To celebrate the IMA’s 60th anniversary in 2024, a number of articles have been chosen by IMA members and MT readers, who introduce their favourite MT articles and explain why they are important to them. Here Nathan Turner CMath MIMA, QinetiQ, introduces …
Stokes Phenomenon Demystified by Richard Paris CMath FIMA and Alistair Wood CMath FIMA
In this 1995 article by R.B. Paris (1946–2022) and his co-author A.D. Wood, a detailed account of the Stokes Phenomenon is provided. The Stokes phenomenon concerns functions whose asymptotic behaviour changes across different regions of the complex plane.
The introduction provides context and includes the ‘poetic, but highly imprecise’ quotation from Sir George Gabriel Stokes on the subject: ‘The inferior term enters as it were into a mist, is hidden for a little from view, and comes out with its coefficient changed’.
The article outlines the history of the phenomenon, from its discovery in the mid-19th century to the more recent developments (in the early 1990s) which ‘dispelled Stokes’ mist’ to reveal the true behaviour of analytic functions in the vicinity of Stokes’ lines.
Thanks to the detailed nature of the article, the reader can ascertain an excellent understanding of the Stokes phenomenon, through many examples and through the application of a variety of mathematical methods which underpin asymptotics.
Moreover, this piece provides a thorough history of the Stokes phenomenon, together with an excellent list of references which provide the reader with an extensive catalogue of information on the subject.
For more on this topic, and the maths of rainbows, see Stokes’s phenomenon: An asymptotic adventure in Plus magazine.
Download the article, Stokes Phenomenon Demystified (pdf) scanned from the 1995 IMA Bulletin, vol. 31, no. 1/2, pp. 21–28.
