pyPRISM.closure.PercusYevick module¶
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class
pyPRISM.closure.PercusYevick.PY(apply_hard_core=False)[source]¶ Bases:
pyPRISM.closure.PercusYevick.PercusYevickAlias of PercusYevick
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class
pyPRISM.closure.PercusYevick.PercusYevick(apply_hard_core=False)[source]¶ Bases:
pyPRISM.closure.AtomicClosure.AtomicClosurePercus Yevick closure evaluated in terms of a change of variables
Mathematial Definition
\[c_{\alpha,\beta}(r) = (\exp(-U_{\alpha,\beta}(r)) - 1.0) (1.0 + \gamma_{\alpha,\beta}(r))\]\[\gamma_{\alpha,\beta}(r) = h_{\alpha,\beta}(r) - c_{\alpha,\beta}(r)\]Variables Definitions
- \(h_{\alpha,\beta}(r)\)
- Total correlation function value at distance \(r\) between sites \(\alpha\) and \(\beta\).
- \(c_{\alpha,\beta}(r)\)
- Direct correlation function value at distance \(r\) between sites \(\alpha\) and \(\beta\).
- \(U_{\alpha,\beta}(r)\)
- Interaction potential value at distance \(r\) between sites \(\alpha\) and \(\beta\).
Description
The Percus-Yevick (PY) is derived by expanding the exponential of the direct correlation function, \(c_{\alpha,\beta}(r)\), in powers of density shift from a reference state. See Reference [1] for a full derivation.
The change of variables is necessary in order to use potentials with hard cores in the computational setting. Written in the standard form, this closure diverges with divergent potentials, which makes it impossible to numerically solve.
This closure has been shown to be accurate for systems with hard cores (strongly repulsive at short distances) and when the potential is short ranged.
References
- Hansen, J.P.; McDonald, I.R.; Theory of Simple Liquids; Chapter 4, Section 4; 4th Edition (2013), Elsevier [link]
Example
import pyPRISM sys = pyPRISM.System(['A','B']) sys.closure['A','A'] = pyPRISM.closure.PercusYevick() sys.closure['A','B'] = pyPRISM.closure.PercusYevick() sys.closure['B','B'] = pyPRISM.closure.HypernettedChain() # ** finish populating system object ** PRISM = sys.createPRISM() PRISM.solve()