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vp.liquids.eos

The Lennard-Jones equation of state at one state point, from the fits of Thol et al.: pressure, energy, heat capacities, chemical potential and activity for the full potential, the same moved to the potential cut (not shifted) at 2.5 sigma by the long-range and delta corrections, and for the potential cut and shifted at 2.5 sigma, with the residual free energy and its derivatives behind each. These are the numbers Allen and Tildesley's simulations are tested against.

Part of the distribution vipyr-liquids; it runs from a checkout of the repository. Planned on PyPI as pip install vipyr-liquids.

Signature

vp.liquids.eos(*, temperature=1.0, density=0.75)

Parameters

temperature : float, default 1.0
The temperature, in units of epsilon / k_B. Range: > 0.
density : float, default 0.75
The number density, in sigma^-3. Range: > 0.

Returns

A frozen EOSResult. Iterating it gives the fields below in order; it also has params, tests, log and check().

p_full : float
The pressure.
e_full : float
The energy per atom, with the ideal gas's 3T/2.
cv_full : float
The heat capacity per atom at constant volume, in units of k_B.
cp_full : float
The heat capacity per atom at constant pressure.
mu_full : float
The chemical potential.
z_full : float
The activity, exp(mu / T) in units of the thermal wavelength cubed.
p_cut : float
The pressure.
e_cut : float
The energy per atom.
mu_cut : float
The chemical potential.
z_cut : float
The activity.
p_cs : float
The pressure.
e_cs : float
The energy per atom.
cv_cs : float
The heat capacity per atom at constant volume.
cp_cs : float
The heat capacity per atom at constant pressure.
mu_cs : float
The chemical potential.
z_cs : float
The activity.
a_res_full_table : ndarray[float64]
The table tau^i delta^j d^(i+j) a_res / d tau^i d delta^j, rows i and columns j from 0 to 2 (entries with i + j > 2 are not used) (rank 2).
a_res_cs_table : ndarray[float64]
The cut-and-shifted fit's table, as a_res_full (rank 2).

Raises

vipyr.ParameterError
A ValueError: an argument outside its range, choices, rank or shape, or one of a group given without the rest; its .param names the argument.
TypeError
An argument of the wrong type, or an unknown keyword.
vipyr.VivBuildError
An ImportError: no C compiler, or the program's C does not build.
RuntimeError
The program stops with its own message (a combination it rejects, or no convergence where the program treats that as an error).

Examples

import vipyr as vp
r = vp.liquids.eos(temperature=1.0, density=0.75)
print(r.p_full, r.e_full, r.cv_full)       # Thol et al. 2016: 0.3996, -3.7212, 2.2630
print(r.p_cs, r.e_cs)                      # cut and shifted at 2.5: 0.9897, -2.9287
assert r.check()
0.3995824497857153 -3.721249230098813 2.2630169185686153
0.9896959151485801 -2.9286513983540416

Each example ran as written when these pages were generated, and the output shown is what it printed.

Checked against

Tests
ports/liquids/test_liquids.py: every tolerance is stated beside its check
Upstream
eos_lj of https://github.com/Allen-Tildesley/examples at 4818bc82, built with gfortran -O2 by ports/liquids/oracle/build.py; same bits from the same start and random numbers

Credits

  • A port of the examples of Allen and Tildesley's Computer Simulation of Liquids, which are CC0-1.0.

Source