diff --git a/doc/src/Howto_peri.rst b/doc/src/Howto_peri.rst index 29eb685c81..fa299e7f84 100644 --- a/doc/src/Howto_peri.rst +++ b/doc/src/Howto_peri.rst @@ -197,7 +197,7 @@ The LPS model has a force scalar state .. math:: \underline{t} = \frac{3K\theta}{m}\underline{\omega}\,\underline{x} + - \alpha \underline{\omega}\,\underline{e}^{\rm d}, \qquad\qquad\textrm{(3)} + \alpha \underline{\omega}\,\underline{e}^\mathrm{d}, \qquad\qquad\textrm{(3)} with :math:`K` the bulk modulus and :math:`\alpha` related to the shear modulus :math:`G` as @@ -242,14 +242,14 @@ scalar state are defined, respectively, as .. math:: - \underline{e}^{\rm i}=\frac{\theta \underline{x}}{3}, \qquad - \underline{e}^{\rm d} = \underline{e}- \underline{e}^{\rm i}, + \underline{e}^\mathrm{i}=\frac{\theta \underline{x}}{3}, \qquad + \underline{e}^\mathrm{d} = \underline{e}- \underline{e}^\mathrm{i}, where the arguments of the state functions and the vectors on which they operate are omitted for simplicity. We note that the LPS model is linear in the dilatation :math:`\theta`, and in the deviatoric part of the -extension :math:`\underline{e}^{\rm d}`. +extension :math:`\underline{e}^\mathrm{d}`. .. note:: diff --git a/doc/src/Howto_triclinic.rst b/doc/src/Howto_triclinic.rst index 3529579d65..24ac66e103 100644 --- a/doc/src/Howto_triclinic.rst +++ b/doc/src/Howto_triclinic.rst @@ -249,23 +249,23 @@ as follows: .. math:: - a = & {\rm lx} \\ - b^2 = & {\rm ly}^2 + {\rm xy}^2 \\ - c^2 = & {\rm lz}^2 + {\rm xz}^2 + {\rm yz}^2 \\ - \cos{\alpha} = & \frac{{\rm xy}*{\rm xz} + {\rm ly}*{\rm yz}}{b*c} \\ - \cos{\beta} = & \frac{\rm xz}{c} \\ - \cos{\gamma} = & \frac{\rm xy}{b} \\ + a = & \mathrm{lx} \\ + b^2 = & \mathrm{ly}^2 + \mathrm{xy}^2 \\ + c^2 = & \mathrm{lz}^2 + \mathrm{xz}^2 + \mathrm{yz}^2 \\ + \cos{\alpha} = & \frac{\mathrm{xy}*\mathrm{xz} + \mathrm{ly}*\mathrm{yz}}{b*c} \\ + \cos{\beta} = & \frac{\mathrm{xz}}{c} \\ + \cos{\gamma} = & \frac{\mathrm{xy}}{b} \\ The inverse relationship can be written as follows: .. math:: - {\rm lx} = & a \\ - {\rm xy} = & b \cos{\gamma} \\ - {\rm xz} = & c \cos{\beta}\\ - {\rm ly}^2 = & b^2 - {\rm xy}^2 \\ - {\rm yz} = & \frac{b*c \cos{\alpha} - {\rm xy}*{\rm xz}}{\rm ly} \\ - {\rm lz}^2 = & c^2 - {\rm xz}^2 - {\rm yz}^2 \\ + \mathrm{lx} = & a \\ + \mathrm{xy} = & b \cos{\gamma} \\ + \mathrm{xz} = & c \cos{\beta}\\ + \mathrm{ly}^2 = & b^2 - \mathrm{xy}^2 \\ + \mathrm{yz} = & \frac{b*c \cos{\alpha} - \mathrm{xy}*\mathrm{xz}}{\mathrm{ly}} \\ + \mathrm{lz}^2 = & c^2 - \mathrm{xz}^2 - \mathrm{yz}^2 \\ The values of *a*, *b*, *c*, :math:`\alpha` , :math:`\beta`, and :math:`\gamma` can be printed out or accessed by computes using the diff --git a/doc/src/compute_cna_atom.rst b/doc/src/compute_cna_atom.rst index 925159951c..33329d88d6 100644 --- a/doc/src/compute_cna_atom.rst +++ b/doc/src/compute_cna_atom.rst @@ -67,7 +67,7 @@ following relation should also be satisfied: .. math:: - r_c + r_s > 2*{\rm cutoff} + r_c + r_s > 2*\mathrm{cutoff} where :math:`r_c` is the cutoff distance of the potential, :math:`r_s` is the skin diff --git a/doc/src/compute_cnp_atom.rst b/doc/src/compute_cnp_atom.rst index 41fdb8324e..94dec390f4 100644 --- a/doc/src/compute_cnp_atom.rst +++ b/doc/src/compute_cnp_atom.rst @@ -74,7 +74,7 @@ following relation should also be satisfied: .. math:: - r_c + r_s > 2*{\rm cutoff} + r_c + r_s > 2*\mathrm{cutoff} where :math:`r_c` is the cutoff distance of the potential, :math:`r_s` is the skin diff --git a/doc/src/compute_efield_wolf_atom.rst b/doc/src/compute_efield_wolf_atom.rst index 93bfa55151..572ca59ab4 100644 --- a/doc/src/compute_efield_wolf_atom.rst +++ b/doc/src/compute_efield_wolf_atom.rst @@ -50,9 +50,9 @@ the potential energy using the Wolf summation method, described in .. math:: E_i = \frac{1}{2} \sum_{j \neq i} - \frac{q_i q_j {\rm erfc}(\alpha r_{ij})}{r_{ij}} + + \frac{q_i q_j \mathrm{erfc}(\alpha r_{ij})}{r_{ij}} + \frac{1}{2} \sum_{j \neq i} - \frac{q_i q_j {\rm erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c + \frac{q_i q_j \mathrm{erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c where :math:`\alpha` is the damping parameter, and *erf()* and *erfc()* are error-function and complementary error-function terms. This diff --git a/doc/src/compute_hexorder_atom.rst b/doc/src/compute_hexorder_atom.rst index 1fb8113a89..ea937f2e00 100644 --- a/doc/src/compute_hexorder_atom.rst +++ b/doc/src/compute_hexorder_atom.rst @@ -40,7 +40,7 @@ is a complex number (stored as two real numbers) defined as follows: .. math:: - q_n = \frac{1}{nnn}\sum_{j = 1}^{nnn} e^{n i \theta({\bf r}_{ij})} + q_n = \frac{1}{nnn}\sum_{j = 1}^{nnn} e^{n i \theta({\textbf{r}}_{ij})} where the sum is over the *nnn* nearest neighbors of the central atom. The angle :math:`\theta` diff --git a/doc/src/compute_stress_atom.rst b/doc/src/compute_stress_atom.rst index e047423640..6c4e0b690c 100644 --- a/doc/src/compute_stress_atom.rst +++ b/doc/src/compute_stress_atom.rst @@ -65,7 +65,7 @@ In case of compute *stress/atom*, the virial contribution is: W_{ab} & = \frac{1}{2} \sum_{n = 1}^{N_p} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) + \frac{1}{2} \sum_{n = 1}^{N_b} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) \\ & + \frac{1}{3} \sum_{n = 1}^{N_a} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + r_{3_a} F_{3_b}) + \frac{1}{4} \sum_{n = 1}^{N_d} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) \\ - & + \frac{1}{4} \sum_{n = 1}^{N_i} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) + {\rm Kspace}(r_{i_a},F_{i_b}) + \sum_{n = 1}^{N_f} r_{i_a} F_{i_b} + & + \frac{1}{4} \sum_{n = 1}^{N_i} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) + \mathrm{Kspace}(r_{i_a},F_{i_b}) + \sum_{n = 1}^{N_f} r_{i_a} F_{i_b} The first term is a pairwise energy contribution where :math:`n` loops over the :math:`N_p` neighbors of atom :math:`I`, :math:`\mathbf{r}_1` @@ -97,7 +97,7 @@ In case of compute *centroid/stress/atom*, the virial contribution is: .. math:: W_{ab} & = \sum_{n = 1}^{N_p} r_{I0_a} F_{I_b} + \sum_{n = 1}^{N_b} r_{I0_a} F_{I_b} + \sum_{n = 1}^{N_a} r_{I0_a} F_{I_b} + \sum_{n = 1}^{N_d} r_{I0_a} F_{I_b} + \sum_{n = 1}^{N_i} r_{I0_a} F_{I_b} \\ - & + {\rm Kspace}(r_{i_a},F_{i_b}) + \sum_{n = 1}^{N_f} r_{i_a} F_{i_b} + & + \mathrm{Kspace}(r_{i_a},F_{i_b}) + \sum_{n = 1}^{N_f} r_{i_a} F_{i_b} As with compute *stress/atom*, the first, second, third, fourth and fifth terms are pairwise, bond, angle, dihedral and improper diff --git a/doc/src/fitpod_command.rst b/doc/src/fitpod_command.rst index de52e0545b..e1f2c47c60 100644 --- a/doc/src/fitpod_command.rst +++ b/doc/src/fitpod_command.rst @@ -263,10 +263,10 @@ then the globally defined weights from the ``fitting_weight_energy`` and POD Potential """"""""""""" -We consider a multi-element system of *N* atoms with :math:`N_{\rm e}` +We consider a multi-element system of *N* atoms with :math:`N_\mathrm{e}` unique elements. We denote by :math:`\boldsymbol r_n` and :math:`Z_n` position vector and type of an atom *n* in the system, -respectively. Note that we have :math:`Z_n \in \{1, \ldots, N_{\rm e} +respectively. Note that we have :math:`Z_n \in \{1, \ldots, N_\mathrm{e} \}`, :math:`\boldsymbol R = (\boldsymbol r_1, \boldsymbol r_2, \ldots, \boldsymbol r_N) \in \mathbb{R}^{3N}`, and :math:`\boldsymbol Z = (Z_1, Z_2, \ldots, Z_N) \in \mathbb{N}^{N}`. The total energy of the diff --git a/doc/src/fix_nh.rst b/doc/src/fix_nh.rst index 0cfbc8f921..0a4076364c 100644 --- a/doc/src/fix_nh.rst +++ b/doc/src/fix_nh.rst @@ -208,19 +208,19 @@ The relaxation rate of the barostat is set by its inertia :math:`W`: .. math:: - W = (N + 1) k_B T_{\rm target} P_{\rm damp}^2 + W = (N + 1) k_B T_\mathrm{target} P_\mathrm{damp}^2 where :math:`N` is the number of atoms, :math:`k_B` is the Boltzmann constant, -and :math:`T_{\rm target}` is the target temperature of the barostat :ref:`(Martyna) `. -If a thermostat is defined, :math:`T_{\rm target}` is the target temperature -of the thermostat. If a thermostat is not defined, :math:`T_{\rm target}` +and :math:`T_\mathrm{target}` is the target temperature of the barostat :ref:`(Martyna) `. +If a thermostat is defined, :math:`T_\mathrm{target}` is the target temperature +of the thermostat. If a thermostat is not defined, :math:`T_\mathrm{target}` is set to the current temperature of the system when the barostat is initialized. If this temperature is too low the simulation will quit with an error. -Note: in previous versions of LAMMPS, :math:`T_{\rm target}` would default to +Note: in previous versions of LAMMPS, :math:`T_\mathrm{target}` would default to a value of 1.0 for *lj* units and 300.0 otherwise if the system had a temperature of exactly zero. -If a thermostat is not specified by this fix, :math:`T_{\rm target}` can be +If a thermostat is not specified by this fix, :math:`T_\mathrm{target}` can be manually specified using the *Ptemp* parameter. This may be useful if the barostat is initialized when the current temperature does not reflect the steady state temperature of the system. This keyword may also be useful in @@ -512,8 +512,8 @@ according to the following factorization of the Liouville propagator .. math:: \exp \left(\mathrm{i} L \Delta t \right) = & \hat{E} - \exp \left(\mathrm{i} L_{\rm T\textrm{-}baro} \frac{\Delta t}{2} \right) - \exp \left(\mathrm{i} L_{\rm T\textrm{-}part} \frac{\Delta t}{2} \right) + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}baro} \frac{\Delta t}{2} \right) + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}part} \frac{\Delta t}{2} \right) \exp \left(\mathrm{i} L_{\epsilon , 2} \frac{\Delta t}{2} \right) \exp \left(\mathrm{i} L_{2}^{(2)} \frac{\Delta t}{2} \right) \\ &\times \left[ @@ -526,8 +526,8 @@ according to the following factorization of the Liouville propagator &\times \exp \left(\mathrm{i} L_{2}^{(2)} \frac{\Delta t}{2} \right) \exp \left(\mathrm{i} L_{\epsilon , 2} \frac{\Delta t}{2} \right) - \exp \left(\mathrm{i} L_{\rm T\textrm{-}part} \frac{\Delta t}{2} \right) - \exp \left(\mathrm{i} L_{\rm T\textrm{-}baro} \frac{\Delta t}{2} \right) \\ + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}part} \frac{\Delta t}{2} \right) + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}baro} \frac{\Delta t}{2} \right) \\ &+ \mathcal{O} \left(\Delta t^3 \right) This factorization differs somewhat from that of Tuckerman et al, in diff --git a/doc/src/fix_npt_cauchy.rst b/doc/src/fix_npt_cauchy.rst index 6764f88eee..862a0b546e 100644 --- a/doc/src/fix_npt_cauchy.rst +++ b/doc/src/fix_npt_cauchy.rst @@ -426,8 +426,8 @@ according to the following factorization of the Liouville propagator .. math:: \exp \left(\mathrm{i} L \Delta t \right) = & \hat{E} - \exp \left(\mathrm{i} L_{\rm T\textrm{-}baro} \frac{\Delta t}{2} \right) - \exp \left(\mathrm{i} L_{\rm T\textrm{-}part} \frac{\Delta t}{2} \right) + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}baro} \frac{\Delta t}{2} \right) + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}part} \frac{\Delta t}{2} \right) \exp \left(\mathrm{i} L_{\epsilon , 2} \frac{\Delta t}{2} \right) \exp \left(\mathrm{i} L_{2}^{(2)} \frac{\Delta t}{2} \right) \\ &\times \left[ @@ -440,8 +440,8 @@ according to the following factorization of the Liouville propagator &\times \exp \left(\mathrm{i} L_{2}^{(2)} \frac{\Delta t}{2} \right) \exp \left(\mathrm{i} L_{\epsilon , 2} \frac{\Delta t}{2} \right) - \exp \left(\mathrm{i} L_{\rm T\textrm{-}part} \frac{\Delta t}{2} \right) - \exp \left(\mathrm{i} L_{\rm T\textrm{-}baro} \frac{\Delta t}{2} \right) \\ + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}part} \frac{\Delta t}{2} \right) + \exp \left(\mathrm{i} L_\mathrm{T\textrm{-}baro} \frac{\Delta t}{2} \right) \\ &+ \mathcal{O} \left(\Delta t^3 \right) This factorization differs somewhat from that of Tuckerman et al, in diff --git a/doc/src/fix_orient.rst b/doc/src/fix_orient.rst index 7e30b7bb01..881ae6c45c 100644 --- a/doc/src/fix_orient.rst +++ b/doc/src/fix_orient.rst @@ -62,19 +62,19 @@ The potential energy added to atom I is given by these formulas .. math:: - \xi_{i} = & \sum_{j=1}^{12} \left| \mathbf{r}_{j} - \mathbf{r}_{j}^{\rm I} \right| \qquad\qquad\left(1\right) \\ + \xi_{i} = & \sum_{j=1}^{12} \left| \mathbf{r}_{j} - \mathbf{r}_{j}^\mathrm{I} \right| \qquad\qquad\left(1\right) \\ \\ - \xi_{\rm IJ} = & \sum_{j=1}^{12} \left| \mathbf{r}_{j}^{\rm J} - \mathbf{r}_{j}^{\rm I} \right| \qquad\qquad\left(2\right)\\ + \xi_\mathrm{IJ} = & \sum_{j=1}^{12} \left| \mathbf{r}_{j}^\mathrm{J} - \mathbf{r}_{j}^\mathrm{I} \right| \qquad\qquad\left(2\right)\\ \\ - \xi_{\rm low} = & {\rm cutlo} \, \xi_{\rm IJ} \qquad\qquad\qquad\left(3\right)\\ - \xi_{\rm high} = & {\rm cuthi} \, \xi_{\rm IJ} \qquad\qquad\qquad\left(4\right) \\ + \xi_\mathrm{low} = & \mathrm{cutlo} \, \xi_\mathrm{IJ} \qquad\qquad\qquad\left(3\right)\\ + \xi_\mathrm{high} = & \mathrm{cuthi} \, \xi_\mathrm{IJ} \qquad\qquad\qquad\left(4\right) \\ \\ - \omega_{i} = & \frac{\pi}{2} \frac{\xi_{i} - \xi_{\rm low}}{\xi_{\rm high} - \xi_{\rm low}} \qquad\qquad\left(5\right)\\ + \omega_{i} = & \frac{\pi}{2} \frac{\xi_{i} - \xi_\mathrm{low}}{\xi_\mathrm{high} - \xi_\mathrm{low}} \qquad\qquad\left(5\right)\\ \\ - u_{i} = & 0 \quad\quad\qquad\qquad\qquad \textrm{ for } \qquad \xi_{i} < \xi_{\rm low}\\ - = & {\rm dE}\,\frac{1 - \cos(2 \omega_{i})}{2} - \qquad \mathrm{ for }\qquad \xi_{\rm low} < \xi_{i} < \xi_{\rm high} \quad \left(6\right) \\ - = & {\rm dE} \quad\qquad\qquad\qquad\textrm{ for } \qquad \xi_{\rm high} < \xi_{i} + u_{i} = & 0 \quad\quad\qquad\qquad\qquad \textrm{ for } \qquad \xi_{i} < \xi_\mathrm{low}\\ + = & \mathrm{dE}\,\frac{1 - \cos(2 \omega_{i})}{2} + \qquad \mathrm{for }\qquad \xi_\mathrm{low} < \xi_{i} < \xi_\mathrm{high} \quad \left(6\right) \\ + = & \mathrm{dE} \quad\qquad\qquad\qquad\textrm{ for } \qquad \xi_\mathrm{high} < \xi_{i} which are fully explained in :ref:`(Janssens) `. For fcc crystals this order parameter Xi for atom I in equation (1) is a sum over the diff --git a/doc/src/min_modify.rst b/doc/src/min_modify.rst index d36f19b0d5..9e4cb4fbc6 100644 --- a/doc/src/min_modify.rst +++ b/doc/src/min_modify.rst @@ -98,14 +98,14 @@ all atoms .. math:: - || \vec{F} ||_{max} = {\rm max}\left(||\vec{F}_1||, \cdots, ||\vec{F}_N||\right) + || \vec{F} ||_{max} = \mathrm{max}\left(||\vec{F}_1||, \cdots, ||\vec{F}_N||\right) The *inf* norm takes the maximum component across the forces of all atoms in the system: .. math:: - || \vec{F} ||_{inf} = {\rm max}\left(|F_1^1|, |F_1^2|, |F_1^3| \cdots, |F_N^1|, |F_N^2|, |F_N^3|\right) + || \vec{F} ||_{inf} = \mathrm{max}\left(|F_1^1|, |F_1^2|, |F_1^3| \cdots, |F_N^1|, |F_N^2|, |F_N^3|\right) For the min styles *spin*, *spin/cg* and *spin/lbfgs*, the force norm is replaced by the spin-torque norm. diff --git a/doc/src/min_spin.rst b/doc/src/min_spin.rst index 9b6841ae8c..c6ae2f26b1 100644 --- a/doc/src/min_spin.rst +++ b/doc/src/min_spin.rst @@ -50,9 +50,9 @@ system: .. math:: - {\Delta t}_{\rm max} = \frac{2\pi}{\kappa \left|\vec{\omega}_{\rm max} \right|} + {\Delta t}_\mathrm{max} = \frac{2\pi}{\kappa \left|\vec{\omega}_\mathrm{max} \right|} -with :math:`\left|\vec{\omega}_{\rm max}\right|` the norm of the largest precession +with :math:`\left|\vec{\omega}_\mathrm{max}\right|` the norm of the largest precession frequency in the system (across all processes, and across all replicas if a spin/neb calculation is performed). diff --git a/doc/src/neb_spin.rst b/doc/src/neb_spin.rst index 62ca9f32cb..ba8ea3a7cd 100644 --- a/doc/src/neb_spin.rst +++ b/doc/src/neb_spin.rst @@ -148,7 +148,7 @@ spin i, :math:`\omega_i^{\nu}` is a rotation angle defined as: .. math:: - \omega_i^{\nu} = (\nu - 1) \Delta \omega_i {\rm ~~and~~} \Delta \omega_i = \frac{\omega_i}{Q-1} + \omega_i^{\nu} = (\nu - 1) \Delta \omega_i \mathrm{~~and~~} \Delta \omega_i = \frac{\omega_i}{Q-1} with :math:`\nu` the image number, Q the total number of images, and :math:`\omega_i` the total rotation between the initial and final spins. diff --git a/doc/src/pair_aip_water_2dm.rst b/doc/src/pair_aip_water_2dm.rst index b84202e69e..65f2e4d912 100644 --- a/doc/src/pair_aip_water_2dm.rst +++ b/doc/src/pair_aip_water_2dm.rst @@ -53,14 +53,14 @@ materials as described in :ref:`(Feng1) ` and :ref:`(Feng2) `. .. math:: E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ - V_{ij} = & {\rm Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} + V_{ij} = & \mathrm{Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ - {\rm Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - + \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + 84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 - 35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1 diff --git a/doc/src/pair_coul.rst b/doc/src/pair_coul.rst index 77c0e0b18b..c8c1581c3c 100644 --- a/doc/src/pair_coul.rst +++ b/doc/src/pair_coul.rst @@ -241,9 +241,9 @@ summation method, described in :ref:`Wolf `, given by: .. math:: E_i = \frac{1}{2} \sum_{j \neq i} - \frac{q_i q_j {\rm erfc}(\alpha r_{ij})}{r_{ij}} + + \frac{q_i q_j \mathrm{erfc}(\alpha r_{ij})}{r_{ij}} + \frac{1}{2} \sum_{j \neq i} - \frac{q_i q_j {\rm erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c + \frac{q_i q_j \mathrm{erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c where :math:`\alpha` is the damping parameter, and *erf()* and *erfc()* are error-function and complementary error-function terms. This diff --git a/doc/src/pair_coul_shield.rst b/doc/src/pair_coul_shield.rst index a7f99500f5..5f580f9037 100644 --- a/doc/src/pair_coul_shield.rst +++ b/doc/src/pair_coul_shield.rst @@ -40,8 +40,8 @@ the pair style :doc:`ilp/graphene/hbn ` .. math:: E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ - V_{ij} = & {\rm Tap}(r_{ij})\frac{\kappa q_i q_j}{\sqrt[3]{r_{ij}^3+(1/\lambda_{ij})^3}}\\ - {\rm Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - + V_{ij} = & \mathrm{Tap}(r_{ij})\frac{\kappa q_i q_j}{\sqrt[3]{r_{ij}^3+(1/\lambda_{ij})^3}}\\ + \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + 84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 - 35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1 diff --git a/doc/src/pair_dpd_ext.rst b/doc/src/pair_dpd_ext.rst index 1caed4689b..e84001235a 100644 --- a/doc/src/pair_dpd_ext.rst +++ b/doc/src/pair_dpd_ext.rst @@ -62,8 +62,8 @@ a sum of 3 terms \mathbf{f} = & f^C + f^D + f^R \qquad \qquad r < r_c \\ f^C = & A_{ij} w(r) \hat{\mathbf{r}}_{ij} \\ - f^D = & - \gamma_{\parallel} w_{\parallel}^2(r) (\hat{\mathbf{r}}_{ij} \cdot \mathbf{v}_{ij}) \hat{\mathbf{r}}_{ij} - \gamma_{\perp} w_{\perp}^2 (r) ( \mathbf{I} - \hat{\mathbf{r}}_{ij} \hat{\mathbf{r}}_{ij}^{\rm T} ) \mathbf{v}_{ij} \\ - f^R = & \sigma_{\parallel} w_{\parallel}(r) \frac{\alpha}{\sqrt{\Delta t}} \hat{\mathbf{r}}_{ij} + \sigma_{\perp} w_{\perp} (r) ( \mathbf{I} - \hat{\mathbf{r}}_{ij} \hat{\mathbf{r}}_{ij}^{\rm T} ) \frac{\mathbf{\xi}_{ij}}{\sqrt{\Delta t}}\\ + f^D = & - \gamma_{\parallel} w_{\parallel}^2(r) (\hat{\mathbf{r}}_{ij} \cdot \mathbf{v}_{ij}) \hat{\mathbf{r}}_{ij} - \gamma_{\perp} w_{\perp}^2 (r) ( \mathbf{I} - \hat{\mathbf{r}}_{ij} \hat{\mathbf{r}}_{ij}^\mathrm{T} ) \mathbf{v}_{ij} \\ + f^R = & \sigma_{\parallel} w_{\parallel}(r) \frac{\alpha}{\sqrt{\Delta t}} \hat{\mathbf{r}}_{ij} + \sigma_{\perp} w_{\perp} (r) ( \mathbf{I} - \hat{\mathbf{r}}_{ij} \hat{\mathbf{r}}_{ij}^\mathrm{T} ) \frac{\mathbf{\xi}_{ij}}{\sqrt{\Delta t}}\\ w(r) = & 1 - r/r_c \\ where :math:`\mathbf{f}^C` is a conservative force, :math:`\mathbf{f}^D` diff --git a/doc/src/pair_hbond_dreiding.rst b/doc/src/pair_hbond_dreiding.rst index a122fc5ea2..2c5059ffa9 100644 --- a/doc/src/pair_hbond_dreiding.rst +++ b/doc/src/pair_hbond_dreiding.rst @@ -68,21 +68,21 @@ force field, given by: .. math:: - E = & \left[LJ(r) | Morse(r) \right] \qquad \qquad \qquad r < r_{\rm in} \\ - = & S(r) * \left[LJ(r) | Morse(r) \right] \qquad \qquad r_{\rm in} < r < r_{\rm out} \\ - = & 0 \qquad \qquad \qquad \qquad \qquad \qquad \qquad r > r_{\rm out} \\ + E = & \left[LJ(r) | Morse(r) \right] \qquad \qquad \qquad r < r_\mathrm{in} \\ + = & S(r) * \left[LJ(r) | Morse(r) \right] \qquad \qquad r_\mathrm{in} < r < r_\mathrm{out} \\ + = & 0 \qquad \qquad \qquad \qquad \qquad \qquad \qquad r > r_\mathrm{out} \\ LJ(r) = & AR^{-12}-BR^{-10}cos^n\theta= \epsilon\left\lbrace 5\left[ \frac{\sigma}{r}\right]^{12}- 6\left[ \frac{\sigma}{r}\right]^{10} \right\rbrace cos^n\theta\\ Morse(r) = & D_0\left\lbrace \chi^2 - 2\chi\right\rbrace cos^n\theta= D_{0}\left\lbrace e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right\rbrace cos^n\theta \\ - S(r) = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2 - \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]} - { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 } + S(r) = & \frac{ \left[r_\mathrm{out}^2 - r^2\right]^2 + \left[r_\mathrm{out}^2 + 2r^2 - 3{r_\mathrm{in}^2}\right]} + { \left[r_\mathrm{out}^2 - {r_\mathrm{in}}^2\right]^3 } -where :math:`r_{\rm in}` is the inner spline distance cutoff, -:math:`r_{\rm out}` is the outer distance cutoff, :math:`\theta_c` is +where :math:`r_\mathrm{in}` is the inner spline distance cutoff, +:math:`r_\mathrm{out}` is the outer distance cutoff, :math:`\theta_c` is the angle cutoff, and :math:`n` is the power of the cosine of the angle :math:`\theta`. @@ -189,8 +189,8 @@ follows: * :math:`\epsilon` (energy units) * :math:`\sigma` (distance units) * *n* = exponent in formula above -* distance cutoff :math:`r_{\rm in}` (distance units) -* distance cutoff :math:`r_{\rm out}` (distance units) +* distance cutoff :math:`r_\mathrm{in}` (distance units) +* distance cutoff :math:`r_\mathrm{out}` (distance units) * angle cutoff (degrees) For the *hbond/dreiding/morse* style the list of coefficients is as @@ -202,7 +202,7 @@ follows: * :math:`\alpha` (1/distance units) * :math:`r_0` (distance units) * *n* = exponent in formula above -* distance cutoff :math:`r_{\rm in}` (distance units) +* distance cutoff :math:`r_\mathrm{in}` (distance units) * distance cutoff :math:`r_{out}` (distance units) * angle cutoff (degrees) diff --git a/doc/src/pair_ilp_graphene_hbn.rst b/doc/src/pair_ilp_graphene_hbn.rst index 36e971ef62..7fa7d6800f 100644 --- a/doc/src/pair_ilp_graphene_hbn.rst +++ b/doc/src/pair_ilp_graphene_hbn.rst @@ -44,14 +44,14 @@ in :ref:`(Kolmogorov) `. .. math:: E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ - V_{ij} = & {\rm Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} + V_{ij} = & \mathrm{Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ - {\rm Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - + \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + 84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 - 35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1 diff --git a/doc/src/pair_ilp_tmd.rst b/doc/src/pair_ilp_tmd.rst index 575bafdc91..133e5f9093 100644 --- a/doc/src/pair_ilp_tmd.rst +++ b/doc/src/pair_ilp_tmd.rst @@ -41,14 +41,14 @@ as described in :ref:`(Ouyang7) ` and :ref:`(Jiang) `. .. math:: E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ - V_{ij} = & {\rm Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} + V_{ij} = & \mathrm{Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ - {\rm Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - + \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + 84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 - 35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1 diff --git a/doc/src/pair_lj_cut_coul.rst b/doc/src/pair_lj_cut_coul.rst index aa5f7a2620..da39ac1645 100644 --- a/doc/src/pair_lj_cut_coul.rst +++ b/doc/src/pair_lj_cut_coul.rst @@ -194,9 +194,9 @@ summation method, described in :ref:`Wolf `, given by: .. math:: E_i = \frac{1}{2} \sum_{j \neq i} - \frac{q_i q_j {\rm erfc}(\alpha r_{ij})}{r_{ij}} + + \frac{q_i q_j \mathrm{erfc}(\alpha r_{ij})}{r_{ij}} + \frac{1}{2} \sum_{j \neq i} - \frac{q_i q_j {\rm erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c + \frac{q_i q_j \mathrm{erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c where :math:`\alpha` is the damping parameter, and erfc() is the complementary error-function terms. This potential is essentially a diff --git a/doc/src/pair_mesodpd.rst b/doc/src/pair_mesodpd.rst index 6674b013ba..269701ee27 100644 --- a/doc/src/pair_mesodpd.rst +++ b/doc/src/pair_mesodpd.rst @@ -200,7 +200,7 @@ force :math:`F_{ij}^C` are expressed as \mathbf{F}_{ij}^{D} & = -\gamma {\omega_{D}}(r_{ij})(\mathbf{e}_{ij} \cdot \mathbf{v}_{ij})\mathbf{e}_{ij} \\ \mathbf{F}_{ij}^{R} & = \sigma {\omega_{R}}(r_{ij}){\xi_{ij}}\Delta t^{-1/2} \mathbf{e}_{ij} \\ \omega_{C}(r) & = 1 - r/r_c \\ - \omega_{D}(r) & = \omega^2_{R}(r) = (1-r/r_c)^{\rm power_f} \\ + \omega_{D}(r) & = \omega^2_{R}(r) = (1-r/r_c)^\mathrm{power_f} \\ \sigma^2 = 2\gamma k_B T The concentration flux between two tDPD particles includes the Fickian @@ -211,7 +211,7 @@ by Q_{ij}^D & = -\kappa_{ij} w_{DC}(r_{ij}) \left( C_i - C_j \right) \\ Q_{ij}^R & = \epsilon_{ij}\left( C_i + C_j \right) w_{RC}(r_{ij}) \xi_{ij} \\ - w_{DC}(r_{ij}) & =w^2_{RC}(r_{ij}) = (1 - r/r_{cc})^{\rm power_{cc}} \\ + w_{DC}(r_{ij}) & =w^2_{RC}(r_{ij}) = (1 - r/r_{cc})^\mathrm{power_{cc}} \\ \epsilon_{ij}^2 & = m_s^2\kappa_{ij}\rho where the parameters kappa and epsilon determine the strength of the diff --git a/doc/src/pair_mgpt.rst b/doc/src/pair_mgpt.rst index 92bf9cd738..13a4bcb079 100644 --- a/doc/src/pair_mgpt.rst +++ b/doc/src/pair_mgpt.rst @@ -33,7 +33,7 @@ elemental bulk material in the form .. math:: - E_{\rm tot}({\bf R}_1 \ldots {\bf R}_N) = NE_{\rm vol}(\Omega ) + E_\mathrm{tot}({\bf R}_1 \ldots {\bf R}_N) = NE_\mathrm{vol}(\Omega ) + \frac{1}{2} \sum _{i,j} \mbox{}^\prime \ v_2(ij;\Omega ) + \frac{1}{6} \sum _{i,j,k} \mbox{}^\prime \ v_3(ijk;\Omega ) + \frac{1}{24} \sum _{i,j,k,l} \mbox{}^\prime \ v_4(ijkl;\Omega ) diff --git a/doc/src/pair_saip_metal.rst b/doc/src/pair_saip_metal.rst index ed011894c9..098edff916 100644 --- a/doc/src/pair_saip_metal.rst +++ b/doc/src/pair_saip_metal.rst @@ -41,14 +41,14 @@ potential (ILP) potential for hetero-junctions formed with hexagonal .. math:: E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ - V_{ij} = & {\rm Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} + V_{ij} = & \mathrm{Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ \rho_{ij}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_i)^2 \\ \rho_{ji}^2 = & r_{ij}^2 - ({\bf r}_{ij} \cdot {\bf n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ - {\rm Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - + \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + 84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 - 35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1 diff --git a/doc/src/pair_spin_dipole.rst b/doc/src/pair_spin_dipole.rst index c38bba03ae..faa2bc7461 100644 --- a/doc/src/pair_spin_dipole.rst +++ b/doc/src/pair_spin_dipole.rst @@ -43,7 +43,7 @@ vector omega and mechanical force between particles I and J. .. math:: - \mathcal{H}_{\rm long} & = + \mathcal{H}_\mathrm{long} & = -\frac{\mu_{0} \left( \mu_B\right)^2}{4\pi} \sum_{i,j,i\neq j}^{N} \frac{g_i g_j}{r_{ij}^3} diff --git a/doc/src/pair_spin_dmi.rst b/doc/src/pair_spin_dmi.rst index 282da39ff7..bb98c72d84 100644 --- a/doc/src/pair_spin_dmi.rst +++ b/doc/src/pair_spin_dmi.rst @@ -52,7 +52,7 @@ particle i: .. math:: \vec{\omega}_i = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times \left(\vec{e}_{ij}\times \vec{D} \right) - ~~{\rm and}~~ + ~~\mathrm{and}~~ \vec{F}_i = -\sum_{j}^{Neighb} \frac{1}{r_{ij}} \vec{D} \times \left( \vec{s}_{i}\times \vec{s}_{j} \right) More details about the derivation of these torques/forces are reported in diff --git a/doc/src/pair_spin_exchange.rst b/doc/src/pair_spin_exchange.rst index 553af72983..a922c45a8d 100644 --- a/doc/src/pair_spin_exchange.rst +++ b/doc/src/pair_spin_exchange.rst @@ -94,7 +94,7 @@ submitted to a force :math:`\vec{F}_{i}` for spin-lattice calculations (see \vec{\omega}_{i} = \frac{1}{\hbar} \sum_{j}^{Neighb} {J} \left(r_{ij} \right)\,\vec{s}_{j} - ~~{\rm and}~~ + ~~\mathrm{and}~~ \vec{F}_{i} = \sum_{j}^{Neighb} \frac{\partial {J} \left(r_{ij} \right)}{ \partial r_{ij}} \left( \vec{s}_{i}\cdot \vec{s}_{j} \right) \vec{e}_{ij} diff --git a/doc/utils/sphinx-config/conf.py.in b/doc/utils/sphinx-config/conf.py.in index e4b461397d..d3a3effe97 100644 --- a/doc/utils/sphinx-config/conf.py.in +++ b/doc/utils/sphinx-config/conf.py.in @@ -290,7 +290,7 @@ rst_prolog = r""" .. only:: html - :math:`\renewcommand{\AA}{\text{Å}}` + :math:`\renewcommand{\AA}{\textup{\r{A}}` .. role:: lammps(code) :language: LAMMPS diff --git a/tools/lammps-gui/org.lammps.lammps-gui.yml b/tools/lammps-gui/org.lammps.lammps-gui.yml index a16ef5fdee..f88ea55bb2 100644 --- a/tools/lammps-gui/org.lammps.lammps-gui.yml +++ b/tools/lammps-gui/org.lammps.lammps-gui.yml @@ -110,5 +110,5 @@ modules: - -D BUILD_WHAM=yes sources: - type: git - url: https://github.com/lammps/lammps.git - branch: release + url: https://github.com/akohlmey/lammps.git + branch: collected-small-fixes