From: W. Trevor King <wking@tremily.us>
Date: Sat, 15 Sep 2012 01:47:01 +0000 (-0400)
Subject: posts:FRC: add reproduction of Livadaru's figure 14.
X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=42894519647394c9c6b5ffc2d114fdb456fe948c;p=blog.git

posts:FRC: add reproduction of Livadaru's figure 14.
---

diff --git a/posts/Comparing_velocity_clamp_experiments/figure-14.png b/posts/Comparing_velocity_clamp_experiments/figure-14.png
new file mode 100644
index 0000000..001f2ed
Binary files /dev/null and b/posts/Comparing_velocity_clamp_experiments/figure-14.png differ
diff --git a/posts/Comparing_velocity_clamp_experiments/frc.py b/posts/Comparing_velocity_clamp_experiments/frc.py
new file mode 100755
index 0000000..e476ec6
--- /dev/null
+++ b/posts/Comparing_velocity_clamp_experiments/frc.py
@@ -0,0 +1,55 @@
+#!/usr/bin/env python
+#
+# Copyright (C) 2012  W. Trevor King <wking@tremily.us>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+"""Freely rotating chain (FRC) following Livadaru et al. [1].
+
+[1]: http://pubs.acs.org/doi/abs/10.1021/ma020751g
+"""
+
+import numpy as _numpy
+import matplotlib.pyplot as _pyplot
+try:  # SciPy >= 0.10.0
+    from scipy.constants import Boltzmann as _kB
+except ImportError:  # SciPy < 0.10.0
+    from scipy.constants import Bolzmann as _kB
+
+from crunch import inverse_frc
+
+
+def figure_14():
+    figure = _pyplot.figure()
+    axes = figure.add_subplot(1, 1, 1)
+    axes.set_xscale('log')
+    axes.set_yscale('log')
+    axes.hold(True)
+    Fs = 10**_numpy.linspace(-4, 2.2, 100)
+    for gamma_degrees in [1, 5, 10, 20, 30, 50, 70]:
+        gamma = gamma_degrees * _numpy.pi / 180
+        xs = _numpy.array([inverse_frc(F, gamma) for F in Fs])
+        axes.plot(Fs, 1/(1-xs))
+    axes.axis([Fs.min(), Fs.max(), 0.9, 500])
+    axes.set_title('FRC force extension')
+    axes.set_xlabel(r'$\frac{fb}{k_B T}$')
+    axes.set_ylabel(r'$\left(1-\frac{R_z}{L}\right)^{-1}$')
+    figure.subplots_adjust(bottom=0.13)
+    return figure
+
+
+if __name__ == '__main__':
+    figure = figure_14()
+    figure.savefig('figure-14.png')
+    #_pyplot.show()
diff --git a/posts/FRC.mdwn_itex b/posts/FRC.mdwn_itex
index c48c08e..4bd0e77 100644
--- a/posts/FRC.mdwn_itex
+++ b/posts/FRC.mdwn_itex
@@ -95,6 +95,16 @@ moves above $l/b$.  For Puchner's revised numbers, this corresponds to
 
 assuming a temperature in the range of 300 K.
 
+I've written an `inverse_frc` implementation in
+[[crunch.py|Comparing_velocity_clamp_experiments/crunch.py]] for
+[[comparing velocity clamp experiments]].  I test the implementation
+with [[frc.py|Comparing_velocity_clamp_experiments/frc.py]] by
+regenerating [Livadaru et al.'s figure 14][livadaru03].
+
+[[!img Comparing_velocity_clamp_experiments/figure-14.png
+  alt="Inverse FRC test matching Livadaru et al.'s figure 14"
+  title="Inverse FRC test matching Livadaru et al.'s figure 14"]]
+
 
 [carrionvazquez99]: http://dx.doi.org/10.1073/pnas.96.20.11288
 [puchner08]: http://dx.doi.org/10.1529/biophysj.108.129999