forked from EduCraft/curriculum-project-hub
sjfhsjfh
c73a2c903f
Real-content fixture for the end-to-end pipeline. TH-141 (39 parts: 22 segment, 15 lemma, 2 example) migrated from the prototype's typst `#let parts` manifest to ADR-0008: declarative manifest.toml (project+info+ordered parts+targets) + per-element element.toml (kind + scalars; examples carry `source`). Content .typ files copied byte-identical (no math corruption); per-element main.typ + meta.toml dropped (wiring is now generated). Part order matches source exactly; 5 lemmas have no proof.typ (optional); no cross-file imports / paralearn refs / figs. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
4 lines
511 B
Typst
4 lines
511 B
Typst
= 开场对照：弹性膜与液面
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$sigma$ 与机械张力同名，却有一个显著不同的性质：肥皂膜的 $sigma$ 与膜的面积无关，而弹性膜的张力随拉伸单调增大。本章从这一对照入手，目的是定位液面张力的微观来源——液面 $sigma$ 来自体相向表面补充新分子，而非把已有分子拉远。本节先把弹性膜的张力机制写一遍，再把液面的拉伸过程写一遍，两者对照得到液面 $sigma$ 与面积无关的物理原因。
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