* Change curvature formalism to match paper

 * Fix charge backwards to go in the proper direction; decrease base to 20

git-svn-id: svn+ssh://hemlock.ucr.edu/srv/svn/misc/trunk/origins_of_life@494 25fa0111-c432-4dab-af88-9f31a2f6ac42

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index d7d8bfee5f8b35e6c6b58bd84f1fac6d576c31e3..5c6dd27719569226daa3885f5d795cc0761ff960 100644 (file)
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -122,16 +122,18 @@ rm(x,y,grid)
 \end{equation}
 
 <<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
 \end{equation}
 
 <<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=

-curve(10^x,from=0,to=sd(c(0.8,1.33)),
+curve(10^x,from=0,to=max(c(sd(abs(log(c(0.8,1.33)))),
+                    sd(abs(log(c(1,1.33)))),
+                    sd(abs(log(c(0.8,1)))))),

       main="Curvature forward",
       main="Curvature forward",

-      xlab="Standard Deviation of Curvature of Vesicle",
+      xlab="Standard Deviation of Absolute value of the Log of the Curvature of Vesicle",

       ylab="Curvature Forward Adjustment")
 @ 
 
 \newpage
 \subsubsection{Length Forward}
 \begin{equation}
       ylab="Curvature Forward Adjustment")
 @ 
 
 \newpage
 \subsubsection{Length Forward}
 \begin{equation}

-  l_f = 3^{\mathrm{stdev}\left|\log l_\mathrm{ves}\right|}
+  l_f = 3^{\mathrm{stdev} l_\mathrm{ves}}

   \label{eq:length_forward}
 \end{equation}
 
   \label{eq:length_forward}
 \end{equation}
 


@@ -178,7 +180,7 @@ rm(grid)
 \newpage
 \subsubsection{Charge Backwards}
 \begin{equation}
 \newpage
 \subsubsection{Charge Backwards}
 \begin{equation}

-  ch_b = 60^{-\left<{ch}_v\right> {ch}_m}
+  ch_b = 20^{\left<{ch}_v\right> {ch}_m}

   \label{eq:charge_backwards}
 \end{equation}
 
   \label{eq:charge_backwards}
 \end{equation}
 


@@ -186,7 +188,7 @@ rm(grid)
 x <- seq(-1,0,length.out=20)
 y <- seq(-1,0,length.out=20)
 grid <- expand.grid(x=x,y=y)
 x <- seq(-1,0,length.out=20)
 y <- seq(-1,0,length.out=20)
 grid <- expand.grid(x=x,y=y)

-grid$z <- as.vector(60^(-outer(x,y)))
+grid$z <- as.vector(20^(outer(x,y)))

 print(wireframe(z~x*y,grid,cuts=50,
           drape=TRUE,
           scales=list(arrows=FALSE),
 print(wireframe(z~x*y,grid,cuts=50,
           drape=TRUE,
           scales=list(arrows=FALSE),


@@ -199,14 +201,14 @@ rm(x,y,grid)
 \newpage
 \subsubsection{Curvature Backwards}
 \begin{equation}
 \newpage
 \subsubsection{Curvature Backwards}
 \begin{equation}

-  cu_f = 4^{\left|\left|\log cu_\mathrm{vesicle}\right|-\left|\log cu_\mathrm{monomer}\right|\right|}
+  cu_f = 7^{1-\left(20\left(\log cu_\mathrm{vesicle}-\log cu_\mathrm{monomer}\right)^2+1\right)^{-1}}

   \label{eq:curvature_backwards}
 \end{equation}
 
 <<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
 grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
                     y=seq(0.8,1.33,length.out=20))
   \label{eq:curvature_backwards}
 \end{equation}
 
 <<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
 grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
                     y=seq(0.8,1.33,length.out=20))

-grid$z <- 10^(abs(3.5^-grid$x-3.5^-grid$y))
+grid$z <- 7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1))

 print(wireframe(z~x*y,grid,cuts=50,
           drape=TRUE,
           scales=list(arrows=FALSE),
 print(wireframe(z~x*y,grid,cuts=50,
           drape=TRUE,
           scales=list(arrows=FALSE),