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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.

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Lecture Notes on the Fermi-Pasta-Ulam-Tsingou Problem
Lecture Notes on the Fermi-Pasta-Ulam-Tsingou Problem Andrew Larkoski November 9, 2016 Because this is a short week, we're going to just discuss some fun aspects of computational physics. Also, because last week's topic was the final homework (due the following Friday), just sit back and relax and forget about everything you have to do. Just kidding. Today, I'm going to discuss the Fermi-Pasta-Ulam-Tsingou (FPUT), problem. Actually, Laura Freeman did her thesis on this topic at Reed in 2008; you can pick up her thesis in the lounge or on the Reed Senior Thesis digital collections if you are interested. Laura actually interviewed Mary Tsingou for her thesis, so this is actually a fascinating historical document. In the early 1950's, Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou per- formed some of the earliest computer simulations on the MANIAC system at Los Alamos. (Remember MANIAC? Metropolis was the leader!) Their problem was very simple, but their results profound. They attempted to simulate a non-linear harmonic oscillator (i.e., spring) on a grid. Recall that Newton's equations for a spring on a grid is: mx¨j = k(xj+1 − 2xj + xj−1) ; (1) which is just a linear problem and so normal modes and eigenfrequencies can be found exactly, etc. The grid spacing is ∆x and so position xj is at xj = j∆x : (2) The problem that FPUT studied was slightly different, modified by non-linearities in x: mx¨j = k(xj+1 − 2xj + xj−1)[1 + α(xj+1 − xj−1)] : (3) When α = 0, this of course returns the linear system, but for α 6= 0 it is non-linear.
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Institute for the Future, Mello Park, Calif: SPONS AGENCY ? National
;10 DOCUMENT RESUME AP ED 110' 011 IR 002 279 AUTHOR Amara, Roy TITLE. Toward Understanding, ,the Socialfmpactof Computers. IFF Report R-29. INSTITUTION 'Institute for the Future, MeLlo Park, Calif: SPONS AGENCY ?National Science Foundation, Washington, D.C. , . 'PUB DATE- ° May 74 . NOTE 141p. j 'AVA'ILABLE FROM Institute for the Future, 2740 Sand Hill Road, Menlo i Park, California 94015 (f10.00) 1.. / . EDRS PRICE MF-$0.76 PLUSATAGE,HC Not Available from EDRS. DESCRIPTORS" Adult Education; *Attitudes;. Computer"Pnograms; *Computers; Computer Science Education; Conference Reports;. Decision Makin Electronic Data Processing; Financial Policy; *,Future (of Society); Puplic Opinion; Scientific Literac .Simulation; Sodial . Attitudes; *Social Change; T_c ological Advancement; *Values 'IDENTIFIERS Computer Literacy; /FP; *Inttitute FOr The Future ABSTRACT r- Summaries of four,. workshops sponsored by the Institute For The Future' (IFF) are presented. Each'focuses on a ,particular aspect'of:the social impact of.computers:(1) computer models and simulatiohs Is aids to decision making;(2) the usd of computers in financitl'operations; 13) perceptions,attitudes, and literacy regarding computers knowledge about the capabilitirs ' and limitation's of computers in meeting humanneeds).; and (4) .individual access to domp ters. Workshop participants and e IFF * staff conclude that there is a need for. th to acqu re a deeper.understanding of 'how computers of ct the decisions individuals and organizations make, -the goods and services they produce, and tfleirorld that individual,perceive. It is also concluded that such improved understan ing must be acquiredin the near future. A programof education p the public 'is lyen propost4.... (Author/DGC) a v .4 , .
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A Bibliography of Publications of Stanis Law M. Ulam
A Bibliography of Publications of Stanislaw M. Ulam Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 17 March 2021 Version 2.56 Abstract This bibliography records publications of Stanis law Ulam (1909–1984). Title word cross-reference $17.50 [Bir77]. $49.95 [B´ar04]. $5.00 [GM61]. α [OVPL15]. -Fermi [OVPL15]. 150 [GM61]. 1949 [Ano51]. 1961 [Ano62]. 1963 [UdvB+64]. 1970 [CFK71]. 1971 [Ula71b]. 1974 [Hua76]. 1977 [Kar77]. 1979 [Bud79]. 1984 [DKU85]. 2000 [Gle02]. 20th [Cip00]. 25th [Ano05]. 49.95 [B´ar04]. 1 2 60-year-old [Ano15]. 7342-438 [Ula71b]. ’79 [Bud79]. Abbildungen [MU31, SU34b, SU34a, SU35a, Ula34, Ula33a]. Abelian [MU30]. Abelsche [MU30]. Above [Mar87]. abstract [Ula30c, Ula39b, Ula78d]. abstrakten [Ula30c]. accelerated [WU64]. Accelerates [Gon96b]. Adam [Gle02]. Adaptive [Hol62]. additive [BU42, Ula30c]. Advances [Ano62, Ula78d]. Adventures [Met76, Ula76a, Ula87d, Ula91a, Bir77, Wil76]. Aerospace [UdvB+64]. ago [PZHC09]. Alamos [DKU85, MOR76a, HPR14, BU90, Ula91b]. Albert [RR82]. algebra [BU78, CU44, EU45b, EU46, Gar01a, TWHM81]. Algebraic [Bud79, SU73]. Algebras [BU75, BU76, EU50d]. Algorithm [JML13]. Algorithms [Cip00]. allgemeinen [Ula30d]. America [FB69]. American [UdvB+64, Gon96a, TWHM81]. Analogies [BU90]. analogy [Ula81c, Ula86]. Analysis [Goa87, JML13, RB12, Ula49, Ula64a, Jun01]. Andrzej [Ula47b]. anecdotal [Ula82c]. Annual [Ano05]. any [OU38a, Ula38b]. applicability [Ula69b]. application [EU50d, LU34]. Applications [Ula56b, Ula56a, Ula81a]. Applied [GM61, MOR76b, TWHM81, Ula67b]. appreciation [Gol99]. Approach [BPP18, Ula42].
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Mathematicians Solve 60-Year-Old Problem 23 March 2015
Mathematicians solve 60-year-old problem 23 March 2015 researchers Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou as a means to study how heat is conducted in solids and metals. At the time the researchers proposed the problem, they expected their numerical calculations would reveal that the system reaches a state of thermal equilibrium - similar to thermal equilibrium exhibited by gasses - in which the energy within the system is evenly divided among each possible movement (called "modes"). When the problem was first simulated with the Mathematical Numerical Integrator and Computer (MANIAC), one of the first digital computers, the researchers were puzzled to discover that after many iterations, energy within the system periodically dispersed and then concentrated to 97 percent of energy within a single mode. This phenomenon became known as "FPU recurrence" and spawned a wealth of questions and research, in addition to thousands of research papers, becoming the foundation of experimental Graphical representation of the resonance manifold in mathematics. the Fermi-Pasta-Ulam problem, plotted in Mathematica. Credit: Yuri Lvov Decades later, using far more powerful computers to run the simulation for greater lengths of time, researchers discovered that energy within the system did eventually reach equilibrium, but the A team of researchers, led by Rensselaer question remained: how precisely was this Polytechnic Institute professor Yuri Lvov, has happening? In the paper "Route to thermalization in found an elegant explanation for the long-standing the ?-Fermi-Pasta-Ulam system," the researchers Fermi-Pasta-Ulam (FPU) problem, first proposed in led by Lvov offer a simple and elegant explanation.
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Chapter Six Conclusion: the Super, the System, and Its Critical Problems
Chapter Six Conclusion: The Super, The System, and Its Critical Problems A decade passed between the time Fermi first proposed the idea of a fusion bomb until the Mike test. Compared to the wartime fission weapon project, Los Alamos appeared to take a considerably longer time to complete research and development of an H-bomb. It is difficult to compare the two projects, however, because the weapons technologies differed from one another excessively, and so did the systems they were developed in. In addition, the Laboratory focused on the Classical Super configuration for the majority of the time, with greater seriousness directed at it than towards any other theory. Up until 1951, the Super represented almost the entire Los Alamos thermonuclear program, with the Alarm Clock and Booster as the only theoretical alternatives. The length of time the U.S. took to develop and test a viable hydrogen bomb, too, is problematic in that it has taken on the form of historical myth. I will elaborate on this later. The period of time that Los Alamos needed to develop and test a fusion device is relative historically. When comparing the time it took Los Alamos to develop a fission bomb as opposed to a fusion bomb it is necessary to consider the characteristics of each project, and the conditions surrounding their development: Compared with the gun and implosion bombs, a fusion weapon involved a much more complicated set of physical problems to solve, 287 fewer people participated in this work, no deadline had been set, and no military directive for this project existed.
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Characterization of Thermalized Fermi-Pasta-Ulam Chains
CHARACTERIZATION OF THERMALIZED FERMI-PASTA-ULAM CHAINS By Boris Gershgorin A Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Mathematics Approved by the Examining Committee: Yuri V. Lvov, Thesis Adviser David Cai, Member Gregor Kovacic, Member Peter Kramer, Member arXiv:0707.2830v1 [math-ph] 19 Jul 2007 Victor Roytburd, Member Rensselaer Polytechnic Institute Troy, New York June 2007 (For Graduation August 2007) CHARACTERIZATION OF THERMALIZED FERMI-PASTA-ULAM CHAINS By Boris Gershgorin An Abstract of a Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Mathematics The original of the complete thesis is on file in the Rensselaer Polytechnic Institute Library Examining Committee: Yuri V. Lvov, Thesis Adviser David Cai, Member Gregor Kovacic, Member Peter Kramer, Member Victor Roytburd, Member Rensselaer Polytechnic Institute Troy, New York June 2007 (For Graduation August 2007) c Copyright 2007 by Boris Gershgorin All Rights Reserved ii CONTENTS LISTOFFIGURES ................................ iv ACKNOWLEDGMENT .............................. ix ABSTRACT .................................... x 0.1 Thesis outline . xi 1. Fermi-Pasta-Ulam problem as a part of nonlinear science . ... 1 1.1 Nonlinearmacroscopicsystems . 1 1.2 History................................... 2 2. Hamiltonian Mechanics of discrete systems . 6 3. Equilibrium statistical physics . 9 3.1 Isolated systems and subsystems . 9 3.2 Liouville’s theorem . 10 3.3 Entropy and the second law of thermodynamics . 13 3.4 TemperatureandGibbsmeasure . 15 4. WaveTurbulence ................................ 19 5. Symplectic integrators for Hamiltonian systems . .. 23 6. Chaosindynamicalsystems . 27 6.1 Logisticmap...............................
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National Security Science Computing Issue
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Fermi, Pasta, Ulam and the Birth of Experimental Mathematics
A reprint from American Scientist the magazine of Sigma Xi, The Scientific Research Society This reprint is provided for personal and noncommercial use. For any other use, please send a request to Permissions, American Scientist, P.O. Box 13975, Research Triangle Park, NC, 27709, U.S.A., or by electronic mail to [email protected]. ©Sigma Xi, The Scientific Research Society and other rightsholders Fermi, Pasta, Ulam and the Birth of Experimental Mathematics A numerical experiment that Enrico Fermi, John Pasta, and Stanislaw Ulam reported 54 years ago continues to inspire discovery Mason A. Porter, Norman J. Zabusky, Bambi Hu and David K. Campbell our years ago, scientists around universally called, sparked a revolu- tunately, because he was at Los Ala- F the globe commemorated the cen- tion in modern science. mos in the early 1950s, he had access tennial of Albert Einstein’s 1905 annus to one of the earliest digital comput- mirabilis, in which he published stun- Time After Time ers. The Los Alamos scientists play- ning work on the photoelectric effect, In his introduction to the version of fully called it the MANIAC (MAth- Brownian motion and special relativ- LA-1940 that was reprinted in Fermi’s ematical Numerical Integrator And ity—thus reshaping the face of physics collected works in 1965, Ulam wrote Computer). It performed brute-force in one grand swoop. Intriguingly, 2005 that Fermi had long been fascinated numerical computations, allowing also marked another important anni- by a fundamental mystery of statisti- scientists to solve problems (mostly versary for physics, although it passed cal mechanics that physicists call the ones involving classified research on unnoticed by the public at large.
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Highlights and Impacts of ASCR's Programs
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Fermi, Pasta, Ulam, and a Mysterious Lady Thierry Dauxois
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