Hard disk model: Difference between revisions
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: <math> | : <math> | ||
\ | \Phi_{12}\left( r \right) = \left\{ \begin{array}{lll} | ||
\infty & ; & r < \sigma \\ | \infty & ; & r < \sigma \\ | ||
0 & ; & r \ge \sigma \end{array} \right. | 0 & ; & r \ge \sigma \end{array} \right. | ||
</math> | </math> | ||
where <math> \ | where <math> \Phi_{12}\left(r \right) </math> is the [[intermolecular pair potential]] between two disks at a distance <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, and <math> \sigma </math> is the diameter of the disk. | ||
==Equations of state== | ==Equations of state== | ||
:''Main article: [[Equations of state for hard disks]]'' | :''Main article: [[Equations of state for hard disks]]'' | ||
Revision as of 15:51, 17 July 2008
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Hard disks are hard spheres in two dimensions. The hard disk intermolecular pair potential is given by
where is the intermolecular pair potential between two disks at a distance , and is the diameter of the disk.
Equations of state
- Main article: Equations of state for hard disks
Virial coefficients
- Main article: Hard sphere: virial coefficients
External links
- Hard disks and spheres computer code on SMAC-wiki.
References
- Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller and Edward Teller, "Equation of State Calculations by Fast Computing Machines", Journal of Chemical Physics 21 pp.1087-1092 (1953)
- Ya G Sinai "Dynamical systems with elastic reflections", Russian Mathematical Surveys 25 pp. 137-189 (1970)
- Katherine J. Strandburg, John A. Zollweg, and G. V. Chester "Bond-angular order in two-dimensional Lennard-Jones and hard-disk systems", Physical Review B 30 pp. 2755 - 2759 (1984)
- Carl McBride and Carlos Vega "Fluid solid equilibrium for two dimensional tangent hard disk chains from Wertheim's perturbation theory", Journal of Chemical Physics 116 pp. 1757-1759 (2002)
- Nándor Simányi "Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems", Inventiones Mathematicae 154 pp. 123-178 (2003)