81 lines
2.2 KiB
ReStructuredText
81 lines
2.2 KiB
ReStructuredText
.. index:: angle_style cosine/shift/exp
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.. index:: angle_style cosine/shift/exp/omp
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angle_style cosine/shift/exp command
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====================================
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Accelerator Variants: *cosine/shift/exp/omp*
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Syntax
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""""""
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.. code-block:: LAMMPS
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angle_style cosine/shift/exp
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Examples
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""""""""
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.. code-block:: LAMMPS
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angle_style cosine/shift/exp
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angle_coeff * 10.0 45.0 2.0
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Description
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"""""""""""
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The *cosine/shift/exp* angle style uses the potential
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.. math::
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E = -U_{\text{min}} \frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1} \quad \text{with} \quad U(\theta,\theta_0) = -0.5 \left(1+\cos(\theta-\theta_0) \right)
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where :math:`U_{\text{min}}`, :math:`\theta`, and :math:`a` are defined for each angle type.
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The potential is bounded between :math:`[-U_{\text{min}}, 0]` and the minimum is
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located at the angle :math:`\theta_0`. The a parameter can be both positive or
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negative and is used to control the spring constant at the
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equilibrium.
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The spring constant is given by :math:`k = A \exp(A) U_{\text{min}} / [2 (\exp(a)-1)]`.
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For :math:`a > 3`, :math:`\frac{k}{U_{\text{min}}} = \frac{a}{2}` to better than 5% relative error. For negative
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values of the :math:`a` parameter, the spring constant is essentially zero,
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and anharmonic terms takes over. The potential is furthermore well
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behaved in the limit :math:`a \rightarrow 0`, where it has been implemented to linear
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order in :math:`a` for :math:`a < 0.001`. In this limit the potential reduces to the
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cosineshifted potential.
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The following coefficients must be defined for each angle type via the
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:doc:`angle_coeff <angle_coeff>` command as in the example above, or in
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the data file or restart files read by the :doc:`read_data <read_data>`
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or :doc:`read_restart <read_restart>` commands:
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* :math:`U_min` (energy)
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* :math:`\theta` (angle)
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* :math:`A` (real number)
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----------
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.. include:: accel_styles.rst
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----------
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Restrictions
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""""""""""""
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This angle style can only be used if LAMMPS was built with the
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EXTRA-MOLECULE package. See the :doc:`Build package <Build_package>` doc
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page for more info.
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Related commands
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""""""""""""""""
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:doc:`angle_coeff <angle_coeff>`,
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:doc:`angle_style cosine/shift <angle_cosine_shift>`,
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:doc:`dihedral_style cosine/shift/exp <dihedral_cosine_shift_exp>`
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Default
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"""""""
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none
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