Parallel hard cubes

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Parallel hard cubes are a simple particle model used in statistical mechanics. They were introduced by B. T. Geilikman [1] in 1950. The virial equation of state (pressure as a power series in the density) was studied by Zwanzig, Temperley, Hoover, and De Rocco [2][3]. The latter two authors computed seven-term series for the models [3]. Both the sixth and seventh terms in the hard-cube series are negative, a counter-intuitive result for repulsive interactions. In 1998 E. A. Jagla [4] investigated the melting transition for both parallel and rotating cube models, finding a qualitative difference in the nature of the transition for the two models. In that same year Martinez-Raton and Cuesta described cubes and mixtures of cubes (See Mixtures [3]).

Usefulness of the Model

Parallel hard cubes have another use, beyond providing a simple model for which seven terms in the Mayers' virial series can be evaluated. In 2009 the Hoovers pointed out [5] that these models can be used as "ideal gas thermometers" capable of measuring the tensor temperature components . Kinetic theory shows that particles colliding with a hard-cube Maxwell-Boltzmann ideal gas at temperature will lose or gain energy according to whether the particle kinetic temperature exceeds or not. The independence of the temperature components for the hard parallel cubes (or squares in two dimensions) allows them to serve as gedanken-experiment thermometers for all three temperature components.

Mixtures

[6] [7] [8]

References

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