From 1f5947c315696b2b57a79494a0e875f32e518e26 Mon Sep 17 00:00:00 2001 From: Craig Warren Date: Thu, 7 Apr 2016 17:05:28 +0100 Subject: [PATCH] Corrected some terminology on the poles for multiple pole Debye and Lorenz materials. --- docs/source/input.rst | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/docs/source/input.rst b/docs/source/input.rst index 21d39c37..79f0bc21 100644 --- a/docs/source/input.rst +++ b/docs/source/input.rst @@ -202,7 +202,7 @@ Allows you to add dispersive properties to an already defined ``#material`` base \chi_p (t) = \frac{\Delta \epsilon_{rp}}{\tau_p} e^{-t/\tau_p}, -where :math:`\Delta \epsilon_{rp} = \epsilon_{rsp} - \epsilon_{r \infty p}`, :math:`\epsilon_{rsp}` is the zero-frequency relative permittivity, :math:`\epsilon_{r \infty p}` is the relative permittivity at infinite frequency, and :math:`\tau_p` is the pole relaxation time. +where :math:`\Delta \epsilon_{rp} = \epsilon_{rsp} - \epsilon_{r \infty}`, :math:`\epsilon_{rsp}` is the zero-frequency relative permittivity for the pole, :math:`\epsilon_{r \infty}` is the relative permittivity at infinite frequency, and :math:`\tau_p` is the pole relaxation time. The syntax of the command is: @@ -211,14 +211,14 @@ The syntax of the command is: #add_dispersion_debye: i1 f1 f2 f3 f4 ... str1 * ``i1`` is the number of Debye poles. -* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp1} = \epsilon_{rsp1} - \epsilon_{r \infty p1}` , for the first Debye pole. +* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp1} = \epsilon_{rsp1} - \epsilon_{r \infty}` , for the first Debye pole. * ``f2`` is the relaxation time (seconds), :math:`\tau_{p1}`, for the first Debye pole. -* ``f3`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp2} = \epsilon_{rsp2} - \epsilon_{r \infty p2}` , for the second Debye pole. +* ``f3`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp2} = \epsilon_{rsp2} - \epsilon_{r \infty}` , for the second Debye pole. * ``f4`` is the relaxation time (seconds), :math:`\tau_{p2}`, for the second Debye pole. * ... * ``str1`` identifies the material to add the dispersive properties to. -For example to create a model of water with a single Debye pole, :math:`\epsilon_{rsp1} = 80.1`, :math:`\epsilon_{r \infty p1} = 4.9` and :math:`\tau_{p1} = 9.231\times 10^{-12}` seconds use: ``#material: 4.9 0 1 0 my_water`` and ``#add_dispersion_debye: 1 75.2 9.231e-12 my_water``. +For example to create a model of water with a single Debye pole, :math:`\epsilon_{rsp1} = 80.1`, :math:`\epsilon_{r \infty} = 4.9` and :math:`\tau_{p1} = 9.231\times 10^{-12}` seconds use: ``#material: 4.9 0 1 0 my_water`` and ``#add_dispersion_debye: 1 75.2 9.231e-12 my_water``. .. note:: @@ -240,9 +240,9 @@ where .. math:: - \beta_p = \sqrt{\omega_p^2 - \delta_p^2} \quad \textrm{and} \quad \gamma_p = \frac{\omega_p^2 \Delta \epsilon_r}{\beta_p}, + \beta_p = \sqrt{\omega_p^2 - \delta_p^2} \quad \textrm{and} \quad \gamma_p = \frac{\omega_p^2 \Delta \epsilon_{rp}}{\beta_p}, -where :math:`\Delta \epsilon_{rp} = \epsilon_{rsp} - \epsilon_{r \infty p}`, :math:`\epsilon_{rsp}` is the zero-frequency relative permittivity, :math:`\epsilon_{r \infty p}` is the relative permittivity at infinite frequency, :math:`\omega_p` is the frequency (Hertz) of the pole pair, :math:`\delta_p` is the damping coefficient (Hertz) , and :math:`j=\sqrt{-1}`. +where :math:`\Delta \epsilon_{rp} = \epsilon_{rsp} - \epsilon_{r \infty}`, :math:`\epsilon_{rsp}` is the zero-frequency relative permittivity for the pole, :math:`\epsilon_{r \infty}` is the relative permittivity at infinite frequency, :math:`\omega_p` is the frequency (Hertz) of the pole pair, :math:`\delta_p` is the damping coefficient (Hertz) , and :math:`j=\sqrt{-1}`. The syntax of the command is: @@ -251,10 +251,10 @@ The syntax of the command is: #add_dispersion_lorentz: i1 f1 f2 f3 f4 f5 f6 ... str1 * ``i1`` is the number of Lorentz poles. -* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp1} = \epsilon_{rsp1} - \epsilon_{r \infty p1}` , for the first Lorentz pole. +* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp1} = \epsilon_{rsp1} - \epsilon_{r \infty}` , for the first Lorentz pole. * ``f2`` is the frequency (Hertz), :math:`\omega_{p1}`, for the first Lorentz pole. * ``f3`` is the damping coefficient (Hertz), :math:`\delta_{p1}`, for the first Lorentz pole. -* ``f4`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp2} = \epsilon_{rsp2} - \epsilon_{r \infty p2}` , for the second Lorentz pole. +* ``f4`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp2} = \epsilon_{rsp2} - \epsilon_{r \infty}` , for the second Lorentz pole. * ``f5`` is the frequency (Hertz), :math:`\omega_{p2}`, for the second Lorentz pole. * ``f6`` is the damping coefficient (Hertz), :math:`\delta_{p2}`, for the second Lorentz pole. * ...