old_contents: """
  Effective Medium Theory Mapping
  ===============================
  
  This example uses Self Consistent Effective Medium Theory to estimate the
  electrical conductivity of a mixture of two phases of materials. Given
  the electrical conductivity of each of the phases (:math:`\sigma_0`,
  :math:`\sigma_1`), the :class:`SimPEG.Maps.SelfConsistentEffectiveMedium`
  map takes the concentration of phase-1 (:math:`\phi_1`) and maps this to an
  electrical conductivity.
  
  This mapping is used in chapter 2 of:
  
  Heagy, Lindsey J.(2018, in prep) *Electromagnetic methods for imaging
  subsurface injections.* University of British Columbia
  
  :author: `@lheagy <https://github.com/lheagy>`_
  
  """
  
  import numpy as np
  import matplotlib.pyplot as plt
  from SimPEG import Maps
  from matplotlib import rcParams
  from string import ascii_lowercase
  rcParams['font.size'] = 12
  
  ###############################################################################
  # Conductivities
  # ---------------
  #
  # Here we consider a mixture composed of fluid (3 S/m) and conductive
  # particles which we will vary the conductivity of.
  #
  
  sigma_fluid = 3
  sigma1 = np.logspace(1, 5, 5) # look at a range of particle conductivities
  phi = np.linspace(0.0, 1, 1000) # vary the volume of particles
  
  ###############################################################################
  # Construct the Mapping
  # ---------------------
  #
  # We set the conductivity of the phase-0 material to the conductivity of the
  # fluid. The mapping will then take a concentration (by volume), of phase-1
  # material and compute the effective conductivity
  #
  
  scemt = Maps.SelfConsistentEffectiveMedium(sigma0=sigma_fluid, sigma1=1)
  
  ###############################################################################
  # Loop over a range of particle conductivities
  # --------------------------------------------
  #
  # We loop over the values defined as `sigma1` and compute the effective
  # conductivity of the mixture for each concentration in the `phi` vector
  #
  
  sige = np.zeros([phi.size, sigma1.size])
  
  for i, s in enumerate(sigma1):
      scemt.sigma1 = s
      sige[:, i] = scemt * phi
  
  ###############################################################################
  # Plot the effective conductivity
  # -------------------------------
  #
  # The plot shows the effective conductivity of 5 difference mixtures. In all
  # cases, the conductivity of the fluid, :math:`\sigma_0`, is 3 S/m. The
  # conductivity of the particles is indicated in the legend
  #
  
  fig, ax = plt.subplots(1, 1, figsize=(7, 4), dpi=350)
  
  ax.semilogy(phi, sige)
  ax.grid(which="both", alpha=0.4)
  ax.legend(["{:1.0e} S/m".format(s) for s in sigma1])
  ax.set_xlabel("Volume fraction of proppant $\phi$")
  ax.set_ylabel("Effective conductivity (S/m)")
  
  
  
new_contents: """
  Effective Medium Theory Mapping
  ===============================
  
  This example uses Self Consistent Effective Medium Theory to estimate the
  electrical conductivity of a mixture of two phases of materials. Given
  the electrical conductivity of each of the phases (:math:`\sigma_0`,
  :math:`\sigma_1`), the :class:`SimPEG.Maps.SelfConsistentEffectiveMedium`
  map takes the concentration of phase-1 (:math:`\phi_1`) and maps this to an
  electrical conductivity.
  
  This mapping is used in chapter 2 of:
  
  Heagy, Lindsey J.(2018, in prep) *Electromagnetic methods for imaging
  subsurface injections.* University of British Columbia
  
  :author: `@lheagy <https://github.com/lheagy>`_
  
  """
  
  import numpy as np
  import matplotlib.pyplot as plt
  from SimPEG import Maps
  from matplotlib import rcParams
  rcParams['font.size'] = 12
  
  ###############################################################################
  # Conductivities
  # ---------------
  #
  # Here we consider a mixture composed of fluid (3 S/m) and conductive
  # particles which we will vary the conductivity of.
  #
  
  sigma_fluid = 3
  sigma1 = np.logspace(1, 5, 5) # look at a range of particle conductivities
  phi = np.linspace(0.0, 1, 1000) # vary the volume of particles
  
  ###############################################################################
  # Construct the Mapping
  # ---------------------
  #
  # We set the conductivity of the phase-0 material to the conductivity of the
  # fluid. The mapping will then take a concentration (by volume), of phase-1
  # material and compute the effective conductivity
  #
  
  scemt = Maps.SelfConsistentEffectiveMedium(sigma0=sigma_fluid, sigma1=1)
  
  ###############################################################################
  # Loop over a range of particle conductivities
  # --------------------------------------------
  #
  # We loop over the values defined as `sigma1` and compute the effective
  # conductivity of the mixture for each concentration in the `phi` vector
  #
  
  sige = np.zeros([phi.size, sigma1.size])
  
  for i, s in enumerate(sigma1):
      scemt.sigma1 = s
      sige[:, i] = scemt * phi
  
  ###############################################################################
  # Plot the effective conductivity
  # -------------------------------
  #
  # The plot shows the effective conductivity of 5 difference mixtures. In all
  # cases, the conductivity of the fluid, :math:`\sigma_0`, is 3 S/m. The
  # conductivity of the particles is indicated in the legend
  #
  
  fig, ax = plt.subplots(1, 1, figsize=(7, 4), dpi=350)
  
  ax.semilogy(phi, sige)
  ax.grid(which="both", alpha=0.4)
  ax.legend(["{:1.0e} S/m".format(s) for s in sigma1])
  ax.set_xlabel("Volume fraction of proppant $\phi$")
  ax.set_ylabel("Effective conductivity (S/m)")
  
  
  
subject: remove the unused import of ascii-lowercase