From aceba1bd01f219d882ab93ce297d8569e9110ed5 Mon Sep 17 00:00:00 2001 From: sjplimp Date: Thu, 12 Sep 2013 17:59:49 +0000 Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@10762 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Section_howto.html | 67 +++++++++++++++++++++++------------------- doc/Section_howto.txt | 67 +++++++++++++++++++++++------------------- 2 files changed, 74 insertions(+), 60 deletions(-) diff --git a/doc/Section_howto.html b/doc/Section_howto.html index a7ac32aabb..967ee19a78 100644 --- a/doc/Section_howto.html +++ b/doc/Section_howto.html @@ -1915,11 +1915,15 @@ LAMMPS.

6.20 Calculating thermal conductivity

The thermal conductivity kappa of a material can be measured in at -least 3 ways using various options in LAMMPS. (See this +least 4 ways using various options in LAMMPS. See the examples/KAPPS +directory for scripts that implement the 4 methods discussed here for +a simple Lennard-Jones fluid model. Also, see this section of the manual for an analogous -discussion for viscosity). The thermal conducitivity tensor kappa is -a measure of the propensity of a material to transmit heat energy in a -diffusive manner as given by Fourier's law +discussion for viscosity. +

+

The thermal conducitivity tensor kappa is a measure of the propensity +of a material to transmit heat energy in a diffusive manner as given +by Fourier's law

J = -kappa grad(T)

@@ -1932,35 +1936,37 @@ scalar.

The first method is to setup two thermostatted regions at opposite ends of a simulation box, or one in the middle and one at the end of a periodic box. By holding the two regions at different temperatures -with a thermostatting fix, the energy added -to the hot region should equal the energy subtracted from the cold -region and be proportional to the heat flux moving between the +with a thermostatting fix, the energy +added to the hot region should equal the energy subtracted from the +cold region and be proportional to the heat flux moving between the regions. See the paper by Ikeshoji and Hafskjold for details of this idea. Note that thermostatting fixes such as fix nvt, fix langevin, and fix temp/rescale store the cumulative energy they -add/subtract. Alternatively, the fix heat command can -used in place of thermostats on each of two regions, and the resulting -temperatures of the two regions monitored with the "compute -temp/region" command or the temperature profile of the intermediate -region monitored with the fix ave/spatial and -compute ke/atom commands. +add/subtract. Alternatively, as a second method, the fix +heat command can used in place of thermostats on each +of two regions to add/subtract specified amounts of energy to both +regions. In both cases, the resulting temperatures of the two regions +can be monitored with the "compute temp/region" command and the +temperature profile of the intermediate region can be monitored with +the fix ave/spatial and compute +ke/atom commands.

-

The second method is to perform a reverse non-equilibrium MD -simulation using the fix -thermal/conductivity command which -implements the rNEMD algorithm of Muller-Plathe. Kinetic energy is -swapped between atoms in two different layers of the simulation box. -This induces a temperature gradient between the two layers which can -be monitored with the fix ave/spatial and -compute ke/atom commands. The fix tallies the +

The third method is to perform a reverse non-equilibrium MD simulation +using the fix thermal/conductivity +command which implements the rNEMD algorithm of Muller-Plathe. +Kinetic energy is swapped between atoms in two different layers of the +simulation box. This induces a temperature gradient between the two +layers which can be monitored with the fix +ave/spatial and compute +ke/atom commands. The fix tallies the cumulative energy transfer that it performs. See the fix thermal/conductivity command for details.

-

The third method is based on the Green-Kubo (GK) formula which relates -the ensemble average of the auto-correlation of the heat flux to -kappa. The heat flux can be calculated from the fluctuations of +

The fourth method is based on the Green-Kubo (GK) formula which +relates the ensemble average of the auto-correlation of the heat flux +to kappa. The heat flux can be calculated from the fluctuations of per-atom potential and kinetic energies and per-atom stress tensor in a steady-state equilibrated simulation. This is in contrast to the two preceding non-equilibrium methods, where energy flows continuously @@ -1980,13 +1986,14 @@ formalism.

6.21 Calculating viscosity

The shear viscosity eta of a fluid can be measured in at least 3 ways -using various options in LAMMPS. (See this +using various options in LAMMPS. See this section of the manual for an analogous -discussion for thermal conductivity). Eta is a measure of the -propensity of a fluid to transmit momentum in a direction -perpendicular to the direction of velocity or momentum flow. -Alternatively it is the resistance the fluid has to being sheared. It -is given by +discussion for thermal conductivity. +

+

Eta is a measure of the propensity of a fluid to transmit momentum in +a direction perpendicular to the direction of velocity or momentum +flow. Alternatively it is the resistance the fluid has to being +sheared. It is given by

J = -eta grad(Vstream)

diff --git a/doc/Section_howto.txt b/doc/Section_howto.txt index 410bc97484..3355469781 100644 --- a/doc/Section_howto.txt +++ b/doc/Section_howto.txt @@ -1902,11 +1902,15 @@ LAMMPS. 6.20 Calculating thermal conductivity :link(howto_20),h4 The thermal conductivity kappa of a material can be measured in at -least 3 ways using various options in LAMMPS. (See "this +least 4 ways using various options in LAMMPS. See the examples/KAPPS +directory for scripts that implement the 4 methods discussed here for +a simple Lennard-Jones fluid model. Also, see "this section"_Section_howto.html#howto_21 of the manual for an analogous -discussion for viscosity). The thermal conducitivity tensor kappa is -a measure of the propensity of a material to transmit heat energy in a -diffusive manner as given by Fourier's law +discussion for viscosity. + +The thermal conducitivity tensor kappa is a measure of the propensity +of a material to transmit heat energy in a diffusive manner as given +by Fourier's law J = -kappa grad(T) @@ -1919,35 +1923,37 @@ scalar. The first method is to setup two thermostatted regions at opposite ends of a simulation box, or one in the middle and one at the end of a periodic box. By holding the two regions at different temperatures -with a "thermostatting fix"_Section_howto.html#howto_13, the energy added -to the hot region should equal the energy subtracted from the cold -region and be proportional to the heat flux moving between the +with a "thermostatting fix"_Section_howto.html#howto_13, the energy +added to the hot region should equal the energy subtracted from the +cold region and be proportional to the heat flux moving between the regions. See the paper by "Ikeshoji and Hafskjold"_#Ikeshoji for details of this idea. Note that thermostatting fixes such as "fix nvt"_fix_nh.html, "fix langevin"_fix_langevin.html, and "fix temp/rescale"_fix_temp_rescale.html store the cumulative energy they -add/subtract. Alternatively, the "fix heat"_fix_heat.html command can -used in place of thermostats on each of two regions, and the resulting -temperatures of the two regions monitored with the "compute -temp/region" command or the temperature profile of the intermediate -region monitored with the "fix ave/spatial"_fix_ave_spatial.html and -"compute ke/atom"_compute_ke_atom.html commands. +add/subtract. Alternatively, as a second method, the "fix +heat"_fix_heat.html command can used in place of thermostats on each +of two regions to add/subtract specified amounts of energy to both +regions. In both cases, the resulting temperatures of the two regions +can be monitored with the "compute temp/region" command and the +temperature profile of the intermediate region can be monitored with +the "fix ave/spatial"_fix_ave_spatial.html and "compute +ke/atom"_compute_ke_atom.html commands. -The second method is to perform a reverse non-equilibrium MD -simulation using the "fix -thermal/conductivity"_fix_thermal_conductivity.html command which -implements the rNEMD algorithm of Muller-Plathe. Kinetic energy is -swapped between atoms in two different layers of the simulation box. -This induces a temperature gradient between the two layers which can -be monitored with the "fix ave/spatial"_fix_ave_spatial.html and -"compute ke/atom"_compute_ke_atom.html commands. The fix tallies the +The third method is to perform a reverse non-equilibrium MD simulation +using the "fix thermal/conductivity"_fix_thermal_conductivity.html +command which implements the rNEMD algorithm of Muller-Plathe. +Kinetic energy is swapped between atoms in two different layers of the +simulation box. This induces a temperature gradient between the two +layers which can be monitored with the "fix +ave/spatial"_fix_ave_spatial.html and "compute +ke/atom"_compute_ke_atom.html commands. The fix tallies the cumulative energy transfer that it performs. See the "fix thermal/conductivity"_fix_thermal_conductivity.html command for details. -The third method is based on the Green-Kubo (GK) formula which relates -the ensemble average of the auto-correlation of the heat flux to -kappa. The heat flux can be calculated from the fluctuations of +The fourth method is based on the Green-Kubo (GK) formula which +relates the ensemble average of the auto-correlation of the heat flux +to kappa. The heat flux can be calculated from the fluctuations of per-atom potential and kinetic energies and per-atom stress tensor in a steady-state equilibrated simulation. This is in contrast to the two preceding non-equilibrium methods, where energy flows continuously @@ -1967,13 +1973,14 @@ formalism. 6.21 Calculating viscosity :link(howto_21),h4 The shear viscosity eta of a fluid can be measured in at least 3 ways -using various options in LAMMPS. (See "this +using various options in LAMMPS. See "this section"_Section_howto.html#howto_20 of the manual for an analogous -discussion for thermal conductivity). Eta is a measure of the -propensity of a fluid to transmit momentum in a direction -perpendicular to the direction of velocity or momentum flow. -Alternatively it is the resistance the fluid has to being sheared. It -is given by +discussion for thermal conductivity. + +Eta is a measure of the propensity of a fluid to transmit momentum in +a direction perpendicular to the direction of velocity or momentum +flow. Alternatively it is the resistance the fluid has to being +sheared. It is given by J = -eta grad(Vstream)