# Difference between revisions of "Bridge function"

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+ | The '''bridge functions''' are infinite series of irreducible [[Cluster diagrams | diagrams]] <math>D_i</math>: | ||

+ | |||

+ | :<math>B^{(2)}(r) = \rho^2 \frac{1}{2} D_1(r) + \rho^3 [D_2(r) + D_3(r)] + \rho^4[...]+...</math> | ||

+ | |||

+ | and | ||

+ | |||

+ | :<math>B^{(1)}(r) = \frac{1}{3} B^{(2)}(r) + \rho^3 \left[\frac{1}{6}D_2(r) - \frac{1}{12}D_3(r)\right] + \rho^4[...]+...</math> | ||

+ | |||

+ | where <math>\rho</math> is the density of the fluid. | ||

+ | ==Universality of the Bridge functional== | ||

+ | For Rosenfeld's principle of the universality of the bridge functional see <ref>[http://dx.doi.org/10.1063/1.464569 Yaakov Rosenfeld "Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas", Journal of Chemical Physics '''98''' pp. 8126-8148 (1993)]</ref>. | ||

+ | |||

==References== | ==References== | ||

− | + | <references/> | |

+ | ;Related reading | ||

+ | *[http://dx.doi.org/10.1063/1.2737046 Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics '''126''' 214504 (2007)] | ||

+ | *[http://dx.doi.org/10.1063/1.1860559 Sang Kyu Kwak and David A. Kofke "Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation", Journal of Chemical Physics '''122''' 104508 (2005)] | ||

+ | *[http://dx.doi.org/10.1063/1.4766465 Stefan M. Kast and Daniel Tomazic "An exact bound on the bridge function in integral equation theories", Journal of Chemical Physics '''137''' 174502 (2012)] | ||

+ | |||

+ | |||

[[category: integral equations]] | [[category: integral equations]] |

## Latest revision as of 16:26, 7 November 2012

The **bridge functions** are infinite series of irreducible diagrams :

and

where is the density of the fluid.

## Universality of the Bridge functional[edit]

For Rosenfeld's principle of the universality of the bridge functional see ^{[1]}.

## References[edit]

- Related reading

- Jean-Marc Bomont and Jean-Louis Bretonnet "Approximative “one particle” bridge function B(1)(r) for the theory of simple fluids", Journal of Chemical Physics
**126**214504 (2007) - Sang Kyu Kwak and David A. Kofke "Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation", Journal of Chemical Physics
**122**104508 (2005) - Stefan M. Kast and Daniel Tomazic "An exact bound on the bridge function in integral equation theories", Journal of Chemical Physics
**137**174502 (2012)