From 3073463598fcd060bad7b16f79305eeb85810e27 Mon Sep 17 00:00:00 2001 From: Zhongwei Li Date: Sun, 30 Nov 2025 08:35:28 +0800 Subject: [PATCH] Initial commit --- .claude-plugin/plugin.json | 12 ++ README.md | 3 + plugin.lock.json | 81 ++++++++++++ skills/hydro-forecast/SKILL.md | 125 ++++++++++++++++++ skills/hydro-forecast/examples.jl | 22 ++++ skills/julia-hydrotools/SKILL.md | 32 +++++ skills/julia-hydrotools/examples.jl | 22 ++++ skills/julia-numerical/SKILL.md | 120 ++++++++++++++++++ skills/julia-numerical/examples.jl | 155 +++++++++++++++++++++++ skills/julia-numerical/test_basic.jl | 34 +++++ skills/typst-physica/SKILL.md | 53 ++++++++ skills/typst-physica/example_physica.typ | 40 ++++++ skills/typst-physica/examples.typ | 36 ++++++ 13 files changed, 735 insertions(+) create mode 100644 .claude-plugin/plugin.json create mode 100644 README.md create mode 100644 plugin.lock.json create mode 100644 skills/hydro-forecast/SKILL.md create mode 100644 skills/hydro-forecast/examples.jl create mode 100644 skills/julia-hydrotools/SKILL.md create mode 100644 skills/julia-hydrotools/examples.jl create mode 100644 skills/julia-numerical/SKILL.md create mode 100644 skills/julia-numerical/examples.jl create mode 100644 skills/julia-numerical/test_basic.jl create mode 100644 skills/typst-physica/SKILL.md create mode 100644 skills/typst-physica/example_physica.typ create mode 100644 skills/typst-physica/examples.typ diff --git a/.claude-plugin/plugin.json b/.claude-plugin/plugin.json new file mode 100644 index 0000000..01c0b63 --- /dev/null +++ b/.claude-plugin/plugin.json @@ -0,0 +1,12 @@ +{ + "name": "Typst", + "description": "Typst文档编写SKILLS", + "version": "0.0.0-2025.11.28", + "author": { + "name": "Dongdong Kong", + "email": "kongdd.sysu@gmail.com" + }, + "skills": [ + "./skills" + ] +} \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..3418ed7 --- /dev/null +++ b/README.md @@ -0,0 +1,3 @@ +# Typst + +Typst文档编写SKILLS diff --git a/plugin.lock.json b/plugin.lock.json new file mode 100644 index 0000000..2c40943 --- /dev/null +++ b/plugin.lock.json @@ -0,0 +1,81 @@ +{ + "$schema": "internal://schemas/plugin.lock.v1.json", + "pluginId": "gh:kongdd/Skills_for_Your_AI_Student:", + "normalized": { + "repo": null, + "ref": "refs/tags/v20251128.0", + "commit": "612887501839f7e669be7f32193e40f041dca2a2", + "treeHash": "a46a0339ed914122c2096f0d7afc6569c8341966161602f9f534013323cd7844", + "generatedAt": "2025-11-28T10:19:56.044404Z", + "toolVersion": "publish_plugins.py@0.2.0" + }, + "origin": { + "remote": "git@github.com:zhongweili/42plugin-data.git", + "branch": "master", + "commit": "aa1497ed0949fd50e99e70d6324a29c5b34f9390", + "repoRoot": "/Users/zhongweili/projects/openmind/42plugin-data" + }, + "manifest": { + "name": "Typst", + "description": "Typst文档编写SKILLS", + "version": null + }, + "content": { + "files": [ + { + "path": "README.md", + "sha256": "bc8f69a6f14ca2bdbda9d1ae10945b2d40ea6ebdbcc8fbb4be23e945fbb7d37b" + }, + { + "path": ".claude-plugin/plugin.json", + "sha256": "c9ea9b269f8dc870871cf00b5820435dbb699a18b3489af4450c76ab85640a0b" + }, + { + "path": "skills/typst-physica/examples.typ", + "sha256": "f29c070d485af884731333a127b9933966faee31d5682c9e77858b93a1822853" + }, + { + "path": "skills/typst-physica/example_physica.typ", + "sha256": "a3aeff09aa965d57419261a9a3d9a206652c5b730c1f59afe7c6eb33a1b66bf9" + }, + { + "path": "skills/typst-physica/SKILL.md", + "sha256": "16a786b033af36f7421bb12f4d9fffcc8cb2782d74c989709d201fe4fd418634" + }, + { + "path": "skills/julia-numerical/examples.jl", + "sha256": "918c3df7fc48fde70bd5bb75f7c6636ff68f5331a61cbe8c1eea666a69662c8d" + }, + { + "path": "skills/julia-numerical/SKILL.md", + "sha256": "381dd118c82ee8631e462c3ab1e137e2cd286d4f0102435036a5265daa88cc11" + }, + { + "path": "skills/julia-numerical/test_basic.jl", + "sha256": "1a47c402edbd91a12024411967d2a427331e6cc9e4cad81e38d10118caf86a85" + }, + { + "path": "skills/julia-hydrotools/examples.jl", + "sha256": "2962c429ca92208da63123ab7234245e19b7710d58fca256f364a741b19fac05" + }, + { + "path": "skills/julia-hydrotools/SKILL.md", + "sha256": "1615b3e2fb09ba38cee4304f3f4f8d2a8da51e1411fe4ceb219002177e71350d" + }, + { + "path": "skills/hydro-forecast/examples.jl", + "sha256": "2962c429ca92208da63123ab7234245e19b7710d58fca256f364a741b19fac05" + }, + { + "path": "skills/hydro-forecast/SKILL.md", + "sha256": "8d38eb768b6bb886729500af7c9e92a951f7edd26186bd91dc62b7c9e3396506" + } + ], + "dirSha256": "a46a0339ed914122c2096f0d7afc6569c8341966161602f9f534013323cd7844" + }, + "security": { + "scannedAt": null, + "scannerVersion": null, + "flags": [] + } +} \ No newline at end of file diff --git a/skills/hydro-forecast/SKILL.md b/skills/hydro-forecast/SKILL.md new file mode 100644 index 0000000..9ae68e1 --- /dev/null +++ b/skills/hydro-forecast/SKILL.md @@ -0,0 +1,125 @@ +--- +name: hydro-forecast +description: +--- + +# 1 运行环境说明 + +- 在Julia中运行 + +- 在julia中首先加载包，`using HydroTools` + +- 若没有包加载出错，则安装之，`using Pkg; Pkg.add("HydroTools")` + + +## 说明 + +先不要立即执行该skills，提醒用户输入的数据的格式。用户需要整理好的数据路径即可。 + +``` + +``` + +`model`模型选择 + ++ MarrMot ++ XAJ ++ TCN ++ LSTM ++ KAN + +如果复杂、参数比较多的模型：要求用户输入模型参数`json`文件。 +按照如下示例 + +```json +{ + "clumping_index": 0.62, + "LAI_max_o": 4.5, + "LAI_max_u": 2.4, + "z00": 1.33, + "mass_overstory": 35, + "mass_understory": 10, + "root_depth": 0.6, + "α_canopy_vis": 0.035, + "α_canopy_nir": 0.23, + "r_root_decay": 0.95, + "minimum_stomatal_resistance": 150, + "z_canopy_o": 20, + "z_canopy_u": 3, + "g1_w": 8, + "VCmax25": 62.5, + "leaf_resp_co": 0.0015, + "stem_resp_co": 0.0020, + "root_resp_co": 0.0020, + "fine_root_resp_co": 0.003, + "N_leaf": 4.45, + "slope_Vc": 0.33152 +} +``` + +## 1.1 任务说明 + +### 1.1.1 `framework`： + +```julia + +function hydro_forecast(f; model, outdir) + res = ... + + fwrite(res.output, ...) + fwrite(res.gof, ...) + fwrite(res.info_flood, ...) + fwrite(res.dat_flood, ...) + fwrite(res.evaluation, ...) +end + +function hydro_forecast(X::AbstractArray, Y::AbstractArray; model::Function, outdir = "OUTPUT") + mkpath(outdir) + res; # return a NamedTuple +end +``` + +**输入**：X, Y, model + +**输出**：Qsim, GOF, Pass_rate + + + `output`: 三类数据集的输出，A DataFrame with columns of `date`, `Qsim`, + + `gof`: 三类数据的拟合优度 + + `info_flood`: 洪水场次信息，`id`, `time_beg`, `time_end`, `duration`, `Q_peak`, `Q_min` + + `dat_flood`：洪水场次的驱动数据， + + `evaluation`: 每个洪水场次上的模拟优度, csv + +**绘图**： + + + 交给他绘图的函数，数据 + +**总结**： + + + `evaluation`总结模型预报精度 （`AI执行`） + + +**内部模块设计**： + + + `flood_division`: 采用R语言，划分洪水场次 + + + `划分数据集`：train, test, valid + + + `loss`: 根据拟合优度指标去设计loss，例如KGE, NSE, RMSE，注意loss越小越优。根据loss去优选模型参数。 + + + `evaluation`: 在三种数据集，train, test, valid。每个洪水场次的洪峰、峰现时间合格率。 + + +### 1.1.2 `model`：水文模型、LSTM、TCN、KAN + + ```julia + Ysim = Model(X, Y; params, state) # Lux的设计哲学 + ``` + +### 1.1.3 文件保存 + +文件保存采用Julia包`DataFrames`，`RTableTools` + +```julia +using RTableTools +fwrite(df, "out.csv") # df is a DataFrame +``` diff --git a/skills/hydro-forecast/examples.jl b/skills/hydro-forecast/examples.jl new file mode 100644 index 0000000..38f4c1e --- /dev/null +++ b/skills/hydro-forecast/examples.jl @@ -0,0 +1,22 @@ +using HydroTools +using Dates + +lat = 20.0 +doy = 120 + +ws = HourAngleSunSet(lat, doy) +# doy +cal_Rsi_toa(lat, doy) + +# date +date = Date(2010, 6, 12) +doy = dayofyear(date) +cal_Rsi_toa(lat, doy) + +# datetime +time = DateTime(2010, 6, 12) +doy = dayofyear(date) +Rsi = cal_Rsi_toa(lat, doy) # [MJ d-1 m-2] + + +MJ2W(Rsi) # [MJ d-1 m-2] to [W m-2] diff --git a/skills/julia-hydrotools/SKILL.md b/skills/julia-hydrotools/SKILL.md new file mode 100644 index 0000000..8f2adb4 --- /dev/null +++ b/skills/julia-hydrotools/SKILL.md @@ -0,0 +1,32 @@ +--- +name: julia-hydrotools +description: 计算短波辐射、长波辐射、潜在蒸散发、日出日落时间、湿度的基本变量处理。 +--- + +# 1 运行环境说明 + +- 在Julia中运行 + +- 在julia中首先加载包，`using HydroTools` + +- 若没有包加载出错，则安装之，`using Pkg; Pkg.add("HydroTools")` + + +## 1.1 函数说明 + +- `cal_Rsi_toa(lat, J)`: daily extraterrestrial radiation in MJ m-2 day-1 + + `lat`: latitude in deg + + `J`: doy of year + > 注意lat和J是scalar + > 如果是vector，按照Julia的语法，采用`cal_Rsi_toa.(lat, J)`调用 + + 默认返回单位是`MJ d-1`，若想转为`W m-2`，需要调用[MJ2W]函数，告诉用户返回的数字单位 + + +## 1.2 文件保存 + +文件保存采用Julia包`DataFrames`，`RTableTools` + +```julia +using RTableTools +fwrite(df, "out.csv") # df is a DataFrame +``` diff --git a/skills/julia-hydrotools/examples.jl b/skills/julia-hydrotools/examples.jl new file mode 100644 index 0000000..38f4c1e --- /dev/null +++ b/skills/julia-hydrotools/examples.jl @@ -0,0 +1,22 @@ +using HydroTools +using Dates + +lat = 20.0 +doy = 120 + +ws = HourAngleSunSet(lat, doy) +# doy +cal_Rsi_toa(lat, doy) + +# date +date = Date(2010, 6, 12) +doy = dayofyear(date) +cal_Rsi_toa(lat, doy) + +# datetime +time = DateTime(2010, 6, 12) +doy = dayofyear(date) +Rsi = cal_Rsi_toa(lat, doy) # [MJ d-1 m-2] + + +MJ2W(Rsi) # [MJ d-1 m-2] to [W m-2] diff --git a/skills/julia-numerical/SKILL.md b/skills/julia-numerical/SKILL.md new file mode 100644 index 0000000..03189a7 --- /dev/null +++ b/skills/julia-numerical/SKILL.md @@ -0,0 +1,120 @@ +--- +name: julia-numerical +description: Execute numerical calculations and mathematical computations using Julia. Use this skill for matrix operations, linear algebra, numerical integration, optimization, statistics, and scientific computing tasks. +--- + +# Julia Numerical Calculation Skill + +This skill enables you to execute numerical calculations using Julia, a high-performance programming language designed for numerical and scientific computing. + +## When to Use + +Use this skill when you need to: +- Perform matrix operations and linear algebra +- Solve differential equations +- Execute numerical integration or optimization +- Calculate statistical measures +- Handle large-scale numerical computations +- Work with complex mathematical operations + +## Setup + +Before using this skill, ensure Julia is installed on your system: + +```bash +# On macOS (using Homebrew) +brew install julia + +# On Linux (Ubuntu/Debian) +sudo apt-get install julia + +# On Windows (using Chocolatey) +choco install julia + +# Or download from https://julialang.org/downloads/ +``` + +## Basic Examples + +### Linear Algebra + +```julia +using LinearAlgebra + +# Create matrices +A = [1 2; 3 4] +B = [5 6; 7 8] + +# Matrix multiplication +C = A * B + +# Eigenvalues and eigenvectors +eigenvals, eigenvecs = eigen(A) + +# Matrix inverse +A_inv = inv(A) +``` + +### Numerical Integration + +```julia +using QuadGK + +# Define a function +f(x) = sin(x) * exp(-x) + +# Integrate from 0 to ∞ +result, error = quadgk(f, 0, Inf) +``` + +### Optimization + +```julia +using Optim + +# Define objective function +f(x) = (x[1] - 2)^2 + (x[2] - 3)^2 + +# Minimize +result = optimize(f, [0.0, 0.0]) +``` + +### Statistics + +```julia +using Statistics + +data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] + +# Statistical measures +mean_val = mean(data) +std_val = std(data) +var_val = var(data) +median_val = median(data) +``` + +## How to Use This Skill + +When you ask me to perform a numerical calculation: +1. I'll identify the appropriate Julia packages needed +2. Write Julia code to solve the problem +3. Execute the code +4. Return results and explanations + +## Common Julia Packages + +- **LinearAlgebra**: Matrix operations and linear algebra +- **Statistics**: Statistical functions +- **QuadGK**: Numerical integration +- **Optim**: Optimization algorithms +- **DifferentialEquations**: Solving differential equations +- **Plots**: Visualization +- **Distributions**: Probability distributions +- **Random**: Random number generation + +## Notes + +- Julia is JIT-compiled, so first runs may include compilation time +- Use `.jl` files for organizing longer scripts +- Install packages with `using Pkg; Pkg.add("PackageName")` +- Results are returned as Julia objects that are converted to readable format diff --git a/skills/julia-numerical/examples.jl b/skills/julia-numerical/examples.jl new file mode 100644 index 0000000..2c527b4 --- /dev/null +++ b/skills/julia-numerical/examples.jl @@ -0,0 +1,155 @@ +# Julia Numerical Calculation Examples +# This file contains common numerical computation patterns + +# ============================================================================ +# Linear Algebra Examples +# ============================================================================ + +function linear_algebra_examples() + using LinearAlgebra + + println("=== Linear Algebra Examples ===") + + # Matrix creation and basic operations + A = [1 2 3; 4 5 6; 7 8 10] + b = [1, 2, 3] + + println("Matrix A:") + println(A) + + # Solve linear system Ax = b + x = A \ b + println("\nSolution to Ax = b:") + println(x) + + # Eigenvalues + eigenvals, eigenvecs = eigen(A) + println("\nEigenvalues:") + println(eigenvals) + + # Singular value decomposition + U, S, V = svd(A) + println("\nSingular values:") + println(S) + + # Determinant and norm + println("\nDeterminant: ", det(A)) + println("Frobenius norm: ", norm(A)) +end + + +# ============================================================================ +# Numerical Integration Examples +# ============================================================================ + +function integration_examples() + using QuadGK + + println("\n=== Numerical Integration Examples ===") + + # Integrate sin(x) from 0 to π + f1(x) = sin(x) + result1, error1 = quadgk(f1, 0, π) + println("∫sin(x)dx from 0 to π = ", result1) + println("Estimated error: ", error1) + + # Integrate exp(-x^2) from -∞ to ∞ (Gaussian) + f2(x) = exp(-x^2) + result2, error2 = quadgk(f2, -Inf, Inf) + println("\n∫exp(-x²)dx from -∞ to ∞ = ", result2) + println("Theoretical value: ", sqrt(π)) + + # Integrate 1/(1+x^2) from 0 to 1 + f3(x) = 1/(1 + x^2) + result3, error3 = quadgk(f3, 0, 1) + println("\n∫1/(1+x²)dx from 0 to 1 = ", result3) + println("Theoretical value (π/4): ", π/4) +end + +# ============================================================================ +# Optimization Examples +# ============================================================================ + +function optimization_examples() + using Optim + + println("\n=== Optimization Examples ===") + + # Simple quadratic function + f(x) = (x[1] - 2)^2 + (x[2] - 3)^2 + + result = optimize(f, [0.0, 0.0]) + println("Minimize f(x,y) = (x-2)² + (y-3)²") + println("Minimum found at: ", Optim.minimizer(result)) + println("Minimum value: ", Optim.minimum(result)) + + # Rosenbrock function (more challenging) + rosenbrock(x) = (1 - x[1])^2 + 100(x[2] - x[1]^2)^2 + + result2 = optimize(rosenbrock, [0.0, 0.0]) + println("\nMinimize Rosenbrock function") + println("Minimum found at: ", Optim.minimizer(result2)) + println("Minimum value: ", Optim.minimum(result2)) +end + +# ============================================================================ +# Statistics Examples +# ============================================================================ + +function statistics_examples() + using Statistics + + println("\n=== Statistics Examples ===") + + data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20] + + println("Data: ", data) + println("\nStatistical measures:") + println("Mean: ", mean(data)) + println("Median: ", median(data)) + println("Standard deviation: ", std(data)) + println("Variance: ", var(data)) + println("Minimum: ", minimum(data)) + println("Maximum: ", maximum(data)) + println("Range: ", maximum(data) - minimum(data)) + + # Quantiles + println("\nQuantiles:") + println("25th percentile: ", quantile(data, 0.25)) + println("50th percentile: ", quantile(data, 0.50)) + println("75th percentile: ", quantile(data, 0.75)) +end + +# ============================================================================ +# Root Finding Examples +# ============================================================================ + +function root_finding_examples() + using Roots + + println("\n=== Root Finding Examples ===") + + # Find root of f(x) = x^3 - 2 + f(x) = x^3 - 2 + root = find_zero(f, 1.0) + println("Root of x³ - 2 = 0: ", root) + println("Verification: f(root) = ", f(root)) + + # Find root of f(x) = sin(x) - 0.5 + f2(x) = sin(x) - 0.5 + root2 = find_zero(f2, 0.5) + println("\nRoot of sin(x) - 0.5 = 0: ", root2) + println("Verification: f(root) = ", f2(root2)) +end + +# ============================================================================ +# Main execution +# ============================================================================ + +if abspath(PROGRAM_FILE) == @__FILE__ + linear_algebra_examples() + integration_examples() + optimization_examples() + statistics_examples() + root_finding_examples() +end diff --git a/skills/julia-numerical/test_basic.jl b/skills/julia-numerical/test_basic.jl new file mode 100644 index 0000000..ca74eb3 --- /dev/null +++ b/skills/julia-numerical/test_basic.jl @@ -0,0 +1,34 @@ +# Basic Julia numerical test +using LinearAlgebra +using Statistics + +println("Testing Julia Numerical Calculation Skill") +println("==========================================\n") + +# Test 1: Basic arithmetic +println("Test 1: Basic Arithmetic") +result = 2 + 2 * 3 +println("2 + 2 * 3 = ", result) + +# Test 2: Vector operations +println("\nTest 2: Vector Operations") +v1 = [1, 2, 3] +v2 = [4, 5, 6] +dot_product = dot(v1, v2) +println("dot([1,2,3], [4,5,6]) = ", dot_product) + +# Test 3: Matrix operations +println("\nTest 3: Matrix Operations") +A = [1 2; 3 4] +println("Matrix A:") +println(A) +println("det(A) = ", det(A)) + +# Test 4: Statistics +println("\nTest 4: Statistics") +data = [10, 20, 30, 40, 50] +println("Data: ", data) +println("mean = ", mean(data)) +println("std = ", std(data)) + +println("\n✓ All basic tests passed!") diff --git a/skills/typst-physica/SKILL.md b/skills/typst-physica/SKILL.md new file mode 100644 index 0000000..9380abd --- /dev/null +++ b/skills/typst-physica/SKILL.md @@ -0,0 +1,53 @@ +--- +name: typst-physica +description: typst公式中的微分、偏微分方程编写，latex公式转typst。 +--- + + +# 引用包 + +应在typst文档的开头，引用包。公式编写、文档排版，依赖`modern-cug-report`。 + +用于如果已经引用了`modern-cug-report`，则无需再重复添加了。 + +```typst +#import "@local/modern-cug-report:0.1.3": * +#show: doc => template(doc, footer: "CUG水文气象学2025", header: "") +``` + + +# 偏微分方程 + +- `(∂ theta) / (∂ t)` + + `\frac{\partial \theta}{\partial t}`采用typst编写会非常简单，`pdv(theta, t)` + + ```typst + (partial.diff theta) / (partial.diff t) // 是错误写法 + pdv(theta, t) // 正确写法 + ``` + +- `(d theta) / (d t)`则是：`dv(theta, t)` + + +# text + +typst公式中的本文需要使用引号： + +```typst +q_(infiltration) // 错误 +q_("infiltration") // 正确 +``` + +# fraction + +- latex的`\frac{y}{x}`，写成typst则是`y/x`； + + 若分子、分母有多个变量，则用括号括起来。例如latex的`\frac{y z}{x}`，写成typst则是`(y z) / x` + + +# 排版 + +- 一级标题之前空两行，凸显章节的层次感。 + +- 第一个一级标题，不用空两行。 diff --git a/skills/typst-physica/example_physica.typ b/skills/typst-physica/example_physica.typ new file mode 100644 index 0000000..38fc995 --- /dev/null +++ b/skills/typst-physica/example_physica.typ @@ -0,0 +1,40 @@ +// Copyright 2023 Leedehai +// Use of this code is governed by a MIT license in the LICENSE.txt file. +// For a manual on this package, see physica-manual.pdf. + +#import "@local/modern-cug-report:0.1.3": * +#show: doc => template(doc, footer: "CUG水文气象学2025", header: "") + +// #import "physica.typ": * + +#show: super-T-as-transpose // Render "..^T" as transposed matrix + +$ + A^T, curl vb(E) = - pdv(vb(B), t), + quad + tensor(Lambda, +mu, -nu) = dmat(1, RR), + quad + f(x,y) dd(x, y), + quad + dd(vb(x), y, [3]), + quad + dd(x, y, 2, d: Delta, p: and), + quad + dv(phi, t, d: upright(D)) = pdv(phi, t) + vb(u) grad phi \ + H(f) = hmat(f; x, y; delim: "[", big: #true), + quad + vb(v^a) = sum_(i=1)^n alpha_i vu(u^i), + quad + Set((x, y), pdv(f, x, y, [2,1]) + pdv(f, x, y, [1,2]) < epsilon) \ + -1/c^2 pdv(, t, 2)psi + laplacian psi = (m^2c^2) / hbar^2 psi, + quad + ket(n^((1))) = sum_(k in.not D) mel(k^((0)), V, n^((0))) / (E_n^((0)) - E_k^((0))) ket(k^((0))), + quad + integral_V dd(V) (pdv(cal(L), phi) - partial_mu (pdv(cal(L), (partial_mu phi)))) = 0 \ + dd(s, 2) = -(1-(2G M)/r) dd(t, 2) + (1-(2G M)/r)^(-1) dd(r, 2) + r^2 dd(Omega, 2) +$ + +$ + "clk:" & signals("|1....|0....|1....|0....|1....|0....|1....|0..", step: #0.5em) \ + "bus:" & signals(" #.... X=... ..... ..... X=... ..... ..... X#.", step: #0.5em) +$ diff --git a/skills/typst-physica/examples.typ b/skills/typst-physica/examples.typ new file mode 100644 index 0000000..3802596 --- /dev/null +++ b/skills/typst-physica/examples.typ @@ -0,0 +1,36 @@ +#import "@local/modern-cug-report:0.1.3": * +#show: doc => template(doc, footer: "CUG水文气象学2025", header: "") + + +== 1 Richards方程 + +Richards方程： + +$ pdv(theta, t) = nabla dot [K(theta) nabla H] + S $ + +其中： +- $theta$：体积含水量 [L^3/L^3] +- $t$：时间 [T] +- $S$：源汇项 [1/T] + +总水头 $H$ 由基质势 $h$ 和重力势 $z$ 组成： +$ H = h + z $ + + +== 2 质量守恒定律 +对于土壤控制体积，质量守恒方程为： +$ pdv(rho theta, t) + nabla dot (rho q) = rho S $ + +假设水密度 $rho$ 为常数，简化为： +$ pdv(theta, t) + nabla dot q = S $ + + +== 3 上边界层条件 + +上边界通常受大气条件控制，主要包括： + +*降雨入渗条件：* +$ -K(theta) pdv(H, z) |_(z=0) = q_("infiltration") $ + +*蒸发条件：* +$ -K(theta) pdv(H, z) |_(z=0) = q_("evaporation") $