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An Exceptional Career in Mathematics

FACM '14 Honors Distinguished Professor Robert M. Miura

Each year for more than a decade, NJIT has hosted Frontiers in Applied and Computational Mathematics — FACM — an international gathering that brings together representatives of academia and preeminent research organizations to share work in mathematics that has significant real-world importance across many scientific and technological disciplines. Once again organized by the Department of Mathematical Sciences and the Center for Applied Mathematics and Statistics at NJIT, FACM ’14, held May 22-23, had an additional special aspect. It was dedicated to Distinguished Professor Robert M. Miura.

The conference’s plenary talks and minisymposium sessions related to mathematical biology, non-linear waves, integrable systems and biostatistics were reflective of the areas in which Miura has made important contributions. In a career of nearly fifty years, he has worked collaboratively to advance mathematics in truly ground-breaking directions.

Outstanding among the many honors Miura has received is the American Mathematical Society’s Leroy P. Steele Prize for Seminal Contribution to Research that he shared in 2006. It recognizes his role in taking the Korteweg-de Vries (KdV) equation to a critical next level of solution, a breakthrough achieved while working with the mathematicians Clifford S. Gardner and Martin D. Kruskal, and nuclear physicist John M. Greene.

The KdV equation, formulated at the end of the 19th century by Diederik Johannes Korteweg and Gustav de Vries was a key step toward the mathematical understanding of an unusual wave form first observed in 1834 on the surface of a canal in Scotland by the engineer John Scott Russell.

Miura first encountered the KdV equation as a research challenge in the mid-1960s at the Princeton Plasma Physics Laboratory, where he was a postdoctoral associate investigating the complexities of nonlinear wave propagation. In addition to MA and PhD degrees in aerospace and mechanical sciences from Princeton, Miura had earned a BS and MS in mechanical engineering from the University of California at Berkeley.

“Every day came with the time to think deeply about new ideas,”Miura says of his Princeton postdoctoral experience. Some of this time was dedicated to building on Kruskal’s earlier work with the physicist Norman Zabusky. They had applied the power of computers, then becoming available, to gain more insight into the wave phenomena at the heart of the KdV equation. Discerning that the waves in their approximate solutions of the KdV equation also had the behavioral qualities of particles, Kruskal and Zabusky coined the term soliton for this type of wave.

Shortly thereafter, Miura and his colleagues took the study of solitons to a new and remarkable plateau of understanding. They showed how it is possible to derive exact solutions of the nonlinear KdV equation by applying inverse scattering theory from quantum mechanics — principles governing the interaction among waves or particles as understood by the middle of the 20th century.

Over the years leading up to the Steele prize in 2006, their work became the basis of theoretical and practical progress in many areas. This progress, which continues today, includes insights relevant to the transport of data in fiber-optic cables, the formation of tornadoes and oceanic waves (possibly tsunamis), high-speed optical computing, plasma physics, and magnetohydrodynamics. Some researchers even postulate a link between solitons and the Great Red Spot on Jupiter.

In subsequent years, Miura focused on differential-difference equations, coauthoring a number of papers on the subject with Charles Lange. These papers were all based on physical applications, including some from mathematical biology, an area to which Miura has made significant contributions.

Much of Miura’s research has involved investigating and modeling spreading cortical depression. In this pathological phenomenon, a self-propagating wave of depolarization and elevated electrolyte concentration slowly spreads through mammalian neocortex. It is the basis of some forms of migraine pain and migraine aura. He has developed several novel models of this phenomenon, and has helped to clarify a more general, related problem of diffusion in cellular environments.

Miura’s research interests are even broader. He has published on such diverse problems as insulin release in beta cells, cell-calcium dynamics, and models of neuronal excitability in cortical, hippocampal and thalamocortical neurons. He has also contributed to the understanding of issues related to the manufacturing of glass electrodes that serve as the main experimental tool in neurophysiology.

In recognition of the work carried out over his long and distinguished career, Miura has been accorded other significant honors in addition to the Steele Prize. He was named an Inaugural Fellow of the Society for Industrial and Applied Mathematics in 2009 and of the American Mathematical Society in 2013. He is also a Fellow of the American Association for the Advancement of Science, the Royal Society of Canada, and of the John Simon Guggenheim Memorial Foundation.

For more about Professor Miura’s achievements, see “In Honor of Robert M. Miura” in the FACM ’14 Program Guide.

Also see “Pursuing Solitons” in the spring 2006 NJIT Magazine.