| delta | 規格化した密度(\(\delta=\rho/\rho_c\))。 The normalized density (\(\delta=\rho/\rho_c\)). |
| tau | 規格化した温度の逆数(\(\tau=T_c/T\))。 Inverse of the normalized temperature (\(\tau=T_c/T\)). |
| メンバ Member |
量 Quantity |
計算式(Wagner and Pruss (2002)の表6.5に基づく) Formula (from Table 6.5 of Wagner and Pruss (2002)) |
| phi_r | 残差項\(\phi^r\)。 The residual part \(\phi^r\). |
\[\begin{eqnarray*} & & \sum_{i=1}^7 n_i \delta^{d_i} \tau^{t_i} \nonumber \\ &+& \sum_{i=8}^{51} n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{c_i}) \nonumber \\ &+& \sum_{i=52}^{54} n_i \delta^{d_i} \tau^{t_i} \exp\left[-\alpha_i(\delta-\epsilon_i)^2 -\beta_i(\tau-\gamma_i)^2\right] \nonumber \\ &+& \sum_{i=55}^{56} n_i \Delta^{b_i}\delta\psi \end{eqnarray*}\] |
| phi_delta_r | \(\phi_{\delta}^r \equiv \PartialDiff{\phi^r}{\delta}\) | \[\begin{eqnarray*} & & \sum_{i=1}^7 n_i d_i \delta^{d_i-1} \tau^{t_i} \nonumber \\ &+& \sum_{i=8}^{51} n_i \exp(-\delta^{c_i}) \delta^{d_i-1} \tau^{t_i} (d_i-c_i\delta^{c_i}) \nonumber \\ &+& \sum_{i=52}^{54} n_i \delta^{d_i} \tau^{t_i} \exp\left[-\alpha_i(\delta-\epsilon_i)^2 -\beta_i(\tau-\gamma_i)^2\right] \nonumber \\ & & \left[\frac{d_i}{\delta}-2\alpha_i(\delta-\epsilon_i)\right] \nonumber \\ &+& \sum_{i=55}^{56} n_i\left[\Delta^{b_i} \left(\psi+\delta\PartialDiff{\psi}{\delta}\right) +\PartialDiff{\Delta^{b_i}}{\delta}\delta\psi\right] \end{eqnarray*}\] |
| phi_deltadelta_r | \(\phi_{\delta\delta}^r \equiv \PartialDDiff{\phi^r}{\delta}\) | \[\begin{eqnarray*} & & \sum_{i=1}^7 n_i d_i (d_i-1) \delta^{d_i-2} \tau^{t_i} \nonumber \\ &+& \sum_{i=8}^{51} n_i \exp(-\delta^{c_i})\delta^{d_i-2}\tau^{t_i} \left[(d_i-c_i\delta^{c_i})(d_i-1-c_i\delta^{c_i}) -c_i^2\delta^{c_i}\right] \nonumber \\ &+& \sum_{i=52}^{54} n_i \tau^{t_i} \exp\left[-\alpha_i(\delta-\epsilon_i)^2 -\beta_i(\tau-\gamma_i)^2\right] \nonumber \\ & & \left[-2\alpha_i\delta^{d_i} +4\alpha_i^2\delta^{d_i}(\delta-\epsilon_i)^2 -4d_i\alpha_i\delta^{d_i-1}(\delta-\epsilon_i)\right. \nonumber \\ & & \left.+d_i(d_i-1)\delta^{d_i-2}\right] \nonumber \\ &+& \sum_{i=55}^{56} n_i\left[ \Delta^{b_i} \left(2\PartialDiff{\psi}{\delta} +\delta\PartialDDiff{\psi}{\delta}\right) +2\PartialDiff{\Delta^{b_i}}{\delta} \left(\psi+\delta\PartialDiff{\psi}{\delta}\right) \right. \nonumber \\ & & \left. +\PartialDDiff{\Delta^{b_i}}{\delta}\delta\psi \right] \end{eqnarray*}\] |
| phi_tau_r | \(\phi_{\tau}^r \equiv \PartialDiff{\phi^r}{\tau}\) | \[\begin{eqnarray*} & & \sum_{i=1}^7 n_i t_i \delta^{d_i} \tau^{t_i-1} \nonumber \\ &+& \sum_{i=8}^{51} n_i t_i \delta^{d_i} \tau^{t_i-1}\exp(-\delta^{c_i}) \nonumber \\ &+& \sum_{i=52}^{54} n_i \delta^{d_i} \tau^{t_i} \exp\left[-\alpha_i(\delta-\epsilon_i)^2 -\beta_i(\tau-\gamma_i)^2\right] \nonumber \\ & & \left[\frac{t_i}{\tau}-2\beta_i(\tau-\gamma_i)\right] \nonumber \\ &+& \sum_{i=55}^{56} n_i \delta \left[ \PartialDiff{\Delta^{b_i}}{\tau}\psi +\Delta^{b_i}\PartialDiff{\psi}{\tau} \right] \end{eqnarray*}\] |
| phi_tautau_r | \(\phi_{\tau\tau}^r \equiv \PartialDDiff{\phi^r}{\tau}\) | \[\begin{eqnarray*} & & \sum_{i=1}^7 n_i t_i (t_i-1) \delta^{d_i} \tau^{t_i-2} \nonumber \\ &+& \sum_{i=8}^{51} n_i t_i (t_i-1) \delta^{d_i} \tau^{t_i-2} \exp(-\delta^{c_i}) \nonumber \\ &+& \sum_{i=52}^{54} n_i \delta^{d_i} \tau^{t_i} \exp\left[-\alpha_i(\delta-\epsilon_i)^2 -\beta_i(\tau-\gamma_i)^2\right] \nonumber \\ & & \left\{ \left[\frac{t_i}{\tau}-2\beta_i(\tau-\gamma_i)\right]^2 -\frac{t_i}{\tau^2}-2\beta_i \right\} \nonumber \\ &+& \sum_{i=55}^{56} n_i\delta\left[ \PartialDDiff{\Delta^{b_i}}{\tau}\psi +2\PartialDiff{\Delta^{b_i}}{\tau}\PartialDiff{\psi}{\tau} +\Delta^{b_i}\PartialDDiff{\psi}{\tau} \right] \end{eqnarray*}\] |
| phi_deltatau_r | \(\phi_{\delta\tau}^r \equiv \PartialCrossDiff{\phi^r}{\delta}{\tau}\) | \[\begin{eqnarray*} & & \sum_{i=1}^7 n_i d_i t_i \delta^{d_i-1} \tau^{t_i-1} \nonumber \\ &+& \sum_{i=8}^{51} n_i t_i \delta^{d_i-1} \tau^{t_i-1} (d_i-c_i\delta^{c_i})\exp(-\delta^{c_i}) \nonumber \\ &+& \sum_{i=52}^{54} n_i \delta^{d_i} \tau^{t_i} \exp\left[-\alpha_i(\delta-\epsilon_i)^2 -\beta_i(\tau-\gamma_i)^2\right] \nonumber \\ & & \left[\frac{d_i}{\delta}-2\alpha_i(\delta-\epsilon_i)\right] \left[\frac{t_i}{\tau}-2\beta_i(\tau-\gamma_i)\right] \nonumber \\ &+& \sum_{i=55}^{56} n_i \left[ \Delta^{b_i}\left( \PartialDiff{\psi}{\tau} +\delta\PartialCrossDiff{\psi}{\delta}{\tau} \right) +\delta\PartialDiff{\Delta^{b_i}}{\delta} \PartialDiff{\psi}{\tau} \right. \nonumber \\ & & \left. +\PartialDiff{\Delta^{b_i}}{\tau} \left(\psi+\delta\PartialDiff{\psi}{\delta}\right) +\PartialCrossDiff{\Delta^{b_i}}{\delta}{\tau}\delta\psi \right] \end{eqnarray*}\] |