def generateData(self, parameters):
h5data = DictTable(self.datafile)
h5key = ''
for key in parameters.keys():
h5key += key + ('%1.2e' % parameters[key]).replace('-', 'm').replace('+', 'p') ## replace due to PyTables natural naming scheme
if h5data.haskey(h5key):
data = h5data[h5key]
else:
print 'generating data for ' + h5key
simulation = Simulation()
simulation.run(totalSteps=1, sweeps=100, dt=1e20, tol=1e-4, **parameters)
data = simulation.parameters
h5data[h5key] = data
return data
def plot(self, filesuffix=('.png',)):
scale = 1e6
simulation = Simulation()
simulation.run(totalSteps=0)
parameters = simulation.parameters
d = parameters['delta'] * scale * 0.5
r = parameters['fieldWidth'] * scale * 1.1
h = parameters['featureDepth'] * scale
w = parameters['trenchWidth'] * scale * 2
L = d + 0.00002 * scale * 2
y1 = L + 0.00001 * scale
x0 = -0.00004 * scale
x1 = 0.00007 * scale
y0 = -h - 0.00001 * scale
eqnFont = 9
fig = pylab.figure()
ax = fig.add_subplot(111, aspect='equal')
ax.add_patch(pylab.Rectangle((-w / 2, -h), w, h, alpha=0.2, color='black', ec='none', zorder=1))
ax.add_patch(pylab.Rectangle((-r / 2, 0), r, d, alpha=0.2, color='black', ec='none', zorder=1))
ax.add_patch(pylab.Rectangle((-r / 2, d), r, L - d, alpha=0.1, color='black', ec='none', zorder=1))
pylab.plot((-r / 2, -w / 2, -w / 2, w / 2, w / 2, r / 2),
(0, 0, -h, -h, 0, 0), 'k', lw=3, alpha=0.5)
pylab.plot((-r / 2, -r / 2),
(d, 0), 'k--', lw=3, alpha=0.5)
pylab.plot((r / 2, r / 2),
(d, 0), 'k--', lw=3, alpha=0.5)
pylab.plot((-r / 2, r / 2),
(L, L), 'k', lw=3, alpha=0.5)
pylab.ion()
pylab.xticks([])
pylab.yticks((-h, 0, d, L), (r'$-h$', 0, r'$\delta$', r'$L$'))
pylab.axes(ax, aspect='equal')
pylab.ylim(ymin=y0)
pylab.ylim(ymax=y1)
pylab.xlim(xmax=x1)
pylab.xlim(xmin=x0)
pylab.xlabel(r'')
pylab.ylabel(r'$z$', fontsize=16, rotation='horizontal')
pylab.text(-20, d / 2 - 10,
r'\['
r'\begin{split}'
r' & \hspace{-25pt} \text{Boundary Layer} \\'
r' \partial_z^2 \eta &= 0 \\'
r' \partial_z^2 C_{\text{Supp}}^{} &= 0 \\'
r' \partial_z^2 C_{\text{Cu}}^{} &= 0'
r'\end{split}'
r'\]', fontsize=eqnFont)
pylab.text(-2, -20, r'Feature', rotation='vertical', fontsize=eqnFont)
kX = 15
kY = -15
pylab.text(kX, kY, r'$k^+ C_{\text{Supp}}^{} \left(1 - \theta\right) = k^- \theta v$', fontsize=eqnFont)
caseX = 13
caseY = -55
pylab.text(caseX, caseY,
r'\['
r'\begin{cases}'
r' & \hspace*{-8pt} \partial_z^2 \eta = \frac{\rho n F}{\Omega} v \frac{P}{a_f}, \\'
r' & \hspace*{-8pt} D_{\text{Supp}}^{} \partial_z^2 C_{\text{Supp}}^{} = \\'
r' & \Gamma k^+ C_{\text{Supp}}^{} \left(1-\theta\right) \frac{P}{a_f},\\'
r' & \hspace*{-8pt} D_{\text{Cu}}^{} \partial_z^2 C_{\text{Cu}}^{} = \frac{v}{\Omega} \frac{P}{a_f}'
r'\end{cases}'
r'\]', rotation='horizontal', fontsize=eqnFont)
pylab.text(-28, d - 7,
r'\['
r' C_{\text{Supp}}^{} = C_{\text{Supp}}^{\infty}, C_{\text{Cu}}^{} = C_{\text{Cu}}^{\infty}'
r'\]', fontsize=eqnFont)
pylab.text(-27, L - 8,
r'\['
r'\begin{split}'
r' & \hspace{-20pt} \text{Reference Electrode} \\'
r' & \eta = E_{\text{Applied}}^{}'
r'\end{split}'
r'\]', fontsize=eqnFont)
y910 = -15
pylab.text(-r / 2 - 3, y910, r'Eqs. (9, 10)', fontsize=eqnFont)
ax.add_patch(FancyArrowPatch((-r / 4 - 5, y910 + 3.5),(-r / 4 + 5, 1.5), arrowstyle='->',mutation_scale=10, lw=1))
y1112 = -h + 15
pylab.text(-r / 2 - 3, y1112, r'Eqs. (11, 12)', fontsize=eqnFont)
ax.add_patch(FancyArrowPatch((-r / 4 - 5, y1112),(0, -h-0.8), arrowstyle='->',mutation_scale=10, lw=1))
afy = -h + h * 0.8
afw = w * 1.1
ax.add_patch(FancyArrowPatch((-afw / 2, afy),(afw / 2, afy), arrowstyle='<->',mutation_scale=10, lw=1))
pylab.text(-2, afy + 2, r'$a_f$', fontsize=eqnFont)
asy = 0 + d * 0.1
asw = r * 1.02
ax.add_patch(FancyArrowPatch((-asw / 2, asy),(asw / 2, asy), arrowstyle='<->',mutation_scale=15, lw=1))
pylab.text(-2, asy + 2, r'$a_s$', fontsize=eqnFont)
caseYY = caseY + 16
caseYYY = caseYY - 8
ax.add_patch(FancyArrowPatch((caseX, caseYY),(-1, caseYYY), arrowstyle='->',mutation_scale=10, lw=1))
kYY = kY + 3
kYYY = kYY + 4
ax.add_patch(FancyArrowPatch((kX, kYY),(w / 2 - 1.5, kYYY), arrowstyle='->',mutation_scale=10, lw=1))
kkYY = kY + 3
ax.add_patch(FancyArrowPatch((kX, kkYY),(w / 2 + 4, 1.5), arrowstyle='->',mutation_scale=10, lw=1))
## break in axes
breakX = d + (L - d) / 2
hX = 10
ls = 10
diag = 5
ax.add_patch(pylab.Rectangle((x0, breakX - hX / 2), x1 - x0 + 0.0, hX, alpha=1.0, color='white', ec='white', zorder=100, clip_on=False))
ax.plot((x0 - ls / 2, x0 + ls / 2), (breakX - hX / 2 + diag / 2, breakX - hX / 2 - diag / 2), 'k', clip_on=False, zorder=101)
ax.plot((x0 - ls / 2, x0 + ls / 2), (breakX + hX / 2 + diag / 2, breakX + hX / 2 - diag / 2), 'k', clip_on=False, zorder=101)
ax.plot((x1 - ls / 2, x1 + ls / 2), (breakX - hX / 2 + diag / 2, breakX - hX / 2 - diag / 2), 'k', clip_on=False, zorder=101)
ax.plot((x1 - ls / 2, x1 + ls / 2), (breakX + hX / 2 + diag / 2, breakX + hX / 2 - diag / 2), 'k', clip_on=False, zorder=101)
for fs in filesuffix:
pylab.savefig('schematic' + fs)