Hard disk model: Difference between revisions
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where <math> \Phi\left(r \right) </math> is the [[intermolecular pair potential]] between two disks at a distance <math> r </math>, and <math> \sigma </math> is the diameter of the disk. | where <math> \Phi\left(r \right) </math> is the [[intermolecular pair potential]] between two disks at a distance <math> r </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]]'' | |||
==Virial coefficients== | |||
:''Main article: [[Hard sphere: virial coefficients]]'' | |||
==External links== | ==External links== | ||
*[http://www.smac.lps.ens.fr/index.php/Programs_Chapter_2:_Hard_disks_and_spheres Hard disks and spheres] computer code on SMAC-wiki. | *[http://www.smac.lps.ens.fr/index.php/Programs_Chapter_2:_Hard_disks_and_spheres Hard disks and spheres] computer code on SMAC-wiki. |
Revision as of 12:08, 19 February 2008
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)