scholarly journals Asymptotology—a cautionary tale

2002 ◽  
Vol 44 (1) ◽  
pp. 33-40 ◽  
Author(s):  
R. L. Dewar

AbstractThe art of asymptotology is a powerful tool in applied mathematics and theoretical physics, but can lead to erroneous conclusions if misapplied. A seemingly paradoxical case is presented in which a local analysis of an exactly solvable problem appears to find solutions to an eigenvalue problem over a continuous range of the eigenvalue, whereas the spectrum is known to be discrete. The resolution of the paradox involves the Stokes phenomenon. The example illustrates two of Kruskal's Principles of Asymptotology.

2000 ◽  
Vol 421 ◽  
pp. 1-14 ◽  
Author(s):  
HERBERT E. HUPPERT

George Batchelor was one of the giants of fluid mechanics in the second half of the twentieth century. He had a passion for physical and quantitative understanding of fluid flows and a single-minded determination that fluid mechanics should be pursued as a subject in its own right. He once wrote that he ‘spent a lifetime happily within its boundaries’. Six feet tall, thin and youthful in appearance, George's unchanging attire and demeanour contrasted with his ever-evolving scientific insights and contributions. His strongly held and carefully articulated opinions, coupled with his forthright objectivity, shone through everything he undertook.George's pervasive influence sprang from a number of factors. First, he conducted imaginative, ground-breaking research, which was always based on clear physical thinking. Second, he founded a school of fluid mechanics, inspired by his mentor G. I. Taylor, that became part of the world renowned Department of Applied Mathematics and Theoretical Physics (DAMTP) of which he was the Head from its inception in 1959 until he retired from his Professorship in 1983. Third, he established this Journal in 1956 and actively oversaw all its activities for more than forty years, until he relinquished his editorship at the end of 1998. Fourth, he wrote the monumental textbook An Introduction to Fluid Dynamics, which first appeared in 1967, has been translated into four languages and has been relaunched this year, the year of his death. This book, which describes the fundamentals of the subject and discusses many applications, has been closely studied and frequently cited by generations of students and research workers. It has already sold over 45 000 copies. And fifth, but not finally, he helped initiate a number of international organizations (often European), such as the European Mechanics Committee (now Society) and the biennial Polish Fluid Mechanics Meetings, and contributed extensively to the running of IUTAM, the International Union of Theoretical and Applied Mechanics. The aim of all of these associations is to foster fluid (and to some extent solid) mechanics and to encourage the development of the subject.


1989 ◽  
Vol 142 (4-5) ◽  
pp. 200-202 ◽  
Author(s):  
Dileep P. Jatkar ◽  
C. Nagaraja Kumar ◽  
Avinash Khare

2010 ◽  
Vol 663 ◽  
pp. 1-1
Author(s):  
Grae Worster

The tenth anniversaries of the deaths of George Batchelor and David Crighton occurred, respectively, in March and April this year. In commemoration and celebration of their lives and works, an afternoon of talks was held in the Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge on 19 April 2010. Three of those talks are summarised here: Keith Moffatt and Shon Ffowcs-Williams give impressions of the lives and spirits of these two prominent figures in the history of Jfm – George its founder and David its Editor from 1996, having been an associate editor since 1979; John Hinch gives insight into MicroHydrodynamics, a term coined by George to describe the research area that dominated the second half of his career.


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