Bridge function: Difference between revisions
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The '''bridge functions''' are infinite series of irreducible [[diagrams]] <math>D_i</math>: | 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> | :<math>B^{(2)}(r) = \rho^2 \frac{1}{2} D_1(r) + \rho^3 [D_2(r) + D_3(r)] + \rho^4[...]+...</math> | ||
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:<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> | :<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 | where <math>\rho</math> is the density of the fluid. | ||
==References== | ==References== | ||
#[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/10.1063/1.2737046 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)] | ||
[[category: integral equations]] | [[category: integral equations]] | ||
Revision as of 10:28, 8 June 2007
The bridge functions are infinite series of irreducible diagrams :
![{\displaystyle B^{(2)}(r)=\rho ^{2}{\frac {1}{2}}D_{1}(r)+\rho ^{3}[D_{2}(r)+D_{3}(r)]+\rho ^{4}[...]+...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3a016aca53933b93dfb7fe63cc9d408238446bb)
and
![{\displaystyle 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}[...]+...}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c9ce1bab48c7699f7cfc86d46a18dd90cc6259ff)
where is the density of the fluid.
