Herr Professor Doctor William Graham Hoover et ux

At our new place, ten miles closer to
Secret Pass and Elko, March 2010

Q: What to wear?
A: Snowshoes and shades.

Bill at our New

Location of Ruby Valley Carol at our New Place

Llamas, or perhaps Alpacas, near
our Home in Ruby Valley, Nevada

Q: Do you know the difference?
A: Four inches at the shoulder.
Llamas or Alpacas, near our Home in Ruby Valley

Spring 2008 in Ruby Valley

Q: Who Pruned this Tree?
A: Tasty Animals.
Spring 2008 in Ruby Valley

Bill and Carol Hoover at Grizzly Flat, California

Q: What is that equation?
A: Something lacking both uniqueness and chaos.
Hoovers, at our Home at Grizzly Flat

Bill and Carol Hoover in Elko, Elko County, Nevada

Q: Who is about to be baptized?
A: The sweet young thing in white ("ux").
Hoovers, in Elko for Baptism

Prior to the 2014 Snook Memorial Meeting in Melbourne

Q: Where were the Hoovers?
A: Alpine National Park, Australia.
Hoovers in 2014 at Alpine National Park
More family pictures

A Second Four-year Dose of Dishonest, Greedy, Cowardly, Lying, Affirmative-Action, Divisive, and Apparently Pro-Islamist and Racist Presidency is underway, Leading from Behind with ISIS "contained" ! Interesting Times indeed! We wish our Republic as well as Israel Good Luck! Fortunately the 2014 electorate saw the Light! Will Hillary be Obama-Lite ? Her Benghazi video lies and classified email shenanigans lie well beyond the pale.

Global Warming Evidence, 2008

Book release 2015 :
"Simulation and Control of Chaotic Nonequilibrium Systems" was released in March 2015. To order the book, click here.


Ian Snook ( 13 June 1945 - 7 April 2013 ) was an Australian computational physicist of the best sort: smart but modest, enthusiastic, tireless, supportive, and optimistic. A detailed biography, written by his colleague Peter Daivis at the Royal Melbourne Institute of Technology, can be found at www.iansnook.com . The Hoovers, joined in 2015 by the journal Computational Methods in Science and Technology ( Poznań ) have chosen to honor his memory through an annual Ian Snook Prize, awarded for the best short paper addressing an interesting problem relevant to statistical mechanics.

The 2013 Prize was awarded to Federico Ricci-Tersenghi for his algorithm generating a time-reversible random number generator, described in arXiv 1305.1805 . The 2014 Prize was awarded to William Hoover, Puneet Patra, and Clint Sprott in recognition of their work establishing the ergodicity of simple time-reversible deterministic thermostats, as outlined in arXiv 1501.03875 . The 2015 Prize was awarded to Puneet Patra for his original work, "Two-Dimensional Time-Reversible Ergodic Maps with Provisions for Dissipation", which has been published in CMST. Puneet Kumar Patra has submitted his Ph D thesis, "Identifying Temperature and Related Statistics of Nonequilibrium Steady States" to the Indian Institute of Technology in Kharagpur and is currently a postdoctoral fellow in the United States. His thesis advisor was Professor Baidurya Bhattacharya of the Kharagpur Institute. The 2016 Ian Snook Prize will be awarded to the author(s) of the most interesting manuscript addressing the ergodicity of dynamical systems in Gibbs' canonical ensemble. Although the harmonic oscillator and single pendulum problem have been successfully addressed the quartic oscillator and the Mexican Hat potential have not. For more details of the 2016 Ian Snook Prize Problem see "2016 Details"

Entries for the 2016 Prize are to be submitted directly to Computational Methods in Science and Technology [ www.cmst.eu ] and are not to exceed ten journal pages in length. The journal has no page charges or charges for color illustrations. Entries for the 2016 Prize can be contributed any time prior to 31 January 2017. Previous winners are ineligible.

Rationale for this Web Page

    "Molecular Dynamics" (Volume 258 in the Springer-Verlag series, Lecture Notes in Physics, published in 1986, and evidently out of print in 2007. I found one copy for sale at $121.17 on Amazon.com in May 2007 and decided to scan the book to make it available for interested readers.) By 2016 both "Molecular Dynamics" and "Computational Statistical Mechanics" were readily available on Amazon.
    "Computational Statistical Mechanics" (A comprehensive treatment of equilibrium and nonequilibrium methods and applications, published by Elsevier in 1991 as Volume 11 of the Studies in Modern Thermodynamics Series). The .pdf file here was provided through the courtesy of the Lawrence Livermore National Laboratory.
    "Time Reversibility, Computer Simulation, and Chaos" (1999, 2001) (An up-to-date description reconciling the irreversible nature of real life with the time-reversible descriptions of nonequilibrium molecular dynamics, published by World Scientific as Volume 13 of the Advanced Series in Nonlinear Dynamics, 1999, reprinted with minor corrections in 2001).
    "Time Reversibility, Computer Simulation, Algorithms, Chaos" (2012) (A revised and expanded up-to-date version of World Scientific's Volume 13 above).
    "Smooth Particle Applied Mechanics---The State of the Art" (Thorough description of the use of mesoscopic/macroscopic particles to simulate the properties of bulk matter, published by World Scientific as Volume 25 of the Advanced Series in Nonlinear Dynamics, 2006). There is a free 107 megabyte draft copy available.
    Koichiro Shida [currently at Tokyo City University] kindly translated all four of these books into Japanese, culminating with publication of the SPAM book just in time for Christmas of 2008. The second printing was finished in time for Christmas 2009.
    "Simulation and Control of Chaotic Nonequilibrium Systems" (This book provides a thorough study of thermodynamic control of nonequilibrium systems and related research topics. It is published by World Scientific as Volume 27 of the Advanced Series in Nonlinear Dynamics). Dr Shida kindly translated this book into Japanese in 2016.

    "Links Between Microscopic and Macroscopic Fluid Mechanics" (with Carol Hoover---this paper was rejected by the American Journal of Physics) [Molecular Physics 101, 1559 (2003)]
    "Mécanique de Nonéquilibre à la Californienne" [Physica A 240, 1 (1997)]
    "Nonequilibrium Molecular Dynamics; the first 25 years" [Physica A 194, 450 (1993)]

Conference Proceedings Contributions and Older Papers with Some Historical or Word-processing Interest:
    "Adiabatic Hamiltonian Deformation, Linear Response Theory, and Nonequilibrium Molecular Dynamics" (presented at Sitges, Spain at a 1980 conference in memory of Mel Green -- typed on an IBM Selectric! A Kewpie Doll drawing accompanying the manuscript was removed by the Editors.) [Springer-Verlag Lecture Notes in Physics 132]
    "Atomistic Computer Simulations" (presented at Boulder, Colorado at Howard Hanley's seminal 1982 conference on Nonlinear Fluid Phenomena -- Looks a bit like teX.) [Physica 118A, 111 (1983)]
    "Nonequilibrium Molecular Dynamics at Livermore and Los Alamos" (presented at Alghero, Sardinia at a 1991 conference celebrating Berni Alder's 65th birthday -- Microscoft Word. The Kewpie Doll Poster from the 1980 Edmonton IUPAP meeting appears here.) [NATO Advanced Science Institutes in Physics, 292B]
    "Computer Simulation of Nonequilibrium Processes" (presented at Monterey, California at the [1987 Shockwaves in Condensed Matter conference] -- B. Moran, B. L. Holian, H. A. Posch, and S. Bestiale are cited as coauthors -- prepared with an IBM Selectric). Two rejection letters from 21 April 1987 are also included. The [first] is from George Bas-Bas at Physical Review Letters (regarding "Second-Law Irreversibility of Reversible Mechanical Systems", which was submitted again on 4 May 1987 and published in [Physical Review Letters 59, 10-13 (1987)] as "Resolution of Loschmidt's Paradox: the Origin of Irreversible Behavior in Reversible Atomistic Dynamics". The latter work is exactly the same as the rejected paper but with the authors' names permuted and the title changed. The [second rejection letter](in his own hand) is from Joel Lebowitz at the Journal of Statistical Physics, regarding the paper "Reversible Mechanics and Time's Arrow", written for a volume he collated honoring Ilya Prigogine. This latter paper was next sent to Physical Review A, also on 4 May 1987, and was published in the 1 January 1988 issue of [Physical Review A 37, 252-257]. These papers illustrate some of the difficulties in publishing novel work.

    "Local Gram-Schmidt and Covariant Lyapunov Vectors and Exponents for Three Harmonic Oscillator Problems" (For our updated book on Time Reversibility, Computer Simulation, and Chaos) A loose translation of some of the covariant literature; with Carol Hoover. This paper was submitted and accepted on 23 June with the help of Stefano Ruffo, appearing electronically in Communications in Nonlinear Science and Numerical Simulation on 25 June 2011 and in printed form in volume 17, pages 1043-1054 in February 2012. This rapid publication is a welcome preview of the internet future.
    "Free Energy Changes, Fluctuations, and Path Probabilities" (For use in our updated book on Time Reversibility) Fluctuation Theorems and Path Probabilities; with Carol Hoover.
    "Maxwell and Cattaneo's Time-Delay Ideas Applied to Shockwaves and the Rayleigh-Bénard Problem" (Originally intended for Physics Letters A) Stability of shockwaves and convective rolls with Maxwell's (as opposed to Cattaneo's) time delay; with Francisco Uribe and Carol Hoover.
    "Three Lectures: NEMD, SPAM, and Shockwaves" (For presentation at La Herradura, Spain,in September 2010) Reviews of nonequilibrium molecular dynamics and smooth particle applied mechanics along with new results on modeling dense-fluid shockwaves and analyzing dynamical instabilities within the waves with local Lyapunov exponents and phase-space growth rates.
    "Flexible Macroscopic Models for Dense-Fluid Shockwaves: Partitioning Heat and Work; Delaying Stress and Heat Flux; Two-Temperature Thermal Relaxation" (For presentation at the 2010 Conference: Advanced Problem in Mechanics, sponsored by the Russian Academy of Science, and delivered at Saint Petersburg in July) Within shockwaves the model described here partitions heat and work separately between the longitudinal and transverse directions of the flow.
    "Time-Reversal Symmetry and Covariant Lyapunov Vectors for Simple Particle Models in and out of Equilibrium" (Physical Review E 82, 046218 (2010)) Comparison (mostly by Bosetti, Posch, and Dellago) of Gram-Schmidt and Covariant Lyapunov Exponents with Local Bounds, emphasising the fractal nature of such analyses. The physical significance of the covariant exponents and vectors is not particularly clear and needs more work.

Memorial Lecture:
    "Nosé-Hoover Nonequilibrium Dynamics and Statistical Mechanics." [41 Vugraphs (19 megabytes!) for the Symposium on Progress and Future Prospects in Molecular Dynamics Simulation in Memory of Professor Shuichi Nosé (Yokohama, 6-8 June 2006)] (8 June 2006)

2016 Lectures:
    "From Ann Arbor to Sheffield : Around the World in 80 Years. I." [19 Vugraphs (15 megabytes) for Bill's 80th Birthday Celebration at Sheffield] (26 July 2016)
    "From Ann Arbor to Sheffield : Around the World in 80 Years. II." [17 Vugraphs (10.4 megabytes) for Bill's 80th Birthday Celebration at Sheffield] (also 26 July 2016)

2015 Lectures:
    "An Appreciation of Berni Julian Alder" [18 Vugraphs (22 megabytes) for the 90th Birthday Symposium of Berni Alder at LLNL-Livermore] (20 August 2015)
    "An Appreciation of Berni Julian Alder" [Manuscript for the Festschrift as resubmitted to the Los Alamos arXiv on 17 October 2015 after the initial submission was placed "on hold" by the arXiv moderators, who suggested it be submitted as a "historical" contribution. After the resubmission as "historical" the manuscript was again put "on hold" on 19 October, "submitted" on October 20, and appeared 21 October, safe and sound ! ] (Manuscript)
    "Shockwaves with Molecular Dynamics and Continuum Mechanics" [38 Vugraphs (17 megabytes) for the Nonequilibrium Simulation School at Sheffield UK] (3 September 2015)
    "Nosé, Posch, Patra, Sprott" [19 Vugraphs (25 megabytes) for the Department of Physics at the University of Vienna] (7 September 2015)

2014 Lectures:
    " 'What is Liquid?' from the Perspective of Simulations" [25 Vugraphs (5 megabytes) for the 80th Birthday Symposium of Doug Henderson at BYU-Provo] (16 August 2014)
    "1984+30, The Legacy of Shuichi Nosé's Work" [29 Vugraphs (11 megabytes) for the 30th Anniversary Symposium at Keio University's Mita Campus (Tokyo)] (10-11 November 2014)
    "Finite Precision, Periodic Orbits, Boltzmann's Constant, Nonequilibrium Entropy" [Poster: (16 Vugraphs, 7 megabytes) for the 30th Anniversary Symposium] (Tokyo Poster)
    "Time Reversibility and Ergodicity - Snook Prize Topics for 2014" [18 Vugraphs (15 megabytes) for the Ian Snook Conference on Chemical Physics (Royal Melbourne Institute of Technology)] (4-5 December 2014)

2012 Lectures:
    "Microscopic Reversibility versus Macroscopic Irreversibility" [36 Vugraphs (23 megabytes) for Saint Petersburg, Russia.] (Bill's Talk, 3 July 2012)
    "Microscopic and Macroscopic Rayleigh-Bénard Flows : Continuum and Particle Simulations, Fluctuations, Time Reversibility, Uniqueness, and Lyapunov Instability" [48 Vugraphs (10 megabytes) for Saint Petersburg, Russia.] (Carol's Talk, 3 July 2012)

2010 Lectures:
    "Two-Temperature Time-Delayed Dense-Fluid Shockwaves with Molecular Dynamics and Continuum Mechanics" [35 Vugraphs (3 megabytes) for Saint Petersburg, Russia and La Herradura, Spain.] ( 1 July 2010)
    "Smooth Particle Applied Mechanics: The Method, with Three Example Problems" [20 Vugraphs (4 megabytes) for Saint Petersburg, Russia.] ( 5 July 2010)
    "Nonequilibrium Molecular Dynamics" [37 Vugraphs (5 megabytes) for La Herradura, Spain.] ( 15 September 2010)

2009 Lectures:
    "Shockwaves with Molecular Dynamics" [35 Vugraphs (29 megabytes!) for Warwick.] (May 2009)
    "Squares, Cubes, Disks, Spheres" [36 Vugraphs (15 megabytes) for Manchester.] (Spring 2009)

2007 Lectures:
    "Hamiltonian Thermostats for Nonequilibrium Molecular Dynamics Simulations." [52 Vugraphs (29 megabytes!) for Mexico, Wien, Gdansk, and Melbourne.] (January 2007)
    "SPAM (Smooth Particle Applied Mechanics)." [39 Vugraphs (15 megabytes) for Mexico City Workshop organized by Paco Uribe.] (Workshop 2007)
    "Computational Physics with Particles." [26 Vugraphs (19 megabytes) for September Meeting on the Hel Peninsula, Poland, and similar to a talk delivered in Melbourne at the November MM2007 meeting.] (Gdansk Talk 2007)
    "Nonequilibrium Statistical Mechanics--The Facts and Fundamentals." [37 Vugraphs (26 megabytes) for a November seminar at Swinburne University (Melbourne, hosted by Billy Todd).] (Swinburne Talk 2007)

Some Publications, from 2000-2010:
    "Shockwaves and Local Hydrodynamics; Failure of the Navier-Stokes Equations" [in New Trends in Statistical Physics, Festschrift in Honor of Leopoldo García-Colín's 80th Birthday, Alfredo Macias and Leonardo Dagdug, Editors (World Scientific, Singapore, 2010)] (Festschrift Paper) pointing out a shortcoming of Navier-Stokes Hydrodynamics.
    "Well-Posed Two-Temperature Constitutive Equations for Stable Dense Fluid Shockwaves using Molecular Dynamics and Generalizations of Navier-Stokes-Fourier Continuum Mechanics" [For Presentation at Saint Petersburg in 2010] [Physical Review E 81, 046302 (2010)]
    "50 Years of Computer Simulation --- a Personal View" [Ensemble 12, 17-29 (2010), in Japanese, translated by Masaharu Isobe with the assistance of our Ruby Valley neighbor, Adam Neff ] (English Version) or (Japanese translation).
    "Single-Speed Molecular Dynamics of Hard Parallel Squares and Cubes" [with Carol Hoover and Marcus Bannerman] (Single-Speed) a study of dynamics and phase transitions for hard parallel squares and cubes; Journal of Statistical Physics, electronic version, 21 July 2009.
    "Tensor Temperature and Shockwave Stability in a Strong Two-Dimensional Shockwave" [with Carol Hoover] (Shock Stability) a study of density, temperature, and overall stability of planar shockwaves in two dimensions; Physical Review E 80, 011128 (July, 2009).
    "Nonlinear Stresses and Temperatures in Transient Adiabatic and Shear Flows via Nonequilibrium Molecular Dynamics -- Three Definitions of Temperature." [with Carol Hoover, a followup of Physical Review E 78, 046701 (2008), appearing as Physical Review E 79, 046705 (2009)] (Three Temperatures) exploring the differences between adiabatic and isoenergetic shear flows which also demonstrates that configurational temperature contains spurious rotational contributions.
    "Microscopic and Macroscopic Stress with Gravitational and Rotational Forces" [with Carol Hoover and Jim Lutsko] (Zhou) a pedagogical study of Zhou's work on the Irving-Kirkwood stress tensor; Physical Review E 79, 036709 (2009).
    "Simulation of Two- and Three-Dimensional Dense-Fluid Shear Viscosities via Nonequilibrium Molecular Dynamics. Comparison of Time-and-Space-Averaged Stresses from Homogeneous Doll's and Sllod Shear Algorithms with those from Boundary-Driven Shear." [Physical Review E 78, 046701 (2008).] (Shear Flow Comparison)
    "Nonequilibrium Temperature and Thermometry in Heat-Conducting Phi-4 Models" [Physical Review E 77, 041104 (2008).] (Kinetic and Configurational Thermostats far from Equilibrium 2008)
    "Computational Physics with Particles" [American Journal of Physics 76, 481-492 (2008).] (Gdansk ms 2007)
    "Computational Physics with Particles---Nonequilibrium Molecular Dynamics and Smooth Particle Applied Mechanics" [this shortened version of our review appears in Computational Methods in Science and Technology 13, 83-93 (2007).] (Gdansk Proceedings 2007)
    "50 Joint Explorations, 1985-2007." [with Carol Hoover; this informal review of our joint work with Harald Posch is archived with the Schroedinger Institute in Vienna as Preprint 1898.] (Wien 2007)
    "Nosé-Hoover Nonequilibrium Dynamics and Statistical Mechanics." [written for the Symposium on Progress and Future Prospects in Molecular Dynamics Simulation in Memory of Professor Shuichi Nosé (Yokohama, 6-8 June 2006); Molecular Simulation 33, 13-19 (2007).] (Spring 2006)
    "Phase-Space Growth Rates, Local Lyapunov Spectra, and Symmetry Breaking for Time-Reversible Dissipative Oscillators." [with Carol Hoover and Florian Grond; Communications in Nonlinear Science and Numerical Simulation 13, 1180-1193 (2008)]. (Fall 2006)
    "Hamiltonian Dynamics of Thermostated Systems: Two-Temperature Heat-Conducting phi-4 Chains." [with Carol Hoover; honoring the 65th Birthday of Harald Posch (Wien); Journal of Chemical Physics 126, 164113 (2007); the Figures which illustrate this preprint can also be found as slides 41, 43, 44, and 46 in the first "January 2007" Lecture below]. (Spring 2007)
    "Nosé Shuichi, 17 June 1951 --- 17 August 2005, In Memorium." [ Butsuri 60, 819 (2005)] (Shuichi)
    "Smooth-Particle Phase Stability with Density and Density-Gradient Potentials." (with C. G. Hoover) [ Physical Review E 73, 016702 (2005)] (Summer 2005)
    "Searching for Auxetics with DYNA3D and ParaDyn." (with C. G. Hoover) [Physica Status Solidi (b) 242, 585-594 (2005)] (October 2004)
    "Nonequilibrium Molecular Dynamics: Reversible Irreversibility from Symmetry Breaking, Thermostats, Entropy Production, and Fractals." [Proceedings of the Segunda Reunión Mexicana sobre Física Matemática y Física Experimental, AIP Conference Proceedings 757, 16-28 (2005)] (September 2004)
    "The Second Law of Thermodynamics and MultiFractal Distribution Functions: Bin Counting, Pair Correlations, and the [definite failure of the] Kaplan-Yorke Conjecture" (with C. G.Hoover, H. A. Posch, and J. A. Codelli; after four inconclusive months at Physica D this paper was rescued by Stefano Ruffo) [Communications in Nonlinear Science and Numerical Simulation, edited by Chen, Li, Luo, and Ruffo]. It became available online 7 April 2005 and eventually appeared in volume 12, pages 214-231 in this Journal (which offers a "rapid exchange of ideas and techniques") sometime in 2007 (about two and a half years after its writing). (August 2004)
    "Nonequilibrium Molecular Dynamics" (with C. G. Hoover)[Condensed Matter Physics 8, 247-260(2005)], from the Festschrift celebrating Doug Henderson's 70th-Birthday Symposium at Brigham Young University] (July 2004)
    "Smooth Particle Applied Mechanics: Conservation of Angular Momentum with Tensile Stability and Velocity Averaging" (with Carol Hoover and Elizabeth Merritt) [Physical Review E 69, 016702 (2004)]
    "Smooth-Particle Boundary Conditions" (with Oyeon Kum) [Physical Review E, 68, 017701 (2003)]
    "Large-System Phase-Space Dimensionality Loss in Stationary Heat Flows" (with Harald Posch) [Physica D 187, 281 (2004)]
    "Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss" (with Harald Posch, Ken Aoki, and Dimitri Kusnezov) [Europhysics Letters 60, 337 (2002)]
    "Time-Reversible Deterministic Thermostats" (with Ken Aoki, Carol Hoover, and Stephanie de Groot) [Physica D 187, 253 (2004)] (Dresden 2004)
    "Time Reversibility, Computer Simulation, and Chaos" [World Scientific, Singapore (1999 and 2001)]
    "Smooth-Particle Simulations Boundary Conditions" (with Carol Hoover) [Computing in Science and Engineering 3(2), 78 (2001)]
    "Liouville's Theorems, Gibbs' Entropy, and Multifractal Distributions for Nonequilibrium Steady States" [Journal of Chemical Physics 109, 4164 (1998)]
    "Dynamical Instabilities, Manifolds, and Local Lyapunov Spectra Far From Equilibrium" (with Carol Hoover and Harald Posch) [Computational Methods in Science and Technology (Poznan, Poland) 7, 55 (2001)]
    "Finite-Precision Stationary States at and away from Equilibrium" (with Christoph Dellago) [Physical Review E 62, 6275 (2000)]

Oldies, but Goodies, arranged by Topic:

  • Equilibrium Statistical Mechanics
  • Nonequilibrium Molecular Dynamics
  • Fractals and Irreversibility
  • Lyapunov Spectra/Singular Value Decomposition
  • SPAM = Smooth Particle Applied Mechanics
  • Chronological Publications, arranged by Decades:
        [ The 1960s ]; [ The 1970s ]; [ The 1980s ]; [ The 1990s ]; [ The 2000s ]; [ The 2010s ].

    Biographical Information for William Graham Hoover

    I was born in Boston on 18 April (remember that famous ride of Paul Revere?) 1936 and lived later, as a boy, in Maryland, Michigan, Pennsylvania, and Washington, DC.  A chemistry teacher at Woodrow Wilson High School in Washington set me on the path that took me to Oberlin College (BA in Chemistry, 1958) and the University of Michigan (MSChem and PhD in Chemical Physics, 1961).  My thesis director at Michigan, Andrew De Rocco, sent me to Jacques Poirier (Duke University) for a postdoctoral year, after which Berni Alder attracted me to Livermore, California. Los Alamos was only number two. I spent the remainder of my research career as a physicist at the University of California's Livermore Laboratory.  I joined the Department of Applied Science (started by Edward Teller through the Davis Campus of the University and dismantled in July 2011, after his death, due to the Livermore Laboratory's growing disinterest in things academic) in 1970 and retired as Professor Emeritus in 1993.  The gradual politization and bureaucratization of the laboratory and the concurrent decline of the University of California toward a rock-bottom level of political correctness (shared at least, and perhaps exceeded, by Oberlin College and the University of Michigan) made an active retired research career much more attractive than continuing "service" to failing institutions. We completed our move to Ruby Valley, Nevada with Carol's retirement (June, 2005). We then completed our work on three books for World Scientific: "Smooth Particle Applied Mechanics---SPAM: The State of the Art", "Time Reversibility, Computer Simulation, and Chaos" and "Simulation and Control of Chaotic Nonequilibrium Systems" (See above for details). Now we are spending more time with the horses ( Majic and the mysterious Mr X [prosaically aka Duke] ).

    Biographical Information for Carol Griswold Hoover ["ux"]

    I met Bill and that was it ... .

    Carol G. Hoover's email address (for .jpg or .pdf or .ps files): hoover1carol@yahoo.com
    William G. Hoover's email address: hooverwilliam@yahoo.com
    William G. Hoover's snail addresses in Nevada: HC 60, Box 601, Ruby Valley, Nevada 89833
    [Our various California mailing addresses and phone numbers are obsolete and should not be used.]