Blog Archives

2024 Snook Prize Problem: Ergodic Algorithms’ Mixing Rates

Hoover William G., Hoover Carol G.

In 1984 Shuichi Nosé invented an isothermal mechanics designed to generate Gibbs’ canonical distribution for the coordinates {q} and momenta {p} of classical N-body systems [1, 2]. His approach introduced an additional timescaling variable s that could speed up or slow down the {q, p} motion i ...

Time-Symmetry Breaking in Hamiltonian Mechanics. Part III. A Memoir for Douglas James Henderson [1934–2020]

Hoover William G., Hoover Carol G.

Following Berni Alder [1] and Francis Ree [2], Douglas Henderson was the third of Bill’s California coworkers from the 1960s to die in 2020 [1, 2]. Motivated by Doug’s death we undertook better to understand Lyapunov instability and the breaking of time symmetry in continuum and atomistic sim ...

Time-Symmetry Breaking in Hamiltonian Mechanics. Part II. A Memoir for Berni Julian Alder [1925–2020]

Hoover William G., Hoover Carol G.

This memoir honors the late Berni Julian Alder, who inspired both of us with his pioneering development of molecular dynamics. Berni’s work with Tom Wainwright, described in the 1959 Scientific American [1], brought Bill to interview at Livermore in 1962. Hired by Berni, Bill enjoyed over 40 ye ...

The 2017 SNOOK PRIZES in Computational Statistical Mechanics

Hoover Wm.G. , Hoover C.G.

The 2017 Snook Prize has been awarded to Kenichiro Aoki for his exploration of chaos in Hamiltonian φ4 models. His work addresses symmetries, thermalization, and Lyapunov instabilities in few-particle dynamical systems. A companion paper by Timo Hofmann and Jochen Merker is devoted to the explor ...

Bit-Reversible Version of Milne’s Fourth-Order Time-Reversible Integrator for Molecular Dynamics

Hoover Wm.G. , Hoover C.G.

We point out that two of Milne’s fourth-order integrators are well-suited to bit-reversible simulations. The fourth-order method improves on the accuracy of Levesque and Verlet’s algorithm and simplifies the definition of the velocity v and energy e = (q2 + v2 )/2. (We use this one-dimensiona ...

Yokohama to Ruby Valley: Around the World in 80 Years. II.

Hoover Wm.G. , Hoover C.G.

We two had year-long research leaves in Japan, working together fulltime with several Japanese plus Tony De Groot back in Livermore and Harald Posch in Vienna. We summarize a few of the high spots from that very productive year (1989-1990), followed by an additional fifteen years’ work in Liver ...

From Ann Arbor to Sheffield: Around the World in 80 Years. I.

Hoover William G.

Childhood and graduate school at Ann Arbor Michigan prepared Bill for an interesting and rewarding career in physics. Along the way came Carol and many joint discoveries with our many colleagues to whom we both owe this good life. This summary of Bill’s early work prior to their marriage and sa ...

Comparison of Very Smooth Cell-Model Trajectories Using Five Symplectic and Two Runge-Kutta Integrators

Hoover Wm.G. , Hoover C.G.

Time-reversible symplectic methods, which are precisely compatible with Liouville’s phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent advantage of such methods. But all numerical methods are susce ...

Why Instantaneous Values of the “Covariant” Lyapunov Exponents Depend upon the Chosen State-Space Scale

Hoover Wm.G. , Hoover C.G.

We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations of its coordinate q and momentum p: { q, p } → { (Q/s), (sP ) }. The time-dependent thermostat ...

Time-Symmetry Breaking in Hamiltonian Mechanics

Hoover Wm.G. , Hoover C.G.

Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates f q g satisfying Hamilton’s motion equations will likewise satisfy them when played “backwards”, with the corresponding momenta changing signs : f +p g