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remove the rest of the example notebooks, import cleanup in electrost…
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…atic_sphere
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@lheagy
lheagy committed Sep 17, 2016
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Expand Up @@ -62,6 +62,11 @@ target/

# Picasa stuff
*.ini

# Windows
content/maxwell1_fundamentals/fundamental_laws/images/~$BC.pptx
*.rst~
content/case_histories/emc/images/figures.pptx

# notebooks
*.ipynb
114 changes: 56 additions & 58 deletions content/maxwell2_dc/fields_from_grounded_sources_dcr/electrostatic_sphere.rst
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Expand Up @@ -30,7 +30,7 @@ The problem setup is shown in the figure below, where we have

.. plot::

from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the whole-space in S/m
sig1 = 10.**-1. # conductivity of the sphere in S/m
Expand All @@ -40,11 +40,11 @@ The problem setup is shown in the figure below, where we have
xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
yr = xr.copy() # Y-axis discretization
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition
colorsphere=[0.1,0.1,0.6]

fig, ax = plt.subplots(1,1, figsize = (6,6))
ax = get_Setup(XYZ,sig0,sig1,R,E0,ax,False,colorsphere)
ax = electrostatic_sphere.get_Setup(XYZ,sig0,sig1,R,E0,ax,False,colorsphere)

plt.show()

Expand All @@ -58,21 +58,21 @@ The governing equation for DC resistivity problem can be obtained from
considering the zero-frequency case, in which case, Maxwell's equations are

.. math::
\nabla \times \mathbf{e} = 0
:label: Faraday_DC
\nabla \times \mathbf{e} = 0
:label: Faraday_DC
.. math::
\nabla \times \mathbf{h} = \mathbf{j}
:label: Ampere_DC
\nabla \times \mathbf{h} = \mathbf{j}
:label: Ampere_DC
Knowing that the curl of the gradient of any scalar potential is always zero,
according to :eq:`Faraday_DC`, we can define a scalar potential so that the
primary electric field is the gradient of a potential. For convenience, we
define it to be the negative gradient of the potential, :math:`V`

.. math::
\mathbf{e} = -\nabla V
:label: DC_Potential
\mathbf{e} = -\nabla V
:label: DC_Potential
To define the potential at a point :math:`p` from an electric field requires integration

Expand All @@ -95,13 +95,13 @@ the integration from :eq:`V_from_e` gives


.. math::
V_p = - E_0 x = -E_0 r \cos\theta
:label: Primary_Potential
V_p = - E_0 x = -E_0 r \cos\theta
:label: Primary_Potential
.. plot::

from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the whole-space in S/m
sig1 = 10.**-1. # conductivity of the sphere in S/m
Expand All @@ -111,29 +111,29 @@ the integration from :eq:`V_from_e` gives
xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
yr = xr.copy() # Y-axis discretization
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition

fig, ax = plt.subplots(1,1, figsize = (8,6))
ax = Plot_Primary_Potential(XYZ,sig0,sig1,R,E0,ax)
ax = electrostatic_sphere.Plot_Primary_Potential(XYZ,sig0,sig1,R,E0,ax)

plt.show()

The total potential outside the sphere :math:`(r > R)` is

.. math::
V_1 = -E_0 \big(1 - \frac{R^3}{r^3}\frac{\sigma_1 - \sigma_0}{\sigma_1 + 2\sigma_0} \big) r \cos\theta
:label: totalP_outside
V_1 = -E_0 \big(1 - \frac{R^3}{r^3}\frac{\sigma_1 - \sigma_0}{\sigma_1 + 2\sigma_0} \big) r \cos\theta
:label: totalP_outside
and inside the sphere :math:`(r < R)`

.. math::
V_2 = -E_0 \frac{3\sigma_0}{\sigma_1+2\sigma_0}r \cos\theta
:label: totalP_inside
V_2 = -E_0 \frac{3\sigma_0}{\sigma_1+2\sigma_0}r \cos\theta
:label: totalP_inside
.. plot::

from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the whole-space in S/m
sig1 = 10.**-1. # conductivity of the sphere in S/m
Expand All @@ -146,17 +146,17 @@ and inside the sphere :math:`(r < R)`
dx = xr[1]-xr[0] # mesh spacing
dy = yr[1]-yr[0] # mesh spacing
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition

fig, ax = plt.subplots(2,2,figsize=(18,12))
ax = mkvc(ax)
ax[0] = Plot_Total_Potential(XYZ,sig0,sig1,R,E0,ax[0])
ax = electrostatic_sphere.mkvc(ax)
ax[0] = electrostatic_sphere.Plot_Total_Potential(XYZ,sig0,sig1,R,E0,ax[0])
ax[0].set_title('Conductive Sphere: \n Total Potential',fontsize=ftsize_title)
ax[1] = Plot_Secondary_Potential(XYZ,sig0,sig1,R,E0,ax[1])
ax[1] = electrostatic_sphere.Plot_Secondary_Potential(XYZ,sig0,sig1,R,E0,ax[1])
ax[1].set_title('Conductive Sphere: \n Secondary Potential',fontsize=ftsize_title)
ax[2] = Plot_Total_Potential(XYZ,sig0,sig2,R,E0,ax[2])
ax[2] = electrostatic_sphere.Plot_Total_Potential(XYZ,sig0,sig2,R,E0,ax[2])
ax[2].set_title('Resistive Sphere: \n Total Potential',fontsize=ftsize_title)
ax[3] = Plot_Secondary_Potential(XYZ,sig0,sig2,R,E0,ax[3])
ax[3] = electrostatic_sphere.Plot_Secondary_Potential(XYZ,sig0,sig2,R,E0,ax[3])
ax[3].set_title('Resistive Sphere: \n Secondary Potential',fontsize=ftsize_title)

plt.tight_layout()
Expand All @@ -183,7 +183,7 @@ according to :eq:`totalP_outside` and :eq:`totalP_inside`, the electric field at
.. plot::

from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the whole-space in S/m
sig1 = 10.**-1. # conductivity of the sphere in S/m
Expand All @@ -196,18 +196,18 @@ according to :eq:`totalP_outside` and :eq:`totalP_inside`, the electric field at
dx = xr[1]-xr[0] # mesh spacing
dy = yr[1]-yr[0] # mesh spacing
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition
ftsize_title = 18 #font size for titles

fig, ax = plt.subplots(2,2,figsize=(18,12))
ax = mkvc(ax)
ax[0] = Plot_Total_ElectricField(XYZ,sig0,sig1,R,E0,ax[0])
ax = electrostatic_sphere.mkvc(ax)
ax[0] = electrostatic_sphere.Plot_Total_ElectricField(XYZ,sig0,sig1,R,E0,ax[0])
ax[0].set_title('Conductive Sphere: \n Total Electric Field',fontsize=ftsize_title)
ax[1] = Plot_Secondary_ElectricField(XYZ,sig0,sig1,R,E0,ax[1])
ax[1] = electrostatic_sphere.Plot_Secondary_ElectricField(XYZ,sig0,sig1,R,E0,ax[1])
ax[1].set_title('Conductive Sphere: \n Secondary Electric Field',fontsize=ftsize_title)
ax[2] = Plot_Total_ElectricField(XYZ,sig0,sig2,R,E0,ax[2])
ax[2] = electrostatic_sphere.Plot_Total_ElectricField(XYZ,sig0,sig2,R,E0,ax[2])
ax[2].set_title('Resistive Sphere: \n Total Electric Field',fontsize=ftsize_title)
ax[3] = Plot_Secondary_ElectricField(XYZ,sig0,sig2,R,E0,ax[3])
ax[3] = electrostatic_sphere.Plot_Secondary_ElectricField(XYZ,sig0,sig2,R,E0,ax[3])
ax[3].set_title('Resistive Sphere: \n Secondary Electric Field',fontsize=ftsize_title)

plt.tight_layout()
Expand Down Expand Up @@ -265,7 +265,7 @@ the charges and not the reverse.

.. plot::

from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the whole space in S/m
sig1 = 10.**-1. # conductivity of the sphere in S/m
Expand All @@ -278,17 +278,17 @@ the charges and not the reverse.
dx = xr[1]-xr[0] # mesh spacing
dy = yr[1]-yr[0] # mesh spacing
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition

fig, ax = plt.subplots(2,2,figsize=(18,12))
ax = mkvc(ax)
ax[0] = Plot_Total_Currents(XYZ,sig0,sig1,R,E0,ax[0])
ax = electrostatic_sphere.mkvc(ax)
ax[0] = electrostatic_sphere.Plot_Total_Currents(XYZ,sig0,sig1,R,E0,ax[0])
ax[0].set_title('Conductive Sphere: \n Total Current Density',fontsize=ftsize_title)
ax[1] = Plot_Secondary_Currents(XYZ,sig0,sig1,R,E0,ax[1])
ax[1] = electrostatic_sphere.Plot_Secondary_Currents(XYZ,sig0,sig1,R,E0,ax[1])
ax[1].set_title('Conductive Sphere: \n Secondary Current Density',fontsize=ftsize_title)
ax[2] = Plot_Total_Currents(XYZ,sig0,sig2,R,E0,ax[2])
ax[2] = electrostatic_sphere.Plot_Total_Currents(XYZ,sig0,sig2,R,E0,ax[2])
ax[2].set_title('Resistive Sphere: \n Total Current Density',fontsize=ftsize_title)
ax[3] = Plot_Secondary_Currents(XYZ,sig0,sig2,R,E0,ax[3])
ax[3] = electrostatic_sphere.Plot_Secondary_Currents(XYZ,sig0,sig2,R,E0,ax[3])
ax[3].set_title('Resistive Sphere: \n Secondary Current Density',fontsize=ftsize_title)

plt.tight_layout()
Expand All @@ -305,26 +305,26 @@ these discontinuities. According to :ref:`gauss_electric`, the electric
charge accumulated on the surface of the sphere can be quantified by

.. math::
\int_V \boldsymbol{\nabla} \cdot \mathbf{e} \; \mathrm{d}V = \int_V \frac{\rho}{\varepsilon_0} \mathrm{d}V = Q
:label: chargeAccumulationIntegral
\int_V \boldsymbol{\nabla} \cdot \mathbf{e} \; \mathrm{d}V = \int_V \frac{\rho}{\varepsilon_0} \mathrm{d}V = Q
:label: chargeAccumulationIntegral
Based on Gauss's theorem, surface charge density at the interface is given by

.. math::
\mathbf{e}_1 \cdot \mathbf{n} - \mathbf{e}_2 \cdot \mathbf{n} = \frac{\rho_s}{\varepsilon_0}
:label: chargeAccumualationInterface
\mathbf{e}_1 \cdot \mathbf{n} - \mathbf{e}_2 \cdot \mathbf{n} = \frac{\rho_s}{\varepsilon_0}
:label: chargeAccumualationInterface
According to :eq:`eField_outside` :eq:`eField_inside`, the charge quantities accumulated at the surface is

.. math::
\oint_S \rho_s \mathrm{d}a = \varepsilon_0 \oint_S (\mathbf{e}_{1n} - \mathbf{e}_{2n}) = \varepsilon_0 \oint_S 3\mathbf{E_0} R^2 \frac{\sigma_1-\sigma_0}{\sigma_1 + 2\sigma_0}\cos\theta \sin\theta \mathrm{d}\phi\mathrm{d}\theta
:label: totalCharge
\oint_S \rho_s \mathrm{d}a = \varepsilon_0 \oint_S (\mathbf{e}_{1n} - \mathbf{e}_{2n}) = \varepsilon_0 \oint_S 3\mathbf{E_0} R^2 \frac{\sigma_1-\sigma_0}{\sigma_1 + 2\sigma_0}\cos\theta \sin\theta \mathrm{d}\phi\mathrm{d}\theta
:label: totalCharge
The figure below shows surface charge density at the surface of sphere.

.. plot::

from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the wholespace in S/m
sig1 = 10.**-1. # conductivity of the sphere in S/m
Expand All @@ -337,13 +337,13 @@ The figure below shows surface charge density at the surface of sphere.
dx = xr[1]-xr[0] # mesh spacing
dy = yr[1]-yr[0] # mesh spacing
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition

fig, ax = plt.subplots(1,2,figsize=(18,6))
ax = mkvc(ax)
ax[0] = Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[0])
ax = electrostatic_sphere.mkvc(ax)
ax[0] = electrostatic_sphere.Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[0])
ax[0].set_title('Conductive Sphere: \n Charge Accumulation',fontsize=ftsize_title)
ax[1] = Plot_ChargesDensity(XYZ,sig0,sig2,R,E0,ax[1])
ax[1] = electrostatic_sphere.Plot_ChargesDensity(XYZ,sig0,sig2,R,E0,ax[1])
ax[1].set_title('Resistive Sphere: \n Charge Accumulation',fontsize=ftsize_title)

plt.tight_layout()
Expand Down Expand Up @@ -372,8 +372,7 @@ The reverse is observed for a resistive sphere.
.. plot::

import matplotlib.pyplot as plt
from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3. # conductivity of the wholespace
sig1 = 10.**-1. # conductivity of the conductive sphere
Expand All @@ -384,7 +383,7 @@ The reverse is observed for a resistive sphere.
xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
yr = xr.copy() # Y-axis discretization
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr) # Space Definition
PlotOpt = 'Total'

xstart=-100.
Expand All @@ -403,7 +402,7 @@ The reverse is observed for a resistive sphere.
ax4 = plt.subplot2grid((20,12), (8, 6),colspan=6,rowspan=6)
ax = [ax0,ax1,ax2,ax3,ax4]

two_configurations_comparison(XYZ,sig0,sig1,sig2,R,R,E0,xstart,ystart,xend,yend,nb_dipole,electrode_spacing,PlotOpt,ax)
electrostatic_sphere.two_configurations_comparison(XYZ,sig0,sig1,sig2,R,R,E0,xstart,ystart,xend,yend,nb_dipole,electrode_spacing,PlotOpt,ax)

#Set Title
ax[0].set_title('Conductive Sphere',fontsize=ftsize_title)
Expand Down Expand Up @@ -431,8 +430,7 @@ The only parameters that have changed are the radius and the conductivity of the

.. plot::

import matplotlib.pyplot as plt
from examples.sphere import *
from em_examples import sphereElectrostatic_example as electrostatic_sphere

sig0 = 10.**-3.
sig1 = 10.**-2.
Expand All @@ -444,7 +442,7 @@ The only parameters that have changed are the radius and the conductivity of the
xr = np.linspace(-100, 100, n)
yr = xr.copy()
zr = np.r_[0]
XYZ = ndgrid(xr,yr,zr)
XYZ = electrostatic_sphere.ndgrid(xr,yr,zr)
xstart = -100.
ystart = 50.
xend = 100.
Expand All @@ -463,7 +461,7 @@ The only parameters that have changed are the radius and the conductivity of the
ax = [ax0,ax1,ax2,ax3,ax4]

#Plot Configuration, Potential and Data
two_configurations_comparison(XYZ,sig0,sig1,sig2,R0,R1,E0,xstart,ystart,xend,yend,nb_dipole,electrode_spacing,PlotOpt,ax)
electrostatic_sphere.two_configurations_comparison(XYZ,sig0,sig1,sig2,R0,R1,E0,xstart,ystart,xend,yend,nb_dipole,electrode_spacing,PlotOpt,ax)

plt.tight_layout()
plt.show()
55 changes: 0 additions & 55 deletions examples/geophysical_surveys/emi_tutorial/InducedCurrents.ipynb
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