Christiansen P., Sorensen M., Scott A. (eds.) Nonlinear science at the dawn of the 21st century (Springer LNP542, 2000)(459s).pdf

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P.L.Christiansen M.P.Sørensen A.C.Scott (Eds.)

Nonlinear Science

at the Dawn

ofthe21stCentury

Editors

P.L. Christiansen

M.P. Sørensen

A.C. Scott

Department of Mathematical Modelling

The Technical University of Denmark

Building 321

2800 Kgs. Lyngby, Denmark

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Die Deutsche Bibliothek - CIP-Einheitsaufnahme

Nonlinear science at the dawn of the 21st century / P. L. Christiansen ... (ed.). -

Berlin;Heidelberg;NewYork;Barcelona;HongKong;London;

Milan ; Paris ; Singapore ; Tokyo : Springer, 2000

(Lecturenotesinphysics;542)

ISBN 3-540-66918-3

ISSN 0075-8450

ISBN 3-540-66918-3 Springer-Verlag Berlin Heidelberg New York

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Remembering Bob

Alwyn Scott

In the summer of 1962, young Robert Dana Parmentier was ﬁnishing a

master’s thesis in the Department of Electrical Engineering at the Univer-

sity of Wisconsin, where it had been decided to support a major expansion

of laboratory facilities in the rapidly developing area of solid state electron-

ics. Jim Nordman and I—both spanking new PhDs—were put in charge of

this eﬀort, and we soon found ourselves involved in a variety of unfamiliar

activities, including the slicing, polishing, cleaning, and doping of semicon-

ductor crystals prior to the formation of p-n junctions by liquid and vapor

phase epitaxy in addition to the more conventional process of dot alloying.

We had much to learn, and welcomed Bob as a collaborator as he worked

toward his doctorate in the area.

It was an exciting time, with research opportunities beckoning to us from

several directions. From a more general perspective than had been origi-

nally contemplated by the Department, we began studying—both exper-

imentally and theoretically—nonlinear electromagnetic wave propagation

on semiconductor junctions with transverse dimensions large compared to a

wave length. And there were many interesting nonlinear eﬀects to consider.

Using ordinary reverse biased semiconductor diodes, the nonlinear ca-

pacitance of the junction causes shock waves, suggesting a means for gen-

eration of short pulses. At high doping levels, the junctions emit light to

become semiconductor lasers, and at yet higher doping levels the negative

conductance discovered by Leo Esaki appears, leading to a family of trav-

eling wave ampliﬁers and oscillators. In 1966, this latter eﬀect was also

realized on insulating junctions between superconducting metals, rendered

nonlinear through Ivar Giaever’s tunneling of normal electrons.

As a basis for our theoretical work, we started with John Scott Russell’s

classic Report on Waves , a massive work that had been resting on a shelf

of the University Library for well over a century, and in 1963 two events

occurred that were to have decisive inﬂuences on Bob’s professional life.

The ﬁrst of these was a Nobel Prize award to the British electrophysiolo-

gists Alan Hodgkin and Andrew Huxley for their masterful experimental,

theoretical and numerical investigations of nonlinear wave propagation on

a nerve ﬁber. This seminal work—to which applied mathematicians made

no contributions whatsoever—pointed the way to Bob’s doctoral research

on the neuristor , a term recently coined for an electronic analog of a nerve

axon.

The other event of 1963 was the experimental veriﬁcation of Brian Joseph-

son’s prediction of tunneling by coupled electron pairs between supercon-

ducting metals, leading to an unusual sort of nonlinear inductor for which

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