Virial pressure

From SklogWiki
Revision as of 16:35, 6 February 2008 by Dduque (talk | contribs) (Indeed, there was - sign missing)
Jump to: navigation, search

This is a common method to obtain the pressure from a general simulation (it is best suited for molecular dynamics since forces are evaluated in this case). For central interactions, one has:

 p  =  \frac{ k_B T  N}{V} - \frac{ 1 }{ d V } \overline{ \sum_{i<j} {\mathbf f}_{ij}  {\mathbf r}_{ij} },

where one can recognize an ideal term and another one due to the virial. The underline is an average, which would be a time average in molecular dynamics, or ensamble average in Monte Carlo; d is the dimension of the system (3 in actual world).  {\mathbf f}_{ij} is the force on particle i exerted by particle j, and {\mathbf r}_{ij} is the vector going from i to j: {\mathbf r}_{ij} = {\mathbf r}_j - {\mathbf r}_i.