added angle_mesocnt documentation

doc/src/angle_mesocnt.rst

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+.. index:: angle_style mesocnt
+
+angle_style mesocnt command
+===========================
+
+Syntax
+""""""
+
+.. code-block:: LAMMPS
+
+   angle_style mesocnt
+
+Examples
+""""""""
+
+.. code-block:: LAMMPS
+
+   angle_style mesocnt
+   angle_coeff 1 buckling C 10 10 20.0
+   angle_coeff 4 harmonic C 8 4 10.0
+   angle_coeff 2 buckling custom 400.0 50.0 5.0
+   angle_coeff 1 harmonic custom 300.0
+
+Description
+"""""""""""
+
+The *mesocnt* angle style uses the potential
+
+.. math::
+
+   E = K_\text{H} \Delta \theta^2 \qquad |\Delta| \theta < \Delta \theta_\text{B} \\ 
+   E = K_\text{H} \theta_\text{B}^2 + K_\text{B} (\Delta \theta - \theta_\text{B}) \qquad |\Delta| \theta \geq \Delta \theta_\text{B}
+
+where :math:`\Delta \theta = \theta - \pi` is the bending angle of the nanotube, :math:`K_\text{H}` and :math:`K_\text{B}` are prefactors for the harmonic and linear regime respectively and :math:`\theta_\text{B}` is the buckling angle. Note that the usual 1/2 factor for the harmonic potential is included in :math:`K_\text{H}`.
+
+The style implements parametrisation presets of :math:`K_\text{H}`, :math:`K_\text{B}` and :math:`\theta_\text{B}` for mesoscopic simulations of 
+carbon nanotubes based on the atomistic simulations of :ref:`(Zhigilei) <Zhigilei>` and buckling considerations of :ref:`(Volkov) <Volkov>`.
+
+The following coefficients must be defined for each angle type via the
+:doc:`angle_coeff <angle_coeff>` command as in the examples above, or in
+the data file or restart files read by the :doc:`read_data <read_data>`
+or :doc:`read_restart <read_restart>` commands:
+
+* mode = *buckling* or *harmonic*
+* preset = *C* or *custom*
+* additional parameters depending on preset
+
+If mode *harmonic* is chosen, the potential is simply harmonic and does not switch to the linear term when the buckling angle is reached. In *buckling* mode, the full piecewise potential is used.
+
+Preset *C* is for carbon nanotubes, and the additional parameters are:
+
+* chiral index :math:`n` (unitless)
+* chiral index :math:`m` (unitless)
+* :math:`r_0` (distance)
+
+Here, :math:`r_0` is the equilibrium distance of the bonds included in the angle, see :doc:`bond_style mesocnt <bond_mesocnt>`.
+
+In harmonic mode with preset *custom*, the additional paramter is:
+
+* :math:`K_\text{H}` (energy)
+
+Hence, this setting is simply a wrapper for :doc:`bond_style harmonic <bond_harmonic>` with an equilibrium angle of 180 degrees.
+
+In harmonic mode with preset *custom*, the additional paramters are:
+
+* :math:`K_\text{H}` (energy)
+* :math:`K_\text{B}` (energy)
+* :math:`\theta_\text{B}` (degrees)
+
+:math:`\theta_\text{B}` is specified in degrees, but LAMMPS converts it to
+radians internally; hence :math:`K_\text{H}` is effectively energy per
+radian\^2 and :math:`K_\text{B}` is energy per radian.
+
+----------
+
+In *buckling* mode, this angle style adds the *buckled* property to all atoms in the simulation, which is an integer flag indicating whether the bending angle at a given atom has exceeded :math:`\theta_\text{B}`. It can be accessed as an atomic variable, e.g. for custom dump commands, as *i_buckled*. 
+
+Restrictions
+""""""""""""
+
+This angle style can only be used if LAMMPS was built with the
+MOLECULE and MESONT packages.  See the :doc:`Build package <Build_package>` doc
+page for more info.
+
+Related commands
+""""""""""""""""
+
+:doc:`angle_coeff <angle_coeff>`
+
+Default
+"""""""
+
+none
+
+----------
+
+.. _Zhigilei:
+
+**(Zhigilei)** Zhigilei, Wei and Srivastava, Phys. Rev. B 71, 165417 (2005).
+
+.. _Volkov:
+
+**(Volkov)** Volkov and Zhigilei, ACS Nano 4, 10, 6187–6195 (2010).