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==
Fluid phase:
:''Main article: [[Equations of state for hard disks]]''
*[[Tejero and Cuesta hard disk equation of state |Tejero and Cuesta]]
==Virial coefficients==
Solid phase:
:''Main article: [[Hard sphere: virial coefficients]]''
*[[Alder-Hoover-Young hard disk equation of state |Alder-Hoover-Young]]
==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 13:08, 19 February 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

References

  1. 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)
  2. Ya G Sinai "Dynamical systems with elastic reflections", Russian Mathematical Surveys 25 pp. 137-189 (1970)
  3. 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)
  4. 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)
  5. Nándor Simányi "Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems", Inventiones Mathematicae 154 pp. 123-178 (2003)