Direct correlation function: Difference between revisions

Revision as of 16:47, 19 February 2008

The direct correlation function, $c(1,2)$ is encountered in the Ornstein-Zernike relation, i.e.

h({\mathbf {r} })-c({\mathbf {r} })=\rho \int h({\mathbf {r} '})~c(|{\mathbf {r} }-{\mathbf {r} '}|){\rm {d}}{\mathbf {r} '}

{\frac {1}{k_{B}T}}\left.{\frac {\partial p}{\partial \rho }}\right\vert _{T}=1-\rho \int _{0}^{\infty }c(r)~4\pi r^{2}~{\rm {d}}r

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 {{Stub-general}}
-<math>c(1,2)</math>
+The '''direct correlation function''', <math>c(1,2)</math> is encountered in the [[Ornstein-Zernike relation]], i.e.
+:<math>h({\mathbf r}) - c({\mathbf r}) = \rho \int  h({\mathbf r'})~c(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}</math>
+and also in the [[compressibility equation]], i.e.
+:<math>\frac{1}{k_BT} \left.\frac{\partial p}{\partial \rho}\right\vert_{T} = 1 - \rho \int_0^{\infty} c(r) ~4 \pi r^2 ~{\rm d}r</math>
 [[Category: Integral equations]]