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fix typing error in doc file

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msvbd
2021-04-16 15:44:20 +02:00
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doc/src/pair_dpdext.rst
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@ -52,7 +52,7 @@ of 3 terms
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}}\\
w(r) = & 1 - r/r_c \\
where :math:`\mathbf{f}^C` is a conservative force, :math:`\mathbf{f}^D` is a dissipative force, and :math:`\mathbf{f}^R` is a random force. :math:`A_{ij}` is the maximum repulsion between the two atoms, :math:`\hat{\mathbf{r}}_{ij}` is a unit vector in the direction :math:`\mathbf{r}_i - \mathbf{r}_j`, :math:`\mathbf{v}_{ij} = \mathbf{v}_i - \mathbf{v}_j` is the vector difference in velocities of the two atoms, :math:`\a` and :math:`\mathbf{\xi}_{ij}` are Gaussian random numbers with zero mean and unit variance, :math:`\Delta t` is the timestep, :math:`w (r) = 1 - r / r_c` is a weight function for the conservative interactions that varies between 0 and 1, :math:`r_c` is the corresponding cutoff, :math:`w_{\alpha} ( r ) = ( 1 - r / \bar{r}_c )^{s_{\alpha}}`, :math:`\alpha \equiv ( \parallel, \perp )`, are weight functions with coefficients :math:`s_\alpha` that vary between 0 and 1, :math:`\bar{r}_c` is the corresponding cutoff, :math:`\mathbf{I}` is the unit matrix, :math:`\sigma_{\alpha} = \sqrt{2 k T \gamma_{\alpha}}`, where :math:`k` is the Boltzmann constant and :math:`T` is the temperature in the pair\_style command.
where :math:`\mathbf{f}^C` is a conservative force, :math:`\mathbf{f}^D` is a dissipative force, and :math:`\mathbf{f}^R` is a random force. :math:`A_{ij}` is the maximum repulsion between the two atoms, :math:`\hat{\mathbf{r}}_{ij}` is a unit vector in the direction :math:`\mathbf{r}_i - \mathbf{r}_j`, :math:`\mathbf{v}_{ij} = \mathbf{v}_i - \mathbf{v}_j` is the vector difference in velocities of the two atoms, :math:`\alpha` and :math:`\mathbf{\xi}_{ij}` are Gaussian random numbers with zero mean and unit variance, :math:`\Delta t` is the timestep, :math:`w (r) = 1 - r / r_c` is a weight function for the conservative interactions that varies between 0 and 1, :math:`r_c` is the corresponding cutoff, :math:`w_{\alpha} ( r ) = ( 1 - r / \bar{r}_c )^{s_{\alpha}}`, :math:`\alpha \equiv ( \parallel, \perp )`, are weight functions with coefficients :math:`s_\alpha` that vary between 0 and 1, :math:`\bar{r}_c` is the corresponding cutoff, :math:`\mathbf{I}` is the unit matrix, :math:`\sigma_{\alpha} = \sqrt{2 k T \gamma_{\alpha}}`, where :math:`k` is the Boltzmann constant and :math:`T` is the temperature in the pair\_style command.
For the style *dpdext/tstat*\ , the force on atom I due to atom J is the same as the above equation, except that the conservative :math:`\mathbf{f}^C` term is dropped. Also, during the run, T is set each timestep to a ramped value from Tstart to Tstop.