Update readme.md

Now use the standard namings.
Corrected spelling errors.

examples/USER/pinning/readme.md

-This example demonstrate using a bias potential that can be used to study solid-liquid transitions with the interface pinning method. This is done by adding a harmonic potential to the Hamiltonian that bias the system towards two-phase configurations. 
+This example demonstrate using a bias potential that can be used to study solid-liquid transitions 
+with the interface pinning method. This is done by adding a harmonic potential to the Hamiltonian 
+that bias the system towards two-phase configurations. 
 
-  U_bias = 0.5*k*(Q-a)^2
+  U_bias = 0.5*K*(Q-a)^2
 
-The bias field couple to an order-parameter of crystallinity Q 
-This implimentation use long-range order: Q=|rho_k|, where rho_k is the collective density field of the wave-vector k.
+The bias field couple to an order-parameter of crystallinity Q. The implementation use long-range order:
+
+  Q=|rho_k|, 
+
+where rho_k is the collective density field of the wave-vector k. 
+For future reference we note that the structure factor S(k) is given by the variance of the collective density field: 
+
+  S(k)=|rho_k|^2.
 
 # Reference
-[Ulf R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] 
 
-Please visit 
+It is recommended to get familiar with the interface pinning method by reading:
+
+  [Ulf R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] 
+
+A detailed bibliography is provided at
+
   urp.dk/interface_pinning.htm 
-for a detailed bibliography. 
 
-# Use
+# Use of rhok fix
 
-   fix [name] [groupID] rhok [nx] [ny] [nz] [spring-constant] [anchor-point]
+For this example we will be using the rhok fix.
 
-include a harmonic bias potential U_bias=0.5*k*(|rho_k|-a)^2 to the force calculation.
-The elements of the wave-vector rho_k is k_x = (2 pi / L_x) * n_x, k_y = (2 pi / L_y) * n_y and k_z = (2 pi / L_z) * n_z.
+   fix [name] [groupID] rhok [nx] [ny] [nz] [K] [a]
 
-# The Interface Pinning method for studying melting transitions
-We will use the interface pinning method to study melting of the Lennard-Jones system
+This fix include a harmonic bias potential U_bias=0.5*K*(|rho_k|-a)^2 to the force calculation.
+The elements of the wave-vector k is given by the nx, ny and nz input: 
+
+  k_x = (2 pi / L_x) * n_x, k_y = (2 pi / L_y) * n_y and k_z = (2 pi / L_z) * n_z. 
+
+We will use a k vector that correspond to a Bragg peak.
+
+# The Interface Pinning method for studying melting transitions of the Lennard-Jones (LJ) system
+
+We will use the interface pinning method to study melting of the LJ system
 at temperature 0.8 and pressure 2.185. This is a coexistence state-point, and the method
-can be used to show this. The present directory contains the input files:
+can be used to show this. The present directory contains the input files that we will use:
 
-  crystal.lmp
-  setup.lmp 
-  pinning.lmp
+  in.crystal
+  in.setup
+  in.pinning
 
-1.  First we will determine the density of the crystal with the LAMMPS input file crystal.lmp.
-    From the output we get that the average density after equbriliation is 0.9731. 
-    We need this density to ensure hydrostatic pressure when in a two-phase simulation.
+1. First we will determine the density of the crystal with the LAMMPS input file in.crystal.
+  From the output we get that the average density after equilibration is 0.9731. 
+  We need this density to ensure hydrostatic pressure when in a two-phase simulation.
 
-2.  Next, we setup a two-phase configuration using setup.lmp.
+2. Next, we setup a two-phase configuration using in.setup.
 
-3.  Finally, we run a two-phase simulation with the bias-field applied using pinning.lmp.
-    The last coulmn in the output show |rho_k|. We note that after a equbriliation period
-	the value fluctuates aroung the anchor point (a) -- showing that this is indeed a coexistence
-	state point.
+3. Finally, we run a two-phase simulation with the bias-field applied using in.pinning.
+  The last column in the output show |rho_k|. We note that after a equilibration period
+  the value fluctuates around the anchor point (a) -- showing that this is indeed a coexistence
+  state point.
 
-The reference [J. Chem. Phys. 139, 104102 (2013)] gives details on using the method to find coexitence state points,
-and the referecee [J. Chem. Phys. 142, 044104 (2015)] show how the crystal growth rate can be computed.
+The reference [J. Chem. Phys. 139, 104102 (2013)] gives details on using the method to find coexistence state points,
+and the reference [J. Chem. Phys. 142, 044104 (2015)] show how the crystal growth rate can be computed from fluctuations.
 That method have been experienced to be most effective in the slightly super-heated regime above the melting temperature.
 
 # Contact
+
   Ulf R. Pedersen
   http://www.urp.dk
   ulf AT urp.dk