National Academy of Engineering Memorial Tributes: National Academy of Engineering, Volume 10
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Memorial Tributes: National Academy of Engineering, Volume 10

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             JULIAN D.COLE                                             55
                               JULIAN D.COLE
                THE ENGINEERING COMMUNITY, and particularly aeronautics,
            suffered a great loss with the death of Julian David Cole on April 17, 1999, at the
            age of seventy-four. He was well known throughout the world and highly admired
            for his mathematical analyses of high-speed flows in aerodynamics, for his
            pioneering work in the development of modern perturbation methods and their
            application to complex nonlinear problems in engineering, for his books on these
            subjects, as an industrial consultant, and as an influential teacher. He was elected
            to the National Academy of Engineering in 1976 and to the National Academy of
            Sciences in the same year.
                Julian was born in Brooklyn, New York, on April 2, 1925. He received his
            B.S. degree in engineering from Cornell University and his Ph.D. degree from the
            California Institute of Technology, where he worked with Hans Liepmann.
            During his career he was a faculty member at Caltech, scientific liaison officer in
            London for the Office of Naval Research, a faculty scholar at Boeing, a faculty
            member and department chair at the University of California at Los Angeles, and a
            chaired professor at Rensselaer Polytechnic Institute. He was a fellow of the
            American Physical Society, the American Institute of Aeronautics and
            Astronautics, and the American Academy of Arts and Sciences. Among other
            awards he received the Theodore von Kármán Prize
             JULIAN D.COLE                                             56
             (Society for Industrial and Applied Mathematics), the Award for Meritorious
             Civilian Service (U.S. Air Force), the Fluid Dynamics Award (American Institute
             of Aeronautics and Astronautics), and the National Academy of Sciences Award
             in Applied Mathematics and Numerical Analysis.
                Julian began his career at the Guggenheim Aeronautical Laboratories in the
             mid-1940s, just at the time when an assault on the sound barrier had become a
             subject of high national priority and when there existed a great and recognized
             need for the development of nonlinear aerodynamics, especially in the transonic
             regime. Unfortunately, transonic flows were poorly understood from a
             fundamental point of view, impossible to calculate, and difficult to study
             experimentally. Quite remarkably, in his first technical paper in 1948 (with Hans
             Liepmann), Cole actually foresaw the possibility of shock-free transonic airfoils,
             in whose development he was later to play a major role. The practical
             development of transonic wings for advanced transport aircraft, based on this
             idea, eventually depended on the availability of a suitable calculating method.
             Great mathematical difficulties stood in the way of this development. The
             difficulties arose from the nonlinear nature of the flow in this regime, with the
             matching of the flow about the lifting wing with the far field, and with the
             development of a stable method of calculation that automatically incorporates
             shock waves. The first and essential breakthrough in this development was
             accomplished by Cole while working with Earll Murman at Boeing from 1968 to
             1969. Their work on transonic foil theory, published in 1971, showed the way and
             provided the inspiration for most future transonic calculations of aircraft
             components and led to important improvements in aircraft efficiency.
                His influence in aerodynamics extends far beyond the preceding specific
             work. From his beginning in 1948, he went on to illuminate the entire field of
             transonics through a long sequence of research papers and the influential book
             Transonic Aerodynamics, 1986, (with Pam Cook). His work was always driven
             by applications and characterized by a fierce determination to find correct
             solutions without compromise and despite mathematical difficulties. He
             influenced and dominated the subject of tran
             JULIAN D.COLE                                             57
             sonic aerodynamic theory for fifty years. He had a similar influence in the field
             of hypersonic aerodynamics, beginning in the mid-1940s. This field grew with a
             focus on warhead problems and then returned to the fore with national interest in
             the Aerospace Plane. Here his early theory of optimum wings based on a
             “waverider” concept is very important.
                The need to cope with nonlinear phenomena, while urgent and highly visible
             in aeronautics, existed then throughout engineering and science. A general
             recognition of this need and response to it began slowly in the 1940s but
             accelerated continuously and continues with great vigor to this day. The effect on
             engineering practice has been profound, and especially after the advent of the
             computer. In this fifty-year development, Julian Cole played a leading and
             decisive role. It began again early in his career with the development, together
             with others in a small group at Caltech around the aerodynamicist-mathematician
             Paco Lagerstrom, of new and innovative general methods of analysis of nonlinear
             problems. Cole continued persistently in this direction for fifty years, both in the
             form of general developments, and in special applications of many kinds. His
             methods have been propogated through many papers and several books:
             Perturbation Methods in Applied Mathematics, first edition 1968, second edition
             (with J.Kevorkian) 1980; SimilarityMethods for Differential Equations, 1974
            (with G.Bluman); and Multiple Scale and Singular Perturbation Methods, 1996
            (with J. Kevorkian). The methods developed in these books have found
            application to nonlinear problems throughout engineering and have provided
            inspiration and a springboard for a whole generation of engineers faced with the
            analysis of nonlinear problems in all fields.
                Throughout his career, and with considerable acclaim from the
            mathematical community, Cole persisted in his interest to find a solution to
            difficult engineering problems, not only in aeronautics, but also in fields as
            disparate as the mechanics of the cochlea in the ear, and in the effect of radiation
            in the generation of holes and electrons in semiconductors. Throughout his career
            he sought to present results of interest directly to his peers at engineering
            conferences. And of course he persisted,
             JULIAN D.COLE                                             58
             with devotion to the education of engineers, in bringing to that task and to the
             university around him a special integrity and wisdom.
                He served as an example for all of us engaged in engineering research and
             education, and not least of all for his wholehearted attention to real engineering
             problems and to the needs of industry and for bringing his solutions and the
             means for finding solutions to real practitioners. He will be much missed.
                A scientific biography of Julian Cole and a list of his papers and of his many
             Ph.D. students may be found in the book Mathematics Is for Solving Problems
             (Society for Industrial and Applied Mathematics, 1996) which was published on
             the occasion of his seventieth birthday.
             JULIAN D.COLE                                                     59
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