Hard disk model: Difference between revisions
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'''Hard disks''' are [[Hard sphere model |hard spheres]] in two dimensions. The hard disk [[intermolecular pair potential]] is given by | |||
: <math> | |||
\Phi\left( r \right) = \left\{ \begin{array}{lll} | |||
\infty & ; & r < \sigma \\ | |||
0 & ; & r \ge \sigma \end{array} \right. | |||
</math> | |||
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. | |||
==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 16:48, 19 November 2007
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Hard disks are hard spheres in two dimensions. The hard disk intermolecular pair potential is given by
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi\left(r \right) } is the intermolecular pair potential between two disks at a distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r } , and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma } is the diameter of the disk.
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)