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Added Einstein version of Green-Kubo 

git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@14847 f3b2605a-c512-4ea7-a41b-209d697bcdaa
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athomps 2016-04-18 23:59:56 +00:00
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doc/Section_howto.txt
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@ -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