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Ferenc Váradi (1959–2014)

Váradi was a Hungarian mathematician whose numerical simulations of solar system evolution extended the role of chaos theory and helped confirm that the dinosaurs went extinct exactly 66 million years ago.

Published onApr 20, 2022
Ferenc Váradi (1959–2014)

Photo credit: unknown.

Ferenc Váradi died suddenly from a heart attack at his home in Worcester, Massachusetts on Nagasaki Day (August 9, 2014). He was 55, the same age as his father was when he died prematurely from the same cause.

Ferenc Váradi was a talented Hungarian mathematician who creatively applied Lie series algebra, Hamiltonian mechanics and dynamical systems theory to numerical simulations of solar system evolution. These investigations dealt with events that reoccur at very different periodicities, ranging from the sonic speeds of helioseismology to the sluggish cycles of solar system dynamics, and deal with phenomena that shape stars and control the motions of planets, thus influencing their environments on timescales of thousands to millions of years.

Ferenc was born in Miskolc, Hungary on March 6, 1959. He earned a diploma in mathematics from Eötvös Loránd University (ELTE) in Budapest and a Ph.D. at the University of California, Los Angeles, where he came to work with his compatriot, Michael Ghil, and was ably assisted by Paul Roberts, who provided the required connection with UCLA’s Department of Mathematics.

Ferenc’s first paper, published in Celestial Mechanics in 1983 [1], was with his distinguished advisor at ELTE, Bálint Érdi. Much of Ferenc’s early work was in perturbation theory as applied to planetary and small-body orbital evolution. He was concurrently expanding his remarkable computational skills and developing symplectic methods during the time when individual computing power moved from mainframes to workstations.

When Ferenc returned to UCLA in 1991 following a few postdoctoral years in industry, he joined forces with W. M. (Bill) Kaula and Michael Ghil to explore with new tools such classical problems as Laplace’s ‘Great Inequality’, the long-observed imperfection in the 2:5 mean-motion resonance between Jupiter and Saturn. He was justifiably proud of the outcome: Jupiter, Saturn and the edge of chaos, which appeared in Icarus in 1999 [2], and had uncovered a mechanism for a transition to chaos in the motions of these two gas giants.

Unfortunately, Bill Kaula died of cancer in 2000 and Michael Ghil’s interests were focused on far shorter timescales. As a researcher without tenure, Ferenc needed a new faculty mentor and joined Bruce Runnegar, who was then directing the UCLA team of the NASA Astrobiology Institute. The goal was to try to explore solar system dynamics in deep time — the last 500 million years — to see if fluctuations in Earth’s orbital elements, particularly eccentricity, could be recognized in sedimentary rock records. At the time, such comparisons were becoming routine for the later Cenozoic but were thought to be useless beyond about 30–50 million years ago.

In order to improve the accuracy of the calculations and thus the hope of seeing beyond the fog induced by solar system chaos, Ferenc developed better integrators and added refinements, such as the effects of some general relativity, to the models. At the turn of the millennium, the calculations were both expensive and time consuming: about 1 million years per day on a Unix workstation. So 500 million years took a long time. The best result (R7) was published in 2003 in the Astrophysical Journal and became known in the trade as Va03 [3]. This nomenclature followed a trend set by Jacques Laskar, who had shown in 1989 with a 200 million-year-long integration that the solar system is chaotic not quasiperiodic. However, Va03 differed significantly from Lascar’s earlier study, La93, in as little as 15–20 million years. Was either correct?

Stratigraphers in northern Spain compared both Va03 and La93 with deep water sediments deposited in the Bay of Biscay area during the great extinction at the end of the Cretaceous. The 100 ka and 400 ka eccentricity cycles of Va03 were a better fit to layers in the rock record generated by changes in Earth’s axial precession and eccentricity than were the same cycles in La93. However, Laskar’s subsequent result, La04, agreed so closely with Va03 that the controversy disappeared. Both integrations helped confirm that the dinosaurs went extinct exactly 66 million years ago.

One other striking thing appeared in the R7 integration, a sudden change — best seen in the eccentricity of Mercury — that occurred about 65 million years ago. Evolutive spectra showed that this transition resulted from a sudden shift in the frequencies and amplitudes of the normal modes that describe the secular resonances of the terrestrial planets. The coincidence in timing between the transition and the extinction of the dinosaurs was appealing, but a mechanism remained elusive. This was an active area of investigation when Ferenc remarried and chose to return to industry. He concluded his career as a creator, developer, and cyberwarrior working for CLK Design Automation in Littleton, Massachusetts, now part of ANSYS, Inc.

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