Green-Kubo formula

Thank you Dr. Tolga for your comment. But if we have a look at the script, we see that to make intensive the flux Jx,Jy and Jz have been divided earlier by three

“variable” commands given by

variable Jx equal c_flux[1]/vol
variable Jy equal c_flux[2]/vol
variable Jz equal c_flux[3]/vol
now the unit of Jx,Jy and Jz is [enerrgy x velocity/volume =energy /m^2/s]. which is the unit of heat flux indeed (flux is intensive now).

Now it is [V/(3KT^2)] which should be multiplied with the integral. But in the script it is [1/(3KT^2V)] has been used in the calculation which is my concern.
please comment.


Amal Giri

Nope. Your problem is that you just didn't read the whole
documentation. Right below the equation for kappa the manual says:
"...the 1/V scaling factor in the equation for J is NOT included in
the calculation performed by this compute..."
and the NOT is pretty noticeable/clear.


Carlos beat me to it :slight_smile: Also note that the variables Jx, Jy, Jz are not used in the correlation function or in calculation of kappa.

fix          JJ all ave/correlate $s $p $d &
             c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running


Thank you Dr. Carlos. Yes , I have read it and that is why those three commands
[ variable Jx equal c_flux[1]/vol
variable Jy equal c_flux[2]/vol
variable Jz equal c_flux[3]/vol ]

are there to include the factor 1/V and it’s OK. now the flux is intensive with dimension [energy/(area x time)]. which should be indeed.

My concern is bit different. After this [V/3KT^2] should be multiplied with the integral which leads the dimension of kappa [ watt/(mK)] but here in the manual script [1/3KT^2V] has been multiplied which leads to a wrong dimension of Kappa given by [watt/(m^7K)] !!!
Please share your veiw.


Amal Giri

This was exactly Tim's point. For the calculation of kappa in the
example it is JJ not Jx,y,z what enters in the correlation function.
And JJ doesn't have the volume normalization included.

Thank you Dr. Timothy. Your point is true. I skipped that point . Now it is OK. Sorry for bothering you people.
Sincere regards and thanks to all of you for your kind cooperation.

Amal Giri