Update documentation

\begin{document}

$$

   U_\text{bias} = \frac{k}{2}(|\rho_{k}| - a)^2

$$

\begin{eqnarray*}

 U &=&  \frac{1}{2} K (|\rho_{\vec{k}}| - a)^2 \\

 \rho_{\vec{k}} &=& \sum_i^N \exp(-i\vec{k} \cdot \vec{r}_i )/\sqrt{N} \\

 \vec{k} &=& (2\pi n_x /L_x , 2\pi n_y  /L_y , 2\pi n_z/L_z ) 

\end{eqnarray*}

\end{document}

ID, group-ID are documented in "fix"_fix.html command

nx, ny, nz = k-vektor of collective density field

k = spring constant of bias potential

K = spring constant of bias potential

a = anchor point of bias potential :ul

[Examples:]

fix bias all rhok 16 0 0 4.0 16.0

fix bias Bs rhok 12 12 0 10.0 32.0 :pre

fix bias Bs rhok 12 12 0 10.0 24.0 :pre

[Description:]

The fix applies an force to atoms 

The fix applies an force to atoms given by the potential

:c,image(Eqs/fix_rhok.jpg)

as described in "(Pedersen)"_#Pedersen. 

The energy and the value of the

collective density field can be written by including

# output                                U_bias rho_k_RE  rho_k_IM |rho_k| 

thermo_style custom step temp pzz pe lz f_bias f_bias\[1\] f_bias\[2\] f_bias\[3\] :pre

to the input script.

This field that bias long-range order 

can be used to study crystal-liquid interfaces,

and determine melting temperatures "(Pedersen)"_#Pedersen.

The folder {examples/pinning} of the source code 

contains an example of using the interface pinning method 

on the Lennard-Jones system.

[Restrictions:]

was built with that package.  See the "Making

LAMMPS"_Section_start.html#start_3 section for more info.

[Related commands:]

"thermo_style"_thermo_style.html

[Default:] none

:line

:link(Pedersen)

[(Pedersen)] Pedersen, J. Chem. Phys., 139, 104102 (2013).