法拉第波

法拉第波（英語：Faraday waves 或 Faraday ripples），以麥可·法拉第（Michael Faraday）為名，是一種振盪容器中液面的非線性駐波，當其振盪頻率超過臨界值時，平靜液面就會開始不穩，這現象稱之為法拉第不穩性。法拉第最早是在1831年皇家學會《自然科學會報》裡的一篇文章附錄中提到法拉第波^[1]^[2]。

若將一層液體放置在垂直振蕩的活塞頂部，在特定的不穩性條件下，會出現以一半活塞頻率振盪的駐波^[3]。這與參數共振問題有關。駐波形式可能會是條紋、緊密堆積六邊形、甚至是正方形或準週期。常在發出鈴鐺聲的葡萄酒酒杯內的葡萄酒表面，觀察到細條紋的法拉第波。法拉第波也能解釋佛教法器「磬」裡的噴泉現象。

法拉第波及其波長，可以用量子力學裡德布羅意-玻姆理論的德布羅意波及其波長來類比^[4]。

應用

微珠在法拉第波上聚集成團^[5]

法拉第波可作為液體模板，用來引導聚集微小物質，包括軟物質、剛體、生物實體(如單一細胞、細胞球體和種有細胞的微珠)。^[5]與固體模板不同，液體模板可以通過調整振動頻率和加速度來動態調整，生成各種具對稱性及週期性的圖案。

這種現象也被鱷魚用來吸引配偶。它們會在略低水面處以低頻振動肺部，導致身上的尖刺移動並引發表面波。這些表面波基本上是法拉第波，可以觀察到特定共振造成的飛濺效應。^[6]^[7]

參見

參考資料

^ Faraday, M. (1831) "On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces", Philosophical Transactions of the Royal Society (London), vol. 121, pages 299–318. "Faraday waves" are discussed in an appendix to the article, "On the forms and states assumed by fluids in contact with vibrating elastic surfaces" （頁面存檔備份，存於網際網路檔案館）. This entire article is also available on-line (albeit without illustrations) at "Electronic Library" （頁面存檔備份，存於網際網路檔案館）.
^ Others who investigated "Faraday waves" include: (1) Ludwig Matthiessen (1868) "Akustische Versuche, die kleinsten Transversalwellen der Flüssigkeiten betreffend" (Acoustic experiments concerning the smallest transverse waves of liquids) （頁面存檔備份，存於網際網路檔案館）, Annalen der Physik, vol. 134, pages 107–117 ; (2) Ludwig Matthiessen (1870) "Über die Transversalschwingungen tönender tropfbarer und elastischer Flüssigkeiten" (On the transverse vibrations of ringing low-viscosity and elastic liquids) （頁面存檔備份，存於網際網路檔案館）, Annalen der Physik, vol. 141, pages 375–393 ; (3) John William Strutt (Lord Rayleigh) (1883), "On the crispations of fluid resting upon a vibrating support," （頁面存檔備份，存於網際網路檔案館） Philosophical Magazine, vol. 16, pages 50–58.
^ Wright, P.H.; Saylor, J.R. (September 2003). Patterning of particulate films using Faraday waves (PDF). Review of Scientific Instruments. 74 (9): 4063–4070. [2017-04-19]. （原始內容存檔 (PDF)於2010-06-09）.
^ John W. M. Bush Department of Mathematics, MIT. Quantum mechanics writ large (PDF). （原始內容存檔 (PDF)於2017-12-15）.
^ ^5.0 ^5.1 引用錯誤：沒有為名為:0的參考文獻提供內容
^ Powell, Devin. Horny Male Alligators Bellow With Their Back Spikes. Wired. 2011-05-25 [4 May 2016]. （原始內容存檔於2021-02-17）.
^ Moriarty, Peter; Holt, R. Glynn. Faraday waves produced by periodic substrates: Mimicking the alligator water dance. The Journal of the Acoustical Society of America. 2011, 129 (4): 2411. Bibcode:2011ASAJ..129.2411M. doi:10.1121/1.3587858.

[1] Faraday, M. (1831) "On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces", Philosophical Transactions of the Royal Society (London), vol. 121, pages 299–318. "Faraday waves" are discussed in an appendix to the article, "On the forms and states assumed by fluids in contact with vibrating elastic surfaces" （頁面存檔備份，存於網際網路檔案館）. This entire article is also available on-line (albeit without illustrations) at "Electronic Library" （頁面存檔備份，存於網際網路檔案館）.

[2] Others who investigated "Faraday waves" include: (1) Ludwig Matthiessen (1868) "Akustische Versuche, die kleinsten Transversalwellen der Flüssigkeiten betreffend" (Acoustic experiments concerning the smallest transverse waves of liquids) （頁面存檔備份，存於網際網路檔案館）, Annalen der Physik, vol. 134, pages 107–117 ; (2) Ludwig Matthiessen (1870) "Über die Transversalschwingungen tönender tropfbarer und elastischer Flüssigkeiten" (On the transverse vibrations of ringing low-viscosity and elastic liquids) （頁面存檔備份，存於網際網路檔案館）, Annalen der Physik, vol. 141, pages 375–393 ; (3) John William Strutt (Lord Rayleigh) (1883), "On the crispations of fluid resting upon a vibrating support," （頁面存檔備份，存於網際網路檔案館） Philosophical Magazine, vol. 16, pages 50–58.

[3] Wright, P.H.; Saylor, J.R. (September 2003). Patterning of particulate films using Faraday waves (PDF). Review of Scientific Instruments. 74 (9): 4063–4070. [2017-04-19]. （原始內容存檔 (PDF)於2010-06-09）.

[4] John W. M. Bush Department of Mathematics, MIT. Quantum mechanics writ large (PDF). （原始內容存檔 (PDF)於2017-12-15）.

[:0-5] 5.0 ^5.1 引用錯誤：沒有為名為:0的參考文獻提供內容

[6] Powell, Devin. Horny Male Alligators Bellow With Their Back Spikes. Wired. 2011-05-25 [4 May 2016]. （原始內容存檔於2021-02-17）.

[7] Moriarty, Peter; Holt, R. Glynn. Faraday waves produced by periodic substrates: Mimicking the alligator water dance. The Journal of the Acoustical Society of America. 2011, 129 (4): 2411. Bibcode:2011ASAJ..129.2411M. doi:10.1121/1.3587858.

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