arXiv:0801.1590v1 [physics.hist-ph] 10 Jan 2008 osmlt hi fprils ikdb ierin- linear a weak by a linked also particles, adding was of but idea chain crys- teraction The a a how simulate equilibrium. study thermal to to towards proposed evolves who tal scientists three the xiain.I a h it fteterm the of birth localized these the of was solve dynamics It the to how of excitations. showed terms they in paradox space space, real Fourier the in in problem the than the and rather spatially to have Looking limit to solutions. continuum known localized [2], so-called equation the Vries between Korteweg-de in link the problem later years the ten emphasized Kruskal and energy. of enough equipartition not is the nonlinearity as guarantee energy known that to the shows result, paradox, remarkable of highly FPU drift the This the occur. authors, not the perfectly does to of almost contrary Thus, expectations be frequency to period. the lowest recurrence seems this the state after to initial recovered time, back the longer was and a be energy after mode surprise, would the great all this their almost that to beginning but suggested The case, indeed the reached. calculation is the pre- physics of energy of statistical drift equipartition by slowly the should until dicted modes, mode other in- Fourier the energy single to the a term, into additional this troduced to due that, thought eertdte5t niesr fteMy15 publica- 1955 have May the seminars why, of and anniversary reason 50th articles the the conferences, is celebrated several This 2005, [5]. in theories Chaos and Solitons [4] obtains equilibrium. one thermal and to destroyed convergence is ’super- fast recurrence resonances a FPU nonlinear the per- that pose’, strong the so If integrable is perturbed quasi-periodic. turbation slightly remain which of systems theorem, orbits Hamiltonian KAM was most the explanation that of convincing discovery states the No ineffi- before the found for transfer. explain looking energy could dynamics, cient that mode Fourier conditions the non-resonance on focused ple paper. 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She gained a Bachelor of Science in 1951 at the Univer- solids. As anticipated, preliminary results confirmed that sity of Wisconsin, and a Master in mathematics in 1955 energy initially introduced in a single Fourier mode drift at University of Michigan. In 1952, following a sugges- to other ones. However, one day, the oversight to stop tion by her mathematics professor, a woman, she applied the computer allows one to discover some unexpected re- for a position at Los Alamos National Laboratory. At currences which were initially hidden by the slowness of that time, women were not encouraged to do mathemat- the computer. It was the start of an ongoing fruitful ics, but because of the Korean war, there was a shortage research. [5] of American young men and staff positions were also pro- The algorithm used by Mary Tsingou in 1955 to sim- posed to young women. She was thus hired with a whole ulate the relaxation of energy in a model crystal on the group of young people right out of college, for doing hand Maniac is reproduced in Fig. 2. Its complexity has to calculations. be compared with the 15 lines Matlab c code, sufficient She was initially assigned to the T1 division (T for The- today to reproduce the original FPU recurrences [7]. oretical) at Los Alamos National Laboratory, led during At the time, programming was a task requiring great the war by Rudolph Peierls and to which the famous spy, insight and originality, and through the 1960s and even Klaus Fuchs, belonged. But she quickly moved to T7 led later, it was common to list programmers as co-authors. by N. Metropolis for working on the first ever computer, It appears that the only reason for the mention “Work the Maniac I, that no one could program. Together with done by FPU+Tsingou, and report written by FPU” is Mary Hunt, she was therefore the first programmer to that she was not involved in the writing. However, Fermi start exploratory work on it. She remembers it as pretty was not either since, as noticed in S. Ulam biographical easy because of the very limited possibilities of the com- book [8], the FPU report was never published because puter: 1000 words. Fermi died before the writing of the paper. Consequently, They were working primarily on weapons but, in paral- Tsingou was not given credit simply because the report lel, they studied other problems like programming chess was never formally presented in a journal and its state- or studying fundamental physics’ problems. Mary Tsin- ment of credit, differentiating between the writing and gou mostly interacted with J. R. Pasta. They were the the work done, was presumably misread by later people. first ones to do actually graphics on the computer, when they considered a problem with an explosion and visual- ized it on an oscilloscope. In addition to Pasta, she interacted also with Stan Ulam, but very little with E. Fermi, at that time pro- fessor in Chicago. He was visiting Los Alamos only for short periods, mostly during the summer. However, she knew Nella, Fermi’s daughter, much better because Nella didn’t want to stay with her parents during their visits to Los Alamos. Both early twenties girls were sleeping in the same dormitory, while Enrico and Laura Fermi were hosted by their good friends, Stan and Fran¸coise Ulam.

FIG. 2: Reproduction of the algorithm used by Mary Tsingou to code the first numerical experiment. Note the date (5-20- 55) at the top right of the figure.

In 1958, Mary Tsingou married Joseph Menzel who was also working at Los Alamos for the Protective Force of the Atomic Energy Commission. She stayed her whole life in this small city but her colleagues changed since Metropolis left Los Alamos for Chicago, Pasta went to Washington, and later Ulam went to Colorado University. FIG. 1: Mary Tsingou in 1955 and in 2007. She worked successively on different problems, always with computers. She became one of the early experts It was Fermi who had the genius to propose that, in- in Fortran (FORmula TRANslator) invented by IBM in stead of simply performing standard calculus, computers 1955, and was assigned to help researchers in the labora- could be used to test a physical idea, inventing the con- tory. cept of numerical experiments. He proposed to check the After her seminal programming work on the Maniac, prediction of statistical physics on the thermalization of in the beginning of the sixties she came back to the 3

FPU problem with Jim Tuck looking for recurrences [6]. husband at Los Alamos, very close to the place where the But she also considered numerical solution of Schr¨odinger FPU problem was designed and discovered: it is time for equations, the mixing problem of two fluids of different a proper recognition of her contribution: let us quote densities with J. Von Neumann, and other problems. Fi- from now on the Fermi-Pasta-Ulam-Tsingou problem. nally, in the eighties during Ronald Reagan’s presidency, she was deeply involved in the Star Wars project calcu- lations. Acknowledgements: I would like to thank T. J. Retired in 1991, Mary T. Menzel is still living with her Gammel and J. Barr´efor helps.

[1] Fermi E., Pasta J., Ulam S., “Studies of nonlinear prob- (1966). lems. I.”, Los Alamos report LA-1940 (1955), published [5] Chaos 15, Focus issue: The “Fermi-Pasta-Ulam” problem- later in Collected Papers of Enrico Fermi, E. Segr´e(Ed.) the first 50 years (2005). (University of Chicago Press, Chicago 1965); also in Non- [6] Tuck J. L., Menzel M. T., The superperiod of the non- linear Wave Motion, Newell A. C. Ed., Lecture in Applied linear weighted string (FPU) problem, Advances in Math- Mathematics 15 (AMS, Providence, Rhode Island, 1974); ematics 9, 399-407 (1972). also in The Many-Body Problem, Mattis C. C. Ed. (World [7] Dauxois T., Peyrard M., Ruffo S., The Fermi-Pasta- Scientific, Singapore, 1993). Ulam “numerical experiment”: history and pedagogical [2] Zabusky N. J., Kruskal M. D., Phys. Rev. Lett. 15, perspectives, European Journal of Physics 26, S3 (2005). 2403 (1965). [8] Ulam S. M., Adventures of a Mathematician, Charles [3] Dauxois T., Peyrard M., Physics of Solitons, Cam- Scribner’s Son, New York, (1976). bridge University Press (2006). [4] Izrailev F. M., Chirikov B. V. Sov. Phys. Dokl. 11 30