def mu_shtrih_0(Atom_weight, z):
x0 = x_0(Atom_weight)
x1 = x_0(Atom_weight + Atom_weight * 0.1)
PHI_0 = progonka(T, 3 * Atom_weight / x0 / 4 / pi / Na / a_0**3, Atom_weight, z)
mu0 = PHI_0[len(PHI_0) - 1]
PHI_1 = progonka(T, 3 * Atom_weight / x1 / 4 / pi / Na / a_0**3, Atom_weight, z)
mu1 = PHI_1[len(PHI_1) - 1]
return (mu1 - mu0) / (x1 - x0)
def delta_P(T, rho):
HI = hi(T, rho)
PHI = progonka(T, rho, 1, 1)
#print("Hi_n = ", HI[N], "len = ", len(HI))
return 8 / (3 * pi**4) * (2 / pi)**(1 / 3) * (
2**(7 / 6) * 3**(2 / 3) * pi**(-5 / 3) * theta(T)**(1 / 2) *
volume(rho, 1)**(2 / 3) *
PHI[0]**2)**(-4 / 3) * (HI[N] * integral_1_2(PHI[N]) + igrek(PHI[N]))
def S(T, rho, Atom_weight, z):
PHI = progonka(T, rho, 1, 1)
# ВСПОМ. ИНТЕГРАЛ
def S_sub_int(T, rho):
max_i = 2
while (PHI[max_i] / X[max_i] >= 10**6) and (max_i < N):
max_i += 1
if max_i % 2 != 0:
max_i -= 1
integr_int_1 = [Z[i] for i in range(max_i + 1)]
integr_int_2 = [Z[i] for i in range(max_i, N + 1)]
integr_func_1 = 0
integr_func_2 = [
5 / 3 * integral_3_2(PHI[i] / X[i]) * X[i]**2 -
PHI[i] / X[i] * integral_1_2(PHI[i] / X[i]) * X[i]**2
for i in range(max_i, N + 1)
]
#integr_res_1 = integrate.simps(integr_func_1, integr_int_1)
integr_res_2 = integrate.simps(integr_func_2, integr_int_2)
return integr_res_2
#ЭЛЕКТРОННАЯ ЭНТРОПИЯ
def S_e(T, rho):
const = 4 * 2**(1 / 2) * theta(T)**(3 / 2) * r_0(rho, 1)**3 / pi
#print(const * S_sub_int(T, rho))
return const * S_sub_int(T, rho)
##ПОЛНАЯ ЭНТРОПИЯ
def S(T, rho):
return 0.9648 * 10**2 / Atom_weight * (S_e(T, rho) + 3 / 2 * log(
1836 * Atom_weight * theta(T) * volume(rho, 1)**
(2 / 3) / 2 / pi, e) + 5 / 3)
return S(T, rho)
def S_integrals(T, rho):
HI = hi_function(T, rho)
PHI = progonka(T, rho)
max_i = 0
for i in range(1, N + 1):
if PHI[i] / X[i] >= 10**6:
max_i = i
subfunc1 = [0] * (max_i + 1)
subfunc2 = []
subx = [0] * (max_i + 1)
for i in range(max_i + 1):
subx[i] = X[i]
nadx = []
for i in range(max_i + 1, N + 1):
nadx.append(X[i])
for i in range(max_i + 1):
subfunc1[i] = 4 / 3 * (22 * PHI[i]**2 * Z[i] + PHI[i]**(3 / 2) * HI[i])
for i in range(max_i + 1, N + 1):
subfunc2.append(X[i] * HI[i] * integral_1_2(PHI[i] / X[i]) +
4 * Z[i]**2 * igrek(PHI[i] / X[i]))
return scipy.integrate.trapz(subfunc1, subx) + scipy.integrate.trapz(
subfunc2, nadx)
def P(T, rho, Atom_weight, z):
PHI = progonka(T, rho, Atom_weight, z)
#return (P_e(T, rho) + theta(T) / volume(rho))
return 32 / (3 * pi**3) * (2 / pi)**(2 / 3) * (
2**(7 / 6) * 3**(2 / 3) * pi**(-5 / 3) * theta(T)**(1 / 2) *
volume(rho, 1)**(2 / 3) * (PHI[0])**2)**(-5 / 3) * integral_3_2(PHI[N])
for j in range(2, m + 1):
TABLE_P[0][j] = TABLE_P[0][1] + (j - 1) * 0.01
for i in range(2, n + 1):
TABLE_P[i][0] = TABLE_P[1][0] + (i - 1) * (-0.02)
for i in range(1, n + 2):
for j in range(1, m + 1):
#print(10 ** TABLE_E[i][0], 10 ** TABLE_E[0][j])
found_rho = mixture_calculation(10**TABLE_E[i][0], 10**TABLE_E[0][j],
mixture)
for k in range(len(mixture)):
T_h = 10**TABLE_E[i][0] / mixture[k]["Z"]**(4 / 3)
rho_h = 10**TABLE_E[0][j] * Na * 11.19 * 1.4818 * 10**(
-25) / mixture[k]["Atom_weight"] / mixture[k]["Z"]
PHI = progonka(T_h, rho_h, 1, 1)
TABLE_P[i][j] += P(T_h, rho_h, PHI) * mixture[k]["Z"]**(
10 / 3) * mixture[k]["amount"] / nuclear_amount
TABLE_E[i][j] += Energy(T_h, rho_h, 1, 1, PHI) * mixture[k]["Z"]**(
7 / 3) * mixture[k]["amount"] / Weight
print(i, j)
f = open('energy_sio2.txt', 'w')
for i in range(len(TABLE_E)):
for j in range(len(TABLE_E[i])):
f.write(str(TABLE_E[i][j]))
f.write(" ")
f.write("\n")
f = open('pressure_sio2.txt', 'w')
for i in range(len(TABLE_P)):
def delta_mu(T, rho):
HI = hi(T, rho)
PHI = progonka(T, rho)
return (2 * theta(T))**(1 / 2) / (6 * math.pi) * (
1 / 2 * integral_minus_1_2(PHI[N]) + HI[N])
def delta_P(T, rho):
HI = hi_function(T, rho)
PHI = progonka(T, rho)
return theta(T)**2 / (3 * math.pi**3) * (HI[N] * integral_1_2(PHI[N]) +
igrek(PHI[N]))
def hi(T, rho):
PHI = progonka(T, rho)
PHI_2N = progonka_2N(T, rho)
Y = [0] * (N + 1)
Z = [0] * (N + 1)
h = [0] * (N + 1)
k1 = [0] * (N + 1)
q1 = [0] * (N + 1)
k2 = [0] * (N + 1)
q2 = [0] * (N + 1)
k3 = [0] * (N + 1)
q3 = [0] * (N + 1)
k4 = [0] * (N + 1)
q4 = [0] * (N + 1)
def priblizhenie_hi(sigma):
const = 4 * (2 * theta(T))**0.5 / pi * (r_0(rho))**2
Y[N] = sigma
Z[N] = sigma
for i_iter in range(N, 1, -1):
h[i_iter] = (-2 * i_iter + 1) / N**2
k1[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI[i_iter] / X[i_iter]) * Y[i_iter] +
X[i_iter] * igrek_sht(PHI[i_iter] / X[i_iter]))
q1[i_iter] = h[i_iter] * Z[i_iter]
#k2[i_iter] = h[i_iter] * const * (integral_sht_1_2(((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2)) * (Y[i_iter] + q1[i_iter] / 2) + ((X[i_iter] + X[i_iter - 1]) / 2) * igrek_sht((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2))
k2[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI_2N[2 * i_iter - 1] / X[i_iter]) *
(Y[i_iter] + q1[i_iter] / 2) +
X[i_iter] * igrek_sht(PHI_2N[2 * i_iter - 1] / X[i_iter]))
q2[i_iter] = h[i_iter] * (Z[i_iter] + k1[i_iter] / 2)
#k3[i_iter] = h[i_iter] * const * (integral_sht_1_2(((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2)) * (Y[i_iter] + q2[i_iter] / 2) + ((X[i_iter] + X[i_iter - 1]) / 2) * igrek_sht((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2))
k3[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI_2N[2 * i_iter - 1] / X[i_iter]) *
(Y[i_iter] + q2[i_iter] / 2) +
X[i_iter] * igrek_sht(PHI_2N[2 * i_iter - 1] / X[i_iter]))
q3[i_iter] = h[i_iter] * (Z[i_iter] + k2[i_iter] / 2)
k4[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI[i_iter - 1] / X[i_iter - 1]) *
(Y[i_iter] + q3[i_iter]) +
X[i_iter - 1] * igrek_sht(PHI[i_iter - 1] / X[i_iter - 1]))
q4[i_iter] = h[i_iter] * (Z[i_iter] + k3[i_iter])
Y[i_iter - 1] = Y[i_iter] + (q1[i_iter] + 2 * q2[i_iter] +
2 * q3[i_iter] + q4[i_iter]) / 6
Z[i_iter - 1] = Z[i_iter] + (k1[i_iter] + 2 * k2[i_iter] +
2 * k3[i_iter] + k4[i_iter]) / 6
Z[0] = Z[1] + 1 / 3 * (Z[1] - Z[2])
i_iter = 1
k1[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI[i_iter] / X[i_iter]) * Y[i_iter] +
X[i_iter] * igrek_sht(PHI[i_iter] / X[i_iter]))
q1[i_iter] = h[i_iter] * Z[i_iter]
k2[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI_2N[2 * i_iter - 1] / X[i_iter]) *
(Y[i_iter] + q1[i_iter] / 2) +
X[i_iter] * igrek_sht(PHI_2N[2 * i_iter - 1] / X[i_iter]))
#k2[i_iter] = h[i_iter] * const * (integral_sht_1_2(((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2)) * (Y[i_iter] + q1[i_iter] / 2) + ((X[i_iter] + X[i_iter - 1]) / 2) * igrek_sht((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2))
q2[i_iter] = h[i_iter] * (Z[i_iter] + k1[i_iter] / 2)
k3[i_iter] = h[i_iter] * const * (
integral_sht_1_2(PHI_2N[2 * i_iter - 1] / X[i_iter]) *
(Y[i_iter] + q2[i_iter] / 2) +
X[i_iter] * igrek_sht(PHI_2N[2 * i_iter - 1] / X[i_iter]))
#k3[i_iter] = h[i_iter] * const * (integral_sht_1_2(((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2)) * Y[i_iter] + q2[i_iter] / 2) + ((X[i_iter] + X[i_iter - 1]) / 2) * igrek_sht((PHI[i_iter] + PHI[i_iter - 1]) / 2) / ((X[i_iter] + X[i_iter - 1]) / 2))
q3[i_iter] = h[i_iter] * (Z[i_iter] + k2[i_iter] / 2)
q4[i_iter] = h[i_iter] * (Z[i_iter] + k3[i_iter])
Y[i_iter - 1] = Y[i_iter] + (q1[i_iter] + 2 * q2[i_iter] +
2 * q3[i_iter] + q4[i_iter]) / 6
return Y
def sigma_2(sigma_0, sigma_1):
HI0_0 = priblizhenie_hi(sigma_0)[0]
HI0_1 = priblizhenie_hi(sigma_1)[0]
print('sigma = ',
sigma_1 - (sigma_1 - sigma_0) * HI0_1 / (HI0_1 - HI0_0))
return sigma_1 - (sigma_1 - sigma_0) * HI0_1 / (HI0_1 - HI0_0)
return priblizhenie_hi(-6.30651686)
import math
import numpy as np
import matplotlib.pyplot as plt
from math import gamma
from Changing_parameters import N, T, rho
from Tabular_values import a_0, Na, E_h
from Dirak_functions import integral_1_2, integral_3_2, integral_minus_1_2
from Atom_parameters import Atom_weight, z
from Cell import z_0, r_0, volume, theta, eta
from working_progonka import progonka, X
PHI = progonka(T, rho, 1, 1)
RESULT_V = [0] * (N + 1)
R = []
F = [0] * (N + 1)
V = [0] * (N + 1)
for i in range(N + 1):
R.append(X[i] * r_0(rho))
mu = PHI[N]
for i in range(N + 1):
if i == 0:
F[0] = z / theta(T)
else:
F[i] = PHI[i] / X[i] * R[i]
for i in range(1, N + 1):
if i == N:
V[N] = 0
else:
V[i] = F[i] / R[i] * theta(T) - mu
def mu(x, Atom_weight, z):
PHI = progonka(T, 3 * Atom_weight / x / 4 / pi / Na / a_0**3, Atom_weight, z)
return PHI[len(PHI) - 1]
def mu_0(Atom_weight, z):
PHI = progonka(T, rho, Atom_weight, z)
return PHI[len(PHI) - 1]
def Energy(T, rho, z, Atom_weight):
PHI = progonka(T, rho, Atom_weight, z)
# ВСПОМ. ИНТЕГРАЛ
def E_sub_int(T, rho):
max_i = 2
while (PHI[max_i] / X[max_i] >= 10**6) and (max_i < N):
max_i += 1
if max_i % 2 != 0:
max_i -= 1
integr_int_1 = [Z[i] for i in range(max_i + 1)]
integr_int_2 = [Z[i] for i in range(max_i, N + 1)]
#integr_int_2 = [X[i] for i in range(max_i, N + 1)]
integr_func_1 = [4/5 * PHI[i]**2.5 for i in range(max_i + 1)]
integr_func_2 = [2 * Z[i]**5 * integral_3_2(PHI[i] / Z[i]**2) for i in range(max_i, N + 1)]
integr_res_1 = integrate.simps(integr_func_1, integr_int_1)
integr_res_2 = integrate.simps(integr_func_2, integr_int_2)
return integr_res_1 + integr_res_2
const = 2**(0.5) / (pi**2) * (theta(T)**2.5) * (4/3) * pi * r_0(rho, 1)**3
# КИНЕТИЧЕСКАЯ ЭНЕРГИЯ
#def E_k(T, rho):
# #return (3 * 2**0.5 / pi**2) * volume(rho) * theta(T)**2.5 * E_sub_int(T, rho)
#
# return 3 * const * E_sub_int(T, rho)
## ПОТЕНЦИАЛЬНАЯ ЭНЕРГИЯ
#def E_p(T, rho):
# #return (2 * 2**0.5 / pi**2) * volume(rho) * theta(T)**2.5 * (integral_3_2(-eta(T, rho)) - 3 * E_sub_int(T, rho))
# return 2 * const * (integral_3_2(-eta(T, rho, 1, 1)) - 3 * E_sub_int(T, rho))
# Проверяем virial theorem
#print(2 * E_k(Temperature_system, rho_system) + E_p(Temperature_system, rho_system))
#print(3 * P_e(Temperature_system, rho_system) * volume(rho_system))
## ВНУТРЕННЯЯ ЭНЕРГИЯ ЭЛЕКТРОНОВ
#def E_e(T, rho):
# return E_k(T, rho) + E_p(T, rho)
#
# ПОЛНАЯ ЭНЕРГИЯ
def E(T, rho):
#return E_e(T, rho) - E_0 + 3/2 * theta(T)
return const * (2 * integral_3_2(-eta(T, rho, 1, 1)) - 3*E_sub_int(T, rho)) + 0.76874512421364*1**(7/3)
return E(T , rho)