Liu hard disk equation of state: Difference between revisions

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<ref>[https://arxiv.org/abs/2010.10624]</ref>.
<ref>[https://arxiv.org/abs/2010.10624]</ref>.


For stable fluid:
For the stable fluid:
:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>
:<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>


where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks.
where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks.


The EoS for stable fluid, liquid-hexatic transition region and hexatic:
The EoS for the stable fluid, liquid-hexatic transition region and hexatic:
:<math>Z = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>
:<math>Z_lh = Z_v + \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math>





Revision as of 19:38, 22 October 2020

The Liu equation of state for hard disks (2-dimensional hard spheres) is given by Eq. 1 of [1].

For the stable fluid:

where the packing fraction is given by where is the diameter of the disks.

The EoS for the stable fluid, liquid-hexatic transition region and hexatic:


References