From 8a3d0caffd27d0db03851fe671f8f9abad887fce Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 12 Apr 2023 03:36:21 -0400 Subject: [PATCH] consistently apply \vec{} macro to only the first text/character and not subscripts --- doc/src/angle_dipole.rst | 22 +++++------ doc/src/compute_ptm_atom.rst | 4 +- doc/src/fix_precession_spin.rst | 18 ++++----- doc/src/pair_dipole.rst | 66 ++++++++++++++++----------------- doc/src/pair_dpd.rst | 4 +- doc/src/pair_dpd_fdt.rst | 8 ++-- 6 files changed, 61 insertions(+), 61 deletions(-) diff --git a/doc/src/angle_dipole.rst b/doc/src/angle_dipole.rst index 8aaed55132..4bc08d9530 100644 --- a/doc/src/angle_dipole.rst +++ b/doc/src/angle_dipole.rst @@ -28,15 +28,15 @@ The *dipole* angle style is used to control the orientation of a dipolar atom within a molecule :ref:`(Orsi) `. Specifically, the *dipole* angle style restrains the orientation of a point dipole :math:`\mu_j` (embedded in atom :math:`j`) with respect to a reference (bond) vector -:math:`\vec{r_{ij}} = \vec{r_i} - \vec{r_j}`, where :math:`i` is another atom of +:math:`\vec{r}_{ij} = \vec{r}_i - \vec{r}_j`, where :math:`i` is another atom of the same molecule (typically, :math:`i` and :math:`j` are also covalently bonded). -It is convenient to define an angle gamma between the 'free' vector :math:`\vec{\mu_j}` -and the reference (bond) vector :math:`\vec{r_{ij}}`: +It is convenient to define an angle gamma between the 'free' vector :math:`\vec{\mu}_j` +and the reference (bond) vector :math:`\vec{r}_{ij}`: .. math:: - \cos\gamma = \frac{\vec{\mu_j}\cdot\vec{r_{ij}}}{\mu_j\,r_{ij}} + \cos\gamma = \frac{\vec{\mu}_j\cdot\vec{r}_{ij}}{\mu_j\,r_{ij}} The *dipole* angle style uses the potential: @@ -53,23 +53,23 @@ potential using the 'chain rule' as in appendix C.3 of .. math:: - \vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\, \vec{r_{ij}} \times \vec{\mu_j} + \vec{T}_j = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\, \vec{r}_{ij} \times \vec{\mu}_j Example: if :math:`\gamma_0` is set to 0 degrees, the torque generated by the potential will tend to align the dipole along the reference -direction defined by the (bond) vector :math:`\vec{r_{ij}}` (in other words, :math:`\vec{\mu_j}` is +direction defined by the (bond) vector :math:`\vec{r}_{ij}` (in other words, :math:`\vec{\mu}_j` is restrained to point towards atom :math:`i`). -The dipolar torque :math:`\vec{T_j}` must be counterbalanced in order to conserve +The dipolar torque :math:`\vec{T}_j` must be counterbalanced in order to conserve the local angular momentum. This is achieved via an additional force -couple generating a torque equivalent to the opposite of :math:`\vec{T_j}`: +couple generating a torque equivalent to the opposite of :math:`\vec{T}_j`: .. math:: - -\vec{T_j} & = \vec{r_{ij}} \times \vec{F_i} \\ - \vec{F_j} & = -\vec{F_i} + -\vec{T}_j & = \vec{r}_{ij} \times \vec{F}_i \\ + \vec{F}_j & = -\vec{F}_i -where :math:`\vec{F_i}` and :math:`\vec{F_j}` are applied on atoms :math:`i` +where :math:`\vec{F}_i` and :math:`\vec{F}_j` are applied on atoms :math:`i` and :math:`j`, respectively. The following coefficients must be defined for each angle type via the diff --git a/doc/src/compute_ptm_atom.rst b/doc/src/compute_ptm_atom.rst index 3d024802ab..a47684224a 100644 --- a/doc/src/compute_ptm_atom.rst +++ b/doc/src/compute_ptm_atom.rst @@ -66,8 +66,8 @@ The deviation is calculated as: \text{RMSD}(\mathbf{u}, \mathbf{v}) = \min_{s, \mathbf{Q}} \sqrt{\frac{1}{N} \sum\limits_{i=1}^{N} - {\left\lVert s[\vec{u_i} - \mathbf{\bar{u}}] - - \mathbf{Q} \cdot \vec{v_i} \right\rVert}^2} + {\left\lVert s[\vec{u}_i - \mathbf{\bar{u}}] + - \mathbf{Q} \cdot \vec{v}_i \right\rVert}^2} Here, :math:`\vec u` and :math:`\vec v` contain the coordinates of the local and ideal structures respectively, :math:`s` is a scale factor, and diff --git a/doc/src/fix_precession_spin.rst b/doc/src/fix_precession_spin.rst index 36a10c8ce6..7440989d7a 100644 --- a/doc/src/fix_precession_spin.rst +++ b/doc/src/fix_precession_spin.rst @@ -103,15 +103,15 @@ possible easy axis for the magnetic spins in the defined group: H_{cubic} = -\sum_{{ i}=1}^{N} K_{1} \Big[ - \left(\vec{s}_{i} \cdot \vec{n_1} \right)^2 - \left(\vec{s}_{i} \cdot \vec{n_2} \right)^2 + - \left(\vec{s}_{i} \cdot \vec{n_2} \right)^2 - \left(\vec{s}_{i} \cdot \vec{n_3} \right)^2 + - \left(\vec{s}_{i} \cdot \vec{n_1} \right)^2 - \left(\vec{s}_{i} \cdot \vec{n_3} \right)^2 \Big] - +K_{2}^{(c)} \left(\vec{s}_{i} \cdot \vec{n_1} \right)^2 - \left(\vec{s}_{i} \cdot \vec{n_2} \right)^2 - \left(\vec{s}_{i} \cdot \vec{n_3} \right)^2 + \left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2 + \left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2 + + \left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2 + \left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 + + \left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2 + \left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 \Big] + +K_{2}^{(c)} \left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2 + \left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2 + \left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 with :math:`K_1` and :math:`K_{2c}` (in eV) the intensity coefficients and :math:`\vec{n}_1`, :math:`\vec{n}_2` and :math:`\vec{n}_3` diff --git a/doc/src/pair_dipole.rst b/doc/src/pair_dipole.rst index 10d0061948..bea80bfc45 100644 --- a/doc/src/pair_dipole.rst +++ b/doc/src/pair_dipole.rst @@ -96,29 +96,29 @@ force (F), and torque (T) between particles I and J. \left(\frac{\sigma}{r}\right)^6 \right] \\ E_{qq} = & \frac{q_i q_j}{r} \\ E_{qp} = & \frac{q}{r^3} (p \bullet \vec{r}) \\ - E_{pp} = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) - - \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r}) \\ + E_{pp} = & \frac{1}{r^3} (\vec{p}_i \bullet \vec{p}_j) - + \frac{3}{r^5} (\vec{p}_i \bullet \vec{r}) (\vec{p}_j \bullet \vec{r}) \\ & \\ F_{qq} = & \frac{q_i q_j}{r^3} \vec{r} \\ F_{qp} = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5} (\vec{p} \bullet \vec{r}) \vec{r} \\ - F_{pp} = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} - - \frac{15}{r^7} (\vec{p_i} \bullet \vec{r}) - (\vec{p_j} \bullet \vec{r}) \vec{r} + - \frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + - (\vec{p_i} \bullet \vec{r}) \vec{p_j} \right] \\ + F_{pp} = & \frac{3}{r^5} (\vec{p}_i \bullet \vec{p}_j) \vec{r} - + \frac{15}{r^7} (\vec{p}_i \bullet \vec{r}) + (\vec{p}_j \bullet \vec{r}) \vec{r} + + \frac{3}{r^5} \left[ (\vec{p}_j \bullet \vec{r}) \vec{p}_i + + (\vec{p}_i \bullet \vec{r}) \vec{p}_j \right] \\ & \\ - T_{pq} = T_{ij} = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\ - T_{qp} = T_{ji} = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\ - T_{pp} = T_{ij} = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) + - \frac{3}{r^5} (\vec{p_j} \bullet \vec{r}) - (\vec{p_i} \times \vec{r}) \\ - T_{pp} = T_{ji} = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) + - \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) - (\vec{p_j} \times \vec{r}) + T_{pq} = T_{ij} = & \frac{q_j}{r^3} (\vec{p}_i \times \vec{r}) \\ + T_{qp} = T_{ji} = & - \frac{q_i}{r^3} (\vec{p}_j \times \vec{r}) \\ + T_{pp} = T_{ij} = & -\frac{1}{r^3} (\vec{p}_i \times \vec{p}_j) + + \frac{3}{r^5} (\vec{p}_j \bullet \vec{r}) + (\vec{p}_i \times \vec{r}) \\ + T_{pp} = T_{ji} = & -\frac{1}{r^3} (\vec{p}_j \times \vec{p}_i) + + \frac{3}{r^5} (\vec{p}_i \bullet \vec{r}) + (\vec{p}_j \times \vec{r}) where :math:`q_i` and :math:`q_j` are the charges on the two -particles, :math:`\vec{p_i}` and :math:`\vec{p_j}` are the dipole +particles, :math:`\vec{p}_i` and :math:`\vec{p}_j` are the dipole moment vectors of the two particles, r is their separation distance, and the vector r = Ri - Rj is the separation vector between the two particles. Note that Eqq and Fqq are simply Coulombic energy and @@ -163,8 +163,8 @@ energy (E), force (F), and torque (T) between particles I and J: 2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\ E_{pp} = & \left[1-4\left(\frac{r}{r_c}\right)^{\!3} + 3\left(\frac{r}{r_c}\right)^{\!4}\right]\left[\frac{1}{r^3} - (\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5} - (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right] \\ + (\vec{p}_i \bullet \vec{p}_j) - \frac{3}{r^5} + (\vec{p}_i \bullet \vec{r}) (\vec{p}_j \bullet \vec{r})\right] \\ & \\ F_{LJ} = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{\!12} - @@ -182,37 +182,37 @@ energy (E), force (F), and torque (T) between particles I and J: \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} + 2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\ F_{pp} = &\frac{3}{r^5}\Bigg\{\left[1-\left(\frac{r}{r_c}\right)^{\!4}\right] - \left[(\vec{p_i}\bullet\vec{p_j}) - \frac{3}{r^2} (\vec{p_i}\bullet\vec{r}) - (\vec{p_j} \bullet \vec{r})\right] \vec{r} + \\ + \left[(\vec{p}_i\bullet\vec{p}_j) - \frac{3}{r^2} (\vec{p}_i\bullet\vec{r}) + (\vec{p}_j \bullet \vec{r})\right] \vec{r} + \\ & \left[1 - 4\left(\frac{r}{r_c}\right)^{\!3}+3\left(\frac{r}{r_c}\right)^{\!4}\right] - \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + (\vec{p_i} \bullet \vec{r}) - \vec{p_j} -\frac{2}{r^2} (\vec{p_i} \bullet \vec{r}) - (\vec{p_j} \bullet \vec{r})\vec{r}\right] \Bigg\} + \left[ (\vec{p}_j \bullet \vec{r}) \vec{p}_i + (\vec{p}_i \bullet \vec{r}) + \vec{p}_j -\frac{2}{r^2} (\vec{p}_i \bullet \vec{r}) + (\vec{p}_j \bullet \vec{r})\vec{r}\right] \Bigg\} .. math:: T_{pq} = T_{ij} = & \frac{q_j}{r^3} \left[ 1 - 3\left(\frac{r}{r_c}\right)^{\!2} + - 2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\ + 2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}_i\times\vec{r}) \\ T_{qp} = T_{ji} = & - \frac{q_i}{r^3} \left[ 1 - 3\left(\frac{r}{r_c}\right)^{\!2} + - 2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\ + 2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p}_j\times\vec{r}) \\ T_{pp} = T_{ij} = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} + - e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\ + e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p}_i \times \vec{p}_j) + \\ & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} + - 3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r}) - (\vec{p_i} \times \vec{r}) \\ + 3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p}_j\bullet\vec{r}) + (\vec{p}_i \times \vec{r}) \\ T_{pp} = T_{ji} = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} + - 3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\ + 3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p}_j \times \vec{p}_i) + \\ & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} + - 3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r}) - (\vec{p_j} \times \vec{r}) + 3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p}_i \bullet \vec{r}) + (\vec{p}_j \times \vec{r}) where :math:`\epsilon` and :math:`\sigma` are the standard LJ parameters, :math:`r_c` is the cutoff, :math:`q_i` and :math:`q_j` are -the charges on the two particles, :math:`\vec{p_i}` and -:math:`\vec{p_j}` are the dipole moment vectors of the two particles, +the charges on the two particles, :math:`\vec{p}_i` and +:math:`\vec{p}_j` are the dipole moment vectors of the two particles, r is their separation distance, and the vector r = Ri - Rj is the separation vector between the two particles. Note that Eqq and Fqq are simply Coulombic energy and force, Fij = -Fji as symmetric forces, diff --git a/doc/src/pair_dpd.rst b/doc/src/pair_dpd.rst index aef085ca6e..815fe46cdc 100644 --- a/doc/src/pair_dpd.rst +++ b/doc/src/pair_dpd.rst @@ -68,13 +68,13 @@ of 3 terms \vec{f} = & (F^C + F^D + F^R) \hat{r_{ij}} \qquad \qquad r < r_c \\ F^C = & A w(r) \\ - F^D = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v_{ij}}) \\ + F^D = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v}_{ij}) \\ F^R = & \sigma w(r) \alpha (\Delta t)^{-1/2} \\ w(r) = & 1 - \frac{r}{r_c} where :math:`F^C` is a conservative force, :math:`F^D` is a dissipative force, and :math:`F^R` is a random force. :math:`\hat{r_{ij}}` is a -unit vector in the direction :math:`r_i - r_j`, :math:`\vec{v_{ij}}` is +unit vector in the direction :math:`r_i - r_j`, :math:`\vec{v}_{ij}` is the vector difference in velocities of the two atoms :math:`\vec{v}_i - \vec{v}_j`, :math:`\alpha` is a Gaussian random number with zero mean and unit variance, *dt* is the timestep size, and :math:`w(r)` is a diff --git a/doc/src/pair_dpd_fdt.rst b/doc/src/pair_dpd_fdt.rst index 133e7ab52c..efe7b3ed66 100644 --- a/doc/src/pair_dpd_fdt.rst +++ b/doc/src/pair_dpd_fdt.rst @@ -56,13 +56,13 @@ given as a sum of 3 terms \vec{f} = & (F^C + F^D + F^R) \hat{r_{ij}} \qquad \qquad r < r_c \\ F^C = & A w(r) \\ - F^D = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v_{ij}}) \\ + F^D = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v}_{ij}) \\ F^R = & \sigma w(r) \alpha (\Delta t)^{-1/2} \\ w(r) = & 1 - \frac{r}{r_c} where :math:`F^C` is a conservative force, :math:`F^D` is a dissipative force, and :math:`F^R` is a random force. :math:`\hat{r_{ij}}` is a -unit vector in the direction :math:`r_i - r_j`, :math:`\vec{v_{ij}}` is +unit vector in the direction :math:`r_i - r_j`, :math:`\vec{v}_{ij}` is the vector difference in velocities of the two atoms, :math:`\vec{v}_i - \vec{v}_j`, :math:`\alpha` is a Gaussian random number with zero mean and unit variance, *dt* is the timestep size, and :math:`w(r)` is a @@ -99,9 +99,9 @@ energies are computed within style *dpd/fdt/energy* as: .. math:: du_{i}^{cond} = & \kappa_{ij}(\frac{1}{\theta_{i}}-\frac{1}{\theta_{j}})\omega_{ij}^{2} + \alpha_{ij}\omega_{ij}\zeta_{ij}^{q}(\Delta{t})^{-1/2} \\ - du_{i}^{mech} = & -\frac{1}{2}\gamma_{ij}\omega_{ij}^{2}(\frac{\vec{r_{ij}}}{r_{ij}}\bullet\vec{v_{ij}})^{2} - + du_{i}^{mech} = & -\frac{1}{2}\gamma_{ij}\omega_{ij}^{2}(\frac{\vec{r}_{ij}}{r_{ij}}\bullet\vec{v}_{ij})^{2} - \frac{\sigma^{2}_{ij}}{4}(\frac{1}{m_{i}}+\frac{1}{m_{j}})\omega_{ij}^{2} - - \frac{1}{2}\sigma_{ij}\omega_{ij}(\frac{\vec{r_{ij}}}{r_{ij}}\bullet\vec{v_{ij}})\zeta_{ij}(\Delta{t})^{-1/2} + \frac{1}{2}\sigma_{ij}\omega_{ij}(\frac{\vec{r}_{ij}}{r_{ij}}\bullet\vec{v}_{ij})\zeta_{ij}(\Delta{t})^{-1/2} where