PUBLIC LECTURE PHI BETA KAPPA FEBRUARY 22, 2016 5 P.M. WILDER AUDITORIUM VISITING SCHOLARS KNIGHT PHYSICS BUILDING UNIVERSITY OF MIAMI DAVID K. CAMPBELL FPU and the Birth of Experimental Mathematics In the summer of 1953, at Los Alamos Scientific Laboratory, Enrico Fermi, John Pasta, and Stanislaw Ulam initiated a series of studies on the MANIAC-1 digital computer. These studies were aimed at exploring how simple, multi-degree of freedom nonlinear mechanical systems obeying reversible deterministic dynamics evolve in time, presumably to an equilibrium state describable by statistical mechanics. FPU’s goal was to gain insight into the fundamental question of “the arrow of time.” Their expectation was that the approach to equilibrium would occur by mixing behavior among the many linear modes. Their intention was then to study more complex nonlinear systems, with the eventual hope of modeling turbulence computationally. The results of this first study of the so-called “Fermi-Pasta-Ulam (FPU) problem,” which were published in 1955 and characterized by Fermi as a “little discovery, ” showed instead of the expected mixing of linear modes a striking series of (near) recurrences of the initial state and no evidence of equipartition. This work heralded the beginning of both computational physics and (modern) nonlinear science. In particular, the work marked the first systematic study of a nonlinear system by digital computers (“experimental mathematics”). I will review the consequences of this remarkable numerical experiment and show how it remains of active interest still today, more than sixty years later. An international leader in the field of nonlinear science, David Campbell is professor of physics, electrical and computer engineering and of materials science and engineering at Boston University. He co- founded and directed the Center for Nonlinear Studies at Los Alamos National Laboratory. A fellow of the AAAS and the American Physical Society, he is co- recipient of the 2010 APS Lilienfeld Prize for “pioneering new approaches to the study of complex systems…and for communicating the excitement of this new field to diverse audiences.” Sponsored by the Phi Beta Kappa Chapter and the Department of Physics.