forked from EduCraft/curriculum-project-hub
hongjr03
9927d38c18
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.
14 lines
654 B
Typst
14 lines
654 B
Typst
设下半空间体相分子的数密度为 $n_v = 1 \/ d^3$。固定一个表面分子作为参考分子，对其与下半空间所有体相分子的相互作用求和。由对称性，相对参考分子距离 $r$ 在下半空间内的体积元为 $dif V = 2 pi r^2 dif r$。下限取 $r = d$，上限取 $infinity$：
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$ Delta U = 2 pi n_v integral_d^infinity u(r) thin r^2 dif r . $
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代入 $u(r)$，用 $integral r^2 dot r^(-n) dif r = r^(3 - n) \/ (3 - n)$ 化简，得
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$ Delta U tilde.op epsilon . $
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把 $Delta U$ 乘以单位面积分子数 $n_s tilde.op 1 \/ d^2$，由 @骨架公式 即得
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$ sigma tilde.op epsilon / d^2 , $
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即 @LJ标度。
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