Merge pull request #1952 from lammps/numdiff-doc

Calculate forces through finite difference calculations of energy

versus position.  These forces can be compared to analytic forces

computed by pair styles, bond styles, etc.  E.g. for debugging

purposes.

computed by pair styles, bond styles, etc.  This can be useful for

debugging or other purposes.

The group specified with the command means only atoms within the group

have their averages computed.  Results are set to 0.0 for atoms not in

the group.

This fix performs a loop over all atoms (in the group).  For each atom

This fix performs a loop over all atoms in the group.  For each atom

and each component of force it adds *delta* to the position, and

computes the new energy of the entire system.  It then subtracts

*delta* from the original position and again computes the new energy

.. note::

   The cost of each energy evaluation is essentially the cost of an MD

   timestep.  This invoking this fix once has a cost of 2N timesteps,

   where N is the total number of atoms in the system (assuming all atoms

   are included in the group).  So this fix can be very expensive to use

   for large systems.

   timestep.  Thus invoking this fix once for a 3d system has a cost

   of 6N timesteps, where N is the total number of atoms in the system

   (assuming all atoms are included in the group).  So this fix can be

   very expensive to use for large systems.

----------

nb3b:     use of nonbonded 3-body harmonic pair style

neb:      nudged elastic band (NEB) calculation for barrier finding

nemd:     non-equilibrium MD of 2d sheared system

numdiff: numerical difference computation of forces

obstacle: flow around two voids in a 2d channel

peptide:  dynamics of a small solvated peptide chain (5-mer)

peri:     Peridynamic model of cylinder impacted by indenter