help with time-step

Hi All,

I apologize for this question. I know that is simple and basic, but I need help.
Can someone tell me (or explain) please, why is time-step (and sample interval, too) use for the calculation of thermal conductivity by Green-Kubo formalism, see below (marked in red):

Thank you very much

Best regards

Roland Rozik

Sample LAMMPS input script for thermal conductivity of solid Ar

units real
variable T equal 70
variable V equal vol
variable dt equal 10.0
variable p equal 200 # correlation length
variable s equal 10 # sample interval
variable d equal $p*$s # dump interval

convert from LAMMPS real units to SI

variable kB equal 1.3806504e-23 # [J/K] Boltzmann
variable kCal2J equal 4186.0/6.02214e23
variable A2m equal 1.0e-10
variable fs2s equal 1.0e-15
variable convert equal {kCal2J}*{kCal2J}/{fs2s}/{A2m}

setup problem

dimension 3
boundary p p p
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
region box block 0 4 0 4 0 4
create_box 1 box
create_atoms 1 box
mass 1 39.948
pair_style lj/cut 13.0
pair_coeff * * 0.2381 3.405
timestep ${dt}
thermo $d

equilibration and thermalization

velocity all create $T 102486 mom yes rot yes dist gaussian
fix NVT all nvt temp $T $T 10 drag 0.2
dump 1 all custom 100 ar_nvt.lammpstrj id type x y z ix iy iz
run 8000

thermal conductivity calculation, switch to NVE if desired

#unfix NVT
#fix NVE all nve

reset_timestep 0
compute myKE all ke/atom
compute myPE all pe/atom
compute myStress all stress/atom NULL virial
compute flux all heat/flux myKE myPE myStress
variable Jx equal c_flux[1]/vol
variable Jy equal c_flux[2]/vol
variable Jz equal c_flux[3]/vol
fix JJ all ave/correlate $s $p d & c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running __variable scale equal {convert}/${kB}/$T/$T/$V*s*{dt}__
variable k11 equal trap(f_JJ[3]){scale} variable k22 equal trap(f_JJ[4])*{scale}
variable k33 equal trap(f_JJ[5])
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
run 100000
variable k equal (v_k11+v_k22+v_k33)/3.0
variable ndens equal count(all)/vol
print “average conductivity: $k[W/mK] @ T K, {ndens} /A^3”

s * dt is the time interval between samples.

It’s used in the trap() function which is doing an integral

and needs to know the spacing between the data points,

i.e. the spacing along the x-axis. Else it can’t scale

the area under the curve correctly.