1

2025-11-20 10:45:27 +08:00
commit 7ea9f9b1b6
12 changed files with 353 additions and 0 deletions
--- a/org/init.py
+++ b/org/init.py
--- a/org/chatgpt2/init.py
+++ b/org/chatgpt2/init.py
@@ -0,0 +1,102 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.interpolate import CubicSpline
+from scipy.constants import h, c, k
+
+# -----------------------------
+# 1. 数据预处理
+# -----------------------------
+# PDMS 可见光折射率数据
+wl_data = np.array([0.3500,0.3535,0.3570,0.3605,0.3640,0.3675,0.3710,0.3745,0.3780,0.3815,
+                    0.3850,0.3885,0.3920,0.3955,0.3990,0.4025,0.4060,0.4095,0.4130,0.4165,
+                    0.4200,0.4235,0.4270,0.4305,0.4340,0.4375,0.4410,0.4445,0.4480,0.4515,
+                    0.4550,0.4585,0.4620,0.4655,0.4690,0.4725,0.4760,0.4795,0.4830,0.4865,
+                    0.4900,0.4935,0.4970,0.5005,0.5040,0.5075,0.5110,0.5145,0.5180,0.5215,
+                    0.5250,0.5285,0.5320,0.5355,0.5390,0.5425,0.5460,0.5495,0.5530,0.5565,
+                    0.5600,0.5635,0.5670,0.5705,0.5740,0.5775,0.5810,0.5845,0.5880,0.5915,
+                    0.5950,0.5985,0.6020,0.6055,0.6090,0.6125,0.6160,0.6195,0.6230,0.6265,
+                    0.6300,0.6335,0.6370,0.6405,0.6440,0.6475,0.6510,0.6545,0.6580,0.6615,
+                    0.6650,0.6685,0.6720,0.6755,0.6790,0.6825,0.6860,0.6895,0.6930,0.6965,
+                    0.7000])
+n_data = np.array([1.4585,1.4576,1.4567,1.4559,1.4550,1.4542,1.4535,1.4527,1.45197,1.45126,
+                   1.45057,1.44990,1.44926,1.44863,1.44802,1.44742,1.44685,1.44628,1.44574,1.44521,
+                   1.44470,1.44420,1.44371,1.44324,1.44277,1.44232,1.44188,1.44145,1.44104,1.44063,
+                   1.44024,1.43985,1.43947,1.43911,1.43875,1.43840,1.43805,1.43772,1.43739,1.43707,
+                   1.43676,1.43645,1.43616,1.43587,1.43558,1.43531,1.43503,1.43477,1.43450,1.43425,
+                   1.43399,1.43375,1.43351,1.43328,1.43305,1.43283,1.43260,1.43238,1.43217,1.43197,
+                   1.43177,1.43157,1.43137,1.43118,1.43098,1.43080,1.43062,1.43044,1.43027,1.43009,
+                   1.42993,1.42976,1.42960,1.42944,1.42929,1.42913,1.42898,1.42883,1.42869,1.42855,
+                   1.42841,1.42827,1.42813,1.42799,1.42787,1.42773,1.42761,1.42749,1.42736,1.42724,
+                   1.42712,1.42701,1.42689,1.42677,1.42666,1.42656,1.42645,1.42634,1.42624,1.42613,
+                   1.42604])
+
+# 三次样条插值
+cs_n = CubicSpline(wl_data, n_data)
+
+# 定义厚度序列（μm）
+thicknesses = [0.5, 1.0, 1.5, 2.0]
+
+# -----------------------------
+# 2. 发射率计算（小问1）
+# -----------------------------
+def fresnel_reflectance(n1, n2):
+    return ((n1 - n2)/(n1 + n2))**2
+
+def thin_film_reflectance(n_film, d, wl):
+    R12 = fresnel_reflectance(1.0, n_film)
+    R23 = fresnel_reflectance(n_film, 1.0)
+    delta = 2 * np.pi * n_film * d / wl
+    R = (R12 + R23 + 2*np.sqrt(R12*R23)*np.cos(2*delta)) / (1 + R12*R23 + 2*np.sqrt(R12*R23)*np.cos(2*delta))
+    return R
+
+# 波长范围 0.35-0.7 μm，步长 0.001
+wl_fine = np.linspace(0.35, 0.7, 500)
+plt.figure(figsize=(8,5))
+
+emission_dict = {}
+for d in thicknesses:
+    R = thin_film_reflectance(cs_n(wl_fine), d, wl_fine)
+    epsilon = 1 - R
+    emission_dict[d] = epsilon
+    plt.plot(wl_fine, epsilon, label=f"d={d} μm")
+
+plt.xlabel("Wavelength (μm)")
+plt.ylabel("Emissivity ε(λ)")
+plt.title("PDMS Thin Film Spectral Emissivity")
+plt.legend()
+plt.grid(True)
+plt.show()
+
+# -----------------------------
+# 3. 净辐射功率计算（小问2）
+# -----------------------------
+# 黑体辐射谱 (Planck)
+def planck_spectrum(wl, T):
+    wl_m = wl * 1e-6  # μm → m
+    return (2*h*c**2 / wl_m**5) / (np.exp(h*c/(wl_m*k*T)) - 1)
+
+T_film = 300  # K
+T_sky = 280   # K
+# 假设太阳吸收率 alpha = 0.1
+alpha = 0.1
+# 假设太阳总辐射 1000 W/m²
+I_sun_total = 1000
+I_sun = np.ones_like(wl_fine) * I_sun_total / len(wl_fine)
+# 假设大气透射率 tau = 0.9
+tau_atm = 0.9
+
+plt.figure(figsize=(8,5))
+for d in thicknesses:
+    epsilon = emission_dict[d]
+    P_emit = np.trapz(epsilon * planck_spectrum(wl_fine, T_film), wl_fine)
+    P_sun = np.trapz(alpha * I_sun, wl_fine)
+    P_atm = np.trapz(epsilon * planck_spectrum(wl_fine, T_sky) * tau_atm, wl_fine)
+    P_net = P_emit - P_sun - P_atm
+    print(f"d={d} μm, P_net = {P_net:.2f} W/m²")
+    plt.bar(d, P_net, width=0.3)
+
+plt.xlabel("Thickness (μm)")
+plt.ylabel("Net Radiative Cooling Power (W/m²)")
+plt.title("PDMS Thin Film Net Radiative Cooling")
+plt.grid(True)
+plt.show()
--- a/org/q1.py
+++ b/org/q1.py
@@ -0,0 +1,103 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.interpolate import InterpolatedUnivariateSpline
+
+# ------------------------------------------------
+# 1. 可见光区 PDMS 折射率数据（题目给定）
+# ------------------------------------------------
+wl_visible = np.array([
+0.3500,0.3535,0.3570,0.3605,0.3640,0.3675,0.3710,0.3745,0.3780,0.3815,
+0.3850,0.3885,0.3920,0.3955,0.3990,0.4025,0.4060,0.4095,0.4130,0.4165,
+0.4200,0.4235,0.4270,0.4305,0.4340,0.4375,0.4410,0.4445,0.4480,0.4515,
+0.4550,0.4585,0.4620,0.4655,0.4690,0.4725,0.4760,0.4795,0.4830,0.4865,
+0.4900,0.4935,0.4970,0.5005,0.5040,0.5075,0.5110,0.5145,0.5180,0.5215,
+0.5250,0.5285,0.5320,0.5355,0.5390,0.5425,0.5460,0.5495,0.5530,0.5565,
+0.5600,0.5635,0.5670,0.5705,0.5740,0.5775,0.5810,0.5845,0.5880,0.5915,
+0.5950,0.5985,0.6020,0.6055,0.6090,0.6125,0.6160,0.6195,0.6230,0.6265,
+0.6300,0.6335,0.6370,0.6405,0.6440,0.6475,0.6510,0.6545,0.6580,0.6615,
+0.6650,0.6685,0.6720,0.6755,0.6790,0.6825,0.6860,0.6895,0.6930,0.6965,
+0.7000
+])
+
+n_visible = np.array([
+1.4585377,1.45761865,1.456730118,1.455870728,1.455039187,1.454234276,1.453454840,
+1.452699788,1.451968089,1.451258766,1.450570894,1.449903597,1.449256044,1.448627445,
+1.448017051,1.447424151,1.446848069,1.446288159,1.445743811,1.445214441,1.444699493,
+1.444198438,1.443710771,1.443236009,1.442773692,1.442323382,1.441884657,1.441457118,
+1.441040380,1.440634076,1.440237854,1.439851378,1.439474326,1.439106388,1.438747267,
+1.438396681,1.438054357,1.437720031,1.437393455,1.437074386,1.436762592,1.436457851,
+1.436159948,1.435868677,1.435583840,1.435305247,1.435032713,1.434766062,1.434505122,
+1.434249731,1.433999730,1.433754966,1.433515292,1.433280566,1.433050651,1.432825415,
+1.432604730,1.432388473,1.432176524,1.431968770,1.431765097,1.431565400,1.431369574,
+1.431177518,1.430989136,1.430804333,1.430623017,1.430445102,1.430270501,1.430099132,
+1.429930914,1.429765771,1.429603626,1.429444407,1.429288044,1.429134467,1.428983610,
+1.428835410,1.428689802,1.428546727,1.428406125,1.428267940,1.428132115,1.427998598,
+1.427867334,1.427738274,1.427611368,1.427486568,1.427363827,1.427243100,1.427124343,
+1.427007511,1.426892565,1.426779463,1.426668165,1.426558634,1.426450831,1.426344720,
+1.426240266,1.426137434,1.426036190
+])
+
+# ------------------------------------------------
+# 2. 插值构建连续 n(λ)
+# ------------------------------------------------
+interp_n = InterpolatedUnivariateSpline(wl_visible, n_visible)
+
+# ------------------------------------------------
+# 3. 红外区 n,k 数据（示例，可替换为真实数据）
+# ------------------------------------------------
+def pdms_nk(lambda_um):
+    """
+    示例：构建红外折射率 n,k（实际请替换 refractiveindex.info 数据）
+    """
+    n = 1.385 + 0.015 * np.exp(-(lambda_um - 10)**2 / 20)
+    k = 0.15 * np.exp(-(lambda_um - 10)**2 / 5)  # 红外区 PDMS 有吸收峰
+    # 可见光区用插值得到的 n
+    n[lambda_um < 0.7] = interp_n(lambda_um[lambda_um < 0.7])
+    k[lambda_um < 0.7] = 0  # 可见光透明
+    return n + 1j*k
+
+# ------------------------------------------------
+# 4. TMM 计算发射率
+# ------------------------------------------------
+def layer_matrix(n_complex, d_um, lambda_um):
+    k0 = 2 * np.pi / (lambda_um * 1e-6)
+    delta = k0 * n_complex * (d_um * 1e-6)
+    q = n_complex
+    M11 = np.cos(delta)
+    M12 = 1j / q * np.sin(delta)
+    M21 = 1j * q * np.sin(delta)
+    M22 = np.cos(delta)
+    return np.array([[M11, M12], [M21, M22]])
+
+def emissivity(lambda_um, d_um):
+    n0 = 1.0  # 空气
+    ns = 1.0  # 基底（可修改）
+    nk = pdms_nk(lambda_um)
+
+    M = layer_matrix(nk, d_um, lambda_um)
+    M11, M12 = M[0,0], M[0,1]
+    M21, M22 = M[1,0], M[1,1]
+
+    numerator = M11 + M12*ns - M21/n0 - M22*ns/n0
+    denominator = M11 + M12*ns + M21/n0 + M22*ns/n0
+
+    R = np.abs(numerator/denominator)**2
+    T = (ns/n0) / np.abs(denominator)**2
+    return 1 - R - T
+
+# ------------------------------------------------
+# 5. 计算发射率与绘图
+# ------------------------------------------------
+lambda_range = np.linspace(0.35, 20, 2000)
+d_pdms = 10   # 10 μm 厚度
+
+eps = emissivity(lambda_range, d_pdms)
+
+plt.figure(figsize=(10,5))
+plt.plot(lambda_range, eps, label=f'd = {d_pdms} μm')
+plt.xlabel("Wavelength (μm)")
+plt.ylabel("Emissivity")
+plt.title("PDMS Thin-film Emissivity Spectrum")
+plt.grid(True)
+plt.legend()
+plt.show()
--- a/org/q2.py
+++ b/org/q2.py
@@ -0,0 +1,95 @@
+import numpy as np
+from scipy.constants import h, c, k
+from scipy.integrate import simps
+import matplotlib.pyplot as plt
+
+from org.q1 import emissivity
+
+
+# ------------------------------------------------
+# 1. 引用第一题的 emissivity() 函数
+# ------------------------------------------------
+# (假设已运行第一题代码)
+# emissivity(lambda_um, thickness_um)
+
+
+# ------------------------------------------------
+# 2. 黑体辐射谱
+# ------------------------------------------------
+def planck_lambda(lambda_um, T):
+    lambda_m = lambda_um * 1e-6
+    return (2*h*c**2)/(lambda_m**5) / (np.exp(h*c/(lambda_m*k*T)) - 1)
+
+# ------------------------------------------------
+# 3. 大气透过率（示例，可替换 MODTRAN 数据）
+# ------------------------------------------------
+def atmosphere_tau(lambda_um):
+    tau = np.ones_like(lambda_um)
+    window = (lambda_um >= 8) & (lambda_um <= 13)
+    tau[window] = 0.8
+    tau[~window] = 0.1
+    return tau
+
+# ------------------------------------------------
+# 4. 太阳辐照谱（简化 AM1.5）
+# ------------------------------------------------
+def solar_spectrum(lambda_um):
+    I0 = 1.5e3  # simplified scaling
+    return I0 * np.exp(-(lambda_um - 0.5)**2 / 0.4)
+
+# ------------------------------------------------
+# 5. 能量项计算
+# ------------------------------------------------
+def P_rad(Ts, lambda_um, eps):
+    return simps(eps * planck_lambda(lambda_um, Ts), lambda_um)
+
+def P_atm(Ta, lambda_um, eps):
+    return simps(eps * planck_lambda(lambda_um, Ta) * (1 - atmosphere_tau(lambda_um)), lambda_um)
+
+def P_solar(lambda_um, eps):
+    A = eps  # approximate absorption
+    return simps(A * solar_spectrum(lambda_um), lambda_um)
+
+def P_conv(Ts, Ta, h=5):
+    return h * (Ts - Ta)
+
+# ------------------------------------------------
+# 6. 净冷却功率
+# ------------------------------------------------
+def P_net(Ts, Ta, lambda_um, eps, h=5):
+    return P_rad(Ts, lambda_um, eps) - P_atm(Ta, lambda_um, eps) - P_solar(lambda_um, eps) - P_conv(Ts, Ta, h)
+
+# ------------------------------------------------
+# 7. 求稳态温度（解 Pnet=0）
+# ------------------------------------------------
+def solve_temperature(Ta, lambda_um, eps):
+    Ts = Ta
+    for _ in range(1000):
+        f = P_net(Ts, Ta, lambda_um, eps)
+        Ts -= 0.1 * f  # simple iteration
+    return Ts
+
+# ------------------------------------------------
+# 8. 运行示例
+# ------------------------------------------------
+lambda_range = np.linspace(0.35, 20, 2000)
+d_pdms = 10
+eps = emissivity(lambda_range, d_pdms)
+
+Ta = 300  # 环境温度
+Ts = solve_temperature(Ta, lambda_range, eps)
+
+print("Steady-state temperature:", Ts)
+
+# 曲线可视化
+T_list = np.linspace(250, 330, 200)
+P_list = [P_net(T, Ta, lambda_range, eps) for T in T_list]
+
+plt.figure(figsize=(10,5))
+plt.plot(T_list, P_list)
+plt.axhline(0, color='r')
+plt.xlabel("Temperature (K)")
+plt.ylabel("Net Cooling Power")
+plt.title("Cooling Power vs Temperature")
+plt.grid(True)
+plt.show()