❊▲❊▼❊◆❚❖❙ ❋■◆■❚❖❙ ❖ ♠ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s é ❜❛s❡❛❞♦ ♥❛ ✐❞❡✐❛ ❞❡ ❞✐✈✐❞✐r ♦❞♦♠í♥✐♦ ♦r✐❣✐♥❛❧ ❞♦ ♣r♦❜❧❡♠❛✱ ♦ ❝♦♥t✐♥✉✉♠✱ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞♦♠í✲♥✐♦s ♠❡♥♦r❡s ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❡❧❡♠❡♥t♦s✳ ❯♠❛ ❢♦r♠✉❧❛çã♦ ♥✉♠ér✐❝❛✱❜❛s❡❛❞❛ ♥❛ t❡♦r✐❛ ❞❛s ✐♥t❡r♣♦❧❛çõ❡s✱ é ❛♣❧✐❝❛❞❛ ❛ ❡ss❡s ❡❧❡♠❡♥t♦s ❞❡❢♦r♠❛ ❛ s❛t✐s❢❛③❡r ❛ ✉♠❛ ❝♦♥❞✐çã♦ ♠❛t❡♠át✐❝❛ ❡ ♣r♦❞✉③✐r ✉♠❛ s♦❧✉çã♦♥✉♠ér✐❝❛✳ ❚r❛t❛✲s❡ ❞❡ ✉♠❛ té❝♥✐❝❛ ♥✉♠ér✐❝❛ ♣❛r❛ ❛ s♦❧✉çã♦✱ ❡♠ ❣r❛♥❞❡❡s❝❛❧❛✱ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ❛❧t❛ ❝♦♠♣❧❡①✐❞❛❞❡ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❡str✉t✉r❛ ❞❡❞❛❞♦s q✉❡ é✱ ❛♦ ♠❡s♠♦ t❡♠♣♦✱ s✐♠♣❧❡s ❡ ✢❡①í✈❡❧ ✭◆❖●❯❊■❘❆❀ ❇❖❯✲❉❊❈✱ ✷✵✵✼✮✳ ❖s ❡❧❡♠❡♥t♦s ✜♥✐t♦s sã♦ ❞❡✜♥✐❞♦s ❝♦♠ ❜❛s❡ ❡♠ s✉❛ ❢♦r♠❛ ❣❡♦♠é✲ tr✐❝❛ ❡ ♥♦ ❣r❛✉ ❞❛ ❢✉♥çã♦ ❞❡ ❛♣r♦①✐♠❛çã♦✳ ❊ss❛ ❢✉♥çã♦ é✱ ♥❛ ♠❛✐♦r✐❛ ❞♦s❝❛s♦s✱ ♣♦❧✐♥♦♠✐❛❧ ❡ ❞❡✜♥❡ ❛ ❢♦r♠❛ ❝♦♠♦ ❛ ✈❛r✐á✈❡❧ ♣r✐♠ár✐❛ ❞❡ ❝á❧❝✉❧♦✱✉s✉❛❧♠❡♥t❡ ✉♠ ♣♦t❡♥❝✐❛❧✱ ❝♦♠♣♦rt❛✲s❡ ♥♦ ♠✐♥ús❝✉❧♦ ❡s♣❛ç♦ ❞❡❧✐♠✐t❛❞♦♣♦r ❝❛❞❛ ❡❧❡♠❡♥t♦ ✜♥✐t♦✳ ▼✉✐t❛s ❢♦r♠❛s ❣❡♦♠étr✐❝❛s ♣♦❞❡♠ s❡r ✉t✐✲❧✐③❛❞❛s ❡♠ ✉♠❛ ❛♥á❧✐s❡ ❜✐❞✐♠❡♥s✐♦♥❛❧❀ ♦ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r é ♦ ♠❛✐s✉s❛❞♦✳ ◆❛ ♠❛✐♦r✐❛ ❞❛s ❛♣❧✐❝❛çõ❡s✱ ❢✉♥çõ❡s ✐♥t❡r♣♦❧❛♥t❡s ❞❡ ♣r✐♠❡✐r♦❣r❛✉ sã♦ s✉✜❝✐❡♥t❡s ♣❛r❛ ❛t❡♥❞❡r ❛♦ ❝♦♠♣r♦♠✐ss♦ ❡♥tr❡ ❛ ♣r❡❝✐sã♦ ♥✉✲♠ér✐❝❛ r❡q✉❡r✐❞❛ ❡ ❛s ❞❡♠❛♥❞❛s ❡♠ t❡r♠♦s ❞❡ ❡s❢♦rç♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ✭❇❆❙❚❖❙✱ ✶✾✾✷✮✳ ◆❛ ❡r❛ ♠♦❞❡r♥❛✱ ♦ ♠ét♦❞♦ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❢♦✐ ❛♣❧✐❝❛❞♦ ✐♥✐✲❝✐❛❧♠❡♥t❡ ♣❛r❛ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❞❡ ❛♥á❧✐s❡ ❡str✉t✉r❛❧ ❡✱ ❥á ♥♦s ❛♥♦s✶✾✺✵✱ ♦ ♠ét♦❞♦ ❢♦✐ ❡♠♣r❡❣❛❞♦ ♥❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ tr❛♥s❢❡rê♥✲❝✐❛ ❞❡ ❝❛❧♦r ❡ ❡s❝♦❛♠❡♥t♦ ❞❡ ✢✉✐❞♦s✳ ❊♠ ✶✾✼✵✱ ✉♠ ❛rt✐❣♦ ❞❡ ❙✐❧✈❡s✲ t❡r ❡ ❈❤❛r✐ ✐♥t✐t✉❧❛❞♦ ✏s♦❧✉çã♦ ♣♦r ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❞❡ ♣r♦❜❧❡♠❛s ❞❡❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ❡♥✈♦❧✈❡♥❞♦ s❛t✉r❛çã♦✑ ✭♥♦ ✐♥❣❧ês✱ ✜♥✐t❡ ❡❧❡♠❡♥t s♦✲❧✉t✐♦♥ ♦❢ s❛t✉r❛❜❧❡ ♠❛❣♥❡t✐❝ ✜❡❧❞ ♣r♦❜❧❡♠s✮ ❛❜r✐✉ ✉♠❛ ♥♦✈❛ ❊r❛ ♣❛r❛♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦ ✭❙■▲❱❊❙❚❊❘❀ ❈❍❆❘■✱ ✶✾✼✵✮✳ ◆❛q✉❡❧❡ tr❛❜❛❧❤♦✱❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s ♦s ❞❡t❛❧❤❡s ❞❛ ✉t✐❧✐③❛çã♦ ❝♦♥❥✉♥t❛ ❞❛ té❝♥✐❝❛ ❞♦s❡❧❡♠❡♥t♦s ✜♥✐t♦s ❝♦♠ ♦ ♠ét♦❞♦ ✈❛r✐❛❝✐♦♥❛❧✳ ❆ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛❛♣r❡s❡♥t❛❞❛ ❢♦r♠♦✉ ❛ ❜❛s❡ ❞❡ ❝á❧❝✉❧♦ ❞♦s ♣r✐♠❡✐r♦s s✐st❡♠❛s ✐♥❢♦r♠á✲ t✐❝♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ♥✉♠ér✐❝♦ ❞❡ ❝❛♠♣♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s✳ ❙✐❧✈❡st❡r ❡❈❤❛r✐ ✭✶✾✼✵✮ ❢♦r♥❡❝❡r❛♠ ❝♦♥tr✐❜✉✐çõ❡s ❞❡ ❢♦r♠❛ ❞❡❝✐s✐✈❛ ♣❛r❛ ♦ ❞❡s❡♥✲✈♦❧✈✐♠❡♥t♦ ❞❡ss❛ té❝♥✐❝❛ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ♥❛ ❡♥❣❡♥❤❛r✐❛ ❡❧étr✐❝❛✳ ✹✽ ✷✳✶ P❖❚❊◆❈■❆■❙ ❊ ▼■◆■▼❆▲■❉❆❉❊ ❊◆❊❘●➱❚■❈❆❆ ❛♥á❧✐s❡ ❞❡ ❝❛♠♣♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s é✱ ❛❧❣✉♠❛s ✈❡③❡s✱ ❢❛❝✐❧✐✲ t❛❞❛ q✉❛♥❞♦✱ ❛♦ ✐♥✈és ❞❡ ❝❛♠♣♦s ✈❡t♦r✐❛✐s✱ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥✲ ❝✐❛✐s é ✉t✐❧✐③❛❞❛ ❝♦♠♦ ❣r❛♥❞❡③❛ ♣r✐♠ár✐❛ ❞❛ ❛♥á❧✐s❡✳ ❆s ❡q✉❛çõ❡s ❞❡P♦✐ss♦♥ ❡ ▲❛♣❧❛❝❡✱ ❡①♣r❡ss❛s ❡♠ t❡r♠♦s ❞❡ ♣♦t❡♥❝✐❛✐s✱ ♣♦❞❡♠ s❡r ❞❡r✐✲✈❛❞❛s ❞❛s ❡q✉❛çõ❡s ❞❡ ▼❛①✇❡❧❧ ❡ r❡s♦❧✈✐❞❛s s♦❜ ❞❡t❡r♠✐♥❛❞❛s ❝♦♥❞✐çõ❡s❞❡ ❝♦♥t♦r♥♦ t❛♠❜é♠ ❡s♣❡❝✐✜❝❛❞❛s ❡♠ t❡r♠♦s ❞❡ ♣♦t❡♥❝✐❛✐s ✭❍❆▼❉■❀◆❖●❯❊■❘❆❀ ❙■▲❱❊❙❚❊❘✱ ✶✾✾✸✮✳ ❆s ❡q✉❛çõ❡s ❞❡ P♦✐ss♦♥ ❡ ▲❛♣❧❛❝❡ sã♦ ❡①❡♠♣❧♦s ❞❡ ❡q✉❛çõ❡s ❞✐✲❢❡r❡♥❝✐❛✐s ♣❛r❝✐❛✐s q✉❡✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❞❡s❝r❡✈❡♠ ♣r♦❜❧❡♠❛s ❡❧❡tr♦s✲ tát✐❝♦s ❡ ♠❛❣♥❡t♦stát✐❝♦s✳ ❆ ❡q✉❛çã♦ ❞❡ P♦✐ss♦♥ ♣♦❞❡ s❡r ❡①♣r❡ss❛❝♦♠♦2 ρ v V =∇ ✭✷✳✶✮ ǫ♦♥❞❡ V é ♦ ♣♦t❡♥❝✐❛❧ ❡❧❡tr♦stát✐❝♦✱ ρ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❡❧étr✐❝❛ ❡ ǫé ❛ ♣❡r♠✐ss✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞♦ ♠❡✐♦ ♠❛t❡r✐❛❧✳ ❆ ❡q✉❛çã♦ ❞❡ ▲❛♣❧❛❝❡ ♣♦❞❡ s❡r ❡①♣r❡ss❛ ❝♦♠♦2 P = 0∇ ✭✷✳✷✮2 ♦♥❞❡ P é ♦ ♣♦t❡♥❝✐❛❧ ❡s❝❛❧❛r ♠❛❣♥ét✐❝♦❡ ∇ é ♦ ♦♣❡r❛❞♦r ❧❛♣❧❛❝✐❛♥♦✳❊♠ ♣r♦❜❧❡♠❛s ❡❧❡tr♦stát✐❝♦s ❡ ♠❛❣♥❡t♦stát✐❝♦s✱ ❛s ❡♥❡r❣✐❛s ❛r✲ ♠❛③❡♥❛❞❛s✱ ❡❧étr✐❝❛ W e ❡ ♠❛❣♥ét✐❝❛ W m ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♣♦❞❡♠ s❡r❡①♣r❡ss❛s ❡♠ t❡r♠♦s ❞❡ ♣♦t❡♥❝✐❛✐s✱ Z ǫ2 W e = dv(∇V ) ✭✷✳✸✮ 2 v❡ Z µ2 W = dv. m (∇P ) ✭✷✳✹✮ 2 v➱ ✐♠♣♦rt❛♥t❡ ♦❜s❡r✈❛r q✉❡ ❛♠❜❛s ❛s ❡♥❡r❣✐❛s sã♦ ❡①♣r❡ss❛s ❡♠ t❡r♠♦s ❞❡ ✈❛❧♦r❡s q✉❛❞rát✐❝♦s ❞♦ ❣r❛❞✐❡♥t❡ ❞❡ ❝❛♠♣♦✱ ✉♠❛ ❝❛r❛❝t❡rís✲t✐❝❛ q✉❡ ♣♦❞❡ s❡r ❡①♣❧♦r❛❞❛ ♣❛r❛ ♦❜t❡r s♦❧✉çõ❡s ♥✉♠ér✐❝❛s✳ ➱ ✐♠♣♦r✲ t❛♥t❡ r❡ss❛❧t❛r q✉❡ ❡①✐st❡♠ ♠✉✐t♦s s✐st❡♠❛s ❢ís✐❝♦s ♥♦s q✉❛✐s ♦ ♣r♦❝❡ss♦❞❡ ♠✐♥✐♠✐③❛çã♦ ❞❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❝♦♥❞✉③ à s♦❧✉çã♦ ♥✉✲♠ér✐❝❛ ❞♦ ♣r♦❜❧❡♠❛✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❛ s♦❧✉çã♦ ♥✉♠ér✐❝❛ ❝♦♥s✐st❡❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❛ss♦❝✐❛❞♦s ❛ ✉♠ ♠í♥✐♠♦ ❧♦❝❛❧ ❡ ♥ã♦ tr✐✈✐❛❧ ❞❛ ❢✉♥çã♦ ❝♦♠♣♦st❛ q✉❡ ❞❡✜♥❡ ❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛✳ ✹✾ ❖s ♣♦t❡♥❝✐❛✐s q✉❡ ❛♣❛r❡❝❡♠ ♥❛s ❡q✉❛çõ❡s ✭✷✳✸✮ ❡ ✭✷✳✹✮ sã♦ ❢✉♥çã♦❞❛ ♣♦s✐çã♦✳ ❊♠ ♣r♦❜❧❡♠❛s ❜✐❞✐♠❡♥s✐♦♥❛✐s ❞❡✜♥✐❞♦s ♥♦ ♣❧❛♥♦ x−y✱ ♣♦r❡①❡♠♣❧♦✱ ❡ss❡s ♣♦t❡♥❝✐❛✐s ♣♦❞❡♠ s❡r ❡①♣r❡ss♦s ❝♦♠♦✿ V = V (x, y),✭✷✳✺✮ P = P (x, y). ✭✷✳✻✮❆ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛ ❛ ❝❛❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛❧ é✱ ♣♦✐s✱ ✉♠❛ ❢✉♥çã♦ ❞♦s ♣♦t❡♥❝✐❛✐s ♦s q✉❛✐s✱ ♣♦r s✉❛ ✈❡③✱ sã♦ ❞❡♣❡♥❞❡♥t❡s ❞❛ ♣♦s✐✲çã♦✳ ❆ ❡♥❡r❣✐❛ é✱ ♣♦rt❛♥t♦✱ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠❛ ❢✉♥çã♦ ❝♦♠♣♦st❛❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❢✉♥❝✐♦♥❛❧ ❡♥❡r❣ét✐❝♦ ✭❙■▲❱❊❙❚❊❘❀ ❋❊❘❘❆❘■✱ ✶✾✾✵✮✳✷✳✷ ❖ ▼➱❚❖❉❖ ❱❆❘■❆❈■❖◆❆▲ ❆ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛ té❝♥✐❝❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s é ♥♦r♠❛❧♠❡♥t❡❢❡✐t❛ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ♠ét♦❞♦s ♠❛t❡♠át✐❝♦s ❝♦♠♦ ♦ ♠ét♦❞♦ ✈❛r✐❛❝✐♦♥❛❧❡ ♦ ♠ét♦❞♦ ❞♦s r❡sí❞✉♦s ♣♦♥❞❡r❛❞♦s✳ ◗✉❛♥❞♦ ♦ ♠ét♦❞♦ ✈❛r✐❛❝✐♦♥❛❧ é❛♣❧✐❝❛❞♦ ♣❛r❛ ♦❜t❡r ❛ s♦❧✉çã♦ ❞❡ ✉♠❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ♣❛r❝✐❛❧ q✉❡❞❡s❝r❡✈❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❝❛♠♣♦✱ ❛ s♦❧✉çã♦ ♣❛r❛ ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧é ♦❜t✐❞❛ ❞❡ ❢♦r♠❛ ✐♥❞✐r❡t❛✳ ◆♦ ❝❛s♦✱ ❞❡✜♥❡✲s❡ ✉♠ ❢✉♥❝✐♦♥❛❧ ❡♥❡r❣ét✐❝♦✱ q✉❡ é ❡①♣r❡ss♦ ❝♦♠♦ ✉♠❛ ✐♥t❡❣r❛❧ ❞❡ ✈♦❧✉♠❡ ❞❡ ✉♠❛ ❢✉♥çã♦ ❞❡✜♥✐❞❛❡♠ t❡r♠♦s ❞❛s ✈❛r✐á✈❡✐s ❞❡♣❡♥❞❡♥t❡s ❞♦ ♣r♦❜❧❡♠❛ ♦r✐❣✐♥❛❧✳ P❛r❛ ✉♠❛ ′ ′ ′❞❛❞❛ ❢✉♥çã♦ P ❝♦♠ ❞❡r✐✈❛❞❛s ♣❛r❝✐❛✐s P x ✱ P y ❡ P z ✱ ♦ ❢✉♥❝✐♦♥❛❧ F é❡①♣r❡ss♦ ❝♦♠♦ Z ′ ′ ′ F = f (P, P , P , P )dv v x y z ✭✷✳✼✮♦♥❞❡ ′ ′ ′ ∂P ∂P ∂P P = ; P = ; P = x y z ✭✷✳✽✮ ∂x ∂y ∂z❖ ♣r♦❝❡ss♦ ❞❡ s♦❧✉çã♦ ❝♦♥s✐st❡ ♥❛ ❜✉s❝❛ ❞❡ ✉♠❛ ❢✉♥çã♦ ♠✉❧t✐✲ ✈❛r✐á✈❡❧ P ♣❛r❛ ❛ q✉❛❧ ♦ ❢✉♥❝✐♦♥❛❧ ❡♥❡r❣ét✐❝♦ F é ❡st❛❝✐♦♥ár✐♦✳ P❛r❛♦❜t❡r ❛ s♦❧✉çã♦ ❛tr❛✈és ❞❡ss❛ ❛❜♦r❞❛❣❡♠✱ ♦ ❢✉♥❝✐♦♥❛❧ F é ❞❡✜♥✐❞♦ ❞❡♠❛♥❡✐r❛ q✉❡ ♦ ✐♥t❡❣r❛♥❞♦ f ❞❛ ❡q✉❛çã♦ ✭✷✳✼✮ s❛t✐s❢❛ç❛ à ❡q✉❛çã♦ ❞❡❊✉❧❡r✿ ∂f ∂ ∂f ∂ ∂f ∂ ∂f= 0 − − − ✭✷✳✾✮ ′ ′ ′∂P ∂x ∂x ∂y ∂y ∂z ∂z ✺✵ ♦♥❞❡ ♦ ♣r♦❜❧❡♠❛ ♦r✐❣✐♥❛❧ ❡stá s✉❥❡✐t♦ ❛ ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ♥❛ ❢r♦♥✲ t❡✐r❛ Ω q✉❡ ❞❡❧✐♠✐t❛ ❛ r❡❣✐ã♦ ♦✉ ❞♦♠í♥✐♦ ❞❡ ❛♥á❧✐s❡✳ ❊♠ ❣❡r❛❧✱ ❛ ❢r♦♥✲t❡✐r❛ Ω ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ❛ ✉♥✐ã♦ ❞❡ ❞✉❛s s✉♣❡r❢í❝✐❡s✿ Ω = Ω D ∪ Ω N ✭✷✳✶✵✮◆❛ s✉♣❡r❢í❝✐❡ Ω D ✱ ❡s♣❡❝✐✜❝❛✲s❡ ✉♠ ✈❛❧♦r ❝♦♥st❛♥t❡ ♣❛r❛ ❛ ❢✉♥çã♦ P❡✱ ♣♦rt❛♥t♦✱ ❛ ✈❛r✐❛çã♦ ∂P é ♥✉❧❛✳ ❊ss❡ t✐♣♦ ❞❡ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥t♦r♥♦ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❝♦♥❞✐çã♦ ❞❡ ❉✐r✐❝❤❧❡t✳ ◆❛ s✉♣❡r❢í❝✐❡ Ω N ✱ ❛s ❝♦♥❞✐çõ❡s❞❡ ❢r♦♥t❡✐r❛ sã♦ r❡❧❛❝✐♦♥❛❞❛s à ❞❡r✐✈❛❞❛ ❞❛ ❢✉♥çã♦ P ❡♠ r❡❧❛çã♦ ❛♦ ✈❡t♦r✉♥✐tár✐♦ n ♣❡r♣❡♥❞✐❝✉❧❛r ♦✉ ♥♦r♠❛❧ ❛♦s ♣♦♥t♦s ❞❛ s✉♣❡r❢í❝✐❡✳ ◗✉❛♥❞♦ s❡ N❡s♣❡❝✐✜❝❛ ❞❡r✐✈❛❞❛ ♥♦r♠❛❧ ♥✉❧❛ ❛♦ ❧♦♥❣♦ ❞❛ s✉♣❡r❢í❝✐❡ Ω ✱ ❛ ❝♦♥❞✐çã♦❞❡ ❝♦♥t♦r♥♦ é ❝❤❛♠❛❞❛ ❞❡ ❝♦♥❞✐çã♦ ❞❡ ◆❡✉♠❛♥♥ ❤♦♠♦❣ê♥❡❛✳ ❊ss❛❝♦♥❞✐çã♦ ❞❡ ❝♦♥t♦r♥♦ é t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥t♦r♥♦♥❛t✉r❛❧✳ ■ss♦ ♣♦rq✉❡ ❛s ❢✉♥çõ❡s P s❡♠ r❡str✐çõ❡s q✉❡ t♦r♥❛♠ ♦ ❢✉♥❝✐♦♥❛❧F (P ) ❡st❛❝✐♦♥ár✐♦ ♣ró①✐♠♦ ❞❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❛✉t♦♠❛t✐❝❛♠❡♥t❡ s❛t✐s❢❛③❡♠ à r❡str✐çã♦ ❞❡ ❞❡r✐✈❛❞❛ ♥♦r♠❛❧ ♥✉❧❛ ♥❛ s✉♣❡r❢í❝✐❡ Ω N ✳❆ ♦❜t❡♥çã♦ ❞❡ ✉♠ ❢✉♥❝✐♦♥❛❧ F q✉❡ é ❡st❛❝✐♦♥ár✐♦ ♥♦ ❡♥t♦r♥♦ ❞❛ s♦❧✉çã♦ ❡ q✉❡ s❛t✐s❢❛③ às ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❞♦ ♣r♦❜❧❡♠❛ r❡q✉❡r ❝♦♥✲s✐❞❡r❛çõ❡s s♦❜r❡ ❛ ♥❛t✉r❡③❛✱ ❡s❝❛❧❛r ♦✉ ✈❡t♦r✐❛❧✱ ❞❛ ✈❛r✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡✱❜❡♠ ❝♦♠♦ ❝♦♥s✐❞❡r❛çõ❡s r❡❧❛t✐✈❛s à ♥ã♦ ❧✐♥❡❛r✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛✳ ❋✉♥✲❝✐♦♥❛✐s ♣❛r❛ ♣♦t❡♥❝✐❛✐s ❡s❝❛❧❛r❡s ❡ ✈❡t♦r✐❛✐s ❡♠ ♣r♦❜❧❡♠❛s ❡❧❡tr♦stát✐❝♦s❡ ♠❛❣♥❡t♦stát✐❝♦s sã♦ ❞♦❝✉♠❡♥t❛❞♦s ❡♠ ✭❇❆❙❚❖❙✱ ✶✾✾✷✮✳ P❛r❛ ❝❛❞❛♣♦t❡♥❝✐❛❧ ❝♦♥s✐❞❡r❛❞♦✱ é ❛♣r❡s❡♥t❛❞❛ ❛ ❞❡❞✉çã♦✴❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛❡q✉❛çã♦ ❞❡ ❊✉❧❡r ❝♦rr❡s♣♦♥❞❡♥t❡✱ ❜❡♠ ❝♦♠♦ ✉♠❛ ❛♥á❧✐s❡ ❞❛s ❝♦♥❞✐çõ❡s❞❡ ❝♦♥t♦r♥♦✳ ❈❆❘❉❖❙❖ ✭✶✾✾✺✮ t❛♠❜é♠ r❡❣✐str❛ ❛❧❣✉♠❛s ❢♦r♠✉❧❛çõ❡s✈❛r✐❛❝✐♦♥❛✐s ❡ ❛♣r❡s❡♥t❛ ✉♠❛ sér✐❡ ❞❡ ❢✉♥❝✐♦♥❛✐s ❡st❛❝✐♦♥ár✐♦s ♦❜t✐❞♦s❡♠ t❡r♠♦s ❞❡ ❝❛♠♣♦s ✈❡t♦r✐❛✐s✳✷✳✸ ❊▲❊▼❊◆❚❖❙ ❚❘■❆◆●❯▲❆❘❊❙ ❉❊ P❘■▼❊■❘❆ ❖❘✲ ❉❊▼P❛r❛ ❛♣❧✐❝❛r ❛ té❝♥✐❝❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ é ♥❡❝❡ssár✐♦ s✉❜❞✐✈✐✲ ❞✐r ❛ r❡❣✐ã♦ ❞♦ ♣r♦❜❧❡♠❛ ❡♠ s✉❜✲r❡❣✐õ❡s ❝❤❛♠❛❞❛s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳❊ss❛ s✉❜❞✐✈✐sã♦ ✭❞✐s❝r❡t✐③❛çã♦✮ é ❢❡✐t❛ ❞❡ ♠♦❞♦ q✉❡ ✉♠ ♠❡s♠♦ ❡❧❡♠❡♥t♦♥ã♦ ♣♦❞❡ ❝♦♥t❡r ♠❛✐s q✉❡ ✉♠ ♠❡✐♦ ♠❛t❡r✐❛❧✳ ❖ ❝♦♥❥✉♥t♦ ❞❡ ❡❧❡♠❡♥t♦sé ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ❡✱ ❡♠ ♣r✐♥❝í♣✐♦✱ ♥ã♦ ❡①✐s✲ t❡♠ r❡str✐çõ❡s ♣❛r❛ ♦ t❛♠❛♥❤♦ ❡ ♦r✐❡♥t❛çã♦ ❞♦s ❡❧❡♠❡♥t♦s✳ ❖ ❡❧❡♠❡♥t♦tr✐❛♥❣✉❧❛r ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❢♦✐ ❡s❝♦❧❤✐❞♦ ♣❛r❛ ❡st❛ ❞✐s❝✉ssã♦ ✐♥tr♦❞✉✲ tór✐❛✳ ❊ss❡ t✐♣♦ ❞❡ ❡❧❡♠❡♥t♦ é ♦ ♠❛✐s ✉s❛❞♦ ♥❛ ❝✐ê♥❝✐❛ ❡ ❡♥❣❡♥❤❛r✐❛✱ ❡ é ✺✶ ❝♦♠✉♠❡♥t❡ ❡♠♣r❡❣❛❞♦ ♥❛ ❛♣r❡s❡♥t❛çã♦ ❞♦s ♣r✐♥❝í♣✐♦s ❡♥✈♦❧✈✐❞♦s ♣❡❧❛ té❝♥✐❝❛ ❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳◗✉❛♥❞♦ ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ sã♦ ✉s❛❞♦s✱ t♦❞♦s ♦s ♣♦♥t♦s ♥♦❞❛✐s ✕ ♦✉ s✐♠♣❧❡s♠❡♥t❡ ✧♥ós✧ ❞❛ ♠❛❧❤❛ ✕ ❞❡✈❡♠ ❝♦✐♥❝✐❞✐r ❝♦♠ ♦s ✈ért✐❝❡s ❞♦s tr✐â♥❣✉❧♦s✳ ❊ss❛ r❡str✐çã♦ é ✐❧✉str❛❞❛ ❝♦♠❛✉①í❧✐♦ ❞❛ ❋✐❣✉r❛ ✷✳✶✳ ❖❜s❡r✈❛✲s❡ ♥❛ ❋✐❣✉r❛ ✷✳✶✭❛✮ ✉♠❛ ♠❛❧❤❛ ✐♥❝♦rr❡t❛❡♠ q✉❡ ✉♠ ❞♦s ♣♦♥t♦s ♥♦❞❛✐s ♥ã♦ ❝♦✐♥❝✐❞❡ ❝♦♠ ✉♠ ✈ért✐❝❡ ❞❡ tr✐â♥❣✉❧♦✳❋✐❣✉r❛ ✷✳✶ ✕ ▼❛❧❤❛s ❢♦r♠❛❞❛s ♣♦r ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ♣r✐♠❡✐r❛♦r❞❡♠❀ ✭❛✮ ♠❛❧❤❛ ✐♥❝♦rr❡t❛❀ ✭❜✮ ♠❛❧❤❛ ❝♦rr❡t❛✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳ ❖ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ t❛♠❜é♠ é ❝♦♥❤❡❝✐❞♦❝♦♠♦ tr✐â♥❣✉❧♦ ❝♦♠ três ♥ós✳ ❖✉tr♦s ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s t❛♠❜é♠♣♦❞❡♠ s❡r ✉s❛❞♦s✳ ➱ ♦ ❝❛s♦ ❞♦ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✱✉♠ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r q✉❡ ♣♦ss✉✐ s❡✐s ♥ós ♦✉ ♣♦♥t♦s ♥♦❞❛✐s✳ ◆♦ ❝❛s♦✱ três ♥ós ❝♦✐♥❝✐❞❡♠ ❝♦♠ ♦s ✈ért✐❝❡s ❡ ♦s ♦✉tr♦s três ♥ós ❡stã♦ ❧♦❝❛❧✐③❛❞♦s♥❛ ♠❡t❛❞❡ ❞❛s ❛r❡st❛s✳ ◆♦ ❝❛s♦✱ ❛ ❝♦♥str✉çã♦ ❞❛ ♠❛❧❤❛ ♣r♦♣r✐❛♠❡♥t❡❞✐t❛ é ❢❡✐t❛ ❡♠♣r❡❣❛♥❞♦✲s❡ tr✐â♥❣✉❧♦s ❝♦♠ três ♥ós✳ ❖s três ♥ós ❞❡❛r❡st❛s sã♦✱ ♥❛ ✈❡r❞❛❞❡✱ ♣❛rt❡ ❞❛ ❞❡✜♥✐çã♦ ❞❛ ❢✉♥çã♦ ✐♥t❡r♣♦❧❛♥t❡ q✉❛✲❞rát✐❝❛ ❡♠♣r❡❣❛❞❛ ♥❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✳ ❊❧❡♠❡♥t♦s ✜♥✐t♦s ❞❡ ♦r❞❡♠ s✉♣❡r✐♦r sã♦ ✉s❛❞♦s ♣❛r❛ s❡ ♦❜t❡r s♦❧✉çõ❡s ♠❛✐s ♣r❡❝✐s❛s✳ ❊♥tr❡t❛♥t♦✱❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ❞❡s❞❡ q✉❡ ❛❞❡q✉❛❞❛♠❡♥t❡✉s❛❞♦s✱ ❝♦♥❞✉③❡♠ ❛ ❡①❝❡❧❡♥t❡s r❡s✉❧t❛❞♦s ❡ ❛♣r❡s❡♥t❛♠ ✈❛♥t❛❣❡♥s ❡♠ ✺✷ ✷✳✹ ❋❯◆➬Õ❊❙ ■◆❚❊❘P❖▲❆◆❚❊❙ ❉❊ P❘■▼❊■❘❖ ●❘❆❯❆ ♠❛✐♦r✐❛ ❞❛s ❢♦r♠✉❧❛çõ❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s sã♦ ❜❛s❡❛❞❛s ❡♠ ♣♦t❡♥❝✐❛✐s✳ P❛r❛ ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ♦ ♣♦t❡♥❝✐❛❧φ p ✈❛r✐❛ ❧✐♥❡❛r♠❡♥t❡ ❞❡♥tr♦ ❞♦ ❡❧❡♠❡♥t♦✱ ♦✉ s❡❥❛✱ φ (x, y) = a + a x + a y. p12 3 ✭✷✳✶✶✮ ❈♦♥s✐❞❡r❡✲s❡ ✉♠ tr✐â♥❣✉❧♦ ♥♦ ♣❧❛♥♦ x − y ♥♦ q✉❛❧ ♦s ✈ért✐❝❡s sã♦♥✉♠❡r❛❞♦s ❝♦♠♦ ✶✱ ✷ ❡ ✸✳ ❙❡ ♦ ♣♦t❡♥❝✐❛❧ ♥❡ss❡s ✈ért✐❝❡s ❛ss✉♠❡ ✈❛❧♦r❡sφ 1 ✱ φ 2 ❡ φ 3 ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ ❡q✉❛çã♦ ✭✷✳✶✶✮ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞❛ ❡♠❝❛❞❛ ✉♠ ❞♦s três ✈ért✐❝❡s✱ r❡s✉❧t❛♥❞♦ ❡♠✿ φ (x, y) = a + a x + a y , p,112131φ (x, y) = a + a x + a y , p,21223 2 ✭✷✳✶✷✮ φ p,3 (x, y) = a 1 + a 2 x 3 + a 3 y 3 .❆ s♦❧✉çã♦ ❞❡ss❡ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s s✐♠✉❧tâ♥❡❛s ❢♦r♥❡❝❡ ♦s ✈❛✲123 ❧♦r❡s ❞♦s ❝♦❡✜❝✐❡♥t❡s a ✱ a ❡ a ❡♠ t❡r♠♦s ❞❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s ✈ért✐❝❡s❡ ❞♦s ✈❛❧♦r❡s ❞♦s ♣♦t❡♥❝✐❛✐s✳ P❛r❛ s❡ ♦❜t❡r ✉♠❛ ❡①♣r❡ssã♦ q✉❡ ❢♦r♥❡❝❡ ♦ ✈❛❧♦r ❞♦ ♣♦t❡♥❝✐❛❧φ p ❡♠ ✉♠❛ ❧♦❝❛❧✐③❛çã♦ ❣❡♥ér✐❝❛ ✭x✱y✮ ❞♦ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r✱ ❞❡✈❡✲s❡ s✉❜st✐t✉✐r ♦s ❝♦❡✜❝✐❡♥t❡s a1 ✱ a 2 ❡ a 3 ♥❛ ❡q✉❛çã♦ ✷✳✶✶✳ ❆♣ós ❛❧❣✉♠❛s ♠❛♥✐♣✉❧❛çõ❡s ❛❧❣é❜r✐❝❛s✱ ♦❜té♠✲s❡ ❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿X3 1 φ (x, y) = (p + q x + r y)φ . p i i i i ✭✷✳✶✸✮D i=1 ◆❛ ❡q✉❛çã♦ ✷✳✶✸✱ D é ✐❣✉❛❧ ❛♦ ❞♦❜r♦ ❞❛ ár❡❛ ❞♦ ❡❧❡♠❡♥t♦ tr✐❛♥✲ i i i❣✉❧❛r✱ ❡ ♦s ❝♦❡✜❝✐❡♥t❡s ❣❡♦♠étr✐❝♦s p ✱ q ❡ r sã♦ ❡①♣r❡ss♦s ❡♠ t❡r♠♦s❞❛s ❝♦♦r❞❡♥❛❞❛s ❞♦s três ✈ért✐❝❡s✱ ❝♦♠♦ s❡❣✉❡✿ p1 = x 2 y3 2 x 3 , q 1 = y2 1 = x3 2 , − y − y3, r − x ✭✷✳✶✹✮ p2 = x 3 y1 3 x 1 , q 2 = y3 2 = x1 3 ,− y − y1, r − x ✭✷✳✶✺✮ p3 = x 1 y2 1 x 2 , q 3 = y1 3 = x2 1 , − y − y2, r − x ✭✷✳✶✻✮ i + q i x + r i y ❱❛❧❡ ♦❜s❡r✈❛r ♥❛ ❡q✉❛çã♦ ✭✷✳✶✸✮ q✉❡ ❛ ❡①♣r❡ssã♦ ❡♥tr❡ ♣❛rê♥t❡s❡s✭p ✮ r❡♣r❡s❡♥t❛ ✉♠❛ ❢✉♥çã♦ ♣❧❛♥❛r✳ ➱ ♣♦ssí✈❡❧✱ ♣♦✐s✱ ❡①♣r❡s✲ ✺✸ s❛r ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ✉♠❛ ❢♦r♠❛ ♠❛✐s ❝♦♠♣❛❝t❛ ❡ ❞❡ ❢á❝✐❧ ✐♥t❡r♣r❡t❛çã♦✳Pr✐♠❡✐r❛♠❡♥t❡✱ sã♦ ❞❡✜♥✐❞❛s ❛s ❢✉♥çõ❡s ❞❡ ❢♦r♠❛✱ α✱ ❝♦♠♦ ❛ s❡❣✉✐r✿ 1 α (x, y) = (p + q x + r y). i i i i ✭✷✳✶✼✮D ❆ ❡①♣r❡ssã♦ ♣❛r❛ ♦ ♣♦t❡♥❝✐❛❧ ♣♦❞❡ ❛❣♦r❛ s❡r ❡s❝r✐t❛ ❝♦♠♦X3 φ(x, y) = α i φ i . i=1 ✭✷✳✶✽✮❊ss❛ ❢♦r♠❛ ❝♦♠♣❛❝t❛ ❞❛ ❡①♣r❡ssã♦ ❢❛❝✐❧✐t❛ ❛ ✐❧✉str❛çã♦ ❞♦ ♣r♦✲ ❝❡ss♦ ❞❡ ❝á❧❝✉❧♦ ❞❡ ✈❛❧♦r❡s ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s✳ ❈❛❞❛ ❢✉♥çã♦❞❡ ❢♦r♠❛ α é ♥✉❧❛ ❡♠ ❞♦✐s ✈ért✐❝❡s ❡ ♣♦ss✉✐ ✈❛❧♦r ✉♥✐tár✐♦ ♥♦ ✈ért✐❝❡ r❡st❛♥t❡✱ ❝♦♠♦ ✐❧✉str❛❞♦ ♥❛s ❋✐❣✉r❛s ✷✳✷ ❡ ✷✳✸✳ ❆ ❡q✉❛çã♦ ✭✷✳✶✽✮ ❢♦r♥❡❝❡ ♦ ♣♦t❡♥❝✐❛❧ ❞❡♥tr♦ ❞❡ ✉♠ ❞❛❞♦ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r ❡ é ✈á❧✐❞❛ ♣❛r❛ t♦❞♦s ♦s ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡ ✉♠❛ ❞❛❞❛♠❛❧❤❛✳ ❱❛❧❡ r❡ss❛❧t❛r q✉❡ ♦ ♣♦t❡♥❝✐❛❧ ❛♦ ❧♦♥❣♦ ❞❡ ✉♠❛ ❞❛❞❛ ❛r❡st❛ é♦❜t✐❞♦ ❛tr❛✈és ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ✐♥t❡r♣♦❧❛çã♦ ❧✐♥❡❛r ❡♥tr❡ ♦s ♣♦t❡♥❝✐✲❛✐s ❞♦s ❞♦✐s ✈ért✐❝❡s q✉❡ ❞❡❧✐♠✐t❛♠ ❛ ❛r❡st❛✳ ◗✉❛♥❞♦ ❞♦✐s tr✐â♥❣✉❧♦s❝♦♠♣❛rt✐❧❤❛♠ ❞♦✐s ✈ért✐❝❡s ✭❡ ❛ ❛r❡st❛ ❝♦rr❡s♣♦♥❞❡♥t❡✮✱ ♦ ♣♦t❡♥❝✐❛❧ s❡rá❝♦♥tí♥✉♦ ❛♦ ❧♦♥❣♦ ❞❛ ❛r❡st❛ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❢r♦♥t❡✐r❛ ❡♥tr❡ ❡ss❡s ❡❧❡✲♠❡♥t♦s✳ (x, y)❋✐❣✉r❛ ✷✳✷ ✕ ❋✉♥çõ❡s ♣❧❛♥❛r❡s α i ✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r P❛r❛ ✉♠ ❞❛❞♦ ♣r♦❜❧❡♠❛ ❞❡✜♥✐❞♦ ❡ ❞✐s❝r❡t✐③❛❞♦ ♥♦ ♣❧❛♥♦ x − y✱❝♦♠ ❛ ✈❛r✐❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ♥♦s ❡❧❡♠❡♥t♦s tr✐❛♥❣✉❧❛r❡s ❞❡s❝r✐t❛ ♣❡❧❛❡q✉❛çã♦ ✭✷✳✶✽✮✱ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❣❧♦❜❛❧ ❞♦ ♣r♦❜❧❡♠❛ ♣♦❞❡ s❡r ❡st❛❜❡✲❧❡❝✐❞♦ ♣❡❧❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠ ♠ét♦❞♦ ✈❛r✐❛❝✐♦♥❛❧✳ ◆❡ss❛ ❛❜♦r❞❛❣❡♠✱ ♦ ✺✹ ❋✐❣✉r❛ ✷✳✸ ✕ ❋✉♥çõ❡s ♣❧❛♥❛r❡s 12(x, y) (x, y) ✭❛✮ ❋✉♥çã♦ α ✭❜✮ ❋✉♥çã♦ α 3✭❝✮ ❋✉♥çã♦ α (x, y) ❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❢✉♥❝✐♦♥❛✐s ❡♥❡r❣ét✐❝♦s ❞♦s ❡❧❡♠❡♥t♦s ✐♥❞✐✈✐❞✉❛✐s✱ F i ✱ ❝♦♠♦ ❛♣r❡s❡♥t❛❞♦❛ s❡❣✉✐r✿X n e F = F i=1 i ✭✷✳✶✾✮♦♥❞❡ n e é ♦ ♥ú♠❡r♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❛ ♠❛❧❤❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ P❛r❛ s❡ ♦❜t❡r ✉♠❛ s♦❧✉çã♦ ❛♣r♦①✐♠❛❞❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ ♦ ❢✉♥✲ ✺✺ ❉✐❢❡r❡♥❝✐❛♥❞♦ ♦ ❢✉♥❝✐♦♥❛❧ F ✱ ❡①♣r❡ss♦ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✶✾✮✱ ❡♠ r❡❧❛çã♦ ❛ ✉♠ ♣♦t❡♥❝✐❛❧ ❣❡♥ér✐❝♦ φ k ❡ ✐❣✉❛❧❛♥❞♦ ❛ ③❡r♦✱ t❡♠✲s❡✿X n e∂F ∂F i = = 0✭✷✳✷✵✮ ∂φ ∂φ p,k p,k i=1♦♥❞❡ k s❡❣✉❡ ❛ ♥✉♠❡r❛çã♦ ❣❧♦❜❛❧ ❞♦s ♥ós ❝♦♠ ♣♦t❡♥❝✐❛✐s s❡♠ r❡str✐çã♦✳ ❱❛❧❡ ♦❜s❡r✈❛r ♥❛ ❡q✉❛çã♦ ✭✷✳✷✵✮ q✉❡ ♦ s♦♠❛tór✐♦ ❡♥❣❧♦❜❛ t♦❞♦s♦s ❡❧❡♠❡♥t♦s ❞❛ ♠❛❧❤❛✳ ❖ ✈❛❧♦r ❞❡ ❝❛❞❛ ❢✉♥❝✐♦♥❛❧ ✐♥❞✐✈✐❞✉❛❧✱ F i ✱ é ♥ã♦♥✉❧♦ ♥♦ ❡❧❡♠❡♥t♦ i ❡ é ✐❣✉❛❧ ❛ ③❡r♦ ❡♠ t♦❞♦s ♦s ♦✉tr♦s ❡❧❡♠❡♥t♦s✳ ◆♦ s♦♠❛tór✐♦ ❡①♣r❡ss♦ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✷✵✮✱ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ✉♠ ❞❡t❡r♠✐✲♥❛❞♦ ♥ó s❡♠ r❡str✐çã♦ s❡ ❧✐♠✐t❛ ❛♦s ❢✉♥❝✐♦♥❛✐s ✐♥❞✐✈✐❞✉❛✐s ❞♦s ❡❧❡♠❡♥t♦s q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ❛q✉❡❧❡ ♥ó✳ ◆♦ ❝❛s♦ s✐♠♣❧❡s ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✹✱❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ♦ s♦♠❛tór✐♦ ❞❛ ❡q✉❛çã♦ ✭✷✳✷✵✮ ❞❡✈✐❞♦ ❛♦ ♥ó ✏❛✑ q✉❡❛♣❛r❡❝❡ ♥♦ ❝❡♥tr♦ ❞❛ ♠❛❧❤❛ é ∂F ∂F 1 ∂F 2 ∂F 3 ∂F4 ✭✷✳✷✶✮ ❋✐❣✉r❛ ✷✳✹ ✕ ❖s ❡❧❡♠❡♥t♦s ✶✱ ✷✱ ✸ ❡ ✹ ❝♦♠♣❛rt✐❧❤❛♠ ♦ ♥ó ✏❛✑✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳ ❆ ♠✐♥✐♠✐③❛çã♦ ❞♦ ❢✉♥❝✐♦♥❛❧ F ❝♦♥❞✉③ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡q✉❛çõ❡s s✐♠✉❧tâ♥❡❛s q✉❡ ♣♦❞❡ s❡r ❡①♣r❡ss♦ ❡♠ ❢♦r♠❛ ♠❛tr✐❝✐❛❧✳ ❖s ❢✉♥❝✐♦♥❛✐ssã♦ ❞✐❢❡r❡♥t❡s ♣❛r❛ ❝❛❞❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛✳ P❛r❛ ♣r♦❜❧❡♠❛s ♠❛❣♥❡✲ ✺✻ ♥ã♦ ❧✐♥❡❛r✐❞❛❞❡ ♠❛❣♥ét✐❝❛✱ ❜❡♠ ❝♦♠♦ ❛ ♣r❡s❡♥ç❛ ❞❡ ❝♦rr❡♥t❡s ❡❧étr✐❝❛s❡ í♠ãs ♣❡r♠❛♥❡♥t❡s✳ ❆ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ✉♠ ❞❛❞♦ ❡❧❡♠❡♥t♦ j ♣❛r❛ ♦ s♦♠❛tór✐♦ ♣r❡s❡♥t❡ ♥❛ ❡q✉❛çã♦ ✭✷✳✷✵✮ é✿    ∂φ S S S φ Q ∂F ∂F j1 j            1112 13 p,11 = S S S φ Q2122 23 p,2 ✭✷✳✷✷✮2 ∂φ3 S S S φ Q3132 33 p,33♦♥❞❡ ♦s ♥ós sã♦ ♥✉♠❡r❛❞♦s ❧♦❝❛❧♠❡♥t❡ ❝♦♠♦ ✶✱ ✷ ❡ ✸✳ ◆❛ ❞❡✜♥✐çã♦ ❞❛ ❡q✉❛çã♦ ♠❛tr✐❝✐❛❧ ❡①♣r❡ss❛ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✷✷✮✱♦s ✈ért✐❝❡s ❞♦ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r j sã♦ ✐❞❡♥t✐✜❝❛❞♦s ♣❡❧♦s ♥ú♠❡r♦s ✶✱✷ ❡ ✸✳ ❆ ♠❛tr✐③ q✉❛❞r❛❞❛ SX (3×3) é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♠❛tr✐③ ❞❡ r✐❣✐❞❡③✱✉♠❛ t❡r♠✐♥♦❧♦❣✐❛ ❤❡r❞❛❞❛ ❞❛ ❛♥á❧✐s❡ ❡str✉t✉r❛❧✳ ❖ t❡r♠♦ ❣❡♥ér✐❝♦ S mné ❡①♣r❡ss♦ ❡♠ t❡r♠♦s ❞❛ ár❡❛ ❞♦ ❡❧❡♠❡♥t♦✱ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❣❡♦♠étr✐❝♦s❞♦ ❡❧❡♠❡♥t♦ ❡ ❞♦ ♣❛râ♠❡tr♦ κ x q✉❡ ❝❛r❛❝t❡r✐③❛ ♦ ♠❡✐♦ ♠❛t❡r✐❛❧✱ κ x SX = (q q + r r ) m = 1, 2, 3 n = 1, 2, 3. mn m n m n ✭✷✳✷✸✮2D ❖ ♣❛râ♠❡tr♦ κ r❡♣r❡s❡♥t❛✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ♣❡r♠✐ss✐✈✐❞❛❞❡ ❡❧é✲ tr✐❝❛ ❡♠ ♣r♦❜❧❡♠❛s ❡❧❡tr♦stát✐❝♦s✱ ❡ ❛ r❡❧✉t✐✈✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ✭✐♥✈❡rs♦❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛✮ ❡♠ ♣r♦❜❧❡♠❛s ♠❛❣♥❡t♦stát✐❝♦s✳ ❖ ✈❡t♦rQ (3×1) ❝♦♥té♠ ✐♥❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s às ❢♦♥t❡s ❡♥❡r❣ét✐❝❛s ❞♦ s✐st❡♠❛❢ís✐❝♦✳ ❊♠ ♣r♦❜❧❡♠❛s ❡❧❡tr♦stát✐❝♦s✱ ❛ m✲és✐♠❛ ♣♦s✐çã♦ ❞♦ ✈❡t♦r Q (3×1)❝♦♥té♠ ♦ ✈❛❧♦r ❞♦ ♣♦t❡♥❝✐❛❧ ❡❧étr✐❝♦ ❡s♣❡❝✐✜❝❛❞♦ ♣❛r❛ ♦ m✲és✐♠♦ ♥ó✳❊♠ ♣r♦❜❧❡♠❛s ❡❧❡tr♦stát✐❝♦s✱ ♠❛❣♥❡t♦stát✐❝♦s ❡ ♠❛❣♥❡t♦❞✐♥â♠✐❝♦s ❛s❢♦♥t❡s ❞❡ ❡♥❡r❣✐❛ ❞❡✈❡♠ r❡♣r❡s❡♥t❛r ♦s ❡❢❡✐t♦s ❞❡ ❝❛r❣❛s ❡❧étr✐❝❛s✱ ❝♦r✲ r❡♥t❡s ♥♦❞❛✐s ❡ í♠ãs ♣❡r♠❛♥❡♥t❡s✳ ❖ s✐st❡♠❛ ❣❧♦❜❛❧ q✉❡ r❡♣r❡s❡♥t❛ ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❡ t♦❞♦s ♦s ♥♥ós ❞❛ r❡❣✐ã♦ ❞✐s❝r❡t✐③❛❞❛ é ❡①♣r❡ss♦ ♣❡❧❛ s❡❣✉✐♥t❡ ❡q✉❛çã♦ ♠❛tr✐❝✐❛❧✿ SS φ = Q . (m×n) (n) (n) ✭✷✳✷✹✮ ❆ ♠❛tr✐③ SS (m×n) é ❛ ♠❛tr✐③ ❣❧♦❜❛❧ ❞♦s ❝♦❡✜❝✐❡♥t❡s✳ ❆ ♠❛tr✐③SS (m×n) ❡ ♦ ✈❡t♦r Q (3×1) sã♦ ❢♦r♠❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦s s❡❣✉✐♥t❡s♣r♦❝❡❞✐♠❡♥t♦s✿ ✶✳ ♣❛r❛ ❝❛❞❛ ❡❧❡♠❡♥t♦ i✱ ❛ s✉❛ ❝♦♥tr✐❜✉✐çã♦✱ ❡①♣r❡ss❛ ♣❡❧❛ ❡q✉❛çã♦✭✷✳✷✷✮✱ ❞❡✈❡ s❡r ✐♥s❡r✐❞❛ ♥❛ ♠❛tr✐③ SS ❡ ♥♦ ✈❡t♦r Q ♦❜❡❞❡❝❡♥❞♦à ♥✉♠❡r❛çã♦ ❣❧♦❜❛❧ ❞♦s ♥ós❀ ✷✳ ❛s r❡str✐çõ❡s ❞❡ ❉✐r✐❝❤❧❡t t❛♠❜é♠ ❞❡✈❡♠ s❡r ✐♥s❡r✐❞❛s ♥❛ ❡q✉❛çã♦♠❛tr✐❝✐❛❧✳ ❙❡ ♦ ♣♦t❡♥❝✐❛❧ ❞♦ ♥ó m t❡♠ ✉♠ ✈❛✶♦r ❡s♣❡❝✐✜❝❛❞♦✱φ ✺✼ ❞✐❛❣♦♥❛❧✱ mm✱ ❡ ③❡r♦s ❡♠ t♦❞❛s ❛s ♣♦s✐çõ❡s r❡st❛♥t❡s✳ ❚❛♠❜é♠✱❛ m✲és✐♠❛ ♣♦s✐çã♦ ❞♦ ✈❡t♦r Q ❛ss✉♠❡ ♦ ✈❛❧♦r φ m ✱ ❡s♣❡❝✐✜❝❛❞♦♣❛r❛ ♦ ♣♦t❡♥❝✐❛❧ ❞❛q✉❡❧❡ ♥ó✳ ❆s ♠❛tr✐③❡s ❞❡ r✐❣✐❞❡③ SX (3×3) r❡♣r❡s❡♥t❛♠ ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞♦s❡❧❡♠❡♥t♦s ✐♥❞✐✈✐❞✉❛✐s ❡ sã♦ s✐♠étr✐❝❛s ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✳ ❖ t❡r♠♦❣❡♥ér✐❝♦✱ ❡①♣r❡ss♦ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✷✸✮✱ ♠♦str❛ q✉❡ ❛ s✐♠❡tr✐❛ é ❣❛r❛♥✲ t✐❞❛ s❡ ♦ ♣r♦❜❧❡♠❛ é ❡st❛❝✐♦♥ár✐♦✳ ❊♠ ❝❡rt❛s ❝❧❛ss❡s ❞❡ ♣r♦❜❧❡♠❛s✱✐♥❝❧✉✐♥❞♦ ❛q✉❡❧❡s q✉❡ r❡♣r❡s❡♥t❛♠ ❝♦r♣♦s ❡♠ ♠♦✈✐♠❡♥t♦✱ ❛s ♠❛tr✐③❡s❞❡ r✐❣✐❞❡③ ♥ã♦ sã♦ s✐♠étr✐❝❛s✳ ❊♠ ♠✉✐t♦s ♣r♦❜❧❡♠❛s✱ ❛ ♠❛tr✐③ ❣❧♦❜❛❧❞❡ ❝♦❡✜❝✐❡♥t❡s SS (m×n) t❡♠ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ s❡r s✐♠étr✐❝❛✱ ❡s♣❛rs❛❡ ❞❡ ❢❛✐①❛✳ ❊ss❛s ♣r♦♣r✐❡❞❛❞❡s sã♦ ❡①tr❡♠❛♠❡♥t❡ ✐♠♣♦rt❛♥t❡s✱ ♣♦✐s♣❡r♠✐t❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ té❝♥✐❝❛s ❛✈❛♥ç❛❞❛s ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦ ❡ ♠❛✲♥✐♣✉❧❛çã♦ ❞❡ ♠❛tr✐③❡s✳ ❈♦♠ r❡s♣❡✐t♦ ❛♦ ♣❛râ♠❡tr♦ κ q✉❡ ❛♣❛r❡❝❡ ♥❛ ❡q✉❛çã♦ ✭✷✳✷✸✮✱ ✈❛❧❡ r❡ss❛❧t❛r q✉❡✱ ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✱ ❛ ♣❡r♠✐ss✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ǫ ❡ ❛ ❝♦♥✲❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ σ sã♦ ❝♦♥st❛♥t❡s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡♠❛❣♥ét✐❝❛ µ ✭♦✉ r❡❧✉t✐✈✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ν✮ ❞❡ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥é✲ t✐❝♦s é r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ q✉❡ é✱ q✉❛s❡s❡♠♣r❡✱ ♥ã♦✲❧✐♥❡❛r✳ ◆❛s r❡❣✐õ❡s ♦❝✉♣❛❞❛s ♣♦r ♠❡✐♦s ♠❛❣♥ét✐❝♦s ♦ ✈❛❧♦r❞❡ ν ✭♦r µ✮ ❡♠ ❝❛❞❛ ❡❧❡♠❡♥t♦ tr✐❛♥❣✉❧❛r é ❢✉♥çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H✱ ν = ν(H). ✭✷✳✷✺✮◆♦ ❝❛s♦✱ ❛ r❡❧❛çã♦ ❡♥tr❡ ♦s ❝❛♠♣♦s B ❡ H é r❡♣r❡s❡♥t❛❞❛ ♠❛t❡✲ ♠❛t✐❝❛♠❡♥t❡ ♣♦rB = kµ(H)kH, ✭✷✳✷✻✮ ❡♠ q✉❡ ❛ ♥♦t❛çã♦ k.k ✐♥❞✐❝❛✱ ❛❧é♠ ❞❛ ♥ã♦✲❧✐♥❡❛r✐❛❞❛❞❡ ❞❛ ❞❡♣❡♥❞ê♥❝✐❛❞♦ ❝❛♠♣♦✱ ✉♠ ♣♦ssí✈❡❧ ❝❛rát❡r t❡♥s♦r✐❛❧ ❞❡ µ(H)✱ ❞❡✈✐❞♦ ❛ ♣r♦♣r✐❡❞❛❞❡s❛♥✐s♦tró♣✐❝❛s ❞♦ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✳ ❙✉r❣❡ ❛ss✐♠✱ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❡♠♣r❡❣❛r ✉♠ ♣r♦❝❡ss♦ ✐t❡r❛t✐✈♦ t❛❧ ❝♦♠♦ ♦ ♠ét♦❞♦ ❞❛s ❛♣r♦①✐♠❛çõ❡s s✉❝❡ss✐✈❛s ✭❇❆❙❚❖❙✱ ✶✾✾✷❀ ❙■▲✲❱❊❙❚❊❘❀ ❋❊❘❘❆❘■✱ ✶✾✾✵✮✳ ❖ ♣r♦❜❧❡♠❛ r❡st❛♥t❡ ❝♦♥s✐st❡ ♥❛ s♦❧✉çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s❧✐♥❡❛r❡s ❡①♣r❡ss♦ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✷✹✮ ♣❛r❛ ♦❜t❡r ♦ ✈❛❧♦r ❞♦ ♣♦t❡♥❝✐❛❧ ♥♦s❞✐✈❡rs♦s ♥ós ❞❛ ♠❛❧❤❛✳ ▼✉✐t♦s ♠ét♦❞♦s ♥✉♠ér✐❝♦s ♣♦❞❡♠ s❡r ❡♠♣r❡✲❣❛❞♦s ❡ ❡ss❡s ✐♥❝❧✉❡♠ ♠ét♦❞♦s ❞✐r❡t♦s ❡ ✐t❡r❛t✐✈♦s✳ ❊①✐st❡ ✉♠❛ ❡①t❡♥s❛❧✐t❡r❛t✉r❛ s♦❜r❡ ♦ ❛ss✉♥t♦ ✭❇❆❙❚❖❙✱ ✶✾✾✷❀ ❙■▲❱❊❙❚❊❘❀ ❋❊❘❘❆❘■✱ ✺✽ ✷✳✺ ❙■❙❚❊▼❆❙ ■◆❋❖❘▼➪❚■❈❖❙ P❆❘❆ ❈➪▲❈❯▲❖ ◆❯▼➱✲❘■❈❖ ❉❊ ❈❆▼P❖❙ ❊▲❊❚❘❖▼❆●◆➱❚■❈❖❙ ❆ ✉t✐❧✐③❛çã♦ ❞❛ té❝♥✐❝❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ r❡s♦❧✈❡r✱ ♥✉✲♠❡r✐❝❛♠❡♥t❡✱ ❛s ❡q✉❛çõ❡s ❞❡ ❝❛♠♣♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ é✱ ❤♦❥❡ ❡♠ ❞✐❛✱ r❡❛❧✐③❛❞❛ ♣♦r ♣r♦❣r❛♠❛s ❞❡ ♣r♦♣ós✐t♦ ❣❡r❛❧ q✉❡ sã♦ rá♣✐❞♦s ❡ ❞❡ ✐♠♣❧❡✲♠❡♥t❛çã♦ r♦❜✉st❛✳ ❊①✐st❡✱ ♥❛ r❡❛❧✐❞❛❞❡✱ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ♥♦ ❞❡s❡♥✈♦❧✲✈✐♠❡♥t♦ ❞❡ s✐st❡♠❛s ❣❡r❛✐s✱ ❡♠ ✈❡③ ❞❡ ♣r♦❣r❛♠❛s ♦r✐❡♥t❛❞♦s ♣❛r❛ ✉♠♣r♦❜❧❡♠❛ ❡s♣❡❝í✜❝♦✳ ❊st❡s s✐st❡♠❛s sã♦ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ s✐st❡♠❛s ❈❆❉ ♣❛r❛ ❝♦♠✲♣✉t❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛✳ ❈❆❉ é ❛ ❛❜r❡✈✐❛t✉r❛ ❞❡ ❈♦♠♣✉t❡r ❆✐❞❡❞❉❡s✐❣♥✱ ✉♠❛ t❡r♠✐♥♦❧♦❣✐❛ q✉❡ r❡❛❧ç❛ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡st❡s s✐st❡♠❛s ♥♦s♣r♦❥❡t♦s ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s✳ ❖s três ♣r✐♥❝✐♣❛✐s ❢❛t♦r❡s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐✲♠❡♥t♦ ❞❡st❡s s✐st❡♠❛s ❢♦r❛♠✿ ✶✳ ♦ ❛❞✈❡♥t♦ ❞♦ ❝♦♠♣✉t❛❞♦r ❞✐❣✐t❛❧❀✷✳ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❝♦♠♣✉t❛çã♦ ❣rá✜❝❛ ✐♥t❡r❛t✐✈❛❀✸✳ ♦s ❛✈❛♥ç♦s ♥❛ ❛♥á❧✐s❡ ♥✉♠ér✐❝❛✱ ♣❡r♠✐t✐♥❞♦ q✉❡ t❛♥t♦ ❛ ❣❡♦♠❡✲ tr✐❛ q✉❛♥t♦ ❛s ❡q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s ♣❛r❝✐❛✐s ❞♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦ ♣♦ss❛♠ s❡r tr❛t❛❞❛s ❞❡ ✉♠❛ ❢♦r♠❛ ❞✐s❝r❡t✐③❛❞❛✳➱ ♣♦ssí✈❡❧ ❛♥❛❧✐s❛r ✉♠ ♥ú♠❡r♦ ❞❡ ❞✐❢❡r❡♥t❡s ❣❡♦♠❡tr✐❛s ❡ ❛s ❝♦♥✲ ❞✐çõ❡s ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦✱ s❡♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❝♦♥str✉çã♦ ❞❡ ✉♠ ♣r♦tó✲ t✐♣♦ ❢ís✐❝♦✳ ❆❧é♠ ❞✐ss♦✱ ❛ s✐♠✉❧❛çã♦ ♥✉♠ér✐❝❛ ♣r♦♣♦r❝✐♦♥❛✱ ♥❛ ♠❛✐♦r✐❛❞♦s ❝❛s♦s✱ ✐♥❢♦r♠❛çõ❡s ❝♦♥✜á✈❡✐s ❡ ♣r❡❝✐s❛s s♦❜r❡ ❝♦♠♣♦rt❛♠❡♥t♦✱ ✐♥✲❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛ ❣❡♦♠❡tr✐❛ ❞♦ ❞✐s♣♦s✐t✐✈♦ ❡ ❞❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s♠❛t❡r✐❛✐s ♥ã♦ ❧✐♥❡❛r❡s ❡♠♣r❡❣❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞♦ ♠❡s♠♦✳ ❆♠❜✐❡♥t❡s ❞❡ s♦❢t✇❛r❡ ♠♦❞❡r♥♦s q✉❡ ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s❝♦♠♦ s✐st❡♠❛s ❈❆❉ ♣❛r❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ❝♦♥✲ tê♠ três ❡❧❡♠❡♥t♦s ♣r✐♥❝✐♣❛✐s✱ q✉❡ tê♠ ❛❝❡ss♦ ❛ ✉♠❛ ❜❛s❡ ❝♦♠✉♠ ❞❡❞❛❞♦s ✭❙■▲❱❊❙❚❊❘❀ ❋❊❘❘❆❘■✱ ✶✾✾✵✮✿ ✶✳ ❖ ♣ré✲♣r♦❝❡ss❛❞♦r✳ P❡r♠✐t❡ q✉❡ ♦ ✉s✉ár✐♦ ❞❡✜♥❛ ❛ ❣❡♦♠❡tr✐❛✱ ❛s❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❡ ❛s ❢♦♥t❡s ❞❡ ❡♥❡r❣✐❛✳ ❆ ❣❡r❛çã♦ ❞❛ ♠❛❧❤❛é t❛♠❜é♠ ✉♠❛ ♦♣❡r❛çã♦ ❞❡ ♣ré✲♣r♦❝❡ss❛♠❡♥t♦❀ ✷✳ ❖ ♣r♦❝❡ss❛❞♦r✳ ➱ ♦ ♣r♦❣r❛♠❛ ♣❛r❛ ♠♦♥t❛❣❡♠ ❡ s♦❧✉çã♦ ❞♦ s✐s✲ t❡♠❛ ❞❡ ❡q✉❛çõ❡s✳ ❆ s♦❧✉çã♦✱ ❡♠ ❣❡r❛❧✱ é ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ✉♠ ✺✾ ✸✳ ❖ ♣ós✲♣r♦❝❡ss❛❞♦r✳ P❡r♠✐t❡ ❛ ✈✐s✉❛❧✐③❛çã♦ ❡ ♠❛♥✐♣✉❧❛çã♦ ❞♦s❞❛❞♦s✳ ❚r❛t❛✲s❡ ❞❡ ❡t❛♣❛ ❛❧t❛♠❡♥t❡ ✐♥t❡r❛t✐✈❛ ♦♥❞❡ sã♦ ❝❛❧❝✉❧❛❞♦s♣❛râ♠❡tr♦s ❝♦♠♦ ❢♦rç❛s✱ ✐♥❞✉tâ♥❝✐❛s ❡ ♣❡r❞❛s✳ ❊①✐st❡♠ ❤♦❥❡ ✐♥ú♠❡r♦s s✐st❡♠❛s ❈❆❉ ❡❧❡tr♦♠❛❣♥ét✐❝♦s✱ ❛❧❣✉♥s❞❡❧❡s ❝♦♠❡r❝✐❛❧♠❡♥t❡ ❞✐s♣♦♥í✈❡✐s ❡ ❡st❡s s✐st❡♠❛s ♣♦❞❡♠ ❞✐❢❡r✐r s✐❣♥✐✜✲❝❛t✐✈❛♠❡♥t❡ ❡♠ s✉❛s ❡str✉t✉r❛s ❡ ❝❛♣❛❝✐❞❛❞❡s✳ ❙✐st❡♠❛s ❈❆❉ ♠♦❞❡r♥♦s ✐♥❝♦r♣♦r❛♠ ♥♦ ♣ré ❡ ♣ós✲♣r♦❝❡ss❛❞♦r❡s✱❛♠❜❛s ❛s ♦♣❡r❛çõ❡s ❞❡ ✐♥t❡r❛çã♦❝♦♠ ♦ ✉s✉ár✐♦ ❡ ❧♦t❡ ✭❣❡r❡♥❝✐❛♠❡♥t♦❞❡ ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s✮✳ ❆ s♦❧✉çã♦ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ❛ ♣❛rt❡♣r✐♥❝✐♣❛❧ ❞♦ s✐st❡♠❛✱ ♠❛s ❛ s✉❛ ♦♣❡r❛çã♦ ♥♦r♠❛❧♠❡♥t❡ ♥ã♦ r❡q✉❡r ✐♥✲ t❡r❛çã♦ ❞♦ ✉s✉ár✐♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ♠♦❞❡❧❛❣❡♠ ❞♦ ♣r♦❜❧❡♠❛ ♥♦r♠❛❧✲♠❡♥t❡ ❡♥✈♦❧✈❡ ✉♠❛ sér✐❡ ❞❡ q✉❡stõ❡s r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❛ ❣❡♦♠❡tr✐❛ ❞♦s❞✐s♣♦s✐t✐✈♦s ❡♠ q✉❡stã♦ ❡ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❡s♣❡r❛❞❛s ❞❡ s❡✉s ❞♦♠í♥✐♦s✳✷✳✻ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ❉❖ ❈❆P❮❚❯▲❖ ◆❡st❡ ❝❛♣ít✉❧♦✱ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞❛s ❛s ❜❛s❡s t❡ór✐❝❛s ❞♦ ♠ét♦❞♦❞♦s ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ❊ss❡ ♠ét♦❞♦ ♥✉♠ér✐❝♦ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛s s✐♠✉❧❛çõ❡s r❡❛❧✐③❛❞❛s ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ tr❛❜❛❧❤♦✳ ◆♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦✱s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠ ❡st✉❞♦ ❞❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r♠♦♥♦❢ás✐❝♦✳ ✻✵ ✻✶✸ ❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❊ ❯▼ ❚❘❆◆❙❋❖❘▼❆❉❖❘ ▼❖◆❖❋➪❙■❈❖ ❊st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ✉♠❛ té❝♥✐❝❛ s✐st❡♠át✐❝❛ ♣❛r❛ ♦❜t❡♥çã♦❞❡ ♣❛râ♠❡tr♦s ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r ♠♦♥♦❢ás✐❝♦✱ ❛tr❛✈és ❞❛ ❝❛r❛❝t❡r✐✲③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✳ ❊ss❛ ❝❛r❛❝t❡r✐③❛çã♦ é r❡❛❧✐③❛❞❛ ❝♦♠♦ ❛✉①í❧✐♦ ❞♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❞♦ ♠❛t❡r✐❛❧✳ ❆ss✐♠✱ ❛♦ ❧♦♥❣♦ ❞♦ ❝❛♣ít✉❧♦ s❡rã♦ ❡①♣❧♦r❛❞♦s✱ ❡♠ ♦r❞❡♠✱ ♦s s❡✲❣✉✐♥t❡s ✐t❡♥s✿ ❼ ❡st✉❞♦ ❞❛s ♣r✐♥❝✐♣❛✐s ❡str✉t✉r❛s ❞❡ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s❀❼ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ♣❡r❞❛s ❞♦s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣✲ ♥ét✐❝♦s❀❼ ❛♣r❡s❡♥t❛çã♦ ❞♦ ❞✐s♣♦s✐t✐✈♦ ❡♠ ❡st✉❞♦❀❼ ♠ét♦❞♦s ❞❡ ❛q✉✐s✐çã♦ ❞♦ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ❡ ♦❜t❡♥çã♦ ❞♦ ♠❡s♠♦❀❼ ❛♣r❡s❡♥t❛çã♦ ❞❡ ❝✉r✈❛s ❞♦s ♣❛râ♠❡tr♦s ❡❧étr✐❝♦s ❞♦ tr❛♥s❢♦r♠❛❞♦r ❡♠ ❡st✉❞♦❀❼ ❛♥á❧✐s❡s ❞❡ ❡♥❡r❣✐❛✱ ♣♦tê♥❝✐❛ ❡ ♣❡r❞❛s ❞♦ ♠♦❞❡❧♦ ❞❡s❡♥✈♦❧✈✐❞♦❀❼ ✈❛❧✐❞❛çã♦ ❞♦ ♠♦❞❡❧♦✱ ❝♦♠ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ✐♥✲r✉s❤✳ ✸✳✶ P❊❘❉❆❙ ❊▼ ▼❆❚❊❘■❆■❙ ❋❊❘❘❖▼❆●◆➱❚■❈❖❙❆ ❛✈❛❧✐❛çã♦ ❞❛s ♣❡r❞❛s ♥♦s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✉s❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❡❧❡tr♦♠❡❝â♥✐❝♦s é ✉♠ ❛ss✉♥t♦ ❝♦♠♣❧❡①♦ ❡♠✉❧t✐❞✐s❝✐♣❧✐♥❛r q✉❡ ❡♥✈♦❧✈❡ ❋ís✐❝❛✱ ❊♥❣❡♥❤❛r✐❛ ❞❡ ▼❛t❡r✐❛✐s ❡ ❊♥❣❡✲♥❤❛r✐❛ ❊❧étr✐❝❛✳ ❆ t❡♦r✐❛ ❞❡ s❡♣❛r❛çã♦ ❞❡ ♣❡r❞❛s ♣❡r♠✐t❡ ❛♥❛❧✐s❛r ✏s❡✲♣❛r❛❞❛♠❡♥t❡✑ ♦s ❞✐❢❡r❡♥t❡s ❢❡♥ô♠❡♥♦s ❢ís✐❝♦s q✉❡ ♣r♦✈♦❝❛♠ ❞✐ss✐♣❛çã♦❞❡ ❝❛❧♦r ❡♠ ♥ú❝❧❡♦s ❞❡ ❡str✉t✉r❛s ❢❡rr♦♠❛❣♥ét✐❝❛s ✭❇❊❘❚❖❚❚■✱ ✶✾✽✽✮✳❉❡ ❛❝♦r❞♦ ❝♦♠ ❡ss❛ t❡♦r✐❛✱ ❛s ♣❡r❞❛s ❡♠ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✻✷ ❛❧t❡r♥❛❞❛ ♣♦❞❡♠ s❡r s❡♣❛r❛❞❛s ❡♠ três ❝♦♠♣♦♥❡♥t❡s✿ ✭✐✮ ❛s ♣❡r❞❛s ♣♦r❤✐st❡r❡s❡✱ ♣♦r ❝✐❝❧♦✱ ❝♦♥s✐❞❡r❛❞❛s ❝♦♥st❛♥t❡s ♣❛r❛ ✉♠❛ ❞❛❞❛ ❢r❡q✉ê♥❝✐❛✱ sã♦ ❞❡t❡r♠✐♥❛❞❛s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥✲t❛çã♦ q✉❡ ♦♣❡r❛ ❡♠ ✉♠❛ ❢r❡q✉ê♥❝✐❛ ♠✉✐t♦ ❜❛✐①❛✱ ❞❛ ♦r❞❡♠ ❞❡ ✶ ❤❡rt③✳❚r❛t❛✲s❡ ❞❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡stát✐❝❛ ♦✉ q✉❛s❡ ❡stát✐❝❛✱ ❡ sã♦ ❝❛✉✲ s❛❞❛s ♣❡❧♦ ❞❡s❧♦❝❛♠❡♥t♦ ❡ r♦t❛çã♦ ❞♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s ❞❡ ✉♠❛❡str✉t✉r❛ s✉❜♠❡t✐❞❛ à ❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥❡t✐③❛♥t❡ ❡①t❡r♥♦❀ ✭✐✐✮❛s ♣❡r❞❛s ❝❛✉s❛❞❛s ♣❡❧❛s ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s✱ ♣r❡s❡♥t❡s ❡♠ ♠❡✐♦s ♠❛✲ t❡r✐❛✐s q✉❡ ❛♣r❡s❡♥t❛♠ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❡❧❡✈❛❞❛❀ ✭✐✐✐✮ ❛s ♣❡r❞❛s❛♥ô♠❛❧❛s✱ t❛♠❜é♠ ❛ss♦❝✐❛❞❛s ❛♦ ♠♦✈✐♠❡♥t♦ ❞♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s❡ ❡①♣❧✐❝❛❞❛s ♣♦r ❇❡rt♦tt✐ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❡♥t✐❞❛❞❡ ❢ís✐❝❛ ❝♦♥❤❡❝✐❞❛❝♦♠♦ ✏♦❜❥❡t♦ ♠❛❣♥ét✐❝♦✑ ✭❇❊❘❚❖❚❚■✱ ✶✾✽✽✮✳ ❊ss❛s ♣❡r❞❛s ♣♦❞❡♠ s❡r❡①♣❧✐❝❛❞❛s✱ ❞❡ ❢♦r♠❛ s✐♠♣❧✐✜❝❛❞❛✱ ❝♦♠♦ s❡♥❞♦ ♦ q✉❡ r❡st❛ ❛♣ós ❛s ♣❡r✲❞❛s ♣♦r ❤✐st❡r❡s❡ ❡ ♣♦r ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s t❡r❡♠ s✐❞♦ s✉❜tr❛í❞❛s ❞❛s♣❡r❞❛s t♦t❛✐s✳ ❊♠ ♠❛t❡r✐❛✐s ❢❡rr♦❝r✐st❛❧✐♥♦s✱ ❛s ♣❡r❞❛s ❛♥ô♠❛❧❛s sã♦ r❡s♣♦♥sá✈❡✐s ♣♦r ✺✵✪ ❞❛s ♣❡r❞❛s t♦t❛✐s✳ ❆s ♠❡❞✐çõ❡s ❞❡ ❣r❛♥❞❡③❛s ♠❛❣♥ét✐❝❛s ✐♥❝❧✉❡♠ ❡♥s❛✐♦s ❡♠ ❝♦r✲ r❡♥t❡ ❝♦♥tí♥✉❛ ✭❈❈✮ ❡ ❡♠ ❝♦rr❡♥t❡ ❛❧t❡r♥❛❞❛ ✭❈❆✮✳ ❖s ❡♥s❛✐♦s ❈❈ sã♦✈♦❧t❛❞♦s ♣❛r❛ ♠❡❞✐çã♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✱ ✢✉①♦ ♠❛❣♥ét✐❝♦✱ ♣❡r✲♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛✱ ❝✉r✈❛s BH ❡ ❧❛ç♦s ❞❡ ❤✐st❡r❡s❡✳ ❏á ❛s ♠❡❞✐çõ❡s❈❆ sã♦ ✈♦❧t❛❞❛s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❛r❛ ❛ ♠❡❞✐çã♦ ❞❛s ♣❡r❞❛s ♥♦s ♠❛t❡✲ r✐❛✐s ♠❛❣♥ét✐❝♦s s♦❜ ❝♦♥❞✐çõ❡s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❛❧t❡r♥❛❞❛✳ ❆ ❞❡t❡r♠✐♥❛çã♦ ❞❛s ♣❡r❞❛s ❡♠ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ❡♠ ✉♥✐✲❞❛❞❡s ❞❡ ✇❛tt✴q✉✐❧♦❣r❛♠❛ ✭❲✴❦❣✮ ✉s✉❛❧♠❡♥t❡ ♣❛rt❡ ❞❡ ❝♦♥❞✐çõ❡s ♣ré✲❡st❛❜❡❧❡❝✐❞❛s✿ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ♠á①✐♠❛ ❞❡ ✶✱✵ ❚ ♦✉ ✶✱✺ ❚ ❡ ❢r❡q✉ê♥✲❝✐❛ ❞❡ ✺✵ ❍③ ♦✉ ✻✵ ❍③✳ ❆♠♣❧❛♠❡♥t❡ ❡♠♣r❡❣❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞❡♠áq✉✐♥❛s ❡ tr❛♥s❢♦r♠❛❞♦r❡s✱ ♦s ♠❛t❡r✐❛✐s ❢❡rr♦❝r✐st❛❧✐♥♦s ♣♦❞❡♠ s❡r❛❣r✉♣❛❞♦s ❡♠ três ❣r❛♥❞❡s ❢❛♠í❧✐❛s✿ ✭✐✮ ❛ç♦s ❡❧étr✐❝♦s ❞❡ ❣rã♦s ♦r✐❡♥t❛✲❞♦s ✭●❖✮ ❡ ❛ç♦s ❡❧étr✐❝♦s ❞❡ ❣rã♦s ♥ã♦ ♦r✐❡♥t❛❞♦s ✭●◆❖✮❀ ✭✐✐✮ ❧✐❣❛s ❞❡❢❡rr♦✲♥íq✉❡❧ ✭❋❡◆✐✮ ❡ ❢❡rr♦✲❝♦❜❛❧t♦ ✭❋❡❈♦✮❀ ✭✐✐✐✮ ❢❡rr✐t❡s ❞❡ ♠❛♥❣❛♥ês✲③✐♥❝♦ ✭▼♥❩♥✮ ❡ ♥íq✉❡❧✲③✐♥❝♦ ✭◆✐❩♥✮✳ ❱❛❧♦r❡s tí♣✐❝♦s ❞❛s ♣❡r❞❛s ❞♦s ♠❛✲ t❡r✐❛✐s ❢❡rr♦❝r✐st❛❧✐♥♦s✱ ❛♦ ❧❛❞♦ ❞❡ ♣r♦♣r✐❡❞❛❞❡s ❡❧❡tr♦♠❛❣♥ét✐❝❛s ❝♦♠♦S ❞❡♥s✐❞❛❞❡ ❞❡ s❛t✉r❛çã♦ ✭B ✮✱ r❡s✐st✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ✭ρ✮ ❡ ♠á①✐♠❛ ♣❡r✲ max♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ ✭µ ✮ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✶✳✸✳✶✳✶ ❆ç♦s ❞❡ ❜❛✐①♦ ❝❛r❜♦♥♦ ❖s ♣r✐♠❡✐r♦s tr❛♥s❢♦r♠❛❞♦r❡s ❝♦♥str✉í❞♦s ♣♦r ✈♦❧t❛ ❞♦s ❛♥♦s ✽✵❞♦ sé❝✉❧♦ ❳■❳ ✉s❛✈❛♠ ❛ç♦s ❞❡ ❜❛✐①♦ ❝❛r❜♦♥♦✱ ✐st♦ é✱ ❝♦♠ t❡♦r❡s ✐♥❢❡r✐✲♦r❡s ❛ ✵✱✵✸✪ ❈ ✭❈❯▲▲■❚❨❀ ●❘❆❍❆▼✱ ✷✵✵✾✮✳ ❊st❡s ❛ç♦s sã♦ ❜❛s✐❝❛✲ ✻✸ ❚❛❜❡❧❛ ✸✳✶ ✕ ▼❛t❡r✐❛✐s ❢❡rr♦❝r✐st❛❧✐♥♦s✿ ♣r♦♣r✐❡❞❛❞❡s ❡❧❡tr♦♠❛❣♥ét✐❝❛s✳B [T] ρ µ [µΩ/m] ❈❛t❡❣♦r✐❛ s max P❡r❞❛s tí♣✐✲❝❛s [W/kg]✯ ❆ç♦ ❜❛✐①♦ ❈ ✷✱✶ ✵✱✹✵ ✺✵✵✵ ✷✱✵ ✭✻✵✴✶✱✵✮❆ç♦ ●◆❖ ✷✱✵ ✵✱✸✺ ✽✵✵✵ ✷✱✼ ✭✻✵✴✶✱✵✮❆ç♦ ●❖ ✭▼✲✹✮ ✷✱✵ ✵✱✹✽ ✹✵✵✵✵ ✵✱✾ ✭✻✵✴✶✱✺✮❆ç♦s ◆✐✲❇ ✷✱✵ ✵✱✹✺ ✲ ✶✱✷ ✭✻✵✴✶✱✼✮❋❡✲✭✹✵✲✺✵◆✐✮ ✶✱✻ ✵✱✹✽ ✶✺✵✱✵✵✵ ✶✶✵ ✭✺✵❦✴✵✱✷✮❋❡✲✭✼✼✲✽✵◆✐✮ ✶✱✶ ✵✱✺✺ ✶✺✵✱✵✵✵ ✹✵ ✭✺✵❦✴✵✱✷✮6 10❋❡✲✭✼✾◆✐✲✹▼♦✮ ✵✱✽ ✵✱✺✽ ✸✸ ✭✺✵❦✴✵✱✷✮❋❡✲✭✹✾❈♦✲✷❱✮ ✷✱✸ ✵✱✸✺ ✺✵✱✵✵✵ ✷✱✷ ✭✻✵✴✷✱✵✮6 ❋❡rr✐t❡s ✭▼♥❩♥✮ ✵✱✺ 2 · 10 ✻✱✵✵✵ ✸✺ ✭✺✵❦✴✵✱✷✮1 10❋❡rr✐t❡s ✭◆✐❩♥✮ ✵✱✸✺ ✹✱✵✵✵ ✲ max [Hz/T] ✯❖s ✈❛❧♦r❡s ❡♥tr❡ ♣❛r❡♥tês❡s ✐♥❞✐❝❛♠ ❛ r❡❧❛çã♦ f/B ♠❡♥t❡ ❢❡rr♦ ❝♦♠❡r❝✐❛❧ ❝♦♠ ❛❧❣✉♠❛s ✐♠♣✉r❡③❛s ✐♥❞❡s❡❥❛❞❛s ❞❡ ❝❛r❜♦♥♦✱♥♦r♠❛❧♠❡♥t❡ s♦❜ ❛ ❢♦r♠❛ ❞❡ ❝❡♠❡♥t✐t❛ ✭❋❡ 3 ❈✮✳ ❆t✉❛❧♠❡♥t❡ ♥ã♦ sã♦✉t✐❧✐③❛❞♦s ♥❛ ❝♦♥str✉çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❡❧étr✐❝♦s ❞❡ ♣♦tê♥❝✐❛✱ ❡♠❜♦r❛❝♦♥t✐♥✉❡♠ ❛ s❡r ✉s❛❞♦s ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ♣❡q✉❡♥♦s ♠♦t♦r❡s ♦♥❞❡❛s ♣❡r❞❛s ❞♦ ❢❡rr♦ ♥ã♦ sã♦ ✉♠ ❢❛t♦r ❞❡t❡r♠✐♥❛♥t❡✱ ♠❛s s✐♠ ♦ ❜❛✐①♦❝✉st♦✳ ❈♦♠♦ ❡①❡♠♣❧♦s ♣♦❞❡♠ ❝✐t❛r✲s❡ ♦s tr❛♥s❢♦r♠❛❞♦r❡s ❞❡ ♣♦tê♥❝✐❛❞❡ r❡❣✉❧❛❞♦r❡s ❡ ❢♦♥t❡ ❞❡ t❡♥sã♦✱ ❢❡✐t♦s ♥❛ ❈❤✐♥❛✳ ❊♠ ✶✾✵✵✱ ♦ ♠❡t❛❧✉r❣✐st❛ ✐♥❣❧ês ❙✐r ❘♦❜❡rt ❍❛❞✜❡❧❞✱ ❞❡s❝♦❜r✐✉ q✉❡ ❛ ❛❞✐çã♦ ❞❡ s✐❧í❝✐♦ ❛♦ ❢❡rr♦✱ ❡♠ ♣❡q✉❡♥❛s q✉❛♥t✐❞❛❞❡s ✭✐♥❢❡r✐♦r❡s ❛✸✪✮✱ ❞✐♠✐♥✉í❛ ❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s ♣❛r❛ ❝❡r❝❛ ❞❡ ✶✴✹ ❞♦s ✈❛❧♦r❡s ♥♦s❛ç♦s ❞❡ ❜❛✐①♦ ❝❛r❜♦♥♦ ✭▼❖❙❊❙✱ ✶✾✾✵✮✳ ❆ ❛♣❧✐❝❛çã♦ ❞❡st❡ t✐♣♦ ❞❡ ❛ç♦s❝♦♠❡ç♦✉ ♥♦s ❊❯❆ ❡♠ ✶✾✵✸ ❡ ♥♦ ❘❡✐♥♦ ❯♥✐❞♦ ❡♠ ✶✾✵✻✳ ❖t✐♠✐③❛♥❞♦✲s❡♦ t❛♠❛♥❤♦ ❞❡ ❣rã♦✱ ❛tr❛✈és ❞❛ ❛❞✐çã♦ ❞❡ s✐❧í❝✐♦✱ ❝♦♥s❡❣✉✐✉✲s❡ q✉❡ ❛s♣❡r❞❛s ♠❛❣♥ét✐❝❛s ❛ ✶✱✺ ❚ ❡ ✺✵ ❍③ ♣❛ss❛ss❡♠ ❞❡ ✼ ❲✴❦❣ ♥♦s ♣r✐♠❡✐r♦s❛ç♦s ♣❛r❛ ✷ ❲✴❦❣ ♥♦s ❞❡ ♠❡❧❤♦r q✉❛❧✐❞❛❞❡ ❤♦❥❡ ❡♠ ❞✐❛✳ ❆ ❛❞✐çã♦ ❞❡ s✐❧í❝✐♦ ❛♦ ❢❡rr♦ t❡♠ ❛s s❡❣✉✐♥t❡s ✈❛♥t❛❣❡♥s✿ ❼ ❆✉♠❡♥t♦ ❞❛ r❡s✐st✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞♦ ♠❛t❡r✐❛❧ ♣r♦✈♦❝❛♥❞♦ ✉♠❛❞✐♠✐♥✉✐çã♦ ❞❛s ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ❡ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ❞❛s♣❡r❞❛s ♠❛❣♥ét✐❝❛s❀ ❼ ❉✐♠✐♥✉✐çã♦ ❞❛ ❛♥✐s♦tr♦♣✐❛ ♠❛❣♥❡t♦❝r✐st❛❧✐♥❛✱ ♦ q✉❡ ♣❡r♠✐t❡ ✉♠❛✉♠❡♥t♦ ♥❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛❀ ❼ ❉✐♠✐♥✉✐çã♦ ❞❛ ♠❛❣♥❡t♦str✐❝çã♦✳ ✻✹ ❼ ❆ ❛❞✐çã♦ ❞❡ ❙✐ ❞✐♠✐♥✉✐ ❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ❞❡ s❛t✉r❛çã♦✱ ❡♠❝❡r❝❛ ❞❡ ✵✱✵✺❚✴✪❙✐ ✭▲❆◆❉●❘❆❋✱ ✷✵✵✷✮✱ ❼ ❖ ♠❛t❡r✐❛❧ s❡ t♦r♥❛ ♠❛✐s ❢rá❣✐❧ ❞✐✜❝✉❧t❛♥❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❡st❛♠✲♣❛❣❡♠✳ P♦r ✐ss♦✱ ♥♦r♠❛❧♠❡♥t❡ ❛s ❛❞✐çõ❡s ❞❡ s✐❧í❝✐♦ ❡stã♦ ❧✐♠✐t❛❞❛s❛ ✸✪✳ ✸✳✶✳✷ ❆ç♦s ❞❡ ❣rã♦ ♦r✐❡♥t❛❞♦❖s ❛ç♦s ❞❡ ❣rã♦ ♦r✐❡♥t❛❞♦ ✭●❖✮ ❢♦r❛♠ ❞❡s❝♦❜❡rt♦s ❡♠ ✶✾✸✸✱ ♣❡❧♦ ♠❡t❛❧✉r❣✐st❛ ❛♠❡r✐❝❛♥♦ ◆♦r♠❛♥ P✳ ●♦ss ✭❈❯▲▲■❚❨❀ ●❘❆❍❆▼✱✷✵✵✾✮✳ ❊❧❡ ❞❡s❝♦❜r✐✉ q✉❡ s❡ ♦s ❛ç♦s s✐❧í❝✐♦ ❢♦ss❡♠ ❧❛♠✐♥❛❞♦s ❛ ❢r✐♦ ❝♦♠ r❡❝♦③✐♠❡♥t♦s ✐♥t❡r♠é❞✐♦s✱ ❛ ✉♠❛ t❡♠♣❡r❛t✉r❛ q✉❡ ♣♦❞❡ ✈❛r✐❛r ❡♥tr❡◦ ✾✵✵ ❡ ✶✶✵✵ ❈ ✭▼❖❙❊❙✱ ✶✾✾✵✮✱ ❡ ❛❝❛❜❛♥❞♦ ♦ ♣r♦❝❡ss♦ ❝♦♠ ✉♠ r❡❝♦✲ ◦③✐♠❡♥t♦ ❛ ❝❡r❝❛ ❞❡ ✶✷✵✵ ❈ ✭❧✐❜❡r❛çã♦ ❞❡ t❡♥sõ❡s✮✱ s❡ ❝♦♥s❡❣✉✐❛ ♦❜t❡r❝❤❛♣❛s ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s ♠✉✐t♦ s✉♣❡r✐♦r❡s às ♦❜t✐❞❛s ♣♦r❧❛♠✐♥❛çã♦ ❛ q✉❡♥t❡ ✭❈❯▲▲■❚❨❀ ●❘❆❍❆▼✱ ✷✵✵✾✮✳ ❊st❡ ♠❡❧❤♦r❛♠❡♥t♦❞❡✈✐❛✲s❡ ❛♦ ❢❛t♦ ❞❡ ❡①✐st✐r ✉♠❛ r❡❝r✐st❛❧✐③❛çã♦ s❡❝✉♥❞ár✐❛ q✉❡ ♦❝♦rr✐❛❞✉r❛♥t❡ ♦ r❡❝♦③✐♠❡♥t♦ ❛ ❛❧t❛ t❡♠♣❡r❛t✉r❛ ❡ q✉❡ ❝♦♥❞✉③✐❛ à ♦❜t❡♥çã♦❞❡ ✉♠❛ t❡①t✉r❛ ♠❛❣♥❡t✐❝❛♠❡♥t❡ ❢❛✈♦rá✈❡❧✱ q✉❡ ♣❛ss♦✉ ❛ s❡r ❝♦♥❤❡❝✐❞❛♣♦r t❡①t✉r❛ ❞❡ ●♦ss✳ ◆❡st❛ t❡①t✉r❛ ✉♠❛ ❞❛s ❞✐r❡çõ❡s ♣r❡❢❡r❡♥❝✐❛✐s ❞❡♠❛❣♥❡t✐③❛çã♦ ❞❡ ❝❛❞❛ ❣rã♦✱ ❛ ❞✐r❡çã♦ ❬✵✵✶❪✱ ❡stá ♣❛r❛❧❡❧❛ à ❞✐r❡çã♦ ❞❡❧❛♠✐♥❛çã♦ ❡ ♣❛r❛❧❡❧❛ ❛♦ ♣❧❛♥♦ ❞❛ ❝❤❛♣❛✱ ❝♦♥s❡❣✉✐♥❞♦✲s❡ ♦❜t❡r ❡①❝❡❧❡♥t❡s♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s s❡❣✉♥❞♦ ❛ ❞✐r❡çã♦ ❞❡ ❛❧✐♥❤❛♠❡♥t♦ ❞♦ ❣rã♦✳ ◆❛s ❋✐❣✉r❛s ✸✳✶ ❡ ✸✳✷ ♣♦❞❡♠ s❡ ♦❜s❡r✈❛r ♠✐❝r♦❣r❛✜❛s ❞❡ ❛ç♦s ❞❡●❖ ❡ ●◆❖✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳✸✳✶✳✸ ▼❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ❛♠♦r❢♦s ✭✈✐❞r♦s ♠❡tá❧✐❝♦s✮ ❆s ❧✐❣❛s ♠❡tá❧✐❝❛s ♣♦ss✉❡♠ ♥♦r♠❛❧♠❡♥t❡ ❡str✉t✉r❛s ❛tô♠✐❝❛s❝r✐st❛❧✐♥❛s ❡♠ q✉❡ ♦s át♦♠♦s ❡stã♦ ♦r❞❡♥❛❞♦s ♥✉♠❛ r❡❞❡ ♦r❞❡♥❛❞❛ ❡ r❡♣❡t✐❞❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛s ❧✐❣❛s ♠❡tá❧✐❝❛s ❛♠♦r❢❛s ❞✐❢❡r❡♠ ❞❛s ❛♥✲t❡r✐♦r❡s ♣❡❧♦ ❢❛t♦ ❞♦s s❡✉s át♦♠♦s ❡st❛r❡♠ ❞✐str✐❜✉í❞♦s ❞❡ ✉♠ ♠♦❞♦♣r❛t✐❝❛♠❡♥t❡ ❛❧❡❛tór✐♦ ❡ ❞❡s♣r♦✈✐❞♦s ❞❡ ♦r❞❡♠ ❛ ❧♦♥❣❛ ❞✐stâ♥❝✐❛ ✭❝♦♠♦♥♦s ✈✐❞r♦s✮✳ ❊ss❛s ❧✐❣❛s ❢♦r❛♠ ❞❡s❝r✐t❛s ♣❡❧❛ ❢ór♠✉❧❛ ❣❡r❛❧ ▼ 70−90 ❨ 10−30 ❩ 0,1−15 ✱♦♥❞❡ ▼ é ✉♠ ♦✉ ♠❛✐s ♠❡t❛✐s ❞❡ tr❛♥s✐çã♦ ❝♦♠♦ ♦ ❋❡✱ ◆✐✱ ❈♦ ❡ ❈r✱ ❨ é✉♠ ❡❧❡♠❡♥t♦ ♥ã♦ ♠❡tá❧✐❝♦ ✭♣♦r ❡①❡♠♣❧♦✱ P✱ ❇ ♦✉ ❈✮ ❡ ❩ é ✉♠ ♠❡t❛❧ó✐❞❡✭❝♦♠♦ ♦ ❙✐✱ ❆❧ ♦✉ ●❡✮ ✭❉❊❈❘■❙❚❖❋❆❘❖✱ ✶✾✾✽❀ ❱■❊■❘❆ ❡t ❛❧✳✱ ✷✵✵✵✮✳ ✻✺ ❋✐❣✉r❛ ✸✳✶ ✕ ●rã♦ ♦r✐❡♥t❛❞♦ ✭●❖✮✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭●❖◆➬❆▲❱❊❙✲▼❖◆❚❊■❘❖✱ ✷✵✶✵✮ ❼ ❋❡ 82 ❇ 12 ❙✐ 6 ❞❡s❝♦❜❡rt❛ ❡♠ ✶✾✼✽ ✭▼❊❚●▲❆❙ ✷✻✵✺❙✮✱❼ ❋❡ 81,5 ❇ 13 ❙✐ 3,5 ❈ 2 ❞❡s❝♦❜❡rt❛ ❡♠ ✶✾✼✾ ✭▼❊❚●▲❆❙ ✷✻✵✺❙❈✮✱❼ ❋❡ 78 ❇ 13 ❙✐ 9 ❞❡s❝♦❜❡rt❛ ❡♠ ✶✾✽✵ ✭▼❊❚●▲❆❙ ✷✻✵✺❙✲✷✮✳ ❆ ❧✐❣❛ ▼❊❚●▲❆❙ ✷✻✵✺❙✲✷ é✱ ❛t✉❛❧♠❡♥t❡✱ ❛ ♠❛✐s ✉s❛❞❛ ❡♠ ♣r♦✲❥❡t♦s ❞❡ s✐st❡♠❛s ❞❡ ♣♦tê♥❝✐❛ ✭❋■❙❍✱ ✶✾✾✵❀ ❱■❊■❘❆ ❡t ❛❧✳✱ ✷✵✵✵✮✳ ❆❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✉s❛❞♦s ❡♠♥ú❝❧❡♦s ❞❡ tr❛♥s❢♦r♠❛❞♦r❡s ❡stã♦ ❛♣r❡s❡♥t❛❞❛s ♥❛ ❚❛❜❡❧❛ ✸✳✷ P❛r❛ ❛❜♦r❞❛r ♦ t❡♠❛ ❞❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s❡ s✉❛ ❛♣❧✐❝❛çã♦ ♥❛ ❛✈❛❧✐❛çã♦ ❞❛s ♣❡r❞❛s é ♥❡❝❡ssár✐♦ ❢❛③❡r ✉♠❛ ❛❜♦r❞❛✲❣❡♠ ❞❛ t❡♦r✐❛ ♠❛❣♥ét✐❝❛✱ ❡①♣❧♦r❛♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❞♦♠í♥✐♦ ♠❛❣♥ét✐❝♦✱ ✻✻ ❋✐❣✉r❛ ✸✳✷ ✕ ●rã♦ ♥ã♦✲♦r✐❡♥t❛❞♦ ✭●◆❖✮✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭●❖◆➬❆▲❱❊❙✲▼❖◆❚❊■❘❖✱ ✷✵✶✵✮✸✳✶✳✹ ▼♦♠❡♥t♦ ♠❛❣♥ét✐❝♦✱ ♠❛❣♥❡t✐③❛çã♦ ❡ ♠❛t❡r✐❛✐s ♠❛❣♥é✲ t✐❝♦s ❖s ♠❛t❡r✐❛✐s q✉❡ s♦❜ ❛ ❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣r♦❞✉③❡♠❡❧❡s ♣ró♣r✐♦s✱ ♥♦ s❡✉ ✈♦❧✉♠❡ ❡ ♥♦ ❡s♣❛ç♦ q✉❡ ♦s ❡♥✈♦❧✈❡✱ ✉♠ ❝❛♠♣♦ ❞❡✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ❇♠❛❣ sã♦ ❝❤❛♠❛❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s✱ ❞✐③❡♥❞♦✲ s❡ q✉❡ ❡①✐❜❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ s❡ ♠❛❣♥❡t✐③❛r ♦✉ s❡ ♣♦❧❛r✐③❛r ♠❛❣♥❡✲t✐❝❛♠❡♥t❡ ✭❘❖❇❊❘❚✱ ✶✾✽✾✮✳ ◆❛ ❡s❝❛❧❛ ♠✐❝r♦s❝ó♣✐❝❛✱ ♦ ♠❛❣♥❡t✐s♠♦ r❡s✉❧t❛ ❞♦ ♠♦✈✐♠❡♥t♦ ❞❡ s♣✐♥ ❞♦s ❡❧étr♦♥s ♥♦ ♠♦✈✐♠❡♥t♦ ♦r❜✐t❛❧ ❞❡st❡s❡♠ t♦r♥♦ ❞♦ ♥ú❝❧❡♦✳ ❊st❡s ♠♦✈✐♠❡♥t♦s ❞ã♦ ♦r✐❣❡♠ ❛♦ ♠♦♠❡♥t✉♠ ❛♥✲❣✉❧❛r ❞❡ ❙♣✐♥ ♦✉ ▼❛❣♥ét♦♥ ❞❡ ❇♦❤r ✭m B ✮✱ q✉❡✱ ♥❛ ór❜✐t❛ ❢✉♥❞❛♠❡♥t❛❧❞♦ át♦♠♦ ❞❡ ❤✐❞r♦❣ê♥✐♦✱ ✈❛❧❡✿ q h −e p242 m = [Am ]B π = 9, 27 · 10 ✻✼ ❚❛❜❡❧❛ ✸✳✷ ✕ ❆❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ✉s❛✲❞♦s ❡♠ ♥ú❝❧❡♦s ❞❡ tr❛♥s❢♦r♠❛❞♦r❡s✳ B [T] H [A/m] ρ [µΩm] P [W/kg] e [mm]▼❛t❡r✐❛❧ sat c mag ▼●✯ ✷✻✵✺ ❙❆✶ ✶✱✺✻ ✷✱✵ ✶✱✸ ✵✱✵✼✵ ✵✱✵✷✺▼●✯ ✷✻✵✺ ❍❇✶ ✶✱✻✹ ✶✱✺ ✶✱✸ ✵✱✵✻✸ ✵✱✵✷✺ ❆ç♦ ●❖ ✷✱✵✸ ✹✱✺ ✵✱✺ ✵✱✹✹✵ ✵✱✷✸✯▼❛t❡r✐❛❧ ♣r♦❞✉③✐❞♦ ♣❡❧❛ ❡♠♣r❡s❛ ▼❊❚●▲❆❙✳ e e p♦♥❞❡ q é ❛ ❝❛r❣❛ ❞♦ ❡❧étr♦♥✱ m é ❛ ♠❛ss❛ ❞♦ ❡❧étr♦♥ ❡♠ r❡♣♦✉s♦✱ h Bé ❛ ❝♦♥st❛♥t❡ ❞❡ P❧❛♥❦✳ ❖ ✈❛❧♦r ❞❡ m ♣♦❞❡ s❡r ♣♦s✐t✐✈♦ ♦✉ ♥❡❣❛t✐✈♦❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ s♣✐♥✳ ❖s ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s ❡stã♦ r❡♣r❡s❡♥t❛❞♦s ♥❛ ❋✐❣✉r❛ ✸✳✸✳❋✐❣✉r❛ ✸✳✸ ✕ ❖ ❞✐♣♦❧♦ ♠❛❣♥ét✐❝♦ t❡♠ ♦r✐❣❡♠ ♥♦ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ❞♦s❡❧étr♦♥s ♥♦s í♦♥s ♦✉ át♦♠♦s q✉❡ ❢♦r♠❛♠ ❛ ♠❛tér✐❛✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r ❆ ❝♦♥❞✐çã♦ ❞❡ s❡r ❣❡r❛❞♦ ✉♠ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ♥ã♦ ♥✉❧♦ s❡❞❡✈❡ à ❡①✐stê♥❝✐❛ ❞❡ s✉❜♥í✈❡✐s ✐♥t❡r♥♦s ✐♥❝♦♠♣❧❡t♦s q✉❡ ❣❡r❛♠ ♠♦♠❡♥✲ t♦s ♠❛❣♥ét✐❝♦s q✉❡ ♥ã♦ sã♦ ❛♥✉❧❛❞♦s ♣❡❧♦ ❡❧étr♦♥ ❝♦♠ s♣✐♥ ❝♦♥trár✐♦✳22626 ◆♦ ❝❛s♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❡❧❡trô♥✐❝❛ ❞♦ ❋❡rr♦ t❡♠✲s❡✿ ✶s ✷s ✷♣26 ✸s ✸♣ ✹s ✸❞ ✳ ❆ ❋✐❣✉r❛ ✸✳✹ ♠♦str❛ ❛ ❝♦♥❞✐çã♦ ❞❡ ♦r❜✐t❛✐s ❡ s♣✐♥s ❛♣❛rt✐r ❞❛ ❞✐str✐❜✉✐çã♦ ❡❧❡trô♥✐❝❛ ❞❡ ▲✐♥✉s P❛✉❧✐♥❣ ❞♦ ❢❡rr♦✳ ❖s ✹ ❡❧étr♦♥s ❞❡s❡♠♣❛r❡❧❤❛❞♦s ❞♦ ú❧t✐♠♦ s✉❜♥í✈❡❧ ❞♦ át♦♠♦ ❞❡❢❡rr♦ ❞ã♦ ❛ ❡❧❡ ✉♠ ♠♦♠❡♥t♦ ❞❡ ❞✐♣♦❧♦ ♠❛❣♥ét✐❝♦ ❞❡ ✹ ♠❛❣♥ét♦♥s ❞❡❇♦❤r✳ ◆♦ ❝❛s♦ ❞♦ ❢❡rr♦✱ ♥♦ s✉❜♥í✈❡❧ ✸❞✱ ♥♦ ♣r✐♠❡✐r♦ ♦r❜✐t❛❧✱ ♦ ♠♦♠❡♥t♦é ♥✉❧♦✱ ❥á ♥♦s ♦✉tr♦s q✉❛tr♦✱ ❝❛❞❛ ♦r❜✐t❛❧ ❛♣♦rt❛ ❝♦♠ ✉♠ ♠♦♠❡♥t✉♠✱ r❡s✉❧t❛♥❞♦ ❛ss✐♠ ♥✉♠ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ❞❡ ✹ ♠❛❣♥ét♦♥s ❞❡ ❇♦❤r✱✐st♦ é✱ ✉♠ ♠❛t❡r✐❛❧ ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❢❡rr♦♠❛❣♥ét✐❝❛s✳ ◆♦s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s✱ ❛❧✐♥❤❛♠❡♥t♦s ❝♦♦♣❡r❛t✐✈♦s ❞❡ ♠♦✲♠❡♥t♦s ❞❡ s♣✐♥ ♦❝♦rr❡♠ ❡♠ ✈♦❧✉♠❡s ❣r❛♥❞❡s ✭❡♠ r❡❧❛çã♦ ❛♦ ✈♦❧✉♠❡ ✻✽ ❋✐❣✉r❛ ✸✳✹ ✕ ❆tr❛✈és ❞♦ ❞✐❛❣r❛♠❛ ❞❡ ▲✐♥✉s P❛✉❧✐♥❣✱ ♦❜té♠✲s❡ ❛ ❞✐s✲ tr✐❜✉✐çã♦ ❞♦s ❡❧étr♦♥s ♥♦s ♦r❜✐t❛✐s✳ ◆♦ ❝❛s♦ ❞♦ ❢❡rr♦ sã♦ ✹ ♠♦♠❡♥t♦s❛♥❣✉❧❛r❡s ❞❡ s♣✐♥ ♥ã♦ ♥✉❧♦s✱ ✐st♦ é✱ ✹ ♠❛❣♥ét♦♥s ❞❡ ❇♦❤r✳ ✭❛✮ ❉✐str✐❜✉✐çã♦ ❞❡ P❛✉❧✐♥❣✳ ✭❜✮ ❙♣✐♥s ♥♦s ❖r❜✐t❛✐s ❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳♠❛❣♥ét✐❝♦ ❞♦s ❞✐♣♦❧♦s ♣♦r ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡✳ ❊st❛ ♠❛❣♥❡t✐③❛çã♦ ❞á♦r✐❣❡♠ ❛♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s✳✸✳✶✳✺ ❉♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s ✭♦✉✱ ❞❡ ❲❡✐ss✮✿ ✉♠❛ q✉❡stã♦ ❡♥❡r✲ ❣ét✐❝❛❱ár✐♦s ✧s♣✐♥s✧❞❡ ❡❧étr♦♥s ♦r✐❡♥t❛❞♦s ❡♠ ✉♠❛ ♠❡s♠❛ ❞✐r❡çã♦ ♥♦ ❝r✐st❛❧ ❞❡ ❢❡rr♦ ❢♦r♠❛♠ ♦ q✉❡ s❡ ❝❤❛♠❛ ❞❡ ❞♦♠í♥✐♦ ♠❛❣♥ét✐❝♦✳ ❊st❡ t❡r♠♦ ❢♦✐ ❝✉♥❤❛❞♦ ♣♦r ❲❡✐ss ❡♠ ✶✾✵✻✱ ❛✐♥❞❛ ❝♦♠♦ s❡♥❞♦ ✉♠❛ ❤✐♣ó✲t❡s❡ ♥❛ q✉❛❧ ❛ ♠❛❣♥❡t✐③❛çã♦ ❡s♣♦♥tâ♥❡❛ é ✐❣✉❛❧ à ♠❛❣♥❡t✐③❛çã♦ ❞❡ s❛t✉r❛çã♦ ❞♦ ❞♦♠í♥✐♦ ❡ s❡✉s ❧✐♠✐t❡s ❞❡✜♥✐❞♦s ♣♦r ✉♠ ❝❛♠♣♦ ♠♦❧❡❝✉✲❧❛r✳ ❙♦♠❡♥t❡ ❡♠ ✶✾✹✾ ❛♣❛r❡❝❡✉ ❛ ❡✈✐❞ê♥❝✐❛ ❡①♣❡r✐♠❡♥t❛❧ ❞♦ ❝♦♥❝❡✐t♦❞❡ ❞♦♠í♥✐♦ ♠❛❣♥ét✐❝♦✱ ❞❡♠♦♥str❛❞♦ ♣♦r ❲✐❧❧✐❛♠s✱ ❇♦r③♦rt ❡ ❙❤♦❝❦❧❡② ✻✾ ❖s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s sã♦ ❝♦♥st✐t✉í❞♦s ♣♦r ❡st❡s ❞♦♠í♥✐♦s❢♦r♠❛♥❞♦ r❡❣✐õ❡s ✈♦❧✉♠étr✐❝❛s ♠✐❝r♦s❝ó♣✐❝❛s ♦♥❞❡ ♦s ♠♦♠❡♥t♦s ❞❡ ❞✐✲♣♦❧♦ ♠❛❣♥ét✐❝♦ s❡ ❡♥❝♦♥tr❛♠ ❛❧✐♥❤❛❞♦s✱ ♣r♦❝✉r❛♥❞♦ ❛ ♠✐♥✐♠✐③❛çã♦ ❞❛❡♥❡r❣✐❛✱ ❝♦♠ ❛s r❡❣✐õ❡s ✈✐③✐♥❤❛s✳ ❆ ♠❛❣♥✐t✉❞❡ ❞♦ ❝❛♠♣♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ M ♣❛r❛ ✉♠ só❧✐❞♦ ❝♦♠♦✉♠ t♦❞♦ é ❛ s♦♠❛ ✈❡t♦r✐❛❧ ❞❛s ♠❛❣♥❡t✐③❛çõ❡s ❞❡ t♦❞♦s ♦s ❞♦♠í♥✐♦s✱♦♥❞❡ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ❝❛❞❛ ❞♦♠í♥✐♦ é ♣♦♥❞❡r❛❞❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ s✉❛ ❢r❛çã♦ ✈♦❧✉♠étr✐❝❛✳ ◆♦ ❝❛s♦ ❞❡ ✉♠❛ ❛♠♦str❛ ♥ã♦ ♠❛❣♥❡t✐③❛❞❛✱ ❛s♦♠❛ ✈❡t♦r✐❛❧ ❛♣r♦♣r✐❛❞❛♠❡♥t❡ ♣♦♥❞❡r❛❞❛ ❞❛s ♠❛❣♥❡t✐③❛çõ❡s ❞❡ t♦❞♦s♦s ❞♦♠í♥✐♦s é ✐❣✉❛❧ ❛ ③❡r♦✳ ❆ ❋✐❣✉r❛ ✸✳✺ ❛♣r❡s❡♥t❛ ✉♠❛ ✐♠❛❣❡♠ ❞❡ ♠❡t❛❧♦❣r❛✜❛ ❡✈✐❞❡♥❝✐✲❛♥❞♦ ♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s✳✸✳✶✳✺✳✶ P❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ ❈❛❞❛ ❞♦♠í♥✐♦ ❡stá s❡♣❛r❛❞♦ ❞♦ ❛❞❥❛❝❡♥t❡ ♣♦r ✉♠❛ ③♦♥❛ ❞❡ tr❛♥✲ s✐çã♦ ✭✐♥t❡r❢❛❝❡✮✳ ❊st❛s ③♦♥❛s ❝❤❛♠❛♠✲s❡ ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ ♦✉ ♣❛r❡✲❞❡s ❞❡ ❇❧♦❝❤✱ ❡♠ ❤♦♠❡♥❛❣❡♠ ❛ ❋❡❧✐① ❇❧♦❝❤ q✉❡✱ ❡♠ ✶✾✸✷✱ ❡❧❛❜♦r♦✉ ❛♣r✐♠❡✐r❛ ❡①♣❧✐❝❛çã♦ t❡ór✐❝❛ ♣❛r❛ ❛ ❡str✉t✉r❛ ❞❛s ♣❛r❡❞❡s ✭❈❯▲▲■❚❨❀●❘❆❍❆▼✱ ✷✵✵✾✮✳ ❆ ❋✐❣✉r❛ ✸✳✻ r❡♣r❡s❡♥t❛ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡ ❛ ❡str✉✲ ◦ t✉r❛ ❞❡ ✉♠❛ ♣❛r❡❞❡ ❞❡ ❞♦♠í♥✐♦ ❞❡ ✶✽✵ ✱ ✐st♦ é✱ ✉♠❛ ♣❛r❡❞❡ q✉❡ s❡♣❛r❛❞♦✐s ❞♦♠í♥✐♦s ❝✉❥❛ ♠❛❣♥❡t✐③❛çã♦ t❡♠ ✐❣✉❛❧ ❞✐r❡çã♦✱ ♠❛s s❡♥t✐❞♦s ♦♣♦s✲ t♦s✳ ❆ ❋✐❣✉r❛ ✸✳✼ ❛♣r❡s❡♥t❛ ✉♠❛ ♠❡t❛❧♦❣r❛✜❛ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r❢❛❜r✐❝❛❞♦ ❝♦♠ ❛ç♦ ✶✵✶✵✱ ♥❛ ❈❤✐♥❛✳ ❆s ♣r♦♣r✐❡❞❛❞❡s ❢❡rr♦♠❛❣♥ét✐❝❛s ❝♦♠ ✐♥t❡r❡ss❡ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛❞♦ ♣r♦❥❡t♦ ❞❡ ♠áq✉✐♥❛s✱ t❛✐s ❝♦♠♦ ❛ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛ ✭❡stát✐❝❛ ❡❞✐♥â♠✐❝❛✮✱ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ ❡t❝✳✱ ❞❡♣❡♥❞❡♠ ❢♦rt❡♠❡♥t❡ ❞❛ ❡str✉t✉r❛❞♦s ❞♦♠í♥✐♦s ❡ ❞❛ ❢♦r♠❛ ❝♦♠♦ ❡st❡s r❡s♣♦♥❞❡♠ s♦❜ ❛ ❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦✳ ❆ ❡str✉t✉r❛ ❞♦s ❞♦♠í♥✐♦s s❡ ❛❥✉st❛ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ t❡♥❞❡ ❛♠✐♥✐♠✐③❛r ❛ ❡♥❡r❣✐❛ ✐♥t❡r♥❛ ❞♦ s✐st❡♠❛ ✭❞❛ ❛♠♦str❛✮✱ ❛ q✉❛❧ é ❝♦♠♣♦st❛♣❡❧❛ s♦♠❛ ❞❡ q✉❛tr♦ t❡r♠♦s ❞✐st✐♥t♦s✿ ❼ ❊♥❡r❣✐❛ ❞❡ ❛♥✐s♦tr♦♣✐❛ ♠❛❣♥❡t♦❝r✐st❛❧✐♥❛✱ E an ❀❼ ❊♥❡r❣✐❛ ♠❛❣♥❡t♦stát✐❝❛✱ E ms ❀❼ ❊♥❡r❣✐❛ ❞❡ tr♦❝❛✱ E t ❀❼ ❊♥❡r❣✐❛ ❞❡ ♠❛❣♥❡t♦str✐❝çã♦✱ ♦✉ ♠❛❣♥❡t♦❡❧ást✐❝❛✱ E mt ✳ ❆ ❋✐❣✉r❛ ✸✳✽ ❛✉①✐❧✐❛ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ss❡ ❢❡♥ô♠❡♥♦✳ ❙✉❛ ❞❡s✲ ✼✵ ❋✐❣✉r❛ ✸✳✺ ✕ ❖ t❛♠❛♥❤♦ ❞♦s ❞♦♠í♥✐♦s ❡stá ♥❛ ❡s❝❛❧❛ ♠✐❝r♦♠étr✐❝❛ ❡✱♣❛r❛ ✉♠ ♠❛t❡r✐❛❧ ♣♦❧✐❝r✐st❛❧✐♥♦✱ ❝❛❞❛ ❣rã♦ ♣♦❞❡ ❝♦♥t❡r ♠❛✐s ❞❡ ✉♠ ❞♦✲♠í♥✐♦✳❋♦♥t❡✿♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ❡♥s❛✐♦ ❞❡ ♠❛t❡r✐❛✐s ♥♦❈❈❚✱ ♥❛ ❯❉❊❙❈✳✸✳✶✳✻ ▼❛❣♥❡t✐③❛çã♦ ❡ s✉s❝❡♣tâ♥❝✐❛ ♠❛❣♥ét✐❝❛ ◗✉❛♥❞♦ ✉♠ ♠❛t❡r✐❛❧ ♠❛❣♥ét✐❝♦ é s✉❜♠❡t✐❞♦ ❛ ✉♠ ❝❛♠♣♦ ❡①✲ t❡r♥♦✱ ❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ é ❞❛❞❛ ♣❡❧❛ s♦♠❛ ❞♦s ❡❢❡✐t♦s ❞❡✈✐❞♦s ❛♦❝❛♠♣♦ ❡①t❡r♥♦ ❡ ❛♦ ✈❡t♦r ❝❤❛♠❛❞♦ ♣♦❧❛r✐③❛çã♦ ♠❛❣♥ét✐❝❛✱ ✐st♦ é✿ B = µ (H + M ). ✼✶ ❋✐❣✉r❛ ✸✳✻ ✕ ■❧✉str❛çã♦ ❞❛ ♣❛r❡❞❡ ❞♦ ❞♦♠í♥✐♦ ♠❛❣♥ét✐❝♦ q✉❡ s❡♣❛r❛ ◦❞♦✐s ❞♦♠í♥✐♦s ❝✉❥♦s ♠♦♠❡♥t♦s ❛tô♠✐❝♦s ♠✉❞❛♠ ❛ ♦r✐❡♥t❛çã♦ ❡♠ ✶✽✵ ✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭●❖◆➬❆▲❱❊❙✲▼❖◆❚❊■❘❖✱ ✷✵✶✵✮ ❊♠ ♠ó❞✉❧♦✱ ❛ ❊q✉❛çã♦ ✭✸✳✶✮ ♣♦❞❡ s❡r ❝♦❧♦❝❛❞❛ s♦❜ ❛ ❢♦r♠❛✿M B = µ 1 + H. ✭✸✳✷✮H ❖ t❡r♠♦ ❡♥tr❡ ♣❛rê♥t❡s❡s r❡♣r❡s❡♥t❛ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ ❞♦ ♠❛t❡r✐❛❧✱ ♣♦rt❛♥t♦✿B = µ µ r ✭✸✳✸✮ H,❡✱ ✜♥❛❧♠❡♥t❡ B = µH. ✭✸✳✹✮❆ ❋✐❣✉r❛ ✸✳✾ ❛✉①✐❧✐❛ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ❢❡♥ô♠❡♥♦ ❞❡ ♠❛❣♥❡t✐✲ ③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ♠❛❣♥ét✐❝♦✳H ◆♦ ❝❛s♦ ❞♦s ♠❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s ♦ ❛♣♦rt❡ ❞♦ t❡r♠♦ µ é♠✉✐t♦ ♣❡q✉❡♥♦✱ ♥❡st❡ ❝❛s♦✱ ♣♦❞❡♠ s❡ ❢❛③❡r ❛❧❣✉♠❛s s✐♠♣❧✐✜❝❛çõ❡s✳ ❆❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ♣♦❞❡ s❡r ❛♣r♦①✐♠❛❞❛ ❛✿ M Mµ = 1 + , r → µ r − 1 = ✼✷ ❋✐❣✉r❛ ✸✳✼ ✕ ▼❡t❛❧♦❣r❛✜❛ ❞♦ ♥ú❝❧❡♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❢❛❜r✐❝❛❞♦ ♥❛❈❤✐♥❛ ❛ç♦ ✶✵✶✵✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ❡♥s❛✐♦ ❞❡ ♠❛t❡r✐❛✐s ♥♦❈❈❚✱ ♥❛ ❯❉❊❙❈✳ r❝♦♠♦ µ ≫ 1 ✭❝♦♥❞✐çã♦ ❞❡ ❢❡rr♦♠❛❣♥❡t✐s♠♦✮✱ M µ r = . ✭✸✳✺✮H ❆ ❝♦♥❞✐çã♦ ❞❡ ❢❡rr♦♠❛❣♥❡t✐s♠♦ ♦❝♦rr❡ ❡♠ ♠❛t❡r✐❛✐s ♣❛r❛ ♦s q✉❛✐s♦s át♦♠♦s tê♠ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ ♣❡r♠❛♥❡♥t❡ r❡❧❛t✐✈❛♠❡♥t❡ ❣r❛♥❞❡✳❆❧é♠ ❞✐st♦✱ ♣♦ss✉❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ s❡r❡♠ ♠❛❣♥❡t✐③❛❞♦s ❢♦rt❡♠❡♥t❡♣♦r ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ♠❛♥t❡♥❞♦ ✉♠ ❣r❛✉ ❝♦♥s✐❞❡rá✈❡❧ ❞❡ ♠❛❣♥❡✲ t✐③❛çã♦ q✉❛♥❞♦ r❡t✐r❛❞♦s ❞♦ ❝❛♠♣♦✳ ❙♦❜r❡ ❡st❛ ❤✐♣ót❡s❡ s❡ ♦❜té♠ ❛ ❝✉r✈❛ ❞♦ ✈❡t♦r ❞❡ ♠❛❣♥❡t✐③❛çã♦M H❡♠ ❢✉♥çã♦ ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H✱ ❡①♣r❡ss♦ ❝♦♠♦ M = µ r ✳ ❆ s✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ χ m ❞❡ ✉♠ ♠❛t❡r✐❛❧ é ❛ s✉❛ ❝❛♣❛✲❝✐❞❛❞❡ ❞❡ ✏❛♠♣❧✐❛r✑ ♦ ♥ú♠❡r♦ ❞❛s ❧✐♥❤❛s ❞❡ ✢✉①♦ q✉❡ ♣❛ss❛♠ ♣♦r ❡❧❡✱❞❡✜♥✐❞♦ ❝♦♠♦✿ M χ = . m ✭✸✳✻✮ ✼✸ ❋✐❣✉r❛ ✸✳✽ ✕ ❆ ❡①✐stê♥❝✐❛ ❞❡ ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s é r❡s✉❧t❛❞♦ ❞❛ ♠✐♥✐✲♠✐③❛çã♦ ❞❡ ❡♥❡r❣✐❛✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳ = µ◆♦ ❝❛s♦ ❞❡ ❢❡rr♦r❡ss♦♥â♥❝✐❛✱ t❡♠♦s q✉❡ χ m r ✳❊st❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ✧❛♠♣❧✐❛r ❛s ❧✐♥❤❛s ❞❡ ❢♦rç❛✧é ✉t✐❧✐③❛❞❛ ♣❛r❛ > 500❝❧❛ss✐✜❝❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❛❣♥ét✐❝♦✱ ♥❡st❡ ❝❛s♦✱ X m s❡❣✉♥❞♦♦ ❣rá✜❝♦ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛✱ ❛t❡♥❞❡♥❞♦ ♦ ✈❛❧♦r ❞❡ X m ♦s ♠❛✲ t❡r✐❛✐s sã♦ ❝❧❛ss✐✜❝❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❚❛❜❡❧❛ ✸✳✸✳❚❛❜❡❧❛ ✸✳✸ ✕ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ♠❛t❡r✐❛✐s q✉❛♥t♦ à s✉s❝❡♣t✐❜✐❧✐❞❛❞❡ ♠❛❣✲♥ét✐❝❛ ❡ ❛ r❡❧❛çã♦ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✳ χ µ/µ▼❛t❡✐❛❧ m P❛r❛♠❛❣♥ét✐❝♦ ❃✵ ❃✶❉✐❛♠❛❣♥ét✐❝♦ ❁✵ ❁✶ ❋❡rr♦♠❛❣♥ét✐❝♦ ≫✵ ≫✶❋❡rr✐♠❛❣♥ét✐❝♦ ≫✵ ≫✶ ❆♥t✐❢❡rr♦♠❛❣♥ét✐❝♦ ❃✵ ❃✶❆ ❋✐❣✉r❛ ✸✳✶✵ ❛♣r❡s❡♥t❛ ❛ ❝✉r✈❛ ❛♣r♦①✐♠❛❞❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❡st✉❞❛❞♦ ♥❡ss❡ tr❛❜❛❧❤♦✳ ✸✳✶✳✻✳✶ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧❯♠ ♠❛t❡r✐❛❧ ♠❛❣♥ét✐❝♦ s✉❜♠❡t✐❞♦ à ❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥é✲ t✐❝♦ ❝r❡s❝❡♥t❡ H ✈❛✐ ❛✉♠❡♥t❛♥❞♦ ❛ s✉❛ ♠❛❣♥❡t✐③❛çã♦ ✭♦✉✱ ❛ s✉❛ ♣♦❧❛r✐✲ ✼✹ ❋✐❣✉r❛ ✸✳✾ ✕ ▼❡❝❛♥✐s♠♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♥ã♦✲❧✐♥❡❛r ❞♦ ♥ú❝❧❡♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r❛té s❡r ❛t✐♥❣✐❞❛ ❛ ❝❤❛♠❛❞❛ ♠❛❣♥❡t✐③❛çã♦ té❝♥✐❝❛✳ ❖ t❡r♠♦ ✏♠❛❣♥❡t✐③❛✲çã♦ té❝♥✐❝❛✑ ❞❡✈❡ ❡ss❡♥❝✐❛❧♠❡♥t❡ ♣❡❧❛ ✈❛r✐❛çã♦ ❞❛ ❞✐r❡çã♦ ❞♦s ❞♦♠í♥✐♦s♠❛❣♥ét✐❝♦s s❛t✉r❛❞♦s ❡ ♥ã♦ ♣❡❧❛ ✈❛r✐❛çã♦ ❞❛ r❡s♣❡❝t✐✈❛ ♠❛❣♥❡t✐③❛çã♦❡s♣♦♥tâ♥❡❛ ✭❈❯▲▲■❚❨❀ ●❘❆❍❆▼✱ ✷✵✵✾✮✳ ▼❡❞✐♥❞♦ ❛ ✐♥❞✉çã♦ ♠❛❣✲♥ét✐❝❛ ♥♦ ♠❛t❡r✐❛❧ ✭♦✉✱ ❞❡♥s✐❞❛❞❡ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦✮✱ B✱ ❡♠ ❢✉♥çã♦❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H ❛♣❧✐❝❛❞♦ ❛ ✉♠❛ ❛♠♦str❛ ❢❡rr♦♠❛❣♥ét✐❝❛ ❞❡s✲♠❛❣♥❡t✐③❛❞❛✱ ♦❜té♠✲s❡ ❛ ❝❤❛♠❛❞❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧ ♦✉✱❝✉r✈❛ ❞❡ ♣r✐♠❡✐r❛ ♠❛❣♥❡t✐③❛çã♦✱ ♦♥❞❡ s❡ ♦❜s❡r✈❛ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦♥ã♦ ❧✐♥❡❛r ❡♥tr❡ ❛ ♠❛❣♥❡t✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ❡ ♦ ❝❛♠♣♦ ❡①t❡r♥♦ ❛♦ q✉❛❧é s✉❜♠❡t✐❞♦✳ ❉✉r❛♥t❡ ❛ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✱❛ ♣❛rt✐r ❞♦ ❡st❛❞♦ ❞❡s♠❛❣♥❡t✐③❛❞♦✱ ♣♦❞❡♠ ❞✐st✐♥❣✉✐r✲s❡ ♥❛ ❝✉r✈❛ BH✈ár✐❛s ③♦♥❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛ ❞✐❢❡r❡♥t❡s ❡t❛♣❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠❛❣✲♥❡t✐③❛çã♦✳ ◆❛ ❋✐❣✉r❛ ✸✳✶✶ ❡stá ❛♣r❡s❡♥t❛❞❛ ❡sq✉❡♠❛t✐❝❛♠❡♥t❡ ✉♠❛❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧✳ ❆ ❋✐❣✉r❛ ✸✳✶✷ ❛♣r❡s❡♥t❛ ♦ ♣r♦❝❡ss♦ ❞❡ ✼✺ ❋✐❣✉r❛ ✸✳✶✵ ✕ ❈✉r✈❛ ❛♣r♦①✐♠❛❞❛ ❞❛ ♠❛❣♥❡t✐③❛çã♦ ❡♠ ✉♠ ♠❛t❡r✐❛❧ ❢❡r✲ r r♦♠❛❣♥ét✐❝♦ ✭♥ã♦ ❧✐♥❡❛r✮ ♦❜t✐❞❛ ♣❡❧♦ ♣r♦❞✉t♦ ♣♦♥t♦ ❛ ♣♦♥t♦ M = Hµ❞♦ ❣rá✜❝♦ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ✈❡rs✉s ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ◆❛ ③♦♥❛ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ✐rr❡✈❡rsí✈❡❧ ❞❛s ♣❛r❡❞❡s✱ ♦s ❞♦♠í♥✐♦s t❛♠❜é♠ r♦❞❛♠ ❞❡ ❢♦r♠❛ ❛ ❛❧✐♥❤❛r ❛ s✉❛ ♠❛❣♥❡t✐③❛çã♦ ❡s♣♦♥tâ♥❡❛ ❝♦♠♦s ❡✐①♦s ❝r✐st❛❧♦❣rá✜❝♦s ♣r❡❢❡r❡♥❝✐❛✐s✱ ❝✉❥❛ ❞✐r❡çã♦ s❡❥❛ ❛ ♠❛✐s ♣ró①✐♠❛❞❛q✉❡❧❛ ❞♦ ❝❛♠♣♦ H✳ ❚♦❞♦ ❡st❡ ♣r♦❝❡ss♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ é ✐rr❡✈❡rsí✲✈❡❧✳ ◆❛ r❡❣✐ã♦✱ ♦ ♠♦✈✐♠❡♥t♦ ❞❛s ♣❛r❡❞❡s ♥ã♦ s❡ ❞á ❞❡ ✉♠ ♠♦❞♦ ❝♦♥tí✲♥✉♦✱ ♠❛s s✐♠ ♣♦r ✈❛r✐❛çõ❡s ❛❜r✉♣t❛s ❝♦♥❤❡❝✐❞❛s ♣♦r s❛❧t♦s ❞❡ ❇❛r❦❤❛✉✲ s❡♥✱ ❡♠ ❤♦♠❡♥❛❣❡♠ ❛♦ ❢ís✐❝♦ ❛❧❡♠ã♦ ❍❡✐♥r✐❝❤ ❇❛r❦❤❛✉s❡♥ q✉❡✱ ❡♠✶✾✶✾✱ ♠♦♥t♦✉ ✉♠❛ ❡①♣❡r✐ê♥❝✐❛ ❡♠ q✉❡ s❡ ♦✉✈✐❛♠ s✉❝❡ss✐✈♦s ❡st❛❧✐❞♦s❝♦rr❡s♣♦♥❞❡♥t❡s às ✈❛r✐❛çõ❡s ❞❡s❝♦♥tí♥✉❛s ♥❛ ♠❛❣♥❡t✐③❛çã♦ ❞♦ ♠❛t❡✲ r✐❛❧✳ ❖s s❛❧t♦s sã♦ ❣❡r❛❞♦s ♣❡❧❛ ❛♥❝♦r❛❣❡♠ ❡ ❧✐❜❡rt❛çã♦ ❞❛s ♣❛r❡❞❡s❞❡ ❞♦♠í♥✐♦s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ♣r❡s❛s ✭♣r♦❞✉t♦ ❞❡ ❞❡❢❡✐t♦s ♥♦ ♠❛t❡r✐❛❧✱✐♠♣✉r❡③❛s✱ t❡♥sõ❡s ❧♦❝❛❧✐③❛❞❛s✱ ❧✐♠✐t❡s ❞❡ ❣rã♦✮✳ ❖ ♠♦✈✐♠❡♥t♦ ❛❜r✉♣t♦♣r♦❞✉③ ✉♠❛ ✈❛r✐❛çã♦ ❛❜r✉♣t❛ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦✱ ♦ q✉❛❧ t❡r♠✐♥❛ ✐♥✲❞✉③✐♥❞♦ ✉♠❛ ❝♦rr❡♥t❡ ♥❛ r❡❣✐ã♦ ❣❡r❛♥❞♦ ✉♠❛ ♣❡r❞❛ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ✼✻ ❋✐❣✉r❛ ✸✳✶✶ ✕ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣✲♥ét✐❝♦✱ ♥❛ r❡❣✐ã♦ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❞♦♠í♥✐♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳❋✐❣✉r❛ ✸✳✶✷ ✕ Pr♦❝❡ss♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ s♦❜ ♦ ❡♥❢♦q✉❡ ❞♦❜❛❧❛♥ç♦ ❡♥❡r❣ét✐❝♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮ ❆s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s t♦t❛✐s q✉❡ ♦❝♦rr❡♠ ♥✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦✲♠❛❣♥ét✐❝♦ q✉❛♥❞♦ s✉❥❡✐t♦ à ❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ❞❡ ✐♥❞✉çã♦ B ✈❛r✐á✈❡❧♥♦ t❡♠♣♦ sã♦ ❞❛❞❛s ♣♦r✿ ✼✼ ♦♥❞❡ P h r❡♣r❡s❡♥t❛ ❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡✱ P h sã♦ ❛s ❝❤❛♠❛❞❛s ♣❡r❞❛s♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ❝❧áss✐❝❛s ❡ P exc sã♦ ❛s ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s❞❡ ❋♦✉❝❛✉❧t ❡①❝❡❞❡♥t❡s ♦✉✱ ❛♥ô♠❛❧❛s✳ P♦r ✈❡③❡s ♣♦❞❡ t❛♠❜é♠ s❡r❛❞♦t❛❞❛ ❛ ❞✐✈✐sã♦ ❡♠ ♣❡r❞❛s ❡stát✐❝❛s ❡ ❞✐♥â♠✐❝❛s ❡♠ q✉❡✱ ❛s ♣r✐♠❡✐r❛s❝♦rr❡s♣♦♥❞❡♠ às ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡✱ ❡ ❛s s❡❣✉♥❞❛s às ♣❡r❞❛s ♣♦r❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ❝❧áss✐❝❛s ❡ ❡①❝❡❞❡♥t❡s✳ ❆t✉❛❧♠❡♥t❡ ❡①✐st❡♠ ❞✉❛s ❧✐♥❤❛s ❞❡ ✐♥✈❡st✐❣❛çã♦ ♣r✐♥❝✐♣❛✐s q✉❛♥t♦à ✐♥t❡r♣r❡t❛çã♦ ❢ís✐❝❛ ❞♦s ✈ár✐♦s ♠❡❝❛♥✐s♠♦s ❞❡ ♣❡r❞❛s✳ ❙❡❣✉♥❞♦ ❇❡r✲ t♦tt✐✱ ❈✉❧❧✐t② ❡ ●r❛❤❛♠ ✭❇❊❘❚❖❚❚■✱ ✶✾✽✽❀ ❈❯▲▲■❚❨❀ ●❘❆❍❆▼✱✷✵✵✾❀ ●❘❆❍❆▼✱ ✶✾✽✷✮✱ ❡♥tr❡ ♦✉tr♦s✱ ♥ã♦ ❡①✐st❡ ❞✐st✐♥çã♦ ❢ís✐❝❛ ❡♥tr❡♦s ♣r♦❝❡ss♦s ❞❡ ♠❛❣♥❡t✐③❛çã♦ q✉❡ ♦❝♦rr❡♠ s♦❜ ❡①❝✐t❛çã♦ ❉❈ ♦✉ ❆❈✱✐st♦ é✱ q✉❡r ❡♠ r❡❣✐♠❡ q✉❛s❡ ❡stát✐❝♦ q✉❡r ❡♠ r❡❣✐♠❡ ✈❛r✐á✈❡❧ ♥♦ t❡♠♣♦✱❡st❡s ❛✉t♦r❡s ❝♦♥s✐❞❡r❛♠ q✉❡ ❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s r❡s✉❧t❛♠ ❞❡ ❞✐ss✐✲♣❛çã♦ ❞❡ ❝❛❧♦r ♣♦r ❡❢❡✐t♦ ❞❡ ❏♦✉❧❡ r❡s✉❧t❛♥t❡ ❞❡ ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t✐♥❞✉③✐❞❛s ♥♦ ♠❛t❡r✐❛❧✳ ❖ q✉❡ ❞✐❢❡r❡ ❡♥tr❡ ♦s ✈ár✐♦s t✐♣♦s ❞❡ ♣❡r❞❛s é q✉❛❧ ♦ ♠❡❝❛♥✐s♠♦ ✐♥t❡r♥♦ q✉❡ ❛s ♦r✐❣✐♥❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ▼✳ ❋✳ ❈❛♠♣♦s❡ ❛ ❡q✉✐♣❡ ❞❡ ❋✳ ▲❛♥❞❣r❛❢ ✭❈❆▼P❖❙❀ ❊▼❯❘❆❀ ▲❆◆❉●❘❆❋✱ ✷✵✵✻❀▲❆◆❉●❘❆❋❀ ❊▼❯❘❆❀ ❈❆▼P❖❙✱ ✷✵✵✽✮✱ ❝♦♥s✐❞❡r❛♠ q✉❡ ❛s ♣❡r❞❛s♣♦r ❤✐st❡r❡s❡ ♥ã♦ tê♠ ♦r✐❣❡♠ ❡♠ ❝♦rr❡♥t❡s ✐♥❞✉③✐❞❛s ♥♦ ♠❛t❡r✐❛❧ ❞✉✲ r❛♥t❡ ♦ ❝✐❝❧♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ♠❛s✱ s✐♠✱ ♥❛ ♥✉❝❧❡❛çã♦ ❡ ❛♥✐q✉✐❧❛çã♦ ❞❡♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s✳✸✳✶✳✼ ▼♦❞❡❧♦s ❞❡ ♣❡r❞❛s ♣❛r❛ ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s ❆ ♣❛rt✐r ❞❛s ❡str✉t✉r❛s t❡ór✐❝❛s q✉❡ ❞❡s❝r❡✈❡♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦❞♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s✱ ❢♦✐ ♣♦ssí✈❡❧ ❞✐st✐♥❣✉✐r três t✐♣♦s ♣r✐♥❝✐♣❛✐s❞❡ ♣❡r❞❛s ♥❡ss❡s ♠❛t❡r✐❛✐s✿ ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡✱ ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s♣❛r❛s✐t❛s ❡ ♣❡r❞❛s ❡①❝❡❞❡♥t❡s✳✸✳✶✳✼✳✶ P❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡ ♣❡r❞❛s ♠❛❣♥ét✐❝❛s t♦t❛✐s h ❆s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡✱ P ✱ ♥✉♠❛ ❛♠♦str❛ ❞❡ ♠❛t❡r✐❛❧ ❢❡rr♦✲♠❛❣♥ét✐❝♦ sã♦ ♣r♦♣♦r❝✐♦♥❛✐s à ár❡❛ ❞♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡✱ ♦❜t✐❞♦ ❡♠ r❡❣✐♠❡ q✉❛s❡ ❡stát✐❝♦✱ ♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦ ✈♦❧✉♠❡ ❞❛ ❛♠♦str❛✱ v ❡ ♣❡❧❛❢r❡q✉ê♥❝✐❛ ❞❡ ♦♣❡r❛çã♦ f✱ ✐st♦ é✱I P = f v HdB h ✭✸✳✽✮ ✼✽ P♦ré♠✱ s❡ ♦ ♠❡s♠♦ ❝á❧❝✉❧♦ ❢♦r ❡❢❡t✉❛❞♦ ❛ ♣❛rt✐r ❞♦ ❝✐❝❧♦ ❞❡ ❤✐st❡✲ r❡s❡ ♦❜t✐❞♦ ♥❛s ❢r❡q✉ê♥❝✐❛s ✐♥❞✉str✐❛✐s ❞❡ ✺✵ ♦✉ ✻✵ ❤❡rt③✱ ♦✉ s✉♣❡r✐♦r❡s✱sã♦ ❛❞q✉✐r✐❞♦s ❞❛❞♦s r❡❧❛t✐✈♦s às ♣❡r❞❛s ♠❛❣♥ét✐❝❛s t♦t❛✐s ❞❛ ❛♠♦str❛✳❖✉ s❡❥❛✱ ❡♠ r❡❣✐♠❡ ❞✐♥â♠✐❝♦✱ ❛ ár❡❛ ❞♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ é ✉♠❛ ♠❡❞✐❞❛❞❛ ❡♥❡r❣✐❛ t♦t❛❧ ❞✐ss✐♣❛❞❛ ♥♦ ♠❛t❡r✐❛❧ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡✳ ◆♦ ✜♠❞♦ sé❝✉❧♦ ❳■❳✱ ❈✳P✳ ❙t❡✐♥♠❡t③ ♦❜t❡✈❡ ✉♠❛ ❢ór♠✉❧❛ ❡♠♣ír✐❝❛ q✉❡ ♣❡r✲♠✐t✐❛ ❝❛❧❝✉❧❛r ❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥❞✉çã♦ ♠á①✐♠❛♥♦ ♠❛t❡r✐❛❧✱ B m ✱ q✉❡ é✱ α h h P = K B f h h m ✭✸✳✾✮❡♠ q✉❡ K é ❛ ❝♦♥st❛♥t❡ ❞❡ ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡ q✉❡ ❞❡♣❡♥❞❡ ❞❛s h♣r♦♣r✐❡❞❛❞❡s ❞♦ ♠❛t❡r✐❛❧ ❡ α é ♦ ❝❤❛♠❛❞♦ ❝♦❡✜❝✐❡♥t❡ ♦✉ ❡①♣♦❡♥t❡ ❞❡❙t❡✐♥♠❡t③ ❡ q✉❡✱ ♥❛ ❡q✉❛çã♦ ♦r✐❣✐♥❛❧ ❞❡ ❙t❡✐♥♠❡t③ ✈❛❧✐❛ ❛♣r♦①✐♠❛❞❛✲♠❡♥t❡ ✶✱✻ ♣❛r❛ ♦s ❛ç♦s✳ h ❆t✉❛❧♠❡♥t❡ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ α ♣♦❞❡ ✈❛r✐❛r ❡♥tr❡ ✶✱✺ ❡ ✷ ✭❋■❙❍✱✶✾✾✵✮ ♣❛r❛ ✐♥❞✉çõ❡s ♠á①✐♠❛s ❛té ✶✱✷ ❚ ✭▲❆◆❉●❘❆❋✱ ✷✵✵✷✮ ❡✱ ❛❝✐♠❛❞❡ss❡ ✈❛❧♦r ❛té ✶✱✻ ❚✱ ♣♦❞❡♠ ❞❡t❡r♠✐♥❛r✲s❡ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ✈❛❧♦✲ = 5 r❡s q✉❡ ♣♦❞❡♠ ❝❤❡❣❛r ❛ α h ✭▲❆◆❉●❘❆❋❀ ❊▼❯❘❆❀ ❈❆▼P❖❙✱✷✵✵✽✮✳ ❖ ❛✉♠❡♥t♦ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❙t❡✐♥♠❡t③ ❛❝✐♠❛ ❞❡ ❞❡t❡r♠✐♥❛❞♦s✈❛❧♦r❡s ❞❡ B m ✱ t❛♠❜é♠ ❢♦✐ r❡❢❡r✐❞♦ ♣♦r ✭❇❖❩❖❘❚❍✱ ✷✵✵✵✮✳ ❖ ♠❡❝❛✲♥✐s♠♦ ❢ís✐❝♦ q✉❡ ❡stá ♥❛ ♦r✐❣❡♠ ❞❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❛✐♥❞❛ ♥ã♦ é❝♦♥s❡♥s✉❛❧✳ ❙❡❣✉♥❞♦ ●✳ ❇❡rt♦tt✐ ✭❇❊❘❚❖❚❚■✱ ✶✾✽✽✮✱ ❈✳ ●r❛❤❛♠ ✭●❘❆❍❆▼✱✶✾✽✷✮ ❡ ❈✉❧❧✐t② ✭❈❯▲▲■❚❨❀ ●❘❆❍❆▼✱ ✷✵✵✾✮✱ ❡♥tr❡ ♦✉tr♦s✱ ❛s ♣❡r❞❛s♣♦r ❤✐st❡r❡s❡ tê♠ ♦r✐❣❡♠ ♥❛s ♠✐❝r♦✲❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ✐♥❞✉③✐❞❛s ♥♦♠❛t❡r✐❛❧✱ t❛✐s ❝♦♠♦ ❛s r❡st❛♥t❡s ❝♦♠♣♦♥❡♥t❡s✳ ❊st❛ ✐❞é✐❛ ❢♦✐ ✐♥✐❝✐❛❧✲♠❡♥t❡ s✉❣❡r✐❞❛ ♣♦r ❇❡❝❦❡r ✭❇❊❈❑❊❘✱ ✶✾✻✸✮✱ ♦ q✉❛❧ ❝♦♥s✐❞❡r♦✉ q✉❡ ♦ú♥✐❝♦ ♠❡❝❛♥✐s♠♦ ❞❡ ♣❡r❞❛s ❡①✐st❡♥t❡ ♥♦s ♠❛t❡r✐❛✐s ♠❛❣♥ét✐❝♦s s❡r✐❛♠❛s ♣❡r❞❛s r❡s✐st✐✈❛s r❡s✉❧t❛♥t❡s ❞❡ ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t✳ ❊♠ s❡✉ ❝♦♥❝❡✐t♦ ❢✉♥❞❛♠❡♥t❛❧✱ ❛ ♦r✐❣❡♠ ❞❛ ❤✐st❡r❡s❡ ❡♥❝♦♥tr❛✲s❡♥♦ ❝❛rát❡r ❞❡s❝♦♥tí♥✉♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ♥❛ ❡s❝❛❧❛ s✉❜✲♠✐❝r♦s❝ó♣✐❝❛✳ ◆❡ss❡ ❡s❝♦♣♦✱ ❛ ♠♦✈✐♠❡♥t❛çã♦ ❞❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦s♦❝♦rr❡ ❞❡ ❢♦r♠❛ ❞✐s❝r❡t❛✱ ✐st♦ é✱ ♣♦r s❛❧t♦s q✉❛♥t✐③❛❞♦s ❡ ♥ã♦ ❛tr❛✈és ❞❡✉♠ ♠♦✈✐♠❡♥t♦ ❝♦♥tí♥✉♦ ❞❛s ♣❛r❡❞❡s✳ ❖✉ s❡❥❛✱ ♠❡s♠♦ ❡♠ ✉♠❛ ❢r❡q✉ê♥✲❝✐❛ ❞❡ ♦♣❡r❛çã♦ ♠✉✐t♦ ❜❛✐①❛ ✭♥❛ ♦r❞❡♠ ❞❡ ♠❍③✮✱ ♥ã♦ ❤á ❝♦♥t✐♥✉✐❞❛❞❡♥♦ ♠♦✈✐♠❡♥t♦✳ ▲♦❣♦✱ ♦s s❛❧t♦s✱ ❝♦♥❤❡❝✐❞♦s ♣♦r s❛❧t♦s ❞❡ ❇❛r❦❤❛✉s❡♥✱♣r♦✈♦❝❛♠ ❧♦❝❛❧♠❡♥t❡ ✈❛r✐❛çã♦ ❞❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ❡✱ ♣♦rt❛♥t♦✱ ♥❛❢♦rç❛ ❡❧❡tr♦♠♦tr✐③ ✐♥❞✉③✐❞❛✳ ❊ss❛ t❡♥sã♦ ♦r✐❣✐♥❛ ♠✐❝r♦❝♦rr❡♥t❡s✱ ❧♦❝❛✲❧✐③❛❞❛s ❡♠ ✈♦❧t❛ ❞♦s s❡❣♠❡♥t♦s ❡♠ ♠♦✈✐♠❡♥t♦ q✉❡ ♣r♦✈♦❝❛♠ ♣❡r❞❛s♣♦r ❡❢❡✐t♦ ❞❡ ❏♦✉❧❡✳ ❆ ♦❝♦rrê♥❝✐❛ ❞♦ ♣r♦❝❡ss♦ ❞❡ ♠♦✈✐♠❡♥t❛çã♦ ♣♦r s❛❧t♦s ❞❡ ❇❛r❦❤❛✉s❡♥ r❡s✉❧t❛ ❞❛ ❛♥❝♦r❛❣❡♠ ❞❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ ❛ ✼✾ ✐♠♣✉r❡③❛s✱ ❞❡❢❡✐t♦s ❝r✐st❛❧✐♥♦s ♦✉ ❧✐♠✐t❡s ❞❡ ❣rã♦✱ ❛s q✉❛✐s só s❡ ❧✐❜❡r✲ t❛♠ q✉❛♥❞♦ ♦ ❝❛♠♣♦ ♥❛ ✈✐③✐♥❤❛♥ç❛ ❞❡ss❛s ♣❛r❡❞❡s é s✉✜❝✐❡♥t❡ ♣❛r❛♣r♦✈♦❝❛r ♦ s❡✉ ❞❡s❧♦❝❛♠❡♥t♦✳✸✳✶✳✼✳✷ ❍✐st❡r❡s❡ ❛tr❛✈és ❞❛ ✈✐sã♦ ❞❡ ❡♥❡r❣✐❛ ♥♦s ❞♦♠í♥✐♦s P♦r ♦✉tr♦ ❧❛❞♦✱ ▼✳ ❈❛♠♣♦s ❡ ❋✳ ▲❛♥❞❣r❛❢ ❡t ❛❧✳ ✭❈❆▼P❖❙❀❊▼❯❘❆❀ ▲❆◆❉●❘❆❋✱ ✷✵✵✻✮✱ ❝♦♥s✐❞❡r❛♠ q✉❡ ❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ r❡s✉❧t❛♠ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❛♥✐q✉✐❧❛çã♦ ❡ ❢♦r♠❛çã♦ ❞❡ ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦♦ q✉❛❧ ♦r✐❣✐♥❛ ❞✐ss✐♣❛çã♦ ✐rr❡✈❡rsí✈❡❧ ❞❡ ❡♥❡r❣✐❛✱ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞❛❡①✐stê♥❝✐❛ ♦✉ ♥ã♦ ❞❡ ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t✳ ❆s ♣❡r❞❛s sã♦ ❞✐r❡t❛♠❡♥t❡♣r♦♣♦r❝✐♦♥❛✐s à ár❡❛ ❞❛s ♣❛r❡❞❡s ♥✉❝❧❡❛❞❛s ❡ ❛♥✐q✉✐❧❛❞❛s ❞✉r❛♥t❡ ✉♠❝✐❝❧♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✭❈❆▼P❖❙❀ ❊▼❯❘❆❀ ▲❆◆❉●❘❆❋✱ ✷✵✵✻✮✳ ❙❡✲❣✉♥❞♦ ❡st❡s ✐♥✈❡st✐❣❛❞♦r❡s ✉♠❛ ❞❛s ♣r♦✈❛s ❞❛ t❡♦r✐❛ q✉❡ ❞❡❢❡♥❞❡♠ é♦ ❢❛t♦ ❞♦ ❡♥✈❡❧❤❡❝✐♠❡♥t♦ ♠❛❣♥ét✐❝♦✱ ♦r✐❣✐♥❛❞♦ ♣❡❧❛s ♠✉❞❛♥ç❛s ❞❛s ❡s✲ tr✉t✉r❛s ❞♦ ❣rã♦ ❞✉r❛♥t❡ ♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞♦s ❛ç♦s ❡❧étr✐❝♦s✱ ❛♣❡♥❛s❢❛③❡♠ ❛✉♠❡♥t❛r ❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ✭❈❆▼P❖❙❀ ❊▼❯❘❆❀ ▲❆◆❉✲●❘❆❋✱ ✷✵✵✻✮✳ ◆♦t❛✲s❡ q✉❡ ♦ ❛✉♠❡♥t♦ ❞♦ ✈♦❧✉♠❡ ❞❡ ♣r❡❝✐♣✐t❛❞♦s ♥♦❛ç♦ ❛✉♠❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ♣♦ssí✈❡✐s ♣♦♥t♦s ❞❡ ♥✉❝❧❡❛çã♦ ❡ ❛♥✐q✉✐❧❛çã♦❞❡ ♣❛r❡❞❡s✳ ❖✉tr♦ ❛s♣❡❝t♦ ❛ ❝♦♥s✐❞❡r❛r é ♦ ❢❛t♦ ❞❛ ♣ró♣r✐❛ ❡str✉t✉r❛ ❞♦s❞♦♠í♥✐♦s✱ ✐st♦ é✱ ♦ ♥ú♠❡r♦ ❞❡ ♣❛r❡❞❡s ❡♠ ♠♦✈✐♠❡♥t♦✱ ✈❛r✐❛r ❝♦♠ ❛❢r❡q✉ê♥❝✐❛ ❞❡ ♦♣❡r❛çã♦ t♦r♥❛♥❞♦ ❞✐s❝✉tí✈❡❧ ♣❛r❛ ❛❧❣✉♥s ❛✉t♦r❡s ❝♦♥✲ s✐❞❡r❛r ❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s t♦t❛✐s ❝♦♠♦ ✉♠❛ s♦♠❛ ❞❛s ♣❡r❞❛s ❡♠r❡❣✐♠❡ ❡stát✐❝♦ ❡ ❞✐♥â♠✐❝♦ ✭❇❊❈❑❊❘✱ ✶✾✻✸✮✳ P❛r❡❝❡✱ ♣♦✐s ❡✈✐❞❡♥t❡ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ r❡s♣♦♥sá✈❡❧ ♣❡❧❛s ♣❡r❞❛s ❤✐st❡r❡s❡s ❛✐♥❞❛ s❡rá ♠♦t✐✈♦❞❡ ♠✉✐t❛ ✐♥✈❡st✐❣❛çã♦✳✸✳✶✳✼✳✸ P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ♦✉ ♣❛r❛s✐t❛s ◗✉❛♥❞♦ ✉♠❛ ♠❛ss❛ ♠❡tá❧✐❝❛ é s✉❜♠❡t✐❞❛ ❛ ✉♠❛ ❞❡♥s✐❞❛❞❡ ❞❡✢✉①♦ ♠❛❣♥ét✐❝♦ ✈❛r✐á✈❡❧✱ ❢♦rç❛s ❡❧❡tr♦♠♦tr✐③❡s s❡rã♦ ✐♥❞✉③✐❞❛s ♥♦ s❡✉✐♥t❡r✐♦r✱ ♣r♦❞✉③✐♥❞♦ ❝♦rr❡♥t❡s q✉❡ ❝✐r❝✉❧❛rã♦ ♣❡❧♦ ♠❡t❛❧✳ ❊ss❛s ❝♦rr❡♥✲ t❡s r❡❝❡❜❡♠ ♦ ♥♦♠❡ ❞❡ ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s ✭♦✉ ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t✮✳ ❆❝✐r❝✉❧❛çã♦ ❞❡ss❛s ❝♦rr❡♥t❡s ♣r♦✈♦❝❛ ❛q✉❡❝✐♠❡♥t♦ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱♣❡r❞❛s ❞❡ ❡♥❡r❣✐❛ ♥♦ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✳ ❆s ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ❝❧áss✐❝❛s✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡♣❡r❞❛s ❋♦✉❝❛✉❧t P f ✱ r❡s✉❧t❛♠ ❞❛ ✈❛r✐❛çã♦ t❡♠♣♦r❛❧ ❞♦ ❝❛♠♣♦ ❞❡ ✐♥❞✉✲çã♦ ♠❛❣♥ét✐❝❛ ♥♦ ♠❛t❡r✐❛❧ ♦ q✉❡ ♦r✐❣✐♥❛ ✉♠❛ ❝♦rr❡♥t❡ ✐♥❞✉③✐❞❛ ❡ s✉❛ ✽✵ ❣r❛♥❞❡③❛ ✈❛✐ ❞❡♣❡♥❞❡r ❞❛ r❡s✐st✐✈✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧✳ ❆s ♣❡r❞❛s ❝❧áss✐✲❝❛s ♣♦r ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s sã♦ ❝❛❧❝✉❧❛❞❛s ❝♦♠ ❜❛s❡ ♥❛s ❡q✉❛çõ❡s ❞❡▼❛①✇❡❧❧✳ ◆♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♠♦❞❡❧♦✱ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ q✉❡ ❛ ❝♦♥❞✉t✐✈✐✲❞❛❞❡ ❡❧étr✐❝❛ ❞♦ ♠❛t❡r✐❛❧ é ❝♦♥st❛♥t❡✱ ❡ ✐s♦tró♣✐❝♦ ♠❛❣♥ét✐❝❛ ❡ ❡❧❡tr✐❝❛✲♠❡♥t❡✳ ◆ã♦ s❡ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦ ❡❢❡✐t♦ ♣❡❧✐❝✉❧❛r ♥❛ ❞✐str✐❜✉✐çã♦❞❛ ❝♦rr❡♥t❡ só ❝♦♥s✐❞❡r❛♥❞♦ ✉♠ ✈❛❧♦r ♠é❞✐♦ ❞❛ ❝♦♥❞✉t✐✈✐❞❛❞❡✳ ❆ ❋✐❣✉r❛ ✸✳✶✸ ✐❧✉str❛ ❛ ❧â♠✐♥❛ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r✳❋✐❣✉r❛ ✸✳✶✸ ✕ ▲â♠✐♥❛ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭●❖◆➬❆▲❱❊❙✲▼❖◆❚❊■❘❖✱ ✷✵✶✵✮ ✽✶ ❈♦♥s✐❞❡r❛♥❞♦ ❛ ❡s♣❡ss✉r❛ e ≪ h✱ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❛❧t✉r❛ ❞❛❧â♠✐♥❛✱ ❛ ♣❛rt✐r ❞❛ ❧❡✐ ❞❡ ❋❛r❛❞❛② t❡♠✲s❡✿ dφ V = ,✭✸✳✶✵✮ dt ❞❡ ♠♦❞♦ q✉❡✱ ❛ t❡♥s❛♦ ✐♥❞✉③✐❞❛ ♥♦ ♣❡r❝✉rs♦ s❡❥❛√ E = 2 2πf B hx m ✭✸✳✶✶✮❡ ❛ r❡s✐stê♥❝✐❛ ❡❧étr✐❝❛ ❞♦ ♣❡r❝✉rs♦ ♠é❞✐♦ l m s❡❥❛ 2hρ R f = . ✭✸✳✶✷✮ l m dx❆ss✐♠ ❛ ❝♦rr❡♥t❡ ✐♥✜♥✐t❡s✐♠❛❧ ✐♥❞✉③✐❞❛ ♥♦ ♣❡r❝✉rs♦ é √E 2πf B l xdx m m di f = = . ✭✸✳✶✸✮R ρ f ❆ ♣♦tê♥❝✐❛ ❞❡ ♣❡r❞❛s ♥♦ ❢❡rr♦✱ ♣♦r ❝✐r❝✉❧❛çã♦ ❞❡ ❝♦rr❡♥t❡s ♣❛r❛✲ s✐t❛s✱ é ❞❛❞❛ ♣♦r✿Z Z 0,5e 0,5e222222234π f B hl x dx π f B hl e m m m m P f = E di f = f = . → Pρ 6ρ ✭✸✳✶✹✮❈♦♥s✐❞❡r❛♥❞♦ ♦ ✈♦❧✉♠❡ t♦t❛❧ ❞❛ ❧â♠✐♥❛ v = hl em ✭✸✳✶✺✮ t❡♠✲s❡ q✉❡ ❛ ♣❡r❞❛ ✧❋♦❝❛✉❧t✧♥♦ ✈♦❧✉♠❡ t♦t❛❧ ❞♦ ❢❡rr♦ é ❞❛❞❛ ♣♦r2 π2222222 P f = B f e f = k f B f e v . m v → P m ✭✸✳✶✻✮6ρ ❡♠ q✉❡ ρ é ❛ r❡s✐st✐✈✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧ ✭✐♥✢✉❡♥❝✐❛❞❛ ♣❡❧♦ t❡♦r ❞❡ s✐❧í❝✐♦✮✱ k fé ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ♣❡r❞❛s ❞❡ ❋♦❝❛✉❧t✱ f é ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ❛❧✐♠❡♥t❛çã♦✱ e é ❛ ❡s♣❡ss✉r❛ ❞❛ ❝❤❛♣❛ ❡ v é ♦ ✈♦❧✉♠❡ t♦t❛❧ ❞♦ ♥ú❝❧❡♦✳✸✳✶✳✼✳✹ P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ❡①❝❡❞❡♥t❡s ▼❡❞✐♥❞♦ ❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s t♦t❛✐s ♥✉♠❛ ❧â♠✐♥❛ ❞❡ ♠❛t❡r✐❛❧❢❡rr♦♠❛❣♥ét✐❝♦ ❛ ♦♣❡r❛r ❡♠ r❡❣✐♠❡ ❞✐♥â♠✐❝♦✱ ♠❡❞✐♥❞♦ t❛♠❜é♠ ❛s r❡s✲ ✽✷ ♣❡❝t✐✈❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡♠ r❡❣✐♠❡ q✉❛s❡ ❡stát✐❝♦ ❡ ❝❛❧❝✉❧❛♥❞♦ ❛s♣❡r❞❛s ❞❡ ❋♦✉❝❛✉❧t ❝❧áss✐❝❛s ♣❡❧❛ ❡q✉❛çã♦ ✭✸✳✶✻✮✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ❛ s♦♠❛P + P h f é ✐♥❢❡r✐♦r às ♣❡r❞❛s t♦t❛✐s✳ ❆ ❡ss❛ ❞✐❢❡r❡♥ç❛ ❝❤❛♠❛✲s❡ ♣❡r❞❛s❡①❝❡❞❡♥t❡s ♦✉✱ ❛♥ô♠❛❧❛s✱ P exc ✱ t❡♥❞♦✲s❡ ❡♥tã♦✱ P = P + P ). exc t − (P f h ✭✸✳✶✼✮ ❆s ♣❡r❞❛s ❡①❝❡❞❡♥t❡s ❡stã♦ ❛ss♦❝✐❛❞❛s ❝♦♠ ♦ ♠♦✈✐♠❡♥t♦ ❡♠ ❧❛r❣❛❡s❝❛❧❛ ❞❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦s ✭❇❊❘❚❖❚❚■✱ ✶✾✽✽❀ ❋■❖❘■▲▲❖✱ ✷✵✵✹✮❡ r❡s♣❡❝t✐✈❛ r♦t❛çã♦ ❞❡ ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s q✉❡ ♦❝♦rr❡ ♥❛ ③♦♥❛ ❞♦s❥♦❡❧❤♦s ❞❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦✳ ❙❡❣✉♥❞♦ ♦ ♠♦❞❡❧♦ ❡st❛tíst✐❝♦ ❞❡ ❇❡rt♦tt✐ ✭❝♦♠ s✉❜í♥❞✐❝❡ B✮✱ ❛s♣❡r❞❛s ❡①❝❡❞❡♥t❡s ♣♦❞❡♠ s❡r tr❛❞✉③✐❞❛s ♣❡❧❛ ❡q✉❛çã♦✿33 r 122 P = K B m f exc,B exc,B ✭✸✳✶✽✮ exc,B ρ ❡♠ q✉❡ K é ✉♠ ♣❛râ♠❡tr♦ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ❡str✉t✉r❛ ❞♦s ❞♦♠í✲♥✐♦s ♠❛❣♥ét✐❝♦s✱ s❡♥❞♦ ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ t❛♠❛♥❤♦ ❞❡ ❣rã♦✱❝♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ σ✱ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❛tr✐t♦ ❞♦ ♦❜❥❡t♦ ♠❛❣♥ét✐❝♦ G✱ s❡çã♦ r❡❢❡r❡♥t❡ ❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ S✱ ❞❡♥s✐❞❛❞❡ ❞❡ ♠❛ss❛ ❡s♣❡❝í✜❝❛m v ❡ ♦ ❡♥t❡ ❡q✉✐✈❛❧❡♥t❡ ❛ ✉♠ ❝❛♠♣♦ ❝♦❡r❝✐t✐✈♦ ❞♦ ♦❜❥❡t♦ ♠❛❣♥ét✐❝♦ V o ✱ ❞❡ ♠♦❞♦ q✉❡✿8, 76363 pσGV K exc,B = o S. ✭✸✳✶✾✮ mvP❛r❛ ▼✳ ❈❛♠♣♦s ✭❈❆▼P❖❙❀ ❊▼❯❘❆❀ ▲❆◆❉●❘❆❋✱ ✷✵✵✻✮✱ ❛s P exc ✭❝♦♠ s✉❜í♥❞✐❝❡ C✮ ✈❛r✐❛♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡q✉❛çã♦ ✭✸✳✷✵✮✱ ❛❝♦♥st❛♥t❡ ♦❜t✐❞❛ ❡♠♣✐r✐❝❛♠❡♥t❡3 122 P = K B f exc,C exc,C ✭✸✳✷✵✮ mρ F e ❡♠ q✉❡ ♦ ♣❛râ♠❡tr♦ K exc,C é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à r❛✐③ q✉❛❞r❛❞❛❞♦ t❛♠❛♥❤♦ ❞❡ ❣rã♦✳ ❈♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❇❡rt♦tt✐ ♣♦❞❡ ❡♥tã♦ ❡s❝r❡✈❡r✲s❡ ♣❛r❛❛s ♣❡r❞❛s ❞❡ ❢❡rr♦ t♦t❛✐s r33 α h222 122 P = K B f + k e vB f + K B m f . t h f excB ✭✸✳✷✶✮ m mρ m ✽✸ ❆s ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ✐♥❞✉③✐❞❛s ❝❛❧❝✉❧❛❞❛s ❞❡ ♠❛♥❡✐r❛ ❝❧áss✐❝❛✱♦ ♣❛râ♠❡tr♦ ♠❛✐s ❞✐❢í❝✐❧ ❞❡ s❡r ♦❜t✐❞♦ é ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞♦♠❛t❡r✐❛❧ ❞❡✈✐❞♦ ❛ ♥ã♦ s❡r ❤♦♠♦❣ê♥❡❛ ❡ ✐s♦tró♣✐❝❛✳✸✳✶✳✽ ❊①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❞❛s s♦❜ r❡❣✐♠❡ ♥ã♦ s❡♥♦✐❞❛❧ ✭P❲▼✮❆ ♣r✐♠❡✐r❛ t❡♥t❛t✐✈❛ ❞❛ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❡❢❡✐t♦s ❞♦ ❝♦♥t❡ú❞♦ ❤❛r♠ô♥✐❝♦ ❞♦ ✢✉①♦ ♠❛❣♥ét✐❝♦✱ ❝♦♠♦ ❛q✉❡❧❡s ♣r♦❞✉③✐❞♦s ♣❡❧❛ ♠♦❞✉❧❛✲çã♦ ♣♦r ❧❛r❣✉r❛ ❞❡ ♣✉❧s♦ ✭P❲▼✮✱ s♦❜r❡ ❛s ♣❡r❞❛s ❡♠ ❧â♠✐♥❛s ♠❛❣♥é✲ t✐❝❛s r❡♠♦♥t❛ ❛♦ ❛♥♦ ❞❡ ✶✾✻✾ ✭❋■❙❍✱ ✶✾✾✵✮✳ ❍♦❧❧✐ts❝❤❡r ✭❍❖▲▲■❚❙✲❈❍❊❘✱ ✶✾✻✾✮ ❛✈❛❧✐❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❛s ♣❡r❞❛s ♥♦ ❢❡rr♦ ❝♦♠ ❛ ♣r❡✲ s❡♥ç❛ ❞❡ ❤❛r♠ô♥✐❝♦s ❞❡ ❜❛✐①❛ ♦r❞❡♠ ♥♦ ✢✉①♦✱ ❝♦♥tr♦❧❛♥❞♦ ♦ ❡❢❡✐t♦❞❡ss❡s ❤❛r♠ô♥✐❝♦s ❡♠ ♠ó❞✉❧♦ ❡ ❡♠ ❢❛s❡✳ ❊st❡ ❡st✉❞♦ ❝♦♥❝❧✉✐✉ q✉❡ ❛♣r❡s❡♥ç❛ ❞❡ ❤❛r♠ô♥✐❝♦s ❛❝❛rr❡t❛ ❞✐r❡t❛♠❡♥t❡ ✉♠ ❢♦rt❡ ❛✉♠❡♥t♦ ♥❛s♣❡r❞❛s ❞♦ ❢❡rr♦✳ ❆tr❛✈és ❞❛ ❡q✉❛çã♦ ❞❡ s❡♣❛r❛çã♦ ❞❡ ♣❡r❞❛s ❞❡ ❙t❡✐♥♠❡③t✲❇❡rt♦tt✐❛♣❧✐❝á✈❡❧ só ❛ ♦♥❞❛s s❡♥♦✐❞❛✐s é ♣♦ssí✈❡❧ ❡st❡♥❞❡r s✉❛ ❛♣❧✐❝❛çã♦ ❛ ♦♥❞❛s♥ã♦ s❡♥♦✐❞❛✐s ❛tr❛✈és ❞❛ sér✐❡ ❞❡ ❋♦✉r✐❡r✳ P❛r❛ ✐st♦✱ é ♥❡❝❡ssár✐♦ ♦❜t❡r♦ ❡s♣❡❝tr♦ ❞❛ ❝♦rr❡♥t❡ ♦ q✉❛❧ é ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ❡s♣❡❝tr♦ ❞❛ ✐♥❞✉çã♦✳ ❆♣❡r❞❛ t♦t❛❧ ✈❛✐ ❝♦rr❡s♣♦♥❞❡r à s♦♠❛ ❞❡ t♦❞♦s ❡st❡s ❛♣♦rt❡s✳ ❆s ❋✐❣✉r❛s✸✳✶✹✱ ✸✳✶✺ ❡ ✸✳✶✻ ❡❧✉❝✐❞❛♠ ❡ss❡s ❢❛t♦s✳❋✐❣✉r❛ ✸✳✶✹ ✕ ❋♦r♠❛s ❞❡ ♦♥❞❛ ❡st✐❧✐③❛❞❛s ❞❡ t❡♥sã♦ P❲▼ ❡ ❞❛ ❝♦rr❡♥t❡ q✉❡ é ♣r♦♣♦r❝✐♦♥❛❧ à ✐♥❞✉çã♦✳ ❆ sér✐❡ ❞❡ ❋♦✉r✐❡r ♣❡r♠✐t❡ r❡♣r❡s❡♥t❛rq✉❛❧q✉❡r ❢✉♥çã♦ ❝♦♠♦ ✉♠❛ s♦♠❛ ❞❡ ♦♥❞❛s s❡♥♦✐❞❛✐s ❝♦♠ ❞✐❢❡r❡♥t❡s❛♠♣❧✐t✉❞❡s ❡ ❢r❡q✉ê♥❝✐❛s✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮ ✽✹ ❋✐❣✉r❛ ✸✳✶✺ ✕ ❆ té❝♥✐❝❛ P❲▼ ❣❡r❛ ✉♠❛ ♦♥❞❛ ❞❡ ❝♦rr❡♥t❡ ❞✐st♦r❝✐❞❛ q✉❡❛❝♦♠♣❛♥❤❛ ❛ s❡♥♦✐❞❡ ❞❡ r❡❢❡rê♥❝✐❛✱ ♣♦r ❡❢❡✐t♦ ❞❛ ✐♥t❡❣r❛çã♦ ❞❛ ❝♦rr❡♥t❡✱❝♦♠ ❜❛s❡ ♥❛ ❝♦♥st❛♥t❡ ❞❡ t❡♠♣♦ RL ❞♦ ❝✐r❝✉✐t♦✳ ❊ss❡ ♣r♦❝❡ss♦ ❞❡✐♥t❡❣r❛çã♦ ❣❡r❛ ❡①♣♦♥❡♥❝✐❛✐s ❝r❡s❝❡♥t❡s ❡ ❞❡❝r❡s❝❡♥t❡s q✉❡ ❞ã♦ ♦ ❝❛rát❡r✧r❡❝♦rt❛❞♦✧❛♦ s✐♥❛❧ ❞❡ ❝♦rr❡♥t❡✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮ ❊♠❜♦r❛ ❝♦♥tr❛r✐❛♠❡♥t❡ ❛♦ ❡s♣❡r❛❞♦ ♦ ❢♦r♠❛t♦ ❞❡ ♦♥❞❛ P❲▼♥ã♦ ❛✉♠❡♥t❛ ❡♠ ❢♦r♠❛ ❡①♣r❡ss✐✈❛ ❛ ♣❡r❞❛ t♦t❛❧✱ ♥♦ ❝❛s♦ ❞❛ ❢♦r♠❛❞❡ ♦♥❞❛ ❞❛ ✐♥❞✉çã♦ ♥❛ ❋✐❣✉r❛ ✸✳✶✼ q✉❡ ✐♥tr♦❞✉③ ❤❛r♠ô♥✐❝❛s ❞❡ ❜❛✐①❛❢r❡q✉ê♥❝✐❛ ✭♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ t❡r❝❡✐r❛ ❡ ❛ q✉✐♥t❛✮ ❣❡r❛♥❞♦ ❧❛ç♦s ♠❡♥♦r❡s✱❛s ♣❡r❞❛s ❛✉♠❡♥t❛♠ ❞❡ ❢♦r♠❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❧❛ç♦s✳ ✽✺ ❋✐❣✉r❛ ✸✳✶✻ ✕ ❋♦r♠❛ ❞❛ ❝✉r✈❛ BH ♣❛r❛ ✉♠❛ ❢♦r♠❛ ❞❡ t❡♥sã♦ P❲▼ ❛s♦♥❞❛s r❡❝♦rt❛❞❛s✱ ❛❢❡t❛♠ só ♦ ❝♦♥t♦r♥♦ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✱ s❡✉ ❡❢❡✐t♦ s♦❜r❡ ❛s ♣❡r❞❛s t♦t❛✐s é ♠í♥✐♠♦✱ ♥✉♠ ✐♥✈❡rs♦r P❲▼ ❛s ♣❡r❞❛s ✜❝❛♠♣♦r ❝♦♥t❛ ❞♦ ❛✉♠❡♥t♦ ❞❛ ❢r❡q✉ê♥❝✐❛✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮❋✐❣✉r❛ ✸✳✶✼ ✕ ❖s ❞♦✐s t✐♣♦s ❜ás✐❝♦s ❞❡ ❢♦r♠❛ ❞❡ ❞✐st♦rçã♦ ❞❛ ✐♥❞✉çã♦♠❛❣♥ét✐❝❛ ♥❛ ❢♦r♠❛çã♦ ❞❡ ❧❛ç♦s ♠❡♥♦r❡s ♥❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ♠❛❣✲♥ét✐❝❛✿ ✭❛✮ s❡♠ ❡①tr❡♠♦s ❧♦❝❛✐s ❡ ✭❜✮ q✉❛tr♦ ✈❛r✐❛çõ❡s ❡①tr❡♠❛s ♥♦♣❡rí♦❞♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮ ✽✻ ✸✳✶✳✾ ▼♦❞❡❧♦ ❞❡ ❏✐❧❡s ❆t❤❡rt♦♥ ❞❡ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛ ❡ s❡✉s♣❛râ♠❡tr♦s ót✐♠♦s❆ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❝♦rr❡s♣♦♥❞❡ ♥❛ ✈❡r❞❛❞❡ ❛ ❡♥❡r❣✐❛ ❞✐ss✐♣❛❞❛ ♣♦r ❝✐❝❧♦✱ q✉❡ ✐♥❝❧✉✐ ❛ ❤✐st❡r❡s❡ ♣r♦♣r✐❛♠❡♥t❡ ❡ ❛s ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s✐♥❞✉③✐❞❛s ♦✉ ❞✐♥â♠✐❝❛s✳ ❯♠❛ ♠♦❞❡❧❛❣❡♠ ❢ís✐❝♦✲♠❛t❡♠át✐❝❛ ❛❞❡q✉❛❞❛❝♦♥tr✐❜✉✐ ♥♦ ♣r♦❥❡t♦ ❞❡ ♠áq✉✐♥❛s ❝♦♠ ♠❡❧❤♦r ❡✜❝✐ê♥❝✐❛ ❡♥❡r❣ét✐❝❛✳ ◆❛♣r♦❝✉r❛ ❞❡ r❡♣r❡s❡♥t❛çõ❡s ♠❛t❡♠át✐❝❛s ♠❛✐s ❡❧❛❜♦r❛❞❛s✱ ♦ ♠♦❞❡❧♦ ♣r♦✲♣♦st♦ ♣♦r ❏✐❧❡s✲❆t❤❡rt♦♥ ✭❏❆✮ ✭❏■▲❊❙ ❉✳ ❈✳❀ ❆❚❍❊❘❚❖◆✱ ✶✾✽✸✮ ♣❛r❛❛ ❤✐st❡r❡s❡ ♠❛❣♥ét✐❝❛ t❡♠ ✉♠ ❢✉♥❞❛♠❡♥t♦ ❢ís✐❝♦ q✉❡ ♣r♦✈é♠ ❞❡ ✉♠❛ sér✐❡ ❞❡ ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ❡①♣❧✐❝❛♥❞♦ ♦ ❢❡♥ô♠❡♥♦ ❞❡ ♣❡r❞❛s ❞❡ ❢❡rr♦♥❛ ❧✐t❡r❛t✉r❛✿ ❼ ❋❡rr♦♠❛❣♥❡t✐s♠♦ ❞❡ ▼❛①✇❡❧❧✱ ✐♥t❡r❛çã♦ ♠út✉❛ ❡♥tr❡ ♠♦♠❡♥t♦s♠❛❣♥ét✐❝♦s❀ ❼ ❲❡❜❡r✱ ❞❡ ❲❡✐❞❡♠❛♥♥✱ ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s ♠♦❧❡❝✉❧❛r❡s❀❼ ❊✇✐♥❣✱ ✐♥t❡r❛çã♦ ♠út✉❛ ❡♥tr❡ ♠♦♠❡♥t♦s ♠❛❣♥ét✐❝♦s❀❼ ▲❛♥❣❡✈✐♥✱ t❡♦r✐❛ ♠❛t❡♠át✐❝❛ ❞♦ P❛r❛♠❛❣♥❡t✐s♠♦❀❼ ❲❡✐ss✱ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s ❡ ❝♦♥❝❡✐t♦ ❞❡ ✐♥✲ ❞✉çã♦ ❡❢❡t✐✈❛ ♠❛❣♥ét✐❝❛ ♥♦ ❢❡♥ô♠❡♥♦ ❢❡rr♦♠❛❣♥ét✐❝♦✳❼ ❑❡rst❡♥✱ ❇❡❝❦❡r ❡ ❉♦r✐♥❣ ♥❛ ✐♥t❡r♣r❡t❛çã♦ ❞❛ ♠✉❞❛♥ç❛ ❞❡ ♠❛❣✲ ♥❡t✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ❡♠ t❡r♠♦s ❞❛ ♠♦✈✐♠❡♥t❛çã♦ ❞❛s ♣❛r❡❞❡s❞♦s ❞♦♠í♥✐♦s✳ ❙✉❛ ❢♦r♠✉❧❛çã♦ é ❡♠ t❡r♠♦s ❞❡ ✉♠❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ tr❛♥s✲❝❡♥❞❡♥t❛❧ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ♥ã♦✲❧✐♥❡❛r ❡♠ ❢✉♥çã♦ ❞❛ ✈❛r✐á✈❡❧ ✐♥❞❡✲♣❡♥❞❡♥t❡ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H✱ ❝♦♥t❡♥❞♦ ❝✐♥❝♦ ♣❛râ♠❡tr♦s ✭M s ✱ χ s ✱ a JA JA JA ✱ α ❡ k ✮✳ ❖s ✈❛❧♦r❡s ✐♥✐❝✐❛✐s sã♦ ♦❜t✐❞♦s ❛tr❛✈és ❞❡ ❝✉r✈❛s ❞❡❤✐st❡r❡s❡ ❡①♣❡r✐♠❡♥t❛✐s✳ ❆ ♦t✐♠✐③❛çã♦ ❞♦s ❝✐♥❝♦ ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ −1 ❏❆ ❡ ❏✐❧❡s✲❆t❤❡rt♦♥ ✐♥✈❡rs♦ ✭❏❆ ✮ ✭❏■▲❊❙ ❉✳ ❈✳❀ ❆❚❍❊❘❚❖◆✱ ✶✾✽✸✮ s❡ ❜❛s❡✐❛ ❡♠ ✉♠ ❣rá✜❝♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ s✉s❝❡♣t✐❜✐❧✐✲m s m m m c c❞❛❞❡ ❞✐❢❡r❡♥❝✐❛❧ χ ✳ ❖s ♣♦♥t♦s ♥♦tá✈❡✐s✿ M ✱ M ✱ H ✱ χ ✱ H ✱ χ ✱M r r in ❡ χ ✱ ❡ χ sã♦ ❞❡✜♥✐❞♦s ❛ ♣❛rt✐r ❞❛s ❢♦r♠✉❧❛çõ❡s ❞❡ ❏✐❧❡s ✭❏■▲❊❙❉✳ ❈✳❀ ❆❚❍❊❘❚❖◆✱ ✶✾✽✸✮ ❡ sã♦ ♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ♣❛r❛ ♦ ❝á❧❝✉❧♦✐t❡r❛t✐✈♦ ❞❛s ✈❛r✐á✈❡✐s a JA ✱ α JA ❡ k JA ✉t✐❧✐③❛♥❞♦ ♦ ❛❧❣♦r✐t♠♦ ✐t❡r❛t✐✈♦♣r♦♣♦st♦ ♣♦r P❡✉❣❡t ✭P❊❯●❊❚✱ ✶✾✾✺✮✳ ◆❛ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥✈❡r❣ê♥❝✐❛❝❤❡❣❛✲s❡ ❛♦s ✈❛❧♦r❡s ✜♥❛✐s ♣❛r❛ ✧a JA ✱ α JA ❡ k JA ✧✭✈❡r✐✜❝❛r ❋✐❣✉r❛ ✸✳✶✽ ✽✼ ❖s ♣❛râ♠❡tr♦s✱ ✐♥✐❝✐❛✐s ♦❜t✐❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❞♦ ❣rá✜❝♦ ❞❡ s✉s❝❡♣t✐❜✐❧✐❞❛❞❡✱ ❛s ❡q✉❛çõ❡s ❜ás✐❝❛s ♣❛r❛ ❡st❡ ✜♠✱ ❛s ❞❡✜♥✐çõ❡s ❞♦s♣❛râ♠❡tr♦s ❡ ♦ ❛❧❣♦r✐t♠♦ ❡stã♦ ♥♦ ❆♥❡①♦ ❇✳❋✐❣✉r❛ ✸✳✶✽ ✕ ❆s s✉s❝❡♣t✐❜✐❧✐❞❛❞❡s ❞✐❢❡r❡♥❝✐❛✐s sã♦ ❛s ✐♥❝❧✐♥❛çõ❡s ❞❛s r❡t❛s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❋✐❣✳ ❖ ❛❧❣♦r✐t♠♦ ❞❡ P❡✉❣❡t ✭P❊❯●❊❚✱ ✶✾✾✺✮é ❛♣❧✐❝❛❞♦ ♣❛r❛ ♦ ❡♥❝♦♥tr♦ ❞❡ ✉♠ ♣r✐♠❡✐r♦ ♣♦ssí✈❡❧ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ✲♠❡tr♦s✳ ❯t✐❧✐③❛✲s❡ ♠❡t❛❞❡ ❞❡ ✉♠ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦s♥♦✈❡ ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮ ✽✽ ❋✐❣✉r❛ ✸✳✶✾ ✕ P♦♥t♦s ❝❤❛✈❡s s✉❣❡r✐❞♦s ♣♦r ❏✐❧❡s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦s ♥♦✈❡ s m m m r r c c in❞❛❞♦s ✭M ✱ M ✱ H ✱ χ ✱ M ✱ χ ✱ H ✱ χ ✱ ❍❝✱ χ ✮ ♥❡❝❡ssár✐♦s ♣❛r❛ ❛✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ❏❆ ❡stã♦ ✐♥❞✐❝❛❞♦s ♥❛ ✜❣✉r❛ tr❛ç❛❞❛ ❛ ✶ ❍③✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❚■❙❚❊▲❆✱ ✷✵✵✶✮✸✳✷ ❉■❙P❖❙■❚■❱❖ ❊▼ ❊❙❚❯❉❖ ❖ ♠♦❞❡❧♦ ♥✉♠ér✐❝♦ ❢♦✐ ❝♦♥str✉í❞♦ s❡❣✉✐♥❞♦ ✉♠ r♦t❡✐r♦ ♣r♦♣♦st♦❆❧❢♦♥s♦ ▼❛rt✐❣♥♦♥✐ ✭▼❆❘❚■●◆❖◆■✱ ✶✾✻✾✮ ❡ ❛♥❛❧✐s❛❞♦ ♥♦ s♦❢t✇❛r❡ ❜✐✲❞✐♠❡♥s✐♦♥❛❧ ❋❊▼▼ ✭❋✐♥✐t❡ ❊❧❡♠❡♥t ▼❡t❤♦❞ ▼❛❣♥❡t✐❝s✮✳ ❖ r♦t❡✐r♦✉t✐❧✐③❛❞♦ é ❛♣r❡s❡♥t❛❞♦ ♥♦ ❆♥❡①♦ ❈✳ ❯♠ ❝♦rt❡ tr❛♥s✈❡rs❛❧ r❡♣r❡s❡♥t❛♥❞♦ ♦ ♠♦❞❡❧♦ ❜✐❞✐♠❡♥s✐♦♥❛❧ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ❋✐❣✉r❛ ✸✳✷✵✳❆♦ r❡❞♦r ❞♦ tr❛♥s❢♦r♠❛❞♦r ✐♥❝❧✉✐✉✲s❡ ✉♠❛ r❡❣✐ã♦ ❝✐r❝✉❧❛r ❝♦♠ ❛r ❝✉❥❛ ❡①tr❡♠✐❞❛❞❡ é ❞❡✜♥✐❞❛ ❝♦♠ ♣♦t❡♥❝✐❛❧ ♠❛❣♥ét✐❝♦ ♥✉❧♦✳ ❊st❛❝♦♥❞✐çã♦ ❞❡ ❢r♦♥t❡✐r❛ é ❞❡♥♦♠✐♥❛❞❛ ❝♦♥t♦r♥♦ ❞❡ ❉✐r✐❝❤❧❡t✱ ❡ t❡♠ ❝♦♠♦ ✽✾ ❋✐❣✉r❛ ✸✳✷✵ ✕ ❚r❛♥s❢♦r♠❛❞♦r ♠♦❞❡❧❛❞♦ ♥♦ ❋❊▼▼✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳✸✳✸ ▼➱❚❖❉❖❙ ❊ ❊◗❯■P❆▼❊◆❚❖❙ P❆❘❆ ❆ ❈❆❘❆❈❚❊✲ ❘■❩❆➬➹❖ ❉❊ ▼❆❚❊❘■❆■❙ ❋❊❘❘❖▼❆●◆➱❚■❈❖❙◆❡ss❛ s❡çã♦✱ ♦ ♦❜❥❡t✐✈♦ é ❛♣r❡s❡♥t❛r ❛s ❢❡rr❛♠❡♥t❛s ❞❡ ❧❛❜♦r❛tó✲ r✐♦ q✉❡ ♣❡r♠✐t❡♠ ✉♠❛ ❛❞❡q✉❛❞❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦s ♠❛t❡r✐❛✐s ✭♣❡r❞❛s ♣♦r ❦❣✱ ❝✉r✈❛ BH✱ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ t❡①t✉r❛ ●❖✮✳ ❆ ✉t✐❧✐③❛çã♦ ❞❡ ❝✐r❝✉✐✲ t♦s ❞❡ ❜❛✐①♦ ❝✉st♦ é ✉♠❛ ❜♦❛ ❛❧t❡r♥❛t✐✈❛✱ ❥á q✉❡ ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s♦ ♣r♦❥❡t✐st❛ ♣r❡❝✐s❛ ❢❛③❡r ❝♦♠♣❛r❛çõ❡s q✉❛❧✐t❛t✐✈❛s ❡♥tr❡ ♦s ♠❛t❡r✐❛✐s q✉❡ ❞✐s♣õ❡ ♣❛r❛ ♦ ♣r♦❥❡t♦ ❞❡ ❢♦r♠❛ ❡①♣❡❞✐t❛ ❡ rá♣✐❞❛✳✸✳✸✳✶ ▼❡❞✐❞♦r ❞❛s ♣❡r❞❛s ❞❡ ❤✐st❡r❡s❡ ❊st❡ ✐♥str✉♠❡♥t♦ ✭✈❡r✐✜❝❛r ❋✐❣✉r❛ ✸✳✷✶✮ é ✉t✐❧✐③❛❞♦ ♥❛s ❡♠♣r❡✲ s❛s ❞❡ ♠❛♥✉❢❛t✉r❛ ❞❡ ♥ú❝❧❡♦s ♣❛r❛ ♠áq✉✐♥❛s ❡❧étr✐❝❛s ♥❛ r❡❝❡♣çã♦ ❞❡♠❛tér✐❛✲♣r✐♠❛✳ ❆tr❛✈és ❞❡ ✉♠❛ ❜♦❜✐♥❛ q✉❡ ♣r♦❞✉③ ✉♠❛ ✐♥❞✉çã♦ ❡s♣❡❝✐✜❝❛❞❛ ✾✵ ❞✐ss✐♣❛❞❛ ♥♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ♥♦ ♣♦♥t♦ ❡s♣❡❝✐✜❝❛❞♦✳ ❖ r❡s✉❧t❛❞♦ é❛♣r❡s❡♥t❛❞♦ ❡♠ ✇❛tt✴❦❣✱ ❞❡ ♠♦❞♦ q✉❡ é ♥❡❝❡ssár✐♦ ❡s♣❡❝✐✜❝❛r ❡s♣❡ss✉r❛❞❛ ❝❤❛♣❛✳❋✐❣✉r❛ ✸✳✷✶ ✕ ❆♣❛r❡❧❤♦ ❞❡ ♠❡❞✐❞❛ ❉❲✷✵✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❯❑❯❍❆❘❆✱ ✷✵✶✵✮✳✸✳✸✳✷ ❖ q✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ❆ ❡st✐♠❛t✐✈❛ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞♦s ♠❛t❡r✐❛✐s❡ ♦❜t❡♥çã♦ ❞❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s ♣♦❞❡ s❡r r❡❛❧✐③❛❞❛ ❛tr❛✈és ❞♦ t❡st❡❞❡ ❊♣st❡✐♥✱ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛❞r♦♥✐③❛❞♦ ♣❡❧❛ ♥♦r♠❛ ❜r❛s✐❧❡✐r❛ ◆❇❘✲✻✶✺✶✭✶✾✾✻✮✳ ❖ q✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ❛ss❡♠❡❧❤❛✲s❡ ❛ ✉♠ tr❛♥s❢♦r♠❛❞♦r ❝♦♥st✐✲ t✉í❞♦ ♣♦r ❞♦✐s ❡♥r♦❧❛♠❡♥t♦s✿ ♣r✐♠ár✐♦ ❡ s❡❝✉♥❞ár✐♦ ✭✈❡r✐✜❝❛r ❋✐❣✉r❛s✸✳✷✷ ❡ ✸✳✷✸✮✳ ❆s ❛♠♦str❛s ❞❡ t❡st❡ ❢♦r♠❛♠ ♦ ♥ú❝❧❡♦ ♠❛❣♥ét✐❝♦ ❞♦ tr❛♥s✲❢♦r♠❛❞♦r✳ ❖ q✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ❛♣r❡s❡♥t❛ ❛✐♥❞❛ ✉♠ ✏✐♥❞✉t♦r ♠út✉♦✑♣❛r❛ ❝♦♠♣❡♥s❛r ♦ ✢✉①♦ ❞✐s♣❡rs♦ ♥♦ ✐♥t❡r✐♦r ❞❛s ❜♦❜✐♥❛s q✉❡ ❡♠ ❝♦♥✲ s❡q✉ê♥❝✐❛ ❞❛ ❞✐s♣♦s✐çã♦ ❞❛s ❜♦❜✐♥❛s é ❛❧t♦✳ ❖ ✐♥❞✉t♦r ❞❡ ❝♦♠♣❡♥s❛çã♦é ❧♦❝❛❧✐③❛❞♦ ♥♦ ❝❡♥tr♦ ❞♦ ❡s♣❛ç♦ ❢♦r♠❛❞♦ ♣❡❧♦s ❡♥r♦❧❛♠❡♥t♦s✳ ❖s ❡♥r♦❧❛♠❡♥t♦s ❛♣r❡s❡♥t❛♠ ✉♠ t♦t❛❧ ❞❡ ✼✵✵ ❡s♣✐r❛s ❡ sã♦ r❡✲❝♦♠❡♥❞❛❞♦s ♣❛r❛ t❡st❡ ♥✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ❢r❡q✉ê♥❝✐❛ ❞❡ ✷✺ ❛ ✹✵✵ ❍③✳❊①❝✐t❛✲s❡ ♦ ❡♥r♦❧❛♠❡♥t♦ ♣r✐♠ár✐♦ ❡ ♠❡❞❡✲s❡ ❛ t❡♥sã♦ s❡❝✉♥❞ár✐❛✳ ❖❝♦♠♣r✐♠❡♥t♦ ❡❢❡t✐✈♦ ♣❛r❛ ♦ ❝❛♠✐♥❤♦ ♠❛❣♥ét✐❝♦ é ❛❞♦t❛❞♦ ❝♦♥✈❡♥❝✐♦✲♥❛❧♠❡♥t❡ ❝♦♠♦ ✵✱✾✹ ♠✱ ♣❛r❛ ♦ q✉❛❞r♦ ❞❡ ✷✺ ❝♠ ✭◆❇❘✲✻✶✺✶✱ ✶✾✾✻✮✳ ❖ ✾✶ ❋✐❣✉r❛ ✸✳✷✷ ✕ ◗✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ✲ ❢♦t♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭P❊❘❊■❘❆ ❏❯◆■❖❘✱ ✷✵✶✶✮✸✳✸✳✸ ❈✐r❝✉✐t♦ ❡sq✉❡♠át✐❝♦ ❖ ❡sq✉❡♠❛ ❞❡ ❧✐❣❛çã♦ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞♦ ❡♥s❛✐♦ ❞❡ ♣❡r❞❛s ♠❛❣✲♥ét✐❝❛s é ✐❧✉str❛❞♦ ♣❡❧♦ ❝✐r❝✉✐t♦ ❡sq✉❡♠át✐❝♦ r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❋✐❣✉r❛✸✳✷✹✳ ❆ ♠❛✐♦r✐❛ ❞♦s q✉❛❞r♦s ❞❡ ❊♣st❡✐♥ ❡①✐st❡♥t❡s ♥♦ ❇r❛s✐❧ ❢♦r❛♠ ❞❡✲ s❡♥✈♦❧✈✐❞♦s ♣❡❧❛ ❡♠♣r❡s❛ ❨♦❦♦❣❛✇❛✳ ❊ss❛ ❡♠♣r❡s❛ ❥á ♥ã♦ ❢❛❜r✐❝❛ ♠❛✐s♦s ♠❡❞✐❞♦r❡s ❞❡ ❊♣st❡✐♥✳ ❚❛✐s ♠❡❞✐❞♦r❡s ♣♦❞❡♠ s❡r ❛❞q✉✐r✐❞♦s ❥✉♥t♦ ❛❡♠♣r❡s❛s ❡str❛♥❣❡✐r❛s ❝♦♠♦ ❛ ❇r♦❝❦❤❛✉s✱ ♦ q✉❡ ❞✐✜❝✉❧t❛ ❡ ❡♥❝❛r❡❝❡ ♦❡♥s❛✐♦✳✸✳✸✳✹ ❖ ❙❡♥s♦r ❞❡ ❧â♠✐♥❛ ú♥✐❝❛ ❖ ❡♥s❛✐♦ ❝♦♠ ♦ s❡♥s♦r ❞❡ ❧â♠✐♥❛ ú♥✐❝❛ ✭s✐♥❣❧❡✲s❤❡❡t t❡st❡r✮ ♥ã♦é ♥♦r♠❛❧✐③❛❞♦✳ ❖ ✧s✐♥❣❧❡✲s❤❡❡t t❡st❡r✧✭❙❙❚✮ é ❝♦♠♣♦st♦ ♣♦r ❞♦✐s ❡♥r♦✲ ✾✷ ❋✐❣✉r❛ ✸✳✷✸ ✕ ◗✉❛❞r♦ ❞❡ ❊♣st❡✐♥ ✲ ✐❧✉str❛çã♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭P❊❘❊■❘❆ ❏❯◆■❖❘✱ ✷✵✶✶✮❋✐❣✉r❛ ✸✳✷✹ ✕ ❈✐r❝✉✐t♦ ❡sq✉❡♠át✐❝♦ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞♦ t❡st❡ ❞❡ ♣❡r❞❛s♠❛❣♥ét✐❝❛s ❡ ❧❡✈❛♥t❛♠❡♥t♦ ❞❛ ❝✉r✈❛ BH✳❋♦♥t❡✿ ◆❇❘✲✻✶✺✶✱ ✶✾✾✻✳ ✾✸ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦ é ❛♣❧✐❝❛❞♦ ♥♦ ❡♥r♦❧❛♠❡♥t♦ ♣r✐♠ár✐♦✱ ♠❛✐s ❡①t❡r♥♦✳❆ ♠❡❞✐çã♦ ❞❡ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ é r❡❛❧✐③❛❞❛ ♥♦ ❡♥r♦❧❛♠❡♥t♦ s❡❝✉♥❞á✲ r✐♦✳❋✐❣✉r❛ ✸✳✷✺ ✕ ❊sq✉❡♠❛ ❞♦ s❡♥s♦r ❙❙❚✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❯❑❯❍❆❘❆✱ ✷✵✶✵✮✳✸✳✸✳✺ ❚é❝♥✐❝❛ ♣❛r❛ ❛ ♠❡❞✐çã♦ ❞♦s ♣r♦❝❡ss♦s ❞❡ ♦r✐❡♥t❛çã♦ ❝r✐s✲ t❛❧♦❣rá✜❝❛ ✭❊❇❙❉✮ ❆ ❞✐❢r❛çã♦ ❞❡ ❡❧étr♦♥s r❡tr♦ ❡s♣❛❧❤❛❞♦s ✭❊❧❡❝tr♦♥ ❇❛❝❦❙❝❛tt❡r❉✐✛r❛❝t✐♦♥✲❊❇❙❉✮ é ✉♠❛ té❝♥✐❝❛ q✉❡ ❢♦r♥❡❝❡ ✐♥❢♦r♠❛çõ❡s ❞❛ ♦r✐❡♥t❛çã♦❝r✐st❛❧♦❣rá✜❝❛ ♦❜t✐❞❛s ❞❡ ❛♠♦str❛s ❛tr❛✈és ❞❛ ❛♥á❧✐s❡ ❞❡ ♣❛❞rõ❡s ❞❡❞✐❢r❛çã♦ ❡♠ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❡❧❡trô♥✐❝♦ ❞❡ ✈❛rr❡❞✉r❛ ✭▼❊❱✮✳ ❆ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s ♦❜t✐❞♦s ♣♦r ❊❇❙❉ é r❡❛❧✐③❛❞❛ ♣❡❧❛ ♦❜s❡r✲✈❛çã♦ ❞♦ ♠❛♣❛ ✭❝♦♥❢❡r✐r ❋✐❣✉r❛ ✸✳✷✼✮ ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ ♦r✐❡♥t❛çõ❡s✭❖r✐❡♥t❛t✐♦♥ ■♠❛❣✐♥❣ ▼✐❝r♦s❝♦♣②✲❖■▼✮✳ ❊st❛ té❝♥✐❝❛ é ❛♣❧✐❝❛❞❛ ♥❛ ❛✈❛❧✐❛çã♦ ❞♦s ♣r♦❝❡ss♦s ❞❡ ❧❛♠✐♥❛çã♦♥❛ ♦❜t❡♥çã♦ ❞❡ ♠❛t❡r✐❛❧ ❞❡ ❣rã♦ ♦r✐❡♥t❛❞♦✳ ❆ t❡❝♥♦❧♦❣✐❛ ❞❡ ♦❜t❡♥çã♦❡ ❝♦♥tr♦❧❡ ❞♦ ❣rã♦ t❡♠ s✐❞♦ ♠✉✐t♦ ❡①♣❧♦r❛❞❛ ❞❡✈✐❞♦ às ✈❛♥t❛❣❡♥s ❞❡❡✜❝✐ê♥❝✐❛ ❡♥❡r❣ét✐❝❛ ❞♦ ❡q✉✐♣❛♠❡♥t♦✳ ❆ ❧❛♠✐♥❛çã♦ r❡❞✉③ ❛ ❡s♣❡ss✉r❛ ✐♥✐❝✐❛❧ ❞❛ ❝❤❛♣❛ ❡ s❡ t♦r♥❛ ✉♠✐♥❞✐❝❛❞♦r ❞♦ ♣r♦❝❡ss♦✳ ❆ té❝♥✐❝❛ ❞❡ ❣rã♦ ♦r✐❡♥t❛❞♦ ♠❡❧❤♦r❛ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ r❡❞✉③✐♥❞♦ ✾✹ ❋✐❣✉r❛ ✸✳✷✻ ✕ ❙❡♥s♦r ❞❡ ❧â♠✐♥❛ ú♥✐❝❛ ❙❙❚✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❯❑❯❍❆❘❆✱ ✷✵✶✵✮✳❋✐❣✉r❛ ✸✳✷✼ ✕ ❊①❡♠♣❧♦ ❞❡ ❖■▼ ❡ ❝ó❞✐❣♦ ❞❡ ❝♦r❡s✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❯❑❯❍❆❘❆✱ ✷✵✶✵✮ ✾✺ ♣❡♥❤♦ ❞♦ ❡q✉✐♣❛♠❡♥t♦ ❡♠ t❡r♠♦s ❞❡ ♣❡r❞❛s ♠❛❣♥ét✐❝❛s✱ ❞❡ ♠♦❞♦ q✉❡✱❡♠ t❡r♠♦s ♣❡r❝❡♥t✉❛✐s✿ er = esp 1 − × 100 ✭✸✳✷✷✮ e ❖ ❝✐r❝✉✐t♦ ♣r♦♣♦st♦ t❛♠❜é♠ ♣♦❞❡r✐❛ ✐♥❞✐❝❛r q✉❡ ♠❛t❡r✐❛❧ ❛♣r❡✲ s❡♥t❛ ♠❡❧❤♦r ♦r✐❡♥t❛çã♦ ✭♦❜s❡r✈❛r ❋✐❣✉r❛s ✸✳✷✽ ❡ ✸✳✷✾✮✳❋✐❣✉r❛ ✸✳✷✽ ✕ ▲❛♠✐♥❛çã♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❯❑❯❍❆❘❆✱ ✷✵✶✵✮✸✳✸✳✻ ❚❡①t✉r❛ ❈r✐st❛❧♦❣rá✜❝❛ ❖s ❣rã♦s ♥ã♦ ❡stã♦ ♦r✐❡♥t❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡✱ ♣r✐✈✐❧❡❣✐❛♥❞♦ ❛❧✲❣✉♠❛s ❞✐r❡çõ❡s ❡♠ r❡❧❛çã♦ à ❞✐r❡çã♦ ❞❛ ❧❛♠✐♥❛çã♦✳ ❆ ❞✐str✐❜✉✐çã♦ ❞❛s♦r✐❡♥t❛çõ❡s ❡♠ r❡❧❛çã♦ à ❧❛♠✐♥❛çã♦ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ t❡①t✉r❛ ❝r✐st❛❧✐♥❛✳❙❡✉ ❝♦♥tr♦❧❡ ♣❡r♠✐t❡ ❛ ❢❛❜r✐❝❛çã♦ ❞❡ ♠áq✉✐♥❛s ❞❡ ❛❧t♦ r❡♥❞✐♠❡♥t♦✳ ❆s t❡①t✉r❛s ✉s✉❛✐s sã♦✿❼ ❚❡①t✉r❛ ●♦ss✳ ❬✶✵✵❪✿ ❢❛✈♦r❡❝❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❣♥ét✐❝❛s✱ é ❝♦✲ ♥❤❡❝✐❞❛ ❝♦♠♦ ❞✐r❡çã♦ ❡s♣♦♥tâ♥❡❛ ♦✉ ❞❡ ❢á❝✐❧ ♠❛❣♥❡t✐③❛çã♦✳ ❊st❛ t❡①t✉r❛ é ❢♦rt❡♠❡♥t❡ ♦r✐❡♥t❛❞❛✳ ❈❛r❛❝t❡r✐③❛ ♦ ❛ç♦ s✐❧í❝✐♦ ❞❡ ❣rã♦♦r✐❡♥t❛❞♦✱ ✐❞❡❛❧ ♣❛r❛ tr❛♥s❢♦r♠❛❞♦r❡s ❡ ♠áq✉✐♥❛s ❡stát✐❝❛s❀ ❼ ❚❡①t✉r❛ ❝ú❜✐❝❛ ❬✶✵✶❪✿ í♥❞✐❝❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♠é❞✐♦✱ ✐❞❡❛❧ ♣❛r❛♠♦t♦r❡s❀ ❼ ❋✐❜r❛ ❣r❛♠❛ ❬✶✶✶❪✿ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞✐❢í❝✐❧✳ ◆ã♦ ❛♣r❡s❡♥t❛ ✉t✐❧✐✲❞❛❞❡ ❡♠ q✉❛❧q✉❡r t✐♣♦ ❞❡ ♠áq✉✐♥❛✳ ✾✻ ❋✐❣✉r❛ ✸✳✷✾ ✕ ▼❛❣♥❡t✐③❛çã♦ ❡♠ r❡❧❛çã♦ ❛♦s í♥❞✐❝❡s ❞❡ ▼✐❧❧❡r ❞❡ ✉♠❛❡str✉t✉r❛ ❈❈❈ ✭❈ú❜✐❝❛ ❞❡ ❈♦r♣♦ ❈❡♥tr❛❞♦✮✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❯❑❯❍❆❘❆✱ ✷✵✶✵✮✸✳✹ ❖❇❚❊◆➬➹❖ ❈❯❘❱❆ ❉❊ ❍■❙❚❊❘❊❙❊ ❖ ❝✐r❝✉✐t♦ ❞❛ ❋✐❣✳ ✸✳✸✵ ♣♦ss✐❜✐❧✐t❛ ✐♥✈❡st✐❣❛r ♦ ❝✐❝❧♦ ❞❡ ❤✐st❡✲ r❡s❡ ❞❡ ✉♠ ♥ú❝❧❡♦ ♠❛❣♥ét✐❝♦✳ ❆ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ❞♦ ♠ét♦❞♦ ❞❡♠❡❞✐çã♦ é ❞❡s❝r✐t❛ ♥♦ ❆♥❡①♦ ❆✳ ◆♦ ♣r❡s❡♥t❡ ❡st✉❞♦✱ ✉t✐❧✐③❛✲s❡ ✉♠ ♥ú❝❧❡♦ ♠❛❣♥ét✐❝♦ ❢❡❝❤❛❞♦ ❞❡✉♠ ♣❡q✉❡♥♦ tr❛♥s❢♦r♠❛❞♦r ❞❡ t❡st❡✳ ❖ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ é ❣❡r❛❞♦♣❡❧❛ ♣❛ss❛❣❡♠ ❞❛ ❝♦rr❡♥t❡ ♥❛ ❜♦❜✐♥❛ ♣r✐♠ár✐❛ ❧✐❣❛❞❛ ❛♦ tr❛♥s❢♦r♠❛❞♦r✈❛r✐á✈❡❧✳ ❖ ❝❛♠♣♦ H é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à ❝♦rr❡♥t❡ q✉❡ ❝✐r❝✉❧❛1 ♥❛ ❜♦❜✐♥❛ ♣r✐♠ár✐❛✳ P♦rt❛♥t♦✱ ❛ q✉❡❞❛ ❞❡ t❡♥sã♦ V R s♦❜r❡ ♦ r❡s✐st♦r t❛♠❜é♠ é ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ❝❛♠♣♦ H✳ ❉❛ ❧❡✐ ❞❡ ❆♠♣❡r❡✱I H dl = N 1 i1✭✸✳✷✸✮ ✾✼ ❋✐❣✉r❛ ✸✳✸✵ ✕ ❈✐r❝✉✐t♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❙■▲❱❆✱ ✶✾✾✺✮ ❈♦♠ ❜❛s❡ ♥❛ ❋✐❣✉r❛ ✸✳✸✵✱ ❛ ✐♠❛❣❡♠ ❡①✐❜✐❞❛ ♥♦ ❝❛♥❛❧ ✶ ❞♦ ♦s❝✐✲❧♦s❝ó♣✐♦ é ♣r♦♣♦r❝✐♦♥❛❧ à ❝♦rr❡♥t❡✿ V (t) ch1 i(t) = ,✭✸✳✷✹✮ R1❧♦❣♦✿ N1 H(t) = V ch1✭✸✳✷✺✮ l Rm1 ♦♥❞❡ l m é ♦ ❝♦♠♣r✐♠❡♥t♦ ♠é❞✐♦ ❞♦ ♥ú❝❧❡♦✱ N 1 é ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s❞♦ ♣r✐♠ár✐♦ ❡ R 1 é ♦ r❡s✐st♦r s❤✉♥t ❞❡ 1 Ω✳ S ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❧❡✐ ❞❡ ❋❛r❛❞❛②✱ ❛ t❡♥sã♦ V ♥❛ ❜♦❜✐♥❛ s❡❝✉♥❞ár✐❛é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à ❞❡r✐✈❛❞❛ ❞♦ ✢✉①♦ t♦t❛❧ ❡♠ r❡❧❛çã♦ ❛♦ S t❡♠♣♦✳ ❊♠♣r❡❣❛♥❞♦✲s❡ ✉♠ ❝✐r❝✉✐t♦ RC ♣❛r❛ ✐♥t❡❣r❛r ♦ s✐♥❛❧ V t❡♠✲s❡✱ ❞❛ ❧❡✐ ❞❡ ❋❛r❛❞❛②✿ dφ(t) V 2 = N 2 ,✭✸✳✷✻✮ dt ❡s❝♦❧❤❡♥❞♦✲s❡ ✉♠ r❡s✐st♦r R 2 ❛♣r♦♣r✐❛❞♦ ❞❡ ❢♦r♠❛ q✉❡ ❛ ♠❛✐♦r ♣❛rt❡❞❛ q✉❡❞❛ ❞❡ t❡♥sã♦ ♦❝♦rr❛ ♥♦ ♠❡s♠♦✿ V = i (t)R . ✾✽ ◆♦ ❝❛s♦✱ ❢♦✐ ❡s❝♦❧❤✐❞♦ ✉♠ r❡s✐st♦r ❞❡ 100 kΩ✱ ❛ss✐♠✱ ❧❡♠❜r❛♥❞♦✲s❡ q✉❡ dV c (t)i (t) = C , c ✭✸✳✷✽✮ dtt❡♠✲s❡ q✉❡ dφ(t) dV c (t) N = C R .2 2 ✭✸✳✷✾✮ c (t) = V ch2 (t) dt dt❈♦♠♦ φ = B(t)S ❡ V ✱ t❡♠✲s❡ q✉❡ R C2 B(t) = V ch2✭✸✳✸✵✮ N S2♦♥❞❡ S é ❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❞♦ ♥ú❝❧❡♦✱ N2 2 é ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❞♦ s❡❝✉♥❞ár✐♦✱ R é ♦ r❡s✐st♦r ❞❡ ✶✵✵ kΩ ❡ C é ♦ ❝❛♣❛❝✐t♦r ❞❡ 1, 5 µF✳r (t) C (t) ◆♦ ❝❛s♦✱ V é ♣r♦♣♦r❝✐♦♥❛❧ ❛ H(t) ❡ V é ♣r♦♣♦r❝✐♦♥❛❧ ❛B(t) ✳ ❊ss❛s ❞✉❛s t❡♥sõ❡s sã♦ ❧✐❞❛s ♣❡❧♦s ❝❛♥❛✐s ✶ ❡ ✷ ❞♦ ♦s❝✐❧♦s❝ó♣✐♦✳❆ ♦♣❡r❛çã♦ ♥♦ ♠♦❞♦ xy ✭❝❛♥❛❧ ✶→❡✐①♦ ①✮ ❡①✐❜❡ ❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡❤✐st❡r❡s❡ B(t) = F (H(t)) ❞♦ ♥ú❝❧❡♦ ♠❛❣♥ét✐❝♦✳ ◆♦ ❝❛s♦ ❞❡ s❡ tr❛t❛r ❞❡ ❞✐s♣♦s✐t✐✈♦s ❝♦♠ ✉♠❛ ú♥✐❝❛ ❜♦❜✐♥❛✱ ❝♦♠♦é ♦ ❝❛s♦ ❞❡ ❝♦♥t❛❝t♦r❡s✱ r❡❛t♦r❡s ❡ ❛té ♠❡s♠♦ ♠♦t♦r❡s ❞❡ ✐♥❞✉çã♦ é♣♦ssí✈❡❧ ✉t✐❧✐③❛r ✉♠❛ ✈❛r✐❛çã♦ ❞♦ ♠❡s♠♦ ❝✐r❝✉✐t♦✱ q✉❡ s❡rá ❛♣r❡s❡♥t❛❞♦♥♦ ❈❛♣ít✉❧♦ ✹✳ ◆❛ ❋✐❣✉r❛ ✸✳✸✶✱ ♦❜tê♠✲s❡ ❛s ❢♦r♠❛s ❞❡ ♦♥❞❛ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦❞❛ t❡♥sã♦ ❡ ❝♦rr❡♥t❡s✱ ❛s q✉❛✐s sã♦ ♣r♦♣♦r❝✐♦♥❛✐s à ✐♥❞✉çã♦ B(t) ❡ à✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H(t)✳ ◆❛ ♠♦♥t❛❣❡♠ ❞♦ ❝✐r❝✉✐t♦ ✐❧✉str❛❞♦ ♥❛❋✐❣✉r❛ ✸✳✸✵✱ ❢♦✐ ✉t✐❧✐③❛❞♦ ✉♠ ♦s❝✐❧♦s❝ó♣✐♦ ❞✐❣✐t❛❧ ❚❊❑❚❘❖◆■❈❙ ❞❡ ✸✵▼❍③✳ ◆❛ ❋✐❣✳ ✸✳✸✷ t❡♠♦s ♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❞♦ ♠❛t❡r✐❛❧ ❛♥❛❧✐s❛❞♦ ❡①✲♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ❊st❛ ❝✉r✈❛ ❢♦✐ ♦❜t✐❞❛ ❛♦ ♠✉❧t✐♣❧✐❝❛r ❛s ✺✵✵ ❛♠♦str❛s❞❛s t❡♥sõ❡s ❞♦s ❝❛♥❛✐s ❞♦ ♦s❝✐❧♦s❝ó♣✐♦ ♣❡❧♦s ❢❛t♦r❡s ❞❡ ❡s❝❛❧❛ q✉❡ ❛♣❛✲ r❡❝❡♠ ♥❛s ❡q✉❛çõ❡s ✭✸✳✷✺✮ ❡ ✭✸✳✸✵✮✳ ◆❡ss❡ ❝❛s♦✱ ✉t✐❧✐③♦✉✲s❡ ♦ ♣r♦❣r❛♠❛❊①❝❡❧ ♣❛r❛ ♣r♦❞✉③✐r ♦s ✈❛❧♦r❡s ❞❡ ❇✭t✮ ❡ ❍✭t✮✳ ❖ ❝á❧❝✉❧♦ ❞♦s ❢❛t♦r❡s ❞❡ ❡s❝❛❧❛ ❜❛s❡✐❛✲s❡ ❡♠ ❞✐♠❡♥sõ❡s ❣❡♦♠é✲ tr✐❝❛s ❞♦ ❡q✉✐♣❛♠❡♥t♦ s♦❜ ❛♥á❧✐s❡✳ ❖ ✉s♦ ❞♦ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s✜♥✐t♦s ❛✉①✐❧✐❛ ♥❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ✈❛❧♦r❡s ❝♦♠♦✿ ✭✐✮ ✈♦❧✉♠❡ ❞❡ ♠❛t❡r✐❛❧♠❛❣♥ét✐❝♦ v❀ ✭✐✐✮ s❡çã♦ ♠❛❣♥ét✐❝❛ S❀ ✭✐✐✐✮ ❝♦♠♣r✐♠❡♥t♦ ♠é❞✐♦ ❞❡ ❝✐r❝✉✲ m❧❛çã♦ ❞♦ ✢✉①♦ ♠❛❣♥ét✐❝♦ l ✳ ❆ss✐♠✱ ❛♦ tr❛ç❛r✲s❡ ♦ ♣❡r❝✉rs♦ ♠é❞✐♦ ❞♦ m = 0, 168602 [m]✢✉①♦ ♥♦ ❋❊▼▼ ✭❝♦♥❢❡r✐r ❋✐❣✉r❛ ✸✳✸✸✮✱ ♦❜té♠✲s❡ l ✳ ❆ ❚❛❜❡❧❛ ✸✳✹ ❛♣r❡s❡♥t❛ ✉♠ r❡s✉♠♦ ❞♦s ❞❛❞♦s ❝♦♥str✉t✐✈♦s ❞♦ tr❛♥s❢♦r♠❛❞♦r ❡♠ ❡st✉❞♦✳ ✾✾ ❋✐❣✉r❛ ✸✳✸✶ ✕ ❋♦r♠❛s ❞❡ ♦♥❞❛ ❞♦s ❝❛♠♣♦s H(t) ❡ B(t)✱ ♣r♦♣♦r❝✐♦♥❛✐s❛♦s s✐♥❛✐s ❞❡ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛ ❡ t❡♥sã♦ s❡❝✉♥❞ár✐❛✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❋✐❣✉r❛ ✸✳✸✷ ✕ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❝♦♥str✉í❞♦ ✉t✐❧✐③❛♥❞♦♦s❝✐❧♦s❝ó♣✐♦ ❞✐❣✐t❛❧ ❝♦♠ ❛♠♦str❛❣❡♠ ❞❡ ✺✵✵ ♣♦♥t♦s✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ✶✵✵ ❋✐❣✉r❛ ✸✳✸✸ ✕ ❉❡✜♥✐çã♦ ❞♦ ❝♦♠♣r✐♠❡♥t♦ ♠é❞✐♦ ❛❞♦t❛❞♦ l m= 0, 1686 m ✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ❚❛❜❡❧❛ ✸✳✹ ✕ ❘❡s✉♠♦ ❞♦s ❞❛❞♦s ❝♦♥str✉t✐✈♦s ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ V 1 ✷✷✵ ❱ V 2 ✷✹ ❱ f✻✵ ❍③ B✶✵✵✵✵ ❣❛✉ss S✼✱✻ ❝♠2 ✭✸✱✾ ❝♠2 ✮ l m ✵✱✶✻✽✻ ♠N 1 ✶✶✵✵ ❡s♣✐r❛sN 2 ✶✷✵ ❡s♣✐r❛sR 1 ✶❘✴✶❲R 2 ✶✵✵❦Ω✴✵✱✷✺❲ C✶✱✺µ❋✴✷✺✵❱ ✶✵✶ ❈♦♥s✐❞❡r❛♥❞♦ ♦s ✈❛❧♦r❡s ❛♣r❡s❡♥t❛❞♦s ♥❛ ❚❛❜❡❧❛ ✸✳✹ ❡ ❛s ❊q✉❛✲çõ❡s ✭✸✳✷✺✮ ❡ ✭✸✳✸✵✮✱ é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❢❛t♦r❡s ❞❡ ❡s❝❛❧❛ ♣❛r❛ ♦s = 6524, 3 [Ae/V] = 1, 644 [T/V]❝❛♠♣♦s H ❡ B✱ ❞❡ ♠♦❞♦ q✉❡✱ f H ❡ f B ✳✸✳✹✳✶ P♦♥t♦s ♥♦tá✈❡✐s ❞❛ ❝✉r✈❛ BH ❈♦♥s✐❞❡r❛♥❞♦ ❛ ❋✐❣✉r❛ ✸✳✸✹✱ é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ♦s ♣♦♥t♦s ♥♦✲ tá✈❡✐s ♥❛ ❝✉r✈❛ BH✳❋✐❣✉r❛ ✸✳✸✹ ✕ ❖ ❡❢❡✐t♦ ❞❡ ❤✐st❡r❡s❡ é ❣❡r❛❞♦ ♣❡❧❛ r❡s✐stê♥❝✐❛ à ♠♦✈✐♠❡♥✲ t❛çã♦ ❞❡ ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r ❊ss❡s ♣♦♥t♦s ♥♦tá✈❡✐s sã♦✿❼ ❆ ❘❡♠❛♥ê♥❝✐❛ ✭B r ✮ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❝❛♠♣♦ B r❡s✐❞✉❛❧ ♥❛ ❛♠♦str❛ ❛♣ós ❛ r❡t✐r❛❞❛ ❞♦ ❝❛♠♣♦ H ✭♦✉ s❡❥❛✱ q✉❛♥❞♦ H = 0✮✳ ◆♦ ❝❛s♦ ❞❛ ✶✵✷ ❼ ❆ ❈♦❡r❝✐✈✐❞❛❞❡ ✭H c ✮ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H ♥❡❝❡s✲ sár✐♦ ♣❛r❛ r❡❞✉③✐r ♦ ❝❛♠♣♦ B ♥♦ ✐♥t❡r✐♦r ❞❛ ❛♠♦str❛ ❛ ③❡r♦✳ ◆♦❝❛s♦ ❞❛ ❝✉r✈❛ BH ♦❜t✐❞❛✱ ❢♦✐ ❡♥❝♦♥tr❛❞♦ ✉♠ ✈❛❧♦r ❞❡ ✶✹✵❬❆✴♠❪♣❛r❛ ❛ ❝♦❡r❝✐✈✐❞❛❞❡✳ ➱ ❡ss❡ ♣❛râ♠❡tr♦ q✉❡ ❞❡✜♥❡ ♦ ♠❛t❡r✐❛❧ ❝♦♠♦♠♦❧❡ ♦✉ ❞♦❝❡✳ max ❼ ❆ ■♥❞✉çã♦ ❞❡ s❛t✉r❛çã♦ ✭B ✮✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ♣♦♥t♦ ❞❡♠á①✐♠❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛✳ ◆♦ ❝❛s♦ ❞❛ ❝✉r✈❛ ♦❜t✐❞❛✱ s❡✉ ✈❛❧♦r❡st❡✈❡ ❡♠ t♦r♥♦ ❞❡ ✶✱✺❬❚❪✳ ◆❛ ❋✐❣✉r❛ ✸✳✸✹✱ ♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ é r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❧✐♥❤❛ só❧✐❞❛ ♥❛ ❝♦r ♣r❡t❛❀ ❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✐♥✐❝✐❛❧ ❡stá r❡♣r❡s❡♥t❛❞❛♥❛ ❝♦r ❛③✉❧✳ ❆ ♣r✐♠❡✐r❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧✱ ❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ ❞❡ ❤✐s✲ t❡r❡s❡✱ s❡ r❡❢❡r❡ ❛♦ ❝❛♠♣♦ ❝♦❡r❝✐t✐✈♦ H c ✳▼❛t❡r✐❛✐s ❢❡rr♦♠❛❣♥ét✐❝♦s q✉❡ ♣♦ss✉❡♠ ✉♠❛ ❝♦❡r❝✐✈✐❞❛❞❡ ❛❧t❛ sã♦ ❞❡♥♦♠✐♥❛❞♦s ❞✉r♦s ✭❝♦❡r❝✐✈✐❞❛❞❡ ♠❛✐♦r q✉❡ ✶✵✹ ❦❆✴♠✮❀ ❛q✉❡❧❡sq✉❡ ♣♦ss✉❡♠ ❝♦❡r❝✐✈✐❞❛❞❡ ❜❛✐①❛ sã♦ ❞❡♥♦♠✐♥❛❞♦s ♠♦❧❡s ♦✉ ❞♦❝❡s ✭❝♦✲❡r❝✐✈✐❞❛❞❡ ♠❡♥♦r q✉❡ ✺✵✵ ❆✴♠✮✳ ❆ ❋✐❣✉r❛ ✸✳✸✺ ❡①❡♠♣❧✐✜❝❛ ♦ ❝♦♠♣♦r✲ t❛♠❡♥t♦ ❞♦ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ♣❛r❛ ❡ss❡s ❝❛s♦s✳❋✐❣✉r❛ ✸✳✸✺ ✕ ❋♦r♠❛t♦ ❞♦ ❧❛ç♦ ❞❡ ❤✐st❡r❡s❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ t✐♣♦ ❞❡♠❛t❡r✐❛❧✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ❆ ❚❛❜❡❧❛ ✸✳✺ ❛♣r❡s❡♥t❛ ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ❝❛❞❛ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧✳❚❛❜❡❧❛ ✸✳✺ ✕ ❊①❡♠♣❧♦s ❞❡ ♠❛t❡r✐❛✐s ❞✉r♦s✱ ♠♦❧❡s ❡ ✐♥t❡r♠❡❞✐ár✐♦s ▼❛t❡r✐❛✐s ❞✉r♦s ▼❛t❡r✐❛✐s ▼♦❧❡s ▼❛t❡r✐❛✐s ✐♥t❡r♠❡❞✐ár✐♦s❋❡rr✐t❡s ❞❡ ❇❛ ❆ç♦ ❙✐❧í❝✐♦ ❋❡ 2 ❖3 ❙♠✲❈♦ ❋❡rr♦ ❈r❖2◆❡✲❋❡✲❇♦ ▼✉♠❡t❛❧ ❚✐♥t❛s ♠❡tá❧✐❝❛s ❞❡ ❋❡ ❡ ❈♦ ✶✵✸ ✸✳✹✳✷ ❖❜t❡♥çã♦ ❞❛ ❝✉r✈❛ BH❆tr❛✈és ❞❡ ✉♠❛ ✐♥t❡r♣♦❧❛çã♦ ♣♦♥t♦ ❛ ♣♦♥t♦ ✭✈❛❧♦r ♠é❞✐♦ ❞❛ s♦♠❛✮✱ ✐♠♣❧❡♠❡♥t❛❞❛ ❝♦♠ ♦ s♦❢t✇❛r❡ ❊①❝❡❧✱ ♦❜t❡✈❡✲s❡ ❛ ❝✉r✈❛ ❞❡ s❛t✉✲r❛çã♦ ♠❛❣♥ét✐❝❛ BH✱ q✉❡ ♣❡r♠✐t❡ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ✭✈❡r✐✜✲❝❛r ❋✐❣✉r❛ ✸✳✸✻✮✳ ❚r❛t❛✲s❡ ❞❡ ✉♠ r❡q✉✐s✐t♦ ❜ás✐❝♦ ♥♦ ♣r♦❥❡t♦ ❡ ❛✈❛❧✐❛çã♦❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❡ ♠áq✉✐♥❛s ❡ ❡q✉✐♣❛♠❡♥t♦s✳❋✐❣✉r❛ ✸✳✸✻ ✕ ❖❜t❡♥çã♦ ♣♦♥t♦ ❛ ♣♦♥t♦ ❞❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ BH❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✹✳✸ ■❞❡♥t✐✜❝❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ❆ r❡❣✐ã♦ q✉❡ ❝❛r❛❝t❡r✐③❛ ✉♠ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦ ❡stá ♣ró✲①✐♠❛ ❞❛ r❡❣✐ã♦ ❞❡ r❡t❡♥t✐✈✐❞❛❞❡ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳ ❆♠♣❧✐❛♥❞♦ ❡st❛③♦♥❛ é ♣♦ssí✈❡❧ ✐❞❡♥t✐✜❝❛r ❞♦✐s ✧❝❛♥❞✐❞❛t♦s✧q✉❡ ♠❛✐s s❡ ❛♣r♦①✐♠❛♠ ❛♦♠❛t❡r✐❛❧ ❧❡✈❛♥t❛❞♦ ♥♦ ❧❛❜♦r❛tór✐♦ ✭✈❡r✐✜❝❛r ❋✐❣✉r❛ ✸✳✸✼✮✳ ◆❡st❡ ❝❛s♦ s❡♣❡r❝❡❜❡ q✉❡ ♦ ❛ç♦ ❝❛r❜♦♥♦ ✶✵✶✵ é ♦ ♠❛✐s ♣ró①✐♠♦ ✭✈❡r✐✜❝❛r ❋✐❣✉r❛ ✸✳✸✽✮✱♥❛ ❜✐❜❧✐♦t❡❝❛ ❞♦ ❋❊▼▼ ❛♣❛r❡❝❡ ❝♦♠ ✉♠❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞❡ ✺✱✽▼❙✴♠ ❡ ◦✉♠ â♥❣✉❧♦ ❞❡ ❤✐st❡r❡s❡ ❞❡ ✷✵ ✳ ❊st❡s ❞❛❞♦s sã♦ ♥❡❝❡ssár✐♦s ♣❛r❛ r♦❞❛r ✶✵✹ ❞❡ ♠❛t❡r✐❛❧ ❡ ❡♠ ❢✉♥çã♦ ❞❡ ❞❛❞♦s ❞❡ ❜✐❜❧✐♦t❡❝❛ s❡ ♦❜té♠ ♣❛râ♠❡tr♦s❡❧❡tr♦♠❛❣♥ét✐❝♦s ✭❝♦♥❞✉t✐✈✐❞❛❞❡✱ â♥❣✉❧♦ ❞❡ ❤✐st❡r❡s❡✮ ❡ ♠❡t❛❧úr❣✐❝♦s✭❧✐❣❛ ❛ç♦ ✶✵✶✵✮✳❋✐❣✉r❛ ✸✳✸✼ ✕ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❧❡✈❛♥t❛❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✺ ❈❆❘❆❈❚❊❘■❩❆➬➹❖ ❉❖ ▼❖❉❊▲❖ ❉❊ ❏■▲❊❙✲❆❚❍❊❘❚❖▼ P❛r❛ tr❛ç❛r ❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ❛ ✐♥❞✉çã♦ B ❞❛ ❝✉r✈❛ ❞❡❤✐st❡r❡s❡ ❞❡✈❡ s❡r ♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦ ✐♥✈❡rs♦ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❞♦ ✈á✲❝✉♦ µ ✱ r❡s✉❧t❛♥❞♦ ♥✉♠ ❣rá✜❝♦ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✳❖s ♣♦♥t♦s ♥♦tá✈❡✐s ♣❛r❛ ❛ ♠♦♥t❛❣❡♠ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❏✐❧❡s❆t❤❡rt♦♠✱ ❡stã♦ ✐♥❞✐❝❛❞♦s ♥❛ ❋✐❣✉r❛ ✸✳✸✾✳ P♦♥t♦s ♥♦tá✈❡✐s ❞❛ ❝✉r✈❛ ❞❡✜♥✐❞♦s ❛ ♣❛rt✐r ❞❛s ❢♦r♠✉❧❛çõ❡s ❞❡❏✐❧❡s✱ ♥♦ ❆♥❡①♦ ❇✱ sã♦ ♦s ♣♦♥t♦s ❞❡ ♣❛rt✐❞❛ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ✐t❡r❛t✐✈♦ ❞❛s✈❛r✐á✈❡✐s a JA ✱ α JA ❡ k JA ✳ ❖ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ♦❜t❡♥çã♦ ❞♦s ✾ ♣♦♥t♦s ❛♣❛rt✐r ❞♦ ❣rá✜❝♦ ❞❡ ♠❛❣♥❡t✐③❛çã♦ é ❝❧❛r❛♠❡♥t❡ ✐❧✉str❛❞♦ ♥❛ ❝✉r✈❛ ❞❛❋✐❣✉r❛ ✸✳✸✾✳ ❆ss✐♠✱5 ∆M in [−5 − (−5, 329)] · 10 χ = = = 632. in ✶✵✺ ❋✐❣✉r❛ ✸✳✸✽ ✕ ❈✉r✈❛ BH ❞❡ ❛ç♦ ❝❛r❜♦♥♦ ✶✵✶✵✳ ◆❡ss❛ ♥♦♠❡♥❝❧❛t✉r❛✱ ♦♥ú♠❡r♦ ✶✵✵✵ ❝♦rr❡s♣♦♥❞❡ ❢❛♠í❧✐❛ ❞❡ ❛ç♦s ❞❡ ❜❛✐①♦ ❝❛r❜♦♥♦✱ ❡♥q✉❛♥t♦♦ ♥ú♠❡r♦ ✶✵ ❝♦rr❡s♣♦♥❞❡ ❛♦ t❡♦r ❞❡ ✵✱✶✪ ❞❡ ❝❛r❜♦♥♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r ❛tr❛✈és ❞❡ ❞❛❞♦s ❞❛ ❜✐❜❧✐♦t❡❝❛ ❞❡ ♠❛t❡r✐❛✐s❞♦ s♦❢t✇❛r❡ ❋❊▼▼❈♦♠ ✐ss♦✱5 M r [A/m], = 2, 8 · 105∆M r [−2, 15 − (−3, 416)] · 10 χ = = = 2694, r∆H r 23, 5 − (−23, 5) H c = 40 [A/m],5∆M c [−9, 49 − (−8, 56)] · 10 χ = = = 90566, c∆H c 56, 24 − 36, 315 M [A/m], m = 4, 5 · 10 H = 175 [A/m], m5∆M c (4, 83 − 3, 99) · 10 χ = = = 90566, m∆H c 197 − 2505 M s = 2M m [A/m]. = 9, 0 · 10 ✶✵✻ ❋✐❣✉r❛ ✸✳✸✾ ✕ ❈✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❡♠ r❡❧❛çã♦ à ✐♥t❡♥s✐❞❛❞❡ ❞❡❝❛♠♣♦✱ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❧❡✈❛♥t❛❞❛ ♣❡❧♦ ❝✐r❝✉✐t♦♣r♦♣♦st♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳✸✳✻ ❈❯❘❱❆❙ ❉❊ ●❘❆◆❉❊❩❆❙ ▼❆●◆➱❚■❈❆❙ ❉❖ ❚❘❆◆❙✲ ❋❖❘▼❆❉❖❘◆❡st❛ s❡çã♦✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❝✉r✈❛s ❞❛ ✈❛r✐❛çã♦ ❞❛s ❣r❛♥❞❡✲ ③❛s ♠❛❣♥ét✐❝❛s ❞♦ tr❛♥s❢♦r♠❛❞♦r✱ ❝♦♠♦ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ ✐♥❞✉tâ♥❝✐❛ ❡ r❡❧✉tâ♥❝✐❛✱ ❡♠ ❢✉♥çã♦ ❞❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♠❛t❡r✐❛❧ q✉❡ ♦ ❝♦♥st✐t✉✐✳✸✳✻✳✶ ❈✉r✈❛ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❞✐❢❡r❡♥❝✐❛❧ ❆tr❛✈és ❞❛ ❝✉r✈❛ BH ♦❜t✐❞❛ ♣♦♥t♦ ❛ ♣♦♥t♦ é ♣♦ssí✈❡❧ ❝❛❧❝✉❧❛r s✉❛ ❞❡r✐✈❛❞❛ ♥♦s ♣♦♥t♦s ❡♠ q✉❡stã♦✱ ❝♦♠ ♦ ❛✉①í❧✐♦ ❞❡ ♣r♦❣r❛♠❛s ❢❡✐t♦s❡♠ ▼❛t▲❛❜ ♦✉ ❊①❝❡❧✱ ♣❛r❛ s❡ ♦❜t❡r ❛ ❝✉r✈❛ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❛❜s♦❧✉t❛ ✶✵✼ ❈♦♠ ❛ ❝✉r✈❛ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❛❜s♦❧✉t❛ ❞♦ ♠❛t❡r✐❛❧ ❡♠ ❢✉♥✲çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✱ ♣♦❞❡♠ s❡r ♦❜t✐❞❛s ♦✉tr❛s ❝✉r✈❛s ❝♦♠♦✿♣❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛✱ ✐♥❞✉tâ♥❝✐❛s ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛✱ ✐♥❞✉tâ♥✲❝✐❛ ♠út✉❛✱ ♠❛❣♥❡t✐③❛çã♦✱ s✉s❝❡♣t✐❜✐❧✐❞❛❞❡✱ r❡❧✉tâ♥❝✐❛ ❡ ♣❡r♠❡â♥❝✐❛✳❆ss✐♠✱ ❝♦♠ ❡ss❛ ✐♥❢♦r♠❛çã♦✱ é ♣♦ssí✈❡❧ t❡r ✉♠❛ ✈✐sã♦ q✉❛❧✐t❛t✐✈❛ ❞❛♦♣❡r❛çã♦ ❞❛ ♠áq✉✐♥❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ❝♦rr❡♥t❡s ❞❡ ♦♣❡r❛çã♦✱ ❛❥✉❞❛♥❞♦❛ ❞❡✜♥✐r ♠❡❧❤♦r ♦s ❝r✐tér✐♦s ❞❡ ♣r♦❥❡t♦ ❛❞♦t❛❞♦s✳ ➱ ✐♠♣♦rt❛♥t❡ ❞❡st❛❝❛r q✉❡ ❡①✐st❡♠ ✈ár✐♦s t✐♣♦s ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛✲❞❡s ♠❛❣♥ét✐❝❛s ♣❛r❛ ✉♠ ❞❛❞♦ ♠❛t❡r✐❛❧ ✭❇❊❘❚❖❚❚■✱ ✶✾✽✽❀ ❇❖❩❖❘❚❍✱✷✵✵✵✮✳ ❙ã♦ ❡❧❡s✿ ❼ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♥♦r♠❛❧✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ µ✱ é❞❛❞❛ ♣❡❧❛ r❛③ã♦ B/H ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞♦ ♠❛t❡r✐❛❧ ♥♦ ❡st❛❞♦ ❞❡s✲♠❛❣♥❡t✐③❛❞♦❀ i ❼ P❡r♠❡❛❜✐❧✐❞❛❞❡ ✐♥✐❝✐❛❧✱ µ ✱ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞♦ ❞❡❝❧✐✈❡ ❞❛ ❝✉r✈❛BH ♥❛ ♦r✐❣❡♠❀❼ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠á①✐♠❛✱ µ max ✱ q✉❡ é ♦ ♠❛✐♦r ✈❛❧♦r ♦❜t✐❞♦ ♣❛r❛ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♥♦r♠❛❧❀❼ P❡r♠❡❛❜✐❧✐❞❛❞❡ ❞✐❢❡r❡♥❝✐❛❧✱ µ dif ✱ q✉❡ é ❝❛❧❝✉❧❛❞❛ ♣❡❧♦ ❞❡❝❧✐✈❡ dB/dH ♣❛r❛ ✉♠ ❞❛❞♦ ♣♦♥t♦ ❞❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦✳❆ ❋✐❣✉r❛ ✸✳✹✵ ❛♣r❡s❡♥t❛ ❛ ❝✉r✈❛ ❞❛ ✈❛r✐❛çã♦ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛ ❞♦ ♠❛t❡r✐❛❧ ♠❛❣♥ét✐❝♦ ❡♠ ❡st✉❞♦✳❖❜s❡r✈❛✲s❡ q✉❡ ✉s✉❛❧♠❡♥t❡ s❡ ✉t✐❧✐③❛ ✉♠❛ ❞❡♥s✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❞❡ ✶✱✵ ❬❚❪ ♥♦ ♣r♦❥❡t♦ ❞❡ tr❛♥s❢♦r♠❛❞♦r❡s✳ ❆ss✐♠✱ ❝♦♠ ❛ ❝✉r✈❛ BH❝❛r❛❝t❡r✐③❛❞❛ ♣♦❞❡✲s❡ ❡st✐♠❛r✱ ❝♦♠ ✉♠ ❡rr♦ ♣❡q✉❡♥♦✱ ❛ ❝♦rr❡♥t❡ ❞❡❡①❝✐t❛çã♦ ❞❡ ✉♠❛ ♠áq✉✐♥❛ ❡ ❝♦♠ ✐st♦ ❛s ♣❡r❞❛s ❛ ✈❛③✐♦✳ ✶✵✽ ❋✐❣✉r❛ ✸✳✹✵ ✕ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥t❡♥s✐✲❞❛❞❡ ❞❡ ❝❛♠♣♦✳ ❚❡♦r✐❝❛♠❡♥t❡✱ ❡st❛ ❝✉r✈❛ ❞❡✈❡r✐❛ ♣❛rt✐r ❞♦ ③❡r♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✻✳✷ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❞♦ ♥ú❝❧❡♦ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦r✲ r❡♥t❡ ♣r✐♠ár✐❛ ❆ ♣❛rt✐r ❞♦ ❣rá✜❝♦ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❡♠ ❢✉♥çã♦ ❞❛✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦✱ é ♣♦ssí✈❡❧ ♣❧♦t❛r ❛ r❡❧❛çã♦ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✈❡rs✉s ❝♦rr❡♥t❡✳ ❊ss❡ ❣rá✜❝♦ ♣❡r♠✐t❡ ✈✐s✉❛❧✐③❛r ❝♦♠♦ ❛ r❡❧❛çã♦ ❞❛s ❝♦r✲ r❡♥t❡s ❞❡ ♦♣❡r❛çã♦ ❡stá ❛tr❡❧❛❞❛ à ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ❞♦ ♠❛t❡✲r✐❛❧✳ ❆ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛ s❡ ♦❜té♠ ❛tr❛✈és ❞❛ r❡❧❛çã♦µ abs µ = rµ ❡ ❛ ❝♦rr❡♥t❡ ❛tr❛✈és ❞❛ ❧❡✐ ❞❡ ❆♠♣❡r❡✱ ❞❡ ♠♦❞♦ q✉❡✿ l 0, 1686m i = H(t) = H(t). 1 ✭✸✳✸✶✮N 11001 ❆ ❋✐❣✉r❛ ✸✳✹✶ ❡①♣r✐♠❡ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ✶✵✾ ❋✐❣✉r❛ ✸✳✹✶ ✕ P❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ r❡❧❛t✐✈❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡❞❡ ❡①❝✐t❛çã♦ ♣r✐♠ár✐❛✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✻✳✸ ■♥❞✉tâ♥❝✐❛s ♣ró♣r✐❛s L1 ❡ L2 ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ♣r✐✲ ♠ár✐❛❉❛ ❧❡✐ ❞❛ ❋❛r❛❞❛② ❡ ❞❡ ❆♠♣❡r❡ s❡ ♦❜té♠ ✉♠❛ ❡①♣r❡ssã♦ ♣❛r❛ ❛s ✐♥❞✉tâ♥❝✐❛s ♣r❡s❡♥t❡s ♥♦ tr❛♥s❢♦r♠❛❞♦r✱ ❞❡ ♠♦❞♦ q✉❡✿ V 1 = N1 dφdt ,✭✸✳✸✷✮ H =N1 i1 lm ,✭✸✳✸✸✮ B = µH,✭✸✳✸✹✮ φ = BS. ✭✸✳✸✺✮❘❡❧❛❝✐♦♥❛♥❞♦ ✭✸✳✸✷✮✱ ✭✸✳✸✸✮✱ ✭✸✳✸✹✮ ❡ ✭✸✳✸✺✮✱ t❡♠♦s q✉❡✿ φ =N1 S lm µ(i)i(t)✭✸✳✸✻✮ ❡ V1 =N21 S µ(i) di(t). ✭✸✳✸✼✮ ✶✶✵ ❉❛ ❞❡✜♥✐çã♦ ❞❡ ✐♥❞✉tâ♥❝✐❛N φ L =, ✭✸✳✸✽✮ it❡♠♦s q✉❡ ❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ é✿2 N S1 L = µ(i) [H]. ✭✸✳✸✾✮ l m■st♦ é✱ ❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ é ♣r♦♣♦r❝✐♦♥❛❧ à ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ q✉❡✱ ♣♦r s✉❛ ✈❡③✱ ❞❡♣❡♥❞❡ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝✐t❛çã♦✳ ✶ ❈♦♠♦ S✱ N 1 ❡ l m sã♦ ❝♦♥st❛♥t❡s✱ ♣♦❞❡♠♦s r❡❡s❝r❡✈❡r ❛ ❊q✉❛çã♦✭✸✳✸✾✮ ❞❡ ♠♦❞♦ q✉❡✿ L = K µ (i),1 L1 r ✭✸✳✹✵✮❝♦♠2 SN µ1 K L1 = = 0, 006855. ✭✸✳✹✶✮ lm❖❜s❡r✈❛r q✉❡ ❛ ❊q✉❛çã♦ ✭✸✳✹✵✮ ❡stá ❡♠ t❡r♠♦s ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ r❡❧❛t✐✈❛✳❉❡ ❢♦r♠❛ ❛♥á❧♦❣❛ ❛ ✐♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞♦ s❡❝✉♥❞ár✐♦ ♣♦❞❡ s❡r ♦❜t✐❞❛✿L = K µ (i),2 L2 r ✭✸✳✹✷✮ ❝♦♠2 SN µ2 K = = 0, 00008153. L2 ✭✸✳✹✸✮ lm❉❛ r❡❧❛çã♦✱ ❡♥tr❡ ❛s ✐♥❞✉tâ♥❝✐❛s s❡ ❝❤❡❣❛ ❛ ✉♠❛ ❡①♣r❡ssã♦ q✉❡ r❡❧❛❝✐♦♥❛ ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❡ ❛ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦✱ q✉❡ s❡rá ✉t✐❧✐③❛❞❛ ♣❛r❛ s✐♠♣❧✐✜❝❛r ❝á❧❝✉❧♦s ♥❛s s❡çõ❡s s❡❣✉✐♥t❡s✿L N112 = = a✭✸✳✹✹✮ L N22 ✶ m❖ ♣❛râ♠❡tr♦ l ✱ ♥❛ r❡❛❧✐❛❞❛❞❡✱ ✈❛r✐❛ ❝♦♠ ❛ s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛ ❞♦ ♠❛t❡r✐❛❧✳ ❈♦♥t✉❞♦✱ ♣❛r❛ ❡❢❡✐t♦s ❞❡ s✐♠♣❧✐✜❝❛çã♦✱ ❝♦♥s✐❞❡r♦✉✲s❡ q✉❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ♠é❞✐♦ ❣❡♦♠étr✐❝♦ é ✐❣✉❛❧ ❛♦ ❝♦♠♣r✐♠❡♥t♦ ♠é❞✐♦ ♠❛❣♥ét✐❝♦ ❞♦ ♠❛t❡r✐❛❧✳ ✶✶✶ ✸✳✻✳✹ ❖❜t❡♥çã♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ❡ s❡❝✉♥✲❞ár✐❛❆tr❛✈és ❞♦s ❢❛t♦r❡s ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ♦❜t✐❞♦s ❛♥t❡r✐♦r♠❡♥t❡ s❡ t♦r♥❛ s✐♠♣❧❡s tr❛ç❛r ❛s ❝✉r✈❛s ❞❡ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛ ❛ ♣❛rt✐r ❞❛ ❝✉r✈❛ ❞❡ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✳❆ ❝✉r✈❛ ❞❛ ✐♥❞✉tâ♥❝✐❛ ✭❝♦♥❢❡r✐r ❋✐❣✉r❛s ✸✳✹✷✱ ✸✳✹✸ ❡ ✸✳✹✹✮ sã♦ ♦❜t✐❞❛s ❞❡r✐✈❛♥❞♦ ❛ ❝✉r✈❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❛tr❛✈és ❞❡ ♣r♦❣r❛♠❛s ❝♦♠♦❊①❝❡❧ ♦✉ ▼❛t▲❛❜✳❋✐❣✉r❛ ✸✳✹✷ ✕ ❆ ❝✉r✈❛ ❞❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ é ♦❜t✐❞❛ ♠✉❧t✐♣❧✐❝❛♥❞♦ ❛s♦r❞❡♥❛❞❛s ❞❛ ❝❛r❛❝t❡ríst✐❝❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ✈❡rs✉s ❝♦rr❡♥t❡ ♣❡❧♦ ❢❛t♦rK L1 ✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ✶✶✷ ❋✐❣✉r❛ ✸✳✹✸ ✕ ❯t✐❧✐③❛♥❞♦ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❛ ✐♥❞✉tâ♥❝✐❛❢♦✐ ❝❛❧❝✉❧❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✺✵ ❬♠❆❪✳▼❛s✱ ❡①✐st❡ ✉♠ ❡rr♦ ♥❡ss❡ ✈❛❧♦r ♣♦rq✉❡ ❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦ é ❛ s♦♠❛ ❞❛❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞❡ ✹✼♠❆ ❡ ✉♠❛ ♦✉tr❛ ❝♦rr❡♥t❡✱ ❛ss♦❝✐❛❞❛ ❛s = 12665 [Ω]♣❡r❞❛s ❞♦ ❢❡rr♦✱ ❝♦♥s✐❞❡r❛♥❞♦ r❡s✐st♦r ❡q✉✐✈❛❧❡♥t❡ R n ✱ ❝✉❥♦✈❛❧♦r é ✶✼ ❬♠❆❪✳ ❆ss✐♠✱ r❡❢❛③❡♥❞♦ ❛s ❝♦♥t❛s ❝♦♠ ✹✼ ❬♠❆❪✱ s❡ ♦❜té♠ ❛❝✉r✈❛ ❝♦rr✐❣✐❞❛✱ s❡♥❞♦ ❡ss❛ ♠✉✐t♦ ♣ró①✐♠❛ ❞❛ ❝✉r✈❛ ❡①♣❡r✐♠❡♥t❛❧✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❋✐❣✉r❛ ✸✳✹✹ ✕ ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ s❡❝✉♥❞ár✐❛✱ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ❢❛t♦r ❞❡♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ K L2 ✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ✶✶✸ V 12 = M12 di1 dt, M 21 = N2 N1 S l mµ(i) [H], ✭✸✳✺✶✮❝♦♠✿ V21 = M21 di2 dt, çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝✐t❛çã♦ s❡❝✉♥❞ár✐❛✱ é ❞❛❞♦ ♣♦r✿ ✭✸✳✺✵✮❆♥❛❧♦❣❛♠❡♥t❡✱ ❛ t❡♥sã♦ ✐♥❞✉③✐❞❛ ♥♦ ❜♦❜✐♥❛❞♦ ♣r✐♠ár✐♦✱ ❡♠ ❢✉♥✲ M 12 = N1 N2 S lm µ(i) [H]. ✭✸✳✹✾✮❝♦♠ ♦ ❢❛t♦r q✉❡ r❡❧❛❝✐♦♥❛ ❛ t❡♥sã♦ ❝♦♠ ❛ ❞❡r✐✈❛❞❛ t❡♠♣♦r❛❧ ❞❛ ❝♦rr❡♥t❡✱❞❡♥♦♠✐♥❛❞♦ ✐♥❞✉tâ♥✐❝❛ ♠út✉❛✱ ❞❛❞♦ ♣♦r✿ ❞ár✐♦✱ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝✐t❛çã♦ ♣r✐♠ár✐❛✱ é ❞❛❞♦ ♣♦r✿ ✸✳✻✳✺ ❈á❧❝✉❧♦ ❞❡ ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s❆ ♣❛rt✐r ❞❛ ▲❡✐ ❞❡ ❋❛r❛❞❛②✱ t❡♠✲s❡ q✉❡ ✭✸✳✹✽✮❆ss✐♠✱ ♣♦❞❡✲s❡ ✐♥❢❡r✐r q✉❡ ❛ t❡♥sã♦ ✐♥❞✉③✐❞❛ ♥♦ ❜♦❜✐♥❛❞♦ s❡❝✉♥✲ µ(i) di1 dt. ✭✸✳✹✼✮ q✉❡ ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❝♦♠♦V 2 = N2 N1 S l m V2 = N2 dφdi1 di1 dt ✭✸✳✹✻✮❆♥❛❧♦❣❛♠❡♥t❡✱ ♣❛r❛ ♦ s❡❝✉♥❞ár✐♦✱ t❡♠✲s❡ q✉❡✿ µ(i) di1 dt. ✭✸✳✹✺✮ q✉❡ ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❝♦♠♦V 1 = N21 S lm V1 = N1 dφdi1 di1 dt ✭✸✳✺✷✮ ✶✶✹ ❞❡ ♠♦❞♦ q✉❡S M 21 = M 12 = L M = N1 N 2 µ(i), ✭✸✳✺✸✮ l m❝✉❥❛ ❡str✉t✉r❛ é s✐♠✐❧❛r à ♦❜s❡r✈❛❞❛ ♥❛s ✐♥❞✉tâ♥❝✐❛s ♣ró♣r✐❛s✿2 S L = N µ(i), 1 ✭✸✳✺✹✮1 lm2 S L = N µ(i). 2 ✭✸✳✺✺✮2 lm❖ q✉♦❝✐❡♥t❡ S/l m ♥❛s ❡q✉❛çõ❡s ✭✸✳✺✸✮✱ ✭✸✳✺✹✮ ❡ ✭✸✳✺✺✮ é ♦ ♠❡s♠♦✳ ■ss♦ ♣❡r♠✐t❡ r❡❧❛❝✐♦♥❛r ♦s três ✈❛❧♦r❡s ❞❡ ✐♥❞✉tâ♥❝✐❛s ❝♦♠♦✿L1 L2 L M = = .22 ✭✸✳✺✻✮ N N N N1212/N ❆ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦ é ❞❡✜♥✐❞❛ ❝♦♠♦ a = N1 2 ✳ ❯t✐✲❧✐③❛♥❞♦ ❡ss❛ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦✱ ❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ♣♦❞❡ s❡r❡①♣r❡ss❛ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ♣r✐♠ár✐❛ ♦✉ s❡❝✉♥❞ár✐❛✿ L L L1 M1= M =2 → L ✭✸✳✺✼✮ N N N a112❡ L L2 M = .2 → M = aL 2 ✭✸✳✺✽✮N N21 N2 ■st♦ é✱ ❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞❛ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥✲❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ♦✉ s❡❝✉♥❞ár✐❛ ❞❡s❞❡ q✉❡ ❛ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦ s❡❥❛ ❝♦♥❤❡❝✐❞❛✳ ❆ ♣❛rt✐r ❞✐ss♦✱ ❢♦✐ ❣❡r❛❞❛ ❛ ❝✉r✈❛ q✉❡ ❡①♣r❡ss❛ ❛ ✐♥✲❞✉tâ♥❝✐❛ ♠út✉❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝✐t❛çã♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r✭❋✐❣✉r❛ ✸✳✹✺✮✳ ❖ ✈❛❧♦r ❡①♣❡r✐♠❡♥t❛❧ ♦❜t✐❞♦ ♣❛r❛ ❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❢♦✐ ❞❡✶✱✶✺❬❍❪✳ ❈♦♥t✉❞♦✱ ❡st❡ ✈❛❧♦r s❡ ❛❧t❡r❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡✲ t✐③❛çã♦✳✸✳✻✳✻ ❈✉r✈❛ ❞❡ ❘❡❧✉tâ♥❝✐❛ ❆♥á❧♦❣❛ ❛ r❡s✐stê♥❝✐❛✱ ❛ r❡❧✉tâ♥❝✐❛ ❡①♣r❡ss❛ ❛ ❞✐✜❝✉❧❞❛❞❡ à ♣❛s✲ l m s❛❣❡♠ ❞❡ ❧✐♥❤❛s ❞❡ ❢♦rç❛✱ ❞❡✜♥✐❞❛ ♣❡❧❛ r❡❧❛çã♦✿ ℜ = ✱ ♦♥❞❡ l mµ(i)S❝♦rr❡s♣♦♥❞❡ ❛♦ ♣❡r❝✉rs♦ ♠é❞✐♦ ❞♦ ✢✉①♦ ❡ S ❛ s❡çã♦ tr❛♥s✈❡rs❛❧ ❞♦ ✶✶✺ ❋✐❣✉r❛ ✸✳✹✺ ✕ ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ✈✐st❛ ❞♦ s❡❝✉♥❞ár✐♦ ♣♦r ❡❢❡✐t♦ ❞❛ ❝♦r✲ r❡♥t❡ ♣r✐♠ár✐❛✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳m = 0, 1686[m] ] 2 ♥ú❝❧❡♦✱ l ❡ S = 0, 76 [cm ✳ ❆ ❝✉r✈❛ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ r❡❧✉tâ♥❝✐❛ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✸✳✹✻✳✸✳✻✳✼ ❈✉r✈❛ ❞❛ ♣❡r♠❡â♥❝✐❛ ❆ P❡r♠❡â♥❝✐❛ p m s❡ ❞❡✜♥❡ ❝♦♠♦ ♦ ✐♥✈❡rs♦ ❞❛ ❘❡❧✉tâ♥❝✐❛ ✭1/ℜ✮✱é ♣r♦♣r✐❡❞❛❞❡ q✉❡ ❢❛❝✐❧✐t❛ ❛ ♣❛ss❛❣❡♠ ❞❡ ✢✉①♦ ♣❡❧♦ ❝✐r❝✉✐t♦ ♠❛❣♥ét✐❝♦✱❡q✉✐✈❛❧❡ à ❝♦♥❞✉tâ♥❝✐❛ ♥♦ ❝✐r❝✉✐t♦ ❡❧étr✐❝♦✿ S p = µ(i) [Wb/A]m ✭✸✳✺✾✮ lm❡♠ q✉❡ ❢❛❝✐❧♠❡♥t❡ s❡ ♣❡r❝❡❜❡ q✉❡ é ♣r♦♣♦r❝✐♦♥❛❧ à ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❛❜✲ s♦❧✉t❛✳ ❆ ❝✉r✈❛ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ ♣❡r♠❡â♥❝✐❛ é ❛♣r❡s❡♥t❛❞❛ ♥❛ ❋✐❣✉r❛ ✶✶✻ ❋✐❣✉r❛ ✸✳✹✻ ✕ ❈✉r✈❛ ❞❛ r❡❧✉tâ♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✻✳✽ ❈♦♥s✐❞❡r❛çõ❡s s♦❜r❡ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❡ ❛ ❝✉r✈❛ BH ❆ ♣❛rt✐r ❞❛ ❝✉r✈❛ BH✱ ❞❡t❡r♠✐♥❛✲s❡ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❞♦ ♠❛t❡✲ r✐❛❧✳ ❆ ❞❡r✐✈❛❞❛ ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❡♠ r❡❧❛çã♦ à ❝♦rr❡♥t❡ é ♣r♦♣♦r❝✐♦♥❛❧❛ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦s ❞❛❞♦s ❣❡♦♠étr✐❝♦s❡ ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❞♦ ❝✐r❝✉✐t♦✳ ❆s ❞❡r✐✈❛❞❛s ❞❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❡♠ r❡❧❛çã♦ ❛s ❝♦rr❡♥t❡s ✈✐st❛s❞♦ ❧❛❞♦ ♣r✐♠ár✐♦ ❡ s❡❝✉♥❞ár✐♦ sã♦ ✐❣✉❛✐s✳ ❆tr❛✈és ❞❛s ❝✉r✈❛s ❧❡✈❛♥t❛❞❛s ❡ ❞❛ ❣❡♦♠❡tr✐❛ ❞♦ ❞✐s♣♦s✐t✐✈♦ é♣♦ssí✈❡❧ r❡❛❧✐③❛r q✉❛❧q✉❡r ❝á❧❝✉❧♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❡♠ ❢♦r♠❛ ❣rá✜❝❛ ❝♦♠✉♠❛ ♣r❡❝✐sã♦ ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s ❡♠ t♦r♥♦ ❞♦s ✺✪✳✸✳✼ ❈➪▲❈❯▲❖ ❉❊ ■◆❉❯❚➶◆❈■❆❙ ❊▼ ❯▼ P❖◆❚❖ ❉❊ ❖P❊❘❆➬➹❖❊st❛ s❡çã♦ ❛♣r❡s❡♥t❛ ♦ ❝á❧❝✉❧♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ❞♦ tr❛♥s❢♦r♠❛❞♦r✱ ✶✶✼ ❋✐❣✉r❛ ✸✳✹✼ ✕ ❈✉r✈❛ ❞❛ ♣❡r♠❡â♥❝✐❛ ❞♦ ❝✐r❝✉✐t♦ ♣r✐♠ár✐♦ ❡♠ ❢✉♥çã♦ ❞❛❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♥♦ ❡♥r♦❧❛♠❡♥t♦ ♣r✐♠ár✐♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✼✳✶ ❈á❧❝✉❧♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ❡ r❡❛tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ♣❡❧♦ ♠ét♦❞♦ ❝♦♥❝❛t❡♥❛❞♦P❛r❛ r❡❛❧✐③❛r ❡ss❡ ❝á❧❝✉❧♦✱ é ♥❡❝❡ssár✐♦ ❝♦♥s✐❞❡r❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦✳ ❆ ❋✐❣✉r❛ ✸✳✹✽ ❛✉①✐❧✐❛ ❛ ❝♦♠♣r❡❡♥❞❡r ❛ ❞✐s✲ tr✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡s ♥♦ ♣r✐♠ár✐♦ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r r❡❛❧✳ ❖❜s❡r✈❛rq✉❡ ❡ss❛s ❝♦rr❡♥t❡s ♣♦ss✉❡♠ ✉♠ ❛s♣❡❝t♦ ❢❛s♦r✐❛❧✳ ➱ ❢á❝✐❧ ♣❡r❝❡❜❡r q✉❡ I r ♣♦❞❡ s❡r ❞❡t❡r♠✐♥❛❞❛ ❝♦♠✿22 V 220 220 R = = = = 16, 4 mA. = 13, 4 kΩ → I rP 3, 6 13400 ❆ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♣♦❞❡ s❡r ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛ ▲❡✐ ❞❡ m = 33, 16❆♠♣❡ré✱ ❞❡ ♠♦❞♦ q✉❡✱ I ❬♠❆❪✳ ❉❡ss❡ ♠♦❞♦✱ t❡♠✲s❡ q✉❡I = I + jI = 16, 4 + 33, 16 R m ❬♠❆❪✳ P❛r❛ ❛ s✐♠✉❧❛çã♦ ♥♦ ❋❊▼▼✱ é = 23, 19 + 46, 9♥❡❝❡ssár✐♦ ✉t✐❧✐③❛r ❛ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦✱ ❛ss✐♠✿ I ❬♠❆❪✱♦❜s❡r✈❛r q✉❡ |I | = 52, 0 ❬♠❆❪✳ ❖ ♠ó❞✉❧♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡♥tr❛❞❛ ♥♦ ♣r✐♠ár✐♦ I ′ 1 é ✶✵✵ ❬♠❆❪✳= I + I = ✶✶✽ ❋✐❣✉r❛ ✸✳✹✽ ✕ ❉✐str✐❜✉✐çã♦ ❞❡ ❝♦rr❡♥t❡s ❡♠ ✉♠ tr❛♥s❢♦r♠❛❞♦r r❡❛❧✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳ ′88, 19 + j46, 9 = I = 65 = ′ ✳ ❈♦♠ ✐ss♦✱ I1 1 − I ❬♠❆❪✳ ❚❡♠✲s❡ q✉❡ I2 aI = 5961 ❬♠❆❪✳ ❯t✐❧✐③❛♥❞♦✲s❡ ❡ss❡s ✈❛❧♦r❡s ♥❛ s✐♠✉❧❛çã♦ ❞♦ ❋❊▼▼✱ t❡♠✲s❡ q✉❡L = 8, 6535 = 0, 1581 = 0, 092 1 ❬❍❪✱ L 2 ❬❍❪ λ 12 ❬❲❜❪✳ ❚❡♠✲s❡ q✉❡✿ λ12 M = = 0, 9422 [H].12 i1❙❛❜❡✲s❡ q✉❡2 M = a M = 8, 6399 [H].2112 ❆ ✐♥❞✉tâ❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ❞♦ ♣r✐♠ár✐♦ l 1 é ❞❛❞❛ ♣♦r✿ l = L1 1 − M 12 ∗ a = 13, 5 [mH.]P♦r ✜♠✱ ❛ ✐♥❞✉tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ❞♦ s❡❝✉♥❞ár✐♦ l 2 é ❞❛❞❛ ♣♦r✿ M21 l = L = 0, 066 [mH.]2 2 − a ✶✶✾ ✸✳✼✳✷ ❈á❧❝✉❧♦ ❞❡ ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ♣♦r ❡♥❡r❣✐❛ ❡♠ ❝♦♥❞✐çõ❡s❞❡ ♣♦❧❛r✐❞❛❞❡ ❛❞✐t✐✈❛ ❡ s✉❜tr❛t✐✈❛ ✭❜✉❝❦✐♥❣ t❡st✮◆♦ tr❛♥s❢♦r♠❛❞♦r ♦s ✢✉①♦s ♣r✐♠ár✐♦s ❡ s❡❝✉♥❞ár✐♦s s❡ ♦♣õ❡♠ ✭❧❡✐ = φ❞❡ ▲❡♥③✮✱ ✐st♦ é✱ φ 1 −φ 2 ✱ ♦ ✢✉①♦ ♠❛❣♥ét✐❝♦ r❡s✉❧t❛♥t❡ ❝♦rr❡s♣♦♥❞❡❛♦ ❣❡r❛❞♦ ♣❡❧❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦✱ ❧❡✈❛♥❞♦ ❛♦ tr❛♥s❢♦r♠❛❞♦r tr❛❜❛❧❤❛r ♥✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣♦♥t♦ ❞❛ ❝✉r✈❛ BH✱ ❝♦♥❞✐çã♦ ♥❛t✉r❛❧ ❞❡♦♣❡r❛çã♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ ❙❡ ♦ tr❛♥s❢♦r♠❛❞♦r ❢♦ss❡ s✐♠✉❧❛❞♦ ♥✉♠❛ ❝♦♥❞✐çã♦ ❞❡ ✢✉①♦s ♣r✐✲♠ár✐♦ ❡ s❡❝✉♥❞ár✐♦ ❡♠ ❛❞✐çã♦✱ ✐st♦ ♥♦s ❧❡✈❛r✐❛ ❛♦ ✈❛❧♦r ♠á①✐♠♦ ❞❡ ✢✉①♦♥❛ ❝✉r✈❛ BH✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ à ✐♥❞✉çã♦ ♠á①✐♠❛ B s ❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡❝❛♠♣♦ ♠á①✐♠❛ H s ✳ ❆tr❛✈és ❞❡st❡ ♣r♦❝❡❞✐♠❡♥t♦ é ♣♦ssí✈❡❧ ♣❡r❝♦rr❡r t♦❞❛ ❛ ❝✉r✈❛ BH❡ ❝❛❧❝✉❧❛r ♣❛râ♠❡tr♦s ❝♦♠♦ ❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡ ❛ r❡❛tâ♥❝✐❛ ❞✐s♣❡rs✐✈❛✳ ❆ss✐♠✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ♥❛ ❝✉r✈❛ BH✱ t❡♠✲s❡ q✉❡✿Z w = H dB,Z ✭✸✳✻✵✮B 12 w = dB, = B . ✭✸✳✻✶✮µ 2µ = N i▲❡♠❜r❛♥❞♦ q✉❡ B = µH ❡ Hl m ✱ t❡♠✲s❡ q✉❡✿ µN i11 B = . ✭✸✳✻✷✮ l m❘❡❡s❝r❡✈❡♥❞♦ ✭✸✳✻✸✮✱ t❡♠✲s❡ q✉❡✿22 1 µ N12 w = i .,21 ✭✸✳✻✸✮ 2µ l m♠✉❧t✐♣❧✐❝❛♥❞♦ ♣❡❧♦ ✈♦❧✉♠❡ v = Sl m ✱ t❡♠✲s❡ q✉❡ ❛ ❡♥❡r❣✐❛ é ❞❛❞❛ ♣♦r✿2 1 µN S12 W = i . 1 ✭✸✳✻✹✮ 2 l m ❆ss✐♠✱ ❛ ❡♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❧✐❣❛çã♦ ❛❞✐t✐✈❛ é❞❛❞❛ ♣♦r✿22 L i L i M i i112212 ✭✸✳✻✺✮ 2 2 2 ✶✷✵ ❡ ❛ ❡♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❧✐❣❛çã♦ s✉❜tr❛t✐✈❛ é ❞❛❞❛ ♣♦r✿22 L i L i M i i112212 W = . b − ✭✸✳✻✻✮ + 2 2 2❋❛③❡♥❞♦ ✭✸✳✻✺✮ ✲ ✭✸✳✻✻✮✿ W a − W b L = . M ✭✸✳✻✼✮ i i12❊st❛ ❡①♣r❡ssã♦ ❡stá ❛♣r❡s❡♥t❛❞❛ s✉♣♦♥❞♦ ✈❛❧♦r❡s ❞❡ ❝♦rr❡♥t❡ ❞♦ t✐♣♦ ❘▼❙✳ ❖ ❋❊▼▼ ✉t✐❧✐③❛ ✈❛❧♦r❡s ❞❡ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦✱ ❞❡st❛ ❢♦r♠❛ ❛ ❡①♣r❡ssã♦ ❡♠ t❡r♠♦s ❞❛ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦ ✜❝❛✿2(W a b ) − W L = . M ✭✸✳✻✽✮ i i12❉❛❞❛s ❛s ❝♦♥s✐❞❡r❛çõ❡s ❞❡ ♦♣❡r❛çã♦ ❞♦ ❡♥s❛✐♦ ❛♥t❡r✐♦r✱ ❛♣ós s✐✲ ♠✉❧❛r ♥♦ ❋❊▼▼ t❛♥t♦ ♥❛ ❝♦♥❞✐çã♦ ❛❝✉♠✉❧❛t✐✈❛ q✉❛♥❞♦ ♥❛ ❞✐❢❡r❡♥❝✐❛❧✱= 0, 0101992 = 0, 0617093 t❡♠✲s❡ q✉❡ W d ❬❏❪ ❡ W a ❬❏❪✳ ❈♦♠ ✐ss♦✱ ✉t✐✲ = 0, 8642 = 8, 6535❧✐③❛♥❞♦ ✭✸✳✻✽✮✱ ♦❜té♠✲s❡ L m ✳ ❆❧é♠ ❞✐ss♦✱ L 1 ❡L = 0, 8642 2 ✳ ❉❡ss❡ ♠♦❞♦✱ ❛ ✐♥❞✉tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ❞♦ ♣r✐♠ár✐♦ l 1 é ❞❛❞❛♣♦r✿ l = L = 729 [mH],1 1 − aL M ❡ ❛ ✐♥❞✉tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ❞♦ s❡❝✉♥❞ár✐♦ l 2 é ❞❛❞❛ ♣♦r✿L Ml 1 = L 1 = 63, 8579 [mH]. − a✸✳✼✳✸ ❈á❧❝✉❧♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ♣❡❧♦ ♠ét♦❞♦ ❣rá✜❝♦ ❈♦♥s✐❞❡r❛♥❞♦ ❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s ❞❡ ❡♥s❛✐♦ ❞♦s t❡st❡s ❛♥t❡r✐♦✲ r❡s✱ ♣♦❞❡✲s❡ ❞❡t❡r♠✐♥❛r ❛s ✐♥❞✉tâ♥❝✐❛s ❛tr❛✈és ❞❛s ❝✉r✈❛s tr❛ç❛❞❛s ♥❛❙❡çã♦ ✸✳✻✳ ❆ss✐♠✱ ❛ ❋✐❣✉r❛ ✸✳✹✾ ❛♣r❡s❡♥t❛ ❛ ❝✉r✈❛ ❞❡ ✐♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛✱❝♦♠ ❛ ✐♥❞✉tâ♥❝✐❛ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦ ❡♠ q✉❡ s❡ tr❛❜❛❧❤❛✳ ❆ss✐♠✱ ❛ ❋✐❣✉r❛ ✸✳✺✵ ❛♣r❡s❡♥t❛ ❛ ❝✉r✈❛ ❞❡ ✐♥❞✉tâ♥❝✐❛ s❡❝✉♥❞ár✐❛✱❝♦♠ ❛ ✐♥❞✉tâ♥❝✐❛ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦ ❡♠ q✉❡ s❡ tr❛❜❛❧❤❛✳ ❆ss✐♠✱ ❛ ❋✐❣✉r❛ ✸✳✺✶ ❛♣r❡s❡♥t❛ ❛ ❝✉r✈❛ ❞❡ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛✱❝♦♠ ❛ ✐♥❞✉tâ♥❝✐❛ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦ ❡♠ q✉❡ s❡ tr❛❜❛❧❤❛✳ ✶✷✶ ❋✐❣✉r❛ ✸✳✹✾ ✕ ■♥❞✉tâ♥❝✐❛ ♣r✐♠ár✐❛ ❞❡ ✽✱✷✽ ❬❍❪ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳❋✐❣✉r❛ ✸✳✺✵ ✕ ■♥❞✉tâ♥❝✐❛ s❡❝✉♥❞❛r✐❛ ❞❡ ✵✱✵✾✺ ❬❍❪ ♥♦ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳ ✶✷✷ ❋✐❣✉r❛ ✸✳✺✶ ✕ ❈✉r✈❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ♣r✐♠❛r✐❛♥❛ ❝♦♥❞✐çã♦ s❡♠ ❝❛r❣❛ ♦ ✈❛❧♦r ♣❛r❛ ❛ ✐♥❞✉tâ♥❝✐❛ ❣r❛✜❝❛♠❡♥t❡ ❡stá ❡♠ t♦r♥♦ ❞❡ ✵✱✾✵✸ ❬❍❪ ♣❛r❛ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ♣r✐♠❛r✐❛ ❞❡ ✶✵✵ ❬♠❆❪❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r✳✸✳✼✳✹ ❋❛t♦r ❞❡ ❛❝♦♣❧❛♠❡♥t♦ ❖ ❢❛t♦r ❞❡ ❛❝♦♣❧❛♠❡♥t♦ é ❞❡✜♥✐❞♦ ❝♦♠♦✿L M K = ,√ ✭✸✳✻✾✮ L1 L2❞❡ ♠♦❞♦ q✉❡ s❡✉ ✈❛❧♦r ♠á①✐♠♦ é ❛ ✉♥✐❞❛❞❡✳ ❉❡ss❛ ❢♦r♠❛✱ ♣❛r❛ ♦ ♠ét♦❞♦ ❞♦s ✢✉①♦s ❝♦♥❝❛t❡♥❛❞♦s✱ ♦ ❢❛t♦r❞❡ ❛❝♦♣❧❛♠❡♥t♦ é K = 0, 81✳ P❛r❛ ♦ ♠é❞♦t♦ ❞❛ ❡♥❡r❣✐❛✱ ♦ ❢❛t♦r ❞❡ ✶✷✸ ✸✳✽ ❉❊❚❊❘▼■◆❆➬➹❖ ❊❳P❊❘■▼❊◆❚❆▲ ❉❆❙ ■◆❉❯❚➶◆✲❈■❆❙ ▼Ú❚❯❆❙ ◆❖ P❖◆❚❖ ❉❊ ❖P❊❘❆➬➹❖ P❛r❛ ✉♠ tr❛♥s❢♦r♠❛❞♦r ✐❞❡❛❧✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✸✳✺✷✱♣♦❞❡♠✲s❡ ♦❜t❡r ❛s s❡❣✉✐♥t❡s ❡q✉❛çõ❡s ♥♦ ❞♦♠í♥✐♦ ❞♦ t❡♠♣♦✿ di di12 V 1 = L 1 + M , ✭✸✳✼✵✮ dt dtdi di21 V = L + M .2 2 ✭✸✳✼✶✮ dt dt ❋✐❣✉r❛ ✸✳✺✷ ✕ ▼♦❞❡❧♦ ✐❞❡❛❧ ❞❡ tr❛♥s❢♦r♠❛❞♦r ♠♦♥♦❢ás✐❝♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r ◆♦ ❞♦♠í♥✐♦ ❞❛ ❢r❡q✉ê♥❝✐❛✱ t❡♠✲s❡✿V = jω(L11 I + L1 M I ), 2 ✭✸✳✼✷✮ V = jω(L22 I + L2 M I ). 1 ✭✸✳✼✸✮P❛r❛ ❛ s✐t✉❛çã♦ ✐♥❞✐❝❛❞❛ ♥❛ ❋✐❣✉r❛ ✸✳✺✸ ♦❜s❡r✈❛✲s❡ q✉❡✿ V = V + V x1 2 ✭✸✳✼✹✮ i = i = i . x1 2 ✭✸✳✼✺✮❈♦♥s✐❞❡r❛♥❞♦ ❛s ❊q✉❛çõ❡s ✭✸✳✼✷✮ ❡ ✭✸✳✼✸✮✱ t❡♠✲s❡ q✉❡✿ V x = ω(L + L + 2M ).|Z x | =1 2 ✭✸✳✼✻✮ ✶✷✹ ❋✐❣✉r❛ ✸✳✺✸ ✕ ❈✐r❝✉✐t♦ ♣❛r❛ ❝á❧❝✉❧♦ ❞❛s ♠út✉❛s✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r P❛r❛ ❛ s✐t✉❛çã♦ ✐♥❞✐❝❛❞❛ ♥❛ ❋✐❣✉r❛ ✸✳✺✹ ♦❜s❡r✈❛✲s❡ q✉❡✿V = V x 1 − V 2 ✭✸✳✼✼✮ i = i . x 1 = −i 2 ✭✸✳✼✽✮ ❈♦♥s✐❞❡r❛♥❞♦ ♥♦✈❛♠❡♥t❡ ❛s ❊q✉❛çõ❡s ✭✸✳✼✷✮ ❡ ✭✸✳✼✸✮✱ t❡♠✲s❡ q✉❡✿ y = ω(L V y 1 + L2|Z | = − 2M). ✭✸✳✼✾✮ I y❋✐❣✉r❛ ✸✳✺✹ ✕ ❈✐r❝✉✐t♦ ♣❛r❛ ❝á❧❝✉❧♦ ❞❛s ♠út✉❛s✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦ ❛✉t♦r ✶✷✺ ❯t✐❧✐③❛♥❞♦ ❛s ❊q✉❛çõ❡s ✭✸✳✼✻✮ ❡ ✭✸✳✼✻✮ ❝❤❡❣❛✲s❡ ✜♥❛❧♠❡♥t❡ ❛❡q✉❛çã♦ ❞❛ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛✿ x y |Z | − |Z | L = . M ✭✸✳✽✵✮4ω ❆♣❧✐❝❛♠✲s❡ ❛s t❡♥sõ❡s ✐♥❞✐❝❛❞❛s ♠❛♥t❡♥❞♦ ❛ ♠❡s♠❛ ❝♦rr❡♥t❡ ❡♠❛♠❜♦s ❡♥s❛✐♦s ✱ ♥❡st❡ ❝❛s♦ ❞❡ ✶✵✵♠❆✱ ♦❜t❡♥❞♦ ❛s ✐♠♣❡❞â♥❝✐❛s ♥❛s❝♦♥❞✐çõ❡s ❞❡ ♣♦❧❛r✐❞❛❞❡ ❛❞✐t✐✈❛ ❡ s✉❜tr❛t✐✈❛ ✱ ✈❛r✐❛♥❞♦ ❛ t❡♥sã♦✳ ❆ss✐♠✿ V x = 319 [V],I x = 71 [mA rms ], V y = 234 [V], I y = 71 [mA rms ].▲♦❣♦✱ V 319 xZ = = = 4493 [Ω], x I x 0, 071V 234 y Z = = = 3296 [Ω], yI 0, 071 y ❡✱ ♣♦r ❝♦♥s❡q✉ê♥❝✐❛✱ 4493 − 3296L M = = 0, 794 [H] ≈ 0, 8 [H]. 4 · 2π · 60✸✳✾ ▼❖❉❊▲❆●❊▼ ❉❖ ❚❘❆◆❙❋❖❘▼❆❉❖❘ P❛r❛ ♠♦❞❡❧❛r ♦ ♥ú❝❧❡♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r r❡❛❧✐③♦✉✲s❡ ♦ ❡♥s❛✐♦ ❞❡✈❛③✐♦✳ P❛r❛ s✐♠✉❧❛r ❛ tr❛♥s❢♦r♠❛❞♦r tr❛❜❛❧❤❛♥❞♦ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ✈❛③✐♦✱♣r✐♠❡✐r❛♠❡♥t❡ ❞❡✈❡✲s❡ ❞❡t❡r♠✐♥❛r ❛ s✉❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦✳ P❛r❛ ❡st❡✜♠✱ ✉t✐❧✐③❛✲s❡ ❛ ❝✉r✈❛ BH ♦❜t✐❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ♣❛r❛ ♦❜t❡r ♦s♣❛râ♠❡tr♦s ❞♦ tr❛♥s❢♦r♠❛❞♦r r❡❧❛❝✐♦♥❛❞♦s ❛ ❡ss❡ ❡♥s❛✐♦✳✸✳✾✳✶ ❈á❧❝✉❧♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦ ✭❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦✮ m sin(ωt) ❈♦♥s✐❞❡r❛♥❞♦ ✉♠ ✢✉①♦ ♠❛❣♥ét✐❝♦ s❡♥♦✐❞❛❧ φ = φ ✱ ❛√ pk m = 220 2 = N φ ω ❡①♣r❡ssã♦ ♣❛r❛ ❛ t❡♥sã♦ ❞❡ ♣✐❝♦ é ❞❛❞❛ ♣♦r V ✳ ✶✷✻ ❆ ❡①♣r❡ssã♦ ♣❛r❛ ❛ ❞❡♥s✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ♠á①✐♠❛✱ ❝♦♥s✐❞❡r❛♥❞♦2 N = 1100 [e] ]❡ S = 7, 6 [cm ✿ V pkB = = 0, 9876 [T], m ✭✸✳✽✶✮ N Sω♦ q✉❡ s❡ ❛♣r♦①✐♠❛ ❞♦ ✈❛❧♦r ❞❡ ✶ ❬❚❪ ❞♦ ❣rá✜❝♦✳ ❆✐♥❞❛ ❞❛ ❝✉r✈❛ BH✱ s❡♦❜té♠ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H ❡ ❞❛ ❧❡✐ ❞❡ ❆♠♣❡r❡✿ 350 [Ae/m] · 0, 1686 [m] Hl = 0, 054 [A], m = N i → i = ✭✸✳✽✷✮ 1100 [e]s❡♥❞♦ q✉❡ ♦ ✈❛❧♦r ❘▼❙ ❞❛ ❝♦rr❡♥t❡ é 0, 054 √ = 0, 038 [A rms ]. 2❈♦♠♦ ♣♦❞❡✲s❡ ✈❡r✱ ♦ ✈❛❧♦r t❡ór✐❝♦ ❛tr❛✈és ❞❛ ❝✉r✈❛ BH ♦❜t✐❞♦ ❡ ♦ ❡①♣❡r✐♠❡♥t❛❧ ❛tr❛✈és ❞❡ ✉♠ ❛♠♣❡rí♠❡tr♦ tr✉❡ ❘▼❙ é ♣ró①✐♠♦✳◆❛s s✐♠✉❧❛çõ❡s é ✉t✐❧✐③❛❞♦ ♦ ✈❛❧♦r ❞❡ ✵✱✵✺✷❬❆❪ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ✈❛❧♦r ❞❡ ❝♦rr❡♥t❡ ❡①♣❡r✐♠❡♥t❛❧ ❞❡ ✸✼ ♠❆ r♠s✳✸✳✾✳✷ ▼♦❞❡❧❛❣❡♠ ❞♦ ♥ú❝❧❡♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❯♠❛ ✈❡③ ❧♦❝❛❧✐③❛❞❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♠❛t❡r✐❛❧ ♥❛ ❜✐❜❧✐♦t❡❝❛❡ ❝♦♠ ❛ ❝♦rr❡♥t❡ ❞❡ ♠❛❣♥❡t✐③❛çã♦ é ♣♦ssí✈❡❧ r♦❞❛r ❛ s✐♠✉❧❛çã♦✳ ❖♣r♦❣r❛♠❛ ✉t✐❧✐③❛ ✉♠ ♠♦❞❡❧♦ sér✐❡ ♣❛r❛ ♦ ♥ú❝❧❡♦ ✭♦❜s❡r✈❛r ❋✐❣✉r❛ ✸✳✺✺✮✱ s❡♥❞♦ q✉❡ ❤❛❜✐t✉❛❧♠❡♥t❡ ❛ ❧✐t❡r❛t✉r❛ ❛♣r❡s❡♥t❛ ✉♠ ♠♦❞❡❧♦ ♣❛r❛❧❡❧♦✳❊♠ ❞❡❝♦rrê♥❝✐❛ ❞✐ss♦✱ ❢❛③✲s❡ ✉♠❛ ♠✉❞❛♥ç❛ ❞❡ ❛ss♦❝✐❛çã♦ sér✐❡ ♣❛r❛❛ss♦❝✐❛çã♦ ❡♠ ♣❛r❛❧❡❧♦ ❛tr❛✈és ❞❡ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❞❡ ✐♠♣❡❞â♥❝✐❛s✳✸✳✾✳✸ ❚r❛♥s❢♦r♠❛çã♦ ❞❡ ✐♠♣❡❞â♥❝✐❛s ❯♠❛ ✐♠♣❡❞â♥❝✐❛ ❢♦r♠❛❞❛ ♣♦r ✉♠ r❡s✐st♦r ❡ ✉♠ ✐♥❞✉t♦r ❡♠ sér✐❡♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♠ ❝✐r❝✉✐t♦ ❡q✉✐✈❛❧❡♥t❡ ♣❛r❛❧❡❧♦✱ ❢♦r♠❛❞♦ t❛♠❜é♠ ♣♦r ✉♠ r❡s✐st♦r ❡ ✐♥❞✉t♦r ❡q✉✐✈❛❧❡♥t❡s ✭♦❜s❡r✈❛r ❋✐❣✉r❛ ✸✳✺✻✮✳ ❙❡♣❛r❛♥❞♦ ♣❛rt❡s r❡❛❧ ❡ ✐♠❛❣✐♥ár✐❛✿2 R p X lpR s =22 ✭✸✳✽✸✮ R + X p lp ✶✷✼ ❋✐❣✉r❛ ✸✳✺✺ ✕ ▼♦❞❡❧♦ sér✐❡ ❞♦ tr❛♥s❢♦r♠❛❞♦r ✉t✐❧✐③❛❞♦ ♣❡❧♦ ❋❊▼▼✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❋✐❣✉r❛ ✸✳✺✻ ✕ ❚r❛♥s❢♦r♠❛çã♦ ❝✐r❝✉✐t♦ sér✐❡ ♣❛r❛ ❝✐r❝✉✐t♦ ♣❛r❛❧❡❧♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❡2 R p X lpX = s ✭✸✳✽✹✮22 ✭✸✳✾✵✮ ❛ r❡s✐stê♥❝✐❛ ♣❛r❛❧❡❧❛ ❡q✉✐✈❛❧❡♥t❡✿R s = 26842 = 2684 "5634 X sR s2 ❆ r❡s✐stê♥❝✐❛ ♣❛r❛❧❡❧❛ ❡q✉✐✈❛❧❡♥t❡ é ❞❛❞❛ ♣♦r✿R p = R s " ❖s ✈❛❧♦r❡s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ r❡s✐st♦r sér✐❡ R s = 2684Ω ❡ ♣❛r❛❛ r❡❛tâ♥❝✐❛ ✐♥❞✉t✐✈❛ sér✐❡ X s = 5634Ω ✳ ♥ú❝❧❡♦ ♥♦ ❋❊▼▼✱ ♦❜té♠✲s❡ ♥♦ ♣r✐♠ár✐♦✿❼ ❈♦rr❡♥t❡ t♦t❛❧ ❂ ✵✱✵✺✷ ❆❀❼ ◗✉❡❞❛ ❞❡ t❡♥sã♦ ❂ ✶✸✾✱✻✶✸✰j✷✾✷✱✾✹✼ ❱❀❼ ❋❧✉①♦ ❝♦♥❝❛t❡♥❛❞♦ ❂ ✵✱✼✼✼✵✻✻✲j✵✱✸✻✽✽✹✸ ❲❜❀❼ ❋❧✉①♦✴❈♦rr❡♥t❡ ❂ ✶✹✱✾✹✸✻✲j✼✱✵✾✸✶✹ ❍❀❼ ❚❡♥sã♦✴❈♦rr❡♥t❡ ❂ ✷✻✽✹✱✽✻✰j✺✻✸✸✱✻ Ω✳ ✭✸✳✽✾✮❈♦♥s✐❞❡r❛♥❞♦ ❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦ ❞❡ ✺✷ ♠❆✱ ❛♦ ♠♦❞❡❧❛r✲s❡ ♦ X s2 X lp = X s "R s ✭✸✳✽✽✮❆♥❛❧♦❣❛♠❡♥t❡ R s2 → R p = R s "X s R p R2 pX2 lp ✭✸✳✽✼✮❊♠ ✭✸✳✽✸✮✱ ❢❛t♦r❛♥❞♦✲s❡ X2 lp ❡ ❝♦♠ ❛s r❡❧❛çõ❡s ❡♠ ✭✸✳✽✼✮ s❡ ♦❜té♠ ✶✷✽ X lp . =R p X sR s X s→ =R p X lpR s ✭✸✳✽✻✮■❣✉❛❧❛♥❞♦ ✭✸✳✽✺✮ ❝♦♠ ✭✸✳✽✻✮ ♦❜té♠✲s❡✿ X2 lpX s . R2 p + X2 lp =R p ✭✸✳✽✺✮❡ X lpR s R2 p ❞❡ ♠♦❞♦ q✉❡✿R2 p + X2 lp = ✶✷✾ ❆ r❡❛tâ♥❝✐❛ ♣❛r❛❧❡❧❛ ❡q✉✐✈❛❧❡♥t❡ é ❞❛❞❛ ♣♦r✿ " # " #22 R 2684 s X lp = X s + 1 = 5634 + 1 = 6914Ω. ✭✸✳✾✶✮X 5634 s ❖ ♠♦❞❡❧♦ sér✐❡ ❛♣r❡s❡♥t❛❞♦ ♣❡❧♦ ♣r♦❣r❛♠❛ ❋❊▼▼ ♣❛r❛ ✉♠❛❞❡t❡r♠✐♥❛❞❛ ❝♦rr❡♥t❡ ❞❡ ♦♣❡r❛çã♦✱ ❡stá ❛tr❡❧❛❞❛ ❛ ✉♠❛ t❡♥sã♦✱ q✉❡ rms♥❡st❡ ❝❛s♦✱ é ❞❡ ✸✷✹ ❱ ✭✷✷✾ V ✮✳ ◆♦ ♠♦❞❡❧♦ ♣❛r❛❧❡❧♦ ❛ t❡♥sã♦❡ ❝♦♥s✐❞❡r❛❞❛ ✷✷✵ ❱✱ ❛ss✐♠ ♣❛r❛ ✐♠♣♦r ❛ ♠❡s♠❛ ❝♦rr❡♥t❡ é ♥❡❝❡ssár✐♦❝♦♠♣❡♥s❛r ❛ ♦s ✈❛❧♦r❡s ❞❡ ✐♠♣❡❞â♥❝✐❛s ♦❜t✐❞♦s ♣♦r ✉♠ ❢❛t♦r ❞❡ ✸✶✶✴✸✷✹✳❉❡ss❛ ❢♦r♠❛✿ 311R p = 14510 = 13927Ω 324❡ 311 X = = 17, 61 [H]. lp 6914 = 6636Ω → L p324 ✸✳✾✳✹ ▼♦❞❡❧♦ ❛tr❛✈és ❞❡ ❡♥s❛✐♦s ❡①♣❡r✐♠❡♥t❛✐sP❡❧♦ ❢❛t♦ ❞❡ s❡r ✉♠ tr❛♥s❢♦r♠❛❞♦r ❞❡ ♣❡q✉❡♥♦ ♣♦rt❡ ♥ã♦ ❢♦✐ ♣♦ssí✈❡❧ ✉t✐❧✐③❛r ✇❛ttí♠❡tr♦s✱ ♣♦r ❝♦♥t❛ ❞♦ ✐♥t❡r✈❛❧♦ ❞❛ ❡s❝❛❧❛ ♥❛q✉❡❧❡s q✉❡ ❡st❛✈❛♠ ❞✐s♣♦♥í✈❡✐s ♥♦ ❧❛❜♦r❛tór✐♦✳ ❖ ♣r♦❜❧❡♠❛ ❢♦✐ ❝♦♥t♦r♥❛❞♦✉t✐❧✐③❛♥❞♦ ♦s❝✐❧♦s❝ó♣✐♦ ❡ ✉♠ ♠✉❧tí♠❡tr♦ tr✉❡ r♠s✱ ❛❧é♠ ❞❡ ❢❡rr❛♠❡♥t❛s❞❛ ♠❛t❡♠át✐❝❛ ❢❛s♦r✐❛❧✳ ◆♦ ❡♥s❛✐♦ ❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦✱ ✉t✐❧✐③♦✉✲s❡ ✉♠❛ t❡♥sã♦ r♠s ❞❡ ✷✼✼ ❱❡ ✉♠❛ ❝♦rr❡♥t❡ tr✉❡ r♠s ❞❡ ✼✶ ♠❆✳ ❖ ❞❡❢❛s❛♠❡♥t♦ ♦❜s❡r✈❛❞♦ ❢♦✐ ❞❡ ✻✷➸✳❆ ❋✐❣✉r❛ ✸✳✺✼ ♠♦str❛ ❛s ❝✉r✈❛s ♦❜t✐❞❛s ♥❡ss❡ ❡♥s❛✐♦✳ ❈♦♠ ❡ss❛ ❞❡❢❛s❛❣❡♠✱ é ♣♦ssí✈❡❧ ♦❜t❡r ❛s ❝♦rr❡♥t❡s s♦❜r❡ ♦ r❡s✐st♦r❡ ♦ ✐♥❞✉t♦r ❞♦ ♠♦❞❡❧♦ ♣❛r❛❧❡❧♦✳ ❉❡ss❛ ❢♦r♠❛✱ I = I cos(62) = 33, 3 [mA] R❡ I = I sin(62) = 62, 68 [mA]. L = 8310Ω❈♦♠ ✐ss♦✱ R n ❡ L = 11, 72 [H]✳P❛r❛ ❛ ❝♦♥❞✐çã♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦✱ ✉t✐❧✐③♦✉✲s❡ t❡♥s❛♦ ❞❡ ✼✱✽ ❱ ❡ ❛ ♠❡s♠❛ ❝♦rr❡♥t❡ ❞❡ ✼✶ ♠❆✳ ❖ ❞❡❢❛s❛♠❡♥t♦ ♦❜t✐❞♦ ♥❡ss❛ ❝♦♥❞✐çã♦ ❢♦✐❞❡ ✺➸✳ ❆ ❋✐❣✉r❛ ✸✳✺✽ ♠♦str❛ ❛s ❝✉r✈❛s ♦❜t✐❞❛s ♥❡ss❡ ❡♥s❛✐♦✳ ✶✸✵ ❋✐❣✉r❛ ✸✳✺✼ ✕ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❞❡ ❡①❝✐t❛çã♦ ❡♠ ✈❛③✐♦ ♣❛r❛✉♠❛ ❝♦rr❡♥t❡ ❞❡ ✶✵✵♠❆✱ t♦r♥❛✲s❡ ♥❡❝❡ssár✐♦ ❛✉♠❡♥t❛r ❛ t❡♥sã♦ ♣❛r❛❛t✐♥❣✐r ❡st❡ ✈❛❧♦r✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦s ❛✉t♦r✳❋✐❣✉r❛ ✸✳✺✽ ✕ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❡ t❡♥sã♦ ♥♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦❝✐r❝✉✐t♦✳❋♦♥t❡✿ ♣r♦❞✉çã♦ ❞♦s ❛✉t♦r✳ ✶✸✶ ◆❡ss❡ ❡♥s❛✐♦✱ t♦♠❛✲s❡ ♦ ♠♦❞❡❧♦ sér✐❡ ❞♦ tr❛♥s❢♦r♠❛❞♦r ✭❝♦♠ ❛ r❡s✐stê♥❝✐❛ ❞♦ ❝♦❜r❡ ❡ ❛ ✐♥❞✉tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦✮✳ ❆ss✐♠✱V = I cos(5) = 7, 77 [mA] R ❡ V = I sin(5) = 0, 6798 [mA]. L= 54, 7Ω = 0, 72Ω = 12, 7 [mH] = ❈♦♠ ✐ss♦✱ R 1 ✱ R 2 ✱ l 1 ❡ l20, 151 [mH] ✳✸✳✶✵ ▼❖❉❊▲❆●❊▼ ❉❆❙ P❊❘❉❆❙ ◆❖ ❚❘❆◆❙❋❖❘▼❆❉❖❘ ❆tr❛✈és ❞♦ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ❛♣r❡s❡♥t❛❞♦ ♥❛ ❋✐❣✉r❛ ✸✳✺✾✱ é♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❛s ♣❡r❞❛s ♥♦ tr❛♥s❢♦r♠❛❞♦r✳ ❈♦♥s✐❞❡r❛r✿ ❼ R 1 ✿ ❘❡s✐stê♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ ♣r✐♠ár✐♦❀❼ x 1 ✿ ❘❡❛tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ♣r✐♠❛r✐❛❀❼ Z 1 ✿ ✐♠♣❡❞â♥❝✐❛ ✈✐st❛ ❞♦ ❧❛❞♦ ♣r✐♠ár✐♦❀❼ R 2 ✿ ❘❡s✐stê♥❝✐❛ ❡q✉✐✈❛❧❡♥t❡ s❡❝✉♥❞ár✐♦❀❼ x 2 ✿ ❘❡❛tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ s❡❝✉♥❞❛r✐❛❀2 ❼ Z ✿ ✐♠♣❡❞â♥❝✐❛ ✈✐st❛ ❞♦ ❧❛❞♦ s❡❝✉♥❞ár✐♦❀ c❼ R ✿ P❡r❞❛s ❞♦ ♥ú❝❧❡♦❀❼ X m ✿ ❘❡❛tâ♥❝✐❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦✳ ❉❛ r❡❧❛çã♦ ❞❡ tr❛♥s❢♦r♠❛çã♦ a✱ ♣♦❞❡✲s❡ r❡♣r❡s❡♥t❛r ❛s ❣r❛♥❞❡✲③❛s ❞♦ s❡❝✉♥❞ár✐♦ ❡♠ ✉♠ ❝✐r❝✉✐t♦ ❡q✉✐✈❛❧❡♥t❡✱ ✈✐st♦ ❞♦ ❧❛❞♦ ♣r✐♠ár✐♦✭❋✐❣✉r❛ ✸✳✻✵✮ ♦✉ s❡❝✉♥❞ár✐♦✳ P❛r❛ ❛ ❝♦♥❞✐çã♦ ❞❡ tr❛♥s❢❡rê♥❝✐❛ ♠á①✐♠❛ ❞❡ ♣♦tê♥❝✐❛ ❛ ✐♠♣❡✲❞â♥❝✐❛ ❞❛ ❢♦♥t❡ ❞❡✈❡ s❡r ✐❣✉❛❧ à ❞❛ ❝❛r❣❛✱ ♥♦ ❝❛s♦ ❡♠ ♣❛rt✐❝✉❧❛r ❞♦❝✐r❝✉✐t♦ ❛♣r❡s❡♥t❛❞♦✿2 Z 1 = a Z2 ✭✸✳✾✷✮❛ss✐♠✱2 R = a R1 2 ✭✸✳✾✸✮ ❡2 x = a x . ✶✸✷ ❋✐❣✉r❛ ✸✳✺✾ ✕ ▼♦❞❡❧♦ ❝✐r❝✉✐t❛❧ ❞♦ tr❛♥s❢♦r♠❛❞♦r✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❋✐❣✉r❛ ✸✳✻✵ ✕ ▼♦❞❡❧♦ ❝✐r❝✉✐t❛❧ ❞♦ tr❛♥s❢♦r♠❛❞♦r r❡✢❡t✐❞♦ ❛♦ ♣r✐♠ár✐♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳22 eq1 = R1 ❆ss♦❝✐❛♥❞♦✲s❡ ❛s ❣r❛♥❞❡③❛s✱ t❡♠✲s❡ ❝♦♠♦ ♣❛rt❡ r❡❛❧ R ✶✸✸ ✸✳✶✵✳✶ ❈á❧❝✉❧♦ ❞❛s r❡s✐stê♥❝✐❛s ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛ ❞♦ ❜♦✲❜✐♥❛❞♦ ❆tr❛✈és ❞❛ s✐♠✉❧❛çã♦ s❡ ♦❜tê♠ ❛s ♣❡r❞❛s ♥♦ ❝♦❜r❡✱ ♥❛s ❜♦❜✐♥❛s= 0, 4197 ♣r✐♠ár✐❛ ❡ s❡❝✉♥❞ár✐❛✳ P❛r❛ ❛s ❝♦rr❡♥t❡s ♣r✐♠ár✐❛ ❞❡ I 1 ❆ ❡= 3, 3718 s❡❝✉♥❞ár✐❛ ❞❡ I2 ❆✱ ❝♦♠ a = 9, 17✳ ❆tr❛✈és ❞❛ s✐♠✉❧❛çã♦ ♥♦ ❋❊▼▼✱ ❛ ♣❡r❞❛ ♥❛ ❜♦❜✐♥❛ ♣r✐♠ár✐❛ é= 0, 9518 = 2, 12 ❞❡ P 1 ❲ ❡ ♥❛ s❡❝✉♥❞ár✐❛ é ❞❡ P 2 ❲✳ ❆ss✐♠✱ ♥♦ t♦t❛❧✱ t❡♠✲s❡ q✉❡ P = 3, 1❲✳ ❈♦♠ ❡ss❡ t♦t❛❧✱ é ♣♦ssí✈❡❧ ❝❛❧❝✉❧❛r ❛ r❡s✐stê♥❝✐❛❡q✉✐✈❛❧❡♥t❡✱ ❞❡ ♠♦❞♦ q✉❡✿ 3.1 R = 2 = 46Ω eq120.3677 ✭❛ ♠✉❧t✐♣❧✐❝❛çã♦ ♣♦r ❞♦✐s s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ s❡r ❛ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦✮✳❆ss✐♠✱ R eq1R = = 23Ω1 2❡ R1 R = = 0, 27Ω.22 a✸✳✶✵✳✷ ❖❜t❡♥çã♦ ❡①♣❡r✐❡♠❡♥t❛❧ ❞❛s ♣❡r❞❛s r❡s✐st✐✈❛s ❡ ❛ ❞✐s✲ ♣❡rsã♦ ♠❛❣♥ét✐❝❛P❡❧♦ ❢❛t♦ ❞❡ ♥ã♦ ❤❛✈❡r ❞✐s♣♦♥í✈❡❧ ♠✐❧✐✇❛tt✐♠❡tr♦s ♣❛r❛ ♣♦tê♥❝✐❛s ❜❛✐①❛s✱ ✉t✐❧✐③♦✉✲s❡ ❛ ♠❛t❡♠át✐❝❛ ❢❛s♦r✐❛❧ ❡ ♦ ✉s♦ ❞❡ ❢♦r♠❛s ❞❡ ♦♥❞❛✭❋✐❣✉r❛ ✸✳✻✶✮ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦✲❝✐r❝✉✐t♦ ❡①♣❡r✐♠❡♥t❛❧✳❆ss✐♠✱ ❢♦✐ ✉t✐❧✐③❛❞♦ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ s❡♠❡❧❤❛♥t❡ ❛♦ ✉t✐❧✐③❛❞♦ ♥♦ ❡♥s❛✐♦❞❡ ❝✐r❝✉✐t♦ ❛❜❡rt♦✳ ❉♦ ❝✐r❝✉✐t♦ ❘▲ sér✐❡ ✭❋✐❣✉r❛ ✸✳✻✷✮✱ ♣r♦♣♦st♦ ♣❛r❛ ❛✈❛❧✐❛r ❛s ♣❡r✲❞❛s ❡ ❞✐s♣❡rsã♦ ♠❛❣♥ét✐❝❛✱ ♦❜t❡✈❡✲s❡✿ = 0, 253❼ I 1cc ❆✱ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛ ♥❛ ❝♦♥❞✐çã♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦❀ = 28, 1❼ V cc ❱ ❂❃ ❚❡♥sã♦ r❡❞✉③✐❞❛ ♣r✐♠ár✐❛❀ ◦❼ ➶♥❣✉❧♦ ❞❡ ❞❡s❢❛s❛♠❡♥t♦ ≈ 4, 085 ✳ ❈♦♠♦ s❡ tr❛t❛ ❞❡ ✉♠ ❝✐r❝✉✐t♦ sér✐❡ ❛ ❝♦rr❡♥t❡ q✉❡ ❣❡r❛ ❛s q✉❡❞❛s❞❡ ♣♦t❡♥❝✐❛❧ é ❛ ♠❡s♠❛✱ ❡ ❞❡♣♦✐s ❞❡ ♦♣❡r❛çõ❡s ♠❛t❡♠át✐❝❛s ♦❜t❡✈❡✲s❡✿ V r V = = 110, 4Ω. r = 28, 1 cos 4, 085 = 27, 93 →= R eq1 ✶✸✹ ❋✐❣✉r❛ ✸✳✻✶ ✕ ❋♦r♠❛ ❞❡ ♦♥❞❛ ❞❛ ❝♦rr❡♥t❡ ❡ t❡♥sã♦ ♥♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦❝✐r❝✉✐t♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❡ V l V = = 7, 72Ω. l = 28, 1 sin 4, 085 = 27, 93 →= X leq1 I cc1❊♠ ❢✉♥çã♦ ❞❛s r❡❧❛çõ❡s ✭✸✳✾✸✮ ❡ ✭✸✳✾✹✮✱ t❡♠✲s❡ X leq1X = = 10, 24 mH l1 = 3, 86Ω → L1 2❡ X leq1 X = = 0, 0122 mH. l2 = 0, 046Ω → L222a R eq1R = = 55, 2 [Ω]1 2❡ R eq1 R = = 0, 656 [Ω].2 ✶✸✺ ❋✐❣✉r❛ ✸✳✻✷ ✕ ▼♦❞❡❧♦ sér✐❡ ❞♦ ❡♥s❛✐♦ ❞❡ ❝✉rt♦ ❝✐r❝✉✐t♦ ♥♦ tr❛♥s❢♦r♠❛❞♦r✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ❊st❛s ♠❡❞✐çõ❡s✱ ❡♠ ❢✉♥çã♦ ❞❛ ❣r❛♥❞❡ ❞✐s❝r❡♣â♥❝✐❛ ❡♥tr❡ ♦s ✈❛✲❧♦r❡s t❡ór✐❝♦s✱ ❢♦r❛♠ r❡❛❧✐③❛❞❛s ✺ ✈❡③❡s ♦❜t❡♥❞♦ ✈❛❧♦r❡s s✐♠✐❧❛r❡s✳ ❯♠❛❤✐♣ót❡s❡ é q✉❡ ♦ ♣r♦❣r❛♠❛ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s é ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ t❛❧❢♦r♠❛ q✉❡ ♦ ✺✵✪ ❞❛ ❡s♣✐r❛ ♥ã♦ é ❝♦♥s✐❞❡r❛❞❛✳✸✳✶✵✳✸ P❡r❞❛s ♥♦ ❢❡rr♦ ❆s ♣❡r❞❛s ❢♦r❛♠ ❞❡t❡r♠✐♥❛❞❛s ❛tr❛✈és ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡✱♦♥❞❡ s✉❛ ár❡❛ ♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦ ✈♦❧✉♠❡ ❞❡ ❢❡rr♦ r❡♣r❡s❡♥t❛ ❛s ♣❡r❞❛s s♦❜r❡ ♦ ❢❡rr♦✳ ❊st❛s ♣❡r❞❛s sã♦ ✐❞❡♥t✐✜❝❛❞❛s ❝♦♠♦✿ P❡r❞❛s ❞❡ ❤✐st❡r❡s❡✱♣❡r❞❛s ❋♦✉❝❛✉❧t ❡ ❛♥ô♠❛❧❛s✳ ❆tr❛✈és ❞❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❛ ❝✉r✈❛ BH s❡ ♦❜t❡✈❡ ❞❛ ❜✐❜❧✐♦t❡❝❛♦ ♠❛t❡r✐❛❧ ♠❛✐s ❛♣r♦①✐♠❛❞♦ à ❝✉r✈❛ ❡①♣❡r✐♠❡♥t❛❧✱ ♥❡st❡ ❝❛s♦✱ ❝♦rr❡s✲♣♦♥❞❡ ❛♦ ♠❛t❡r✐❛❧ ❞❡ ❛ç♦ ❞❡ ❜❛✐①♦ t❡♦r ❞❡ ❝❛r❜♦♥♦✱ ❛ç♦ ✶✵✶✵✳ ◆❡st❡ ✶✸✻◦ ❤✐st❡r❡s❡ ♠á①✐♠❛ ❞❡ ✷✵ ✳ ❈♦♠ ❡st❡s ❞❛❞♦s ❛s ♣❡r❞❛s ❛t✐♥❣✐r❛♠ ✸✱✻❲❛tts ♥❛s ❝♦♥❞✐çõ❡s ♥♦♠✐♥❛✐s ♦♥❞❡ ❛ ❝♦rr❡♥t❡ ♣r✐♠ár✐❛ ♥♦♠✐♥❛❧ é ❞❡I = 0, 4197 = 3, 3718 1 ❬❆❪ ❡ ✉♠❛ s❡❝✉♥❞ár✐❛ I 2 ❬❆❪✳ ❖ ✈❛❧♦r ♦❜t✐❞♦ ♣❛r❛ ❛s ♣❡r❞❛s ❞❡ ❝♦❜r❡ ❡ ❢❡rr♦ ✜❝❛r❛♠ ♣ró①✐♠♦s✱♦ q✉❡ ❢❛③ ❝♦♥❝❧✉✐r q✉❡ ♦s ✈❛❧♦r❡s ✉t✐❧✐③❛❞♦s ♥♦ ♣r♦❥❡t♦ ❡stã♦ ❝♦rr❡t♦s✳✸✳✶✵✳✹ P❡r❞❛s ❚♦t❛✐s ❆s ♣❡r❞❛s t♦t❛✐s sã♦ ❞❛❞❛s ♣❡❧♦ s♦♠❛tór✐♦ ❞❛s ♣❡r❞❛s ♥♦ ❝♦❜r❡❜♦❜✐♥❛ ♣r✐♠ár✐❛✱ ❞❛s ♣❡r❞❛s ♥♦ ❝♦❜r❡ ❜♦❜✐♥❛ s❡❝✉♥❞ár✐❛✱ ❞❛s ♣❡r❞❛s ♥♦❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❡ ❞❛s ♣❡r❞❛s ❋♦✉❝❛✉❧t✱ ❧♦❣♦✿ P = (P + P ) + P + P t f h cu1 cu2 ✭✸✳✾✺✮❛ss✐♠ P = 3, 6 + 1, 19565 + 2, 088 = 6, 88 [W]. t ✭✸✳✾✻✮✸✳✶✶ ❊◆❊❘●■❆ ❉■❙❙■P❆❉❆ ◆❆ ❈❯❘❱❆ ❉❊ ❍■❙❚❊❘❊❙❊ ❆ ❡♥❡r❣✐❛ ❞✐ss✐♣❛❞❛ ♥❛ ❝✉r✈❛ ❞♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❝♦♠♦ ❝♦♥✲ s❡q✉ê♥❝✐❛ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s ❞♦ ♠❛t❡r✐❛❧ ❛❝❛r✲r❡t❛ ✉♠❛ ♣❡r❞❛✱ ♥♦ ♥ú❝❧❡♦ ❡ ❝♦rr❡s♣♦♥❞❡ ❛ ár❡❛ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡♠✉❧t✐♣❧✐❝❛❞❛ ♣❡❧♦ ✈♦❧✉♠❡ ❞❡ ❢❡rr♦ ❛tr❛✈❡ss❛❞♦ ♣❡❧♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ❆ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ♦❜t✐❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ❝♦♠♦ ✐❧✉str❛ ❛❋✐❣✳ ✸✳✻✸✱ ♥❛ ✈❡r❞❛❞❡ ❝♦rr❡s♣♦♥❞❡ ❛ s♦♠❛ ❞❡ três t✐♣♦s ❞❡ ♣❡r❞❛s ❥á❝♦♠❡♥t❛❞❛s✿ ❼ ❙♦♠❡♥t❡ ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ✭❝✉r✈❛ ❛③✉❧✱ ♥❛ ❋✐❣✳ ✸✳✻✸✮✳❼ P❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡ ❝♦rr❡♥t❡s ❞❡ ❋♦✉❝❛✉❧t ✭❝✉r✈❛ ✈❡r♠❡❧❤❛✱ ♥❛ ❋✐❣✳ ✸✳✻✸✮✳❼ P❡r❞❛s ♣♦r ❤✐st❡r❡s❡✱ ❝♦rr❡♥t❡s ❋♦✉❝❛✉❧t ❡ ❡①❝❡❞❡♥t❡s ✭❝✉r✈❛ ✈❡r❞❡✱ ♥❛ ❋✐❣✳ ✸✳✻✸✮✳❆ ár❡❛ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞❛ ♣❡❧❛ s♦❧✉çã♦ ❞❛ ✐♥t❡❣r❛❧ Z~ w = B H · d ~ ✭✸✳✾✼✮❝♦♥s✐❞❡r❛♥❞♦ ✶✸✼ ❋✐❣✉r❛ ✸✳✻✸ ✕ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦s ❝✐❝❧♦s ❞❡ ♣❡r❞❛s❞♦ ❢❡rr♦✿ ✭❛✮ ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡❀ ✭❜✮ ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ❞❡ ❋♦❝❛✉❧t❀✭❝✮ ♣❡r❞❛s ❡①❝❡❞❡♥t❡s✳❋♦♥t❡✿❛❞❛♣t❛❞♦ ✭●❯❊❘❘❆✱ ✷✵✶✵✮ t❡♠✲s❡ q✉❡✿Z22 H B BH3 w = = = [J/m ].H · µdH → w = µ ✭✸✳✾✾✮ 2 2µ 2❈♦♥s✐❞❡r❛♥❞♦ ♦ ✈♦❧✉♠❡ ❞♦ ❢❡rr♦ v = Sl m ✱ t❡♠✲s❡ q✉❡ ❛ ❡♥❡r❣✐❛ é ❞❛❞❛ ♣♦r 1 W = BHSl . m ✭✸✳✶✵✵✮ 22= 0, 1686 [m] ] ❈♦♥s✐❞❡r❛♥❞♦ q✉❡ l m ✱ S = 84, 66 [cm ❡ v =3142, 6 [cm ] ✱ ❞❛ ❝✉r✈❛ ❧❡✈❛♥t❛❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ♦❜t❡♠♦s ❛ r❡❧❛✲ ✶✸✽ ❢❡rr♦ s❡ ♦❜té♠ ❛ ❡♥❡r❣✐❛ ❞✐ss✐♣❛❞❛ ♥♦ ❝✐❝❧♦✳ ❆ss✐♠ ❝❛❧❝✉❧❛♥❞♦ ❛ ár❡❛❣r❛✜❝❛♠❡♥t❡ ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ♦❜t✐❞❛✱ t❡♠♦s q✉❡ 1 W = BHSl = 0, 048 [J]. m 2 P❛r❛ ♦❜t❡r ❛ ♣♦tê♥❝✐❛ ♣♦r ❝✐❝❧♦ ❜❛st❛ ❞✐✈✐❞✐r ❛ ❡♥❡r❣✐❛ ♣❡❧♦ t❡♠♣♦❝♦rr❡s♣♦♥❞❡♥t❡ ❞❡ ✉♠ ❝✐❝❧♦ ♦✉ s✐♠♣❧❡s♠❡♥t❡ ♠✉❧t✐♣❧✐❝❛r ♣❡❧❛ ❢r❡q✉ê♥❝✐❛0, 052 ∗ 60 = 3, 12 [W] ✭❡rr♦ ✶✵✪✮✳ ◆❛ s✐♠✉❧❛çã♦✱ ✉t✐❧✐③♦✉✲s❡ ❛ ❝♦rr❡♥t❡❞❡ ✈❛③✐♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❡ ✺✷ ♠❆ ♦ r❡s✉❧t❛❞♦ ❛♣r❡s❡♥t❛❞♦ ✸✱✻ ✇❛tt✳ ◆♦ ❝❛s♦ ❞❛ ♦♣❡r❛çã♦ ❡♠ ✈❛③✐♦ ❝♦♠ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦ ❞❡✺✷❬♠❆❪ ❛ ❡♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ❢♦✐ ❞❡ ✶✵✱✻❬♠❏❪ ♥❛ s✐♠✉❧❛çã♦✳ ❉♦s ♣♦♥t♦s ❞♦ ❣rá✜❝♦ ❞❛ ❝✉r✈❛ BH ❛tr❛✈és ❞❡ ✐t❡r❛çõ❡s ♦❜t❡♠♦s❛ ár❡❛ ❝♦rr❡s♣♦♥❞❡♥t❡ à ❡♥❡r❣✐❛ ♣❛r❛ ♦s ✈❛❧♦r❡s ♠á①✐♠♦s ❞❡ ✐♥❞✉çã♦B = 0, 9544 [T] = 337 [A/m] ❡ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H ♥❛ ❝♦♥❞✐çã♦❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦ ✭✺✷♠❆✮✳ ❆ss✐♠✿ H = 322❼ ❊♥❡r❣✐❛ ♠á①✐♠❛ ❂ B ❬❏✴♠✸❪ ✭ ♦❜t✐❞♦ ❞❛ ❝✉r✈❛ BH✮✳❼ ❈♦❡♥❡r❣✐❛ ❂ ✶✻✽❬❏✴♠✸❪ ✭ ❝á❧❝✉❧♦ ❞❡ ❝♦❡♥❡r❣✐❛ r❡❛❧✐③❛❞♦ ♥♦ ❣rá✜❝♦ ❡♠ ❊①❝❡❧✱ ❛tr❛✈és ❞❛ té❝♥✐❝❛ ❞♦s tr❛♣é③✐♦s✮✳❼ ❊♥❡r❣✐❛ ❂✸✷✷✲✶✻✽✱ ♦❜t❡♥❞♦ ❛ ✉♠❛ ❡♥❡r❣✐❛ t♦t❛❧ ❞❡ ✶✺✹❬❏✴♠✸❪ P❛r❛ ❝❛❧❝✉❧❛r ❛ ♣♦tê♥❝✐❛ ❞♦ tr❛♥s❢♦r♠❛❞♦r ♥❡st❛s ❝♦♥❞✐çõ❡s✱ ❜❛st❛♠✉❧t✐♣❧✐❝❛r ♣♦r ✻✵❍③✳ P❛r❛ ❞❡t❡r♠✐♥❛r ❛ ♣♦tê♥❝✐❛ ❞❡ ♣r♦❥❡t♦ t❡rí❛♠♦s q✉❡ ♦❜t❡r ❛ ❡♥❡r✲❣✐❛ ❛❝✉♠✉❧❛❞❛ ♥♦ ♥ú❝❧❡♦ ♣❛r❛ ❛ ❝♦rr❡♥t❡ ♥♦♠✐♥❛❧ ❞♦ ♣r✐♠ár✐♦ ❛❝r❡s❝✐❞❛❞❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦✳ ◆♦ ♣r❡s❡♥t❡ ❝❛s♦✱ ❛ ❝♦rr❡♥t❡ ❞❡ s✐♠✉❧❛çã♦ ❢♦✐ ❞❡✸✻✼✱✼ ♠❆ ✭tr❛♥s❢❡rê♥❝✐❛✮ ✰ ✺✷ ♠❆ ✭♠❛❣♥❡t✐③❛çã♦ ✰ ❝♦rr❡♥t❡ ❞❡ ♣❡r❞❛♥ú❝❧❡♦✮✳ P❛r❛ ❛t✐♥❣✐r ❛ ár❡❛ ♠á①✐♠❛✱ é ♥❡❝❡ssár✐♦ ❢❛③❡r ♦ tr❛♥s❢♦r♠❛✲ ✷ ❞♦r ♦♣❡r❛r ♥❛ ❝♦♥❞✐çã♦ ❛❝✉♠✉❧❛t✐✈❛ ✳ ❘❡❛❧✐③❛♥❞♦ ❛ s✐♠✉❧❛çã♦ ♥❡st❛❝♦♥❞✐çã♦✱ ♦❜té♠✲s❡ ❛ ❡♥❡r❣✐❛ ♥♦ ✈❛❧♦r ❞❡ ✵✱✽✷ ❥♦✉❧❡ ♣♦r ❝✐❝❧♦✳ ❊ss❛ ✐♥✲❢♦r♠❛çã♦ ✐♥❞✐❝❛ q✉❡ ❛ ♣♦tê♥❝✐❛ ♠á①✐♠❛ q✉❡ ♦ tr❛♥s❢♦r♠❛❞♦r ♣♦❞❡r✐❛❢♦r♥❡❝❡r✱ ♥❡st❡ ❝❛s♦✱ é ❞❡ ❞❡ ✺✵ ❲✳ ❖ tr❛♥s❢♦r♠❛❞♦r ❢♦✐ ♣r♦❥❡t❛❞♦ s❡❣✉♥❞♦ ✉♠ r♦t❡✐r♦ ♣r♦♣♦st♦ ♣♦r❆❧❢♦♥s♦ ▼❛rt✐♥❣♥♦♥✐ ✭✈❡r✐✜❝❛r ❆♥❡①♦ ❈✮✳ ❆ ♣♦tê♥❝✐❛ ❞❡ ♣r♦❥❡t♦ s❡❡♥❝♦♥tr❛ ❡♥tr❡ ✺✵ ❱❆ ❡ ✺✼ ❱❆ ❞❡♣❡♥❞❡♥❞♦ ❞♦s ❢❛t♦r❡s ❞❡ ❧❛♠✐♥❛çã♦❝♦♥s✐❞❡r❛❞♦s ♣❛r❛ ❛ ❝❤❛♣❛ ✭✵✳✽✺✲✵✱✾✮ ❡ ❞♦s ❢❛t♦r❡s ♠❛❣♥ét✐❝♦s B =1, 3 ❬❚❪ ❡ H = 140❬❆✴♠❪ ❞♦ ❣rá✜❝♦✳ ❆ss✐♠✱ ♦❜s❡r✈❛✲s❡ q✉❡ ♣♦❞❡r✐❛ s❡r ✷❆ ❝♦♥❞✐çã♦ ❛❝✉♠✉❧❛t✐✈❛ ♦❝♦rr❡ q✉❛♥❞♦ ♦s ✢✉①♦s ❞❡ ♣r✐♠ár✐♦ ❡ s❡❝✉♥❞ár✐♦ s❡ s♦♠❛♠✳ ❊ss❛ ❝♦♥❞✐çã♦ ♣❡r♠✐t❡ ✈❡r✐✜❝❛r ❛ ❝❛♣❛❝✐❞❛❞❡ ♠á①✐♠❛ ❞❡ ✢✉①♦ ♣♦ssí✈❡❧ ♥♦ ✐♥t❡r✐♦r ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ ◆❛ ♣rát✐❝❛✱ ♣♦ré♠✱ ♦❝♦rr❡ ❛♣❡♥❛s ❛ ❝♦♥❞✐çã♦ ❞✐❢❡r❡♥❝✐❛❧ ✭♦✉ s✉❜tr❛t✐✈❛✮✱ ❡♠ q✉❡ ♦s ✢✉①♦s s❡ ❝♦♥tr❛♣õ❡♠✱ r❡s♣❡✐t❛♥❞♦ ❛ ▲❡✐ ❞❡ ▲❡♥③✳ ✶✸✾ ♦❜t✐❞❛ ✉♠❛ ♣♦tê♥❝✐❛ ❛♣❛r❡♥t❡ ✉♠ ♣♦✉❝♦ ♠❛✐♦r ❞♦ q✉❡ ❛ ♣r❡✈✐st❛ ♣❡❧♦♣r♦❥❡t♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛✳✸✳✶✶✳✶ P❡r❞❛s ♣♦r ✉♥✐❞❛❞❡ ❞❡ ♠❛ss❛ ❡ ✈♦❧✉♠❡ ❆tr❛✈és ❞❛ ❝✉r✈❛ ❞❡ ❤✐st❡r❡s❡ ❢♦✐ ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❛s ♣❡r❞❛s s♦❜r❡ ♦ ✈♦❧✉♠❡ ❞❡ ❢❡rr♦✱ ✐st♦ é✱ ❛s ♣❡r❞❛s ♣♦r ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡ ❞♦♠❛t❡r✐❛❧ ♦ q✉❡ é ♠✉✐t♦ út✐❧ ♣❛r❛ ♦ ♣r♦❥❡t♦ ❞❛s ♠áq✉✐♥❛s✱ ❥á q✉❡ ♥❛❢❛s❡ ❞❡ ♣r♦❥❡t♦ ❡ s✐♠✉❧❛çã♦ ♦ ✈♦❧✉♠❡ ❞♦ ❞✐s♣♦s✐t✐✈♦ é ✉♠❛ ✐♥❢♦r♠❛çã♦❞✐s♣♦♥í✈❡❧✳ ❙❡ ❛ ❞❡♥s✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧ ❞❛ ❝❤❛♣❛ é ✉♠ ❞❛❞♦ ❝♦♥❤❡❝✐❞♦é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❛s ♣❡r❞❛s ♣♦r ❦❣ ❞❡ ❢❡rr♦✱ ♥❡st❡ ❝❛s♦✿ ❼ P❡r❞❛s ♣♦r ✈♦❧✉♠❡ ❂ ✸✱✻ ❲✴✵✱✵✵✵✶✹✷✼✸✽♠✸ ❂ ✷✺❬❑✇✴♠✸❪❼ P❡s♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❂ ✼✾✵✵ ❦❣✴♠✸✯ ✵✱✵✵✵✶✹✷✼✸✽♠✸ ❂ ✶✱✶✹❬❦❣❪❼ P❡r❞❛s ♣♦r ❦❣ ❂ ✸✱✻❲✴✶✱✶✹❣ ❂ ✸✱✷❲✴❦❣ ❆ ❚❛❜❡❧❛ ✸✳✻ ❛♣r❡s❡♥t❛ ✈❛❧♦r❡s ✉s✉❛✐s ♣❛r❛ ♣❡r❞❛s ♣♦r ✉♥✐❞❛❞❡ ❞❡♠❛ss❛✱ ❡♠ ♠áq✉✐♥❛s ❞❡ ❝♦rr❡♥t❡ ❛❧t❡r♥❛❞❛✱ ♥❛ ❝♦♥❞✐çã♦ ❞❡ f = 50 [Hz]✱ g = 0, 5 [mm] ❡ B = 1 [T]✳❚❛❜❡❧❛ ✸✳✻ ✕ P❡r❞❛s ♣♦r ♠❛ss❛ ✉s✉❛✐s ❡♠ ♠áq✉✐♥❛s ❞❡ ❝♦rr❡♥t❡ ❛❧t❡r✲♥❛❞❛ ◗✉❛❧✐❞❛❞❡ ❞❛ ❧â♠✐♥❛ P❡r❞❛s ♣♦r ♠❛ss❛ [W/kg]❆✉sê♥❝✐❛ ❞❡ sí❧✐❝✐♦ ✸✱✻❇❛✐①❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ s✐❧í❝✐♦ ✸✱✵❆❧t❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ s✐❧í❝✐♦ ✶✱✼ ✭❆❧❢♦♥s♦ ▼❛rt✐❣♥♦♥✐✱ ▼áq✉✐♥❛s ❞❡ ❈♦rr❡♥t❡ ❆❧t❡r♥❛❞❛✮✳✸✳✶✶✳✷ P♦tê♥❝✐❛ ❛t✐✈❛ ♣♦r ✉♥✐❞❛❞❡ ❞❡ ♠❛ss❛ ❆tr❛✈és ❞❛ ❝✉r✈❛ BH ❡ ❛ ♦♣❡r❛çã♦ ❡♠ ❝♦♥❞✐çã♦ ❛❝✉♠✉❧❛t✐✈❛ ❢♦✐♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ❛ ❡♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ s♦❜r❡ ♦ ✈♦❧✉♠❡ ❞❡ ❢❡rr♦✳ ❊st❛❡♥❡r❣✐❛ ❛❝✉♠✉❧❛❞❛ ♣♦r ❝✐❝❧♦ ♣❡r♠✐t❡ ♦ ❝á❧❝✉❧♦ ❞❛ ♣♦tê♥❝✐❛ ♠á①✐♠❛ ❞♦❞✐s♣♦s✐t✐✈♦✳ ❈♦♠♦ é ❝♦♥❤❡❝✐❞♦ ♦ ✈♦❧✉♠❡ ❡ ❛ ❞❡♥s✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧ é ♣♦ssí✈❡❧❞❡t❡r♠✐♥❛r ❛ ♣♦tê♥❝✐❛ ♠á①✐♠❛ ❛ss♦❝✐❛❞❛ à ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡ ❡ ❞❡ ✶✹✵33 ❼ P♦tê♥❝✐❛ ♣♦r ✈♦❧✉♠❡ ❂ ✺✵❲✴✵✱✵✵✵✶✹✷✼✸✽ m ❂ ✸✼✵ ❦❲✴ m3❼ P❡s♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r ❂ ✼✾✵✵ ❦❣✴ m ✯ ✵✱✵✵✵✶✹✷✼✸✽♠✸ ❂ ✶✱✶✹ ❦❣❼ P♦tê♥❝✐❛ ♣♦r ❦❣ ❂✺✵ ❲✴✶✱✶✹ ❦❣ ❂ ✹✻✱✺ ❲✴❦❣3 ❆ ❞❡♥s✐❞❛❞❡ tí♣✐❝❛ ❞♦ ❢❡rr♦ é ❞❡ ✼✾✵✵ ❦❣✴ m ✱ ✈❛r✐❛♥❞♦ ❧❡✈❡♠❡♥t❡ s❡✲❣✉♥❞♦ ❛ ❧✐❣❛ ❢♦r♠❛❞❛✳✸✳✶✶✳✸ ❘❡♥❞✐♠❡♥t♦ ♠á①✐♠♦ ❆♦ ❞✐s♣♦r ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ♣♦tê♥❝✐❛ ♠á①✐♠❛ ❡ ♣❡r❞❛s ♠á①✐✲♠❛s é ♣♦ssí✈❡❧ ❡st✐♠❛r ♦ r❡♥❞✐♠❡♥t♦ ❞♦ ❞✐s♣♦s✐t✐✈♦✳ ❆s ♣❡r❞❛s ❞♦ ❢❡rr♦❡ ❝♦❜r❡ ♣♦r s✐♠✉❧❛çã♦ r❡s✉❧t❛r❛♠ s❡r❡♠ ♣ró①✐♠❛s✱ ✉s✉❛❧♠❡♥t❡ ♥♦ ♣r♦✲❥❡t♦ ❞❡ ♠áq✉✐♥❛s ❡st❡s ✈❛❧♦r❡s sã♦ ♣ró①✐♠♦s✳ ◆❛ s✐♠✉❧❛çã♦ s❡ ♦❜t❡✈❡❛ ♣❡r❞❛ ❞♦ ❢❡rr♦ ❞❡ ✸✱✻ ❲ ❡ ❛s ♣❡r❞❛s ❞♦ ❝♦❜r❡ ❞❡ ✸✱✶❲ ✭❝♦♥❞✐çã♦❞❡ ♣r♦❥❡t♦ ót✐♠❛ ♥♦ ❢❡rr♦ ❡ ♥♦ ❝♦❜r❡✮✳ ❉❡ss❛ ❢♦r♠❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛♣♦tê♥❝✐❛ ❝❛❧❝✉❧❛❞❛ ♥♦ ❣rá✜❝♦ BH ✭❞❡ ✺✵ ❲✮✱ t❡♠✲s❡ q✉❡ ♦ r❡♥❞✐♠❡♥t♦♠á①✐♠♦ é ❛ r❛③ã♦✿ 50 − 3, 6 η = = 0, 87. 50 + 3, 1 + 3, 6■st♦ é✱ ❝♦♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❛s ❝❤❛♣❛s ✉t✐❧✐③❛❞❛s só s❡rá ♣♦s✲ sí✈❡❧ ♦❜t❡r ✉♠ tr❛♥s❢♦r♠❛❞♦r ❝♦♠ ✉♠❛ ❡✜❝✐ê♥❝✐❛ ♠á①✐♠❛ ❞❡ ✽✼✪✳ ✸✳✶✶✳✹ P♦♥t♦ ót✐♠♦ ❞❡ ♦♣❡r❛çã♦❆tr❛✈és ❞❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ♥♦ ❣rá✜❝♦ ❞❡ ♣❡r♠❡❛❜✐✲ ❧✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ♣❡r❝❡❜❡✲s❡ q✉❡ ♦ ♠❡s♠♦ ♥ã♦ ❡stá ♦♣❡r❛♥❞♦ ❡♠ s❡✉♣♦♥t♦ ✧ót✐♠♦✧✳ ❖ ♣♦♥t♦ ót✐♠♦ ❞❡ ♦♣❡r❛çã♦ ❝♦rr❡s♣♦♥❞❡ àq✉❡❧❡ ❞❡ ♣❡r✲♠❡❛❜✐❧✐❞❛❞❡ ♠á①✐♠❛✱ ❛t✐♥❣✐❞❛ ❝♦♠ ✉♠❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ ❞❡ ✶✵✵❆✴♠ ❡ ✉♠❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ❞❡ ✵✱✸ ❚✱ ❝♦♠♦ ♠♦str❛ ♦ ❣rá✜❝♦ ❞❛❋✐❣✉r❛ ✸✳✻✹✳ m sin(ωt) ❈♦♥s✐❞❡r❛♥❞♦ ✉♠ ✢✉①♦ ♠❛❣♥ét✐❝♦ s❡♥♦✐❞❛❧ φ = φ ✱ ❛❡①♣r❡ssã♦ ♣❛r❛ ❛ t❡♥sã♦ ❞❡ ♣✐❝♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ▲❡✐ ❞❡ ❋❛r❛❞❛②✱ é ❞❛❞❛♣♦r✿ V pk = N φ m ω = 220 p(2)❆ ❡①♣r❡ssã♦ ♣❛r❛ ❛ ❞❡♥s✐❞❛❞❡ ♠❛❣♥ét✐❝❛ ♠á①✐♠❛✿ V pk pk V B = m → N = → N = 3620 [e]. ✶✹✶ ❋✐❣✉r❛ ✸✳✻✹ ✕ ❉❡r✐✈❛♥❞♦ ❛ ❝✉r✈❛ BH s❡ ♦❜té♠ ❛ ❝✉r✈❛ ❞❡ ♣❡r♠❡❛❜✐❧✐✲❞❛❞❡ ✐♥❝r❡♠❡♥t❛❧✱ ❡♠ q✉❡ ♣❡r❝❡❜❡✲s❡ q✉❡ ♦ ♣♦♥t♦ ❞❡ ♠❡♥♦r r❡❧✉tâ♥❝✐❛❝♦✐♥❝✐❞❡ ❝♦♠ ✉♠❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H = 100 [A/m]✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❉❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❝❛♠♣♦ H✱ ❛tr❛✈és ❞❛ ❧❡✐ ❞❡ ❆♠♣❡r❡✱ ♦❜té♠✲s❡ ❛❝♦rr❡♥t❡ ❞❡ ♣✐❝♦ ❞❡ ✹✱✼ ❬♠❆ ❪✳ ❖s ❞❡♠❛✐s ❞❛❞♦s ♣♦r ❝♦♥s❡q✉ê♥❝✐❛ ❞♦s q✉❡s✐t♦s ❞❡ t❡♥sã♦ ❡ ❝♦rr❡♥t❡ ♥♦ s❡❝✉♥❞ár✐♦ sã♦✿1 = 3620 [e] ❼ ◆ú♠❡r♦ ❞❡ ❡s♣✐r❛s ♣r✐♠ár✐❛s✿ N ❀ 2 = 394 [e]❼ ◆ú♠❡r♦ ❞❡ ❡s♣✐r❛s s❡❝✉♥❞ár✐❛s✿ N ❀❼ ▼❛t❡r✐❛❧✿ ❆ç♦ ✶✵✶✵❀❼ ❘❡❧❛çã♦ tr❛♥s❢♦r♠❛çã♦✿ a = 9, 17✳ ❙✐♠✉❧❛♥❞♦ ❝♦♠ ❡st❡s ♣❛râ♠❡tr♦s✱ s❡ ♦❜tê♠ ♣❡r❞❛s ♥♦ ❢❡rr♦ ❞❡ ✶✹✷ r❡♥t❡ ❞❡ ♣✐❝♦ ❞❡ ✷✵ ❬♠❆❪✱ ❛ ♣❡r❞❛ ♦❜t✐❞❛ ♥♦ ♥ú❝❧❡♦ ❡r❛ ❞❡ ✸✱✻❲✱ ✐st♦ é✱✶✶ ✈❡③❡s ♠❛✐♦r✳ ❈♦♠ ✐ss♦✱ ✈❡r✐✜❝❛✲s❡ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ♥♦ ♣r♦❥❡t♦ ♦r✐❣✐♥❛❧❡r❛ ❞❡ ✶✶✵✵✱ ❡ ❛✉♠❡♥t❛♥❞♦ ✸ ✈❡③❡s ❡st❡ ✈❛❧♦r✱ ❛s ♣❡r❞❛s sã♦ r❡❞✉③✐❞❛s❡♠ ♠❛✐s ❞❡ ✶✶ ✈❡③❡s✳ ▲♦❣✐❝❛♠❡♥t❡✱ ❞❡✈❡✲s❡ ❛✈❛❧✐❛r s❡ ♥❛ ♣rát✐❝❛ ❛ ❢❛❝t✐❜✐❧✐❞❛❞❡ ❞❛❝♦♥str✉çã♦ ❞❡ss❡ tr❛♥s❢♦r♠❛❞♦r ót✐♠♦✱ ✉♠❛ ✈❡③ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐✲ r❛s é ♠✉✐t♦ ❛❧t♦ ❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❛ ❥❛♥❡❧❛ ❞♦ tr❛♥s❢♦r♠❛❞♦r é ❧✐♠✐t❛❞❛✳✸✳✶✶✳✺ ❚r✐â♥❣✉❧♦ ❞❡ ♣♦tê♥❝✐❛s P❛r❛ ❞❡t❡r♠✐♥❛r ❛ ♣♦tê♥❝✐❛ ❛♣❛r❡♥t❡ ♥❛ ❝♦♥❞✐çã♦ ♥♦♠✐♥❛❧ s❡rá✉t✐❧✐③❛❞❛ ❛ ❝♦rr❡♥t❡ ❞❡ ♣✐❝♦ ♥♦♠✐♥❛❧ ❛❝r❡s❝✐❞❛ ❞❛ ❝♦rr❡♥t❡ ❞❡ ✈❛③✐♦✿I1 = 0, 3677 [A] + 0, 052 (vazio) = 0, 4197 [A] ✱ ❛ t❡♥sã♦ ♥❡st❛ ❝♦♥❞✐çã♦❢♦✐ ❞❡ ✷✷✵❱✱ ❛ss✐♠✿ √= I V = 1/ ❼ P♦tê♥❝✐❛ ❛♣❛r❡♥t❡✿ S11 1 2 · 0, 4197 · 220 = 65, 3 [VA]❀= 53, 1 [W] ❼ P♦tê♥❝✐❛ ❛t✐✈❛✿ P 1 ✭♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❛s ❝❛r❛❝t❡ríst✐❝❛s♠❛❣♥ét✐❝❛s ❝✉r✈❛ BH✮❀1 = 38 [VAR] ❼ P♦tê♥❝✐❛ ❘❡❛t✐✈❛✿ Q ❀❼ ❋❛t♦r ❞❡ ♣♦tê♥❝✐❛ F P = 0, 81✳ P♦rt❛♥t♦✱ ❛ ❡✜❝✐ê♥❝✐❛ ❡♥❡r❣ét✐❝❛ ❞♦ ♣❡q✉❡♥♦ tr❛♥s❢♦r♠❛❞♦r ❝♦♥✲ s✐❞❡r❛♥❞♦ s❡✉ r❡♥❞✐♠❡♥t♦ ❡ ❢❛t♦r ❞❡ ♣♦tê♥❝✐❛ é ❜❛✐①❛✱ ❞❛ ♦r❞❡♠ ❞♦s✼✵✱✺✪ ✭0, 87·0, 81✮✳ ■st♦ s❡ ❞❡✈❡✱ ♥❡st❡ ♣r♦❥❡t♦ ❡♠ ♣❛rt✐❝✉❧❛r✱ à ❝♦rr❡♥t❡❞❡ ✈❛③✐♦✱ ❝✉❥♦ ✈❛❧♦r s❡ ♠♦str♦✉ ♠❛✐♦r ❞♦ q✉❡ ♦ t✐♣✐❝❛♠❡♥t❡ ❡s♣❡r❛❞♦❡♠ r❡❧❛çã♦ à ❝♦rr❡♥t❡ ♥♦♠✐♥❛❧✳✸✳✶✷ ❙❊P❆❘❆➬➹❖ ❉❆❙ P❊❘❉❆❙ ❖❜t❡♥❞♦ ❞✐❢❡r❡♥t❡s ❝✉r✈❛s ❞❡ ❤✐st❡r❡s❡ ✉t✐❧✐③❛♥❞♦ ❛ ❢r❡q✉ê♥❝✐❛ f❝♦♠♦ ♣❛râ♠❡tr♦ ✈❛r✐á✈❡❧ ❡ ♠❛♥t❡♥❞♦ ❝♦♥st❛♥t❡ ❛ ✐♥❞✉çã♦ B é ♣♦ssí✈❡❧✉t✐❧✐③❛r ♦ ♠♦❞❡❧♦ ❞❡ ❙t❡✐♠❡t③ ❡ ❇❡rt♦tt✐ ♣❛r❛ s❡♣❛r❛r ❛s ♣❡r❞❛s✱ ♠♦♥✲ t❛♥❞♦ ✉♠ s✐st❡♠❛ ❞❡ ❡q✉❛çõ❡s ❧✐♥❡❛r❡s ❞❡ ✸ ✈❛r✐á✈❡✐s ❝♦rr❡s♣♦♥❞❡♥t❡s ✶✹✸ ✸✳✶✷✳✶ P❡r❞❛ ❞❡ ❤✐st❡r❡s❡❈✳P✳ ❙t❡✐♥♠❡t③ ♣r♦♣ôs ✉♠❛ ❢ór♠✉❧❛ ❡♠♣ír✐❝❛ q✉❡ ♣❡r♠✐t❡ ❝❛❧✲ ❝✉❧❛r ❛s ♣❡r❞❛s ♣♦r ❤✐st❡r❡s❡ ❡♠ ❢✉♥çã♦ ❞❛ ✐♥❞✉çã♦ ♠á①✐♠❛ B m ✱ ♥♦♠❛t❡r✐❛❧✿ α h P = K B h h ✭✸✳✶✵✶✮ m f,❡♠ q✉❡ α h ♣♦❞❡ ✈❛r✐❛r ❡♥tr❡ ✶✱✺ ❡ ✷ ♣❛r❛ ✐♥❞✉çõ❡s ❞❡ ❛té ✶✱✺❬❚❪✳✸✳✶✷✳✷ P❡r❞❛s ♣♦r ❝♦rr❡♥t❡s ♣❛r❛s✐t❛s ✭❋♦✉❝❛✉❧t✮ ❊st❛ ❡q✉❛çã♦ ❢♦✐ ♠♦❞❡❧❛❞❛ ❛ ♣❛rt✐r ❞❛s ❡q✉❛çõ❡s ❞❛s ❝♦rr❡♥t❡s✐♥❞✉③✐❞❛s ❞❡ ❋❛r❛❞❛②✿2 pi222222 P = B f e = K B f e v. f v → P f f ✭✸✳✶✵✷✮ m m 6ρ✸✳✶✷✳✸ P❡r❞❛s ❡①❝❡❞❡♥t❡s ✭♠♦❞❡❧♦ ❇❡rt♦tt✐✮ ❋♦✐ ❝♦♥s✐❞❡r❛❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❇❡rt♦tt✐ ♣❛r❛ ❛✈❛❧✐❛r ❛s ♣❡r❞❛s ❡①✲❝❡❞❡♥t❡s✱2323 P = K B f . excB excB m ✭✸✳✶✵✸✮ ✸✳✶✷✳✹ ❆♣❧✐❝❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❞❛s❋♦r❛♠ r❡❛❧✐③❛❞♦s ❧❡♥✈❛♥t❛♠❡♥t♦s ❞♦ ❝✐❝❧♦ ❞❡ ❤✐st❡r❡s❡ ❡♠♣r❡✲ ❣❛♥❞♦ ♦ ♠❡s♠♦ ❝✐r❝✉✐t♦ ❞❡s❝r✐t♦ ❛♥t❡r✐♦r♠❡♥t❡ ♥❛s ❢r❡q✉ê♥❝✐❛s ❞❡ ✶✵✱✺✵ ❡ ✻✵ ❍③✳ ❈♦♥s✐❞❡r♦✉✲s❡ ✉♠❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ♠á①✐♠❛ B m ❂✵✱✼ ❚✳◆❡ss❛s ❝♦♥❞✐çõ❡s✱ ❢♦✐ ♣♦ssí✈❡❧ ❛✈❛❧✐❛r ❛s ♣❡r❞❛s t♦t❛✐s ❞♦ ❢❡rr♦✳ ❈♦♠ ❛s ♣❡r❞❛s ❞♦ ❢❡rr♦ ❛ss♦❝✐❛❞❛s às ❞✐❢❡r❡♥t❡s ❢r❡q✉ê♥❝✐❛s✱ ♦s❝♦❡✜❝❡♥t❡s ❞♦s ♠♦❞❡❧♦s ❞❡ ❝❛❞❛ ♣❛r❝❡❧❛ ♣♦❞❡♠ s❡r ❞❡t❡r♠✐♥❛❞♦s✱ r❡✲ s♦❧✈❡♥❞♦ ✉♠ s✐st❡♠❛ ❧✐♥❡❛r ❞❡ 3 × 3 ❡q✉❛çõ❡s✱ ❝♦♠ ❜❛s❡ ♥♦ ♠♦❞❡❧♦♣r♦♣♦st♦✿ α h2323222 P = K B f + K B m f + K e vB f . t h excB f ✭✸✳✶✵✹✮ m m ✶✹✹ ❯♠❛ ✈❡③ r❡s♦❧✈✐❞♦ ♦ s✐st❡♠❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❡s♣❡ss✉r❛ ❞❛ ❝❤❛♣❛30, 5 ❬♠♠❪ ❡ ♦ ✈♦❧✉♠❡ ❞♦ ♠❛t❡r✐❛❧ ♠❛❣♥ét✐❝♦ ✵✱✵✵✵✶✹✷✼✸✽ ❬ m ❪✱ sã♦♦❜t✐❞♦s ♦s s❡❣✉✐♥t❡s ❝♦❡✜❝✐❡♥t❡s✿ α h23326222 P = 0, 0454B f + 0, 00068B m f e vB f . t + 4, 48 · 10 ✭✸✳✶✵✺✮ m m ❆ ❚❛❜❡❧❛ ✸✳✼ ❛♣r❡s❡♥t❛ ❛ ❞✐str✐❜✉✐çã♦ ♣❡r❝❡♥t✉❛❧ ❞❛s ♣❡r❞❛s t♦✲ t❛✐s ❡♠ ❢✉♥çã♦ ❞❛ ✐♥❞✉çã♦ ❡ ❢r❡q✉ê♥❝✐❛✳ ❆ s✐♠✉❧❛çã♦ ❢♦✐ ❢❡✐t❛ ❝♦♠ ❛❝♦rr❡♥t❡ ❞❡ ✵✱✵✹✶ ❬❆❪ q✉❡ ❝♦rr❡s♣♦♥❞❡✱ s❡❣✉♥❞♦ ❛ ❝✉r✈❛ BH✱ ❛ ✉♠❛✐♥❞✉çã♦ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✵✱✽ ❬❚❪✳❚❛❜❡❧❛ ✸✳✼ ✕ P❡r❞❛s ♣❛r❛ ❞✐❢❡r❡♥t❡s ❢r❡q✉ê♥❝✐❛s ❞❡ ♦♣❡r❛çã♦✱ ❡♠ ❬❍③❪✳ s e❆ ♣❡r❞❛ t♦t❛❧ s✐♠✉❧❛❞❛ P ❡ ❛ ♣❡r❞❛ t♦t❛❧ ❞♦ ♠♦❞❡❧♦ P sã♦ ❛♣r❡s❡♥t❛✲❞❛s ❡♠ ❬❲❪✳ ❆s ♣❛r❝❡❧❛s ❞❡ ♣❡r❞❛s ❞♦s ♠♦❞❡❧♦s sã♦ ❡①♣r❡ss❛s ❡♠ ❬❲❪❡ ❡♠ ✪✳ ◆❡ss❡ ú❧t✐♠♦ ❝❛s♦✱ r❡♣r❡s❡♥t❛ ♦ q✉❛♥t♦ ❡ss❛ ♣❛r❝❡❧❛ ❝♦♥tr✐✲❜✉✐ ♣❡r❝❡♥t✉❛❧♠❡♥t❡ ♣❛r❛ ❛s ♣❡r❞❛s ❞♦ ❞✐s♣♦s✐t✐✈♦ ❡♠ ✉♠❛ ❢r❡q✉ê♥❝✐❛❡s♣❡❝í✜❝❛✳ f P s P m P h h exc exc F F ❬❲❪ P ✪ P ❬❲❪ P ✪ P ❬❲❪ P ✪✻✵ ✷✱✷✾ ✷✱✸✹ ✶✱✼✹ ✼✹ ✵✱✷✷ ✾✱✹ ✵✱✸✹ ✶✹✱✺✺✵ ✶✱✽✻ ✶✱✽✽ ✶✱✹✺ ✼✼ ✵✱✶✼ ✾ ✵✱✷✻ ✶✸✱✽✶✵ ✵✱✸✶✼ ✵✱✸✷ ✵✱✷✾ ✾✵ ✵✱✵✶✺ ✹✱✼ ✵✱✵✶✵✷ ✸✱✷ ❉❛ ❚❛❜❡❧❛ ✸✳✼ s❡ ♣♦❞❡ ❛✜r♠❛r q✉❡✱ ♥❛ ❢❛✐①❛ ❞❡ ❢r❡q✉ê♥❝✐❛s ✉t✐✲❧✐③❛❞❛s ♥❛ ✐♥❞ústr✐❛✱ ❛s ♣❡r❞❛s ♣♦r ❝❛✉s❛ ❞❛ ❤✐st❡r❡s❡ sã♦ ♠✉✐t♦ s✐❣♥✐✲✜❝❛t✐✈❛s ❡ t❡♥❞❡♠ ❛ ❛✉♠❡♥t❛r ♣r♦♣♦r❝✐♦♥❛❧♠❡♥t❡ q✉❛♥❞♦ ❛ ❢r❡q✉ê♥❝✐❛❞✐♠✐♥✉✐✳ ❯t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❤✐st❡r❡s❡ ♥❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ✶ ❬❍③❪ s❡♦❜t❡✈❡ ✉♠❛ ♣❡r❞❛ ❞❛ ♦r❞❡♠ ❞♦s ✾✽✪✱ ♥❛ s✐♠✉❧❛çã♦✳ ❈♦♥❝❧✉✐✲s❡ q✉❡ ❛❡✜❝✐ê♥❝✐❛ ❞❛s ♠áq✉✐♥❛s ❡stá ❢♦rt❡♠❡♥t❡ ❛tr❡❧❛❞❛ às ♣❡r❞❛s ❞❡ ❡♥❡r❣✐❛♥♦s ❞♦♠í♥✐♦s ♠❛❣♥ét✐❝♦s✳ ❈♦♠♦ ❢♦r❛♠ ❛♣r❡s❡♥t❛❞♦s ♥❛ ♣❛rt❡ ✐♥tr♦❞✉✲ tór✐❛✱ ♦s ✈✐❞r♦s ♠❡tá❧✐❝♦s ♣❛r❡❝❡♠ s❡r ♣r♦♠✐ss♦r❡s✳ ✶✹✺ ❋✐❣✉r❛ ✸✳✻✺ ✕ ❈✉r✈❛ ❞❡ ❤✐st❡r❡s❡ tr❛ç❛❞❛ ❛ ✶✵ ❍③✱ ♣♦r ♠ét♦❞♦s ❣rá✲3✜❝♦s s❡ ♦❜t❡✈❡ ✉♠❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❞❡ ✸✵❬❏✴ m ❪✱ ❝♦rr❡s♣♦♥❞❡ ❛✉♠❛ ♣♦tê♥❝✐❛ ❞❡ ✵✱✸✷ ✇❛tt✳ ❙❡❣✉♥❞♦ ❛ ❧✐t❡r❛t✉r❛ ❛s ✐rr❡❣✉❧❛r✐❞❛❞❡s ♥♦❝♦♥t♦r♥♦ ♣♦❞❡♠ s❡r ❝❛✉s❛ ❞♦s s❛❧t♦s ❞❡ ❇❛r❦❛✉s❡♥✱ ❡♠❜♦r❛ ❡①✐st❡ ❛♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❝♦♥t❛♠✐♥❛çã♦ ❝♦♠ r✉í❞♦✱ ♦ q✉❛❧ s❡ t♦r♥❛ ♥♦tór✐♦❡♠ ❜❛✐①❛s ❢r❡q✉ê♥❝✐❛s✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ❉♦ ❣rá✜❝♦ ❞❛ ❋✐❣✉r❛ ✸✳✻✻ s❡ ♣❡r❝❡❜❡ q✉❡ ❛s ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡s♣❛r❛s✐t❛s t♦r♥❛♠✲s❡ ♠❛✐♦r❡s ❡♠ ❢r❡q✉ê♥❝✐❛s ♣ró①✐♠❛s ❛ ✸✵✵ ❍③✱ ❡st❛é ❛ ❢r❡q✉ê♥❝✐❛ ♠á①✐♠❛ q✉❡ ♣♦❞❡ ♦♣❡r❛r ✉♠ ✐♥✈❡rs♦r✱ ♥❡st❡ ❝❛s♦ ❛ ❡s✲ tr❛té❣✐❛ ♠❛✐s r❡♥tá✈❡❧ é ❞✐♠✐♥✉✐r ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧✱ ♥♦ ❝❛s♦❞♦s ♠❛t❡r✐❛✐s ❛♠♦r❢♦s✱ ✐st♦ s❡ ❝♦♥s❡❣✉❡ ♣❡❧❛ ❛❞✐çã♦ ❞❡ ❇♦r♦ ❡ s✐❧í❝✐♦✳❖❜s❡r✈❛r t❛♠❜é♠ ❋✐❣✉r❛s ✸✳✻✺✱ ✸✳✻✼ ❡ ✸✳✻✽ ♣❛r❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦❞❡ss❡s ❢❡♥ô♠❡♥♦s✳ ✶✹✻ ❋✐❣✉r❛ ✸✳✻✻ ✕ ❙❡♣❛r❛çã♦ ♣❡r❞❛s ❡♠ ❢✉♥çã♦ ❞❛ ■♥❞✉çã♦✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳❋✐❣✉r❛ ✸✳✻✼ ✕ ❖♣❡r❛çã♦ ❡♠ r❡❣✐♠❡ q✉❛s❡ ❡stát✐❝♦✿ ❛s ♣❡r❞❛s ❞❡ ❤✐st❡r❡s❡ sã♦ ♠✉✐t♦ ♣ró①✐♠❛s ❞❛s ♣❡r❞❛s t♦t❛✐s✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳ ✶✹✼ ❋✐❣✉r❛ ✸✳✻✽ ✕ ❙❡♣❛r❛çã♦ ❞❛s ♣❡r❞❛s ❡♠ ❢✉♥çã♦ ❞❛ ❢r❡q✉ê♥❝✐❛✳❋♦♥t❡✿ Pr♦❞✉çã♦ ❞♦ ❆✉t♦r✳✸✳✶✸ ❈❖❘❘❊◆❚❊ ❉❊ ■◆✲❘❯❙❍ ❖s ♣❛râ♠❡tr♦s ❧❡✈❛♥t❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ s❡rã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛♠♦❞❡❧❛r ❛ ❝♦rr❡♥t❡ ❞❡ ✐♥✲r✉s❤ ❞♦ tr❛♥s❢♦r♠❛❞♦r✳ ❊st❛ ❝♦rr❡♥t❡ ❛♣❛✲ r❡❝❡ ❞✉r❛♥t❡ ❛ ❡♥❡r❣✐③❛çã♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r✱ ❞❡✈✐❞♦ à ♠❛❣♥❡t✐③❛çã♦❡ à s❛t✉r❛çã♦ ❞♦ s❡✉ ♥ú❝❧❡♦✱ s❡♥❞♦ s✉❛ ♠❛❣♥✐t✉❞❡ ❞❡t❡r♠✐♥❛❞❛ ♣❡❧❛❞❡❝❧✐✈✐❞❛❞❡ ❞❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ♥❛ r❡❣✐ã♦ s❛t✉r❛❞❛✳ ◆♦s tr❛♥s❢♦r♠❛❞♦r❡s ❞❡ ❡❧❡✈❛❞❛ ♣♦tê♥❝✐❛✱ ❛❧t❛s ❝♦rr❡♥t❡s ❞❡ ✐♥✲ r✉s❤ ♣♦❞❡♠ s❡r ❛t✐♥❣✐❞❛s✳❖s tr❛♥s❢♦r♠❛❞♦r❡s ✉s❛❞♦s ♥♦s s✐st❡♠❛s ❡❧étr✐❝♦s ❞❡ ♣♦tê♥❝✐❛ r❡q✉❡r❡♠✱ ❡♠ r❡❣✐♠❡ ♣❡r♠❛♥❡♥t❡✱ ❝♦rr❡♥t❡s ❞❡ ❡①❝✐t❛çã♦ ❞❛ ♦r❞❡♠ ❞❡ ✵✱✺✪ ❛ ✷✪ ❞❛ ❝♦rr❡♥t❡ ♥♦♠✐♥❛❧✳✸✳✶✸✳✶ ❈♦♠♣♦rt❛♠❡♥t♦ ❡♠ r❡❣✐♠❡ ♥ã♦✲s❛t✉r❛❞♦ ❖ ❝✐r❝✉✐t♦ ❘▲ ❞❛ ❋✐❣✳ ✸✳✻✾ ❞❡st✐♥❛✲s❡ ❛♦ ❡st✉❞♦ ❞♦ tr❛♥s✐tór✐♦❞❡ ❝♦rr❡♥t❡ ❞✉r❛♥t❡ ❛ ❡♥❡r❣✐③❛çã♦ ❞❡ ✉♠ tr❛♥s❢♦r♠❛❞♦r ♠♦♥♦❢ás✐❝♦ ♣♦r❢♦♥t❡ ❞❡ t❡♥sã♦ s❡♥♦✐❞❛❧✱ ❝♦♠ ♦ s❡❝✉♥❞ár✐♦ ❡♠ ❛❜❡rt♦✳ ❖ ✐♥❞✉t♦r ♥ã♦✲ ✶✹✽ ❋✐❣✉r❛ ✸✳✻✾ ✕ ❈✐r❝✉✐t♦ ♥ã♦✲❧✐♥❡❛r ♣❛r❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ tr❛♥s❢♦r✲♠❛❞♦r ❝♦♠ s❡❝✉♥❞ár✐♦ ❡♠ ✈❛③✐♦✳❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭●❯❊❘❘❆✱ ✷✵✶✵✮é ♦ ✢✉①♦ ❞❡ ❡♥❧❛❝❡ ♥♦ ♣r✐♠ár✐♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ sã♦ ❞❡s♣r❡③❛❞❛s ❛s ♣❡r❞❛s♥♦ ♥ú❝❧❡♦✳ ❆♣ós ♦ ❢❡❝❤❛♠❡♥t♦ ❞❛ ❝❤❛✈❡✱ t❡♠✲s❡✿ dλ ❈♦♠♦ ❛ r❡❧❛çã♦ i = f(λ) é ♥ã♦✲❧✐♥❡❛r✱ ❛ ❊q✉❛çã♦ ✭✸✳✶✵✻✮ só♣♦❞❡rá s❡r r❡s♦❧✈✐❞❛ ♥✉♠❡r✐❝❛♠❡♥t❡✳ ❊♥tr❡t❛♥t♦✱ s❡ ❢♦r ❛ss✉♠✐❞♦ q✉❡♦ ♥ú❝❧❡♦ ♠❛❣♥ét✐❝♦ ♥ã♦ ❛t✐♥❣❡ ❛ s❛t✉r❛çã♦✱ ♣♦❞❡✲s❡ ❢❛③❡r i = f(λ) =λ/L m ✱ ♦♥❞❡ L m ❡ ❛ ✐♥❞✉tâ♥❝✐❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞♦ tr❛♥s❢♦r♠❛❞♦r✱ q✉❡❝♦rr❡s♣♦♥❞❡ ❛ ✐♥❝❧✐♥❛çã♦ ❞❛ r❡t❛ q✉❡ ♣❛ss❛ ♣❡❧❛ ♦r✐❣❡♠ ❡ ♣❡❧♦ ♣♦♥t♦ ❞❡❥♦❡❧❤♦ ❞❛ ❝✉r✈❛ λ − i❀ ❛ss✐♠✱ ✭✸✳✶✵✻✮ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦✿ dλ ✭✸✳✶✵✼✮ dtP❛r❛ s✐♠♣❧✐✜❝❛r✱ s✉♣õ❡ q✉❡ λ(0) = 0❀ ❛ss✐♠✱ ❡st❛ ❡q✉❛çã♦ t❡♠ ♣♦r s♦❧✉çã♦✿22ωL U − ωL U R m (R/L m )t m m m λ(t) = + e2222 sin ωt − cos ωtR + (ωL ) R + (ωL ) ωL m m m ✭✸✳✶✵✽✮ m m m = U /ω❈♦♥s✐❞❡r❛♥❞♦ R ≪ ωL ❡ ❢❛③❡♥❞♦ λ ✱ r❡s✉❧t❛ − (R/L )t m λ(t) = λ [e m − cos ωt] ✭✸✳✶✵✾✮❆ s♦❧✉çã♦ ❞❡s❡❥❛❞❛ é ❝♦♠♣♦st❛ ♣♦r ❞✉❛s ♣❛rt❡s ❢✉♥❞❛♠❡♥t❛✐s✿ ❛ ✶✹✾