add convex-hull-of-stability.typ converted from convex-hull-of-stabil…

…ity.tex

add skip-connection.typ converted from skip-connection.tex

assets/convex-hull-of-stability/convex-hull-of-stability.typ

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+#import "@preview/cetz:0.3.1": canvas, draw, vector
+#import draw: line, content, rect, circle, intersections
+
+#set page(width: auto, height: auto, margin: 3pt)
+
+#canvas({
+  // Diagram dimensions and styles
+  let width = 12
+  let height = 8
+  let point_radius = 0.15
+  let line_thickness = 1.5pt
+  let arrow_style = (mark: (end: "stealth"), stroke: black + line_thickness, fill: black)
+  let hull_style = (stroke: blue.darken(20%) + 2.5pt)
+  let hyp_hull_style = (stroke: (paint: gray, thickness: line_thickness, dash: "dashed"))
+
+  // Draw axes first to establish named positions
+  line((0, 0), (0, height), ..arrow_style, name: "y-axis-left")
+  line((0, 0), (width, 0), ..arrow_style, name: "x-axis")
+  line((width, 0), (width, height), ..arrow_style, name: "y-axis-right")
+
+  // Draw stable points
+  let stable_point(pos, label, anchor: "north", padding: none, ..rest) = {
+    circle(pos, radius: point_radius, fill: blue.darken(20%), ..rest)
+    content(pos, label, anchor: anchor, padding: padding)
+  }
+
+  stable_point((0, height - 1), "A", anchor: "west", padding: (left: 10pt), name: "a")
+  stable_point((width / 2, 2), "AX", anchor: "north", padding: (top: 10pt), name: "ax")
+  stable_point((width * 5 / 7, 1.5), $A_2X_5$, anchor: "north", padding: (top: 10pt), name: "a2x5")
+  stable_point((width, height - 1.5), "X", anchor: "east", padding: (right: 10pt), name: "x")
+
+  // Draw unstable points
+  let unstable_point(pos, label, ..rest) = {
+    let (x, y) = pos
+    rect((x, y - 0.15), (x + 0.3, y + 0.15), fill: red, stroke: .5pt, ..rest)
+    content(pos, label, anchor: "south", padding: (bottom: 8pt))
+  }
+
+  unstable_point((width / 3, height - 1.5), $A_2X$, name: "a2x")
+  unstable_point((width * 7 / 9, 3.7), $A_2X_7$, name: "a2x7")
+
+  // Draw convex hull
+  line("a", "ax", ..hull_style, name: "hull-a-ax")
+  line("ax", "a2x5", ..hull_style, name: "hull-ax-a2x5")
+  line("a2x5", "x", ..hull_style, name: "hull-a2x5-x")
+  content(
+    (rel: (-1.8, -.8), to: "ax"),
+    text(fill: blue.darken(20%), size: 12pt)[convex hull\ of stability],
+    frame: "rect",
+    stroke: none,
+    padding: (left: 5pt),
+    fill: white,
+    name: "hull-label",
+  )
+  line(
+    "hull-label.north",
+    "hull-a-ax.90%",
+    stroke: (paint: blue.darken(20%), thickness: .5pt),
+    padding: 1pt,
+    name: "hull-label-line",
+  )
+
+  // Draw hypothetical hull
+  line("ax", "a2x7", ..hyp_hull_style, name: "hyp-hull-ax-a2x7")
+  line("a2x7", "x", ..hyp_hull_style, name: "hyp-hull-a2x7-x")
+  content(
+    (rel: (0, 0.3), to: "hyp-hull-a2x7-x.mid"),
+    text(fill: gray, size: 13pt)[hypothetical hull for\ evaluating $A_2X_5$],
+    anchor: "east",
+  )
+
+  // Draw decomposition energy arrows
+  // First draw invisible lines to find intersections
+  line(
+    (rel: (0, 3), to: "a2x"),
+    (rel: (0, -3), to: "a2x"),
+    stroke: none,
+    name: "a2x-vertical",
+  )
+  intersections("a2x-isect", "a2x-vertical", "hull-a-ax", "hull-ax-a2x5")
+
+  // Draw arrow between intersection points
+  line(
+    "a2x-isect.0",
+    "a2x",
+    mark: (end: ">", fill: red),
+    stroke: red + line_thickness,
+    name: "arrow-a2x",
+  )
+  content(
+    (rel: (-0.5, 0), to: "arrow-a2x.60%"),
+    text(fill: red)[$Delta E_d$],
+  )
+  content(
+    (rel: (.2, 0), to: "arrow-a2x.30%"),
+    text(fill: red, size: 12pt)[A + AX → A₂X],
+    frame: "rect",
+    padding: (1pt, 3pt),
+    stroke: red + .3pt,
+    name: "box1",
+    anchor: "west",
+    fill: red.lighten(90%),
+  )
+
+  // Second arrow - find intersections first
+  line(
+    (rel: (0, 3), to: "a2x5"),
+    (rel: (0, -3), to: "a2x5"),
+    stroke: none,
+    name: "a2x5-vertical",
+  )
+  intersections("a2x5-isect", "a2x5-vertical", "hyp-hull-ax-a2x7", "hyp-hull-a2x7-x")
+
+  // Draw arrow between intersection points
+  line(
+    "a2x5-isect.0",
+    "a2x5",
+    mark: (end: ">", fill: rgb("#4d8000")),
+    stroke: rgb("#4d8000") + line_thickness,
+    name: "arrow-a2x5",
+  )
+  content(
+    "arrow-a2x5.mid",
+    text(fill: rgb("#4d8000"))[$Delta E_d$],
+    anchor: "east",
+    padding: (right: 3pt),
+  )
+  content(
+    (rel: (0.1, 0), to: "arrow-a2x5.mid"),
+    text(fill: rgb("#4d8000"), size: 10pt)[4/5 AX + 3/5 A₂X₇ → A₂X₅],
+    frame: "rect",
+    padding: (1pt, 3pt),
+    stroke: rgb("#4d8000") + .3pt,
+    name: "box2-label",
+    anchor: "west",
+    fill: rgb("#4d8000").lighten(90%),
+  )
+
+  // Draw chemical potential range
+  line(
+    (0, height - 4.5),
+    "ax",
+    stroke: (paint: orange, thickness: line_thickness, dash: "dashed"),
+    name: "mu-line",
+  )
+  content(
+    (rel: (2.4, 0), to: "mu-line.start"),
+    rotate(14deg)[#text(fill: orange, size: 13pt)[$μ_A$ range\ where AX is stable]],
+  )
+
+  // Draw orange double arrow
+  line(
+    "hull-a-ax.2%",
+    "mu-line.4%",
+    mark: (start: ">", end: ">", fill: orange),
+    stroke: orange + line_thickness,
+    name: "mu-arrow",
+  )
+
+  // Draw legend
+  circle((0.5, 1), radius: point_radius, fill: blue.darken(20%), name: "legend-stable")
+  content(
+    "legend-stable.east",
+    "stable",
+    anchor: "west",
+    padding: (left: 5pt),
+  )
+  rect(
+    (rel: (-0.15, -0.6), to: "legend-stable"),
+    (rel: (0.15, -0.3), to: "legend-stable"),
+    fill: red,
+    stroke: red,
+    name: "legend-unstable",
+  )
+  content(
+    "legend-unstable.east",
+    "unstable",
+    anchor: "west",
+    padding: (left: 5pt),
+  )
+
+  // Add axis labels
+  content(
+    (rel: (-0.5, 0), to: "y-axis-left.mid"),
+    [#rotate(-90deg)[$Delta E_f$ (energy/atom)]],
+  )
+  content((width / 2, -0.5), $x "in" A_(1-x)X_x$)
+})

assets/skip-connection/skip-connection.typ

@@ -0,0 +1,106 @@
+#import "@preview/cetz:0.3.1": canvas, draw
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#canvas({
+  import draw: line, content, rect, hobby
+
+  let node-sep = 2.5 // Horizontal separation between nodes
+  let arrow-style = (mark: (end: "stealth", fill: black, scale: 0.5), stroke: black)
+
+
+  // Draw main nodes
+  content(
+    (0, 0),
+    [layer 1],
+    fill: rgb("#ffd699"),
+    name: "l1",
+    frame: "rect",
+    padding: (3pt, 6pt),
+    stroke: none,
+  ) // orange!50
+  content(
+    (node-sep, 0),
+    $a(arrow(x))$,
+    name: "act1",
+    frame: "rect",
+    padding: (0, 3pt),
+    stroke: none,
+  )
+  content((rel: (0, -0.3), to: "act1.south"), "activation")
+  content(
+    (2 * node-sep, 0),
+    [layer 2],
+    fill: rgb("#7dc3c3"),
+    name: "l2",
+    frame: "rect",
+    padding: (3pt, 6pt),
+    stroke: none,
+  ) // teal!50
+  content(
+    (3 * node-sep, 0),
+    text(size: 1.8em)[$plus.circle$],
+    name: "add",
+  )
+  content((rel: (0, -0.3), to: "add.south"), "add")
+  content(
+    (3.75 * node-sep, 0),
+    $a(arrow(x))$,
+    name: "act2",
+    frame: "rect",
+    padding: (0, 3pt),
+    stroke: none,
+  )
+  content((rel: (0, -0.3), to: "act2.south"), "activation")
+
+  // Draw main flow arrows
+  line("l1", "act1", ..arrow-style)
+  line("act1", "l2", ..arrow-style)
+  line("l2", "add.west", ..arrow-style)
+  line("add.east", "act2", ..arrow-style)
+
+  // Draw input arrow
+  line(
+    (rel: (-2, 0), to: "l1"),
+    "l1",
+    stroke: black,
+    name: "input",
+    mark: (end: "stealth", fill: black, scale: 0.5),
+  )
+  content((rel: (0, -0.2), to: "input.10%"), $arrow(x)$)
+
+  // Draw skip connection using hobby curve
+  hobby(
+    (rel: (-1.5, 0), to: "l1"),
+    (rel: (0, 2.2), to: "act1"),
+    "add.north",
+    close: false,
+    tension: 0.8,
+    ..arrow-style,
+    name: "skip",
+  )
+  content((rel: (0, 0.3), to: "skip.mid"), $arrow(x)$)
+  content(
+    (rel: (0, -0.3), to: "skip.mid"),
+    align(center, text(size: 0.8em)[skip connection\ (identity)]),
+    anchor: "north",
+  )
+
+  // Draw F(x) curly brace
+  content(
+    (rel: (0, -1.2), to: "act1"),
+    [#math.underbrace(box(width: 17em), text(size: 1.4em)[$cal(F)(arrow(x))$])],
+    name: "fx-brace",
+  )
+
+  // Add F(x) + x label
+  content(
+    (rel: (0.8, 0.8), to: "add"),
+    $cal(F)(arrow(x)) + arrow(x)$,
+    name: "fx-label",
+    frame: "rect",
+    stroke: none,
+    padding: 1pt,
+  )
+  line("fx-label.south", "add.north-east", stroke: .2pt, name: "fx-arrow")
+})