From 1c7c2a99c96144e89a45f6ecc5b56d1c2588a22e Mon Sep 17 00:00:00 2001
From: majsylw <58003896+majsylw@users.noreply.github.com>
Date: Mon, 16 Aug 2021 11:08:04 +0200
Subject: [PATCH] add plot to documentation
---
user_libs/DebyeFit/Readme.rst | 36 ++++++++++++++++++++++++----
user_libs/DebyeFit/docs/epsilon.png | Bin 0 -> 50299 bytes
2 files changed, 31 insertions(+), 5 deletions(-)
create mode 100644 user_libs/DebyeFit/docs/epsilon.png
diff --git a/user_libs/DebyeFit/Readme.rst b/user_libs/DebyeFit/Readme.rst
index 1c5daab8..8523afe7 100644
--- a/user_libs/DebyeFit/Readme.rst
+++ b/user_libs/DebyeFit/Readme.rst
@@ -1,17 +1,43 @@
Fitting multi-pole Debye model to dielectric data
=================================================
-In the ``user_libs`` sub-package is a module called ``DebyeFit`` which can be used to to fit a multi-Debye expansion to dielectric data, defined as
+All electromagnetic phenomena are governed by the Maxwell's equations, which describing how electric and magnetic fields are distributed due to charges and currents,
+and how they are changing in time. gprMax is open source software that simulates electromagnetic wave propagation by using
+Yee's algorithm to solve (3+1)D Maxwell’s equations with Finite-Difference Time-Domain (FDTD) method.
+The behavior of the electromagnetic wave is closely dependent on the material in which it propagates.
+Some dispersive media have quite complex electromagnetic properties depending on the wavelength.
+This, for example, means that for different frequencies the wave can propagate with a different speed in different materials.
+This significantly affects the solver’s output. The main goal of the GSoC 2021 project was to enhance series of scripts,
+which modelled electromagnetic properties of the variety range of materials.
+
+Multi-pole Debye model
+======================
+
+Electric permittivity is a complex function with both real and imaginary parts.
+In general, as a hard and fast rule, the real part dictates the velocity of the medium while the imaginary part is related to the electromagnetic losses.
+The generic form of dispersive media takes a form of
+
+.. math::
+
+ \epsilon(\omega) = \epsilon^{'}(\omega) - j\epsilon^{''}(\omega),
+
+where :math:`\omega` is the angular frequency, :math:`\epsilon^{'}` and :math:`\epsilon^{''}` are the real and imaginary parts of the permittivity respectively.
+
+In the ``user_libs`` sub-package is a module called ``DebyeFit`` which can be used to fit a multi-Debye expansion to dielectric data, defined as
.. math::
\epsilon(\omega) = \epsilon_{\infty} + \sum_{i=1}^{N}\frac{\Delta\epsilon_{i}}{1+j\omega t_{0,i}},
-where :math:`\epsilon(\omega)` is frequency dependent dielectric properties, :math:`\Delta\epsilon` - difference between the real permittivity at zero and infinity frequency.
+where :math:`\epsilon(\omega)` is frequency dependent dielectric permittivity, :math:`\Delta\epsilon` - difference between the real permittivity at zero and infinity frequency.
:math:`\tau_{0}` is relaxation time (s), :math:`\epsilon_{\infty}` - real part of relative permittivity at infinity frequency, and :math:`N` is number of the Debye poles.
The user can choose between Havriliak-Negami, Jonscher, Complex Refractive Index Mixing models, and arbitrary dielectric data derived experimentally
-or calculated using some other function.
+or calculated using some other function to fit the data to a multi-Debye expansion.
+
+
+
+