Length Scale in LJ Units

In one of the worked examples in Lammps documentation for calculating thermal conductivity using NEMD simulation, the length scale in the x and y directions were 18.82 in the calculation of thermal conductivity, while the input for both was 10. How did we come up with 18.82?

sample LAMMPS input script for thermal conductivity of liquid LJ

thermostatting 2 regions via fix langevin

settings

variable x equal 10
variable y equal 10
variable z equal 20

variable rho equal 0.85
variable t equal 0.7
variable rc equal 3.0
variable tlo equal 0.3
variable thi equal 1.0

setup problem

units lj
atom_style atomic

lattice fcc ${rho}
region box block 0 $x 0 $y 0 $z
create_box 1 box
create_atoms 1 box
mass 1 1.0

velocity all create $t 87287

pair_style lj/cut ${rc}
pair_coeff 1 1 1.0 1.0

neighbor 0.3 bin
neigh_modify delay 0 every 1

heat layers

region hot block INF INF INF INF 0 1
region cold block INF INF INF INF 10 11
compute Thot all temp/region hot
compute Tcold all temp/region cold

1st equilibration run

fix 1 all nvt temp $t $t 0.5
thermo 100
run 1000

velocity all scale $t

unfix 1

2nd equilibration run

fix 1 all nve
fix hot all langevin {thi} {thi} 1.0 59804 tally yes
fix cold all langevin {tlo} {tlo} 1.0 287859 tally yes
fix_modify hot temp Thot
fix_modify cold temp Tcold

variable tdiff equal c_Thot-c_Tcold
thermo_style custom step temp c_Thot c_Tcold f_hot f_cold v_tdiff
thermo 1000
run 10000

thermal conductivity calculation

reset langevin thermostats to zero energy accumulation

compute ke all ke/atom
variable temp atom c_ke/1.5

fix hot all langevin {thi} {thi} 1.0 59804 tally yes
fix cold all langevin {tlo} {tlo} 1.0 287859 tally yes
fix_modify hot temp Thot
fix_modify cold temp Tcold

fix ave all ave/time 10 100 1000 v_tdiff ave running
thermo_style custom step temp c_Thot c_Tcold f_hot f_cold v_tdiff f_ave

fix 2 all ave/spatial 10 100 1000 z lower 0.05 v_temp &
file profile.langevin units reduced

run 20000

The lattice command — LAMMPS documentation determines the lattice spacing and the region command — LAMMPS documentation then uses these to create a rectangular region which is then converted into the simulation box with the create_box command — LAMMPS documentation

The screen and logfile will then show the box dimensions and thus the length scales for the system (they can also be output via a custom thermo style or print commands).