62 citations · 331 across the 60 of their papers we have counts for
38 papers · 1 filter
Chaos in Nonequilibrium Two-Temperature Nosé-Hoover Cell Models
Hesam Arabzadeh, Carol Griswold Hoover, William Graham Hoover +1
We revisit a two-temperature Nosé-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at to explore…
Canonical Temperature Control by Molecular Dynamics
William Graham Hoover, Carol Griswold Hoover
"Pedagogical derivations for Nosé's dynamics can be developed in two different ways, (i) by starting with a temperature-dependent Hamiltonian in which the variable scales the t…
Thermodynamic Entropy from Sadi Carnot's Cycle using Gauss' and Doll's-Tensor Molecular Dynamics
William Graham Hoover, Carol Griswold Hoover
Carnot's four-part ideal-gas cycle includes both isothermal and adiabatic expansions and compressions. Analyzing this cycle provides the fundamental basis for statistical thermodyn…
Computational Implementation of Maxwell's Knudsen-Gas Demon and Its Extension to a Two-Dimensional Soft-Disk Fluid
William Graham Hoover, Carol Griswold Hoover
An interesting preprint by Puru Gujrati, "Maxwell's Demon Must Remain Subservient to Clausius' Statement" [ of the Second Law of Thermodynamics ], traces the development and applic…
Nonequilibrium Time Reversibility with Maps and Walks
William Graham Hoover, Carol Griswold Hoover, Edward R. Smith
Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zermélo's paradoxes. That is, computational time-reversible simulations invariably pr…
What is Liquid ? [in two dimensions]
Karl P. Travis, William Graham Hoover, Carol Griswold Hoover +1
We consider the practicalities of defining, simulating, and characterizing "Liquids" from a pedagogical standpoint based on atomistic computer simulations. For simplicity and clari…
From Hard Spheres and Cubes to Nonequilibrium Maps with Thirty-Some Years of Thermostatted Molecular Dynamics
William Graham Hoover, Carol Griswold Hoover
This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it develo…
Nonequilibrium Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps
William Graham Hoover, Carol Griswold Hoover
Deterministic and time-reversible nonequilibrium molecular dynamics simulations typically generate "fractal" [ fractional-dimensional ] phase-space distributions. Because these dis…
2020 Ian Snook Prize Problem : Three Routes to the Information Dimensions for a One-Dimensional Stochastic Random Walk and for an Equivalent Prototypical Two-Dimensional Baker Map
William Graham Hoover, Carol Griswold Hoover
The $1000 Ian Snook Prize for 2020 will be awarded to the author(s) of the most interesting paper exploring a pair of relatively simple, but fractal, models of nonequilibrium syst…
Aspects of Nosé and Nosé-Hoover Dynamics Elucidated
W. G. Hoover, C. G. Hoover
Some paradoxical aspects of the Nosé and Nosé-Hoover dynamics of 1984 and Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of thermostated harmonic oscillator d…
The Nosé-Hoover, Dettmann, and Hoover-Holian Oscillators
William Graham Hoover, Julien Clinton Sprott, Carol Griswold Hoover
To follow up recent work of Xiao-Song Yang on the Nosé-Hoover oscillator we consider Dettmann's harmonic oscillator, which relates Yang's ideas directly to Hamiltonian mechanics. W…
Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble Averages
William Graham Hoover, Carol Griswold Hoover
Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs' canonical distribution for simple ( small ) dynamical problems. Adding one or two thermostat…
The 2017 SNOOK PRIZES in Computational Statistical Mechanics
Wm. G. Hoover, Carol G. Hoover
The 2017 Snook Prize has been awarded to Kenichiro Aoki for his exploration of chaos in Hamiltonian models. His work addresses symmetries, thermalization, and Lyapunov instab…
Time-Irreversibility is Hidden Within Newtonian Mechanics
William Graham Hoover, Carol Griswold Hoover
We develop a bit-reversible implementation of Milne's Fourth-order Predictor algorithm so as to generate precisely time-reversible simulations of irreversible processes. We apply o…
Instantaneous Pairing of Lyapunov Exponents in Chaotic Hamiltonian Dynamics and the 2017 Ian Snook Prize
William Graham Hoover, Carol Griswold Hoover
The time-averaged Lyapunov exponents support a mechanistic description of the chaos generated in and by nonlinear dynamical systems. The exponents are ordered from largest to small…
Singly-Thermostated Ergodicity in Gibbs' Canonical Ensemble and the 2016 Ian Snook Prize
William Graham Hoover, Carol Griswold Hoover
For a harmonic oscillator, Nosé's single-thermostat approach to simulating Gibbs' canonical ensemble with dynamics samples only a small fraction of the phase space. Nosé's approach…
A Tutorial: Adaptive Runge-Kutta Integration for Stiff Systems : Comparing the Nosé and Nosé-Hoover Oscillator Dynamics
William Graham Hoover, Julien Clinton Sprott, Carol Griswold Hoover
"Stiff" differential equations are commonplace in engineering and dynamical systems. To solve them we need flexible integrators that can deal with rapidly-changing righthand sides.…
The Equivalence of Dissipation from Gibbs' Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators
Puneet Kumar Patra, William Graham Hoover, Carol Griswold Hoover +1
Gibbs' thermodynamic entropy is given by the logarithm of the phase volume, which itself responds to heat transfer to and from thermal reservoirs. We compare the thermodynamic diss…
Time-Reversible Ergodic Maps and the 2015 Ian Snook Prize
William Graham Hoover, Carol Griswold Hoover
The time reversibility characteristic of Hamiltonian mechanics has long been extended to nonHamiltonian dynamical systems modeling nonequilibrium steady states with feedback-based…
Nonequilibrium Systems : Hard Disks and Harmonic Oscillators Near and Far From Equilibrium
William Graham Hoover, Carol Griswold Hoover, Julien Clinton Sprott
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible d…
Ergodicity of a Singly-Thermostated Harmonic Oscillator
William Graham Hoover, Julien Clinton Sprott, Carol Griswold Hoover
Although Nose's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nose-Hoover ( harmonic ) oscillator, with its mean kinetic temperatur…
Ergodicity of the Martyna-Klein-Tuckerman Thermostat and the 2014 Snook Prize
William Graham Hoover, Carol Griswold Hoover
Nosé and Hoover's 1984 work showed that although Nosé and Nosé-Hoover dynamics were both consistent with Gibbs' canonical distribution neither dynamics, when applied to the harmoni…
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion
Wm. G. Hoover, C. G. Hoover
Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-…
Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient
Julien Clinton Sprott, William Graham Hoover, Carol Griswold Hoover
We use nonequilibrium molecular dynamics to analyze and illustrate the qualitative differences between the one-thermostat and two-thermostat versions of equilibrium and nonequilibr…