(By: Bernard Goodman, Professor Emeritus of Physics)
On May 20, 2010, our colleague Tai-Fu Tuan passed away. He came to UC in 1965 after four years in the research group of the distinguished theorist Rudolph Peierls, then Professor at Birmingham University in England and later at Oxford University, who was one of the pioneering physicists of the second quarter of the 20th century in applying the new quantum theory to a wide range of physical problems. Tuan probably acquired his eclectic style in physics from this association with Peierls. His research tastes and his special personality, livened the academic life of the department for both students and faculty - but more on this later.
Following work (with his first student at UC) on pion nucleon scattering - which is a so called two-body problem - he tackled three-body scattering, at that time a much less developed area. (It is a common and correct rumor that, even in classical mechanics, there is no exact solution for the three-body systems which are common in celestial mechanics of the solar system.) The quantum three-body problem, which he tackled with a student, Chester Carpenter, was the capture rate of free electrons by hydrogen atoms (two electrons and one proton). Using the so-called Faddeev formalism for three body scattering, they derived the now definitive value n = 12 for the energy dependence of the capture rate.
After these researches in what might be considered in some sense as 'conventional' phenomenological issues in the quantum theory of scattering (so-called S-matrix theory), Tai-Fu shifted, beginning in the early 1970's, to the development of a truly remarkable, unconventional and unexpected application of the S-matrix to the theory of long waves in the earth's atmosphere. These are known as atmospheric gravity waves (not to be confused with the oscillations of space -time itself, the still elusive gravitational waves, whose future detection is being pursued by putting satellites in space to form giant interferometers). Long-wave atmospheric oscillations are sound waves and are very difficult to treat quantitatively because of the large range of variation of propagation properties like density and temperature at different altitudes, starting from sea level to the evanescent densities in the upper atmosphere. Sound propagation in the oceans has a similar feature of depth dependence of velocity; but, although the relative degree of the variation is much smaller proportionately than in the atmosphere, it is still important. For example, in World War II the cat and mouse game of submarine detection involved figuring out where sonar waves could be deflected away from the submarine through sound refraction and so permit it to hide. Aeronomists tried to deal with the inhomogeneous atmosphere by modeling it as a number of homgeneous layers (slabs). If you have ever looked through a glass stack of different optical densities in an art gallery, you will have seen intriguing artifacts coming from the reflection of light at the interfaces between the layers. Similar artifacts confused the interpretation of the calculated gravity wave patterns in the layer models. In a very different context, the scattering of elementary particles is determined by the strong distance dependence of the forces between them. A sophisticated (S-matrix) theory had been developed which allows a coherent quantitative phenomenology of such processes. It seems to have been during Tai-Fu's sabbatical in Zagreb at the Institute Ruger Boscovich in the early 1970's in discussions there about atmospheric physics with Dubravko Tadic his friend from the Peierls days, that he recognized the possibility of a corresponding S-matrix approach. This could give an artifact-free computational method for atmospheric gravity waves. Of course, such a possibility would be a bold departure because, among other things, the theory of the dynamics of gases and liquids is inherently non-linear, while the Schroedinger equation of Quantum Mechanics is linear. In what can only be called a tour de force, Tuan did manage to devise a mathematical transformation of classical fluid dynamics to Schroedinger form and so to an S-matrix. Once he had this, the die was cast and he found himself converted into the full fledged theoretical aeronomist that he was to remain for the rest of his researches - but for one piece of research in 1977. A talented student Shadia Habbal from Syria and he worked out a model of the breaking and recombination of magnetic field lines which take place when solar-wind magnetic field lines collide with the earth's field. The essential physics of field line recombination is quite challenging to understand and was really satisfactorily clarified only much later. Nevertheless, Tai-Fu and Shadia did a very nice piece of work. She is now a chaired professor of solar-terrestrial physics at the University of Wales.
His new mathematical approach to atmospheric waves was a hard sell to the aeronomy community - for evident reasons - and the fact that S-matrix methodology was outside its normal background and so the formulation was assumed to be in some way unsound. His papers in the Journal of the Geophysical Union were published only after protracted exchanges with referees, but Tai-Fu never relented in submitting them. His now 'full fledged' fledging to the field of aeronomy attracted his scientific interests to a large number of other phenomena associated with upper-atmosphere wave dynamics beyond just wave dynamics which he could now study in detail. To name some, he wrote on the time dependence of chemical processes in the upper atmosphere, on air glow, etc. In the process he trained fifteen PhD students, five postdocs plus two MS students; and garnered $1.2-3 million in research support. Together with four other PhD's, three already mentioned earlier, he has the department record! One of his very last students, however, did a thesis on a different application of the S-matrix to inhomogeneous media, namely to the propagation of light along optical fibers. In these fibers the optical density is graded (to lower values) at the surface where the losses from scattering are strongest, in order to channel the wave away from there. When one thinks about it, the complex poles of the different optical modes relate to their propagation 'lifetimes' or attenuation lengths, for which the S-matrix language is natural. Practical technological usefulness of this approach is not yet clear. Tai-Fu gave a series of lectures on this subject at a number of institutions in China around the time of his retirement.
Some words about him as an academician: He was very attentive to his students, worked closely with them; and they all are fond of him. A measure of one's academic contribution is the success of one's students - and his have done generally quite well. He also taught with dedication, offering a total of six advanced courses on special subjects which he considered important but unrepresented in the curriculum.
His personality was described at the beginning as 'special' as distinct from the term 'colorful', the latter suggesting some degree of conscious showmanship - which Tai-Fu did not have. He was a cultured gentleman, admiring of course of Chinese culture but, from his youth, he was also devoted to the culture of the West, its literature, especially its music and later to American universities. But he did have an intriguing personal story. His father moved about as a diplomat and Tai-Fu went to a high school in Australia. There rugby was the important sport, and he loved to regale us with an account of his terror over having to play it. He managed to avoid it by choosing boxing(!) instead. He went to England with his father and undertook to study engineering at Cambridge. They told him there that he was completely deficient in mathematics. To make up for this, he sought help in the US from a mathematician relative; and went on, improbably it might appear, to earn his PhD in theoretical physics at Carnegie-Mellon University. He loved sports cars and could be seen coming to campus in a Porsche Boxster.
We miss him.
Tai-Fu Tuan (1929-2010)
(By: Bernard Goodman, Professor Emeritus of Physics)