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b/org/chatgpt2/__init__.py index 90ca8d8..31758fc 100644 --- a/org/chatgpt2/__init__.py +++ b/org/chatgpt2/__init__.py @@ -69,35 +69,45 @@ plt.grid(True) plt.show() # ----------------------------- -# 3. 净辐射功率计算（小问2） +# 问题2 +# ----------------------------- +T_film = 420 # 薄膜温度 K +T_sky = 280 # 天空温度 K +alpha = 0.1 # 吸收可见光比例 +I_sun_total = 1000 # W/m²，太阳总辐射 +I_sun = np.ones_like(wl_fine) * I_sun_total / len(wl_fine) # 均匀分布 +tau_atm = 0.9 # 大气透射率假设 + +# ----------------------------- +# 4. Planck 黑体辐射函数 # ----------------------------- -# 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)) +# ----------------------------- +# 5. 计算净辐射功率 +# ----------------------------- +P_net_list = [] 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) + P_net_list.append(P_net) -plt.xlabel("Thickness (μm)") +# ----------------------------- +# 6. 绘图：净辐射功率 vs 厚度 +# ----------------------------- +plt.figure(figsize=(8,5)) +plt.plot(thicknesses, P_net_list, marker='o', linestyle='-', color='blue', label='Net Radiative Cooling') +for x, y in zip(thicknesses, P_net_list): + plt.text(x, y, f"{y:.1f}", ha='center', va='bottom') + +plt.xlabel("Film Thickness (μm)") plt.ylabel("Net Radiative Cooling Power (W/m²)") -plt.title("PDMS Thin Film Net Radiative Cooling") +plt.title("PDMS Thin Film Radiative Cooling Performance") plt.grid(True) +plt.legend() plt.show() diff --git a/org/chatgpt2/q1_2.py b/org/chatgpt2/q1_2.py new file mode 100644 index 0000000..933472e --- /dev/null +++ b/org/chatgpt2/q1_2.py @@ -0,0 +1,182 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.interpolate import CubicSpline + + +# ----------------------------- +# 1. 从data.txt读取分块格式数据（先wl+n，再wl+k） +# ----------------------------- +def read_split_data(file_path): + """ + 解析分块数据格式： + 第一部分：wl n（多行数据） + 第二部分：wl k（多行数据） + 返回：sorted_wl, n, k（波长已排序，保证n和k一一对应） + """ + with open(file_path, 'r', encoding='utf-8') as f: + lines = [line.strip() for line in f if line.strip() and not line.startswith('#')] + + # 分割n数据和k数据（以"wl k"为分界） + split_idx = None + for i, line in enumerate(lines): + if line == 'wl k': # 找到k数据的表头 + split_idx = i + break + + # 提取n数据（表头后到split_idx前） + n_lines = lines[1:split_idx] # 跳过"wl n"表头 + wl_n = [] + n_list = [] + for line in n_lines: + wl, n_val = line.split() + wl_n.append(float(wl)) + n_list.append(float(n_val)) + + # 提取k数据（split_idx后） + k_lines = lines[split_idx + 1:] # 跳过"wl k"表头 + wl_k = [] + k_list = [] + for line in k_lines: + wl, k_val = line.split() + wl_k.append(float(wl)) + k_list.append(float(k_val)) + + # 转换为numpy数组 + wl_n = np.array(wl_n) + n_list = np.array(n_list) + wl_k = np.array(wl_k) + k_list = np.array(k_list) + + # 确保n和k的波长完全一致（否则插值会出错） + assert np.allclose(wl_n, wl_k), "n和k的波长列表不一致！" + + # 排序（按波长递增，避免插值异常） + sorted_idx = np.argsort(wl_n) + sorted_wl = wl_n[sorted_idx] + sorted_n = n_list[sorted_idx] + sorted_k = k_list[sorted_idx] + + return sorted_wl, sorted_n, sorted_k + + +# 读取数据 +wl_all, n_all, k_all = read_split_data('/Users/spasolreisa/IdeaProjects/asiaMath/data.txt') + +# 三次样条插值（覆盖全波段，保证计算精度） +cs_n = CubicSpline(wl_all, n_all) # 折射率n的插值函数 +cs_k = CubicSpline(wl_all, k_all) # 消光系数k的插值函数 + +# 定义待研究的PDMS薄膜厚度（μm），可按需调整 +thicknesses = [0.5, 1.0, 1.5, 2.0] + + +# ----------------------------- +# 2. 核心物理模型：薄膜发射率计算 +# ----------------------------- +def fresnel_reflectance(n1, k1, n2, k2): + """ + 菲涅尔反射率（垂直入射近似，考虑消光系数k） + 输入：介质1的n/k，介质2的n/k + 输出：垂直入射时的反射率R（0-1） + """ + m1 = n1 + 1j * k1 # 介质1的复折射率 + m2 = n2 + 1j * k2 # 介质2的复折射率 + return np.abs((m1 - m2) / (m1 + m2)) ** 2 + + +def thin_film_emissivity(n_film, k_film, d, wl, n_air=1.0, k_air=0.0): + """ + 薄膜发射率计算（考虑多光束干涉和吸收） + 输入： + n_film/k_film: 薄膜的折射率/消光系数 + d: 薄膜厚度（μm） + wl: 波长（μm） + n_air/k_air: 空气的折射率/消光系数（默认n=1, k=0） + 输出： + epsilon: 发射率（0-1） + """ + # 1. 计算上下表面的菲涅尔反射率 + R12 = fresnel_reflectance(n_air, k_air, n_film, k_film) # 空气→薄膜 + R23 = fresnel_reflectance(n_film, k_film, n_air, k_air) # 薄膜→空气 + + # 2. 计算相位差和吸收衰减 + delta = 2 * np.pi * n_film * d / wl # 干涉相位差（无吸收时） + alpha = 4 * np.pi * k_film * d / wl # 吸收导致的振幅衰减系数 + + # 3. 多光束干涉反射率（考虑吸收） + numerator = R12 + R23 * np.exp(-alpha) + 2 * np.sqrt(R12 * R23 * np.exp(-alpha)) * np.cos(2 * delta) + denominator = 1 + R12 * R23 * np.exp(-alpha) + 2 * np.sqrt(R12 * R23 * np.exp(-alpha)) * np.cos(2 * delta) + R_total = numerator / denominator + + # 4. 多光束干涉透射率（考虑吸收） + T_total = (1 - R12) * (1 - R23) * np.exp(-alpha) / denominator + + # 5. 基尔霍夫定律：ε = 1 - R - T（局部热平衡） + epsilon = 1 - R_total - T_total + return epsilon + + +# ----------------------------- +# 3. 计算并绘制不同厚度的发射率光谱 +# ----------------------------- +# 定义计算波长范围（覆盖数据的有效波长区间，步长0.01μm保证平滑） +wl_min = wl_all.min() +wl_max = wl_all.max() +wl_fine = np.linspace(wl_min, wl_max, int((wl_max - wl_min) / 0.01) + 1) + +# 创建绘图 +plt.figure(figsize=(12, 7)) +plt.rcParams['font.sans-serif'] = ['Arial'] # 统一字体 + +# 存储不同厚度的发射率结果（用于后续分析） +emission_dict = {} + +for d in thicknesses: + # 插值得到当前波长下的n和k + n_film = cs_n(wl_fine) + k_film = cs_k(wl_fine) + + # 计算发射率 + epsilon = thin_film_emissivity(n_film, k_film, d, wl_fine) + emission_dict[d] = epsilon + + # 绘制光谱曲线 + plt.plot(wl_fine, epsilon, linewidth=2, label=f'Thickness = {d} μm') + +# ----------------------------- +# 4. 图表美化与标注（突出辐射制冷关键波段） +# ----------------------------- +# 标注大气透明窗口（8-13μm，辐射制冷核心波段） +if wl_min <= 13 and wl_max >= 8: # 仅当数据覆盖该波段时才标注 + plt.axvspan(8, 13, alpha=0.15, color='red', label='Atmospheric Window (8-13 μm)') + +# 坐标轴与标题 +plt.xlabel('Wavelength (μm)', fontsize=14) +plt.ylabel('Emissivity ε(λ)', fontsize=14) +plt.title('PDMS Thin Film Spectral Emissivity for Different Thicknesses', fontsize=16, fontweight='bold') + +# 网格、图例与范围设置 +plt.grid(True, alpha=0.3, linestyle='--') +plt.legend(fontsize=12, loc='best') +plt.ylim(0, 1.05) # 发射率范围0-1.05（留出余量） +plt.xlim(wl_min, wl_max) + +# 保存图片（高分辨率） +plt.tight_layout() +plt.savefig('PDMS_emissivity_spectrum.png', dpi=300, bbox_inches='tight') +plt.show() + +# ----------------------------- +# 5. 输出关键波段（8-13μm）的平均发射率（若数据覆盖该波段） +# ----------------------------- +if wl_min <= 13 and wl_max >= 8: + print("=== 8-13 μm 大气窗口平均发射率 ===") + wl_window = np.linspace(8, 13, 500) # 大气窗口内的波长点 + for d in thicknesses: + n_window = cs_n(wl_window) + k_window = cs_k(wl_window) + epsilon_window = thin_film_emissivity(n_window, k_window, d, wl_window) + avg_epsilon = np.mean(epsilon_window) + print(f"厚度 {d} μm: 平均发射率 = {avg_epsilon:.4f}") +else: + print("数据未覆盖8-13μm大气窗口，跳过该波段平均发射率计算。") \ No newline at end of file