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 ...

Information Dimensions of Simple Four-Dimensional Flows

Hoover William G., Hoover Carol G., Travis Karl P.

Baker Maps have long served as pedagogical tools for understanding chaos and fractal phase-space distributions. Recent work [1], following earlier efforts from 1997 [2], shows that the Kaplan-Yorke formula for information dimension disagrees wit ...

The Simplest Viscous Flow

Hoover William G., Hoover Carol G.

We illustrate an atomistic periodic two-dimensional stationary shear flow, u_x = ( x˙ ) = E˙y, using the simplest possible example, the periodic shear of just two particles! We use a short-ranged “realistic” pair potential, ...

$1000 SNOOK PRIZES FOR 2021: The Information Dimensions of a Two-Dimensional Baker Map

Hoover William G., Hoover Carol G.

The fractal information dimension can be computed in three ways: (1) mapping points, (2) mapping regions (two-dimensional areas here), and (3) applying the Kaplan-Yorke conjecture. For the simplest nonequilibrium Baker N2 Map these three approaches can give different results. A pedagogical explor ...

2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps

Hoover William G., Hoover Carol G.

The $1000 Ian Snook Prize for 2020 will be awarded to the author(s) of the most interesting paper exploring pairs of relatively simple, but fractal, models of nonequilibrium systems, dissipative time-reversible Baker Maps and their equivalent stochastic random walks. Two-dimensional deterministic ...