Editing Percus Yevick
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 1: | Line 1: | ||
If one defines a class of | If one defines a class of diagrams by the linear combination (Eq. 5.18 Ref.1) | ||
(See G. Stell in Ref. 2) | (See G. Stell in Ref. 2) | ||
:<math>\left.D(r)\right. = y(r) + c(r) -g(r)</math> | :<math>\left.D(r)\right. = y(r) + c(r) -g(r)</math> | ||
one has the exact | one has the exact integral equation | ||
:<math>y(r_{12}) - D(r_{12}) = 1 + n \int (f(r_{13})y(r_{13})+D(r_{13})) h(r_{23})~dr_3</math> | :<math>y(r_{12}) - D(r_{12}) = 1 + n \int (f(r_{13})y(r_{13})+D(r_{13})) h(r_{23})~dr_3</math> | ||
| Line 13: | Line 13: | ||
:<math>\left.h-c\right.=y-1</math> | :<math>\left.h-c\right.=y-1</math> | ||
The | The ''PY'' closure can be written as (Ref. 3 Eq. 61) | ||
:<math>\left.f [ \gamma (r) ]\right. = [e^{-\beta \Phi} -1][\gamma (r) +1]</math> | :<math>\left.f [ \gamma (r) ]\right. = [e^{-\beta \Phi} -1][\gamma (r) +1]</math> | ||
| Line 29: | Line 29: | ||
:<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math> | :<math>\left.g(r)\right. = e^{-\beta \Phi} (1+ \gamma(r))</math> | ||
or in terms of the bridge function | |||
:<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math> | :<math>\left.B(r)\right.= \ln (1+\gamma(r) ) - \gamma(r)</math> | ||
| Line 38: | Line 36: | ||
Note: the restriction <math>-1 < \gamma (r) \leq 1</math> arising from the logarithmic term Ref. 6. | Note: the restriction <math>-1 < \gamma (r) \leq 1</math> arising from the logarithmic term Ref. 6. | ||
A critical look at the PY was undertaken by Zhou and Stell in Ref. 7. | A critical look at the PY was undertaken by Zhou and Stell in Ref. 7. | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)] | #[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)] | ||