clarify LJ energy function component of the quartic bond style
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@ -28,11 +28,18 @@ The *quartic* bond style uses the potential
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.. math::
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.. math::
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E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 + 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
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E & = E_q + E_{LJ} \\
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E_q & = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 \\
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E_{LJ} & = \left\{ \begin{array} {l@{\quad:\quad}l}
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4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon & r < 2^{\frac{1}{6}}, \epsilon = 1, \sigma = 1 \\
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0 & r >= 2^{\frac{1}{6}}
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\end{array} \right.
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to define a bond that can be broken as the simulation proceeds (e.g.
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to define a bond that can be broken as the simulation proceeds (e.g.
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due to a polymer being stretched). The :math:`\sigma` and :math:`\epsilon` used in the
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due to a polymer being stretched). The :math:`\sigma` and
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LJ portion of the formula are both set equal to 1.0 by LAMMPS.
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:math:`\epsilon` used in the LJ portion of the formula are both set
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equal to 1.0 by LAMMPS and the LJ portion is cut off at its minimum,
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i.e. at :math:`r_c = 2^{\frac{1}{6}}`.
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The following coefficients must be defined for each bond type via the
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The following coefficients must be defined for each bond type via the
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:doc:`bond_coeff <bond_coeff>` command as in the example above, or in
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:doc:`bond_coeff <bond_coeff>` command as in the example above, or in
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@ -46,9 +53,9 @@ or :doc:`read_restart <read_restart>` commands:
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* :math:`U_0` (energy)
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* :math:`U_0` (energy)
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This potential was constructed to mimic the FENE bond potential for
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This potential was constructed to mimic the FENE bond potential for
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coarse-grained polymer chains. When monomers with :math:`\sigma = \epsilon = 1.0`
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coarse-grained polymer chains. When monomers with :math:`\sigma =
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are used, the following choice of parameters gives a quartic potential that
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\epsilon = 1.0` are used, the following choice of parameters gives a
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looks nearly like the FENE potential:
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quartic potential that looks nearly like the FENE potential:
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.. math::
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.. math::
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