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Fixed a couple more mathbf->boldsymbol errors in fix brownian doc

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This commit is contained in:
Karl Hammond
2022-10-15 10:47:33 -05:00
parent 09a14d558d
commit 9e43e9792c
1 changed files with 9 additions and 9 deletions
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18
doc/src/fix_brownian.rst
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@ -93,15 +93,15 @@ updated. This style therefore requires the hybrid atom style
.. math::
\mathbf{\mu}(t+dt) = \frac{\mathbf{\mu}(t) + \mathbf{\omega} \times \mathbf{\mu}dt
}{|\mathbf{\mu}(t) + \mathbf{\omega} \times \mathbf{\mu}|}
\boldsymbol{\mu}(t+dt) = \frac{\boldsymbol{\mu}(t) + \boldsymbol{\omega} \times \boldsymbol{\mu}dt
}{|\boldsymbol{\mu}(t) + \boldsymbol{\omega} \times \boldsymbol{\mu}|}
which correctly reproduces a Boltzmann distribution of orientations and
rotational diffusion moments (see :ref:`(Ilie) <Ilie1>`) when
.. math::
\mathbf{\omega} = \frac{\mathbf{T}}{\gamma_r} + \sqrt{\frac{2 k_B T_{rot}}{\gamma_r}\frac{d\mathbf{W}}{dt}},
\boldsymbol{\omega} = \frac{\mathbf{T}}{\gamma_r} + \sqrt{\frac{2 k_B T_{rot}}{\gamma_r}\frac{d\mathbf{W}}{dt}},
with :math:`d\mathbf{W}` being a random number with zero mean and variance :math:`dt`
and :math:`T_{rot}` is *rotation_temp*.
@ -118,15 +118,15 @@ the quaternion
\mathbf{q}(t+dt) = \frac{\mathbf{q}(t) + d\mathbf{q}}{\lVert\mathbf{q}(t) + d\mathbf{q}\rVert}
which correctly reproduces a Boltzmann distribution of orientations and rotational
diffusion moments [see :ref:`(Ilie) <Ilie1>`] when the quaternion step given by
diffusion moments [see :ref:`(Ilie) <Ilie1>`] when the quaternion step is given by
.. math::
d\mathbf{q} = \mathbf{\Psi}\mathbf{\omega}dt
d\mathbf{q} = \boldsymbol{\Psi}\boldsymbol{\omega}dt
where :math:`\boldsymbol{\Psi}` has rows :math:`(-q_1,-q_2,-q_3)`,
:math:`(q_0,-q_3,q_2)`, :math:`(q_3,q_0,-q_1)`, and :math:`(-q_2,q_1,q_0)`.
:math:`\mathbf{\omega}` is evaluated in the body frame of reference where the
:math:`\boldsymbol{\omega}` is evaluated in the body frame of reference where the
friction tensor is diagonal. See :ref:`(Delong) <Delong1>` for more details of
a similar algorithm.
@ -186,8 +186,8 @@ The *gamma_r_eigen*, and *gamma_t_eigen* keywords are the eigenvalues of
the rotational and viscous damping tensors (having the same units as
their isotropic counterparts). Required for (and only compatible with)
*brownian/asphere*. For a 2D system, the first two values of
*gamma_r_eigen* must be inf (only rotation in xy plane), and the third
value of *gamma_t_eigen* must be inf (only diffusion in xy plane).
*gamma_r_eigen* must be *inf* (only rotation in *x*\ --\ *y* plane), and the third
value of *gamma_t_eigen* must be *inf* (only diffusion in the *x*\ --\ *y* plane).
If the *dipole* keyword is used, then the dipole moments of the particles
are updated as described above. Only compatible with *brownian/asphere*
@ -198,7 +198,7 @@ will be occur at this prescribed temperature instead of *temp*. Only
compatible with *brownian/sphere* and *brownian/asphere*.
If the *planar_rotation* keyword is used, then rotation is constrained
to the xy plane in a 3D simulation. Only compatible with
to the *x*\ -- *y* plane in a 3D simulation. Only compatible with
*brownian/sphere* and *brownian/asphere* in 3D.
----------