2121212

这篇博客讲述了作者对数学的热爱,认为数学是一种强大的逻辑工具,能锻炼思维并解决实际问题。数学在各个学科中都有应用,随着科技的发展,其重要性日益凸显。尽管学习数学具有挑战性,但努力和毅力是掌握它的关键。数学的不断发展也在推动科技进步。
部署运行你感兴趣的模型镜像

私は勉強していた科目の中で、一番好きなのは数学だ。数学は強力な論理を備えたツールで人々の思考能力を訓練することができる。それは私たちの思考をより鋭くすることができる。また、いくつかの実際的な問題を解決するのにも役立つ。数学は基本科目だ。言語科目を除いて、数学は基本的に他の科目で使用される。数学は科学のすべての分野にも適用できる。数学はすべての科目の母だとよく言われる。

 

 今、数学は急速に発展している。科学技術の発展において、数学の助けによってのみ解決することができるいくつかの問題が現れ続けている。逆にそれを通して数学も速くに発展している。

 

 ただし、数学を勉強しているのは簡単じゃない。発達な知力が必要だ。数学の試験に失敗した子供がいっぱいだが簡単に対処できた子供もいる。その原因は多分知力かもしれない。しかし、数学をマスターする上で最も重要なことは自分の努力だと思う。ある人は非常に賢くないが、勤勉を通してそれを習得することができる。数え切れないほどの事実がこれを証明している。数学は挑戦だがそれは好きな原因だ。

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Stable-Diffusion-3.5

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Stable Diffusion 3.5 (SD 3.5) 是由 Stability AI 推出的新一代文本到图像生成模型,相比 3.0 版本,它提升了图像质量、运行速度和硬件效率

Variables = "x", "T", "P", "N", "Y", "r" 0.0000000E+00 1.0000000E+03 5.0000000E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 2.0202020E-02 1.0000000E+03 4.9898375E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 4.0404040E-02 1.0000000E+03 4.9795496E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 6.0606062E-02 1.0000000E+03 4.9691359E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 8.0808081E-02 1.0000000E+03 4.9585922E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 1.0101010E-01 1.0000000E+03 4.9479172E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 1.2121212E-01 1.0000000E+03 4.9371070E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 1.4141414E-01 1.0000000E+03 4.9261602E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 1.6161616E-01 1.0000000E+03 4.9150742E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 1.8181819E-01 1.0000000E+03 4.9038465E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 2.0202020E-01 1.0000000E+03 4.8924727E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 2.2222222E-01 1.0000000E+03 4.8809523E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 2.4242425E-01 1.0000000E+03 4.8692809E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 2.6262626E-01 1.0000000E+03 4.8574566E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 2.8282827E-01 1.0000000E+03 4.8454746E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 3.0303031E-01 1.0000000E+03 4.8333336E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 3.2323232E-01 1.0000000E+03 4.8210289E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 3.4343433E-01 1.0000000E+03 4.8085586E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 3.6363637E-01 1.0000000E+03 4.7959184E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 3.8383839E-01 1.0000000E+03 4.7831051E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 4.0404040E-01 1.0000000E+03 4.7701148E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 4.2424244E-01 1.0000000E+03 4.7569445E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 4.4444445E-01 1.0000000E+03 4.7435898E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 4.6464646E-01 1.0000000E+03 4.7300473E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 4.8484850E-01 1.0000000E+03 4.7163125E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 5.0505048E-01 1.0000000E+03 4.7023812E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 5.2525252E-01 1.0000000E+03 4.6882492E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 5.4545456E-01 1.0000000E+03 4.6739133E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 5.6565654E-01 1.0000000E+03 4.6593668E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 5.8585858E-01 1.0000000E+03 4.6446074E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 6.0606062E-01 1.0000000E+03 4.6296297E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 6.2626261E-01 1.0000000E+03 4.6144281E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 6.4646465E-01 1.0000000E+03 4.5989980E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 6.6666669E-01 1.0000000E+03 4.5833336E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 6.8686867E-01 1.0000000E+03 4.5674297E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 7.0707071E-01 1.0000000E+03 4.5512820E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 7.2727275E-01 1.0000000E+03 4.5348836E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 7.4747473E-01 1.0000000E+03 4.5182293E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 7.6767677E-01 1.0000000E+03 4.5013121E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 7.8787881E-01 1.0000000E+03 4.4841266E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00 8.0808079E-01 Infinity Infinity Infinity NaN NaN 8.2828283E-01 NaN NaN NaN NaN 0.0000000E+00 8.4848487E-01 NaN NaN NaN NaN 0.0000000E+00 8.6868685E-01 NaN NaN NaN NaN 0.0000000E+00 8.8888890E-01 NaN NaN NaN NaN 0.0000000E+00 9.0909094E-01 NaN NaN NaN NaN 0.0000000E+00 9.2929292E-01 NaN NaN NaN NaN 0.0000000E+00 9.4949496E-01 NaN NaN NaN NaN 0.0000000E+00 9.6969700E-01 NaN NaN NaN NaN 0.0000000E+00 9.8989898E-01 NaN NaN NaN NaN 0.0000000E+00 1.0101010E+00 NaN NaN NaN NaN 0.0000000E+00 1.0303030E+00 NaN NaN NaN NaN 0.0000000E+00 1.0505050E+00 NaN NaN NaN NaN 0.0000000E+00 1.0707071E+00 NaN NaN NaN NaN 0.0000000E+00 1.0909091E+00 NaN NaN NaN NaN 0.0000000E+00 1.1111112E+00 NaN NaN NaN NaN 0.0000000E+00 1.1313131E+00 NaN NaN NaN NaN 0.0000000E+00 1.1515151E+00 NaN NaN NaN NaN 0.0000000E+00 1.1717172E+00 NaN NaN NaN NaN 0.0000000E+00 1.1919192E+00 NaN NaN NaN NaN 0.0000000E+00 1.2121212E+00 NaN NaN NaN NaN 0.0000000E+00 1.2323233E+00 NaN NaN NaN NaN 0.0000000E+00 1.2525252E+00 NaN NaN NaN NaN 0.0000000E+00 1.2727273E+00 NaN NaN NaN NaN 0.0000000E+00 1.2929293E+00 NaN NaN NaN NaN 0.0000000E+00 1.3131313E+00 NaN NaN NaN NaN 0.0000000E+00 1.3333334E+00 NaN NaN NaN NaN 0.0000000E+00 1.3535353E+00 NaN NaN NaN NaN 0.0000000E+00 1.3737373E+00 NaN NaN NaN NaN 0.0000000E+00 1.3939394E+00 NaN NaN NaN NaN 0.0000000E+00 1.4141414E+00 NaN NaN NaN NaN 0.0000000E+00 1.4343435E+00 NaN NaN NaN NaN 0.0000000E+00 1.4545455E+00 NaN NaN NaN NaN 0.0000000E+00 1.4747474E+00 NaN NaN NaN NaN 0.0000000E+00 1.4949495E+00 NaN NaN NaN NaN 0.0000000E+00 1.5151515E+00 NaN NaN NaN NaN 0.0000000E+00 1.5353535E+00 NaN NaN NaN NaN 0.0000000E+00 程序输出结果如上,修改程序module constants implicit none ! 物理常数 real, parameter :: pi = 3.141592653589793 real, parameter :: R_univ = 8.314462618 ! 通用气体常数 [J/(mol·K)] real, parameter :: k_B = 1.380649e-23 ! 玻尔兹曼常数 [J/K] real, parameter :: N_A = 6.02214076e23 ! 阿伏伽德罗常数 [1/mol] ! 水物性参数 real, parameter :: M_H2O = 0.018015 ! 水的摩尔质量 [kg/mol] real, parameter :: rho_l = 1000.0 ! 液态水密度 [kg/m³] real, parameter :: sigma_H2O = 0.072 ! 表面张力 [N/m] real, parameter :: h_fg = 2.257e6 ! 汽化潜热 [J/kg] real, parameter :: cp_v = 1410.0 ! 水蒸气比热 [J/(kg·K)] ! 发动机参数 real, parameter :: De = 0.2 ! 喷口直径 [m] real, parameter :: T0 = 1000.0 ! 喷口温度 [K] real, parameter :: P0 = 50000.0 ! 喷口压力 [Pa] real, parameter :: U0 = 2000.0 ! 喷口速度 [m/s] real, parameter :: X_H2O = 0.22 ! 水蒸气摩尔分数 ! 数值参数 integer, parameter :: nx = 100 ! 空间网格数 integer, parameter :: nt = 1000 ! 时间步数 real, parameter :: dt = 1e-5 ! 时间步长 [s] real, parameter :: L_domain = 10.0 * De ! 计算域长度 [m] ! 共享变量 real, allocatable :: P_g(:) ! 压力场 end module constants program condensation_model use constants implicit none ! 场变量定义 real :: x(nx), dx real :: T_g(nx), U_g(nx), rho_g(nx) real :: N_d(nx), Y_d(nx), r_d(nx) ! 液滴数密度、质量分数、半径 real :: m_v(nx), J_nuc(nx), dr_dt(nx) ! 凝结速率、成核率、半径增长率 ! 辅助变量 real :: S(nx), r_c(nx), P_sat(nx) integer :: i, t_step ! 分配共享数组 allocate(P_g(nx)) ! 初始化网格 dx = L_domain / (nx - 1) do i = 1, nx x(i) = (i - 1) * dx end do ! 初始化流场 (简化线性分布) do i = 1, nx P_g(i) = P0 * (1.0 - 0.8 * x(i)/L_domain) T_g(i) = T0 * (1.0 - 0.6 * x(i)/L_domain) U_g(i) = U0 * (1.0 - 0.3 * x(i)/L_domain) rho_g(i) = P_g(i) / (287.0 * T_g(i)) ! 空气气体常数 end do ! 初始化液相变量 N_d = 0.0 Y_d = 0.0 r_d = 0.0 ! 时间迭代循环 do t_step = 1, nt ! 计算过饱和比和临界半径 call calculate_saturation_ratio(P_g, T_g, S, P_sat, r_c) ! 初始化成核和生长参数 J_nuc = 0.0 dr_dt = 0.0 ! 应用Schmidt-Appleman冷凝判据 (显式循环代替where) do i = 1, nx if (S(i) > 1.0) then call nucleation_model_element(T_g(i), rho_g(i), S(i), r_c(i), J_nuc(i)) call droplet_growth_model_element(T_g(i), rho_g(i), r_d(i), r_c(i), S(i), dr_dt(i)) end if end do ! 计算凝结质量速率 do i = 1, nx if (r_d(i) > 0.0) then m_v(i) = 4.0 * pi * r_d(i)**2 * rho_l * dr_dt(i) * N_d(i) else m_v(i) = 0.0 endif end do ! 更新液相控制方程 call update_liquid_phase(N_d, Y_d, r_d, J_nuc, m_v, dr_dt, U_g, dx) ! 更新气相控制方程 call update_gas_phase(T_g, P_g, U_g, rho_g, m_v, dx) ! 输出数据 if (mod(t_step, 100) == 0) then call output_data(t_step, x, T_g, P_g, N_d, Y_d, r_d) end if end do ! 输出最终结果 call output_data(nt, x, T_g, P_g, N_d, Y_d, r_d) deallocate(P_g) contains ! 计算饱和比和临界半径 subroutine calculate_saturation_ratio(P, T, S, P_sat, r_c) real, intent(in) :: P(:), T(:) real, intent(out) :: S(:), P_sat(:), r_c(:) integer :: i do i = 1, nx P_sat(i) = 611.0 * exp(5423.0 * (1.0/273.0 - 1.0/T(i))) ! 简化Antoine方程 S(i) = (X_H2O * P(i)) / P_sat(i) r_c(i) = merge(2.0 * sigma_H2O / (rho_l * (R_univ/M_H2O) * T(i) * log(S(i))), & 1e-9, S(i) > 1.0) end do end subroutine ! 单元素成核模型 subroutine nucleation_model_element(T, rho_g, S, r_c, J_nuc) use constants, only: pi, sigma_H2O, k_B real, intent(in) :: T, rho_g, S, r_c real, intent(out) :: J_nuc real :: A, B, DeltaG if (S > 1.0) then DeltaG = 4.0 * pi * r_c**2 * sigma_H2O / 3.0 A = 1e30 ! 指前因子 B = 4.0 * pi * r_c**2 * sigma_H2O / (3.0 * k_B * T) J_nuc = A * exp(-B) else J_nuc = 0.0 end if end subroutine ! 单元素液滴生长模型 subroutine droplet_growth_model_element(T, rho_g, r, r_c, S, dr_dt) use constants, only: M_H2O, R_univ, rho_l, h_fg, sigma_H2O, pi, P_g real, intent(in) :: T, rho_g, r, r_c, S real, intent(out) :: dr_dt real :: lambda_v, Kn, Pr_v, T_sat if (S > 1.0 .and. r > 0.0) then lambda_v = 0.026 ! 导热系数 Kn = sqrt(pi * M_H2O / (2.0 * R_univ * T)) / r Pr_v = 0.71 ! 普朗特数 T_sat = 373.0 - (P_g(i) - 101325.0) * 0.00025 ! 简化计算 dr_dt = lambda_v * (T_sat - T) * (1.0 - r_c/r) & / (rho_l * h_fg * r * (1.0 + 3.78*(1.0 - 0.82*Kn)/Pr_v * Kn)) else dr_dt = 0.0 end if end subroutine ! 更新液相变量 subroutine update_liquid_phase(N_d, Y_d, r_d, J_nuc, m_v, dr_dt, U, dx) use constants, only: dt, rho_l, pi real, intent(inout) :: N_d(:), Y_d(:), r_d(:) real, intent(in) :: J_nuc(:), m_v(:), dr_dt(:), U(:), dx integer :: i do i = 2, nx-1 ! 数密度守恒 N_d(i) = N_d(i) + dt*(J_nuc(i) - U(i)*(N_d(i)-N_d(i-1))/dx) ! 质量分数守恒 Y_d(i) = Y_d(i) + dt*(m_v(i)/rho_l - U(i)*(Y_d(i)-Y_d(i-1))/dx) ! 更新液滴半径 if (N_d(i) > 0.0) then r_d(i) = (3.0 * Y_d(i) / (4.0 * pi * rho_l * N_d(i)))**(1.0/3.0) else r_d(i) = 0.0 end if end do end subroutine ! 更新气相变量 subroutine update_gas_phase(T, P, U, rho, m_v, dx) use constants, only: dt, h_fg, cp_v real, intent(inout) :: T(:), P(:), U(:), rho(:) real, intent(in) :: m_v(:), dx integer :: i do i = 2, nx-1 ! 连续方程 rho(i) = rho(i) - dt * m_v(i) ! 动量方程 U(i) = U(i) - dt * U(i) * (U(i)-U(i-1))/dx - dt*(P(i)-P(i-1))/(dx*rho(i)) ! 能量方程 T(i) = T(i) - dt * U(i) * (T(i)-T(i-1))/dx + dt * m_v(i) * h_fg / (rho(i)*cp_v) ! 状态方程 P(i) = rho(i) * 287.0 * T(i) end do end subroutine ! 数据输出 subroutine output_data(step, x, T, P, N, Y, r) integer, intent(in) :: step real, intent(in) :: x(:), T(:), P(:), N(:), Y(:), r(:) character(len=50) :: filename integer :: i write(filename, '(a,i6.6,a)') 'output_', step, '.dat' open(unit=10, file=filename, status='replace') write(10, '(A)') 'Variables = "x", "T", "P", "N", "Y", "r"' do i = 1, nx write(10, '(6ES16.7)') x(i), T(i), P(i), N(i), Y(i), r(i) end do close(10) end subroutine end program condensation_model
06-03
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