##########################################################
#   Summary:
# The following example uses fix wall/region to apply an inward harmonic force
#    -2*k*(r - (rc0-rc))
# to every particle (group "all") whose distance from the origin, r,
# exceeds the inner radius, rc0-rc, (which is currently set to 30.0)
#
#  here "rc" is the wall thickness parameter (used with fix wall/region)
#   and "rc0" is the size of the region (defined with the region command.)
#   (= 30.0 + wall_thickness in this example)
#
# How "hard" the surface is can be controlled by the "k" parameter
# (currently set to 50.0 in the example below.)
# 
##########################################################




# Define "rSphere", a spherical region (used by LAMMPS fix wall/region)
#
#                     sphere_center radius
#                      x0  y0   z0   rc0
#                      |    |    |    |
#                     \|/  \|/  \|/  \|/
#                      V    V    V    V

region rSphere sphere  0    0    0  230.0   side in

# This sets the parameter "rc0" equal to 230.0.
# The "230.0" means we assume no particle will ever be further than 230.0
# from the center of the sphere (which we placed at the origin in this example).
# I made this radius extremely large to make sure that this never happens.
# (Depending on the size of your system, you may have to adjust this.)



# Now apply an inward force applied to every particle which lies outside
# a spherical region (of radius rc0-rc)
# The energy of each particle (due to that force) is:
#
# Uexternal(r) = k*(rsurf-rc)^2 
#       where "rsurf" = the distance from the particle to the surface = rc0 - r
#              = k*((rc0-rc) - r)^2
#                 
#                                             k   ignore rc
#                                             |     |    |
#                                            \|/   \|/  \|/
#                                             V     V    V

fix fxWall all wall/region rSphere harmonic  50.0  0.0  200.0

# Uexternal(r) = k*(r - (rc0-rc))^2    (if (rc0-rc) < r < rc0,  0 otherwise)
# 
#     Note that rc0-rc = 30.0
#                      = the "inner" sphere radius


# For an explanation of these commands go here:
# http://lammps.sandia.gov/doc/fix_wall_region.html
# http://lammps.sandia.gov/doc/region.html