From 8e5dca6674b9c04e5b8c8614e5dc0add6505bd9d Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Fri, 8 Jan 2021 10:03:52 -0500 Subject: [PATCH 01/23] Convert binary phase field example to use steppyngstounes --- examples/phase/binary.py | 35 +++++++++++++++++++++++++---------- 1 file changed, 25 insertions(+), 10 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index f3938969a2..d51174f162 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -572,19 +572,34 @@ def deltaChemPot(phase, C, T): >>> dt = 1.e-5 >>> if __name__ == '__main__': -... timesteps = 100 +... timesteps = 1000000 ... else: ... timesteps = 10 ->>> from builtins import range ->>> for i in range(timesteps): -... phase.updateOld() -... C.updateOld() -... phaseRes = 1e+10 -... diffRes = 1e+10 -... while phaseRes > 1e-3 or diffRes > 1e-3: -... phaseRes = phaseEq.sweep(var=phase, dt=dt) -... diffRes = diffusionEq.sweep(var=C, dt=dt, solver=solver) +>>> phaseScale = 1e-3 +>>> diffScale = 1e-3 + +>>> phase.updateOld() +>>> C.updateOld() + +>>> from steppyngstounes import PIDStepper, ScaledStepper, FixedStepper, PseudoRKQSStepper +>>> for outer in FixedStepper(start=0., stop=timesteps*dt, tryStep=dt * 100): +... for inner in PseudoRKQSStepper(start=outer.begin, stop=outer.end, tryStep=dt): +... # print("step", inner.begin, inner.size) +... for sweep in range(5): +... phaseRes = phaseEq.sweep(var=phase, dt=inner.size) / phaseScale +... diffRes = diffusionEq.sweep(var=C, dt=inner.size, solver=solver) / diffScale +... # print(" ", sweep, phaseRes, diffRes) +... res = max(phaseRes, diffRes) +... if inner.succeeded(error=res, value=None): +... phase.updateOld() +... C.updateOld() +... print(inner.size) +... else: +... phase.value = phase.old +... C.value = C.old +... dt = inner.want +... outer.succeeded(value=None, error=1.) ... if __name__ == '__main__': ... viewer.plot() From 6e94f8552475253f134f59150aa2d98a0669e4f6 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Sat, 9 Jan 2021 21:02:46 -0500 Subject: [PATCH 02/23] Convert to quadratic time stepper for very long times --- examples/phase/binary.py | 30 ++++++++++++++++++++++++------ 1 file changed, 24 insertions(+), 6 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index d51174f162..76d4992207 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -572,9 +572,9 @@ def deltaChemPot(phase, C, T): >>> dt = 1.e-5 >>> if __name__ == '__main__': -... timesteps = 1000000 +... totaltime = 1e10 ... else: -... timesteps = 10 +... totaltime = 1e-4 >>> phaseScale = 1e-3 >>> diffScale = 1e-3 @@ -583,25 +583,43 @@ def deltaChemPot(phase, C, T): >>> C.updateOld() >>> from steppyngstounes import PIDStepper, ScaledStepper, FixedStepper, PseudoRKQSStepper ->>> for outer in FixedStepper(start=0., stop=timesteps*dt, tryStep=dt * 100): -... for inner in PseudoRKQSStepper(start=outer.begin, stop=outer.end, tryStep=dt): + +>>> class SquareStepper(FixedStepper): +... def _adaptStep(self): +... dt = (self.current - self.start) +... if dt == 0: +... dt = super(FixedStepper, self)._adaptStep() +... return dt + +>>> solve = 0 + +>>> t = viewer.axes.text(0.00025, 0.2, "t = 0") + +>>> for outer in SquareStepper(start=0., stop=totaltime, size=dt): +... #print(outer.size) +... for inner in PIDStepper(start=outer.begin, stop=outer.end, size=dt): #, maxStep=2.5): ... # print("step", inner.begin, inner.size) ... for sweep in range(5): ... phaseRes = phaseEq.sweep(var=phase, dt=inner.size) / phaseScale ... diffRes = diffusionEq.sweep(var=C, dt=inner.size, solver=solver) / diffScale ... # print(" ", sweep, phaseRes, diffRes) +... solve += 1 ... res = max(phaseRes, diffRes) ... if inner.succeeded(error=res, value=None): ... phase.updateOld() ... C.updateOld() -... print(inner.size) +... #print("", inner.size) ... else: +... #print("", inner.size, "FAILED", phaseRes, diffRes) ... phase.value = phase.old ... C.value = C.old ... dt = inner.want ... outer.succeeded(value=None, error=1.) ... if __name__ == '__main__': -... viewer.plot() +... t.set_text("t = {:f}".format(outer.end)) +... viewer.plot(filename="binary-{}.png".format(outer.end)) + +>>> print(solve, "total solves") >>> from fipy import input >>> if __name__ == '__main__': From ba57a517b7a7db3d47e49fb40ae9fbf12736af12 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Tue, 12 Jan 2021 18:25:03 -0500 Subject: [PATCH 03/23] Visualize interface position --- examples/phase/binary.py | 30 ++++++++++++++++++++++++++++-- 1 file changed, 28 insertions(+), 2 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 76d4992207..723ddd3214 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -465,7 +465,15 @@ def deltaChemPot(phase, C, T): module: fipy.viewers >>> if __name__ == '__main__': -... viewer = Viewer(vars=(phase, C, sharp), +... from matplotlib import pyplot as plt +... fig = plt.figure(constrained_layout=True, figsize=[4, 6]) +... gs = fig.add_gridspec(ncols=1, nrows=3) +... viewax = fig.add_subplot(gs[1:, 0]) +... viewax.set_xlabel(r"$x / \mathrm{cm}$") +... posax = fig.add_subplot(gs[0, 0], sharex=viewax) +... posax.set_ylabel(r"$t / \mathrm{s}$") +... posax.label_outer() +... viewer = Viewer(vars=(phase, C, sharp), axes=viewax, ... datamin=0., datamax=1.) ... viewer.plot() @@ -595,6 +603,17 @@ def deltaChemPot(phase, C, T): >>> t = viewer.axes.text(0.00025, 0.2, "t = 0") +>>> def tanhResiduals(p, y, x): +>>> x0, d = p +>>> return y - 0.5 * (1 - numerix.tanh((x - x0) / (2*d))) +>>> from scipy.optimize import leastsq # doctest: +SCIPY +>>> x = mesh.cellCenters[0] + +>>> positions = [0.001] +>>> times = [1e-5] +>>> posax.set_ylim(dt, totaltime) +>>> line, = posax.semilogy(positions, times, color="blue") +>>> bug, = posax.semilogy([], [], linestyle="", marker="o", color="red") >>> for outer in SquareStepper(start=0., stop=totaltime, size=dt): ... #print(outer.size) ... for inner in PIDStepper(start=outer.begin, stop=outer.end, size=dt): #, maxStep=2.5): @@ -616,7 +635,14 @@ def deltaChemPot(phase, C, T): ... dt = inner.want ... outer.succeeded(value=None, error=1.) ... if __name__ == '__main__': -... t.set_text("t = {:f}".format(outer.end)) +... if posax is not None: +... (x0_fit, d_fit), msg = leastsq(tanhResiduals, [L/2., deltaA], +... args=(phase.globalValue, x.globalValue)) # doctest: +SCIPY +... positions.append(x0_fit) +... times.append(outer.end) +... line.set_data(positions, times) +... bug.set_data([positions[-1]], [times[-1]]) +... t.set_text(r"$t = {:f}\,\mathrm{{s}}$".format(outer.end)) ... viewer.plot(filename="binary-{}.png".format(outer.end)) >>> print(solve, "total solves") From 665c04dca29ed8aa4d31e54eaf7ea47c5085edd8 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Tue, 12 Jan 2021 18:26:03 -0500 Subject: [PATCH 04/23] Add discussion of binary phase field behavior --- examples/phase/binary.py | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 723ddd3214..efa11d25b5 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -662,6 +662,26 @@ def deltaChemPot(phase, C, T): could again verify the final concentrations and phase fraction against the expected values. +The interface moves :math:`\approx 3.4\,\mathrm{\mu m}` in +:math:`80\,\mathrm{ms}`, driven by diffusion in the liquid phase +(:math:`(10\,\mathrm{\mu m})^2 / (10^{-5}\,\mathrm{cm^2/s}) = 0.1 s` is a +rough estimate of how long this process should take). For the next +:math:`20\,\mathrm{s}`, the interface stalls while the solute step trapped +in the solid phase diffuses outward (:math:`(3.4\,\mathrm{\mu m})^2 / +(10^{-9}\,\mathrm{cm^2/s}) = \mathcal{O}(100\,\mathrm{s})`). Once the +solute gradient in the solid reaches the new position of the interface, the +solidification front begins to move, driven by diffusion in the solid. +When the solute in the solid becomes uniform, the interface stalls again +after :math:`\approx 4000\,\mathrm{s}`, having moved another +:math:`3.2\,\mathrm{\mu m}` (:math:`(17\,\mathrm{\mu m})^2 / +(10^{-9}\,\mathrm{cm^2/s}) = \mathcal{O}(3000\,\mathrm{s})`). After this +point, there is essentially no further motion of the interface and barely +perceptable changes in the concentration field. The fact that the +interface does not reach the predicted phase fraction is due to the fact +that this phase field model exhibits adsorption at the interface, resulting +in the bulk phases not having exactly the concentrations assumed in the +sharp interface treatment. + .. rubric:: Footnotes .. [#phi] We will find that we need to "sweep" this non-linear problem From 2b817050e31d5930fa42a510da752bcaca442c45 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Tue, 12 Jan 2021 18:27:38 -0500 Subject: [PATCH 05/23] Add mass conservation to step size control --- examples/phase/binary.py | 15 +++++++-------- 1 file changed, 7 insertions(+), 8 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index efa11d25b5..bb465c8051 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -584,9 +584,6 @@ def deltaChemPot(phase, C, T): ... else: ... totaltime = 1e-4 ->>> phaseScale = 1e-3 ->>> diffScale = 1e-3 - >>> phase.updateOld() >>> C.updateOld() @@ -618,13 +615,15 @@ def deltaChemPot(phase, C, T): ... #print(outer.size) ... for inner in PIDStepper(start=outer.begin, stop=outer.end, size=dt): #, maxStep=2.5): ... # print("step", inner.begin, inner.size) -... for sweep in range(5): -... phaseRes = phaseEq.sweep(var=phase, dt=inner.size) / phaseScale -... diffRes = diffusionEq.sweep(var=C, dt=inner.size, solver=solver) / diffScale +... for sweep in range(2): +... phaseRes = phaseEq.sweep(var=phase, dt=inner.size) +... diffRes = diffusionEq.sweep(var=C, dt=inner.size, solver=solver) ... # print(" ", sweep, phaseRes, diffRes) ... solve += 1 -... res = max(phaseRes, diffRes) -... if inner.succeeded(error=res, value=None): +... err = max(phaseRes / 1e-3, +... diffRes / 1e-3, +... abs(C.cellVolumeAverage.value - 0.5) / 1e-6) +... if inner.succeeded(error=err, value=None): ... phase.updateOld() ... C.updateOld() ... #print("", inner.size) From bc4e900aef3bb3f01f704c0fcddffc6333344d71 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Tue, 12 Jan 2021 18:28:37 -0500 Subject: [PATCH 06/23] Reduce simulation time It's done for all intents and purposes --- examples/phase/binary.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index bb465c8051..bc3ddf52a8 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -580,7 +580,7 @@ def deltaChemPot(phase, C, T): >>> dt = 1.e-5 >>> if __name__ == '__main__': -... totaltime = 1e10 +... totaltime = 300 * 3600 # 300 h ... else: ... totaltime = 1e-4 From 4edca5a780fa74298a9544c362326bb40545cff1 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 27 Jan 2021 14:22:10 -0500 Subject: [PATCH 07/23] Create a custom viewer --- examples/phase/binary.py | 242 +++++++++++++++++++++++++-------------- 1 file changed, 153 insertions(+), 89 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index bc3ddf52a8..1f0d1fb58d 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -461,20 +461,70 @@ def deltaChemPot(phase, C, T): >>> sharp.setValue(Cs, where=x < L * fraction) >>> sharp.setValue(Cl, where=x >= L * fraction) +>>> elapsed = Variable(value=0.) # s + .. index:: module: fipy.viewers >>> if __name__ == '__main__': -... from matplotlib import pyplot as plt -... fig = plt.figure(constrained_layout=True, figsize=[4, 6]) -... gs = fig.add_gridspec(ncols=1, nrows=3) -... viewax = fig.add_subplot(gs[1:, 0]) -... viewax.set_xlabel(r"$x / \mathrm{cm}$") -... posax = fig.add_subplot(gs[0, 0], sharex=viewax) -... posax.set_ylabel(r"$t / \mathrm{s}$") -... posax.label_outer() -... viewer = Viewer(vars=(phase, C, sharp), axes=viewax, -... datamin=0., datamax=1.) +... try: +... from fipy import Matplotlib1DViewer +... from scipy.optimize import leastsq # doctest: +SCIPY +... from matplotlib import pyplot as plt +... +... class PhaseViewer(Matplotlib1DViewer): +... def __init__(self, phase, C, sharp, elapsed, title=None, +... tmin=None, tmax=None, **kwlimits): +... self.phase = phase +... self.x = self.phase.mesh.cellCenters[0] +... self.elapsed = elapsed +... +... fig = plt.figure(constrained_layout=True, figsize=[4, 6]) +... gs = fig.add_gridspec(ncols=1, nrows=3) +... self.viewax = fig.add_subplot(gs[1:, 0]) +... self.viewax.set_xlabel(r"$x / \mathrm{cm}$") +... self.posax = fig.add_subplot(gs[0, 0], sharex=self.viewax) +... self.posax.set_ylabel(r"$t / \mathrm{s}$") +... self.posax.label_outer() +... self.posax.set_ylim(tmin, tmax) +... +... self.times = [] +... self.positions = [] +... self.line, = self.posax.semilogy([0.], [0.], +... color="blue") +... self.bug, = self.posax.semilogy([], [], +... linestyle="", marker="o", color="red") +... +... super(PhaseViewer, self).__init__(vars=(phase, C, sharp), +... axes=self.viewax, +... **kwlimits) +... +... self.timer = self.viewax.text(0.00025, 0.2, "t = 0") +... +... @staticmethod +... def tanhResiduals(p, y, x): +... x0, d = p +... return y - 0.5 * (1 - numerix.tanh((x - x0) / (2*d))) +... +... def _plot(self): +... (x0_fit, d_fit), msg = leastsq(self.tanhResiduals, [L/2., deltaA], +... args=(self.phase.globalValue, +... self.x.globalValue)) +... self.positions.append(x0_fit) +... self.times.append(float(self.elapsed)) +... self.line.set_data(self.positions, self.times) +... self.bug.set_data([self.positions[-1]], [self.times[-1]]) +... +... self.timer.set_text(r"$t = {:f}\\,\\mathrm{{s}}$".format(float(self.elapsed))) +... +... super(PhaseViewer, self)._plot() +... +... viewer = PhaseViewer(phase=phase, C=C, sharp=sharp, +... elapsed=elapsed, tmin=1e-5, tmax=300 * 3600, +... datamin=0., datamax=1.) +... except ImportError: +... viewer = Viewer(vars=(phase, C, sharp), +... datamin=0., datamax=1.) ... viewer.plot() Because the phase field interface will not move, and because we've seen in @@ -561,14 +611,14 @@ def deltaChemPot(phase, C, T): \\vec{u}_\\phi &= \\frac{D_\\phi}{C} \\nabla \\phi \\\\ &\\approx - \\frac{Dl \\frac{1}{2} V_m}{R T} + \\frac{D_l \\frac{1}{2} V_m}{R T} \\left[ \\frac{L_B\\left(T - T_M^B\\right)}{T_M^B} - \\frac{L_A\\left(T - T_M^A\\right)}{T_M^A} \\right] \\frac{1}{\\Delta x} \\\\ &\\approx - \\frac{Dl \\frac{1}{2} V_m}{R T} + \\frac{D_l \\frac{1}{2} V_m}{R T} \\left(L_B + L_A\\right) \\frac{T_M^A - T_M^B}{T_M^A + T_M^B} \\frac{1}{\\Delta x} \\\\ @@ -577,109 +627,121 @@ def deltaChemPot(phase, C, T): To get a :math:`\\text{CFL} = \\vec{u}_\\phi \\Delta t / \\Delta x < 1`, we need a time step of about :math:`\\unit{10^{-5}}{\\second}`. ->>> dt = 1.e-5 +>>> dt0 = 1.e-5 + +>>> from builtins import range +>>> for i in range(8): +... phase.updateOld() +... C.updateOld() +... phaseRes = 1e+10 +... diffRes = 1e+10 +... while phaseRes > 1e-3 or diffRes > 1e-3: +... phaseRes = phaseEq.sweep(var=phase, dt=dt0) +... diffRes = diffusionEq.sweep(var=C, dt=dt0, solver=solver) +... elapsed.value = (i + 1) * dt0 +... if __name__ == '__main__': +... viewer.plot() +>>> from fipy import input >>> if __name__ == '__main__': -... totaltime = 300 * 3600 # 300 h -... else: -... totaltime = 1e-4 +... input("Moving phase field. Press to proceed...") + +We see that the composition on either side of the interface approaches the +sharp-interface solidus and liquidus, but it will take a great many more +timesteps to reach equilibrium. If we waited sufficiently long, we +could again verify the final concentrations and phase fraction against the +expected values. + +We can estimate the time to equlibration by examining the time for the +diffusion field to become uniform. In the liquid, this will take +:math:`\\mathcal{O}((\\unit{10}{\\micro\\meter})^2 / D_l) = +\\unit{0.1}{\\second}` and in the solid +:math:`\\mathcal{O}((\\unit{10}{\\micro\\meter})^2 / D_s) = +\\unit{1000}{\\second}`. + +Not wanting to take a hundred-million steps, we employ adaptive time +stepping, using the steppyingstounes package. This package takes care of +many of the messy details of stepping, like ???, while keeping the +structure of our solve loop largely intact. + +>>> from steppyngstounes import SequenceStepper, PIDStepper +>>> from itertools import count + +Assuming the process is dominated by diffusion, we can take steps that +increase parabolically. +Since we're unsure if diffusion is the only process controlling dynamics, +we take each parabolic step with an adaptive stepper that uses a `PID +controller`_ to keep the equation residuals and mass conservation within +acceptable limits. The total number of solves is not strongly sensitive to +the number of sweeps, but two sweeps seems to be both sufficient and +efficient. + +We'll only advance the step if it's successful, so we need to update the +old values before we get started. >>> phase.updateOld() >>> C.updateOld() ->>> from steppyngstounes import PIDStepper, ScaledStepper, FixedStepper, PseudoRKQSStepper - ->>> class SquareStepper(FixedStepper): -... def _adaptStep(self): -... dt = (self.current - self.start) -... if dt == 0: -... dt = super(FixedStepper, self)._adaptStep() -... return dt - ->>> solve = 0 - ->>> t = viewer.axes.text(0.00025, 0.2, "t = 0") - ->>> def tanhResiduals(p, y, x): ->>> x0, d = p ->>> return y - 0.5 * (1 - numerix.tanh((x - x0) / (2*d))) ->>> from scipy.optimize import leastsq # doctest: +SCIPY ->>> x = mesh.cellCenters[0] - ->>> positions = [0.001] ->>> times = [1e-5] ->>> posax.set_ylim(dt, totaltime) ->>> line, = posax.semilogy(positions, times, color="blue") ->>> bug, = posax.semilogy([], [], linestyle="", marker="o", color="red") ->>> for outer in SquareStepper(start=0., stop=totaltime, size=dt): -... #print(outer.size) -... for inner in PIDStepper(start=outer.begin, stop=outer.end, size=dt): #, maxStep=2.5): -... # print("step", inner.begin, inner.size) +>>> if __name__ == '__main__': +... totaltime = 300 * 3600 # 300 h +... else: +... totaltime = 32e-5 # 320 us + +>>> dt = dt0 + +>>> for checkpoint in SequenceStepper(start=float(elapsed), stop=totaltime, +... sizes=(dt0 * 2**(n/2) for n in count(7))): +... for step in PIDStepper(start=checkpoint.begin, +... stop=checkpoint.end, +... size=dt): ... for sweep in range(2): -... phaseRes = phaseEq.sweep(var=phase, dt=inner.size) -... diffRes = diffusionEq.sweep(var=C, dt=inner.size, solver=solver) -... # print(" ", sweep, phaseRes, diffRes) -... solve += 1 +... phaseRes = phaseEq.sweep(var=phase, dt=step.size) +... diffRes = diffusionEq.sweep(var=C, dt=step.size, solver=solver) ... err = max(phaseRes / 1e-3, ... diffRes / 1e-3, ... abs(C.cellVolumeAverage.value - 0.5) / 1e-6) -... if inner.succeeded(error=err, value=None): +... if step.succeeded(error=err): ... phase.updateOld() ... C.updateOld() -... #print("", inner.size) +... elapsed.value = step.end ... else: -... #print("", inner.size, "FAILED", phaseRes, diffRes) ... phase.value = phase.old ... C.value = C.old -... dt = inner.want -... outer.succeeded(value=None, error=1.) +... # the last step might have been smaller than possible, +... # if it was near the end of the checkpoint range +... dt = step.want +... checkpoint.succeeded() ... if __name__ == '__main__': -... if posax is not None: -... (x0_fit, d_fit), msg = leastsq(tanhResiduals, [L/2., deltaA], -... args=(phase.globalValue, x.globalValue)) # doctest: +SCIPY -... positions.append(x0_fit) -... times.append(outer.end) -... line.set_data(positions, times) -... bug.set_data([positions[-1]], [times[-1]]) -... t.set_text(r"$t = {:f}\,\mathrm{{s}}$".format(outer.end)) -... viewer.plot(filename="binary-{}.png".format(outer.end)) - ->>> print(solve, "total solves") +... viewer.plot() >>> from fipy import input >>> if __name__ == '__main__': -... input("Moving phase field. Press to proceed...") +... input("Re-equilbrated phase field. Press to proceed...") .. image:: binary/moving.* :width: 90% :align: center - :alt: phase and composition fields in during solidification, compared with final phase diagram concentrations - -We see that the composition on either side of the interface approach the -sharp-interface solidus and liquidus, but it will take a great many more -timesteps to reach equilibrium. If we waited sufficiently long, we -could again verify the final concentrations and phase fraction against the -expected values. - -The interface moves :math:`\approx 3.4\,\mathrm{\mu m}` in -:math:`80\,\mathrm{ms}`, driven by diffusion in the liquid phase -(:math:`(10\,\mathrm{\mu m})^2 / (10^{-5}\,\mathrm{cm^2/s}) = 0.1 s` is a -rough estimate of how long this process should take). For the next -:math:`20\,\mathrm{s}`, the interface stalls while the solute step trapped -in the solid phase diffuses outward (:math:`(3.4\,\mathrm{\mu m})^2 / -(10^{-9}\,\mathrm{cm^2/s}) = \mathcal{O}(100\,\mathrm{s})`). Once the -solute gradient in the solid reaches the new position of the interface, the -solidification front begins to move, driven by diffusion in the solid. -When the solute in the solid becomes uniform, the interface stalls again -after :math:`\approx 4000\,\mathrm{s}`, having moved another -:math:`3.2\,\mathrm{\mu m}` (:math:`(17\,\mathrm{\mu m})^2 / -(10^{-9}\,\mathrm{cm^2/s}) = \mathcal{O}(3000\,\mathrm{s})`). After this + :alt: phase and composition fields during solidification, compared with final phase diagram concentrations + +The interface moves :math:`\\approx \\unit{3.4}{\\micro\\meter}` in +:math:`\\unit{80}{\\milli\\second}`, driven by diffusion in the liquid +phase (compare the estimate above of \\unit{0.1}{\\second}}). For the next +:math:`\\unit{20}{\\second}`, the interface stalls while the solute step +trapped in the solid phase diffuses outward +(:math:`(\\unis{3.4}{\\micro\\meter})^2 / D_s = +\mathcal{O}(\\unit{100}{\\second})`). Once the solute gradient in the +solid reaches the new position of the interface, the solidification front +begins to move, driven by diffusion in the solid. When the solute in the +solid becomes uniform, the interface stalls again after :math:`\\approx +\\unit{4000}{\\second}`, having moved another +:math:`\\unit{3.2}{\\micro\\meter}` (recall the estimate of +:math:`\\unit{1000}{\\second}` for equilibration in the solid). After this point, there is essentially no further motion of the interface and barely perceptable changes in the concentration field. The fact that the interface does not reach the predicted phase fraction is due to the fact -that this phase field model exhibits adsorption at the interface, resulting -in the bulk phases not having exactly the concentrations assumed in the -sharp interface treatment. +that this phase field model accounts for adsorption at the interface, +resulting in the bulk phases not having exactly the concentrations assumed +in the sharp interface treatment. .. rubric:: Footnotes @@ -693,6 +755,8 @@ def deltaChemPot(phase, C, T): as a :class:`~fipy.variables.variable.Variable` .. _CFL limit: http://en.wikipedia.org/wiki/Courant-Friedrichs-Lewy_condition + +.. _PID controller: https://en.wikipedia.org/wiki/PID_controller """ from __future__ import unicode_literals From 97b6b6f8e3c773321040e413fb9023df2921c58e Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 27 Jan 2021 16:01:33 -0500 Subject: [PATCH 08/23] Correct description of time steps Time steps increase geometrically, not parabolically. Parabolically increasing timesteps (`dt0 * (n/2)**2`) do not perform as well. --- examples/phase/binary.py | 13 ++++++------- 1 file changed, 6 insertions(+), 7 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 1f0d1fb58d..0f520637d5 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -668,13 +668,12 @@ def deltaChemPot(phase, C, T): >>> from itertools import count Assuming the process is dominated by diffusion, we can take steps that -increase parabolically. -Since we're unsure if diffusion is the only process controlling dynamics, -we take each parabolic step with an adaptive stepper that uses a `PID -controller`_ to keep the equation residuals and mass conservation within -acceptable limits. The total number of solves is not strongly sensitive to -the number of sweeps, but two sweeps seems to be both sufficient and -efficient. +increase geometrically. Since we're unsure if diffusion is the only +process controlling dynamics, we take each increasing step with an adaptive +stepper that uses a `PID controller`_ to keep the equation residuals and +mass conservation within acceptable limits. The total number of solves is +not strongly sensitive to the number of sweeps, but two sweeps seems to be +both sufficient and efficient. We'll only advance the step if it's successful, so we need to update the old values before we get started. From fa4c4d45fd152ee63fe9895dcdad408b08c1d494 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 27 Jan 2021 16:03:24 -0500 Subject: [PATCH 09/23] Explain merits of steppyngstounes --- examples/phase/binary.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 0f520637d5..3f9ca74395 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -661,8 +661,9 @@ def deltaChemPot(phase, C, T): Not wanting to take a hundred-million steps, we employ adaptive time stepping, using the steppyingstounes package. This package takes care of -many of the messy details of stepping, like ???, while keeping the -structure of our solve loop largely intact. +many of the messy details of stepping, like overshoot, underflow, and step +size adaptation, while keeping the structure of our solve loop largely +intact. >>> from steppyngstounes import SequenceStepper, PIDStepper >>> from itertools import count From 875174a3360cdca4cb4be19f1c9e5fed53a787b1 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 27 Jan 2021 17:52:37 -0500 Subject: [PATCH 10/23] Apply steppyngstounes to binaryCoupled --- examples/phase/binary.py | 2 +- examples/phase/binaryCoupled.py | 177 ++++++++++++++++++++++++++++---- 2 files changed, 160 insertions(+), 19 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 3f9ca74395..2de11e87b7 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -699,7 +699,7 @@ def deltaChemPot(phase, C, T): ... diffRes = diffusionEq.sweep(var=C, dt=step.size, solver=solver) ... err = max(phaseRes / 1e-3, ... diffRes / 1e-3, -... abs(C.cellVolumeAverage.value - 0.5) / 1e-6) +... abs(Cavg.value - 0.5) / 1e-6) ... if step.succeeded(error=err): ... phase.updateOld() ... C.updateOld() diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index 6324ce3fa6..38d4ea6a31 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -479,12 +479,70 @@ def deltaChemPot(phase, C, T): >>> sharp.setValue(Cs, where=x < L * fraction) >>> sharp.setValue(Cl, where=x >= L * fraction) +>>> elapsed = Variable(value=0.) # s + .. index:: module: fipy.viewers >>> if __name__ == '__main__': -... viewer = Viewer(vars=(phase, C, sharp), -... datamin=0., datamax=1.) +... try: +... from fipy import Matplotlib1DViewer +... from scipy.optimize import leastsq # doctest: +SCIPY +... from matplotlib import pyplot as plt +... +... class PhaseViewer(Matplotlib1DViewer): +... def __init__(self, phase, C, sharp, elapsed, title=None, +... tmin=None, tmax=None, **kwlimits): +... self.phase = phase +... self.x = self.phase.mesh.cellCenters[0] +... self.elapsed = elapsed +... +... fig = plt.figure(constrained_layout=True, figsize=[4, 6]) +... gs = fig.add_gridspec(ncols=1, nrows=3) +... self.viewax = fig.add_subplot(gs[1:, 0]) +... self.viewax.set_xlabel(r"$x / \mathrm{cm}$") +... self.posax = fig.add_subplot(gs[0, 0], sharex=self.viewax) +... self.posax.set_ylabel(r"$t / \mathrm{s}$") +... self.posax.label_outer() +... self.posax.set_ylim(tmin, tmax) +... +... self.times = [] +... self.positions = [] +... self.line, = self.posax.semilogy([0.], [0.], +... color="blue") +... self.bug, = self.posax.semilogy([], [], +... linestyle="", marker="o", color="red") +... +... super(PhaseViewer, self).__init__(vars=(phase, C, sharp), +... axes=self.viewax, +... **kwlimits) +... +... self.timer = self.viewax.text(0.00025, 0.2, "t = 0") +... +... @staticmethod +... def tanhResiduals(p, y, x): +... x0, d = p +... return y - 0.5 * (1 - numerix.tanh((x - x0) / (2*d))) +... +... def _plot(self): +... (x0_fit, d_fit), msg = leastsq(self.tanhResiduals, [L/2., deltaA], +... args=(self.phase.globalValue, +... self.x.globalValue)) +... self.positions.append(x0_fit) +... self.times.append(float(self.elapsed)) +... self.line.set_data(self.positions, self.times) +... self.bug.set_data([self.positions[-1]], [self.times[-1]]) +... +... self.timer.set_text(r"$t = {:f}\\,\\mathrm{{s}}$".format(float(self.elapsed))) +... +... super(PhaseViewer, self)._plot() +... +... viewer = PhaseViewer(phase=phase, C=C, sharp=sharp, +... elapsed=elapsed, tmin=1e-5, tmax=300 * 3600, +... datamin=0., datamax=1.) +... except ImportError: +... viewer = Viewer(vars=(phase, C, sharp), +... datamin=0., datamax=1.) ... viewer.plot() Because the phase field interface will not move, and because we've seen in @@ -516,7 +574,7 @@ def deltaChemPot(phase, C, T): >>> initialRes = None >>> sweep = 0 ->>> while res > 1e-4 and sweep < 20: +>>> while res > 1e-8 and sweep < 100: ... res = eq.sweep(dt=dt, solver=solver) ... if initialRes is None: ... initialRes = res @@ -578,14 +636,14 @@ def deltaChemPot(phase, C, T): \\vec{u}_\\phi &= \\frac{D_\\phi}{C} \\nabla \\phi \\\\ &\\approx - \\frac{Dl \\frac{1}{2} V_m}{R T} + \\frac{D_l \\frac{1}{2} V_m}{R T} \\left[ \\frac{L_B\\left(T - T_M^B\\right)}{T_M^B} - \\frac{L_A\\left(T - T_M^A\\right)}{T_M^A} \\right] \\frac{1}{\\Delta x} \\\\ &\\approx - \\frac{Dl \\frac{1}{2} V_m}{R T} + \\frac{D_l \\frac{1}{2} V_m}{R T} \\left(L_B + L_A\\right) \\frac{T_M^A - T_M^B}{T_M^A + T_M^B} \\frac{1}{\\Delta x} \\\\ @@ -594,22 +652,18 @@ def deltaChemPot(phase, C, T): To get a :math:`\\text{CFL} = \\vec{u}_\\phi \\Delta t / \\Delta x < 1`, we need a time step of about :math:`\\unit{10^{-5}}{\\second}`. ->>> dt = 1.e-5 - ->>> if __name__ == '__main__': -... timesteps = 100 -... else: -... timesteps = 10 +>>> dt0 = 1.e-5 >>> from builtins import range ->>> for i in range(timesteps): +>>> for i in range(8): ... phase.updateOld() ... C.updateOld() ... res = 1e+10 ... sweep = 0 ... while res > 1e-3 and sweep < 20: -... res = eq.sweep(dt=dt, solver=solver) +... res = eq.sweep(dt=dt0, solver=solver) ... sweep += 1 +... elapsed.value = (i + 1) * dt0 ... if __name__ == '__main__': ... viewer.plot() @@ -617,16 +671,101 @@ def deltaChemPot(phase, C, T): >>> if __name__ == '__main__': ... input("Moving phase field. Press to proceed...") -.. image:: binary/moving.* - :width: 90% - :align: center - -We see that the composition on either side of the interface approach the +We see that the composition on either side of the interface approaches the sharp-interface solidus and liquidus, but it will take a great many more timesteps to reach equilibrium. If we waited sufficiently long, we could again verify the final concentrations and phase fraction against the expected values. +We can estimate the time to equlibration by examining the time for the +diffusion field to become uniform. In the liquid, this will take +:math:`\\mathcal{O}((\\unit{10}{\\micro\\meter})^2 / D_l) = +\\unit{0.1}{\\second}` and in the solid +:math:`\\mathcal{O}((\\unit{10}{\\micro\\meter})^2 / D_s) = +\\unit{1000}{\\second}`. + +Not wanting to take a hundred-million steps, we employ adaptive time +stepping, using the steppyingstounes package. This package takes care of +many of the messy details of stepping, like overshoot, underflow, and step +size adaptation, while keeping the structure of our solve loop largely +intact. + +>>> from steppyngstounes import SequenceStepper, PIDStepper +>>> from itertools import count + +Assuming the process is dominated by diffusion, we can take steps that +increase geometrically. Since we're unsure if diffusion is the only +process controlling dynamics, we take each increasing step with an adaptive +stepper that uses a `PID controller`_ to keep the equation residuals and +mass conservation within acceptable limits. The total number of solves is +not strongly sensitive to the number of sweeps, but two sweeps seems to be +both sufficient and efficient. + +We'll only advance the step if it's successful, so we need to update the +old values before we get started. + +>>> phase.updateOld() +>>> C.updateOld() + +>>> if __name__ == '__main__': +... totaltime = 300 * 3600 # 300 h +... else: +... totaltime = 32e-5 # 320 us + +>>> dt = dt0 + +>>> for checkpoint in SequenceStepper(start=float(elapsed), stop=totaltime, +... sizes=(dt0 * 2**(n/2) for n in count(7))): +... for step in PIDStepper(start=checkpoint.begin, +... stop=checkpoint.end, +... size=dt): +... for sweep in range(2): +... res = eq.sweep(dt=step.size, solver=solver) +... err = max(res / 1e-3, +... abs(Cavg.value - 0.5) / 1e-6) +... if step.succeeded(error=err): +... phase.updateOld() +... C.updateOld() +... elapsed.value = step.end +... else: +... phase.value = phase.old +... C.value = C.old +... # the last step might have been smaller than possible, +... # if it was near the end of the checkpoint range +... dt = step.want +... checkpoint.succeeded() +... if __name__ == '__main__': +... viewer.plot() + +>>> from fipy import input +>>> if __name__ == '__main__': +... input("Re-equilbrated phase field. Press to proceed...") + +.. image:: binary/moving.* + :width: 90% + :align: center + :alt: phase and composition fields during solidification, compared with final phase diagram concentrations + +The interface moves :math:`\\approx \\unit{3.4}{\\micro\\meter}` in +:math:`\\unit{80}{\\milli\\second}`, driven by diffusion in the liquid +phase (compare the estimate above of \\unit{0.1}{\\second}}). For the next +:math:`\\unit{20}{\\second}`, the interface stalls while the solute step +trapped in the solid phase diffuses outward +(:math:`(\\unis{3.4}{\\micro\\meter})^2 / D_s = +\mathcal{O}(\\unit{100}{\\second})`). Once the solute gradient in the +solid reaches the new position of the interface, the solidification front +begins to move, driven by diffusion in the solid. When the solute in the +solid becomes uniform, the interface stalls again after :math:`\\approx +\\unit{4000}{\\second}`, having moved another +:math:`\\unit{3.2}{\\micro\\meter}` (recall the estimate of +:math:`\\unit{1000}{\\second}` for equilibration in the solid). After this +point, there is essentially no further motion of the interface and barely +perceptable changes in the concentration field. The fact that the +interface does not reach the predicted phase fraction is due to the fact +that this phase field model accounts for adsorption at the interface, +resulting in the bulk phases not having exactly the concentrations assumed +in the sharp interface treatment. + .. rubric:: Footnotes .. [#phi] We will find that we need to "sweep" this non-linear problem @@ -639,6 +778,8 @@ def deltaChemPot(phase, C, T): as a :class:`~fipy.variables.variable.Variable` .. _CFL limit: http://en.wikipedia.org/wiki/Courant-Friedrichs-Lewy_condition + +.. _PID controller: https://en.wikipedia.org/wiki/PID_controller """ from __future__ import unicode_literals From 3656079e9faa19f8c7bff0f3ba38f5255e809fc1 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 27 Jan 2021 22:40:07 -0500 Subject: [PATCH 11/23] Update figures for binary phase field examples --- examples/phase/binary.py | 17 ++++++++++----- examples/phase/binaryCoupled.py | 20 ++++++++++++------ .../generated/binary/binary-0.000899.pdf | Bin 0 -> 14697 bytes .../generated/binary/binary-0.000899.png | Bin 0 -> 20239 bytes .../binary/binary-1080000.000000.pdf | Bin 0 -> 14374 bytes .../binary/binary-1080000.000000.png | Bin 0 -> 20878 bytes .../generated/binary/binary-8.949963.pdf | Bin 0 -> 15379 bytes .../generated/binary/binary-8.949963.png | Bin 0 -> 21173 bytes .../binary/binaryCoupled-0.000899.pdf | Bin 0 -> 14655 bytes .../binary/binaryCoupled-0.000899.png | Bin 0 -> 20140 bytes .../binary/binaryCoupled-1080000.000000.pdf | Bin 0 -> 14364 bytes .../binary/binaryCoupled-1080000.000000.png | Bin 0 -> 20888 bytes .../binary/binaryCoupled-8.949963.pdf | Bin 0 -> 15373 bytes .../binary/binaryCoupled-8.949963.png | Bin 0 -> 21133 bytes .../generated/binary/coupled-stationary.pdf | Bin 0 -> 13931 bytes .../generated/binary/coupled-stationary.png | Bin 0 -> 18433 bytes examples/phase/generated/binary/moving.pdf | Bin 20847 -> 0 bytes examples/phase/generated/binary/moving.png | Bin 37747 -> 0 bytes .../phase/generated/binary/stationary.pdf | Bin 20419 -> 13940 bytes .../phase/generated/binary/stationary.png | Bin 36201 -> 18446 bytes examples/phase/index.rst | 1 + 21 files changed, 27 insertions(+), 11 deletions(-) create mode 100644 examples/phase/generated/binary/binary-0.000899.pdf create mode 100644 examples/phase/generated/binary/binary-0.000899.png create mode 100644 examples/phase/generated/binary/binary-1080000.000000.pdf create mode 100644 examples/phase/generated/binary/binary-1080000.000000.png create mode 100644 examples/phase/generated/binary/binary-8.949963.pdf create mode 100644 examples/phase/generated/binary/binary-8.949963.png create mode 100644 examples/phase/generated/binary/binaryCoupled-0.000899.pdf create mode 100644 examples/phase/generated/binary/binaryCoupled-0.000899.png create mode 100644 examples/phase/generated/binary/binaryCoupled-1080000.000000.pdf create mode 100644 examples/phase/generated/binary/binaryCoupled-1080000.000000.png create mode 100644 examples/phase/generated/binary/binaryCoupled-8.949963.pdf create mode 100644 examples/phase/generated/binary/binaryCoupled-8.949963.png create mode 100644 examples/phase/generated/binary/coupled-stationary.pdf create mode 100644 examples/phase/generated/binary/coupled-stationary.png delete mode 100644 examples/phase/generated/binary/moving.pdf delete mode 100644 examples/phase/generated/binary/moving.png diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 2de11e87b7..7f5103373a 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -563,7 +563,7 @@ def deltaChemPot(phase, C, T): ... input("Stationary phase field. Press to proceed...") .. image:: binary/stationary.* - :width: 90% + :width: 50% :align: center :alt: phase and composition fields in equilibrium, compared with phase diagram concentrations @@ -718,10 +718,17 @@ def deltaChemPot(phase, C, T): >>> if __name__ == '__main__': ... input("Re-equilbrated phase field. Press to proceed...") -.. image:: binary/moving.* - :width: 90% - :align: center - :alt: phase and composition fields during solidification, compared with final phase diagram concentrations +.. image:: binary/binary-0.000899.* + :width: 30% + :alt: phase and composition fields at t=0.000899, compared with final phase diagram concentrations + +.. image:: binary/binary-8.949963.* + :width: 30% + :alt: phase and composition fields at t=8.949963, compared with final phase diagram concentrations + +.. image:: binary/binary-1080000.000000.* + :width: 30% + :alt: phase and composition fields at t=1080000, compared with final phase diagram concentrations The interface moves :math:`\\approx \\unit{3.4}{\\micro\\meter}` in :math:`\\unit{80}{\\milli\\second}`, driven by diffusion in the liquid diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index 38d4ea6a31..a8fb83e1a6 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -586,9 +586,10 @@ def deltaChemPot(phase, C, T): ... viewer.plot() ... input("Stationary phase field. Press to proceed...") -.. image:: binary/stationary.* - :width: 90% +.. image:: binary/coupled-stationary.* + :width: 50% :align: center + :alt: phase and composition fields in equilibrium, compared with phase diagram concentrations We verify that the bulk phases have shifted to the predicted solidus and liquidus compositions @@ -741,10 +742,17 @@ def deltaChemPot(phase, C, T): >>> if __name__ == '__main__': ... input("Re-equilbrated phase field. Press to proceed...") -.. image:: binary/moving.* - :width: 90% - :align: center - :alt: phase and composition fields during solidification, compared with final phase diagram concentrations +.. image:: binary/binaryCoupled-0.000899.* + :width: 30% + :alt: phase and composition fields at t=0.000899, compared with final phase diagram concentrations + +.. image:: binary/binaryCoupled-8.949963.* + :width: 30% + :alt: phase and composition fields at t=8.949963, compared with final phase diagram concentrations + +.. image:: binary/binaryCoupled-1080000.000000.* + :width: 30% + :alt: phase and composition fields at t=1080000, compared with final phase diagram concentrations The interface moves :math:`\\approx \\unit{3.4}{\\micro\\meter}` in :math:`\\unit{80}{\\milli\\second}`, driven by diffusion in the liquid diff --git a/examples/phase/generated/binary/binary-0.000899.pdf b/examples/phase/generated/binary/binary-0.000899.pdf new file mode 100644 index 0000000000000000000000000000000000000000..63a8fa3940aa555494094e2565a7acfb9becbac2 GIT binary patch literal 14697 zcmeHucRZHg`?wh%dneLkXFmIR>^-wbQB?NMe2lC}(Lf4`P>75oBS|V*S*1ZGQe>1p z65b8Jb3am&-}~F|^ZmYFzkj}ZozA(h`2uGOMxj6a5(EwrwM_3&8ae^Z>?1*-r-Y#%uWtfwfBh*oL-2km%qK-My zj_3r(t`5@n_9DVDt8EiIBGJju3yy;xVF(jHZwGTHBHS9_(bNX>I|UQr2)#o9r}~dt z<43Ir-w#KayV^OrdAY#xtHZ5~?cJRmh;RaF@?YejkN~j8fSQ+=H_;!U0OK_PDNbJC zNp5ul9Y5~?A2`IOhB+Le=@jVZ;AEx)P=hB6KRYjfA3HxMFNecxoUir=h!BQOj&649 z-oapA2pL*d7LLWBAsi;q5aOD|%$)qa1NihHEV!hW{T6b2?^@JBTvRQzp zn4?01(0Xm?T8`T;2~$LyX+*@m=8nf?4Lx~#${tB@roN^4K%@Lgf2f~vXeuLUdS?2f zP|)!sLD3HnE>ac`E`IsPn&N%Zr6c!wV&2BIU%K&$T(TraZSDe^U5mSZt8lXY7k~bW z(F?&^Z*T1^juRJ_4jc*5r0L8FW(%NMxI9*1!gZ99CnuqCOlx0{WQ$YR-cK`pFCuue z4&G_M)Ot4P<$cCM0ZDg*i2uv!K9!PK2_k$hcSx0QpBv*p z$ExccOb@Cv9B5Cdu4YXQwlIrvzh2E5uFj{&M=543@Fj!4JvaWaf$tR#t2?1Kbyu%& z-qDyl-YV8}wyG?_oIlsH`ab)u9OIVvC(Ol7KRQXK06<3PzmFCnCi~eo=3WpDMg{kvoc7X;NtuQ9DujED|NrD{`Q3Y9T#IS8?;S{HR zI0g^LDR%^O&7SHw&(5z%Wf08I+Lf~`or0oL4@;Z12{RQgZ23IFa#fN^EK!$i3S+f1 z%h~F|&I@Lzngm{$+3}^#oI9sq&C$Ya7qeT$Bk)|a8LXt?U0iQu47vDrOErFkdyIZ0 zmFA%5fY6tazY?Xpqv+f%gqb>#o1FfDL-{Nn zm(BKAvw7DzPfgTTnb=)uQ)ULq=RHW#U>|3D$4{+$tn(w`wdo~wue4$h#-vU$U#=2L z?6sFm&UFp@jAZK2JzzZB^Nfk!hEw9wq@n6l}L2`loVfpe~ zyoJH4UoYBtI_*$=XyL0UkJ!Ck(Ge}fljX}~$V#@r?t>7qR1{;&%X-au=IGTBij`bl z?^(t94u2En9{PnnPpYRbCVkc6IJ(16dX{RyXeMbNU!bmPURw7=v*AF()w(yY7nPPg zZ+)CjjmUoKdH?n6X*Hj|0|@^km8lP6F!DKG0jY~d8Pmmw%vCgR^4541+vvxB5H;x$ z^pw)dEL~{Y_p$lf8Ob-L{tt@61$vWfj+9Eaz^*Vj@3K1edY>i(9fFg}qxg+)Ndg@m z9blG}e;kDL2`jHVEFOQ)ncInzzeYDnhE5-+SFVZQhbWpj+l@m;o z=FfCxQs$5!ePT~$#AfoK|6qSKq0@W2Cb7G!r0C^|GuJCEdN1|YMpP?x^%}YjJl-k2 zEk*k6NLu(|W@T%qJB+;4cf451G$!t~~wpQa zyAI=HpJNH7_rv5}RnC;Yo=sJ$oe&KU4W`hFe;YH+Ijy~~-n}W%=#6HvR_8X?o6maB zaq#dXIQ zZ?_+cRgm=eLAz3Ny&OO2pJi-rHg3Kx^D+Jy8=C-acR_gcT++)%J(-t6g90vLcya#e zm&?oSRSkIoMUF~Oh%k%#5f_Bl+q>UiPT#NnJ~K1%eKPj#j=s}pTI54D1cDixSce~3 zxkec)P^Imd6?RUp>U%+E>-5$9>w~w$%-F>F<+1FEWTu_>%zDVFW2XN>F#q1F~x?NRc^%dvTC2d5+<35sw-z3 zb6CDl^kxoNJ4s9uF)vhT7F^{z-hKHveN^Wrok7fKoHl#O%!kwzb>(+jPo9gtgYnhO zW>f2Q53$w_Xnv;NJ{(75&RZBs`wgwU<3( ziG4y}*Q6M<#Ja1uE7pWMRanbtur=Xfw#<#vm9yDlY@IDC894*wcf+2#(FSl>dK6kS9D&?d(4L-!2f8o)J~>c(ey2BGIQTfYkGX0 zpT3^7IwLPKFg&BOMUgujGBSUdJ3q`#k{JZqOK3C!zh;A?AfxcFj3|QaZx)nNqCOj? 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For the next -:math:`\\unit{20}{\\second}`, the interface stalls while the solute step +:math:`\\unit{12}{\\second}`, the interface stalls while the solute step trapped in the solid phase diffuses outward -(:math:`(\\unis{3.4}{\\micro\\meter})^2 / D_s = -\mathcal{O}(\\unit{100}{\\second})`). Once the solute gradient in the +(:math:`(\\unit{2.8}{\\micro\\meter})^2 / D_s = +\mathcal{O}(\\unit{80}{\\second})`). Once the solute gradient in the solid reaches the new position of the interface, the solidification front begins to move, driven by diffusion in the solid. When the solute in the solid becomes uniform, the interface stalls again after :math:`\\approx \\unit{4000}{\\second}`, having moved another -:math:`\\unit{3.2}{\\micro\\meter}` (recall the estimate of +:math:`\\unit{2.9}{\\micro\\meter}` (recall the estimate of :math:`\\unit{1000}{\\second}` for equilibration in the solid). After this point, there is essentially no further motion of the interface and barely -perceptable changes in the concentration field. The fact that the -interface does not reach the predicted phase fraction is due to the fact -that this phase field model accounts for adsorption at the interface, -resulting in the bulk phases not having exactly the concentrations assumed -in the sharp interface treatment. +perceptable changes in the concentration field. + +.. note:: + + This evolution is qualitatively consistent with that seen in + :mod:`examples.phase.binary`, but the interface does not move as far and + the bulk concentrations are further from the phase diagram values. The + computation also takes substantially longer than the uncoupled variant. .. rubric:: Footnotes From cd469d6af24a467360b4b45d7ae21204d9b63fa2 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 09:20:07 -0500 Subject: [PATCH 13/23] Deprecate fipy.steppers Can't deprecate base class for some reason. Don't really need to. --- documentation/glossary.rst | 5 +++++ fipy/__init__.py | 2 -- fipy/steppers/__init__.py | 17 +++++++++++++++++ fipy/steppers/pidStepper.py | 3 +++ fipy/steppers/pseudoRKQSStepper.py | 3 +++ fipy/steppers/stepper.py | 4 ++++ 6 files changed, 32 insertions(+), 2 deletions(-) diff --git a/documentation/glossary.rst b/documentation/glossary.rst index b9abaee4d6..f2839f5b31 100644 --- a/documentation/glossary.rst +++ b/documentation/glossary.rst @@ -186,6 +186,11 @@ Glossary See http://sphinx.pocoo.org/. + steppyngstounes + This package provides iterators that simplify both deterministic and + adaptive time (or other independent variable) stepping. + See https://github.com/guyer/steppyngstounes. + TravisCI A cloud-based :term:`Continuous Integration` tool. See https://travis-ci.org. diff --git a/fipy/__init__.py b/fipy/__init__.py index 0d328c18d3..1d73bd6dab 100644 --- a/fipy/__init__.py +++ b/fipy/__init__.py @@ -40,7 +40,6 @@ from fipy.boundaryConditions import * from fipy.meshes import * from fipy.solvers import * -from fipy.steppers import * from fipy.terms import * from fipy.tools import * from fipy.variables import * @@ -50,7 +49,6 @@ __all__.extend(boundaryConditions.__all__) __all__.extend(meshes.__all__) __all__.extend(solvers.__all__) -__all__.extend(steppers.__all__) __all__.extend(terms.__all__) __all__.extend(tools.__all__) __all__.extend(variables.__all__) diff --git a/fipy/steppers/__init__.py b/fipy/steppers/__init__.py index 360029815f..701f59dd42 100644 --- a/fipy/steppers/__init__.py +++ b/fipy/steppers/__init__.py @@ -5,11 +5,14 @@ from fipy.steppers.stepper import Stepper from fipy.steppers.pseudoRKQSStepper import PseudoRKQSStepper from fipy.steppers.pidStepper import PIDStepper +from fipy.tools.decorators import deprecate __all__ = ["L1error", "L2error", "LINFerror", "sweepMonotonic"] from future.utils import text_to_native_str __all__ = [text_to_native_str(n) for n in __all__] +@deprecate(version="3.4.3", + message="Pass a ``residualFn`` to :meth:`~fipy.terms.term.Term.sweep`.") def residual(var, matrix, RHSvector): r""" Determines the residual for the current solution matrix and variable. @@ -34,6 +37,9 @@ def residual(var, matrix, RHSvector): Lx = matrix * array(var) return LINFnorm(Lx - RHSvector) +@deprecate(version="3.4.3", + message="Calculate error explicitly with " + ":mod:`~fipy.tools.numerix`.") def error(var, matrix, RHSvector, norm): r""" .. math:: @@ -60,6 +66,9 @@ def error(var, matrix, RHSvector, norm): denom = L1norm(var.old) return L1norm(var - var.old) / (denom + (denom == 0)) +@deprecate(version="3.4.3", + message="Calculate error explicitly with " + ":mod:`~fipy.tools.numerix.L1norm`.") def L1error(var, matrix, RHSvector): r""" .. math:: @@ -81,6 +90,9 @@ def L1error(var, matrix, RHSvector): from fipy.tools.numerix import L1norm return error(var, matrix, RHSvector, L1norm) +@deprecate(version="3.4.3", + message="Calculate error explicitly with " + ":mod:`~fipy.tools.numerix.L2norm`.") def L2error(var, matrix, RHSvector): r""" .. math:: @@ -102,6 +114,9 @@ def L2error(var, matrix, RHSvector): from fipy.tools.numerix import L2norm return error(var, matrix, RHSvector, L2norm) +@deprecate(version="3.4.3", + message="Calculate error explicitly with " + ":mod:`~fipy.tools.numerix.LINFnorm`.") def LINFerror(var, matrix, RHSvector): r""" .. math:: @@ -123,6 +138,8 @@ def LINFerror(var, matrix, RHSvector): from fipy.tools.numerix import LINFnorm return error(var, matrix, RHSvector, LINFnorm) +@deprecate(version="3.4.3", + message="Use the :term:`steppyngstounes` package instead.") def sweepMonotonic(fn, *args, **kwargs): """ Repeatedly calls :func:`fn(*args, **kwargs)` until the residual returned by diff --git a/fipy/steppers/pidStepper.py b/fipy/steppers/pidStepper.py index 6de962f224..3b1ec30bb2 100644 --- a/fipy/steppers/pidStepper.py +++ b/fipy/steppers/pidStepper.py @@ -1,11 +1,14 @@ from __future__ import division from __future__ import unicode_literals from fipy.steppers.stepper import Stepper +from fipy.tools.decorators import deprecate __all__ = ["PIDStepper"] from future.utils import text_to_native_str __all__ = [text_to_native_str(n) for n in __all__] +@deprecate(version="3.4.3", + message="Use the :term:`steppyngstounes` package instead.") class PIDStepper(Stepper): """ Adaptive stepper using a PID controller, based on:: diff --git a/fipy/steppers/pseudoRKQSStepper.py b/fipy/steppers/pseudoRKQSStepper.py index 20a9dd6694..8ba0d764e7 100644 --- a/fipy/steppers/pseudoRKQSStepper.py +++ b/fipy/steppers/pseudoRKQSStepper.py @@ -1,10 +1,13 @@ from __future__ import unicode_literals from fipy.steppers.stepper import Stepper +from fipy.tools.decorators import deprecate __all__ = ["PseudoRKQSStepper"] from future.utils import text_to_native_str __all__ = [text_to_native_str(n) for n in __all__] +@deprecate(version="3.4.3", + message="Use the :term:`steppyngstounes` package instead.") class PseudoRKQSStepper(Stepper): """ Adaptive stepper based on the ``rkqs`` (Runge-Kutta diff --git a/fipy/steppers/stepper.py b/fipy/steppers/stepper.py index dce9b3c062..4cdd2e2544 100644 --- a/fipy/steppers/stepper.py +++ b/fipy/steppers/stepper.py @@ -2,10 +2,14 @@ from builtins import object __docformat__ = 'restructuredtext' +# from fipy.tools.decorators import deprecate + __all__ = ["Stepper"] from future.utils import text_to_native_str __all__ = [text_to_native_str(n) for n in __all__] +# @deprecate(version="3.4.3", +# message="Use the :term:`steppyngstounes` package instead.") class Stepper(object): def __init__(self, vardata=()): self.vardata = vardata From e1ff04a47acabc5a8d9444a7f2c48f930427ffd0 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 09:29:16 -0500 Subject: [PATCH 14/23] Add discussion of adaptive stepping to USAGE --- documentation/USAGE.rst | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/documentation/USAGE.rst b/documentation/USAGE.rst index 553c03ec6b..f27fc15207 100644 --- a/documentation/USAGE.rst +++ b/documentation/USAGE.rst @@ -937,6 +937,19 @@ Nothing different needs to be done when % \subsection{Internal boundary conditions} +----------------- +Adaptive Stepping +----------------- + +Step size can be controlled with the :term:`steppyngstounes` package. +Demonstrations of its use are found in :mod:`examples.phase.binary` and +:mod:`examples.phase.binaryCoupled.` + +.. note:: + + The old :mod:`fipy.steppers` classes are now deprecated. They were + undocumented and did not work very well. + .. _RunningUnderPython2: ---------------------- From 8e185630244bfae4b65d068d79f27f546b441972 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 10:50:41 -0500 Subject: [PATCH 15/23] Fix spelling errors --- examples/phase/binary.py | 12 ++++++------ examples/phase/binaryCoupled.py | 12 ++++++------ 2 files changed, 12 insertions(+), 12 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 7f5103373a..9addc8a946 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -652,7 +652,7 @@ def deltaChemPot(phase, C, T): could again verify the final concentrations and phase fraction against the expected values. -We can estimate the time to equlibration by examining the time for the +We can estimate the time to equilibration by examining the time for the diffusion field to become uniform. In the liquid, this will take :math:`\\mathcal{O}((\\unit{10}{\\micro\\meter})^2 / D_l) = \\unit{0.1}{\\second}` and in the solid @@ -660,10 +660,10 @@ def deltaChemPot(phase, C, T): \\unit{1000}{\\second}`. Not wanting to take a hundred-million steps, we employ adaptive time -stepping, using the steppyingstounes package. This package takes care of -many of the messy details of stepping, like overshoot, underflow, and step -size adaptation, while keeping the structure of our solve loop largely -intact. +stepping, using the :term:`steppyingstounes` package. This package takes +care of many of the messy details of stepping, like overshoot, underflow, +and step size adaptation, while keeping the structure of our solve loop +largely intact. >>> from steppyngstounes import SequenceStepper, PIDStepper >>> from itertools import count @@ -744,7 +744,7 @@ def deltaChemPot(phase, C, T): :math:`\\unit{3.2}{\\micro\\meter}` (recall the estimate of :math:`\\unit{1000}{\\second}` for equilibration in the solid). After this point, there is essentially no further motion of the interface and barely -perceptable changes in the concentration field. The fact that the +perceptible changes in the concentration field. The fact that the interface does not reach the predicted phase fraction is due to the fact that this phase field model accounts for adsorption at the interface, resulting in the bulk phases not having exactly the concentrations assumed diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index 07b4dac190..baf53bacbc 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -678,7 +678,7 @@ def deltaChemPot(phase, C, T): could again verify the final concentrations and phase fraction against the expected values. -We can estimate the time to equlibration by examining the time for the +We can estimate the time to equilibration by examining the time for the diffusion field to become uniform. In the liquid, this will take :math:`\\mathcal{O}((\\unit{10}{\\micro\\meter})^2 / D_l) = \\unit{0.1}{\\second}` and in the solid @@ -686,10 +686,10 @@ def deltaChemPot(phase, C, T): \\unit{1000}{\\second}`. Not wanting to take a hundred-million steps, we employ adaptive time -stepping, using the steppyingstounes package. This package takes care of -many of the messy details of stepping, like overshoot, underflow, and step -size adaptation, while keeping the structure of our solve loop largely -intact. +stepping, using the :term:`steppyingstounes` package. This package takes +care of many of the messy details of stepping, like overshoot, underflow, +and step size adaptation, while keeping the structure of our solve loop +largely intact. >>> from steppyngstounes import SequenceStepper, PIDStepper >>> from itertools import count @@ -768,7 +768,7 @@ def deltaChemPot(phase, C, T): :math:`\\unit{2.9}{\\micro\\meter}` (recall the estimate of :math:`\\unit{1000}{\\second}` for equilibration in the solid). After this point, there is essentially no further motion of the interface and barely -perceptable changes in the concentration field. +perceptible changes in the concentration field. .. note:: From 272e249717fed586fe91a5dda207281b9194f607 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 11:00:03 -0500 Subject: [PATCH 16/23] Install steppyngstounes on CIs --- .appveyor.yml | 1 + .circleci/config.yml | 1 + .travis.yml | 1 + 3 files changed, 3 insertions(+) diff --git a/.appveyor.yml b/.appveyor.yml index 4449b28bfe..d42d80e56e 100644 --- a/.appveyor.yml +++ b/.appveyor.yml @@ -93,6 +93,7 @@ install: - cmd: if "%TARGET_ARCH%" == "x86" if "%FIPY_SOLVERS%" == "pysparse" conda.exe install --quiet --name root pysparse - cmd: pip install scikit-fmm + - cmd: pip install git+https://github.com/guyer/steppyngstounes.git # Skip .NET project specific build phase. build: off diff --git a/.circleci/config.yml b/.circleci/config.yml index c02914de20..550fe66909 100644 --- a/.circleci/config.yml +++ b/.circleci/config.yml @@ -40,6 +40,7 @@ commands: source activate ~/project/<< parameters.condaenv >> conda remove --quiet --channel conda-forge --force fipy pip install scikit-fmm + pip install git+https://github.com/guyer/steppyngstounes.git test_fipy: description: "Run FiPy Tests" diff --git a/.travis.yml b/.travis.yml index 2d246a3007..6609c90f25 100644 --- a/.travis.yml +++ b/.travis.yml @@ -54,6 +54,7 @@ before_install: # Useful for debugging any issues with conda - conda info -a - pip install scikit-fmm + - pip install git+https://github.com/guyer/steppyngstounes.git install: - python setup.py install before_script: From f72d1f8fc36cb33a1c439a7e577add2c2daee882 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 11:14:44 -0500 Subject: [PATCH 17/23] Discard result of succeeded() --- examples/phase/binary.py | 2 +- examples/phase/binaryCoupled.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 9addc8a946..7d4bdf2979 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -710,7 +710,7 @@ def deltaChemPot(phase, C, T): ... # the last step might have been smaller than possible, ... # if it was near the end of the checkpoint range ... dt = step.want -... checkpoint.succeeded() +... _ = checkpoint.succeeded() ... if __name__ == '__main__': ... viewer.plot() diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index baf53bacbc..0c33fd72ff 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -734,7 +734,7 @@ def deltaChemPot(phase, C, T): ... # the last step might have been smaller than possible, ... # if it was near the end of the checkpoint range ... dt = step.want -... checkpoint.succeeded() +... _ = checkpoint.succeeded() ... if __name__ == '__main__': ... viewer.plot() From 1ca252d6f0c1dd7f6dfe44251b0c1a31c9231f7f Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 11:24:46 -0500 Subject: [PATCH 18/23] Fix typo --- examples/phase/binary.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 7d4bdf2979..d9d35fea24 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -735,7 +735,7 @@ def deltaChemPot(phase, C, T): phase (compare the estimate above of \\unit{0.1}{\\second}}). For the next :math:`\\unit{20}{\\second}`, the interface stalls while the solute step trapped in the solid phase diffuses outward -(:math:`(\\unis{3.4}{\\micro\\meter})^2 / D_s = +(:math:`(\\unit{3.4}{\\micro\\meter})^2 / D_s = \mathcal{O}(\\unit{100}{\\second})`). Once the solute gradient in the solid reaches the new position of the interface, the solidification front begins to move, driven by diffusion in the solid. When the solute in the From 1f5a3c523bddc9992c3f207567e298d6458e79f2 Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Thu, 28 Jan 2021 13:22:16 -0500 Subject: [PATCH 19/23] Fix math --- examples/phase/binary.py | 3 ++- examples/phase/binaryCoupled.py | 3 ++- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index d9d35fea24..7becea1ff9 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -732,7 +732,8 @@ def deltaChemPot(phase, C, T): The interface moves :math:`\\approx \\unit{3.4}{\\micro\\meter}` in :math:`\\unit{80}{\\milli\\second}`, driven by diffusion in the liquid -phase (compare the estimate above of \\unit{0.1}{\\second}}). For the next +phase (compare the estimate above of :math:`\\unit{0.1}{\\second}}`). +For the next :math:`\\unit{20}{\\second}`, the interface stalls while the solute step trapped in the solid phase diffuses outward (:math:`(\\unit{3.4}{\\micro\\meter})^2 / D_s = diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index 0c33fd72ff..243f9aeebf 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -756,7 +756,8 @@ def deltaChemPot(phase, C, T): The interface moves :math:`\\approx \\unit{2.8}{\\micro\\meter}` in :math:`\\unit{70}{\\milli\\second}`, driven by diffusion in the liquid -phase (compare the estimate above of \\unit{0.1}{\\second}}). For the next +phase (compare the estimate above of :math:`\\unit{0.1}{\\second}}`). +For the next :math:`\\unit{12}{\\second}`, the interface stalls while the solute step trapped in the solid phase diffuses outward (:math:`(\\unit{2.8}{\\micro\\meter})^2 / D_s = From 5682e258504e6b33583804f0ca2a48523361634a Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Tue, 2 Feb 2021 22:20:14 -0500 Subject: [PATCH 20/23] Ensure mass conservation of early evolution --- examples/phase/binary.py | 4 ++-- examples/phase/binaryCoupled.py | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 7becea1ff9..63a871f15f 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -554,7 +554,7 @@ def deltaChemPot(phase, C, T): >>> C.updateOld() >>> phaseRes = 1e+10 >>> diffRes = 1e+10 ->>> while phaseRes > 1e-3 or diffRes > 1e-3: +>>> while phaseRes > 1e-3 or diffRes > 1e-3 or abs(Cavg.value - 0.5) > 5e-7: ... phaseRes = phaseEq.sweep(var=phase, dt=dt) ... diffRes = diffusionEq.sweep(var=C, dt=dt, solver=solver) >>> from fipy import input @@ -635,7 +635,7 @@ def deltaChemPot(phase, C, T): ... C.updateOld() ... phaseRes = 1e+10 ... diffRes = 1e+10 -... while phaseRes > 1e-3 or diffRes > 1e-3: +... while phaseRes > 1e-3 or diffRes > 1e-3 or abs(Cavg.value - 0.5) > 1e-6: ... phaseRes = phaseEq.sweep(var=phase, dt=dt0) ... diffRes = diffusionEq.sweep(var=C, dt=dt0, solver=solver) ... elapsed.value = (i + 1) * dt0 diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index 243f9aeebf..a1c765b314 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -661,7 +661,7 @@ def deltaChemPot(phase, C, T): ... C.updateOld() ... res = 1e+10 ... sweep = 0 -... while res > 1e-3 and sweep < 20: +... while (res > 1e-3 or abs(Cavg.value - 0.5) > 1e-8) and sweep < 20: ... res = eq.sweep(dt=dt0, solver=solver) ... sweep += 1 ... elapsed.value = (i + 1) * dt0 From 4fe044bac01a5ba4509d126c66281a8ebcf87eac Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 3 Feb 2021 10:30:45 -0500 Subject: [PATCH 21/23] Fix LaTeX --- examples/phase/binaryCoupled.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/phase/binaryCoupled.py b/examples/phase/binaryCoupled.py index a1c765b314..895ecbc207 100755 --- a/examples/phase/binaryCoupled.py +++ b/examples/phase/binaryCoupled.py @@ -756,7 +756,7 @@ def deltaChemPot(phase, C, T): The interface moves :math:`\\approx \\unit{2.8}{\\micro\\meter}` in :math:`\\unit{70}{\\milli\\second}`, driven by diffusion in the liquid -phase (compare the estimate above of :math:`\\unit{0.1}{\\second}}`). +phase (compare the estimate above of :math:`\\unit{0.1}{\\second}`). For the next :math:`\\unit{12}{\\second}`, the interface stalls while the solute step trapped in the solid phase diffuses outward From e6842e9da8f60b0e8ea144bc97b40adf1be1552d Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 3 Feb 2021 12:33:55 -0500 Subject: [PATCH 22/23] Fix LaTeX --- examples/phase/binary.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/phase/binary.py b/examples/phase/binary.py index 63a871f15f..2b8f0456c9 100755 --- a/examples/phase/binary.py +++ b/examples/phase/binary.py @@ -732,7 +732,7 @@ def deltaChemPot(phase, C, T): The interface moves :math:`\\approx \\unit{3.4}{\\micro\\meter}` in :math:`\\unit{80}{\\milli\\second}`, driven by diffusion in the liquid -phase (compare the estimate above of :math:`\\unit{0.1}{\\second}}`). +phase (compare the estimate above of :math:`\\unit{0.1}{\\second}`). For the next :math:`\\unit{20}{\\second}`, the interface stalls while the solute step trapped in the solid phase diffuses outward From f15c915741eb7aba149d5da7c5ef89de535d53af Mon Sep 17 00:00:00 2001 From: Jonathan Guyer Date: Wed, 1 Dec 2021 18:30:06 -0500 Subject: [PATCH 23/23] ping the build --- .azure/templates/install.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.azure/templates/install.yml b/.azure/templates/install.yml index 2d6ed2cefd..baabc25695 100644 --- a/.azure/templates/install.yml +++ b/.azure/templates/install.yml @@ -61,3 +61,4 @@ steps: fi pip install git+https://github.com/guyer/steppyngstounes.git displayName: Install pip packages +