From 42894519647394c9c6b5ffc2d114fdb456fe948c Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Fri, 14 Sep 2012 21:47:01 -0400 Subject: [PATCH] posts:FRC: add reproduction of Livadaru's figure 14. --- .../figure-14.png | Bin 0 -> 67105 bytes .../frc.py | 55 ++++++++++++++++++ posts/FRC.mdwn_itex | 10 ++++ 3 files changed, 65 insertions(+) create mode 100644 posts/Comparing_velocity_clamp_experiments/figure-14.png create mode 100755 posts/Comparing_velocity_clamp_experiments/frc.py 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 0000000000000000000000000000000000000000..001f2edca207b492bd1b0afea6adbbb2475fe559 GIT binary patch literal 67105 zcmeFZWmr~Q)HMu(f}}J^DGkyf9ZH8ZN;guH(%s$N-O?c4($XN^-QE4JoAW&1_xt_- z-q&@mbAWxXz4uykjXCC+W1T=*X;EZ^w+K*BP{`t9Lh?{hFz=wCUMR!A0>4SJ^Rfj0 zg0&V9SA+*27kK>u@bha+F%@elC{!KDKhOpI`NmLC@1VqmJ}Ww;>@V0mV1AwJIXTLE z!<8v$^f`#?I>^HVUJPyL9U*KC$qSmd#xwz}a*GeM(^+p+f@S!>h}uvlNFII|QD&vS3__2}aIc?LXxusEiFdM8Lk>>PmF49&i`EB&y>hab*LQbo%gdjpN;S*~g8~8|(;dk=*xtSp$bYsq z9B#&KI$iFt#q#~HP@#P8_DmHe4uhu4K1VnaukLDR;J-ozf0vunmDN>&p%hMV1%j6A z1(uteTVR;ua+~LuRIb=~Ew{vWZ#WjyX~xs7;ioU|{^w+yT!#ydQR;GR<7END@}#F<5qXb}w&lPRCO+y`He|`_mN!TsBngCy!=p-Jv{B z_h-dwwe&j{-{fQe_##?w4&eP<@739p6%u+5rW`~q_XpdoxyfH&KS(=wFdEJNrcP$J zF!)y>H;~NEa5Qb)Nhyv)Y>y3o#8t{I_UK)_dHgt&lS1!Y?72AiE1Z6|9zYbkr<`KYKwJj-Xp z{Dy5F&?ix-9wfp+<@$Z-zrK~+c3PQC{KC4s<#oR7l!htNXtXm;-rhDc7)WR@Dr=Fb zF`em6`uG9Ni9vS=-s?rno~Fm{Q2eH+$2&|KMR-ced=7=-Fal12M!N$l#ez3@EC!u} zgQ2$dka4kieR6)DV|OrH*U%6} ztw5paaw04e`c~M%!ND}St?kqN!a`pH6Dg&1O2FAIcqEgl(ok=2m|z@+S8WRmsc57k zP@QSPH#hmq%i1k>hunYT8Du7lRr=!S@F#wK)dN#&UxNvTr5 zPoPA#`uOrP>?#Qkm5A}@y4c^?52D}|deeBh$tB}*T<(h_s55SD^cybz(}c z?S)46p`jtxACn>Sxe``u-N<2t+}-CpOyhWYdkW~&_>9Y=E|<2l?L zaX)|l4B68P`Oy zHT_qj77xDI#n;D(^Dal1gT)Fqxov%Wh7<0OFaw(tLsI?MD-#qs3-U*IQPw zCpWi8v+r-V($@hr$W4g~kqP6GkQgU)=`zt`2QvY%(E~VQ<+eGPjFW#bk|~HB+@*^| z%*Qiy(%UPR?e=i%2QCHs0LR&--RmXf2a|sVk^4*l2)P$eK%n7b2X_@HS7e=l8%?hP zykn;M`b!^dUA?|2@{`+2W!i4%qh>=PVc{-L``dHlj=sLW-c;_|695F=_(vdWD_YZe zohL2r?AQQUeOGUG`Y7E9!sl&RSeQsKHXZuK{w&_fzh?tmIN)6N0Xn+5Q_LC*&Bi;_(3S0nq zq1HUCtpC7_djgEtPT{hpxx5DZK<_CG0_JB)0KeXX_qsmrK-CL>xSX?qytrzOY2xy= zr>AE{>)p)_9{4*5kRK^*7R?uNIu*(xAXTspod9g>)~xbJCGI8)ze(oe=Eet@5_Fct z(0V^s4kiP{1A2(4Q0FX2xME4z)@unP!>tyldgkgs0D>jwfZ*w&QpgK|j0h&Dr{3}Y z@$P7C9+T2=;5GR>i zCbX}kqXTkdu*4WVPvBkfL6ljU2NCCkj3nZRgcss`b=bv?gNJ9l-WT0dpkDv8$r>4- zEu@*6LAg95l3WsdEu8-`VCqo(buYLrvZ!be>>WE&2Z!x$4CGNfVc@!ng2g|fOR$oX zkRVY~Qm#!XX@&A)M|(7#4RODIf_{9T3A;X)D+!rJfDxg+y}b@)JM;BbkgvZ)#O{QA zoy-34ewu0axAECO2asnzE0hb74OS`Bg2*9nXpWD^(bUwm3TwXIE!tmfP98{Pp|p1h zv|H_bO+ZM9K`UFPQbmD+f&y8~MNWHr`_uJ4jH7Fi_@IoY%U2Y7!V0aYs|-=W!i3pB zg1G?0T3znXIE)8BQgd)5fP@y?23zQ0_jLszN2!R3aT|Na;zno=eY>;==sCQiGSmgHo7D5X;M3JLYA!v#|N z!+8$Qt|yt==x7Yb)Ag0hgSnHTu7A$=YO=C#u!DUCd=YqU_qpv4p&0G}I_F`R8f-t*DBoMTKB%SfI2Oodzv_>pBb7LSOWcx>fMB}%2M(!7i1xIs1ulw%FHKWfb8xAGl%L7rkXK1!L;JFB&;gSo3fy`%Yh zmOj^~=%S(zYdztV@7_UaX=#DvA_dY-0tl{V=PPN&kf|~)nPZoMAiY^`K*v5n=yV{X z`8)?;2e^DL4*PCIfI>FiY$p5o`0$+ceF|}>XSmZ+ERgjqC@63k?|`~IT#&S}ImgK7 zf0+AG)(n6P;1&6(S-P$L2?#X#8dH_W>$Pw)sn=j%5J0lW&FRJ(*r5N4RiZ(zt^$`k znCa!wk;il@7Rq<+Hs-`r$$6PCG^}iF2*=T?D7U&jV9fQXcRbu(QC<_-9W4^(rv`|b zK&k>Vv>;4s0f5zY)>|lm@CEboIiBiQ8V(QHFS+(ypR8dt=^(+wXMmLW`Vc1)6C@p& z<$i`%GVr-{u(V{L_;mEcjzC%V!6IXMa>5oRWTm=NX^K|Sc5{6cLde|gMeV*{^rce+8UBIK(0zo z<8}VI^2e8>EL_Fpa|~0t=w;WT{4QYb!rM%zTiU0uPUTaWu67yq)h( z1S@Ge`T`76sMHrfoUiW~%@*y8B!vTs;>9w^)mtDn=7Cv?p;LHxV@m3&w&TDs%v;S9MHef5;gWbspMB}ZJsck zR;#e!0!TvlP;qCmSma4!Gm`)}P4YK z{_5Ud|CE;dAb=#thl{DcbbfwNM{Ja}KCXhLpw(z#ZRZt2UjuaLx9Ln2NLi4%o1dSr zv)#i6(??1}LsLVsE)JpMdu6Rd9?&q?8}V9zGLXd6YXEkQ1u88jfLfH3kpThIAJrH- z$N?OH><&_ML_rNC)e{g9tRBFe%78b3{CCLX!(9*OV#Ho897Es~;Y&mO|+@8gRkGvVa{P0s;h|q4_*&v`C3T z4}fl1^tkihSGR{;QHwlgL263^}0`74hV=c2CO?44gt8`Sre+_ zcV(512$Ed3!^vvJ)7|Mte|N@b?+~y|3skZh9-z+D1+=)+2vD^O+r3GSGS_*&cYZpD z9b=957TL-by3ctZayiOHG%re z$NwwI!1dEUge=U|nBfB?lvyZ{fanax3}j@m?(XipQ)M8lIGPel|H^^w3^Sdp2?g70 zh6@QIPdEmF{W)5pC#vQjNka`?LE06J12=$rj>yoYJyF5S!;`>al{IlEZhDtr?L2nl zGsN4^^kd{=~#LEtr9Vu4O%Lu}oAxjC@k_ zsrmdNmw`}o_fzZC?FpE+Q4r|UcWmNZCdsz*|KBq{K`$*W%?4ETawp{M8mJoKIlrea%BA@mh+a!tOl7Or$0smCH`w`# zgf5TEtc0@L@Q%&461#c2{Zoq$Yk0aUs_5Thx2P0VWOR}S4nD07G{SNW|vRAie zO5V`dpimAfAVXxfUVa`I_@gG6WVZGk@sWH~W!joB3HiSw>7nPd)4`}(4-ua~zMA1m zvHASp=u0nNWT>#zS+*Bn8BLEsp82$8U1|=?%=prUg@QdHL^v_;>wn@NbQl3sba)8f z%JOF_r6I_rT&`!Vq4BJFQEKGawdw?h@z&xhzaTaT4v%?y)!yzXNn%rq*jRsPK z*n{u|by7Cf9(OTiv^9mAe@yA~xREyfjM|;>MoUDh)m|En0~>ba2Mrh7*cNn7h&Yru zHFmQ>KSY$k<%dRqqXh)yNM>e^l;Ar!{ppQlbSMuR9B+WrK{fiFgLWlwWR)=oji67b zy%#Y?4)#)SM+XehE4Xa7Gg1}7l*_k;;vZkmS?*%eYN43TPIHln8|y^sG&S#=xg1_E zPjm&N*GrJ?T!2`2aB@P&#EcO@%OjTfv_H}rh*4dY7Z4zZaPweqGzR;pL+41-;o_^B zC>b>!4Ofu#4=$^B%TRM%X4x*Dr{agCo53pysUsV$|1C=nelpwVYLkc$@hYaJ>!b%P zNZzRI?!CLM->Ql)m=`VGJ0{=fIzOwSWP>b72^^#92DQ?J)3vBUm=(5)QDaCQ%V&h? 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Trevor King +# +# This program is free software: you can redistribute it and/or modify +# it under the terms of the GNU General Public License as published by +# the Free Software Foundation, either version 3 of the License, or +# (at your option) any later version. +# +# This program is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU General Public License for more details. +# +# You should have received a copy of the GNU General Public License +# along with this program. If not, see . + +"""Freely rotating chain (FRC) following Livadaru et al. [1]. + +[1]: http://pubs.acs.org/doi/abs/10.1021/ma020751g +""" + +import numpy as _numpy +import matplotlib.pyplot as _pyplot +try: # SciPy >= 0.10.0 + from scipy.constants import Boltzmann as _kB +except ImportError: # SciPy < 0.10.0 + from scipy.constants import Bolzmann as _kB + +from crunch import inverse_frc + + +def figure_14(): + figure = _pyplot.figure() + axes = figure.add_subplot(1, 1, 1) + axes.set_xscale('log') + axes.set_yscale('log') + axes.hold(True) + Fs = 10**_numpy.linspace(-4, 2.2, 100) + for gamma_degrees in [1, 5, 10, 20, 30, 50, 70]: + gamma = gamma_degrees * _numpy.pi / 180 + xs = _numpy.array([inverse_frc(F, gamma) for F in Fs]) + axes.plot(Fs, 1/(1-xs)) + axes.axis([Fs.min(), Fs.max(), 0.9, 500]) + axes.set_title('FRC force extension') + axes.set_xlabel(r'$\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 -- 2.26.2