# Obituaries: Chia-Chiao Lin, 1916-2013

The focus of Lin’s early research was fluid mechanics, in particular hydrodynamic stability and turbulence, and the aerodynamics of gas turbines, oscillating airfoils, and shock waves. In his doctoral dissertation, under the supervision of Theodore von Kármán, he solved an outstanding problem stemming from work of Werner Heisenberg concerning the stability of parallel flows. He also resolved a longstanding problem concerning the theory of asymptotic solutions of ordinary differential equations of order higher than 2 that are uniformly valid around turning points.

With von Kármán, Lin proposed a spectral theory for homogeneous turbulence, further developing von Kármán’s similarity theory and the statistical theory of turbulence. These investigations in hydrodynamic stability and turbulence greatly influenced engineers and scientists working on fluid flow, including geophysical fluid dynamicists. Lin’s 1955 monograph, *The Theory of Hydrodynamic Stability*, was the first such publication in this developing field.

Lin then turned to problems in the hydrodynamics of superfluid helium and astrophysics. In 1964, with Frank Shu of the University of California at Berkeley, Lin advanced the density-wave theory of galaxy formation (based on earlier work of Bertil Lindblad) to account for sustained spiral structures. He also contributed to work on related problems in gravitational collapse and star formation. In 1996, Lin and Giuseppe Bertin published the monograph *Spiral Structure in Galaxies: A Density Wave Theory*.

In 1967, at the SIAM Annual Meeting in Toronto, Lin gave the John von Neumann Lecture. His paper based on the lecture, “Dynamics of Self-gravitating Systems: Structure of Galaxies,” was published in *SIAM Review* in April 1969. He concluded the paper with two general remarks:

*“First, in statistical mechanics, combinatorial analysis is extremely important: the problem is discrete. At the same time, when one goes into the consideration of the limiting form of the distribution function, one finds it is continuous (in phase space). Thus, it would be unwise to divide applied mathematics artificially in terms of discrete (or finite) and continuous (or infinite) parts. One often has to consider both and to carry out the limiting process in a single theory that deals with one particular subject.*

*“Second, the current revival in the theoretical study of galactic structure is largely stimulated by the recent improvement in observational technique (especially radio astronomy). In turn, these mathematical studies enable us to understand better the nature of collective modes and to raise again, in sharper focus, some fundamental questions on the relaxation process in a ‘collisionless’ system. These studies certainly involve quite sophisticated mathematical concepts and theorems. They point toward the interest and the importance of the study of nonlinear random processes, and might, by example, contribute to the stimulation and the development of a general mathematical theory, even as the study of the physical process of Brownian motion did. It is in the hope that more general mathematical theories will be stimulated by these studies that I wish to dedicate this survey paper to the late John von Neumann.”*

It was shortly after the von Neumann lecture and *SIAM Review* paper that Lin was elected SIAM president. Further securing his place in SIAM history was the 1974 publication of *Mathematics Applied to Deterministic Problems in the Natural Sciences*, by Lin and his student Lee Segel (1932–2005). SIAM reprinted the book in 1988 as the first volume in the Classics in Applied Mathematics series. In 2010, reappraising one of the problems from the book, S.G.B. O’Brien [2] commented on what made the book and its modeling approach innovative for its time: Lin and Segel “demonstrate how to deal with a real problem from a qualitative description through the mathematical formulation, simplification, and approximate solution, and, importantly, the interpretation of the mathematical results in terms of the original process.” The book has a recent descendant: *A Primer on Mathematical Models in Biology*, by Segel and his student Leah Edelstein-Keshet, which SIAM will publish this month.

In 2002, Lin returned to his alma mater, Tsinghua University in Beijing, as Distinguished Professor. There he founded and served as honorary director of the Zhou Pei-Yuan Center for Applied Mathematics (ZCAM)—now an active hub of research in quantitative biology, applied partial differential equations, scientific computation, and other interdisciplinary subjects linking mathematics, the natural sciences, and engineering.

On his return to China, Lin worked to promote the application of mathematics to the biological sciences. He suggested that new developments in the area should be regarded as part of the natural evolution of applied mathematics with an expanded scope. His own research was on the problem of protein folding—one of the most basic intellectual challenges in computational molecular biology. Instead of concentrating on the prediction of protein structure, Lin tried to understand the mechanism of the process of fast folding toward an equilibrium state. In an analogy with Heisenberg’s energy cascade theory, Lin sketched an application of the kinetic theory for dissipative systems to the study of the structure and function of protein molecules. In this way he showed that traditional concepts and methods of statistical physics can be successfully applied to yield predictions for comparison with empirical data [1]. This work provides a completely new idea for the formulation of protein folding as a nonlinear stochastic process, and moves the problem of protein folding closer to resolution.

Though in his 90s, Lin worked tirelessly at Tsinghua to set an example for young researchers. In recent years he oversaw the research of more than 10 PhD students and junior faculty. Until two years ago, he met every week with colleagues and students in his office; when failing health prevented these meetings, he often held them at home, and he continued to participate in academic activities.

C.C. Lin provided guidance and support to ZCAM from its inception. Along with academic advice, Lin contributed substantial personal financial support for the development of the center. In addition to previous gifts to Tsinghua University, in recent years he donated his salary from the Chinese government to help defray the operating expenses of ZCAM. In 2007, he sold some of his property in the U.S. and donated the collected money to the Tsinghua University Education Foundation, which used it to establish the Lin-Liang Research Fund for the long-term development of the center.

*This obituary was adapted from “Pioneering Applied Mathematician Chia-Chiao Lin Dies at 96,” MIT News, January 14, 2013, with contributions from Jinzhi Lei, Tsinghua University.*

**References**

[1] C.C. Lin, *On the evolution of applied mathematics*, Acta Mech. Sinica, 19:2 (2003), 97–102.

[2] S.B.G. O’Brien, *Lin & Segel’s standing gradient problem revisited: A lesson in mathematical modeling and asymptotics*, SIAM Rev., 53:4 (2011), 775–796.