media/src/asy: Add Asympote graphics from my thesis

diff --git a/media/src/asy/afm.asy b/media/src/asy/afm.asy
new file mode 100644 (file)
index 0000000..432bdbb
--- /dev/null
+++ b/media/src/asy/afm.asy
@@ -0,0 +1,33 @@
+// AFM operating principle graphic
+
+//size(x=9cm,keepAspect=true);
+
+import base_afm; // for Cantilever, Substrate, ...
+
+defaultpen(fontsize(size=10pt, lineskip=10pt));
+
+Cantilever c = Cantilever();
+// position base so tip touches substrate when bent
+c.set_tip_for_dx(8pt);
+c.align_tip((0,0));
+// unbend the tip and draw it in grey
+c.set_tip_for_dx(0);
+pair unbent_tip = c.tip;
+filldraw(c.tip_guide(), fillpen=grey, grey);
+draw(c.arm_guide(), grey);
+// rebend the tip and draw it in black
+c.set_tip_for_dx(8pt);
+filldraw(c.tip_guide(), fillpen=black);
+draw(c.arm_guide(), black);
+label("Cantilever", c.base-(0,14pt), SW);
+
+Substrate s = Substrate();
+s.draw();
+
+Photodiode p = Photodiode(center=(-40pt, 40pt));
+p.draw();
+label("Photodiode", p.center+(0,p.radius), N);
+
+Laser s = Laser(start=(-5pt,40pt), dir=S, cantilever=c, photodiode=p);
+s.draw();
+label("Laser", s.start, N);

diff --git a/media/src/asy/base_afm.asy b/media/src/asy/base_afm.asy
new file mode 100644 (file)
index 0000000..2a58f37
--- /dev/null
+++ b/media/src/asy/base_afm.asy
@@ -0,0 +1,246 @@
+// AFM drawing utilities.
+
+struct Cantilever {
+  // draw an AFM cantilever with the tip at TIP (x,y) position on page
+  // the cantilever arm is roughly parallel to DIR_TO_BASE (x,y) vector
+  // POINT_SCALE x gives the height of the tip.
+  pair tip;          // point of the tip
+  pair tip_top;      // center of the back side of the tip
+  pair tip_distal;   // distal back corner of the tip
+  pair tip_proximal; // proximal back corner of the tip
+
+  pair uty;          // unit vector pointing distally at the tip
+  pair utx;          // unit vector pointing tip-side at the tip
+
+  pair base;         // location of the cantilever base (chip attachment point)
+
+  pair uy;           // unit vector pointing distally at the base
+  pair ux;           // unit vector pointing tip-side at the base
+
+  real arm_length;   // cantilever path length
+  real tip_height;   // distance from tip_top to tip
+  real rest_angle;   // in degrees.  uy = dir(rest_angle)
+  real dx;           // (tip_top offset from unbent) <dot> (ux)
+  real theta;        // in radians
+  real r_curve;
+
+
+  void align_tip(pair tip) {
+    // shift the whole cantilever setup so the tip rests on TIP.
+    pair offset = tip - this.tip;
+    this.tip += offset;
+    this.tip_top += offset;
+    this.tip_distal += offset;
+    this.tip_proximal += offset;
+    this.base += offset;
+  }
+
+  real dx_error(real theta) {
+    /* Call the radius of curvature, r_curve=R
+     * arm_length=L lies along the perimiter, so
+     *   R\theta = L
+     * The perpendicular deflection dx is then
+     *   R(1-\cos\theta) = L(1-\cos\theta)/\theta = dx
+     * and the horizontal displacement L' from the base is
+     *   R\sin\theta = L\sin\theta/\theta = L\sinc\theta= L'
+     */
+     return this.arm_length * (1.0 - cos(theta)) / theta  -  this.dx;
+  }
+
+  real dx_prime(real theta) {
+    /* d(dx)/d(\theta) = L/\theta * [(\cos\theta-1)/\theta + \sin\theta]  */
+    return this.arm_length/theta * ((cos(theta)-1)/theta + sin(theta));
+  }
+
+  void set_tip_for_dx(real dx) {
+    /* invert dx(theta) using bracketed Newton-Raphson bisection.
+     * First order theta from
+     *   dx = L(1-\cos\theta)/\theta
+     *      = L[1-(1-\theta^2/2!+...)]/\theta
+     *      ~= L\theta/2
+     *   \theta != 2dx/L
+     */
+    this.dx = dx;
+    real Lp;
+    if (dx == 0) {
+      this.theta = 0;
+      this.r_curve = -1;
+      Lp = this.arm_length;
+    } else {
+      real first_order_theta = 2.0*dx/this.arm_length;
+      this.theta = newton(this.dx_error, this.dx_prime,
+                          0.1 * first_order_theta,
+                          min(3.0 * first_order_theta, pi/2.0));
+      /* because we ignored tip_height when we calculated theta, cheat a
+       * bit and pretend the tip is directly under our caculated
+       * tip_top.  Then adjust tip_top accordingly.  This throws off the
+       * bend (and maybe the arm length) a bit, but ah well :p.
+       */
+      this.r_curve = this.arm_length / this.theta;
+      Lp = this.r_curve * sin(this.theta);
+    }
+    this.uy = dir(this.rest_angle);
+    this.ux = dir(this.rest_angle+90);
+    this.uty = dir(this.rest_angle+degrees(this.theta));
+    this.utx = dir(this.rest_angle+90+degrees(this.theta));
+    this.tip = this.base + Lp*this.uy + (dx+this.tip_height)*this.utx;
+    this.tip_top = this.tip - this.tip_height*this.utx;
+    this.tip_distal = this.tip_top + this.tip_height/3.0*this.uty;
+    this.tip_proximal = this.tip_top - this.tip_height/3.0*this.uty;
+  }
+
+  guide tip_guide() {
+    path p;
+    p = this.tip -- this.tip_distal -- this.tip_proximal -- cycle;
+    return p;
+  }
+
+  guide arm_guide() {
+    path p;
+    if (this.dx == 0) {
+      // all three points should be colinear
+      p = this.tip_distal -- this.tip_proximal -- this.base;
+    } else {
+      p = this.tip_distal -- this.tip_proximal{-this.uty}
+          .. tension 0.75 .. {-this.uy}this.base;
+      /*      real angle_tip_proximal, angle_base;
+      pair center = this.base + this.r_curve*dx;
+      angle_tip_proximal = angle(tip_proximal - center);
+      angle_base = angle(this.base - center);
+      p = tip_distal -- arc(center, this.r_curve, angle_tip_proximal, angle_base);
+      tip_proximal{-uty} .. tension 0.75 .. {uy}this.base;
+      */
+    }
+    return p;
+  }
+
+  void operator init (pair base=(0,0), real arm_length=2.5cm, real tip_height=0.5cm, real rest_angle=195, real dx=0) {
+    this.base = base;
+    this.arm_length = arm_length;
+    this.tip_height = tip_height;
+    this.rest_angle = rest_angle;
+    this.set_tip_for_dx(dx);
+  }
+}
+
+struct Substrate {
+  pair prot_connect_point;
+  real substrate_width = 3cm;
+  real substrate_height = 10pt;
+  real piezo_width = 1.5cm;
+  real piezo_height = 0.75cm;
+  pen substrate_fill = grey;
+
+  path box(pair top_center, real width, real height) {
+    real w = width/2;
+    pair ul = top_center+(-w,0);
+    pair ur = top_center+( w,0);
+    pair ll = top_center+(-w,-height);
+    pair lr = top_center+( w,-height);
+    path p = ul -- ur -- lr -- ll -- cycle;
+    return p;
+  }
+
+  void draw(pair dir=(0,0)) {
+    pair piezo_top = this.prot_connect_point - (0,this.substrate_height);
+    pair piezo_bot = this.prot_connect_point - (0,this.substrate_height+this.piezo_height);
+    filldraw(this.box(this.prot_connect_point, this.substrate_width, this.substrate_height),
+             fillpen=this.substrate_fill);
+    label("Substrate", this.prot_connect_point - (0,this.substrate_height/2));
+    draw(this.box(piezo_top, this.piezo_width, this.piezo_height));
+    label("Piezo", piezo_top, S);
+    if (dir != (0,0)) {
+      real arrow_length = this.piezo_height/3;
+      pair arrow_center = piezo_bot + (0, arrow_length/2 + 2pt);
+      arrow(b=arrow_center + dir*arrow_length/2, dir=-dir,
+            length=this.piezo_height/3, Arrow(size=8pt),
+            margin=NoMargin, L="");
+    }
+  }
+
+  void operator init(pair prot_connect_point=(0,0)) {
+    this.prot_connect_point = prot_connect_point;
+  }
+}
+
+struct Photodiode {
+  pair center;
+  real radius = 8pt;
+  real x_scale = 0.5;
+
+  void draw(pen fillpen=grey, pen drawpen=defaultpen) {
+    pair c = this.center;
+    pair y = (0, this.radius);
+    pair x = (this.x_scale*this.radius, 0);
+    filldraw(shift(this.center)*xscale(this.x_scale)*scale(this.radius)
+             *unitcircle, fillpen, drawpen);
+    draw((c-x)--(c+x)--c--(c-y)--(c+y), drawpen);
+  }
+
+  void operator init(pair center=(0,0)) {
+    this.center = center;
+  }
+}
+
+// extension() added sometime between asy v1.40 and v1.91
+pair extension(pair P, pair Q, pair p, pair q)
+{
+  pair ac=P-Q;
+  pair bd=q-p;
+  real det=ac.x*bd.y-ac.y*bd.x;
+  if(det == 0) return (infinity,infinity);
+  return P+((p.x-P.x)*bd.y-(p.y-P.y)*bd.x)*ac/det;
+}
+
+struct Laser {
+  pair start;
+  real width = 2pt; // width at start (the laser source)
+  real spot = 1pt;  // width at the cantilever reflection point (minimum)
+  pair dir;
+  Cantilever cantilever;
+  Photodiode photodiode;
+
+  void draw(pen fillpen=red) {
+    pair w = scale(this.width/2)*rotate(90)*this.dir;
+    pair rw = scale(this.spot/2)*this.cantilever.uty;
+    if (dot(w, rw) < 0) rw = -rw; // ensure similar direction
+    // find point of reflection off cantilever.
+    pair ref = extension(this.start, this.start+this.dir,
+                         this.cantilever.tip_distal,
+                         this.cantilever.tip_proximal);
+    // find direction of reflection post-cantilever
+    pair post_dir = reflect((0,0), this.cantilever.uty)*dir;
+    pair contact = extension(ref, ref+post_dir,
+                             this.photodiode.center,
+                             this.photodiode.center+N);
+    real contact_width = this.width; ///length(ref-this.start)*length(ref-contact);
+    pair cw = scale(contact_width)*rotate(90)*post_dir;
+    if (dot(cw, rw) < 0) cw = -cw; // ensure similar direction
+    // laser -> cant.
+    fill((start+w)--(start-w)--(ref-rw)--(ref+rw)--cycle, fillpen);
+    // cant. -> photo.
+    fill((contact+cw)--(contact-cw)--(ref-rw)--(ref+rw)--cycle, fillpen);
+  }
+
+  void operator init(pair start, pair dir=S, Cantilever cantilever,
+                     Photodiode photodiode) {
+    this.start = start;
+    this.dir = unit(dir);
+    this.cantilever = cantilever;
+    this.photodiode = photodiode;
+  }
+}
+
+void distance(Label L, pair start, pair end) {
+  pair center = (start+end)/2;
+  pair u = unit(end-start);
+  picture picL;
+  label(picL, L);
+  pair label_size = 1.2 * (max(picL)-min(picL));
+  real arrow_length = length(end-start)/2 - label_size.y;
+  if (arrow_length > 4pt) {
+    arrow(b=start, dir=u, length=arrow_length, Arrow(size=4pt), L="");
+    arrow(b=end, dir=-u, length=arrow_length, Arrow(size=4pt), L="");
+  }
+  label(L, center);
+}

diff --git a/media/src/asy/expt-sawtooth-Ls.dat b/media/src/asy/expt-sawtooth-Ls.dat
new file mode 100644 (file)
index 0000000..17b1f7c
--- /dev/null
+++ b/media/src/asy/expt-sawtooth-Ls.dat
@@ -0,0 +1,9 @@
+4.19963e-08
+6.52187e-08
+8.84682e-08
+1.10442e-07
+1.33067e-07
+1.55498e-07
+1.77802e-07
+1.99098e-07
+2.2189e-07

diff --git a/media/src/asy/expt-sawtooth.asy b/media/src/asy/expt-sawtooth.asy
new file mode 100644 (file)
index 0000000..f80d5ca
--- /dev/null
+++ b/media/src/asy/expt-sawtooth.asy
@@ -0,0 +1,71 @@
+import wtk_graph;
+
+size(6cm,4cm,IgnoreAspect);
+
+scale(Linear, Linear);
+real k = infinity; /* spring constant in N/m, already accounted for (0.05) */
+real xscale=1e9;
+real fscale=1e12;
+
+real xmin = -5e-9;
+real xmax = 300e-9;
+real fmin = -100e-12;
+real fmax = 1000e-12;
+real fnmax = 300e-12;
+
+real kB = 1.3806504e-23;
+real T = 300;
+real p = 3.7e-10;
+real WLC(real x, real L, real p=p, real T=T, real kB=kB,
+         real xLmax=0.99, real fmax=fnmax) {
+  real f = infinity;
+  if (x < 0)
+    return infinity;
+  if (x/L <= xLmax)
+    f = kB*T/p*(0.25*(1/(1-x/L)^2 - 1) + x/L);
+  if (f > fnmax)
+    return infinity;
+  return f;
+}
+
+void graphSawtooth(string file="datafile", real k,
+                   int xcol=0, int fcol=1,
+                   real xscale=1, real fscale=1, real dx=0, real df=0,
+                   pen p=red) {
+  file fin=input(file).line();
+  real[][] a=fin.dimension(0,0);
+  a=transpose(a);
+  real[] x=a[xcol];
+  real[] f=a[fcol];
+  x = x - f/k; /* Remove cantilever extension */
+  graphData(x=x, y=f, xscale=xscale, yscale=fscale,
+            dx=dx, dy=df, p=p, dots=false);
+}
+
+/* expt-sawtooth.dat already scaled to nm and pN */
+graphSawtooth("expt-sawtooth.dat", k=k, p=psoft);
+
+file fin = input('expt-sawtooth-Ls.dat').line();
+real[][] a = fin.dimension(0,0);
+a = transpose(a);
+real[] Ls = a[0];
+int i;
+for (i=0; i<Ls.length; ++i) {
+  real fn(real x) {
+    real f = WLC(x / xscale, L=Ls[i]);
+    if (f == infinity) {
+      write(x, fnmax*fscale * 1.1);
+      return fnmax*fscale * 1.1;
+    }
+    write(x, f*fscale);
+    return f*fscale;
+  }
+  draw(graph(fn, a=0, b=0.9*Ls[i]*xscale), p=phard);
+}
+
+xlimits(xmin*xscale, xmax*xscale, crop=true);
+ylimits(fmin*fscale, fmax*fscale, crop=true);
+
+xaxis(sLabel("Distance (nm) ($x_t-x_c$)"), BottomTop, LeftTicks);
+yaxis(sLabel("Force (pN)"), LeftRight, RightTicks);
+label(sLabel("Poly-ubiquitin force curve"), point(N), N);

diff --git a/media/src/asy/expt-sawtooth.dat b/media/src/asy/expt-sawtooth.dat
new file mode 100644 (file)
index 0000000..3314289
--- /dev/null
+++ b/media/src/asy/expt-sawtooth.dat
@@ -0,0 +1,1200 @@
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diff --git a/media/src/asy/fit-valley.asy b/media/src/asy/fit-valley.asy
new file mode 100644 (file)
index 0000000..bf4c9e8
--- /dev/null
+++ b/media/src/asy/fit-valley.asy
@@ -0,0 +1,15 @@
+import wtk_graph;
+
+usepackage("amsmath");
+
+size(8cm,6cm,IgnoreAspect);
+
+scale(Log, Linear, Log);
+real xscale=1;
+real yscale=1e9;
+
+graphMatrixFile("fit-valley.dat", xscale=xscale, yscale=yscale,
+                x_label="$k_{uo}$ (s$^{-1}$)", y_label="$\Delta x_u$ (nm)",
+                palette_label="$D_\text{JS}$");
+
+label(sLabel("Fit quality"), point(N),N);

diff --git a/media/src/asy/fit-valley.dat b/media/src/asy/fit-valley.dat
new file mode 100644 (file)
index 0000000..0eb615b
--- /dev/null
+++ b/media/src/asy/fit-valley.dat
@@ -0,0 +1,9900 @@
+#k0 (1/s)      dx (nm) D_JS
+0.002  1.2e-10 0.584348
+0.002  1.21061e-10     0.590907
+0.002  1.22121e-10     0.59638
+0.002  1.23182e-10     0.581554
+0.002  1.24242e-10     0.5991
+0.002  1.25303e-10     0.595028
+0.002  1.26364e-10     0.591126
+0.002  1.27424e-10     0.605027
+0.002  1.28485e-10     0.609652
+0.002  1.29545e-10     0.609193
+0.002  1.30606e-10     0.613042
+0.002  1.31667e-10     0.624632
+0.002  1.32727e-10     0.604166
+0.002  1.33788e-10     0.615662
+0.002  1.34848e-10     0.627717
+0.002  1.35909e-10     0.612443
+0.002  1.3697e-10      0.627952
+0.002  1.3803e-10      0.625526
+0.002  1.39091e-10     0.602265
+0.002  1.40152e-10     0.622571
+0.002  1.41212e-10     0.598247
+0.002  1.42273e-10     0.616676
+0.002  1.43333e-10     0.611893
+0.002  1.44394e-10     0.599424
+0.002  1.45455e-10     0.60453
+0.002  1.46515e-10     0.602248
+0.002  1.47576e-10     0.613267
+0.002  1.48636e-10     0.609558
+0.002  1.49697e-10     0.595195
+0.002  1.50758e-10     0.581741
+0.002  1.51818e-10     0.582815
+0.002  1.52879e-10     0.578112
+0.002  1.53939e-10     0.569439
+0.002  1.55e-10        0.564881
+0.002  1.56061e-10     0.565041
+0.002  1.57121e-10     0.562134
+0.002  1.58182e-10     0.529712
+0.002  1.59242e-10     0.534463
+0.002  1.60303e-10     0.514022
+0.002  1.61364e-10     0.509806
+0.002  1.62424e-10     0.499266
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+0.002  1.65606e-10     0.476443
+0.002  1.66667e-10     0.449323
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+0.002  1.76212e-10     0.372035
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+0.002  1.82576e-10     0.277863
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+0.002  1.86818e-10     0.218545
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+0.002  1.91061e-10     0.179728
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+0.002  1.94242e-10     0.15771
+0.002  1.95303e-10     0.135922
+0.002  1.96364e-10     0.13312
+0.002  1.97424e-10     0.123062
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+
+0.00210383     1.2e-10 0.587268
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+0.285194       1.91061e-10     0.710034
+0.285194       1.92121e-10     0.700603
+0.285194       1.93182e-10     0.709002
+0.285194       1.94242e-10     0.701592
+0.285194       1.95303e-10     0.711888
+0.285194       1.96364e-10     0.707693
+0.285194       1.97424e-10     0.712484
+0.285194       1.98485e-10     0.712467
+0.285194       1.99545e-10     0.714336
+0.285194       2.00606e-10     0.708259
+0.285194       2.01667e-10     0.708261
+0.285194       2.02727e-10     0.700121
+0.285194       2.03788e-10     0.701097
+0.285194       2.04848e-10     0.698518
+0.285194       2.05909e-10     0.696277
+0.285194       2.0697e-10      0.688415
+0.285194       2.0803e-10      0.69349
+0.285194       2.09091e-10     0.68701
+0.285194       2.10152e-10     0.684413
+0.285194       2.11212e-10     0.684701
+0.285194       2.12273e-10     0.681806
+0.285194       2.13333e-10     0.674635
+0.285194       2.14394e-10     0.672314
+0.285194       2.15455e-10     0.660047
+0.285194       2.16515e-10     0.659411
+0.285194       2.17576e-10     0.656122
+0.285194       2.18636e-10     0.64255
+0.285194       2.19697e-10     0.63884
+0.285194       2.20758e-10     0.639428
+0.285194       2.21818e-10     0.623498
+0.285194       2.22879e-10     0.61895
+0.285194       2.23939e-10     0.618009

diff --git a/media/src/asy/fjc-model.asy b/media/src/asy/fjc-model.asy
new file mode 100644 (file)
index 0000000..50c3c3a
--- /dev/null
+++ b/media/src/asy/fjc-model.asy
@@ -0,0 +1,9 @@
+import wiggle;  // for RandomWalk
+
+RandomWalk w = RandomWalk(dx=1cm);
+w.align(90);
+guide g = w.straight_guide();
+draw(g, red);
+dot(g, linewidth(2pt) + blue);
+dot(w.start);
+dot(w.end);

diff --git a/media/src/asy/kramers-integrand.asy b/media/src/asy/kramers-integrand.asy
new file mode 100644 (file)
index 0000000..a4fcd74
--- /dev/null
+++ b/media/src/asy/kramers-integrand.asy
@@ -0,0 +1,52 @@
+import palette;
+import wtk_graph;
+
+real a = 0.2;
+real b = 0.7;
+real x_min = 0;
+real x_max = 1;
+real f_min = 0;  // zoom in on region of interest
+real f_max = 1;
+real n = 20;     // number of integration traces
+
+real f_raw(real x) {return -(x-a)*(x-b)**2;}
+real f_raw_min = f_raw(x_max);
+real f_raw_max = f_raw(x_min);
+real f(real x) {return (f_raw(x)-f_raw_min)/(f_raw_max-f_raw_min);}
+
+real ep(real x) {return (exp(f(x)));}
+real em(real x) {return (exp(-f(x)));}
+real integrand(real x, real y) {return (ep(y) * em(x));}
+
+picture pic1;
+scale(pic1, Linear, Linear);
+image(pic1, integrand, (x_min, x_min), (x_max, x_max), BWRainbow());
+real x;
+for (int i = 1; i <= n; ++i) {
+  x = x_min + i*(x_max-x_min)/(n + 1);
+  draw(pic1, (0, x) -- (x, x));
+}
+size(pic1, 5cm, 5cm, point(pic1, SW), point(pic1, NE));
+label(pic1, sLabel("Kramers integrand"), point(pic1, N), align=N);
+frame f1 = shift((2cm, 0)) * pic1.fit();
+add(f1);
+
+picture pic2;
+scale(pic2, Linear, Linear);
+draw(pic2, graph(em, x_min, x_max, operator ..), red);
+size(pic2, 5cm, 1cm, point(pic2, SW), point(pic2, NE));
+xaxis(pic2, sLabel("$x'$"), Bottom);
+frame f2 = pic2.fit();
+f2 = shift((min(f1).x - min(f2).x, min(f1).y - max(f2).y)) * f2;
+add(f2);
+label(Label("$e^{-U(x')}$"), (max(f2)+min(f2))/2 + (-18pt, 0));
+
+picture pic3;
+scale(pic3, Linear, Linear);
+draw(pic3, rotate(90)*graph(ep, x_min, x_max, operator ..), red);
+size(pic3, 1cm, 5cm, point(pic3, SW), point(pic3, NE));
+yaxis(pic3, sLabel("$x$"), Left);
+frame f3 = pic3.fit();
+f3 = shift((min(f1).x - max(f3).x, min(f1).y - min(f3).y)) * f3;
+add(f3);
+label(rotate(90)*Label("$e^{U(x)}$"), (max(f3)+min(f3))/2 + (0, -18pt));

diff --git a/media/src/asy/landscape-bell.asy b/media/src/asy/landscape-bell.asy
new file mode 100644 (file)
index 0000000..f2a8d2e
--- /dev/null
+++ b/media/src/asy/landscape-bell.asy
@@ -0,0 +1,40 @@
+import wtk_graph;
+
+size(6cm, 4cm, IgnoreAspect);
+
+scale(Linear, Linear);
+
+real x_min = 0;
+real x_max = 1;
+real f_min = 0;  // zoom in on region of interest
+real f_max = 1;
+pair folded = (0.2, 0.2);
+pair transition = (0.8, 0.8);
+pair forced_transition = (0.8, 0.5);
+real dx = 0.1;  // width of energy level lines
+
+void draw_level(pair center, Label label, pen p=currentpen) {
+  draw(Scale(center-(dx/2,0)) -- Scale(center+(dx/2,0)), p);
+  dot(label, Scale(center));
+}
+
+void draw_rate(pair a, pair b, Label label, pen p=currentpen) {
+  path arrow_path = Scale(a){dir(70)} .. {dir(-60)}Scale(b);
+  draw(arrow_path, p, Arrows, Margin(1, 1));
+  label(label, point(arrow_path, length(arrow_path)/2));
+}
+
+draw_level(folded, Label("folded", align=S));
+draw_level(transition, Label("transition", align=S));
+draw_level(forced_transition, Label(
+  minipage("\center{forced transition}", 60), align=S), dashed);
+
+draw_rate(folded, transition, Label("$k_{u0}$", align=NW));
+draw_rate(folded, forced_transition, Label("$k_{uF}$", align=SE), dashed);
+
+xlimits(x_min, x_max, Crop);
+ylimits(f_min, f_max, Crop);
+
+label(sLabel("Bell model unfolding"), point(N), N);
+xaxis(sLabel("End-to-end distance $x$"), BottomTop);
+yaxis(sLabel("Free energy $U_F$"), LeftRight);

diff --git a/media/src/asy/landscape-cant.asy b/media/src/asy/landscape-cant.asy
new file mode 100644 (file)
index 0000000..c14a82c
--- /dev/null
+++ b/media/src/asy/landscape-cant.asy
@@ -0,0 +1,43 @@
+// This graphic is very similar to landscape.asy
+
+import wtk_graph;
+
+size(6cm, 4cm, IgnoreAspect);
+
+scale(Linear, Linear);
+
+real a = 0.2;
+real b = 0.7;
+real F = 0.3;
+real k = 0.5;
+real x_min = 0;
+real x_max = 1;
+real f_min = 0;
+real f_max = 1;
+
+real f_raw(real x) {return -(x-a)*(x-b)**2;}
+real f_raw_min = f_raw(x_max);
+real f_raw_max = f_raw(x_min);
+real f(real x) {return (f_raw(x)-f_raw_min)/(f_raw_max-f_raw_min);}
+
+real x_fold = (2*a+b)/3;
+real x_barrier = b;
+
+real const_force(real x) {return f(x_fold)-F*(x-x_fold);}
+real force(real x) {return const_force(x)+1/2*k*(x-x_fold)**2;}
+real f_force(real x) {return f(x)+(force(x)-f(x_fold));}
+
+draw(graph(f, x_min, x_max, operator ..), blue);
+draw(graph(const_force, x_min, x_max, operator ..), dashed);
+draw(graph(force, x_min, x_max, operator ..), black);
+draw(graph(f_force, x_min, x_max, operator ..), red);
+
+label(sLabel("folded", align=S), Scale((x_fold, f(x_fold))));
+label(sLabel("barrier", align=N), Scale((x_barrier, f(x_barrier))));
+
+xlimits(x_min, x_max, Crop);
+ylimits(f_min, f_max, Crop);
+
+label(sLabel("Cantilever-altered energy landscape"), point(N), N);
+xaxis(sLabel("End-to-end distance $x$"), BottomTop);
+yaxis(sLabel("Free energy $U_F$"), LeftRight);

diff --git a/media/src/asy/landscape.asy b/media/src/asy/landscape.asy
new file mode 100644 (file)
index 0000000..2cb5aa9
--- /dev/null
+++ b/media/src/asy/landscape.asy
@@ -0,0 +1,63 @@
+import wtk_graph;
+
+size(6cm, 4cm, IgnoreAspect);
+
+scale(Linear, Linear);
+
+real a = 0.2;
+real b = 0.6;
+real x_min = 0;
+real x_max = 1;
+real f_min = 0.5;  // zoom in on region of interest
+real f_max = 0.8;
+real x_arrow = 0.2;  // range around x_barrier
+real y_arrow = 0.08;  // offset above U_F(x)
+real state_size = 7pt;  // size of current-state dot
+
+real f_raw(real x) {return -(x-a)*(x-b)**2;}
+real f_raw_min = f_raw(x_max);
+real f_raw_max = f_raw(x_min);
+real f(real x) {return (f_raw(x)-f_raw_min)/(f_raw_max-f_raw_min);}
+real f_arrow(real x) {return (f(x) + y_arrow);}
+
+// df/dx = -(x-b)**2 - 2(x-a)(x-b)
+// at the extremes, df/dx = 0, so
+//   (x-b)**2 = -2(x-a)(x-b)
+//   so
+//        x-b = 0
+//          x = b
+//   or
+//    -2(x-a) = (x-b)
+//          x = (2a + b)/3
+
+real x_fold = (2*a+b)/3;
+real x_barrier = b;
+real x_unfold = (3*b + x_max)/4;
+real x_state = (3*x_fold + x_barrier)/4;
+
+path f_path = graph(f, x_min, x_max, operator ..);
+draw(f_path, blue);
+
+path arrow_path = graph(f_arrow, x_barrier-x_arrow/2, x_barrier+x_arrow/2,
+  operator ..);
+draw(arrow_path, Arrow);
+label(sLabel("$k_u$", align=N), point(arrow_path, length(arrow_path)/2));
+
+real[] state_ts = intersect(f_path, (x_state, f_min)--(x_state, f_max));
+real state_t = state_ts[0];  // time along f_path
+pair state_perp = scale(1/10cm)*rotate(90)*dir(f_path, state_t);
+pair state_point = (x_state, f(x_state)) + state_perp*state_size/2;
+pen state_pen = linewidth(state_size) + currentpen;
+
+label(sLabel("folded", align=S), Scale((x_fold, f(x_fold))));
+label(sLabel("barrier", align=N), Scale((x_barrier, f(x_barrier))));
+label(sLabel("unfolded", align=NE), Scale((x_unfold, f(x_unfold))));
+dot(Scale(state_point), state_pen);
+label(sLabel("state", align=N), Scale(state_point) + (0, state_size/20cm));
+
+xlimits(x_min, x_max, Crop);
+ylimits(f_min, f_max, Crop);
+
+label(sLabel("Unfolding energy landscape"), point(N), N);
+xaxis(sLabel("End-to-end distance $x$"), BottomTop);
+yaxis(sLabel("Free energy $U_F$"), LeftRight);

diff --git a/media/src/asy/monte-carlo.asy b/media/src/asy/monte-carlo.asy
new file mode 100644 (file)
index 0000000..e3de598
--- /dev/null
+++ b/media/src/asy/monte-carlo.asy
@@ -0,0 +1,189 @@
+// A die roll decides which of two doors to enter.
+
+//import unicode;
+//from three access rotate;
+
+/* Copy three.asy's relevant rotate function, since including three
+ * adds an uneccessary movie15 LaTeX dependency.
+ */
+transform3 rotate(real angle, triple v)
+{
+  v=unit(v);
+  real x=v.x, y=v.y, z=v.z;
+  real s=Sin(angle), c=Cos(angle), t=1-c;
+  return new real[][] {
+    {t*x^2+c,   t*x*y-s*z, t*x*z+s*y, 0},
+      {t*x*y+s*z, t*y^2+c,   t*y*z-s*x, 0},
+        {t*x*z-s*y, t*y*z+s*x, t*z^2+c,   0},
+          {0,         0,         0,         1}};
+}
+
+struct Door {
+  pair center;
+  real angle;
+  Label L;
+  real width = 3cm;
+  real aspect_ratio = (1+sqrt(5))/2; // Golden ratio
+  real knob_ratio = 0.10;
+  triple inward = (0, 0.4, -1); // x component must be zero for current implementation.
+
+  void draw() {
+    picture p; // the door panel
+    guide g = yscale(this.aspect_ratio)*scale(this.width)*shift((-0.5,-0.5))*
+      unitsquare;
+    fill(p, g, white);
+    label(p, Label(this.L, (0,0), embed=Scale), (0,0));
+    p = shift((-this.width/2.0,0))*xscale(Cos(this.angle))*rotate(-90)*
+      slant(-unit(this.inward).y*Sin(this.angle))*
+      rotate(90)*shift((this.width/2.0,0))*
+      p; // open the door if angle > 0
+    clip(p, g);
+    fill(shift(this.center)*g); // fill the hole
+    add(p, this.center);        // add the door panel
+    draw(shift(this.center)*g); // outline the hole again
+  }
+
+  void operator init (pair center=(0,0), Label L="", real angle=0) {
+    this.center = center;
+    this.L = L;
+    this.angle = angle;
+  }
+}
+
+struct Die {
+  pair center;
+  int top;
+  int left;
+  bool righthanded = true;
+  real side = 1cm;
+  real dot_ratio = 0.2;
+  triple up = (0, 1, 0.4); // up, but tilted out of the page
+  real theta = -20;
+  pair[][] pips;
+
+  int right() {
+    /* It is traditional to combine pairs of numbers that total seven
+     * to opposite faces; this implies that at one vertex the faces 1,
+     * 2 and 3 intersect. It leaves one other abstract design choice:
+     * the faces representing 1, 2 and 3 respectively can be placed in
+     * either clockwise or counterclockwise order about this
+     * vertex. If the 1, 2 and 3 faces run counterclockwise around
+     * their common vertex, the die is called "right handed"; if they
+     * run clockwise it is called "left handed". Standard modern
+     * Western dice are right-handed, whereas Chinese dice are often
+     * left-handed.
+     *  - http://en.wikipedia.org/wiki/Dice
+     */
+    int little_top = min(this.top, 7-this.top);
+    int little_left = min(this.left, 7-this.left);
+    int little_right = 6 - little_top - little_left;
+    bool righthanded;
+    int little_ccw[] = {little_top, little_left, little_right};
+    int i = 0;
+    little_ccw.cyclic = true;
+    while (little_ccw[i] != 1 && i < 3)  i += 1;
+    if (i == 3)  return -1;
+    if (little_ccw[i+1] == 2)      righthanded = true;
+    else                           righthanded = false;
+    if (this.top != little_top)    righthanded = !righthanded;
+    if (this.left != little_left)  righthanded = !righthanded;
+    if (righthanded == this.righthanded)  return little_right;
+    return 7-little_right;
+  }
+
+  void setup_pips() {
+    real d = 1.0/3.5;
+    this.pips = new pair[7][];
+    this.pips[0] = null;
+    this.pips[1].push((0,0));
+    this.pips[2].push((-d,d));
+    this.pips[2].push((d,-d));
+    this.pips[3] = copy(this.pips[2]);
+    this.pips[3].push((0,0));
+    this.pips[4] = copy(this.pips[2]);
+    this.pips[4].push((d,d));
+    this.pips[4].push((-d,-d));
+    this.pips[5] = copy(this.pips[4]);
+    this.pips[5].push((0,0));
+    this.pips[6] = copy(this.pips[4]);
+    this.pips[6].push((-d,0));
+    this.pips[6].push((d,0));
+  }
+
+  // z coordinate in face unitvectors will end up facing this.up
+  pair transform(pair face_coords, triple face_x, triple face_y) {
+    triple face_z = cross(unit(face_x), unit(face_y));
+    triple f_c = face_coords.x*face_x + face_coords.y*face_y +0.5*face_z;
+    triple u = cross(unit(this.up), (0,0,1));
+    if (length(u) > sqrtEpsilon) {
+      // rotate z coordinate to point along this.up
+      f_c = rotate(-aSin(length(u)), u) * f_c;
+    }
+    triple c = rotate(this.theta, this.up) * f_c;
+    return shift(this.center)*scale(this.side)*(c.x, c.y);
+  }
+
+  guide transform(guide face_coords, triple face_x, triple face_y) {
+    guide g;
+    pair p;
+    pair[] c; // for holding Bezier control points
+    for (int i=0; i < length(face_coords); ++i) {
+      p = this.transform(point(face_coords, i), face_x, face_y);
+      if (i == 0) {
+        g = g--p;
+      } else {
+        c = controlSpecifier(face_coords, i-1); // {outgoing, incoming)
+        c[0] = this.transform(c[0], face_x, face_y);
+        c[1] = this.transform(c[1], face_x, face_y);
+        g = g..controls c[0] and c[1]..p;
+      }
+    }
+    if (cyclic(face_coords)) {
+      c = controlSpecifier(face_coords, -1);
+      c[0] = this.transform(c[0], face_x, face_y);
+      c[1] = this.transform(c[1], face_x, face_y);
+      g = g..controls c[0] and c[1]..cycle;
+    }
+    return g;
+  }
+
+  void draw_pip(pair z, triple face_x, triple face_y) {
+    fill(this.transform(shift(z)*scale(this.dot_ratio/2.0)*unitcircle,
+                            face_x, face_y));
+  }
+
+  /* azimuth = 0, elevation=90  ->  facing up
+   * azimuth = 0, elevation=0   ->  facing out of the page
+   * azimuth = 90, elevation=0  ->  facing right
+   */
+  void draw_face(int number, triple face_x, triple face_y) {
+    filldraw(this.transform(shift((-0.5,-0.5))*unitsquare, face_x, face_y),
+             white);
+    for (pair z : this.pips[number])
+      this.draw_pip(z, face_x, face_y);
+  }
+
+  void draw() {
+    this.draw_face(this.top, face_x=(1,0,0), face_y=(0,1,0));
+    this.draw_face(this.left, face_x=(1,0,0), face_y=(0,0,1));
+    this.draw_face(this.right(), face_x=(0,0,-1), face_y=(0,1,0));
+  }
+
+  void operator init (pair center=(0,0), int top=1, int left=2) {
+    this.center = center;
+    this.top = top;
+    this.left = left;
+    this.setup_pips();
+  }
+}
+
+Door L = Door((-2cm,0),
+              L=minipage("\centering{\Large Unfold}\\$P=1/3$\\(\epsdice{1}\epsdice{2})"));
+Door R = Door((2cm,0),
+              L=minipage("\centering{\Large Stay folded}\\$Q=1-P$\\(\epsdice{3}\epsdice{4}\epsdice{5}\epsdice{6})"),
+              angle=30);
+Die d = Die((-0.3cm, -2.5cm), top=3, left=5);
+
+L.draw();
+R.draw();
+d.draw();

diff --git a/media/src/asy/pbs-hist.asy b/media/src/asy/pbs-hist.asy
new file mode 100644 (file)
index 0000000..8603a09
--- /dev/null
+++ b/media/src/asy/pbs-hist.asy
@@ -0,0 +1,19 @@
+import wtk_graph;
+
+
+size(6cm, 4cm, IgnoreAspect);
+
+scale(Linear, Log);
+real fscale=1e12;
+
+pen p = psoft;
+
+histFile("pbs-hist.hist", bin_scale=fscale, fillpen=(p+opacity(0.3)),
+    drawpen=p);
+
+//set xrange [100:400]
+//#set yrange [0.0001:1]
+//xlimits(pic, xmin, xmax);
+//ylimits(pic, ymin, ymax);
+xaxis(sLabel("Force (pN)"), BottomTop, LeftTicks, above=true);
+yaxis(sLabel("Frequency"), LeftRight, RightTicks, above=true);

diff --git a/media/src/asy/pbs-hist.dat b/media/src/asy/pbs-hist.dat
new file mode 100644 (file)
index 0000000..e9c177d
--- /dev/null
+++ b/media/src/asy/pbs-hist.dat
@@ -0,0 +1,131 @@
+1.84458445371e-10
+2.36485186373e-10
+1.91553000963e-10
+1.08783185732e-10
+5.49828058318e-11
+1.12921676493e-10
+1.01097417175e-10
+1.24154722846e-10
+2.2820820485e-10
+2.51856723488e-10
+2.35302760442e-10
+1.92735426894e-10
+2.05150899179e-10
+1.97465130622e-10
+2.39441251203e-10
+2.22296075191e-10
+2.32346695612e-10
+1.94509065792e-10
+2.11063028838e-10
+2.41214890101e-10
+1.22381083948e-10
+1.63765991564e-10
+2.06333325111e-10
+2.42988528999e-10
+2.41806103067e-10
+2.52447936454e-10
+2.67819473568e-10
+2.37667612305e-10
+1.5844507487e-10
+1.76772676814e-10
+2.21704862225e-10
+9.63677134472e-11
+1.90370575031e-10
+2.25843352987e-10
+2.02194834349e-10
+1.81502380542e-10
+2.27025778919e-10
+1.82093593508e-10
+1.89188149099e-10
+1.93917852826e-10
+1.56671435972e-10
+1.76181463848e-10
+2.13427880702e-10
+2.73140390261e-10
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+2.11063028838e-10
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diff --git a/media/src/asy/pbs-hist.hist b/media/src/asy/pbs-hist.hist
new file mode 100644 (file)
index 0000000..a037bbc
--- /dev/null
+++ b/media/src/asy/pbs-hist.hist
@@ -0,0 +1,18 @@
+4e-11  1
+6e-11  1
+8e-11  4
+1e-10  5
+1.2e-10        6
+1.4e-10        8
+1.6e-10        13
+1.8e-10        18
+2e-10  25
+2.2e-10        26
+2.4e-10        10
+2.6e-10        7
+2.8e-10        4
+3e-10  0
+3.2e-10        0
+3.4e-10        2
+3.6e-10        0
+3.8e-10        1

diff --git a/media/src/asy/piezo.asy b/media/src/asy/piezo.asy
new file mode 100644 (file)
index 0000000..fa61a6f
--- /dev/null
+++ b/media/src/asy/piezo.asy
@@ -0,0 +1,232 @@
+// Cylindrical piezo operating principle graphic
+
+//size(x=9cm,keepAspect=true);
+
+import graph3;
+import three;
+
+pen piezo_pen = opacity(0.1) + grey;
+pen x_electrode_pen = opacity(0.4) + red;
+pen y_electrode_pen = opacity(0.4) + blue;
+pen z_electrode_pen = opacity(0.4) + green;
+pen outline_pen = linewidth(1pt) + black;
+
+real R = 1.1cm;
+real r = 0.9cm;
+real h = 5cm;
+real ethick = 1pt;
+real espace = 1cm;
+real theta1 = 0.4*pi;
+real dtheta = 2*asin(espace/(R+r)/4);
+real theta2 = theta1 + pi/2 - dtheta;
+real tavg = (theta1 + theta2)/2;
+real dr = 4pt;
+real dR = 6pt;
+
+currentprojection = FrontView;
+
+triple cylinder(real r, real theta, real z) {
+    return (r*cos(theta), r*sin(theta), z);
+}
+
+struct Cylinder {
+    real r;
+    real R;
+    real z1;
+    real z2;
+    real theta1;
+    real theta2;
+
+    void operator init(real r=0, real R=1, real z1=0, real z2=1,
+            real theta1=0, real theta2=2pi) {
+        this.r = r;
+        this.R = R;
+        this.z1 = z1;
+        this.z2 = z2;
+        this.theta1 = theta1;
+        this.theta2 = theta2;
+    }
+
+    triple _cap(pair t) {
+        return cylinder(t.x, t.y, 0);
+    }
+
+    triple _inner_wall(pair t) {
+        return cylinder(this.r, t.x, t.y);
+    }
+
+    triple _outer_wall(pair t) {
+        return cylinder(this.R, t.x, t.y);
+    }
+
+    triple _box1(pair t) {
+        return cylinder(t.x, this.theta1, t.y);
+    }
+
+    triple _box2(pair t) {
+        return cylinder(t.x, this.theta2, t.y);
+    }
+
+    surface cap() {
+        // surface() described in graph3 documentation.
+        return surface(
+            this._cap, (this.r, this.theta1), (this.R, this.theta2), 8, 8, Spline);
+    }
+
+    surface[] surfaces() {
+        surface ret[];
+        surface cap = this.cap();
+        ret.push(shift(0, 0, this.z1)*cap);
+        ret.push(shift(0, 0, this.z2)*cap);
+        ret.push(surface(
+            this._outer_wall, (this.theta1, this.z1), (this.theta2, this.z2),
+            8, 8, Spline));
+        ret.push(surface(
+            this._inner_wall, (this.theta1, this.z1), (this.theta2, this.z2),
+            8, 8, Spline));
+        if (this.theta1 % 2pi != this.theta2 % 2pi) {
+            ret.push(surface(this._box1, (this.r, this.z1), (this.R, this.z2)));
+            ret.push(surface(this._box2, (this.r, this.z1), (this.R, this.z2)));
+        }
+        return ret;
+    }
+
+    path3[] cap_paths() {
+        triple c = (0, 0, 0);
+        real t1 = degrees(this.theta1);
+        real t2 = degrees(this.theta2);
+        return new path3[] {
+            arc(c, this.r, 90, t1, 90, t2, (0, 0, 1)),
+            arc(c, this.R, 90, t1, 90, t2, (0, 0, 1)),
+            };
+    }
+
+    path3[] outline() {
+        path3 ret[];
+        path3 caps[] = this.cap_paths();
+        ret.push(shift(0, 0, this.z1)*caps[0]);
+        ret.push(shift(0, 0, this.z1)*caps[1]);
+        ret.push(shift(0, 0, this.z2)*caps[0]);
+        ret.push(shift(0, 0, this.z2)*caps[1]);
+        if (this.theta1 % 2pi != this.theta2 % 2pi) {
+            ret.push(
+                cylinder(this.r, this.theta1, this.z1) --
+                cylinder(this.r, this.theta1, this.z2) --
+                cylinder(this.R, this.theta1, this.z2) --
+                cylinder(this.R, this.theta1, this.z1) -- cycle);
+            ret.push(
+                cylinder(this.r, this.theta2, this.z1) --
+                cylinder(this.r, this.theta2, this.z2) --
+                cylinder(this.R, this.theta2, this.z2) --
+                cylinder(this.R, this.theta2, this.z1) -- cycle);
+        }
+        return ret;
+    }
+
+    void draw(pen surface_pen, pen outline_pen, transform3 t=identity4) {
+        surface surfaces[] = this.surfaces();
+        path3 paths[] = this.outline();
+        for (int i=0; i < surfaces.length; ++i) {
+            draw(t*surfaces[i], surface_pen, nolight);
+        }
+        for (int i=0; i < paths.length; ++i) {
+            draw(t*paths[i], outline_pen, nolight);
+        }
+    }
+
+    void cap(pen surface_pen, pen outline_pen, transform3 t=identity4) {
+        surface cap = this.cap();
+        path3 paths[] = this.cap_paths();
+        draw(t*cap, surface_pen, nolight);
+        for (int i=0; i < paths.length; ++i) {
+            draw(t*paths[i], outline_pen, nolight);
+        }
+    }
+}
+
+void wire(Label label="", triple a, triple b, transform3 t=identity4,
+        align align=NoAlign) {
+    draw(t*(a--b));
+    dot(t*a);
+    dot(label, t*b, align=align);
+}
+
+Cylinder piezo = Cylinder(r, R, -h/2, h/2);
+Cylinder z_in = Cylinder(r-ethick, r, espace/2, h/2-espace/2, 0, 2pi);
+Cylinder z_out = Cylinder(R, R+ethick, espace/2, h/2-espace/2, 0, 2pi);
+Cylinder xa_in = Cylinder(
+    r-ethick, r, -h/2+espace/2, -espace/2, theta1, theta2);
+Cylinder xa_out = Cylinder(
+    R, R+ethick, -h/2+espace/2, -espace/2, theta1, theta2);
+Cylinder ya_in = Cylinder(
+    r-ethick, r, -h/2+espace/2, -espace/2, theta1+pi/2, theta2+pi/2);
+Cylinder ya_out = Cylinder(
+    R, R+ethick, -h/2+espace/2, -espace/2, theta1+pi/2, theta2+pi/2);
+Cylinder xb_in = Cylinder(
+    r-ethick, r, -h/2+espace/2, -espace/2, theta1+pi, theta2+pi);
+Cylinder xb_out = Cylinder(
+    R, R+ethick, -h/2+espace/2, -espace/2, theta1+pi, theta2+pi);
+Cylinder yb_in = Cylinder(
+    r-ethick, r, -h/2+espace/2, -espace/2, theta1-pi/2, theta2-pi/2);
+Cylinder yb_out = Cylinder(
+    R, R+ethick, -h/2+espace/2, -espace/2, theta1-pi/2, theta2-pi/2);
+
+transform3 piezo_transform = shift(-1.5*R, 0, 0)*rotate(12, (1, 0, 0));
+
+piezo.draw(piezo_pen, outline_pen, piezo_transform);
+z_in.draw(z_electrode_pen, outline_pen, piezo_transform);
+z_out.draw(z_electrode_pen, outline_pen, piezo_transform);
+xa_in.draw(x_electrode_pen, outline_pen, piezo_transform);
+xa_out.draw(x_electrode_pen, outline_pen, piezo_transform);
+ya_in.draw(y_electrode_pen, outline_pen, piezo_transform);
+ya_out.draw(y_electrode_pen, outline_pen, piezo_transform);
+xb_in.draw(x_electrode_pen, outline_pen, piezo_transform);
+xb_out.draw(x_electrode_pen, outline_pen, piezo_transform);
+yb_in.draw(y_electrode_pen, outline_pen, piezo_transform);
+yb_out.draw(y_electrode_pen, outline_pen, piezo_transform);
+
+
+transform3 z_transform = shift((1.5*R, 0, 1.3*R))*rotate(90, (1, 0, 0));
+transform3 label_transform = shift((0, 1cm, 0));
+
+piezo.draw(piezo_pen, invisible, z_transform);
+z_in.draw(z_electrode_pen, invisible, z_transform);
+z_out.draw(z_electrode_pen, invisible, z_transform);
+wire("$z_-$", (-R-ethick, 0, 0), (-R-ethick, 3R/4, 0),
+    label_transform*z_transform, align=W);
+wire("$z_+$", (-r+ethick, 0, 0), (-r/3, 0, 0),
+    label_transform*z_transform, align=E);
+
+transform3 xy_transform = shift((1.5*R, 0, -1.3*R))*rotate(90, (1, 0, 0));
+
+piezo.draw(piezo_pen, invisible, xy_transform);
+xa_in.draw(x_electrode_pen, invisible, xy_transform);
+xa_out.draw(x_electrode_pen, invisible, xy_transform);
+ya_in.draw(y_electrode_pen, invisible, xy_transform);
+ya_out.draw(y_electrode_pen, invisible, xy_transform);
+xb_in.draw(x_electrode_pen, invisible, xy_transform);
+xb_out.draw(x_electrode_pen, invisible, xy_transform);
+yb_in.draw(y_electrode_pen, invisible, xy_transform);
+yb_out.draw(y_electrode_pen, invisible, xy_transform);
+wire("$x_-$", cylinder(r-ethick, tavg, 0), cylinder(r-ethick-dr, tavg, 0),
+    label_transform*xy_transform, align=-expi(tavg));
+wire("$x_+$", cylinder(R+ethick, tavg, 0), cylinder(R+ethick+dR, tavg, 0),
+    label_transform*xy_transform, align=expi(tavg));
+wire("$y_-$", cylinder(r-ethick, tavg + pi/2, 0),
+    cylinder(r-ethick-dr, tavg + pi/2, 0),
+    label_transform*xy_transform, align=-expi(tavg + pi/2));
+wire("$y_+$", cylinder(R+ethick, tavg + pi/2, 0),
+    cylinder(R+ethick+dR, tavg + pi/2, 0),
+    label_transform*xy_transform, align=expi(tavg + pi/2));
+wire("$x_+$", cylinder(r-ethick, tavg + pi, 0),
+    cylinder(r-ethick-dr, tavg + pi, 0),
+    label_transform*xy_transform, align=-expi(tavg + pi));
+wire("$x_-$", cylinder(R+ethick, tavg + pi, 0),
+    cylinder(R+ethick+dR, tavg + pi, 0),
+    label_transform*xy_transform, align=expi(tavg + pi));
+wire("$y_+$", cylinder(r-ethick, tavg - pi/2, 0),
+    cylinder(r-ethick-dr, tavg - pi/2, 0),
+    label_transform*xy_transform, align=-expi(tavg - pi/2));
+wire("$y_-$", cylinder(R+ethick, tavg - pi/2, 0),
+    cylinder(R+ethick+dR, tavg - pi/2, 0),
+    label_transform*xy_transform, align=expi(tavg - pi/2));

diff --git a/media/src/asy/unfolding.asy b/media/src/asy/unfolding.asy
new file mode 100644 (file)
index 0000000..00e6623
--- /dev/null
+++ b/media/src/asy/unfolding.asy
@@ -0,0 +1,111 @@
+// Protein unfolding graphic
+
+//size(x=9cm,keepAspect=true);
+
+import base_afm; // for Cantilever, Substrate, ...
+import wiggle;   // for Wiggle
+
+struct ProteinChain {
+  // Generate and draw a mixed protein (2nd protein unfolded)
+  // starting at START (x,y)
+  // of folded length LEN, with NUM segments
+  // with the unfolded protein's dimensions given by UNFOLD_LEN and UNFOLD_WID
+  // (so the final length with be LEN - LEN/NUM + UNFOLD_LEN
+  pair start;
+  pair end;
+  real angle;
+  real len_u = 2cm;
+  real len_f = 0.5cm;
+  real rough_u = 0.4cm;
+  real rough_f = 0.6cm;
+  Wiggle prot_u;
+  Wiggle prot_f;
+  bool folded[];
+
+  void gen_prots() {
+    this.prot_u = Wiggle(end=(0,this.len_u), roughness=this.rough_u);
+    this.prot_f = Wiggle(end=(0,this.len_f), roughness=this.rough_f);
+  }
+
+  pair prot_start(int n) {
+    assert(n < this.folded.length);
+    pair start = this.start;
+    pair u = dir(this.angle);
+    for (int i; i < n; i+=1) {
+      if (this.folded[i] == true)
+        start += u*this.len_f;
+      else
+        start += u*this.len_u;
+    }
+    return start;
+  }
+
+  Wiggle prot(int n) {
+    assert(n < this.folded.length);
+    if (this.folded[n] == true)
+      return this.prot_f;
+    else
+      return this.prot_u;
+  }
+
+  guide guide() {
+    guide g;
+    guide p;
+    for (int i=0; i < this.folded.length; i+=1) {
+      p = shift(this.prot_start(i))*this.prot(i).guide();
+      g = g .. p;
+    }
+    return g;
+  }
+
+  void operator init(pair start=(0,0), real angle=90,
+                     bool folded[]={true,true,false,true}) {
+    this.start = start;
+    this.angle = angle;
+    this.folded = folded;
+    this.gen_prots();
+    guide g = this.guide();
+    this.end = point(g, length(g));
+  }
+}
+
+defaultpen(fontsize(size=10pt, lineskip=10pt));
+
+bool folded[] = {true,true,false,true};
+ProteinChain p = ProteinChain(folded=folded);
+draw(p.guide(), red);
+label("\vbox{\hbox{Folded}\hbox{protein}}", p.prot_start(1)+(1.4*p.rough_f, 0)/2, E);
+label("\vbox{\hbox{Unfolded}\hbox{protein}}", p.prot_start(2)+(1.3*p.rough_u, p.len_u)/2, E);
+
+
+Cantilever c = Cantilever();
+// position base so tip touches protein when bent
+c.set_tip_for_dx(12pt);
+c.align_tip(p.end);
+// unbend the tip and draw it in grey
+c.set_tip_for_dx(0);
+pair unbent_tip = c.tip;
+filldraw(c.tip_guide(), fillpen=grey, grey);
+draw(c.arm_guide(), grey);
+// rebend the tip and draw it in black
+c.set_tip_for_dx(12pt);
+filldraw(c.tip_guide(), fillpen=black);
+draw(c.arm_guide(), black);
+label("Cantilever", c.base-(0,16pt), SW);
+
+Substrate s = Substrate();
+s.draw(dir=S);
+
+real xt_x = -0.45*s.substrate_width;
+real xi_x = -0.27*s.substrate_width;
+real bar_extra = 6pt;
+distance("$x_t$", (xt_x, 0), (xt_x, unbent_tip.y));
+distance("$x_c$", (xi_x, c.tip.y), (xi_x, unbent_tip.y));
+distance("$x_{f1}$", (xi_x, p.prot_start(3).y), (xi_x, c.tip.y));
+distance("$x_u$", (xi_x, p.prot_start(2).y), (xi_x, p.prot_start(3).y));
+distance("$x_{f2}$", (xi_x, 0), (xi_x, p.prot_start(2).y));
+real y;
+y = unbent_tip.y;      draw((xt_x-bar_extra,y)--(xi_x+bar_extra,y));
+y = p.prot_start(2).y; draw((xi_x-bar_extra,y)--(xi_x+bar_extra,y));
+y = p.prot_start(3).y; draw((xi_x-bar_extra,y)--(xi_x+bar_extra,y));
+y = c.tip.y;           draw((xi_x-bar_extra,y)--(xi_x+bar_extra,y));

diff --git a/media/src/asy/wiggle.asy b/media/src/asy/wiggle.asy
new file mode 100644 (file)
index 0000000..8ea6546
--- /dev/null
+++ b/media/src/asy/wiggle.asy
@@ -0,0 +1,122 @@
+// Define Wiggle structure for drawing random wiggles.
+
+struct Wiggle {
+  // Generate a horizontal wiggly line, centered at CENTER (x,y)
+  // with a width WIDTH x
+  // and randomly distributed heights.
+  // The random points are unformly distributed within an envelope
+  // with the maximum possible deviation given by ROUGHNESS x
+
+  pair start;
+  pair end;
+  real roughness;
+  real tense;
+  int num;
+  int random_seed;
+  pair points[];
+
+  void generate(bool labels=false) {
+    int n = this.num;
+    pair step = (this.end-this.start) / (n-1);
+    pair perp = scale(this.roughness)*rotate(90)*unit(step);
+    real y, envelope;
+    srand(this.random_seed);
+    for (int i=0; i < n; i+=1) {
+      if (i == (n-1)/2 || i == 0 || i == n-1) {
+        y = 0.0;
+      } else {
+        real frac = i/n;
+        envelope = (frac*(1.0-frac)*4)**3;
+        y = (2*unitrand()-1.0) * envelope;
+      }
+      this.points.push(this.start + i*step + perp*y);
+      if (labels==true)
+        dot(format("%d", i), this.points[-1], S);
+    }
+  }
+
+  guide guide() {
+    guide g;
+    for (int i=0; i < this.points.length; i+=1) {
+      g = g .. tension this.tense .. this.points[i];
+    }
+    this.end = point(g, length(g));
+    return g;
+  }
+
+  void operator init(pair start=(0,0), pair end=(1cm,0), real roughness=1cm,
+                     real tense=1, int num=15, int random_seed=5) {
+    this.start = start;
+    this.end = end;
+    this.roughness = roughness;
+    this.tense = tense;
+    this.num = num;
+    this.random_seed = random_seed;
+    this.generate();
+  }
+}
+
+struct RandomWalk {
+  // Generate a random walk starting from START (x,y)
+  // with NUM steps, each of step-size DX,
+  // and randomly distributed step directions.
+
+  pair start;
+  pair end;
+  real dx;
+  int num;
+  real tense;
+  int random_seed;
+  pair points[];
+
+  void generate(bool labels=false) {
+    int n = this.num;
+    srand(this.random_seed);
+    pair p = this.start;
+    this.points.push(p);
+    if (labels==true)
+      dot("0", this.points[0], S);
+    for (int i=1; i <= this.num; i+=1) {
+      real theta = 360*unitrand();
+      p += rotate(theta)*(this.dx, 0);
+      this.points.push(p);
+      if (labels==true)
+        dot(format("%d", i), this.points[i], S);
+    }
+    this.end = p;
+  }
+
+  void align(real dir) {
+    real dtheta = dir - degrees(this.end - this.start);
+    for (int i=1; i < this.points.length; i+=1) {
+      this.points[i] = rotate(dtheta, this.start)*this.points[i];
+    }
+    this.end = this.points[this.num];
+  }
+
+  guide curved_guide() {
+    guide g;
+    for (int i=0; i < this.points.length; i+=1) {
+      g = g .. tension this.tense .. this.points[i];
+    }
+    return g;
+  }
+
+  guide straight_guide(interpolate join=operator ..) {
+    guide g;
+    for (int i=0; i < this.points.length; i+=1) {
+      g = g -- this.points[i];
+    }
+    return g;
+  }
+
+  void operator init(pair start=(0,0), real dx=3mm,
+                     real tense=1, int num=15, int random_seed=25) {
+    this.start = start;
+    this.dx = dx;
+    this.tense = tense;
+    this.num = num;
+    this.random_seed = random_seed;
+    this.generate();
+  }
+}

diff --git a/media/src/asy/wlc-model.asy b/media/src/asy/wlc-model.asy
new file mode 100644 (file)
index 0000000..e8e6034
--- /dev/null
+++ b/media/src/asy/wlc-model.asy
@@ -0,0 +1,7 @@
+import wiggle;  // for RandomWalk
+
+RandomWalk w = RandomWalk(dx=1cm);
+w.align(90);
+draw(w.curved_guide(), red);
+dot(w.start);
+dot(w.end);

diff --git a/media/src/asy/wtk_graph.asy b/media/src/asy/wtk_graph.asy
new file mode 100644 (file)
index 0000000..77e1395
--- /dev/null
+++ b/media/src/asy/wtk_graph.asy
@@ -0,0 +1,228 @@
+import graph;
+import palette;
+import stats;
+
+
+Label sLabel(string s, align align=NoAlign, int extra_spaces=0) {
+  string spaces = "";
+  int i;
+  for (i=0; i<extra_spaces; ++i) {
+    spaces += " ";
+  }
+  return Label(s+spaces, s+spaces, align=align);
+}
+
+void graphData(picture pic=currentpicture, real[] x, real[] y,
+               real xscale=1, real yscale=1, real dx=0, real dy=0, pen p=red,
+               path mpath=scale(0.8mm)*unitcircle,
+               markroutine markroutine=marknodes,
+               string t="Title",
+               bool dots=false) {
+  pen pline=p;
+  marker mk = nomarker;
+  if (dots == true) {
+    pline = invisible;
+    mk = marker(mpath, markroutine, p);
+  }
+  if (t != "Title") {
+    draw(pic=pic, graph(pic,xscale*(x+dx),yscale*(y+dy)), p=pline,
+         legend=sLabel(t,extra_spaces=1), marker=mk);
+  } else {
+    draw(pic=pic, graph(pic,xscale*(x+dx),yscale*(y+dy)), p=pline, marker=mk);
+  }
+}
+
+void graphFile(picture pic=currentpicture, string file="datafile",
+               int xcol=0, int ycol=1,
+               real xscale=1, real yscale=1, real dx=0, real dy=0, pen p=red,
+               path mpath=scale(0.8mm)*unitcircle,
+               markroutine markroutine=marknodes,
+               string t="Title",
+               bool dots=false) {
+  file fin = input(file).line();
+  real[][] a = fin.dimension(0,0);
+  a = transpose(a);
+  real[] x;
+  real[] y = a[ycol];
+  if (xcol >= 0)
+    x = a[xcol];
+  else
+    x = sequence(y.length);
+  graphData(pic=pic, x=x, y=y, xscale=xscale, yscale=yscale, dx=dx, dy=dy, p=p,
+            mpath=mpath, markroutine=markroutine, t=t, dots=dots);
+}
+
+void fitFile(picture pic=currentpicture, string file="fitparamfile",
+             int pcol=0, real f(real x, real[] params),
+             real xmin=realMin, real xmax=realMax,
+             real xscale=1, real yscale=1, pen p=red,
+             string t="Title") {
+  file fin=input(file).line();
+  real[][] a=fin.dimension(0,0);
+  a=transpose(a);
+  real[] params=a[pcol];
+  real fn(real x) {
+    return f(x / xscale, params) * yscale;
+  }
+  /* should be able to extract xmin and xmax from the figure...
+  if (xmin == realMin)
+    xmin = point(pic, W).x / xscale;
+  if (xmax == realMax)
+    xmax = point(pic, E).x / xscale;
+  */
+  if (t != "Title") {
+    draw(pic=pic, graph(pic, fn, a=xmin*xscale, b=xmax*xscale), p=p,
+         legend=sLabel(t,extra_spaces=1));
+  } else {
+    draw(pic=pic, graph(pic, fn, a=xmin*xscale, b=xmax*xscale), p=p);
+  }
+}
+
+void histFile(picture pic=currentpicture, string file="datafile",
+              int bin_col=0, int count_col=1,
+              real bin_scale=1, real count_scale=1, real low=-infinity,
+              pen fillpen=red, pen drawpen=nullpen, bool bars=false,
+              string t="Title") {
+  file fin = input(file).line();
+  real[][] a = fin.dimension(0,0);
+  a = transpose(a);
+  real[] bins = a[bin_col] * bin_scale;
+  real[] count = a[count_col] * count_scale;
+  /* Convert bin-center marks to bin-edge marks */
+  real bin_width = bins[1]-bins[0];
+  bins = bins - bin_width / 2;               /* shift centers to the left */
+  bins.push(bins[bins.length-1]+bin_width);  /* add terminal edge on right */
+  /* Normalize counts -> frequency */
+  real total = sum(count);
+  count = count / total;
+  if (t != "Title") {
+    histogram(pic=pic, bins=bins, count=count, low=low,
+              fillpen=fillpen, drawpen=drawpen, bars=bars,
+              legend=sLabel(t,extra_spaces=1));
+  } else {
+    histogram(pic=pic, bins=bins, count=count, low=low,
+              fillpen=fillpen, drawpen=drawpen, bars=bars);
+  }
+}
+
+real[] identity_zfn(real[] z) {
+  return z;
+}
+
+/* Return a sorted list of unique entries in an array x */
+real[] set(real[] x) {
+  int i=1;
+  x = sort(x);
+  while (i < x.length){
+    if (x[i] == x[i-1])
+      x.delete(i);
+    else
+      i += 1;
+  }
+  return x;
+}
+
+/* Convert x,y,z arrays to a z matrix */
+real[][] extract_matrix(real[] xs, real[] ys, real[] zs) {
+  int i, j, k;
+  real[] x_set = set(xs);
+  real[] y_set = set(ys);
+  real[] z_col = array(y_set.length, 0);
+  real[][] z_matrix = array(n=x_set.length, z_col);
+  //assert zs.length == x_set.length*y_set.length;
+  for (i=0; i<x_set.length; ++i) {
+    for (j=0; j<y_set.length; ++j) {
+      for (k=0; k<x_set.length*y_set.length; ++k) {
+        if (xs[k] == x_set[i] && ys[k] == y_set[j]) {
+          z_matrix[i][j] = zs[k];
+          break;
+        }
+      }
+    }
+  }
+  return z_matrix;
+}
+
+void graphMatrixFile(picture pic=currentpicture, string file="datafile",
+                     int xcol=0, int ycol=1, int zcol=2,
+                     real xscale=1, real yscale=1,
+                     real[] zfn(real[] z)=identity_zfn,
+                     pen[] p=BWRainbow(8192), Label x_label=null,
+                     Label y_label=null, Label palette_label=null,
+                     real palette_offset=6pt, real palette_width=12pt) {
+  file fin = input(file).line();
+  real[][] a = fin.dimension(0,0);
+  /* drop blank lines used to separate Gnuplot blocks. */
+  for (int i=a.length-1; i >= 0; --i)
+    if (a[i].length < 3)
+      a.delete(i);
+  a = transpose(a);
+  real[] xs = a[xcol];
+  real[] ys = a[ycol];
+  real[] zs = zfn(a[zcol]);
+  real[][] z = extract_matrix(xs, ys, zs);
+  pair initial = (xscale*min(xs), yscale*min(ys));
+  pair final = (xscale*max(xs), yscale*max(ys));
+  //bounds range = image(pic=pic, x=xscale*x, y=yscale*y, f=z, palette=p);
+  bounds range = image(pic=pic, z, initial, final, range=Automatic, palette=p);
+  // Add axes before palette or palette will end up in same box as the image
+  if (x_label != null)
+    xaxis(pic, x_label, BottomTop,LeftTicks,above=true);
+  if (y_label != null)
+    yaxis(pic, y_label, LeftRight,RightTicks,above=true);
+  transform graph_to_pic = pic.calculateTransform();
+  transform pic_to_graph = inverse(graph_to_pic);
+  pair p_SE_pic = graph_to_pic * (xscale*max(xs), yscale*min(ys));
+  pair p_initial_graph = pic_to_graph * (p_SE_pic + palette_offset*E);
+  pair p_NE_pic = graph_to_pic * (xscale*max(xs), yscale*max(ys));
+  pair p_final_graph = pic_to_graph * (p_NE_pic
+                                       + (palette_offset+palette_width)*E);
+  if (palette_label == null)
+    palette(pic, bounds=range, initial=p_initial_graph, final=p_final_graph,
+            axis=Right, palette=p);
+  else
+    palette(pic, L=palette_label, bounds=range, initial=p_initial_graph,
+            final=p_final_graph, axis=Right, palette=p);
+}
+
+string math(string contents) {
+  return "$" + contents + "$";
+}
+
+string Exp(string value) {
+  return "\cdot 10^{" + value + "}";
+}
+
+string units(string value, string units) {
+  return value+"\mbox{ "+units+"}";
+}
+
+pen phard=blue;
+pen pmed=green;
+pen psoft=red;
+
+path m1=(0,0)--(1,0)--(.5,1)--cycle;
+m1 = scale(3mm)*shift(-.5,-.33)*m1;
+path m8=scale(2mm)*shift(-.5,-.5)*unitsquare;
+path m30=scale(1.5mm)*unitcircle;
+path mdot=scale(0.2pt)*unitcircle;
+
+markroutine marksize(string file="datafile", pen p=red, path mpath=scale(0.8mm)*unitcircle, real size=1) {
+  return new void(picture pic=currentpicture, frame f, path g) {
+    /* frame f is the marker we setup in graphFile().  We can't scale
+       that directly though, since the drawn line thickness would change.
+       Instead, we give marksize() the same p and mpath that graphFile()
+       got, so it can scale the path and stroke it with the unscaled pen.
+     */
+    file fin=input(file).line();
+    real[][] a=fin.dimension(0,0);
+    a=transpose(a);
+    real[] s=a[3];
+    for (int i=0; i <= length(g); ++i) {
+      pair z = point(g, i);
+      frame f;
+      draw(f, scale(sqrt(s[i]/size))*mpath, p);
+      add(pic, f, z);
+    }
+  };
+}