Wiktor Eckhaus (28 June 1930 – 1 October 2000) was a Polish–Dutch

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, known for his work on the field of

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

. He was Professor Emeritus of Applied Mathematics at the

Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollme ...

Biography

Eckhaus was born into a wealthy family, and raised in

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...

where his father was managing a fur company. During the German occupation of Poland, he, his mother and sister had to hide because of their Jewish descent. His father, after being a prisoner of war, joined the Russian Army. After the war, in 1947, the re-united family came to

Amsterdam Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...

– via a refugee camp in Austria. Wiktor passed the state exam of the Hogere Burgerschool in 1948, and started to study

aeronautics Aeronautics is the science or art involved with the study, design, and manufacturing of air flight–capable machines, and the techniques of operating aircraft and rockets within the atmosphere. The British Royal Aeronautical Society identifies ...

at the Delft University of Technology. Following his graduation he worked with the National Aerospace Laboratory in Amsterdam, from 1953 till 1957. In the period 1957–1960 he worked at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

, where Eckhaus earned a PhD in 1959 under

Leon Trilling Leon Trilling (July 15, 1924 Białystok, Poland - April 20, 2018), an aeronautical engineer and historian of technology, was professor emeritus in MIT’s Department of Aeronautics and Astronautics and the Program in Science, Technology, and Socie ...

on a dissertation entitled ''"Some problems of unsteady flow with discontinuities"''. In 1960, he became a "maître de recherches" (senior research fellow) at the Department of Mechanics of the Sorbonne. In 1964 he was a visiting professor at the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...

and the

Mathematical Centre The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Cou ...

. Thereafter, in 1965, he became professor at the Delft University of Technology, in pure and applied mathematics and mechanics. From 1972 until his retirement in 1994, Eckhaus was professor of applied mathematics at the Utrecht University. Initially he studied the

flow Flow may refer to: Science and technology * Fluid flow, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathematics), a group action of the real numbers on a set * Flow (psych ...

around

airfoil An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. ...

s, leading to his research on the stability of solutions to (weakly

nonlinear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...

)

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s. This resulted in what is now known as the ''Eckhaus instability criterion'' and ''Eckhaus instability'', appearing for instance as a secondary instability in models of Rayleigh–Bénard convection. Later, Eckhaus worked on

singular perturbation theory In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion : ...

and

soliton In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium ...

equations. In 1983 he treated strongly singular relaxation oscillations – called ''"canards"'' (French for ''"ducks"'') – resulting in his most-read paper ''"Relaxation oscillations including a standard chase on French ducks"''. Eckhaus used standard methods of

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

, on a problem qualified before, by Marc Diener, as an example of a problem only treatable through the use of non-standard analysis. He became a member of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...

in 1987.

Publications

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Notes

References

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Also appeared as:

External links

* {{DEFAULTSORT:Eckhaus, Wiktor 1930 births 2000 deaths People from Ivano-Frankivsk People from Stanisławów Voivodeship Ukrainian Jews Polish emigrants to the Netherlands Dutch people of Ukrainian-Jewish descent Aerodynamicists 20th-century Dutch mathematicians MIT School of Engineering alumni Academic staff of Utrecht University Academic staff of the Delft University of Technology Members of the Royal Netherlands Academy of Arts and Sciences