Verlet modified

2015-09-01T17:00:42Z

158.49.50.230:

The '''Verlet modified''' (1980) (Ref. 1) [[Closure relations | closure relation]] for [[hard sphere model | hard sphere]] fluids,
in terms of the [[cavity correlation function]], is (Eq. 3)

:<math>\ln y(r) = \gamma (r) - A \frac{1}{2} \gamma^2(r) \left[ \frac{1}{1+ B \gamma(r) /2} \right]</math>

where several sets of values are tried for ''A'' and ''B'' (Note, when ''A=0'' the [[HNC| hyper-netted chain]] is recovered).
Later (Ref. 2) Verlet used a Padé (2/1) approximant (Eq. 6) fitted to obtain the best [[hard sphere model | hard sphere]] results
by minimising the difference between the pressures obtained via the [[Pressure equation | virial]] and [[Compressibility equation | compressibility]] routes:

:<math>\ln y(r) = \gamma (r) - A \frac{1}{2} \gamma^2(r) \left[ \frac{1+ \lambda \gamma(r)}{1+ \mu \gamma(r)} \right]</math>

with <math>A= 0.80</math>, <math>\lambda= 0.03496</math> and <math>\mu = 0.6586</math>.

==References==
#[http://dx.doi.org/10.1080/00268978000102671 Loup Verlet "Integral equations for classical fluids I. The hard sphere case", Molecular Physics '''41''' pp. 183-190 (1980)]
#[http://dx.doi.org/10.1080/00268978100100971 Loup Verlet "Integral equations for classical fluids II. Hard spheres again", Molecular Physics '''42''' pp. 1291-1302 (1981)]
[[Category: Integral equations]]

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Verlet modified