def d(s=s_current):
x()
for i in range(1, N):
D[i] = const * (X[i + 1] - X[i - 1]) * (
((X[i] / 2) * integral_1_2(PHI_S[s_current][i] / X[i]) -
PHI_S[s_current][i] / 4 *
integral_minus_1_2(PHI_S[s_current][i] / X[i])))
def beta(s=s_current):
x()
for i in range(N - 1, -1, -1):
if i == N - 1:
BETA[i] = -h(N)**2 / 2 * const * (
integral_1_2(PHI_S[s_current][N]) - PHI_S[s_current][i] / 2 *
integral_minus_1_2(PHI_S[s_current][N])) * ALPHA[N - 1]
else:
BETA[i] = (D[i + 1] - C[i + 1] * BETA[i + 1]) / (
B[i + 1] + C[i + 1] * ALPHA[i + 1])
def progonka(s):
s_current = 0
while s_current < s:
for i in range(1, N):
B[i] = -A[i] - C[i] - const / 4 * (X[i + 1] -
X[i - 1]) * integral_minus_1_2(
PHI_S[s_current][i] / X[i])
D[i] = const * (X[i + 1] - X[i - 1]) * (
(X[i] / 2 * integral_1_2(PHI_S[s_current][i] / X[i])) -
PHI_S[s_current][i] / 4 *
integral_minus_1_2(PHI_S[s_current][i] / X[i]))
for i in range(N - 1, -1, -1):
if i == N - 1:
ALPHA[i] = 1 / (1 - h(N) + h(N)**2 / 4 * const *
integral_minus_1_2(PHI_S[s_current][N]))
BETA[i] = -h(N)**2 / 2 * const * (
integral_1_2(PHI_S[s_current][N]) - PHI_S[s_current][i] /
2 * integral_minus_1_2(PHI_S[s_current][N])) * ALPHA[N - 1]
else:
ALPHA[i] = -A[i + 1] / (B[i + 1] + C[i + 1] * ALPHA[i + 1])
BETA[i] = (D[i + 1] - C[i + 1] * BETA[i + 1]) / (
B[i + 1] + C[i + 1] * ALPHA[i + 1])
# ИСКОМОЕ УРАВНЕНИЕ
for i in range(N + 1):
if i == 0:
Y[i] = z / (theta(T) * r_0(rho))
else:
Y[i] = ALPHA[i - 1] * Y[i - 1] + BETA[i - 1]
for i in range(N + 1):
RESULT[s_current][i] = PHI_S[s_current][i] * theta(T)
for i in range(N + 1):
PHI_S[s_current + 1][i] = Y[i]
s_current += 1
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_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 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
def progonka_2N(T, rho):
# константа а в уравнении
const_a = 4 * (2 * theta(T))**0.5 / pi * (r_0(rho))**2
PHI_S = [[0 for i in range(N + 1)] for j in range(s + 1)]
RESULT = [[0 for i in range(N + 1)] for j in range(s)]
for i in range(N + 1):
if i == 0:
PHI_S[0][0] = z / (theta(T) * r_0(rho))
else:
PHI_S[0][i] = z / (theta(T) *
r_0(rho)) * (1 - 3 / 2 * U[i] + 1 / 2 *
(U[i])**3) - eta_0(T, rho) * U[i]
s_current = 0
while s_current < s:
B = [0] + [
-4 * U[i] * (1 + const_a * h_N**2 * U[i]**2 *
integral_minus_1_2(PHI_S[s_current][i] / U[i]**2))
for i in range(1, N)
]
D = [0] + [
4 * const_a * h_N**2 * U[i]**3 *
(2 * U[i]**2 * integral_1_2(PHI_S[s_current][i] / U[i]**2) -
PHI_S[s_current][i] *
integral_minus_1_2(PHI_S[s_current][i] / U[i]**2))
for i in range(1, N)
]
ALPHA = [0] * (N + 1)
BETA = [0] * (N + 1)
for i in range(N - 1, -1, -1):
if i == N - 1:
ALPHA[i] = 1 / (
1 - 2 * h_N + h_N**2 *
(1 + const_a * integral_minus_1_2(PHI_S[s_current][N])))
BETA[i] = -h_N**2 * const_a * (
2 * integral_1_2(PHI_S[s_current][N]) - PHI_S[s_current][i]
* integral_minus_1_2(PHI_S[s_current][N])) * ALPHA[N - 1]
else:
ALPHA[i] = -A[i + 1] / (B[i + 1] + C[i + 1] * ALPHA[i + 1])
BETA[i] = (D[i + 1] - C[i + 1] * BETA[i + 1]) / (
B[i + 1] + C[i + 1] * ALPHA[i + 1])
# ИСКОМОЕ УРАВНЕНИЕ
Y = [0] * (N + 1)
for i in range(N + 1):
if i == 0:
Y[i] = z / (theta(T) * r_0(rho))
else:
Y[i] = ALPHA[i - 1] * Y[i - 1] + BETA[i - 1]
for i in range(N + 1):
RESULT[s_current][i] = PHI_S[s_current][i] * theta(T)
for i in range(N + 1):
PHI_S[s_current + 1][i] = Y[i]
s_current += 1
PHI = [RESULT[8][i] / theta(T) for i in range(N + 1)]
return PHI
def z_0(T, rho, Atom_weight):
return 317.5 * Atom_weight * T**1.5 * 2 * integral_1_2(
-eta(T, rho)) / pi**0.5 / rho
def n_e_0():
return (const/(betta**1.5))*integral_1_2(betta*(Chem_potential_e()))
def n_e_full(i):
return (const / (betta ** 1.5))*integral_1_2(betta*(Chem_potential_e() - V(i)))
def rho_e(i):
return c1*integral_1_2((V(i)+Chem_potential_e())/theta(T))
def n_e_full1(i):
return (((2*theta(T))**1.5)/(2*(math.pi)**2))*integral_1_2((V(i)+Chem_potential_e())/theta(T))
def n_e_pribl():
return (((2*theta(T))**1.5)/(2*(math.pi)**2))*integral_1_2((Chem_potential_e())/theta(T))
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 n_e_full(r):
return (const/(betta**1.5))*integral_1_2(betta*(Chem_potential_e()-V_Ne_eff(r)))
def progonka(T, rho, Atom_weight, z):
# константа а в уравнении
const_a = 4 * (2 * theta(T))**0.5 / pi * (r_0(rho, Atom_weight))**2
PHI_S = [[0 for i in range(N + 1)] for j in range(s + 1)]
RESULT = [[0 for i in range(N + 1)] for j in range(s)]
for i in range(N + 1):
if i == 0:
PHI_S[0][0] = z / (theta(T) * r_0(rho, Atom_weight))
else:
PHI_S[0][i] = z / (theta(T) * r_0(rho, Atom_weight)) * (
1 - 3 / 2 * X[i] + 1 / 2 * (X[i])**3) - eta_0(T, rho) * X[i]
s_current = 0
while s_current < s:
B = [0] + [
-A[i] - C[i] - const_a / 4 * (X[i + 1] - X[i - 1]) *
integral_minus_1_2(PHI_S[s_current][i] / X[i])
for i in range(1, N)
]
D = [0] + [
const_a * (X[i + 1] - X[i - 1]) *
((X[i] / 2 * integral_1_2(PHI_S[s_current][i] / X[i])) -
PHI_S[s_current][i] / 4 *
integral_minus_1_2(PHI_S[s_current][i] / X[i]))
for i in range(1, N)
]
ALPHA = [0] * (N + 1)
BETA = [0] * (N + 1)
for i in range(N - 1, -1, -1):
if i == N - 1:
ALPHA[i] = 1 / (1 - h_N + h_N**2 / 4 * const_a *
integral_minus_1_2(PHI_S[s_current][N]))
BETA[i] = -h_N**2 / 2 * const_a * (
integral_1_2(PHI_S[s_current][N]) - PHI_S[s_current][i] /
2 * integral_minus_1_2(PHI_S[s_current][N])) * ALPHA[N - 1]
else:
ALPHA[i] = -A[i + 1] / (B[i + 1] + C[i + 1] * ALPHA[i + 1])
BETA[i] = (D[i + 1] - C[i + 1] * BETA[i + 1]) / (
B[i + 1] + C[i + 1] * ALPHA[i + 1])
# ИСКОМОЕ УРАВНЕНИЕ
Y = [0] * (N + 1)
for i in range(N + 1):
if i == 0:
Y[i] = z / (theta(T) * r_0(rho, Atom_weight))
else:
Y[i] = ALPHA[i - 1] * Y[i - 1] + BETA[i - 1]
for i in range(N + 1):
RESULT[s_current][i] = PHI_S[s_current][i] * theta(T)
for i in range(N + 1):
PHI_S[s_current + 1][i] = Y[i]
s_current += 1
PHI = [RESULT[8][i] / theta(T) for i in range(N + 1)]
##СТРОИМ ГРАФИК
#fig = plt.figure()
#for i in range(s):
# graph1 = plt.plot(X, PHI)
#plt.title("T = 0 keV")
#plt.grid(True)
#
#plt.xlabel('x')
#plt.ylabel('y(s)')
#plt.savefig('progonka1')
#plt.show()
return PHI
def int1_2(x):
if x>10**7:
return (x**1.5)*(2/3)
else:
return integral_1_2(x)
