From d5d0a879e8a454cf1a3b6ce3a2a008bdf9b0e732 Mon Sep 17 00:00:00 2001 From: athomps Date: Mon, 18 Apr 2016 23:59:56 +0000 Subject: [PATCH] Added Einstein version of Green-Kubo git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@14847 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Section_howto.txt | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/doc/Section_howto.txt b/doc/Section_howto.txt index c252a39a14..6774e4a4f6 100644 --- a/doc/Section_howto.txt +++ b/doc/Section_howto.txt @@ -2005,9 +2005,9 @@ formalism. 6.21 Calculating viscosity :link(howto_21),h4 -The shear viscosity eta of a fluid can be measured in at least 4 ways +The shear viscosity eta of a fluid can be measured in at least 5 ways using various options in LAMMPS. See the examples/VISCOSITY directory -for scripts that implement the 4 methods discussed here for a simple +for scripts that implement the 5 methods discussed here for a simple Lennard-Jones fluid model. Also, see "this section"_Section_howto.html#howto_20 of the manual for an analogous discussion for thermal conductivity. @@ -2055,7 +2055,7 @@ See the "fix viscosity"_fix_viscosity.html command for details. The fourth method is based on the Green-Kubo (GK) formula which relates the ensemble average of the auto-correlation of the -stress/pressure tensor to eta. This can be done in a steady-state +stress/pressure tensor to eta. This can be done in a fully equilibrated simulation which is in contrast to the two preceding non-equilibrium methods, where momentum flows continuously through the simulation box. @@ -2122,6 +2122,13 @@ variable v equal (v_v11+v_v22+v_v33)/3.0 variable ndens equal count(all)/vol print "average viscosity: $v \[Pa.s/] @ $T K, $\{ndens\} /A^3" :pre +The fifth method is related to the above Green-Kubo method, +but uses the Einstein formulation, analogous to the Einstein +mean-square-displacement formulation for self-diffusivity. The +time-integrated momentum fluxes play the role of Cartesian +coordinates, whose mean-square displacement increases linearly +with time at sufficiently long times. + :line 6.22 Calculating a diffusion coefficient :link(howto_22),h4