add jensens-inequality.typ converted from jensens-inequality.tex

add ergodic.typ converted from ergodic.tex

change readme title from gear icon with TikZ text to "Scientific Diagrams"
update-readme-table.py now errors on typst/latex code files without a corresponding YAML metadata file
rename shell.tex to momentum-shell.tex and add momentum-shell.typ typst translation
rename hea.tex to high-entropy-alloy.tex
rename sign-plane.tex to complex-sign-plane.tex
move "Open in overleaf" link into CodeBlock.svelte buttons for LaTeX code
fix app.css overriding svelte-multiselect remove-option button styles

Author: janosh

assets/aviary/aviary.yml

@@ -5,3 +5,4 @@ tags:
   - materials informatics
 description: |
   Aviary logo: a repo of machine learning models for representation learning in materials discovery from stoichiometry and symmetries via graph convolutions. For <https://github.com/CompRhys/aviary>.
+hide: true

assets/sign-plane/sign-plane-hd.png assets/complex-sign-plane/complex-sign-plane-hd.png

@@ -1,4 +1,4 @@
-title: Sign Plane
+title: Complex Sign Plane
 tags:
   - physics
   - quantum field theory

assets/sign-plane/sign-plane.pdf assets/complex-sign-plane/complex-sign-plane.pdf

@@ -0,0 +1,113 @@
+#import "@preview/cetz:0.3.1": canvas, draw
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#canvas({
+  import draw: content, line, rect, scale
+
+  let orange-fill = rgb(100%, 80%, 70%)
+  let red-fill = rgb(100%, 80%, 80%)
+  let gray-fill = rgb(90%, 90%, 90%)
+  let blue-fill = rgb(80%, 80%, 100%)
+
+  // Helper function for rounded rectangles with text
+  let node(pos, text, fill: none, name: none) = {
+    rect(
+      (pos.at(0) - 1.2cm, pos.at(1) - 0.8cm),
+      (pos.at(0) + 1.2cm, pos.at(1) + 0.8cm),
+      fill: fill,
+      stroke: black + 1pt,
+      radius: 2mm,
+      name: name,
+    )
+    content(
+      pos,
+      scale(300%, text),
+      anchor: "center",
+    )
+  }
+
+  // Helper for comment nodes
+  let comment(pos, text, name: none) = {
+    content(
+      pos,
+      text,
+      anchor: "center",
+      name: name,
+    )
+  }
+
+  // Main equation components
+  content((0cm, 0cm), scale(400%, $($), anchor: "center")
+  node((4cm, 0cm), $-frac(h^2, 2m) nabla^2_bold(r)$, fill: orange-fill, name: "kinetic")
+  content((6.5cm, 0cm), $+$, anchor: "center", scale: 300%)
+  node((9cm, 0cm), $v_"ext"(bold(r))$, fill: red-fill, name: "external")
+  content((11.5cm, 0cm), $+$, anchor: "center", scale: 300%)
+  node((14cm, 0cm), $v_H(bold(r))$, fill: red-fill, name: "hartree")
+  content((16.5cm, 0cm), $+$, anchor: "center", scale: 300%)
+  node((19cm, 0cm), $v_"xc"$, fill: red-fill, name: "xc")
+  content((21cm, 0cm), $)$, anchor: "center", scale: 400%)
+  node((24cm, 0cm), $phi_i(bold(r))$, fill: gray-fill, name: "phi1")
+  content((26.5cm, 0cm), $=$, anchor: "center", scale: 300%)
+  node((29cm, 0cm), $E_i$, fill: blue-fill, name: "energy")
+  node((32cm, 0cm), $phi_i(bold(r))$, fill: gray-fill, name: "phi2")
+
+  // Comments with line breaks
+  comment(
+    (4cm, 4cm),
+    [#set align(center)
+      #text(24pt)[non-rel. Schrödinger equation\
+        or relativistic Dirac equation]],
+    name: "kinetic-comment",
+  )
+  comment(
+    (9cm, -4cm),
+    [#set align(center)
+      #text(24pt)[pseudopotential\
+        (ultrasoft/PAW/norm-conserving)\
+        or all-electron]],
+    name: "external-comment",
+  )
+  comment(
+    (14cm, -4cm),
+    [#set align(center)
+      #text(24pt)[Hartree potential\
+        from solving Poisson eq.\
+        or integrating charge density]],
+    name: "hartree-comment",
+  )
+  comment(
+    (19cm, 4cm),
+    [#set align(center)
+      #text(24pt)[LDA or GGA\
+        or hybrids]],
+    name: "xc-comment",
+  )
+  comment(
+    (28cm, 4cm),
+    [#set align(center)
+      #text(24pt)[physical orbitals or not\
+        mesh density and basis set]],
+    name: "phi-comment",
+  )
+  comment(
+    (29cm, -4cm),
+    [#set align(center)
+      #text(24pt)[view EVs as mere Lagrange\
+        multipliers or band structure approx]],
+    name: "energy-comment",
+  )
+
+  // Arrows
+  let arrow-style = (
+    mark: (end: "stealth"),
+    stroke: 2pt,
+  )
+  line("kinetic-comment", "kinetic.north", ..arrow-style)
+  line("external-comment", "external.south", ..arrow-style)
+  line("hartree-comment", "hartree.south", ..arrow-style)
+  line("xc-comment", "xc.north", ..arrow-style)
+  line("phi-comment", "phi1.north", ..arrow-style)
+  line("phi-comment", "phi2.north", ..arrow-style)
+  line("energy-comment", "energy.south", ..arrow-style)
+})

assets/sign-plane/sign-plane.png assets/complex-sign-plane/complex-sign-plane.png

@@ -1,7 +1,8 @@
-title: Kohn-Sham DFT User Choices
+title: DFT Choices
+description: A diagram illustrating the various choices and components in density functional theory (DFT) calculations, including kinetic energy, external potential, Hartree potential, and exchange-correlation terms.
 tags:
   - physics
-  - quantum-mechanics
-  - density-functional-theory
-  - Kohn-Sham
-description: Visualization of the many choices involved in a Kohn-Sham calculation. It can be non-relativistic based on the classical Schrödinger equation or fully relativistic based on the Dirac equation which includes spin-orbit coupling. The near-core electrons can be modeled explicitly in an all-electron calculation or, much more commonly, incorporated along with the nucleus into an effective pseudo-potential. The Hartree energy can be obtained by integrating the charge density or by solving the Poisson equation. The exchange-correlation potential can be treated with a huge library of density functionals, most commonly LDA and GGA. The wave functions can be computed on a numerical mesh and expanded in one of many possible basis sets, e.g. plane waves, APW, or PAW. Inspired by fig. 3 in [arxiv:cond-mat/0211443](https://arxiv.org/abs/cond-mat/0211443).
+  - quantum mechanics
+  - dft
+  - equations
+  - schematic

assets/sign-plane/sign-plane.svg assets/complex-sign-plane/complex-sign-plane.svg

@@ -0,0 +1,73 @@
+#import "@preview/cetz:0.3.1": canvas, draw
+
+#set page(width: auto, height: auto, margin: 3pt)
+
+#canvas({
+  import draw: line, content, circle, rect, hobby
+
+  let rx = 5
+  let ry = 3
+  let arrow-style = (mark: (end: "stealth", fill: black), stroke: 1pt)
+
+  // Axes
+  line((-rx - 0.5, 0), (rx + 0.5, 0), ..arrow-style)
+  content((rx + 0.5, 0), $q_1$, anchor: "west", padding: 2pt)
+
+  line((0, -ry - 0.5), (0, ry + 0.5), ..arrow-style)
+  content((0, ry + 0.5), $q_2$, anchor: "south", padding: 2pt)
+
+  // Ellipse
+  circle(
+    (0, 0),
+    radius: (rx, ry),
+    stroke: blue,
+    fill: rgb(0%, 0%, 100%, 5%),
+    name: "ellipse",
+  )
+
+  // Labels for radii
+  content((rx + .2, 1), $sqrt(2E \/ m)$, anchor: "south-west", padding: 1pt, name: "r1")
+  line((rx, 0), "r1.south", stroke: 0.2pt)
+  content((0.5, ry + .5), $sqrt(2E \/ k)$, anchor: "south-west", padding: 1pt, name: "r2")
+  line((0, ry), "r2.south-west", stroke: 0.2pt)
+
+  // Label P
+  content((rx - 0.6, 0.2), text(fill: blue)[$P$])
+
+  let rect-scale = calc.sqrt(2) / 2 // scale rectangle so corners touch ellipse
+  rect(
+    (-rx * rect-scale, -ry * rect-scale),
+    (rx * rect-scale, ry * rect-scale),
+    stroke: rgb("#ffa500"),
+    fill: rgb(100%, 65%, 0%, 10%),
+    name: "rect",
+  )
+  content((-rx / 4, ry / 2), text(fill: rgb("#ffa500"))[$R$ for $omega in.not QQ$])
+
+  // Trajectory
+  hobby(
+    (-rx * rect-scale, ry * rect-scale),
+    (-1.1, -ry * rect-scale + 0.4),
+    (-.5, -ry * rect-scale + 0.1),
+    (.1, -ry * rect-scale + 0.4),
+    (rx * rect-scale, ry * rect-scale),
+    omega: 0,
+    stroke: red,
+  )
+  hobby(
+    (-rx * rect-scale, ry * rect-scale),
+    (-.1, -ry * rect-scale + 0.4),
+    (.5, -ry * rect-scale + 0.1),
+    (1.1, -ry * rect-scale + 0.45),
+    (rx * rect-scale, ry * rect-scale),
+    omega: 0,
+    stroke: red,
+  )
+  content(
+    (2.5, -1.3),
+    align(
+      center,
+      text(fill: red)[$R$ for\ $omega = 2 in QQ$],
+    ),
+  )
+})

assets/sign-plane/sign-plane.tex assets/complex-sign-plane/complex-sign-plane.tex

@@ -0,0 +1,42 @@
+#import "@preview/cetz:0.3.1": canvas, draw
+#import "@preview/cetz-plot:0.1.0": plot
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#canvas({
+  let mark = (end: "stealth", fill: black, scale: 0.7)
+  draw.set-style(
+    axes: (
+      y: (label: (anchor: "north-west", offset: -0.2), mark: mark),
+      x: (label: (anchor: "south-east", offset: -0.25), mark: mark),
+    ),
+  )
+
+  plot.plot(
+    size: (8, 6),
+    x-label: $x$,
+    y-label: $log x$,
+    y-min: -1,
+    x-tick-step: none,
+    y-tick-step: none,
+    axis-style: "school-book",
+    {
+      // Main logarithmic curve
+      plot.add(
+        style: (stroke: rgb(0%, 0%, 80%) + 1.5pt),
+        domain: (11, 150),
+        samples: 150,
+        x => calc.ln(x - 10) - 2,
+      )
+
+      // Dashed line
+      plot.add(
+        style: (
+          stroke: (paint: orange, thickness: 1.5pt, dash: "dashed"),
+        ),
+        domain: (8, 120),
+        x => 0.2 + (3 - 0.2) * (x - 8) / (120 - 8),
+      )
+    },
+  )
+})

assets/sign-plane/sign-plane.typ assets/complex-sign-plane/complex-sign-plane.typ

@@ -0,0 +1,36 @@
+#import "@preview/cetz:0.3.1": canvas, draw
+
+#set page(width: auto, height: auto, margin: 3pt)
+
+#canvas({
+  import draw: line, content, circle
+
+  let rx = 4
+  let ry = 2.2
+  let arrow-style = (mark: (end: "stealth", fill: black), stroke: 1pt)
+
+  // Axes
+  line((-rx - 0.5, 0), (rx + 0.5, 0), ..arrow-style)
+  content((rx + 0.5, 0), $q_1$, anchor: "west", padding: 2pt)
+
+  line((0, -ry - 0.5), (0, ry + 0.5), ..arrow-style)
+  content((0, ry + 0.5), $q_2$, anchor: "south", padding: 2pt)
+
+  // Ellipse
+  circle(
+    (0, 0),
+    radius: (rx, ry),
+    stroke: blue,
+    fill: rgb(0%, 0%, 100%, 5%),
+    name: "ellipse",
+  )
+
+  // Labels for radii
+  content((rx + .2, 1), $sqrt(2E \/ m)$, anchor: "south-west", padding: 1pt, name: "r1")
+  line((rx, 0), "r1.south", stroke: 0.2pt)
+  content((0.5, ry + .5), $sqrt(2E \/ k)$, anchor: "south-west", padding: 1pt, name: "r2")
+  line((0, ry), "r2.south-west", stroke: 0.2pt)
+
+  // Label P
+  content((3, 1), text(fill: blue)[$P$])
+})

assets/sign-plane/sign-plane.yml assets/complex-sign-plane/complex-sign-plane.yml

@@ -0,0 +1,5 @@
+title: Momentum Shell
+tags:
+  - physics
+  - statistical mechanics
+description: See also https://diagrams.janosh.dev/ergodic.

assets/dft-choices/dft-choices.typ

@@ -3,3 +3,4 @@ tags:
   - info-graphics
 description: |
   Useless Gantt chart for my Scientific Computing MPhil project at Cambridge University titled "Data-Driven Risk-Conscious Thermoelectric Materials Discovery". See <https://github.com/janosh/thermo>.
+hide: true