The Center for Nonlinear Studies (CNLS) was an integral part of my scientific career starting as a Postdoctoral Fellow in 1983 up to my tenure as CNLS Director from 2004 to 2015. As such, I experienced a number of scientific phases of CNLS through almost four decades of foundation, evolution, and transition. Throughout this entire interval, the inspiration and influence of David Campbell guided my way. A proper history of CNLS encompassing all of the many contributors to the CNLS story is beyond my means or purpose here. Instead, I present the history as I experienced it. I emphasize the main scientific accomplishments achieved at CNLS over more than 40 years, but I will also attempt to describe and quantify the attributes that made and continue to make the Center for Nonlinear Studies a special institution of remarkable impact and longevity. Throughout its existence, CNLS owes much to the enduring legacy of David Campbell who laid down the foundations and operating principles that have made it so successful.

This paper is about the development and evolution of the Center for Nonlinear Studies (CNLS) at Los Alamos National Laboratory from its founding in 1980 through 2016. The early emphasis was driven by the emergence of revolutionary concepts in the study of nonlinear systems: Low-dimensional chaos, universal routes to chaotic states and their ubiquity in real physical systems, the discovery and investigation of solitons and related coherent structures, dynamical system concepts on turbulence, and the concept of adaptation in natural systems and in computing. David Campbell identified these main areas as “paradigms of nonlinear science” in four distinct classes: Solitons and Coherent Structures, Deterministic Chaos and Fractals, Complex Configurations and Pattern Formation, and Adaptive Nonlinear Systems. Through many decades, this early structure evolved to include other sources of nonlinearity and tools for their analysis including many-body systems such as in quantum magnetism and statistical physics analysis, respectively. Themes such as soft matter, quantitative biology, and information-theory/machine-learning emerged as active areas of research. Throughout the 35 years that I address in this paper, I interacted with CNLS as a postdoctoral fellow, as an active experimental researcher, as an adviser and acting Deputy Director, and finally, as the CNLS Director from 2004 to 2015. I present here the CNLS history from my personal perspective, highlighting many of its key scientific discoveries and accomplishments but also giving the reader an understanding of what makes CNLS a unique scientific entity and relating a few personal anecdotes regarding its personalities and culture.

Nonlinear science in the mid to late 1970s was exploding into the scientific consciousness.1 Chaos, nonlinear dynamics, solitons, and a whole host of related topics spanned traditional disciplinary boundaries.2 The challenge was to create and maintain an organization to capitalize on this paradigm shift and to provide an interactive space for collaborations across but also within scientific disciplines. Los Alamos National Laboratory (LANL or Los Alamos Scientific Laboratory (LASL) prior to 1981) played an important role in a number of developments that contributed to the foundations of this exciting era. Most significant was the 1954 Fermi–Pasta–Ulam–Tsingou (FPUT) numerical simulations to test the equipartition of energy in a system of coupled anharmonic oscillators on the MANIAC supercomputer.3,4 Rather than reaching equilibrium equipartition, the initial state recurred in an unexpected manner, only later explained by the concepts of solitons and chaos. Another, achieved in 1975 by Mitchell Feigenbaum of LANL’s Theoretical Division, was based on earlier work by Los Alamos researchers Stan Ulam, Nick Metropolis, and Paul Stein5 and on the related academic research of Mark Kac, John von Neumann, and Stephen Smale. Feigenbaum analyzed the properties of a simple mathematical equation, the logistic map, and predicted that the properties of the period-doubling sequence would be universal.6–8 (I first learned about period-doubling universality circa 1979 while a graduate student at the University of Washington Leo Kadanoff featured the result in the Boris Jacobsen Public Lecture series using the same HP calculator on which Feigenbaum performed his first calculations. Little did I know that 4 years later I would wind up researching these very questions as a Director’s Funded Postdoc at LANL.) When the universality of period doubling was demonstrated by Libchaber and Mauer9 in a physical experiment of thermal convection in liquid helium, the enormity of this universality prediction and its relevance to experimental physics was confirmed.

In 1973, two events helped shape the future CNLS. First, the LASL Director Harold Agnew, in an effort to revitalize the Theoretical Division, hired Peter Carruthers from Cornell University as its Division Leader, and one of his strategic new hires was Mitchell Feigenbaum. Second, a new distinguished postdoctoral position, the J. Robert Oppenheimer Postdoctoral Fellowship, was created to attract outstanding scientific talent to the Lab; its first awardee was David Campbell, Fig. 1. In 1978, soon after Feigenbaum’s discovery of period-doubling universality in the logistic map, a working group of scientists emerged to ponder how nonlinear dynamics and chaos were evolving. With tongue very much in cheek, the group styled itself the “Unstable Working Group,” Fig. 2, with members that included Campbell, Feigenbaum, Alan Bishop, Basil Nicolaenko, Mac Hyman, Darryl Holm, Nick Metropolis, and Lab Senior Consultants Stan Ulam, Joel Lebowitz, and David McLaughlin. From these beginnings arose the idea of creating a new Lab entity to capitalize on the emerging paradigm of nonlinear science. The co-founders who developed the concept and presented it to Lab management were a very interdisciplinary group: Campbell (nonlinear field theory), Bishop (solitons and condensed matter physics), Nicolaenko (pure math of nonlinear systems), Hyman (nonlinear PDEs and computational algorithms), and Holm (nonlinear fluid dynamics). The Center for Nonlinear Studies was formally created in 1980 with Campbell and Nicolaenko sharing the initial administrative responsibilities.10 To reflect the strong external scientific support for the new CNLS structure, the Lab appointed an External Advisory Committee (EAC), chaired by Mark Kac (Rockefeller) and which included Rutherford Aris (Minnesota), Roger Dashen (Institute for Advanced Study, Princeton), Martin Kruskal (Princeton), Alwyn Scott (Wisconsin), Robert Schrieffer (UC Santa Barbara), and Isadore Singer (UC Berkeley). Regarding the EAC, Kac and Stan Ulam argued that it contains a potential candidate for the first CNLS Director, an insight that provided providential as Al Scott became intrigued by the CNLS concept and accepted the CNLS Director position in 1981. As an influential leader in soliton theory,11 Scott provided instant external credibility and stature to this new enterprise.

FIG. 1.

CNLS co-founder and Director 1987-1992.

FIG. 1.

CNLS co-founder and Director 1987-1992.

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FIG. 2.

Original list of participants in the first meeting of the “Unstable Working Group” held on December 3, 1978 and chaired by Campbell. (Holm is added as regular member although not present at this meeting.)

FIG. 2.

Original list of participants in the first meeting of the “Unstable Working Group” held on December 3, 1978 and chaired by Campbell. (Holm is added as regular member although not present at this meeting.)

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A little background about Los Alamos National Laboratory helps in understanding the structure upon which CNLS was developed. LANL has always had many missions under the auspices of the U.S. Department of Energy, most centrally the maintenance of nuclear weapons and the understanding and characterization of the physics behind them. A broad range of science emerged from the recognition that a diverse portfolio of research from engineering and applied science to basic science was vital in maintaining a vibrant scientific laboratory. Researchers resided in Groups that were combined into Divisions. A unique aspect of this structure that followed from the Manhattan project (where the Theory Division was headed by Hans Bethe) was that the Theoretical Division housed theorists across the scientific spectrum including physics (field theory, nuclear, atomic, condensed matter, astrophysics, plasma, and biological), physical chemistry, materials, and applied mathematics. This was arguably the largest and most diverse concentration of theoretical science collocated together in a single organization and included what was in the 1980s one of the first theoretical biology groups (an opinion voiced by many biologists at the time was that there was no such thing as “theoretical” biology). Physics Division represented most of the experimental efforts in traditional areas of physics including the Condensed Matter and Thermal Physics Group, which was my first home at LANL. Another Division of importance to CNLS was the Computing Division (later the Computer and Computational Sciences Division). The main contributors to CNLS are the postdocs of which there are several types in the LANL repertoire: Postdoctoral Associates (sponsors pay), Director’s Funded Postdoctoral Fellows (about 30/year for whole Lab and the Lab pays), and Distinguished Postdoctoral Fellows (four each per year) named for J. Robert Oppenheimer, Richard Feynman, and Fred Reines [Oppenheimer, Feynman (computation and theory), and Reines (experimental) Fellows].

To maximize the internal impact of CNLS, to maintain external ties to the academic and industrial scientific community, and to provide a productive and innovative scientific environment for the emerging interdisciplinary field of nonlinear science, a number of components of CNLS practice12 that have survived through over 40 years are as follows:

  1. Postdocs shared with Groups/Divisions to resist isolation and encourage internal engagement.

  2. Visitors (short- and long-term) to maintain strong external scientific connections.

  3. Conferences to focus attention on emerging areas of science, particularly those of an interdisciplinary nature.

  4. Co-locating CNLS participants together to encourage and nurture collaboration.

  5. Establishing an internal Executive Committee (EC) of Lab scientists with different backgrounds to help guide the direction and evolution of the CNLS.

  6. Funding developed through CNLS accrued to Groups/Divisions.

  7. Maintain an exciting, novel, and transformational institution within the larger scientific mission of Los Alamos National Laboratory.

Over the intervening decades, there have been many contributors to the scientific and managerial administration of the CNLS. Without naming the numerous individuals who played an acting role in bridging the gaps in this record, the list of permanent Directors and Deputy Directors with their years of service is presented here:
  1. 1980–1981: David Campbell and Basil Nicolaenko, co-administrators10 

  2. 1981–1985: Alwyn Scott, 1st CNLS Director

  3. 1985–1993: David Campbell, Director

  4. 1987–1995: Gary Doolen, 1st Deputy Director

  5. 1996–1997: Don Cohen, Director

  6. 1996–1997: Charlie Doering, Deputy Director

  7. 1997–2003: Hans Frauenfelder, Director

  8. 1997–2000: Shiyi Chen, Deputy Director

  9. 2000–2003: Len Margolin, Deputy Director

  10. 2004–2015: Robert Ecke, Director

  11. 2004–2006: Zoltán Toroczkai, Deputy Director

  12. 2008–2010: Eddy Timmermans, Deputy Director

  13. 2012–2015: Aric Hagberg, Deputy Director

  14. 2016–2022: Angel Garcia, Director

  15. 2016–Present: Enrique Batista, Deputy Director

  16. 2022–Present: Chris Fryer, Director

Below, I have divided the CNLS history into three chronological sections: 1980–1994, 1994–2004, and 2004–2015 corresponding roughly to the tenure and influence of the three longest serving CNLS Directors: David Campbell (1987–1992), Hans Frauenfelder (1997–2003), and Robert Ecke (2004–2015). Al Scott was very influential in getting the CNLS started in 1981, but his stay was rather brief so I have included it in the first era. Don Cohen served for only a year in 1996–1997 and had minimal impact on the CNLS. The period 2015-Present saw Angel Garcia and most recently Chris Fryer serving as CNLS Director, but I will have little to say about those years except to note the continuation of efforts begun earlier. I have also emphasized my own research results as representative of particular nonlinear science topics, e.g., nonlinear dynamics and chaos, pattern formation, turbulence, etc., owing to my familiarity with those results. I have tried to encompass as much of the outstanding science that was done at CNLS, but much has been left out for which I bear full responsibility. Finally, I have focused on David Campbell’s contributions to CNLS over other worthy participants since this article is being written in tribute to David’s investment and efforts on behalf of CNLS.

The Center for Nonlinear Studies began with a very small footprint consisting of several small offices and a meeting room in the Theoretical Division Building. With a burgeoning group of distinguished visitors, new postdocs arriving at a rapid rate, and the need to organize workshops and conferences, space was at a premium. Al Scott summarized the situation to upper management with what became known as the “milk-stool” memo in which he pointed out that “When distinguished visitors including Nobel Prize winners and National Academy of Science Members visit CNLS, I can’t even offer them a milk stool in the corner of my office on which to sit!” This space pressure would lead eventually to CNLS obtaining its own building around 1990, but in the meantime, this was an exciting time at CNLS. The two main themes in the early days were solitons and nonlinear dynamical systems. The term “soliton” was coined by Martin Kruskal to describe analytical integrable solutions to the Korteweg de Vries (KdV) equation, discovered by Martin and Norm Zabusky.13 Solitons result from a balancing of wave dispersion with nonlinearity and they have the unexpected property that two solitons can emerge unscathed from interactions with each other, see Fig. 3. Al Scott, a pioneer in soliton science,11 led research on solitons in biological systems, i.e., Davydov solitons,14 David Campbell, and Alan Bishop developed novel applications of solitons in materials science,15,16 and others investigated solitons in phi-4 theory, in the Sine-Gordon equation, and in other nonlinear wave equations. On the nonlinear dynamics front, the contributions of Feigenbaum included the analysis of universality in two-frequency nonlinear systems17 as modeled by the torus mapping called the Circle map described by the iterative mapping θ n + 1 = θ n + Ω K / ( 2 π ) sin ( 2 π θ n ) (more on this later). Other early prominent scientific results were the nonlinear stability of fluids and plasmas,18 the characterization of the fractal dimension of chaotic attractors,19 and the mathematical20 and dynamical system21 properties of the one-dimensional (1-D) Kuramoto Sivashinsky equation: t u ( x , t ) + x x u ( x , t ) + x x x x u ( x , t ) 12 ( x u ( x , t ) ) 2 = 0.

FIG. 3.

Space–time plot of the collision of two KdV solitons that pass through each other undisturbed.

FIG. 3.

Space–time plot of the collision of two KdV solitons that pass through each other undisturbed.

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The first CNLS postdoctoral fellows were Erica Jen, an applied mathematician who specialized in the emerging field of cellular automata, and Doyne Farmer, a physicist who was part of the self-styled “Dynamical Systems Collective” at UC Santa Cruz (with Norm Packard, Rob Shaw, and Jim Crutchfield). Doyne had a wide variety of interests including state-space reconstruction of chaotic attractors that allowed for the computation of their fractal dimension.19 Erica and Doyne collaborated with members of Harry Swinney’s group at UT Austin to apply these concepts to data from a Taylor–Couette fluid experiment,22 demonstrating their utility in analyzing real physical systems with potentially very large degrees of freedom. Doyne became an Oppenheimer Fellow in 1983 and led CNLS in a number of new exciting research areas. One thing he did was to have CNLS purchase a number of SUN UNIX workstations to create a local area network at CNLS. In the spirit of the times, the machines included named computers with one set that included Groucho, Chico, and Harpo while another set included Trotsky and Lenin. To pull these apparently disparate groupings together was a computer named Marx, leaving ambiguous whether it went with the first set, the Marx Brothers, or the second, after Karl Marx. The vision that small-scale computing on a network would be the future of computing, supplemented by large supercomputers for which Los Alamos was famous, was critical to many of the early successes of CNLS.12 In those early days, one was allocated a set amount of computer time on the supercomputers and one needed to be judicious about its use. In a moment of overzealous fascination, two students in CNLS set out to investigate the fractal structure produced by iteration of the area-preserving Standard Map,
p n + 1 = p n + K sin ( θ n ) ,
(1)
θ n + 1 = θ n + p n + 1 ,
(2)
where p n and θ n are taken modulo 2 π. The fractal island structure of the Standard Map is shown in Fig. 4. While continuing to go to smaller and smaller scales, the students burned through the entire year’s worth of computer allocation! Only after urgent plies from Campbell was the allocation restored.
FIG. 4.

Fractal structure of iterations of the Standard Map.

FIG. 4.

Fractal structure of iterations of the Standard Map.

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The importance of computing was encapsulated in the insight that computing would make unique and critical contributions to the mathematics of nonlinear systems23 through the notion of “experimental mathematics.” This idea has certainly been extraordinarily prescient. Even in 1985, their statement that “It would be hard to exaggerate the role that computers and numerical simulations have played in the recent progress of nonlinear science” now seems a significant understatement.

Another adventure of the early days was in response to the lack of available office space in CNLS. Doyne organized the “El Rancho Institute” in the nearby community of El Rancho one summer in the mid-1980s where he rented a charming adobe house, brought along his whole computer network, and spent the summer doing science without interruption in a lovely location near the Rio Grande river. I recently asked David Campbell how he got approval for such an inventive solution to the space problem and he replied: “We just did it!” On another occasion, things did not go according to plan. The poster for the 1987 conference “Nonlinearity in Biology and Medicine” was supposed to use the famous Botticelli painting “Birth of Venus” as the background, representing birth as a foundational biological process. A senior administrator considered it too politically incorrect and demanded that Campbell and another organizer Byron Goldstein present the request to a then existing Lab committee that considered such issues. Despite the conclusion of the committee that this was a famous piece of art and perfectly fine for the poster, it was disapproved and the background was changed to a computer on a shell (alluding to the UNIX c-shell); David commissioned an artist to paint the new background and has the original to this day. Win some and lose some.

One of the early successes and enduring traditions of CNLS was the identification and molding of international conferences on important new topics in nonlinear science. Of the conferences in the first decade enumerated below, several stand out as particularly compelling and influential. The second CNLS Annual Conference in 1982 was entitled “Order in Chaos,” Fig. 5, and included many of the most influential researchers in chaotic dynamics including Mitch Feigenbaum, Doyne Farmer, Martin Gutzwiller, Phil Holmes, Albert Libchaber, Benoit Mandelbrot, Ed Ott, David Ruelle, and Jim Yorke. The field of chaotic dynamics was exploding, and this conference helped pave the way for future advances in the field. Another noteworthy conference was “Evolution, Games, and Learning” in 1985 organized by Farmer, Alan Lapedes, and Norm Packard which brought the interdisciplinary approach of nonlinear dynamics to the interconnected topics of adaptation underlying biological evolution, game theory, and machine learning, Fig. 6. A contribution to the Conference Proceedings in Physica D: Nonlinear Phenomena 22 by Farmer, Alan Perelson, and Norm Packard that applied these ideas to the immune system24 has been extremely influential. A related important conference, organized in 1989 by Stephanie Forrest,25 was entitled “Emergent Computation: Self-Organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks” where “interesting global behavior emerges from many local interactions. When the emergent behavior is also a computation, we refer to the system as an emergent computation.” (Stephanie was a postdoc in CNLS, and I had recently organized a large CNLS conference so she asked me whether she should organize the conference. I replied encouragingly but warned her that she would wind up doing all the work despite well-intentioned senior co-organizers. And so it went: the conference helped cement her leadership in this field and she did all the work!). In 1987 and again in 1988, Chris Langton organized the first conferences on “Artificial Life” (ALIFE) as a collaborative effort between CNLS and the Santa Fe Institute. His vision for the conference was “Artificial Life is the study of man-made systems that exhibit behaviors characteristic of natural living systems. It complements the traditional biological sciences concerned with the analysis of living organisms by attempting to synthesize life-like behaviors within computers and other artificial media. By extending the empirical foundation upon which biology is based beyond the carbon-chain life that has evolved on earth, Artificial Life can contribute to theoretical biology by locating life-as-we-know-it within the larger picture of life-as-it-could-be.” The legacy of this foundational conference is reflected in its continuation up to the present day.

FIG. 5.

Poster for the 1982 Second CNLS Annual Conference entitled “Order in Chaos.”

FIG. 5.

Poster for the 1982 Second CNLS Annual Conference entitled “Order in Chaos.”

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FIG. 6.

Poster for the 1985 Fifth CNLS Annual Conference entitled “Evolution, Games, and Learning.”

FIG. 6.

Poster for the 1985 Fifth CNLS Annual Conference entitled “Evolution, Games, and Learning.”

Close modal

A list of the CNLS Annual Conferences spanning the time up to 1992 includes a wide diversity of topics of the impact and influence of nonlinearity in mathematics, fluid dynamics, condensed matter physics, biology and medicine, the interface of evolution, game theory, adaptation, and machine learning, and materials science. Other more targeted workshops were widespread and helped bring the focus of nonlinearity to an even wider set of topics. As we will see these conferences have had important internal and external impacts. The CNLS contracted with Physica D to publish the Annual Conference Proceedings:

  1. 1981 Nonlinear Problems: Present and Future, North Holland Mathematical Studies 61 (1981).

  2. 1982 Order in Chaos, Physica D 7 (1983).

  3. 1983 Fronts, Interfaces, and Patterns, Physica D 12 (1984).

  4. 1984 Transport and Propagation in Nonlinear Systems, Journal of Statistical Physics 39 (1985).

  5. 1985 Evolution, Games, and Learning, Physica D 22 (1986).

  6. 1986 Nonlinearity in Condensed Matter, Springer Series in Solid State Sciences 69 (1987).

  7. 1987 Nonlinearity in Biology and Medicine, Proceedings of 7th CNLS Annual Conference, Elsevier Mathematical Biosciences Series (1988).

  8. 1988 Advances in Fluid Turbulence, Physica D 37 (1989).

  9. 1989 Emergent Computation, Physica D 42 (1990).

  10. 1990 Nonlinear Science: The Next Decade, Physica D 51 (1992).

  11. 1992 Nonlinearity in Materials Science, Physica D 66 (1993).

I arrived in Los Alamos in late 1983 as a Director’s-Funded Postdoc working with John Wheatley in the Condensed Matter and Thermal Physics Group on nonlinear dynamics and chaos in cryogenic helium where early results revealed a rich set of nonlinear phenomena including period-doubling, see Fig. 7, and quasiperiodic and mode-locked states evocative of circle map dynamics. Although I was not officially a CNLS postdoc, I wanted to learn from Doyne about nonlinear dynamics, so we started a collaboration on demonstrating fat fractal scaling in the circle map. A fractal set is one in which an iterative procedure produces, in the limit of infinite iterations, a set of measure zero. For example, a center-1/3 Cantor set is formed by taking the center 1/3 segment from the real number line between 0 and 1, which results in 2N segments of length ( 1 / 3 ) N. As N , the fraction of the real number line occupied by segments goes to zero. If instead, one takes a reducing fraction at each level, i.e., { 1 / m , 1 / m 2 , 1 / m 3 , }, there is a finite measure of the line upon infinite iteration. Dave Umberger, a CNLS graduate student working with Doyne, established that a fat fractal was formed under certain Hamiltonian maps (including the Standard Map, see Fig. 4),27 i.e., that the fractal measure was consistent with the form μ ( ε ) μ ( 0 ) ε β, where ε is the coarse-grained resolution. For the circle map, the intervals of interest are formed through the nonlinearity of mode-locking such that for K = 0, the set of integer fractions corresponding to the rational ratio of frequencies has measure zero on the real number line (corresponding to μ ( 0 ) = 1), whereas for the critical value K = 1, the mode-locked intervals have unity measure such that μ ( 0 ) = 0 and fractal scaling with β = 0.13. The mode-locked ratios form Arnold Tongues as K varies from 0 to 1 as shown in Fig. 8, and fat fractal scaling emerges28 as shown in Fig. 9 where power-law scaling of μ ( ε ) μ ( 0 ) ε β is demonstrated for K = 0.8 over 3 decades in ε. The measure μ ( 0 ) also has a power-law dependence on K of μ ( 0 ) = ( 1 K ) γ as shown in the upper left inset of Fig. 9 where the dashed line is the γ = 0.314 scaling conjecture.29 Although β seems to vary continuously toward its fractal value of 0.13 at K = 1, the convergence to statistical stationarity is slow, and we conjectured that β = 2 / 3 for 0 < K < 1. This numerical work introduced me to many of the subtleties of circle-map properties and paved the way for our experimental studies of the quasiperiodic route to chaos.30 

FIG. 7.

(a) Power spectrum of Rayleigh–Bénard convection in 3He/ 4He mixtures26 at bifurcation parameter ε = 0.26 with labels for the main frequency f 0, the mode-locked frequency f 1 = 2 / 3 f 0, the difference frequency f 0 f 1 = f 0 / 3, and 2 period-doubling peaks at f 0 / 6 and f 0 / 12; (b) power spectrum of the weakly aperiodic state after the transition to chaos; (c) schematic illustration of the bifurcation diagram showing the period-doubling branches vs ε where vertical dashed lines indicate amplitudes from power spectral peaks at measured ε values.

FIG. 7.

(a) Power spectrum of Rayleigh–Bénard convection in 3He/ 4He mixtures26 at bifurcation parameter ε = 0.26 with labels for the main frequency f 0, the mode-locked frequency f 1 = 2 / 3 f 0, the difference frequency f 0 f 1 = f 0 / 3, and 2 period-doubling peaks at f 0 / 6 and f 0 / 12; (b) power spectrum of the weakly aperiodic state after the transition to chaos; (c) schematic illustration of the bifurcation diagram showing the period-doubling branches vs ε where vertical dashed lines indicate amplitudes from power spectral peaks at measured ε values.

Close modal
FIG. 8.

Arnold Tongues of nonlinear parameter K vs bare winding number W. The tongues consist of mode-locked intervals that become broader as K increases. Major intervals are shown corresponding to rational ratios p / q: 0/1, 1/5, 1/4, 1/3, 3/8, 2/5, 3/7, 1/2, where the intervals form a Faery tree constructed as ( p 1 + p 2 ) / ( q 1 + q 2 ). For example, the ratios 0/1 and 1/1 are the generators of the tree with 1/2 in level 1, 1/3 and 2/3 in level 2, 1/4, 2/5, 3/5, 3/4, etc. Here, we only show half the interval owing to its symmetry about 1/2.

FIG. 8.

Arnold Tongues of nonlinear parameter K vs bare winding number W. The tongues consist of mode-locked intervals that become broader as K increases. Major intervals are shown corresponding to rational ratios p / q: 0/1, 1/5, 1/4, 1/3, 3/8, 2/5, 3/7, 1/2, where the intervals form a Faery tree constructed as ( p 1 + p 2 ) / ( q 1 + q 2 ). For example, the ratios 0/1 and 1/1 are the generators of the tree with 1/2 in level 1, 1/3 and 2/3 in level 2, 1/4, 2/5, 3/5, 3/4, etc. Here, we only show half the interval owing to its symmetry about 1/2.

Close modal
FIG. 9.

Power-law scaling of the measure μ ( ε ) μ ( 0 ) vs coarse-graining resolution ε for the circle map with K = 0.8.28, μ ( 0 ) and β are obtained from a least-squares fit to the relationship μ ( ε ) μ ( 0 ) = A ε β. The upper left inset shows μ ( 0 ) vs K, consistent with the scaling conjecture of Jensen:29  μ ( 0 ) = ( 1 K ) 0.314 (dashed line). The lower right inset shows the fat fractal exponent β vs K. A direct numerical value (solid points) appears to show a smooth crossover from a value β = 0.68 ± 0.05 to the thin fractal value β 0.13. Other scalings suggested that this smoothness was a result of insufficient convergence of β for achievable resolution ε as K 1 and the conjecture was that β = 2 / 3 over the interval 0 < K < 1.

FIG. 9.

Power-law scaling of the measure μ ( ε ) μ ( 0 ) vs coarse-graining resolution ε for the circle map with K = 0.8.28, μ ( 0 ) and β are obtained from a least-squares fit to the relationship μ ( ε ) μ ( 0 ) = A ε β. The upper left inset shows μ ( 0 ) vs K, consistent with the scaling conjecture of Jensen:29  μ ( 0 ) = ( 1 K ) 0.314 (dashed line). The lower right inset shows the fat fractal exponent β vs K. A direct numerical value (solid points) appears to show a smooth crossover from a value β = 0.68 ± 0.05 to the thin fractal value β 0.13. Other scalings suggested that this smoothness was a result of insufficient convergence of β for achievable resolution ε as K 1 and the conjecture was that β = 2 / 3 over the interval 0 < K < 1.

Close modal

A short time later, I met Ronnie Mainieri who was a student at NYU. He was an expert in the theory of chaos and mode-locking. Together with my experimental CNLS postdoc Tim Sullivan, we made a unique characterization of the universal route to chaos through quasiperiodicity and mode-locking.31 A short time later, he joined CNLS as a postdoc and we continued our collaboration32 in which we were able to compute the universal trajectory scaling function for the quasiperiodic route to chaos, Fig. 10. The universal trajectory scaling function was computed by Feigenbaum33 and is the ultimate test of circle-map universal criticality. Ours was the only experimental measurement of this precise test but sadly the nature of the discrete function (several referees said it was not a function at all!) made it a complex object to understand.

FIG. 10.

Comparison of a 5-segment universal trajectory scaling function σ f ( s ) obtained from experimental data32 (solid blue circles and corresponding dashed blue line), which represents how intervals in θ i are created by each iteration of the the effective circle-map. The much more detailed Feigenbaum result33 is shown as solid red line. This is the most precise test of universality in the quasiperiodic route to chaos.

FIG. 10.

Comparison of a 5-segment universal trajectory scaling function σ f ( s ) obtained from experimental data32 (solid blue circles and corresponding dashed blue line), which represents how intervals in θ i are created by each iteration of the the effective circle-map. The much more detailed Feigenbaum result33 is shown as solid red line. This is the most precise test of universality in the quasiperiodic route to chaos.

Close modal

Ioannis Kevrekidis came to CNLS as a postdoc in 1987 and was very interested in our results because he was an expert in bifurcation analysis and had worked on mode-locking in general 2D maps of the plane. We collaborated on a description and qualitative bifurcation analysis of our experimental data,34 see Fig. 11, in a region above criticality for the circle map and demonstrated bifurcations consistent with 2D mappings. Later, Kevrekidis, I, and others35 made this more quantitative using machine learning to fit the experimental data and perform numerical bifurcation analysis on the resulting fitted maps. In 2016, I was giving an overview of CNLS activities for a banquet talk at a CNLS workshop on applications of machine learning and recalling our work using machine learning and a joke Kevrekidis told me during the break, paraphrasing I commented “This is all wrong and besides we did it all before.” As we will see, machine learning and neural networks came in and out of fashion at CNLS over many years.

FIG. 11.

Mode-locking Arnold Tongue data in the space of P r 1 vs R a / R a c for Rayleigh–Bénard convection in a 3He/ 4He mixture at about 1 Kelvin30,34 where roughly speaking the nonlinear coupling parameter K P r 1 and W = f 1 / f 2 R a / R a c, where P r is the fluid Prandtl Number and R a is the Rayleigh Number with R a c its critical value at the onset of convection. The critical line is at about P r 1 14.7 although the critical transition occurs along a more complicated path in parameter space. The lower left inset shows experimental data at constant P r 15.04, which determines the hysteresis shown in the main figure. The lower right inset shows a typical Poincaré section of the data in a state-space reconstruction.

FIG. 11.

Mode-locking Arnold Tongue data in the space of P r 1 vs R a / R a c for Rayleigh–Bénard convection in a 3He/ 4He mixture at about 1 Kelvin30,34 where roughly speaking the nonlinear coupling parameter K P r 1 and W = f 1 / f 2 R a / R a c, where P r is the fluid Prandtl Number and R a is the Rayleigh Number with R a c its critical value at the onset of convection. The critical line is at about P r 1 14.7 although the critical transition occurs along a more complicated path in parameter space. The lower left inset shows experimental data at constant P r 15.04, which determines the hysteresis shown in the main figure. The lower right inset shows a typical Poincaré section of the data in a state-space reconstruction.

Close modal

Our experimental data of a chaotic time series in weakly chaotic regime of quasiperiodicity and mode-locking (fractal dimension D f = 3.1) were also used by Farmer and Sidorowich36 as one test of their seminal analysis techniques for predicting nonlinear time series. These approaches were early results that led to the creation of the Prediction Company by Farmer and Norm Packard in 1991.37 

I became a Technical Staff Member in 1986 and quickly became closely connected with CNLS. In the early days, CNLS had a yearly rotating unofficial Deputy Director who was part of the CNLS Executive Committee and I filled that role in 1987. This was the beginning of a long association with CNLS lasting for over 40 years. At that time, there was movement to get both a permanent CNLS building and also a permanent Deputy Director position. The latter came first and Gary Doolen was named the first Deputy in 1988. CNLS had a great impact on my scientific career when they approved Victor Steinberg as the 1987/1988 CNLS Ulam Scholar. He had applied to me for a year-long visit, but I did not have the resources for such an appointment. The Ulam Scholar position had been created in 1984 to honor the enduring legagy of Stan Ulam.38 The first Ulam Scholar was James Murray, an Oxford University mathematical biologist, who published an important paper entitled “On the spatial spread of rabies in foxes39 with CNLS postdocs Ann Stanley and David Brown. The next Ulam Scholars were Adrian Patrascioiu (U. Arizona) and John Holland (U. Michigan). During Victor’s year at CNLS, we attempted to visualize thermal convection in cryogenic helium (without much success), but he also introduced me to the problem of rotating thermal convection, a problem I wound up studying off and on for the next 30 years. We were both low-temperature physicists who had abundant experience avoiding and/or finding/fixing leaks in difficult cryogenic environments. When our first test of a room-temperature apparatus with water cooling erupted in fountains of water in every direction, we were amused, wet, and decidedly more humble. Once we solved these problems, Fang Zhong, Victor, and I made some significant progress. In particular, we solved a mystery about heat transport in rotating Rayleigh–Bénard convection found by Tom Rossby.40 It turns out that there is a state of rotating convection consisting of thermal convection at the sidewalls, so-called “wall modes,” that is, unstable at a smaller Rayleigh number than the critical Rayleigh number for bulk convection,41,42 see Fig. 12. Our observation that the wall modes precess in the rotating frame was explained by Edgar Knobloch as resulting from the breaking of azimuthal reflection symmetry by rotation.43 Through my association with CNLS, Darryl Holm obtained financial support for rotating convection from DARPA, and this project was off and running.

FIG. 12.

(a) Shadowgraph image of m=5 wall mode,41 (b) space–time plot of wall mode precession, (c) shadowgraph image of m = 6 wall mode coexisting with bulk convection, and (d) shadowgraph image of m = 31 wall mode for much larger diameter to height ratio.44 

FIG. 12.

(a) Shadowgraph image of m=5 wall mode,41 (b) space–time plot of wall mode precession, (c) shadowgraph image of m = 6 wall mode coexisting with bulk convection, and (d) shadowgraph image of m = 31 wall mode for much larger diameter to height ratio.44 

Close modal

The Stanislaw M. Ulam Distinguished Scholar position was established in 1984 as an annual award that enables a distinguished scientist to spend time at the Center for Nonlinear Studies (CNLS) at Los Alamos National Laboratory carrying out research in collaboration with staff scientists of the Laboratory. The Ulam Scholarship honors the memory of the brilliant Polish-American mathematician Stan Ulam (Fig. 13), who was among the founders of what has now become “nonlinear science.” Many of these scientists made significant contributions to Lab research and maintained collaborations with CNLS for many years.

FIG. 13.

Stan Ulam.

Stanislas Ulam Distinguished Visiting Scholars

  1. 1985 James D. Murray (Oxford University)

  2. 1986 Adrian Patrascioiu (University of Arizona)

  3. 1987 John H. Holland (University of Michigan)

  4. 1988 Victor Steinberg (Weizmann Institute, Israel)

  5. 1989 Kunihiko Kaneko (Tokyo, Japan)

  6. 1990 Stephen R. Wiggins (Cal Tech)

  7. 1991 William I. Newman (UCLA)

  8. 1992 Serge Aubry (Saclay, France) and Phillip Rosenau (Technion, Israel)

  9. 1993 Lee Segel (Weizmann Institute, Israel)

  10. 1994 Thomas Manteuffel (University of Colorado)

  11. 1995 Yannis G. Kevrekidis (Princeton)

  12. 1996 David Sherrington (Oxford, UK)

  13. 1997 David Pines (University of Illinois UC)

  14. 1998 Ciprian Foias (Indiana University)

  15. 1999 David K. Campbell (University of Illinois UC)

  16. 2000 William Klein (Boston University)

  17. 2001 Kyozi Kawasaki (Chubu University, Japan)

  18. 2002 Edriss Titi (UC Irvine/Weizmann Institute)

  19. 2003 Carlos Castillo-Chavez (Cornell)

  20. 2004 Matthew Ernst (Utrecht, Netherlands)

  21. 2005 Sidney Redner (Boston University)

  22. 2006 Gregory Eyink (Johns-Hopkins University)

  23. 2007 Carl Bender (Washington University)

  24. 2008 Yves Pomeau (Ecole Normale Superieure Paris)

  25. 2009 Michael Savageau (UC Davis)

  26. 2010 Ekhard Salje (Cambridge University)

  27. 2011 David Wolpert (NASA Ames Research Center)

  28. 2013 Geoff Vallis (Princeton)

  29. 2014 Gregory Voth (U. Chicago)

  30. 2015 Panagiotis Kevrekidis (U. Massachusetts)

  31. 2016 Andrey Chubukov (U. Wisconsin, Madison) and Dmitrii Maslov (U. Florida)

  32. 2017 Adrian E. Roitberg (U. Florida)

  33. 2018 Hannes Jonsson (University of Iceland)

  34. 2019 Qimiao Si (Rice University)

  35. 2020 Andreas Waechter (Northwestern U.)

  36. 2023 Eric Bittner (University of Houston) and Nuno Gomes Loureiro (MIT)

Another way to promote interaction with external researchers and to expose CNLS to emerging research in the national and international science arena was through visitors from academic institutions, industry, and other national laboratories. Often there would be at least one if not more talks per day by these visitors at CNLS on a staggeringly diverse set of topics. A particular highlight of the CNLS year was the Mark Kac (Fig. 14) Memorial Lectures given by scientists of the highest caliber. These lectures were established to honor the founding Chairman of the CNLS External Advisory Committee and served as a fitting and continuing tribute to his lifelong commitment, not only to the pursuit of scientific research of the highest quality but also to the broad dissemination of the results of this research. Below is a list of the Kac Lecturers and their lecture topics.

FIG. 14.

Mark Kac.

Mark Kac Memorial Lectures:

  1. 1986 Joel L. Lebowitz, Rutgers University, Microscopic and Macroscopic Time Evolutions

  2. 1987 Joseph Ford, Georgia Tech, FPU Problem, Chaos

  3. 1988 Jerry P. Gollub, Haverford College, Waves, Transport, Patterns

  4. 1989 Philip Holmes, Cornell University, Dynamical Systems and Chaos

  5. 1990 Alan Newell, University Arizona, Nonlinear Optics

  6. 1991 Harry Swinney, University Texas, Austin, Chaos and Pattern Formation

  7. 1992 Nancy Kopell, Boston University, Mathematical Biophysics

  8. 1993 Israel Gelfand, Rutgers University, Spectral Theory and Integrable Systems

  9. 1994 Pierre Hohenberg, ATT Bell Labs, Pattern Formation, Fluctuations

  10. 1995 Joseph Keller, Stanford University, Waves, Semiclassical Mechanics

  11. 1996 Edward Spiegel, Columbia University Waves, Patterns, Bifurcations

  12. 1998 Isadore Singer, MIT, Atiyah-Siner Index Theorem

  13. 1999 Richard Garwin, IBM Watson Research Center, Ballistic Missile Defense, Nuclear Power

  14. 2000 Guenter Ahlers, UC Santa Barbara, Rayleigh–Bénard Convection

  15. 2001 John Hopfield, Cal Tech, Neural Computing, Perception

  16. 2002 Alex M u ¨ller, IBM Zurich, Hi-Tc Superconductors

  17. 2004 David Thouless, University Washington, Quantum Numbers, Quantized Vortices

  18. 2005 Leo Kadanoff, University Chicago, Computer Simulations, Droplets, Loewner Evolution

  19. 2006 Peter Wolynes, UC San Diego, Glasses, Energy Landscapes, Quantum Chaos

  20. 2007 David R. Nelson, Harvard University, Viruses, Luttinger Liquids, Evolution

  21. 2008 Michael Fisher, University of Maryland, Critical Phenomena

  22. 2009 James S. Langer, UC Santa Barbara, Physics of Glassy Solids

  23. 2010 Robert Austin, Princeton University, Physics of Cancer

  24. 2011 Subir Sachdev, Harvard University, Quantum Criticality

  25. 2012 Paul Chaikin, NYU, Topological Defects, Self-replication, Dynamic Phase Transition

  26. 2013 Joe Pedlosky, Woods Hole Oceanographic Institute, Ocean physics

  27. 2014 Susan Coppersmith, University Wisconsin Madison, Quantum-Dot Qubits

  28. 2015 Mehran Kardar, MIT Fluctuation-Induced Forces

  29. 2016 Jose Onuchic, Rice University, Folding and Cancer

  30. 2019 Nigel Goldenfeld, University Illinois Urbana Champaign, Turbulence

During Victor Steinberg’s year at CNLS, we co-organized with Doolen and Holm, the 1988 CNLS Annual Conference entitled “Advances in Fluid Turbulence.”45 We invited a diverse array of researchers from the traditional turbulence community such as Tony Leonard, Bob Kraichnan, Steve Orszag, and David Youngs and from the emerging transition-to-turbulence physics community including Pierre Hohenberg, Michael Cross, Paul Kolodner, Eric Siggia, Hassan Aref, Harry Swinney, Yves Couder, and Vincent Croquette. This was the first large international conference that I had helped organize and CNLS support was the critical factor in making this a remarkable conference at the crossroads of traditional and emergent approaches to turbulence in fluids.

In 1986, Brosl Hasslacher contributed to an extremely influential paper on lattice-gas hydrodynamics46 where particles move in discrete time steps between sites on a hexagonal lattice with collisions at vertices that satisfy particle number and momentum conservation as illustrated schematically in Fig. 15. In certain limits, this discrete automaton approximates the Navier–Stokes equation for fluid flow. These insights and the emergence of parallel computing launched a cottage industry at CNLS on these algorithms, evolving eventually into the extremely influential lattice-Boltzman computational fluid methods.47 Key players in this arena were Doolen (team leader), Hasslacher, Tsutomu Shimomura, Shiyi Chen, and Hudong Chen, the latter two newly arrived CNLS postdocs. Shiyi, who obtained his PhD at Peking University where he worked with the famous Chinese turbulence theorist Pei-Yuan Chou, had been attracted to CNLS partly by the close proximity of Robert Kraichnan who lived in Los Alamos County. Kraichnan was arguably the most gifted turbulence theorist of the 20th century, had been an assistant of Albert Einstein, and was uniquely funded by numerous government agencies as a private researcher. As Shiyi related to me, he had aspirations of following in Kraichnan’s footsteps. Shiyi, Hudong Chen, and Kraichnan came up with an idea for a new closure model. Shiyi and Hudong spent many days working intensively to establish the details of the model.48 Proudly reporting to Kraichnan that they had found the solution, Bob replied that yes this was correct, he had worked it out the evening they had first discussed it! Shiyi realized at that point that Bob was in an entirely different league, and he turned to computational fluid dynamics, an area in which he had great success. In particular, he played a vital role in implementing and evolving lattice hydrodynamic algorithms on the new Thinking Machines Connection Machine (CM) computers (CM-2, CM-5) obtained in the late 1980s49 at Los Alamos by the Advanced Computing Lab. He also performed some of the world’s most advanced 3D computer simulations of isotropic turbulence in an ongoing collaboration with Kraichnan and others.50 

FIG. 15.

Schematic illustration of lattice gas dynamics of discrete particle motion on an hexagonal (triangular) lattice where there is scattering at vertices and momentum conservation of the scattering particles. Black arrows represent motions at step i and red arrows the resultant motions at step i+1. The black dot is a stationary particle.

FIG. 15.

Schematic illustration of lattice gas dynamics of discrete particle motion on an hexagonal (triangular) lattice where there is scattering at vertices and momentum conservation of the scattering particles. Black arrows represent motions at step i and red arrows the resultant motions at step i+1. The black dot is a stationary particle.

Close modal

In the early days at CNLS, applied mathematics played a very important part in the activities and topics of the Center. Mac Hyman had a strong summer student program, jointly funded between CNLS and the DOE Applied Math Program, which was focused on the development of novel and efficient algorithms for the computation of nonlinear partial differential equations. Mac used these algorithmic approaches to simulate many of the interesting and important nonlinear problems of the day, e.g., the Kuramoto–Sivashinsky Equation.21 Mac also began a continuing workshop collaboration with the University of Arizona Applied Mathematics Department with which he had strong academic connections. This workshop, begun in 1986 was called Arizona Days, was held alternately at CNLS and at U.A., consisted mostly of graduate student and postdoc presentations, and has continued, with some interruptions, to this day. Other influential results included CNLS postdoc Charlie Doering’s work on the complex Ginzburg–Landau Equation51 and Holm’s work on fluids.18 In 1992, Philip Rosenau spent 6 months as the CNLS Ulam Scholar and collaborated with Mac Hyman in exploring an interesting variation on the classical nonlinear soliton. Solitons, in general, are functions that are localized in space, decaying rapidly but smoothly with infinite tails, whereas the new object named a “compacton” had finite support, e.g., its solution was precisely 0 outside of its finite amplitude domain.52 Compactons are solutions to a KdV-like equation: u t + a ( u n ) x + ( u n ) x x x = 0, where n is an integer.

One of the early conundrums of nonlinear studies/science was What is it? It was not an academic discipline like physics, mathematics, biology, etc. It was uniquely interdisciplinary with applications everywhere one looked. In a tribute to Stan Ulam,12 David Campbell began his description of nonlinearity: “Let me start from a very simple, albeit circular, definition: Nonlinear science is the study of those mathematical systems and natural phenomena that are not linear. Ever attuned to the possibility of bons mots, Stan once remarked that this was ‘like defining the bulk of zoology by calling it the study of non-elephant animals.’ His point, clearly, was that the vast majority of mathematical equations and natural phenomena are nonlinear, with linearity being the exceptional, but important, case.” From this general comment, David continued “…the absence of a systematic mathematical framework and the complexity of natural nonlinear phenomena suggest that nonlinear behavior is best comprehended by classifying its various manifestations in many different systems and by identifying and studying their common features.” He defined four areas of central interest in nonlinear science at the time: Solitons and Coherent Structures, Deterministic Chaos and Fractals, Complex Configurations and Pattern Formation, and Adaptive Nonlinear Systems. This enumeration of nonlinear science paradigms was extremely useful in the early days of nonlinear science; it served to differentiate aspects of nonlinear science that reflected overarching principles as opposed to the more general category of complicated systems. The term “Complex Systems” is an even more general basket of phenomena, tools, and approaches, which I will not try to categorize here.

Another main emphasis area in the early days was nonlinearity in condensed matter physics and materials science. The sixth CNLS annual conference entitled “Nonlinearity in Condensed Matter53 was introduced by Rolf Landauer and summarized by Gordon Baym and included topics (speakers) on low-dimensional magnetism (J. Boucher, Bishop), conducting polymers (A. Heeger, S. Mazumdar—CNLS postdoc) , experimental and theoretical methods (P. Chaikin, Z. Fisk, A. Leggett, D. Scalapino, and D. Campbell), structural phase transitions (K. A. M u ¨ller, J. Krumhansl), spin glasses and random field systems (V. Jaccarino, R. Bruinsma, and G. Gruner), and frustrated/incommensurate/Nonequilbrium systems (M. Widom, D. Fisher, and H. Levine). Important contributions by CNLS researchers in this area include solitons in polyacetylene,15 soliton energetics in Peierls–Hubbard models, and DNA denaturation.54 In 1992, Bishop, Jim Gubernatis, and I organized the Twelfth CNLS Annual Conference entitled “Nonlinearity in Material Science,” jointly sponsored with the Los Alamos National Laboratory Center for Materials Science (CMS). Topics included crystal growth, spinodal decomposition, fracture, surface dynamics using STM, DNA denaturation, and melting/pinning in magnetic bubble arrays. This conference built important bridges in materials science between experimentalists in CMS and Material Science and Technology (MST) Division with theorists in CNLS and T-Division.

In the years leading up to 1990, CNLS had a Senior Scientist Y. C. Lee who was part time at CNLS and at the University of Maryland. He was a very versatile scientist including early interests in neural networks and machine learning. When Roger Jones and Chris Barnes from the Applied Physics Division were tasked with automating the control and tuning of the source for a negative-ion accelerator, Roger consulted with CNLS and Y. C. Lee. Roger spent an internal sabbatical at CNLS, developed a neural-network based software control package nicknamed “CNLS Network” (Connectionist Normalized Local Spline) with Y. C. Lee,55 and successfully tested and implemented it for the ion accelerator.56 In that article, Jones stated “The field is still in an early stage of development and it is not clear yet what the capabilities and limitations of it will be.” Soon after, in 1995, Jones left the Laboratory to co-found a start-up company Center for Adaptive Systems Applications (CASA) in collaboration with Citibank that used neural network and adaptive technology to address issues in consumer banking. This example illustrates the scientific flexibility and ability to create new capability through collaborative interactions that have been a hallmark of CNLS over many years and a testament to the legacy of Campbell’s leadership and vision.

A number of important events in and around 1990 greatly impacted the CNLS. In 1988, Doyne Farmer became the leader of a new “Complex Systems” Group in the Theoretical Division and attracted a number of outstanding postdocs including Chris Langton (ALIFE Organizer), Walter Fontana (Harvard), Steen Rasmussen (U. So. Denmark, SFI), David Wolpert (SFI), Stephanie Forrest (Arizona State University, SFI), James Theiler (LANL Fellow), and Seth Lloyd (MIT). James Theiler built on Doyne’s work on state-space imbedding and fractal dimension estimation by introducing the method of surrogate data testing for nonlinearity in time series.57 Seth Lloyd proposed an early version of a realizable quantum computer,58 and Stephanie Forrest became a pioneer in the burgeoning field of “emergent computation.”25 A short time later, the permanent CNLS building was constructed, featuring a (then) state-of-the-art computer facility and office space for the administration, visitors, postdocs, and students. A direct connection was made to the Advance Computing Lab so that CNLS had early and efficient access to the new Connection Machine parallel computers. In early 1990s, David Campbell took a sabbatical leave at the Santa Fe Institute. Gary Doolen became the Acting Director, and I was asked to serve as the Acting Deputy Director. I came to appreciate David Campbell’s motto for CNLS: “Never peak early!.” David was always rushing about fixing or finishing things as he headed out on travel or came up on an impending deadline. I thought this was just an excuse for procrastination until it was my turn then—gasp—I understood. It remained a motto for CNLS, selectively used by those of us who knew it, for the next 25 years! David fully intended to return to CNLS in 1992 but received an offer he could not refuse at the University of Illinois Urbana-Champaign and left the Lab and CNLS late in 1992. Thus, my one-year tenure as Deputy stretched to two years after which Jen and Mainieri (who became a technical staff member in the Complex Systems Group) successively filled the role while the position of new Director was considered.

The University of California (UC) was the contractor for Los Alamos National Laboratory since its inception in 1945. Thus, it was natural for the CNLS to engage with other UC campuses in the area of nonlinear science. In 1984, through the efforts of Campbell, Henry Abarbanel (UC San Diego), and others, the California Coordinating Committee on Nonlinear Science (CCCNLS) was formed joint between CNLS and participating UC campuses at Berkeley, Davis, Los Angeles, Santa Barbara, and Santa Cruz. Campbell was the CCCNLS representative from CNLS from 1984 to 1992 and I followed in that role in 1993. A small amount of money was allocated by UC to facilitate interactions, primarily in the form of an annual workshop at one of the participating entities. Efforts to expand this group to a Multi-Campus Research Unit (MRU) that would have been funded at a much higher level did not succeed. Nevertheless, UC did provide additional funding from its contract fee with LANL in the form of grants to be jointly administered between CNLS and UC campuses. Campbell encouraged me to develop a joint research collaboration with Professor Guenter Ahlers, the UCSB representative on the CCCNLS, that involved funding a student (Yuchou Hu) from UCSB who would perform his PhD research at LANL with me. Ahlers and I were both involved in research on Rayleigh–Bénard convection (RBC), and we converged on studying pattern formation in rotating RBC. Guenter spent several summers at LANL through various funding channels and Hu spent time at UCSB and at LANL in a very successful collaboration. His thesis work produced 10 papers on both non-rotating and rotating convection including Science,60 see Fig. 16, three Physical Review Letters,61–63 and four longer Physical Review E papers.

FIG. 16.

False color shadowgraph image of spiral defect chaos in RBC (discovered by Morris et al., 199359) of high-pressure gas where the light/dark variations are the convection rolls. There are characteristic spirals of both clock-wise and counter clockwise handedness that occur with about 50% statistical probability. When one rotates the system about a vertical axis, this statistical symmetry is broken with a preference for spirals with the handedness of the rotation direction.60 

FIG. 16.

False color shadowgraph image of spiral defect chaos in RBC (discovered by Morris et al., 199359) of high-pressure gas where the light/dark variations are the convection rolls. There are characteristic spirals of both clock-wise and counter clockwise handedness that occur with about 50% statistical probability. When one rotates the system about a vertical axis, this statistical symmetry is broken with a preference for spirals with the handedness of the rotation direction.60 

Close modal

One last example of the serendipity and unintended consequences of the interactive environment of CNLS was a series of events that led to the creation of the Ultra Safe Nuclear Corporation and the production of an innovative next-generation of intrinsically safe modular nuclear reactors. It all began around 1995 with a discussion at a party between Roberto Camassa, a CNLS affiliate staff member, and Francesco Venneri, an Italian compatriot who was working on the Advanced Transmutation of Waste Program at LANL. This program explored the use of spallation neutrons produced by the LANL proton accelerator to produce nuclear reactions in a mixture of molten salt and actinide fuel (including waste radioactive material). A significant problem that limited the project was how to perform real-time fuel cleanup to prevent lanthanide reaction products from degrading the reactor efficiency. The cleaning scheme that had been proposed was to use centrifugal separation owing to the density differences of actinide and lanthanides. There were some complicated technical challenges owing to rapid rotation, internal heating from radioactive decay, and the unknown separation parameters involved. Owing to my involvement with CNLS and my research on rotating thermal convection, Camassa thought of me and we had a discussion about the problem. My Director’s Funded CNLS postdoc, Ning Li, became interested in the problem, and we figured out a way to start a little experimental project on the side to figure out if the scheme was feasible—this would be very difficult today at LANL with the strict rules about activities and funding. We made some measurements, Camassa did some calculations, and we were able to estimate the operating efficiency of the separation scheme that appeared to rely on extreme engineering obstacles. Nevertheless, Li became a partner with Venneri on related parts of the project and was hired as a staff member to pursue other aspects of innovative nuclear reactor concepts. After detours in mid-career for both of them at other institutions, in 2011 Li and Venneri co-founded the Ultra Safe Nuclear Corporation that promises to deliver a revolution in reliable, green electrical power generation for the 21st century. And it all started from a serendipitous discussion and CNLS connections.

The process for choosing a new CNLS Director was in the hands of the T-Division Leader, Dick Slansky. Previous selections had been made using a search committee to solicit and recommend candidates. Dick decided to not use that approach and instead appointed Don Cohen, a distinguished applied mathematician from Cal Tech as the third CNLS Director in 1993. Cohen obtained a leave from Cal Tech to take the position and maintained his faculty appointment. Cohen decided he would like to have his own Deputy Director so Gary Doolen left to become the Group Leader of the Complex Systems Group and a extensive search succeeded in attracting Charlie Doering, a former CNLS postdoc and then a Clarkson University Physics Professor, to that position in 1994. Cohen’s tenure was a short one as he never really embraced the role CNLS played at the Lab, preferring to think of CNLS as an independent island of excellence within the greater Laboratory. Because CNLS has no scientific staff outside of the Director and Deputy, this was not an effective leadership strategy. Thus, his tenure lasted only a few years before he returned to Cal Tech by mutual agreement. Charlie Doering then became the bridge to a new CNLS Director, this time chosen by a search committee of which I was the Chair. Erica Jen, also a member of the committee, learned that Hans Frauenfelder had recently joined Physics Division after an illustrious career at Urbana-Champaign (one of the last forced 70-year retirements of that era) and might be interested in joining CNLS. A member of the National Academy of Sciences (among many honors), he had pioneered the study of energy landscapes in biophysics as applied to the problem of protein folding. Although his background was not “nonlinear science” as we had come to define it, we recommended Hans to be the new CNLS Director and Dick Slansky concurred.

Hans brought a new emphasis on biology to CNLS in which the role of statistical physics played a large part. Although not strongly nonlinear in either its alignment with the paradigms defined earlier or in its novelty, statistical physics played a key role in 20th century physics. Nevertheless, tools of statistical physics were being applied to many non-traditional problems across many disciplines and came to play an important role in CNLS moving forward. Some prominent examples were the concepts of energy landscapes, an important idea in understanding protein folding, the modeling of spin glasses, and the application of statistical physics based equations to problems in epidemiology. Several of Frauenfelder’s contributions to biological physics during this period included a comprehensive review of the subject written with Peter Wolynes and Bob Austin64 and an innovative exploration of the importance of the solvent environment in the process of protein folding, joint with two CNLS postdocs Ben McMahon and Paul Fenimore.65 

The first conference that Hans helped organize was the 16th CNLS Annual Conference entitled “Landscape paradigms in physics and biology—Concepts, structures and dynamics66 in 1997, organized by Frauenfelder, Bishop, Angel Garcia, Alan Perelson, Peter Schuster, David Sherrington, and Pieter Swart. David Sherrington, CNLS Ulam Scholar at the time, gave the first talk introducing the broad range of the energy landscape concept spanning proteins to spin glasses.67 This was Hans’ first CNLS conference, and he had very strong feelings about the nature of talks—known among the community as the “Frauenfelder Rules”—in which he insisted that invited talks should be 30 min with 15 min of questions. It was a great conference with many excellent talks. One was particularly memorable. A rather famous speaker was giving a very interesting talk with many questions arising during the talk. The chair of the session decided to let the speaker continue past the 2/3 time limit in lieu of those questions. Finally, Hans rose from his seat, walked past the session chair muttering about not keeping to the rules, stood in front of the viewgraph projector, and announced to the startled speaker (and the audience) that his talk was over! Rules were rules after all.

Several other seminal Annual CNLS conferences occurred during this middle period. One was the 21st Annual conference in 2001 entitled Principles of Soft Matter organized by CNLS Feynman Fellow David Egolf, Eli Ben-Naim, David Weitz (Harvard), and me, see Fig. 17. The term “soft matter”68 had begun to emerge to describe a set of complex fluid systems such as polymers, lipids, membranes, etc., led to prominence to a large degree by the awarding of the Nobel Prize in Physics to Pierre de Gennes in 1992. By the end of the decade, there were numerous researchers in this nascent field, and we worked hard to bring many of them together in Santa Fe. One of our hopes was that de Gennes would accept our invitation to give the introductory keynote address at the conference. To our disappointment, he politely declined. Sometime later, he sent another email saying that Hans said it would be an exciting meeting so of course he would come! When I asked Hans about this change of heart, he replied “He owed me one.” The conference was a huge success with over 300 participants and a wonderful set of speakers. Several years later, Zoltan Torozckai, Eli Ben Naim, Frauenfelder, and others organized the 2003 CNLS Annual Conference Networks: Structure, Function, and Dynamics, see Fig. 18, that again consolidated the emerging area of network science in mathematics, physics, and biology and attracted over 350 participants. A conference proceedings recording this event69 included contributions by Mark Newman,70 Barabási, Albert, Redner, Torozckai, and others.

FIG. 17.

Poster for the 21st CNLS Annual Conference Principles of Soft Matter 2001.

FIG. 17.

Poster for the 21st CNLS Annual Conference Principles of Soft Matter 2001.

Close modal
FIG. 18.

Poster for the 23rd CNLS Annual Conference Networks: Structure, Function, and Dynamics 2003.

FIG. 18.

Poster for the 23rd CNLS Annual Conference Networks: Structure, Function, and Dynamics 2003.

Close modal

Hans had an unparalleled set of professional colleagues from his decades at the very peak of physics. As a graduate student at ETH Zurich with Paul Scherrer in the late 1940s, Hans shared an office with one of Wolfgang Pauli’s students/assistants, Robert Schafroth, who had the only coffee machine in the building. After the war, Pauli would bring many famous visitors to have coffee with Robert and Hans. These included many of the important luminaries of 20th century physics including Bohr, Heisenberg, Kramers, Weisskopf, Zwicky, Glauber, Dyson, and Kallen. Hans knew everyone in physics and could call on them in the service of CNLS. Several examples come to mind. In 1997, David Pines was the CNLS Ulam Scholar. David, with Zack Fisk, had been developing novel concepts of “adaptive” matter to describe complex phenomena in f-electron and high-T c superconductors. These early ideas morphed into a general model for an Institute for Complex Adaptive Matter (ICAM), joint between LANL and the University of California, that expanded to include other adaptive systems such as biological systems. At one early formative workshop at LANL, I gave a talk about how superstructures or patterns formed in condensed matter systems were fundamentally different from the physics of similar looking patterns arising in systems far from equilibrium, e.g., fluid dynamics, biology, etc. In discussions afterward, I impressed upon a group that included five members of the NAS and that there is no free-energy minimization principle that determines the state of the system when the state is far from equilibrium. They insisted that this could not be true until Peter Wolynes showed up and confirmed my point; some beliefs are strongly held.

Later, David Pines asked to present the ICAM concept to the annual meeting of the CNLS External Advisory Committee (EAC). After an impassioned presentation in which David argued that the theoretical principles of condensed matter physics could, among other things, help solve hard problems in biology,71 Ivar Giaver, a Nobel Laureate for the experimental discovery of the Josephson effect who later turned to biological research, was an EAC member and made (as best I remember) the following remark: “I have worked in the fields of superconductivity and biology, and I can tell you that they have nothing to do with each other.” I thought that this was rather a dagger in the whole business, but undeterred, David continued with unbridled optimism and, indeed, ICAM exists to the present day! A later EAC meeting involved Nobel Laureate Robert Laughlin who had numerous insightful remarks about more applied aspects of CNLS research based on his years at Livermore National Laboratory. Finally, in 1999, language was inserted as an amendment into a funding bill in Congress that implied that “Centers” at national laboratories could not exist owing to the belief that they were a mechanism to subvert the intent of the funding. Although this was not the case with CNLS, there was intense concern that the fallout could be disastrous. Hans talked to Director John Browne, called the Presidential Science Advisor Neal Lane, and all turned out fine. I never learned the details and perhaps it was all just a “tempest in a teapot,” although the Center for Materials Science was shut down at that time (there may have been additional issues that contributed to its demise).

In 1998, CNLS collaborated with Mike Warren from the T-Division Astrophysics Group to build a commodity Beowulf cluster computer based on DEC-alpha machines running LINUX. Completed in just 28 person-hours from the arrival of the machines, Mike was joined by former CNLS postdocs (then staff in the Applied Math Group) Aric Hagberg and Dave Moulton and by Dave Neal (CNLS systems administrator) in its construction and operation. The machine, nicknamed “Avalon,” see Fig. 19, achieved 10 GFlops for a total cost of about $150,000, within a factor a 2–3 of machines costing millions with a performance-to-price increase of 5–20 on the parallel Linpack benchmark compared to those other machines and was the 1998 second-prize winner of the 1998 Gordon Bell Award for Price/Performance.72 This effort demonstrated the power of commodity computing via LINUX clusters, which would become the paradigm for computing for the next several decades.

FIG. 19.

Mike Warren is shown in front of 40 of the Avalon DEC alpha processors.

FIG. 19.

Mike Warren is shown in front of 40 of the Avalon DEC alpha processors.

Close modal

During the 1990s, the influence and involvement of CNLS in nonlinear dynamics and chaos had diminished significantly. One of the last influential papers in this area was written by my former CNLS postdoc Mainieri who became a staff member in the Complex Systems Group and CNLS postdoc Jan Rehacek entitled “Projective synchronization in three-dimensional chaotic systems.”73 They addressed the circumstances under which two three-dimensional chaotic systems could become synchronized including the new projective synchronization scheme. Soon after this paper, Mainieri left LANL to build a start-up company, the Institute for Physical Sciences, which was based on the interpretation of data from the Internet and that had a successful tenure of over 15 years in the Washington, DC area. This was effectively the end of chaos research at CNLS.

In 1993, CNLS postdoc Roberto Camassa and Darryl Holm published a Physical Review Letter entitled “An integrable shallow-water equation with peaked solitons,” introducing what later became known as the Camassa–Holm (CH) equation: u t + 2 K u x u x x t + 3 u u x = 2 u x u x x + u u x x x, where u is the wave amplitude and K is a control parameter. For finite K, the CH equation yields smooth soliton solutions, but for K = 0, “peakons” form with a discontinuous slope at the amplitude maximum. A modified version of this equation, the viscous Camassa–Holm equation, was explored as an efficient fluid turbulence closure model, the Navier–Stokes alpha model,74,75 and has been tested for a wide variety of applications from a turbulent channel flow to ocean circulation models.76 Very involved in this effort was Shiyi Chen who had been appointed CNLS Deputy Director in 1997 when Charlie Doering left CNLS for a position at the University of Michigan. Shiyi’s three-year tenure at CNLS brought a renewed vigor to the area of fluid turbulence77 and to Lattice-Boltzmann computational fluid methods.47 

A very influential paper written by CNLS postdoc Stefan Boettcher and Carl Bender78 introduced a novel approach to quantum mechanics using non-Hermitian Hamiltonians with PT (space-time reflection) symmetry. The eigenvalues remain real, and this interesting reformulation of quantum mechanics has attracted enormous attention over the last 25 years. Later, in 2007, Bender was the CNLS Ulam Scholar and continued his work on PT symmetric quantum mechanics during his time at CNLS.79 For his work on PT Symmetric quantum mechanics, Bender was awarded the 2017 American Physical Society Dannie Heineman Prize for Mathematical Physics following in the footsteps of Feigenbaum who won the same prize in 2008 for his theory of the universal period doubling route to deterministic chaos.

There were also many collaborations in condensed matter physics including the investigation of coupled electronic and elastic degrees of freedom to explain colossal magnetoresistance in a perovskite manganite material.80 The work provided the framework to understand a set of experimental results and upon which one might engineer nano-scale structure of insulating and metallic phases.

Another effort that was facilitated by CNLS was the development of climate modeling at LANL. In the early 1990s, Bob Malone, Rick Smith, and John Dukowicz81 implemented an ocean climate model on the CM-2 parallel computer, nicknamed POP for parallel ocean program. CNLS held its 1995 Annual Conference82 on Nonlinear Phenomena in Ocean Dynamics which served to advertise this new capability to the ocean modeling community. A related contribution to this effort was the development of a novel model for the dynamics of sea ice by CNLS postdoc Elizabeth Hunke and Dukowicz.83 Long-term funding from DOE for climate modeling was obtained for a model named the Climate Ocean Sea Ice Model (COSIM). Many years later I collaborated with Beth Wingate, a member of the COSIM team, on addressing a small-scale mixing process that needed to be parameterized in the coarse-grained models. That problem is the turbulent mixing of stratified flow in overflows that are part of the global thermohaline circulation of the ocean. We performed a laboratory experiment on turbulent stratified shear flows to address this issue,84,85 see Fig. 20.

FIG. 20.

Image of stratified shear flow with heavy fluid flow as indicated by the arrow at mean velocity U underneath quiescent lighter fluid. Density is color coded red (heavier) and blue (lighter).

FIG. 20.

Image of stratified shear flow with heavy fluid flow as indicated by the arrow at mean velocity U underneath quiescent lighter fluid. Density is color coded red (heavier) and blue (lighter).

Close modal
There were also exciting results in pattern formation and spatiotemporal dynamics at CNLS during the 1990s. John Pearson performed large-scale simulations of reaction–diffusion equations86 to understand experimental results from the Swinney group at UT Austin. An example shown in Fig. 21 represents the patterns produced by the dynamics reaction of a two-species chemical reaction evolving according to the following reaction–diffusion equations:
t U = D u 2 U U V 2 + F ( 1 U ) ,
(3)
t V = D v 2 V + U V 2 + ( F + k ) V ,
(4)
where F is the feed rate, k is a reaction rate, and D u and D v are diffusion coefficients for species U and V, respectively. Another example is the analysis of spatiotemporal dynamics in the Rayleigh–Bénard convection state of spiral defect chaos59,62 using direct numerical simulations and a unique method for finding the Lyapunov spectrum for evolving patterns developed by David Egolf (CNLS Feynman Fellow).87  Figure 22 shows the Lyapunov spectral density λ ( i / L 2 ) as a function of the i th orthogonal Lyapunov exponent normalized by the lateral system size L. The Lyapunov dimension density is given by the condition: 0 δ λ ( i / L 2 ) d ( i / L 2 ) = 0, which yields δ = 0.019 corresponding to a total fractal dimension of 44 < D L < 78 for system sizes 48 < L < 64.
FIG. 21.

Images of a reaction diffusion system86 showing, for different values of F and k, (a) a heterogeneous spot pattern and (b) a labyrinth roll pattern, quantitatively similar to experimental results from Harry Swinney’s group at UT Austin.

FIG. 21.

Images of a reaction diffusion system86 showing, for different values of F and k, (a) a heterogeneous spot pattern and (b) a labyrinth roll pattern, quantitatively similar to experimental results from Harry Swinney’s group at UT Austin.

Close modal
FIG. 22.

(a) Image of the spiral defect chaos state with black (white) being hot (cold) fluid and (b) Lyapunov spectral density vs i th Lyapunov exponent.

FIG. 22.

(a) Image of the spiral defect chaos state with black (white) being hot (cold) fluid and (b) Lyapunov spectral density vs i th Lyapunov exponent.

Close modal

When Shiyi Chen left in 2000 to join Johns Hopkins University, LANL was struggling in the wake of the Wen Ho Lee incident and from other negative national publicity that eventually led to the resignation of Laboratory Director John Browne. During these turbulent times, Hans appointed Len Margolin, a computational fluid dynamicist from the Applied Physics Division as the CNLS Deputy Director. Margolin was not a good fit with the culture of CNLS, and it started to drift; it was time for a change.

Hans Frauenfelder stepped down as CNLS Director in 2003, returning to research in the Theoretical Biology Group as a Senior Laboratory Fellow. During the interim period while a search was conducted for a new Director, several people served in an Acting role including Dan Strotman, T-Division Deputy, and Pieter Swart from the Applied Mathematics Group. I volunteered to head the search committee, and after a lengthy search, we offered the position to an external candidate who turned it down. I consulted with T-Division Leader Alan Bishop about whether we should go down the list of other candidates. At the time, the Lab was entering uncertain times because the long-time UC contract to run the Laboratory had not been renewed, a new contract process was under way, and Laboratory Director John Browne had unexpectedly resigned. Alan suggested that we postpone a decision and that I serve as Acting CNLS Director while we awaited developments. I worried that this would take away from my experimental program but rather quickly decided that I’d give it a try—after all it was only temporary. CNLS had come off the rails a bit without a permanent Director so there was much to do. Just as I was getting my feet under me, the summer of 2004 brought the combined laser-eye accident and the apparent loss of classified materials that caused then LANL Director Pete Nanos to close the Lab to all scientific activities, and we all had to undergo lengthy training and exercises. It was the summer, and CNLS was filled to the brim with summer students, visitors, and a new Ulam Scholar, Sid Redner, none of whom had any contact with lasers or classified materials. For several weeks, no one was allowed to do any science, and people were wondering why they were there at all and what was happening at this crazy place. Nevertheless, we managed to get things back operating again with long-term damage averted. By 2005, I was hooked at the opportunity to direct, encourage, and develop an amazing cadre of talented postdocs, students, and young aspiring technical staff members. Thus, I began my 11-year tenure as the 5th CNLS Director.

I had been a member of the CNLS Executive Committee since 1987, so I had seen its evolution over more than two decades. One thing that had become apparent to me was that nonlinear science had not succeeded in becoming its own entity but rather had made significant impact on many fields including fluid mechanics, geophysics, condensed matter physics, soft matter, biology, etc. The enthusiasm for universality had subsided, however, replaced instead by the necessity and desire to probe more deeply into the specifics of a given problem within an established discipline. To some extent, nonlinear science was the revolution that succeeded beyond its wildest expectations, going from “There is no such thing as chaos in physical systems!” to “There is chaos everywhere one looks carefully.” Thus, these concepts became tools for the analysis and understanding of topics in many disciplines rather than a discipline itself. My view was that CNLS needed to expand its horizons beyond the original nonlinear science paradigms in order to grow with the times. I saw the opportunity for CNLS to contribute in the areas of computational materials chemistry, computer science, biology, geosciences, and network science as well as in traditional areas such as turbulence and plasma physics.

In line with developing different research directions, Toroczkai, a former CNLS Director’s Fellow from the Complex Systems Group was named CNLS Deputy Director in 2004, and he worked very hard to make key changes to the CNLS portfolio until 2006 when he left for a faculty position at Notre Dame University. His main line of research emphasis was graphical networks with many interdisciplinary applications. One example performed with CNLS visitor Kevin Bassler was the analysis of transport and flow on scale-free networks.88 He also brought a number of outstanding postdocs in the area of networks to CNLS including Hasan Guclu (Director’s Fellow)89 and Adilson Motter (Director’s Fellow).90 Toroczkai’s emphasis on networks remained at CNLS for many years, although it quickly evolved away from generic graphical models toward real networks such as the national electrical grid, robustness of infrastructure networks, and network approaches to cybersecurity. In 2005, Sid Redner joined CNLS as the Ulam Scholar and contributed a number of important results on graphical network including voter-model networks91 and on scientific citation statistics.92 

The Laboratory started the Quantum Institute in about 2000 in response to the collective activities of outstanding researchers in Theoretical, Physics, and Computing Divisions in the fundamentals of quantum mechanics and in quantum information. This group included Howard Barnum, Dana Berkland, Malcolm Boshier, Chris Hammel, Richard Hughes, Daniel James, Emanuel Knill, Paul Kwiat, Ray Laflamme, Jane Nordholt, Eddy Timmermans, and Woijeck Zurek as well as younger postdocs and staff including John Chiaverini, Diego Dalvit, Gerardo Ortiz, Danna Rosenberg, and Rolando Somma. Within about 5 or 6 years, almost all of these scientists had left the Laboratory leaving Boshier (laser trapping) and the Hughes/Nordholt (quantum communication) team in Physics Division and Dalvit, Somma (postdoc), Timmermans, and Zurek in Theoretical Division. These departures undermined the potential for scientific leadership in quantum information, so the Quantum Institute was dissolved in terms of its financial support, and its main functions were turned over to CNLS. Although this was perhaps a controversial decision and mistakes were made in the transition, CNLS moved forward in support of the remaining quantum information portfolio, hiring CNLS postdocs in quantum information including Jon Yard (Feynman Fellow), Robin Blume-Kohout, Spiros Michalakis, and Adolfo del Campo (Oppenheimer Fellow), formalizing the organization and funding of the quantum lunch series, supporting the hire of Somma in Theoretical Division, supporting newly converted CNLS Feynman Fellow Matt Hastings, co-funding experimental postdocs and capability development projects in Physics Division, and establishing a lecture series entitled “The CNLS Distinguished Quantum Lectures” that featured Charlie Bennett (IBM), Alexander Fetter (Stanford), David Wineland (NIST), Tony Leggett, William Phillips (NIST), and Deborah Jin (U. Colorado Boulder)—see list below. We also combined efforts in quantum chemistry and condensed matter physics, particularly in quantum magnetism and superconductivity, into a larger quantum project that allowed better collaboration across the quantum spectrum. Some important scientific papers from this quantum effort include work by Yard and Hastings on quantum capacity,93,94 Hastings on fundamental quantum theory,95–97 Sergei Tretiak on quantum chemistry98 including the application of density functional theory (DFT) for modeling perovskite thin films with applications as high-efficiency solar cells,99,100 and Cristian Batista on quantum magnetism.101,102 In this effort, Eddy Timmermans who served as CNLS Deputy from 2008 to 2010 played an influential and positive role. CNLS helped keep quantum science alive at LANL, which was ultimately rewarded by a reinvigorated DOE/Lab investment in quantum information and quantum computing around 2016 after I had stepped down from CNLS. It is a thriving part of the Laboratory research portfolio today.

In recognition of the important contributions of Los Alamos Scientists to many aspects of quantum science, the CNLS established in 2009 the Distinguished Quantum Lecture.

  1. 2009 Charles H. Bennett, IBM Research Center, Entanglement, Quantum Darwinism, and the Fate of Jimmy Hoffa

  2. 2010 Alexander L. Fetter, Stanford University, Bose–Einstein Condensates

  3. 2011 David Wineland, NIST, Quantum Information & Quantum-Limited Metrology with Trapped Ions

  4. 2013 Tony Leggett, University Illinois Urbana-Champaign, Limits of Quantum Mechanics and Superfluidity & Bose–Einstein Condenstates

  5. 2014 William Phillips, NIST, Laser Cooling and Trapping

  6. 2015 Deborah Jin, University Colorado, Ultracold Gases & Polar Molecules

CNLS engaged in extended and successful program development in collaboration with different LANL Groups and Divisions, facilitated by energetic and talented staff members. We built teams at LANL, evaluated the status and national viability of research areas as well as advertising LANL accomplishments in those areas through targeted workshops and conferences, assisted PIs in the development, evaluation, and review of internally funded Laboratory Research and Development proposals, and helped leverage external funding support for ongoing conference efforts. I will discuss three such efforts: (1) smart grid science, (2) quantitative biology, and (3) neural computation approaches to computer vision. Two of them fall within the broader context of a main theme of CNLS research in Information Science and Technology, which we helped contribute toward at LANL over about 15 years. Alan Bishop had articulated a general position that a significant part of LANL’s future lay at the interface of the computer science concept of information theory and the computer-based simulation of complex physical systems, the traditional hard science areas of physics–chemistry–biology, and applied science and technological development, i.e., the encompassing area of Information, Science, and Technology (IST). He asked me to explore this area through the tools of CNLS. We already had some emerging efforts in this area in Misha Chertkov’s research at the intersection of computer science and physics in optimization theory,103 so this was a natural new research direction.

The beginnings of the CNLS IST effort were a combination of the use of novel algorithms for message passing,104 the newly emerging recognition of the commonality of optimization algorithms between computer science (belief propagation algorithm) and physics (Bethe approximation),105 the associations of spin-glass physics and graphical networks, and the arrival of a number of extremely talented postdocs including Misha Stepanov (CNLS Postdoc 2004), Konstantin Turitsyn (CNLS Oppenheimer Fellow 2009), and Lenka Zdeborova (CNLS Director’s Funded Postdoc 2008). CNLS sponsored a series of conferences on this subject (Applications of Statistical Physics to Coding Theory 2005, Optimization in Complex Networks 2006, Algorithms, Inference, and Statistical Physics 2007, and Physics of Algorithms 2009) to explore its potential and develop connections and collaborations with external institutions—Misha Chertkov was superb at finding new connections and working with top groups around the world in his evolving research areas. In 2009, Chertkov approached me about his desire to apply his emerging interest in algorithms to a practical problem such as understanding, controlling, and optimizing the electrical power grid. This seemed very interesting and I knew just the person he should involve in his efforts to develop a new funding stream: Scott Backhaus, an extremely talented applied physicist who was looking for new directions and had talked to me about possible applications in smart grid design. In a moment of serendipity, I got Scott and Misha together to discuss opportunities. In the beginning, Misha was too “theoretical” for Scott and Scott too “applied” for Misha, but they soon realized that their skills were complementary and their interests converged. Together with Russell Bent, they developed a successful internal LDRD proposal that sought to illuminate the science of the smart electrical grid of the future. The existing electrical grid was based on large and very constant energy generation, e.g., coal-fired, nuclear, or hydroelectric, with rapid natural gas-based generation for irregular load demand. Grid stability was then established by evaluating Kirchoff’s laws on the known electrical network under the perturbation of removing one large generation station (“N-1 stability”). The inclusion of ever increasing fluctuating and intermittent electric generation from wind and solar (both large scale and home solar panels) posed an extreme challenge to standard stability approaches, and something new was needed. What resulted was a series of highly influential publications106–108 varying from theoretical approaches to practical implementation, a seminal conference organized by Backhaus, Bent, and Chertkov bringing together the new concept of “smart grid science” (32nd CNLS Annual Conference—Optimization and Control of Smart Grids 2012, see Fig. 23), and a successful program funded by the Department of Energy Office of Electricity with total funding in excess of $10M. A large number of outstanding CNLS postdocs were hired by the Laboratory to form the backbone of this new energy program opportunity, currently led by Russell Bent. In 2015, CNLS developed a new biennial Winter School and Conference on Grid Science (with Backhaus, Bent, and Chertkov and partially funded by the DOE Office of Electricity) to teach students, postdocs, and practitioners this new scientific approach to understand the electrical grid that continues to this day. The topics were wide spread from control algorithms based on the physics concept of instantons109 to the economics, stability, and control of energy generation in response to fluctuating supply and demand through the implementation of “chance-constrained optimal power flow.”110 The impact of this program has been tremendous with nine of the early papers from 2010 to 2017 having been cited over 5000 times (Google Scholar).

FIG. 23.

Top: Poster of the 32nd CNLS Annual Conference Optimization and Control of Smart Grids 2012. Bottom: Poster heading for Grid Science Summer School.

FIG. 23.

Top: Poster of the 32nd CNLS Annual Conference Optimization and Control of Smart Grids 2012. Bottom: Poster heading for Grid Science Summer School.

Close modal

The success of this endeavor required sustained support from CNLS over the better part of a decade, the perseverance and talent of hard working younger researchers anxious to make an impact, and the critical role of internal research funding provided by the LDRD program. Because the latter funding is limited to 3 years in duration, the role of CNLS in sustaining such efforts was essential to its eventual success.

A similar process played out in another area that evolved over many years. It began with a CNLS-fostered collaboration that drew from Laboratory interests in brain function on the one hand and novel brain-inspired methods of computation on the other. CNLS sponsored two conferences with organizers Luis Bettencourt, Ilya Nemenman, John George, and Garrett Kenyon Grand Challenges in Neural Computation I & II on this topic in 2007 and 2011. An LDRD project with the organizers of the first conference investigated a wide array of concepts in neural computation before settling on a computer vision approach for identifying disparate images in digital images using neural network learning methods. A second round of LDRD funding that involved a different set of researchers included Steve Brumby, Mike Warren, and Rick Chartrand. The project incorporated more sophisticated deep-learning approaches and transformational high-speed data access methods to develop unique approaches to computer vision. In 2014, key members of this team (Warren, Brumby, and Chartrand) founded Descartes Labs to capitalize on the insights developed through this 7-year effort supported by CNLS. The company, with Warren as CTO, provided real-time access to peta-bytes of geo-spatial data using peta-flop cloud-based supercomputing for various imaging and analysis applications.111 With over 100 employees and valuations of many $10 M dollars, this is one of the most successful LANL company spinoffs in its history. Warren was a remarkable innovator in computing and information science who I consulted frequently to learn from over my time at CNLS; his early death in 2023 was a tremendous loss to many of us.

Finally, I want to discuss the tremendously successful combined summer school and conference series entitled The q-bio Conference and Summer School on Cellular Information Processing, which CNLS ran for 7 years beginning in 2007 at Saint John’s College in Santa Fe, NM.112 These combined events have continued and evolved to the present day under different auspices with major leadership from former CNLS Feynman Fellow Brian Munsky (U. Colorado State University). Los Alamos has a proud tradition as one of the early innovators in theoretical biology (a separate group in Theoretical Division), which for many years was an unrecognized and unappreciated approach to biology. Members of the group included Byron Goldstein in theoretical immunology,113 Alan Perelson in theoretical virology with seminal applications to the multi-drug treatment of HIV114 and Hepatitis C,115 and Bette Korber in computational approaches to characterizing and developing a vaccine for HIV.116 From these roots, a group of young LANL staff including Ilya Nemenman, Bill Hlavacek, Mike Wall, Yi Jiang, and Jim Faeder, joined a bit later by S. Gnanakaran and Munsky, developed the concept of a combined summer school and conference to encourage and promote the concept of quantitative biology (q-bio). This approach was emerging in the mid-2000s as a novel approach to developing theoretical models of biological systems, particularly at the molecular and cellular level, and the q-bio school and conference drew many aspiring students and postdocs to this seminal and important event. This is an example of how CNLS can act as a consolidator and amplifier of important emerging trends in science. In parallel to this conference series was a very active and productive program in CNLS on theoretical biophysics including work on the processing of cellulose for biofuels,117,118 the elucidation of transport phenomena in the cellular nuclear pore complex by CNLS Oppenheimer Fellow Anton Zilman,119 the role of gene expression noise in understanding gene regulation by Munsky,120 and information processing and analysis of mutations in cancer cells by Oppenheimer Fellow Ludmil Alexandrov.121,122

Before and during my tenure as Director, one area of my research benefitted greatly from CNLS interactions. Earlier in 1998, my CNLS postdoc Peter Vorobieff attended a CNLS seminar by Walter Goldberg (U. Pittsburgh) on turbulence in flowing soap films. Walter wondered if it was possible to do particle image velocimetry (PIV) in such films at which point Vorobieff went to the lab and had preliminary data on PIV in soap films by the next day! A collaboration developed with Goldberg who sent a CNLS-funded summer student Mike Rivera to work with Vorobieff on this project resulting in several nice results on decaying two-dimensional turbulence in soap films,123 see Fig. 24. In 2003, Rivera who had then become a CNLS Director’s postdoc had implemented the filter approach for the analysis of our much improved experimental data while Shiyi Chen and Greg Eyink at Johns Hopkins were performing direct numerical simulations with students. Both groups initially explored the forward enstrophy cascade of 2D turbulence. In a pair of papers in Physical Review Letters,124,125 we used the filter approach to elucidate the physical mechanisms of that cascade. We next turned our attention to the more subtle case of the 2D inverse energy cascade. In 2006, Eyink came to CNLS as the Ulam Scholar and developed a very sophisticated theory of the inverse cascade,126 which we then used to demonstrate its effectiveness in describing the physical mechanisms of the inverse cascade,127 see Fig. 25. In 2007–2008, Guido Boffetta spent a year as a Fulbright Fellow at CNLS. Together we consolidated our research on two-dimensional turbulence, combining direct numerical simulations, the theory from Kraichnan, Eyink and others, and experiments into an invited review in the Annual Reviews of Fluid Mechanics.128 This rewarding scientific collaboration was facilitated by student, postdoc, visitor, and Ulam Scholar support in fine CNLS tradition.

FIG. 24.

False color visualization of soap film thickness for (a) periodic vortex shedding behind a disk and (b) 2D turbulence owing to the interaction of the shedding behind a lateral array of disks.

FIG. 24.

False color visualization of soap film thickness for (a) periodic vortex shedding behind a disk and (b) 2D turbulence owing to the interaction of the shedding behind a lateral array of disks.

Close modal
FIG. 25.

Instantaneous filtered energy flux from (a) and (b) DNS and (c) and (d) physical experiment in an electromagnetically forced stratified fluid system. The colors represent positive [red-orange in (a) and (b), red in (c) and (d)] and negative [blue-green (a) and (b) and blue (c) and (d)] energy flux. The exact flux distribution in (a) and (c) compares well with the theoretical model spatial distribution (b) and (d).

FIG. 25.

Instantaneous filtered energy flux from (a) and (b) DNS and (c) and (d) physical experiment in an electromagnetically forced stratified fluid system. The colors represent positive [red-orange in (a) and (b), red in (c) and (d)] and negative [blue-green (a) and (b) and blue (c) and (d)] energy flux. The exact flux distribution in (a) and (c) compares well with the theoretical model spatial distribution (b) and (d).

Close modal

Although CNLS is perhaps best suited to a theoretical and computational approach to scientific problems owing to the colocation of postdocs in the CNLS, there were a number of successful CNLS postdocs associated with experimental programs and diverse parts of the Laboratory. Eric Daub was a postdoc with Paul Johnson from the Earth and Environmental Sciences Division and contributed to the analysis and model building of friction models to describe seismic activity in real earthquake faults.129 This interaction developed a sustained interaction with Johnson on machine learning and geophysics. Doug Shepherd combined laser spectroscopy in the Center for Integrated Nanotechnology and theoretical modeling with Munsky.130 Claire White did neutron scattering experiments in Physics Division and detailed numerical simulations in CNLS of materials that could substitute for traditional cement that uses a huge amount of energy to produce.131 From the Ulam Scholar perspective, Ekhard Salje was well suited to combine experimental, theoretical, and numerical expertise and was successful in all three during his tenure at CNLS. One example was large-scale simulations of grain boundary dynamics over different ranges of temperature132 and the other an experimental and theoretical analysis of tin telluride using spectroscopic (resonant ultrasound, Mössbauer), thermodynamic (specific heat, magnetization), and magneto-striction and -transport measurements. Hardening and softening elastic behavior were associated with co-elastic and ferro-elastic states, respectively.133 Finally, Backhaus, CNLS Oppenheimer Fellow Kostya Turitsyn, and I explored fluid mass transport in a laboratory analog of the dissolution of CO 2 into aqueous porous media for carbon sequestration.134 An example of the plume structures from that experiment is shown in Fig. 26.

FIG. 26.

False color representation of solutal plumes in a Hele–Shaw geometry.134 

FIG. 26.

False color representation of solutal plumes in a Hele–Shaw geometry.134 

Close modal

The CNLS exploration of topics in IST took another turn circa 2010 that coincided with the hiring of Aric Hagberg as CNLS Deputy Director. Aric is a talented and diverse applied mathematician with interests in pattern formation, networks, cybersecurity, and broader IST concepts. Another partner in the IST arena was Frank Alexander who was the head of the fledgling Information Science and Technology Institute. The so-called approach of “deep learning” using Artificial Neural Networks and multi-layered structures was emerging into machine learning supremacy owing to its very efficient performance on GPUs and improvements in associated computer algorithms.135 I was initially both excited and skeptical about machine learning for science as there were no exceptional success stories at the time. CNLS became involved through the neural computation project mentioned early and in a series of workshops to explore the potential of deep learning for science. CNLS workshops in this area included Information Discovery for Materials Discover and Design (2009 and 2014), Physics Informed Machine Learning (2016 and 2018), Machine Learning in Solid State Geoscience (2018 and 2019), and Machine Learning for Computational Fluid and Solid Dynamics 2019. An important contributor in this area was Chertkov on the physics-informed direction136 where the algorithms were constrained to satisfy known laws of physics, e.g., conservation of energy, etc. In the geoscience arena, Johnson promoted this machine-learning approach to address the extremely challenging problem of earthquake prediction.137 This was an exciting area and Hagberg, Alexander, and I constantly debated its future, providing guidance and feedback to the many researchers in T-Division and CCS-Division who were preparing research proposals to take advantage of the promise of these deep learning approaches. Whether machine learning can produce the revolution in scientific discovery and technological development that it has achieved in computer vision, speech recognition, and natural language processing remains a topic of intensive research.

I hope I have given a flavor of the history, atmosphere, and accomplishments of the Center for Nonlinear Studies. Of course, there is so much more to be told; one could write an entire book on the subject. I apologize in advance to the many fine scientists and outstanding accomplishments whose contributions I have failed to include or give proper acknowledgment.

Let me conclude by giving my insights into what has made CNLS such an enduring center of excellence at LANL with importance to the national and international science communities. Here are my summary conclusions:

  1. The mechanisms of CNLS established by Campbell and others remain equally valuable today. Namely, CNLS engages both within the Lab and among the external scientific community through visitors, postdocs, students, and conferences. It builds scientific collaborations, is the generator of new research directions, participates in the national dialog on science, helps create the foundation for successful start-up spinoffs of Laboratory science, and creates an environment for scientific creativity within the larger Laboratory structure.

  2. When postdocs or students were funded completely by CNLS, they could become disconnected from the Groups that originally sponsored them. CNLS had the tradition of co-sponsorship of postdocs which I made more exact by having, on the one hand, the Groups be their funding home, while on the other, CNLS was their physical location and scientific home.

  3. Colocation is critical. Science happens on a personal level so having the CNLS building with shared offices that was often overflowing created an environment for postdocs, students, staff, and visitors to learn from and collaborate with each other. In 2005, we purchased an automatic espresso machine to attract people to CNLS to talk and interact. It grew to be very popular, supported by voluntary contributions from users. My job as the resident experimentalist was to keep the coffee coming!

  4. CNLS is most helpful for young staff members who are acquiring resources and building careers. Sharing the cost of a postdoc means a lot to a young person. Not so much for a senior researcher with many sources of support: 1/2 is much bigger than 1/N! Nevertheless, senior scientists have much to offer, and it is important to engage with all interested parties, something David impressed upon me over many years through discussion and actions.

  5. CNLS does not have scientific staff that need to compete for funding with scientists in Divisions. Rather it assists in building projects or programs such that the financial support flows to the Divisions. The LANL Center for Materials Science had many staff scientists who competed for funding, ultimately leading at least in part to its demise. This condition means that CNLS is tied to the research and personnel at LANL—it is not an island. The key to success is to find the technical staff who are willing to participate in the CNLS enterprise—CNLS is not a funding entity. Shared postdocs are given the freedom to explore some of their own ideas including interacting with and collaborating with other postdocs and technical staff. Some mentors do not like to share control of the postdocs experience, whereas others both contribute to and benefit from the opportunity. Thus, a key role for the CNLS leadership (Director and Deputy) is in choosing partners wisely.

  6. The CNLS Executive Committee (EC) is an essential communication venue for understanding the role of CNLS within the Laboratory and for developing new lines of research. It met weekly during my time at CNLS, usually at lunch where in the early days we all chipped in for pizza. It is an unusual aspect of the CNLS EC that scientists are willing to volunteer their time to engage with CNLS in this regular way. I heard on a number of occasions from other Center and Institute Directors at LANL that they were envious of this sense of community.

  7. The CNLS has had to evolve in its scientific breadth in response to similar trends in the nonlinear science community. While keeping traditionally nonlinear topics such as fluid turbulence and solitons, new opportunities in effective nonlinearities owing to many-body interactions in condensed matter physics, in statistical physics and kinetic theory applied to a diverse spectrum of problems from physics to epidemiology, in soft matter and biological physics, and in machine learning applied to scientific questions. Perhaps “complexity” better describes the research activities of the CNLS today as opposed to the narrower earlier paradigms. Nevertheless, the framework on which CNLS was established and how it adapted to changing times has stood the test of time. It is in an invaluable resource for Los Alamos National Laboratory, and I hope it remains so in the future.

It would be impossible to thank everyone to whom I am indebted for my time at CNLS. David Campbell was an inspiring leader, and I learned much under his tutelage. He, more than anyone, created the aura, environment, and spirit of CNLS. It was fun working with Doyne Farmer in the early days. I benefitted greatly from personal interactions with members of the CNLS EC including Gary Doolen, Darryl Holm, Mac Hyman (we often disagreed!), Alan Bishop (later my boss), and Erica Jen. My CNLS mediated collaborations with Victor Steinberg (Ulam Scholar) and Guenter Ahlers (UC INCOR collaborator) were transformational for me, shaping my personal research in many ways. Early CNLS postdocs that I interacted with included Ioannis Kevrekidis, Roberto Camassa, Shiyi Chen, and Stephanie Forrest. Of my numerous postdoctoral researchers, a number stand out as particularly connected with CNLS: Tim Sullivan, Ronnie Mainieri, Ning Li, Yuanming Liu, Peter Vorobieff, David Egolf, Michael Rivera, Zahir Daya, Tamás Börzsönyi, and Mahesh Bandi. The CNLS External Advisory Committee (EAC) was essential for providing useful criticism and analysis on the one hand and for support for CNLS with LANL management on the other. I very much enjoyed my interactions over the years with Martin Kruskal, Al Scott, and Guenter Ahlers and during my tenure as Director with Sue Coppersmith, David Campbell (he always wrote the report!), Tom Witten, Dave Levermore, Peter Wolynes, and Herbie Levine. Everyone who served on the EAC was a pleasure to interact with. Special thanks to a variety of CNLS visitors with whom I had interactions including Philippe Odier, Guido Boffetta, Florent Krzakala, Greg Eyink, Carl Bender, Bill Klein, and Ekhard Salje. Thanks to former Deputy Directors Charlie Doering and Shiyi Chen, to my Deputy Directors Zoltán Toroczkai, Eddy Timmermans, and especially Aric Hagberg. During my time as a Director, I greatly valued my interactions with CNLS affiliates Misha Chertkov, Scott Backhaus, Sergei Tretiak, Cristian Batista, Beth Wingate, Frank Alexander, Eli Ben-Naim, Avadh Saxena, Charlie Doering, Shiyi Chen, S. Gnanakaran, and Gian Luca Delzanno and with CNLS postdocs Colm Connaughton, Cristiano Nisoli, Claire White, Hussein Aluie, Matt Hastings, Jon Yard, Rolando Somma, David Roberts, Anton Zilman, Ivan Christov, and Lenka Zdeborova. As with any institution much of what was accomplished was expertly facilitated by the administrative staff with special thanks to Frankie Gomez, Marian Martinez, Barbara Rhodes, and Dorthy Garcia in the early years and later Christie Salazar, Ellie Vigil, Adam Shipman, Lysa Intrator, and Kacy Hopwood. Of course, an organization that depends on computation needs a superior systems administrator including Peter Ford who set up the CNLS network in the new building, Susan Coghlan who was always so accessible and helpful, and Don Thompson who I worked closely with during my tenure as Director. Thanks also to David Campbell for providing stories about CNLS and for feedback on this manuscript and to Greg Swift, a longtime friend and colleague, who also helped with proofreading. Finally, I would like to thank Los Alamos National Laboratory for its wisdom in creating CNLS in 1980, for its continued financial and institutional support over 40 years including from the LANL LDRD program for its support of CNLS scientific research, and for the willingness to allow CNLS the flexibility to prosper under ever more constrained operating conditions. I would like to give special tribute to three individuals with whom I had close personal interactions through CNLS who passed away recently:

  1. Charlie Doering was a long-time friend, first as a CNLS postdoc, later as CNLS Deputy Director, and finally as an academic colleague. He and I organized our first conference together in 1987 at CNLS on noise in nonlinear systems. Our tracks were parallel for many years through our joint interest in turbulent convection and in geophysical fluid dynamics. I miss his joyous spirit, his intense sense of scientific integrity, and his ability to frame complex questions with deep mathematical roots in the most straightforward of terms.

  2. Erica Jen was, in my opinion, the conscience of CNLS throughout her tenure there. She served with me on the CNLS Executive Committee, and I learned much from her mature, knowledgeable, and community-spirited approach to CNLS. When I was thrown into the deep end of the pool to serve as the Acting CNLS Deputy in 1991, I often turned to her for advice, knowing that I would get the straight scoop, never tainted by self-interest or ulterior motives.

  3. Mike Warren was a brilliant computational astrophysicist who I first learned about during the construction of Avalon mentioned earlier. Later when I became CNLS Director in 2004, I would talk to Mike about astrophysics, computing, and IST. He would regale me with ways to extract data from disk storage with much lower access times than were currently available and how we should build a peta-byte storage capability that would be revolutionary (it only happened once he went to Descartes Labs). He suggested we form a group discussion on topics in IST, which he named “Threat-down” in homage to The Colbert Report. The group, which consisted of Aric Hagberg, Luis Bettencourt, Dan Holz, Pieter Swart, Mike and me, would meet once a week to discuss what was important in IST (or anything else interesting); it was truly enlightening. Mike would often quietly listen to the rest of us and then announce confidently that the real issue was something we had all missed.

The authors have no conflicts to disclose.

Robert E. Ecke: Conceptualization (lead); Methodology (lead); Writing – original draft (lead); Writing – review & editing (lead).

The data presented in this paper are from the previously published work.

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