Add HMA examples

The example input script sets up a simple FCC crystal using the Lennard-Jones

potential. The script sets up the HMA compute to calculate the energy, pressure

and heat capacity.  The output columns are:

1: timestep

2: measured temperature

3: potential energy

4: HMA potential energy

5: pressure

6: HMA pressure

7: HMA heat capacity contribution

Averages of the potential energy (#3 and #4) agree although #4 (HMA) is more precise.

Averages of the pressure (#5 and #6) agree once the ideal gas

contribution is included; #6 (HMA) is more precise.

The heat capacity can be computed from colume #3 (convential) as

Cv = Var(#3)/(k T^2)

With HMA, the heat capacity can be computed from column #4 and #7 as

Cv = #7 + Var(#4)/(k T^2)

# Harmonically mapped average example

units lj 

dimension 3 

boundary p p p 

atom_style atomic 

atom_modify map array

# ---------- Create Atoms ----------------------------

lattice 	fcc 1.0

region	box block 0 4 0 4 0 4 units lattice

create_box	1 box

lattice	fcc 1.0 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1  

create_atoms 1 region box

# ---------- Define Interatomic Potential --------------------- 

pair_style lj/smooth/linear 3

pair_coeff * * 1.0 1.0 

mass 1 1.0

atom_modify sort 0 1

velocity all create 0.1 45678 dist gaussian

compute u all pe 

compute p all pressure NULL pair  

compute hma all HMA settemp u p 9.579586686264458 cv

timestep 0.005

fix settemp all nvt temp 1.0 1.0 0.5

thermo_style custom elapsed temp c_u c_hma[1] c_p c_hma[2] c_hma[3]

thermo_modify format float '%22.15e'

thermo 500

run 20000

thermo 20

run 200000