The required teaching order completes generic jet mechanics before introducing laser/PFC sources. The physical causal order still starts with the laser. We first solve mechanics with a declared source, then derive that source from optical heating and phase thermodynamics.
必学顺序先完成通用射流力学，再引入激光／PFC 源。实际因果顺序仍从激光开始。先使用声明源求解力学，再从光学加热和相变热力学推导该源。
Chapter 章节 | Theoretical work completed in the chapter 章节完成的理论工作 | Inputs held explicit 明确保留的输入 |
|---|---|---|
Integrate Rayleigh energy/time, derive spatial pressure impulse and anisotropy; separate radial and jet speed. 积分 Rayleigh 能量／时间，推导空间压力冲量及不对称性；区分径向与射流速度。 | Supplied cavity/source, liquid properties and boundary geometry. 给定腔体／源、液体物性与边界几何。 | |
J02 · Moving interfaces, jet formation and geometric focusing | Close potential-flow interface motion; recover radial signs; solve flux-limited and pressure-limited focusing. 闭合势流界面运动；还原径向符号；求解限流量及限压力聚焦。 | Initial surfaces/potential, gas law or pressure history, all boundaries. 初始表面／势、气体规律或压力历程及全部边界。 |
Derive slender conservation, capillary spectrum and finite-flight growth; distinguish threshold from actual pinch. 推导细长守恒、毛细增长谱及有限飞行增长；区分阈值与真实夹断。 | Formed jet profile, finite mass/length, noise and continuing supply. 已形成射流轮廓、有限质量／长度、噪声及持续供给。 | |
Derive receiver force/impulse and acoustic impact; define pressure observation and finite conditional bounds. 推导接收体受力／冲量及声学冲击；定义压力观察及有限条件界限。 | Arrival field, receiver response, fixed area/time observation and energy budget. 到达场、接收体响应、固定面积／时间观察与能量预算。 |
What “close the chain” means
“完成理论链”的含义
Each stage states its governing equations, closure laws, initial/boundary data, conserved quantities and output definitions. The analytic controls are solved and numerically checked. State and budgets are passed to the next stage. A specified nonlinear free-surface geometry still requires a spatial solution; a table of models is not an experimental verification or a universal closed-form maximum.
每阶段明确支配方程、闭合规律、初始／边界数据、守恒量及输出定义。解析对照已求解并数值核验，状态与预算传到下一阶段。指定非线性自由表面几何仍需空间求解；模型表格不是实验验证，也不是通用闭式最高值。
The substantial arrangement follows the earlier pressure-limit chapter: start with a soluble control, derive the refinement, calculate its implications, identify its transition, and end with a multi-part problem. Original chapters and accepted solutions are retained. Every displayed formula is followed by its own physical variable map, and every reference answer begins with the original formulas.
完整安排参考早期压力极限章节：从可解对照开始，推导改进，计算其含义，确定阶段转换，最后以多部分综合题收尾。原章节及已接受解答保留。每个显示公式后都有相应物理变量图，每个参考答案先列原始公式。
After J04: specialize the supplied source and compare architectures
J04 之后：特化给定源并比较结构
L01 becomes the bridge to optical deposition, heat flow and finite PFC phase inventory. The subsequent project route keeps PFC in a finite water-droplet stamp, the primary PFC-containing liquid layer below film/PVC, and PFC embedded in hydrogel. Both direct liquid-to-film and intact-PVC-mediated loading remain. Compare mechanisms and both output envelopes without forced early selection.
L01 成为连接光学沉积、热流与有限 PFC 相存量的桥梁。后续项目路线保留有限水滴印章中的 PFC、主要薄膜／PVC 下含 PFC 液层及水凝胶嵌入 PFC。液体直接作用于薄膜及完整 PVC 介导载荷均保留。比较机制及两类输出范围，不强制提前选一个分支。
Harmonic acoustic forcing is not a prerequisite detour. Linear capillary perturbation in J03 and the arrest wave in J04 serve jet survival and impact prediction directly. Each chapter asks one brief synthesis after a comprehensive worked calculation; new chapters remain pending until understanding is demonstrated.
简谐声学驱动不是必修绕行。J03 的线性毛细扰动和 J04 的制动波直接服务于射流存续与冲击预测。每章在综合计算后要求一次简短综合回答；理解得到展示之前，新章保持待完成。
Primary sources and reproducible calculations
主要来源与可复现计算
Radial collapse: Brennen. Pressure impulse: Cooker & Peregrine. Internal-jet scaling and interface computation: Supponen et al.. Focused exit example: Tagawa et al.. Free-thread conservation: Eggers & Dupont. Each result stays with its own geometry and observer definition.
径向塌缩：Brennen。压力冲量：Cooker 与 Peregrine。内部射流尺度律及界面计算：Supponen 等。聚焦出口实例：Tagawa 等。自由液丝守恒：Eggers 与 Dupont。每项结果均保持其自身几何与观察定义。
Equation and physical-variable manifest · Executable benchmark verification · Required sequence. All rendering resources are local in the forwardable course folder; primary citation links are optional reading.