Files
curriculum-project-hub/examples/TH-141/收束/segments/算不准背后的真实物理/textbook.typ
T
hongjr03 9927d38c18 feat(cph): implement nested outline manifest and batch/combined export
ADR-0029 — nested outline manifest, supersedes ADR-0008's flat [[parts]]:
- cph-model: recursive loader over manifest.toml containers / element.toml
  leaves; Lesson.parts (pure elements, DFS order) + Lesson.outline (elements
  interleaved with section headings at their DFS-open position); rejects
  ambiguous/incomplete folders and root-vs-container table misplacement
- cph-diag: new DiagCode::ManifestMalformed for carrier-document structure
  errors (discharges an existing TODO)
- cph-typst: augmented manifest now serializes the outline (element/section
  entries) instead of a flat parts array
- render/lib.typ: render-lesson renders section headings at their depth
- examples/TH-141 migrated to 5 nested section containers + 3 root segments,
  byte-identical element order; smoke-verified via cph check/build + pdftotext

ADR-0030 — batch & combined export, extends ADR-0009/0011:
- cph build with no --target batches every declared target (repeatable
  --target for an explicit subset); any target failure => non-zero exit,
  per-target ledger, independent per-target execution
- cph-model: bundle.toml loader (directory + [info]/[targets.*]/ordered
  lessons with per-lesson target overrides)
- cph-typst: augmented bundle manifest (path-prefixed member outlines),
  Engine::{compile_check_bundle,build_bundle_pdf}
- render/lib.typ: render-bundle assembles member lessons under per-lesson
  headings, depth-shifts their own section headings, resets example/lemma
  counters at each lesson boundary by default
- cph-cli: `cph bundle <path> --target <name>` subcommand, same batching
  contract as `cph build`
- new bundle fixtures/tests (cph-model unit + cph-typst through-template PDF
  compile), smoke-verified via a real 2-lesson merged PDF

Verification: cargo fmt/clippy/test clean across the workspace (68 tests);
real cph check/build/bundle runs against TH-141 and a bundle fixture, PDF
content inspected via pdftotext.
2026-08-05 18:34:05 +08:00

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Typst

@模型对照表 中的偏差并非来源不明,每一条都可追溯到一项物理简化。
分子作用力的各向异性。缺键模型把每对分子之间的键能简化为同一个 $epsilon$,但真实的分子间相互作用具有方向性,水的氢键尤甚。各向异性对应的研究方向是液晶与晶体表面物理。
参数 $zeta$ 的有效性。Stefan $zeta = 1\/2$ 只是为得到不依赖晶格的最简表达;FCC (111) 给出 $zeta = 3\/4$ 是基于严格晶格的几何计数。真实液体并没有严格晶格,$zeta$ 应当被视为有效参数。如何从液体的局部结构出发反推 $zeta$ 是液体统计物理的一个分支。
氢键带来的极性贡献。缺键模型把所有相互作用都归为单一键能,忽略了水分子之间的氢键贡献。@GG公式 在水/聚合物体系下与实验偏差较大就是这一简化的具体后果,Fowkes 分解就是针对这一偏差的修正路径。
表面层并非严格二维。我们建模时把表面分子当作一个零厚度的层,但真实液体的表面层有 nm 量级的厚度,密度随深度连续变化。这条偏差对应的研究方向是液气界面的密度剖面与梯度理论。
逐条看下来,每一条偏差都对应一个仍在活跃的研究方向。本章的微观模型给出"理论从分子到宏观浸润如何一步步推出来"的完整链条,但同时也指明了链条上每一段还能被怎么继续精细化。这才是建模在物理学里的常态。