fix viscosity

Dear All

Who can help me on this "fix viscosity"?
1) in the lammps example, the unit is lj. we also can use another unit in the system, right?
2) variable, dVx equal f_5[11][3] - f_5[1][3] Can you explain clearly on this equation?
3) for units reduced, does this relate to unit in the system or something else?
4) variable visc equal -(f_4/(2*(step*0.005-125)*lx+1.0e-10))/(v_dVx/(ly/2))
from lammps help website, 1.0e-10 is a fudge factor to avoid a divide-by-0.0 on the 1st time step, right?
ly/2 is the distance over which that delta occurs, so dividing by it gives a slope, right?
if 3 dimension here, what are the parameters?

Thanks for your time.
Look forward to your reply.

Example from lammps:

# sample LAMMPS input script for viscosity of 2d LJ liquid
# Muller-Plathe via fix viscosity

# settings

variable x equal 20
variable y equal 20

variable rho equal 0.6
variable t equal 1.0
variable rc equal 2.5

# problem setup

units lj
dimension 2
atom_style atomic
neigh_modify delay 0 every 1

lattice sq2 ${rho}
region simbox block 0 $x 0 $y -0.1 0.1
create_box 1 simbox
create_atoms 1 box

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

mass * 1.0
velocity all create $t 97287

fix 1 all nve
fix 2 all langevin $t $t 0.1 498094
fix 3 all enforce2d

# equilibration run

thermo 1000
run 5000

unfix 2

# turn on Muller-Plathe driving force and equilibrate some more

velocity all scale $t

fix 4 all viscosity 100 x y 20
fix 5 all ave/spatial 20 50 1000 y center 0.05 vx &
           units reduced file profile.mp.2d

# equilibration run

variable dVx equal f_5[11][3]-f_5[1][3]

thermo 1000
thermo_style custom step temp epair etotal press f_4 v_dVx
run 20000

# data gathering run
# reset fix viscosity to zero flux accumulation

unfix 4
fix 4 all viscosity 100 x y 20

variable visc equal -(f_4/(2*(step*0.005-125)*lx+1.0e-10))/(v_dVx/(ly/2))
fix vave all ave/time 1000 1 1000 v_visc ave running start 26000

thermo_style custom step temp f_4 v_dVx v_visc f_vave

# only need to run for 10000 steps to make a good 100-frame movie

#dump 1 all custom 100 dump.mp.2d id type x y z vx

#dump 1 all image 100 image.*.jpg vx type zoom 1.6 adiam 1.2
#dump_modify 1 pad 5 amap -0.7 0.7 ca 0.0 2 min blue max red

run 50000

I suggest you read the Muller-Plathe paper cited
on the fix viscosity doc page, as well as the
doc pages for all the commands you have Qs
about. Most of your questions are answered there.
And you can treat the input script like a program

and examine the intermediate values it produces

​and processes.

Steve