updated dynamics section and others

Doc/pages/R_notation.rst

@@ -4,41 +4,46 @@
 Frequently Used Symbols and Notations
 =====================================
 
-============================================ ===============
-**Symbol**                                   **Description**
-:math:`\alpha, \beta, \gamma, \ldots`        atom types
-:math:`j, k, l, \ldots`                      atom indices
-:math:`c_{\alpha}`                           concentration of atom-type :math:`\alpha` where :math:`c_{\alpha} = N_{\alpha} / N`
-:math:`D`                                    diffusion constant
-:math:`F(\mathbf{q}, t)`                     intermediate scattering function
-:math:`F_{\mathrm{coh}}(\mathbf{q}, t)`      coherent intermediate scattering function
-:math:`F_{\mathrm{inc}}(\mathbf{q}, t)`      incoherent intermediate scattering function
-:math:`g(\mathbf{r})`                        pair distribution function
-:math:`G(\mathbf{r}, t)`                     the van Hove function
-:math:`G_{\mathrm{d}}(\mathbf{r}, t)`        distinct part of the van Hove function
-:math:`G_{\mathrm{s}}(\mathbf{r}, t)`        self part of the van Hove function
-:math:`t`                                    time
-:math:`t_{\mathrm{cor}}`                     the total time of the correlation function
-:math:`t_{\mathrm{tot}}`                     the total time of the MD simulation
-:math:`\Delta t`                             the MD time step
-:math:`S(\mathbf{q})`                        static structure factor
-:math:`S(\mathbf{q}, \omega)`                dynamic structure factor
-:math:`S_{\mathrm{coh}}(\mathbf{q}, \omega)` dynamic coherent structure factor
-:math:`S_{\mathrm{inc}}(\mathbf{q}, \omega)` dynamic incoherent structure factor
-:math:`T`                                    temperature
-:math:`M`                                    number of atom types in the system
-:math:`n_{\mathrm{c}}`                       total number of time steps calculated for the correlation function
-:math:`n_{\mathrm{t}}`                       total number of time steps in the MD simulation
-:math:`N`                                    total number of atoms in the unit cell, simulation or volume :math:`V`
-:math:`N_\alpha`                             number of atom of type :math:`\alpha`
-:math:`\rho`                                 density
-:math:`r`                                    distance
-:math:`q`                                    wavenumber
-:math:`\mathbf{q}`                           wavevector
-:math:`\mathbf{r}(t)`                        the position of an atom at time :math:`t`
-:math:`\mathbf{v}(t)`                        the velocity of an atom at time :math:`t`
-:math:`W_\alpha`                             weighting factor for atom-type :math:`\alpha`
-:math:`W_\alpha\beta`                        weighting factor for atom-type pair :math:`\alpha\beta`
-:math:`\omega`                               angular frequency
-:math:`\Delta \omega`                        the frequency step
-============================================ ===============
+======================================================= ===============
+**Symbol**                                              **Description**
+:math:`\alpha, \beta, \gamma, \ldots`                   atom types
+:math:`j, k, l, \ldots`                                 atom indices
+:math:`c_{\alpha}`                                      concentration of atom-type :math:`\alpha` where :math:`c_{\alpha} = N_{\alpha} / N`
+:math:`C_{\mathbf{vv}jj}(t)`                            the velocity autocorrelation function of particle :math:`j`
+:math:`C_{\mathbf{vv}jj}(\omega)`                       the Fourier transform of the velocity autocorrelation function of particle :math:`j`
+:math:`D`                                               diffusion constant
+:math:`\mathrm{DOS}(\omega)`                            density of states
+:math:`F(\mathbf{q}, t)`                                intermediate scattering function
+:math:`F_{\mathrm{coh}}(\mathbf{q}, t)`                 coherent intermediate scattering function
+:math:`F_{\mathrm{inc}}(\mathbf{q}, t)`                 incoherent intermediate scattering function
+:math:`F_{\mathrm{inc}}^{\text{G}}(\mathbf{q}, t)`      Gaussian approximation of the incoherent intermediate scattering function
+:math:`g(\mathbf{r})`                                   pair distribution function
+:math:`G(\mathbf{r}, t)`                                the van Hove function
+:math:`G_{\mathrm{d}}(\mathbf{r}, t)`                   distinct part of the van Hove function
+:math:`G_{\mathrm{s}}(\mathbf{r}, t)`                   self part of the van Hove function
+:math:`t`                                               time
+:math:`t_{\mathrm{cor}}`                                the total time of the correlation function
+:math:`t_{\mathrm{tot}}`                                the total time of the MD simulation
+:math:`\Delta t`                                        the MD time step
+:math:`S(\mathbf{q})`                                   static structure factor
+:math:`S(\mathbf{q}, \omega)`                           dynamic structure factor
+:math:`S_{\mathrm{coh}}(\mathbf{q}, \omega)`            dynamic coherent structure factor
+:math:`S_{\mathrm{inc}}(\mathbf{q}, \omega)`            dynamic incoherent structure factor
+:math:`S_{\mathrm{inc}}^{\text{G}}(\mathbf{q}, \omega)` Gaussian approximation of the dynamic incoherent structure factor
+:math:`T`                                               temperature
+:math:`M`                                               number of atom types in the system
+:math:`n_{\mathrm{c}}`                                  total number of time steps calculated for the correlation function
+:math:`n_{\mathrm{t}}`                                  total number of time steps in the MD simulation
+:math:`N`                                               total number of atoms in the unit cell, simulation or volume :math:`V`
+:math:`N_\alpha`                                        number of atom of type :math:`\alpha`
+:math:`\rho`                                            density
+:math:`r`                                               distance
+:math:`q`                                               wavenumber
+:math:`\mathbf{q}`                                      wavevector
+:math:`\mathbf{r}(t)`                                   the position of an atom at time :math:`t`
+:math:`\mathbf{v}(t)`                                   the velocity of an atom at time :math:`t`
+:math:`W_\alpha`                                        weighting factor for atom-type :math:`\alpha`
+:math:`W_\alpha\beta`                                   weighting factor for atom-type pair :math:`\alpha\beta`
+:math:`\omega`                                          angular frequency
+:math:`\Delta \omega`                                   the frequency step
+======================================================= ===============