diff --git a/examples/ReproducableCode/DoubleLayerCapacity/CompressibleValidationAnalyticalMethod.py b/examples/ReproducableCode/DoubleLayerCapacity/CompressibleValidationAnalyticalMethod.py
index db4b3e5726b0c28bfde61bd083054754a35c3809..992b84d9b4db907449a8c256d29ef76bf5c30c97 100644
--- a/examples/ReproducableCode/DoubleLayerCapacity/CompressibleValidationAnalyticalMethod.py
+++ b/examples/ReproducableCode/DoubleLayerCapacity/CompressibleValidationAnalyticalMethod.py
@@ -75,12 +75,13 @@ nR_m = nR_mol * NA * 1/(1e-3)# [1/m^3]
pR = 1.01325 * 1e+5 # [Pa]
LR = 20e-8
chi = 80 # [-]
-
+K_vec = ['incompressible', 50_000, 15_000, 1_500, 500] # Working
+# ! Not working: 100_000, 20_000
# Parameter and bcs for the electrolyte
Lambda2 = (k*T*epsilon0*(1+chi))/(e0**2 * nR_m * (LR)**2)
a2 = (pR)/(nR_m * k * T)
-K = 1_000#'incompressible'
kappa = 0
+K = 50_000
Molarity = 0.01
y_R = Molarity / nR_mol
z_A, z_C = -1.0, 1.0
@@ -103,26 +104,26 @@ phi_left_dimless = np.linspace(Vol_start, Volt_end, n_Volts) * e0/(k*T)
# Numerical calculations
# Solution vectors
-# y_A_num, y_C_num, y_S_num, phi_num, p_num, x_num = [], [], [], [], [], []
-# for i, phi_bcs in enumerate(phi_left_dimless):
-# y_A_, y_C_, phi_, p_, x_ = solve_System_4eq(phi_bcs, phi_right, p_right, z_A, z_C, y_R, y_R, K, Lambda2, a2, number_cells, solvation=kappa, refinement_style='hard_log', rtol=1e-4, max_iter=2500, return_type='Vector', relax_param=relax_param)
-# y_S_ = 1 - y_A_ - y_C_
-# y_A_num.append(y_A_)
-# y_C_num.append(y_C_)
-# y_S_num.append(y_S_)
-# phi_num.append(phi_)
-# p_num.append(p_)
-# x_num.append(x_)
+y_A_num, y_C_num, y_S_num, phi_num, p_num, x_num = [], [], [], [], [], []
+for i, phi_bcs in enumerate(phi_left_dimless):
+ y_A_, y_C_, phi_, p_, x_ = solve_System_4eq(phi_bcs, phi_right, p_right, z_A, z_C, y_R, y_R, K, Lambda2, a2, number_cells, solvation=kappa, refinement_style='hard_log', rtol=1e-4, max_iter=2500, return_type='Vector', relax_param=relax_param)
+ y_S_ = 1 - y_A_ - y_C_
+ y_A_num.append(y_A_)
+ y_C_num.append(y_C_)
+ y_S_num.append(y_S_)
+ phi_num.append(phi_)
+ p_num.append(p_)
+ x_num.append(x_)
-# Q_num = []
-# for j in range(len(phi_left_dimless)):
-# Q_num.append(Q_num_(y_A_num[j], y_C_num[j], n(p_num[j], K), x_num[j]))
-# Q_num = np.array(Q_num)
+Q_num = []
+for j in range(len(phi_left_dimless)):
+ Q_num.append(Q_num_(y_A_num[j], y_C_num[j], n(p_num[j], K), x_num[j]))
+Q_num = np.array(Q_num)
-# dx_ = phi_left_dimless[1] - phi_left_dimless[0] # [1/V], Assumption: phi^L is uniformly distributed
-# C_DL_num = (Q_num[1:] - Q_num[:-1])/dx_ # [µAs/cm³]
-# C_DL_num = np.array(C_DL_num)
-# C_dl_num = C_dl(Q_num, phi_left_dimless)
+dx_ = phi_left_dimless[1] - phi_left_dimless[0] # [1/V], Assumption: phi^L is uniformly distributed
+C_DL_num = (Q_num[1:] - Q_num[:-1])/dx_ # [µAs/cm³]
+C_DL_num = np.array(C_DL_num)
+C_dl_num = C_dl(Q_num, phi_left_dimless)
# Analytical calculations
# K = K_vec[0]
@@ -137,7 +138,7 @@ plt.figure()
# plt.plot(phi_left, Q_num[1] - Q_ana, label='Difference')
# plt.plot(phi_left_dimless, Q_num - Q_ana, label='Difference')
# plt.plot(phi_left_dimless, Q_num[1], label='Numerical')
-# plt.plot(phi_left_dimless, Q_num, label='Numerical')
+plt.plot(phi_left_dimless, Q_num, label='Numerical')
plt.plot(phi_left_dimless, Q_ana, label='Analytical')
plt.grid()
plt.legend()
@@ -150,7 +151,7 @@ plt.figure()
# plt.plot(Phi_pot_center(phi_left), C_DL_num[1] - C_DL_ana, label='Difference')
# plt.plot(Phi_pot_center(phi_left_dimless), C_DL_num - C_DL_ana, label='Difference')
# plt.plot(Phi_pot_center(phi_left_dimless), C_DL_num[1], label='Numerical')
-# plt.plot(Phi_pot_center(phi_left_dimless), C_DL_num, label='Numerical')
+plt.plot(Phi_pot_center(phi_left_dimless), C_DL_num, label='Numerical')
plt.plot(Phi_pot_center(phi_left_dimless), C_DL_ana, label='Analytical')
plt.grid()
plt.legend()
diff --git a/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py b/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py
index f23debe52dda6274fbd5bbe9e9b560982c320b66..cf633d74c996677331b7514f712ba88733078ea0 100644
--- a/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py
+++ b/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py
@@ -44,7 +44,7 @@ chi = 80 # [-]
Lambda2 = (k*T*epsilon0*(1+chi))/(e0**2 * nR_m * (LR)**2)
a2 = (pR)/(nR_m * k * T)
K = 'incompressible'
-kappa = 0
+kappa = 5
Molarity = 0.01
y_R = Molarity / nR_mol
z_A, z_C = -1.0, 1.0
@@ -61,7 +61,7 @@ rtol = 1e-4 # ! Change back to 1e-8
# phi^L domain
Vol_start = 0.1 # ! Change back to 0
Volt_end = 0.75
-n_Volts = 5#0
+n_Volts = 10#0
phi_left = np.linspace(Vol_start, Volt_end, n_Volts) * e0/(k*T)
@@ -99,7 +99,7 @@ C_DL_ana = C_dl(Q_ana, phi_left)
# Plotting
plt.figure()
# plt.plot(phi_left, Q_num - Q_ana, label='Difference')
-# plt.plot(phi_left, Q_num, label='Numerical')
+plt.plot(phi_left, Q_num, label='Numerical')
plt.plot(phi_left, Q_ana, label='Analytical')
plt.grid()
plt.legend()
@@ -110,7 +110,7 @@ plt.show()
plt.figure()
# plt.plot(Phi_pot_center(phi_left), C_DL_num - C_DL_ana, label='Difference')
-# plt.plot(Phi_pot_center(phi_left), C_dl_num, label='Numerical')
+plt.plot(Phi_pot_center(phi_left), C_dl_num, label='Numerical')
plt.plot(Phi_pot_center(phi_left), C_DL_ana, label='Analytical')
plt.grid()
plt.legend()
@@ -120,5 +120,5 @@ plt.tight_layout()
plt.show()
print('phi_left:', phi_left)
-print('Q_num:', Q_num)
+# print('Q_num:', Q_num)
print('Q_ana:', Q_ana)
\ No newline at end of file
diff --git a/examples/ReproducableCode/ValidationSimplifiedSystem.py b/examples/ReproducableCode/ValidationSimplifiedSystem.py
index 9d5c47de097d75288059fcb021f945aa1fed9fb4..dc925522852aded581e8aa0d6141a8ede0e603bf 100644
--- a/examples/ReproducableCode/ValidationSimplifiedSystem.py
+++ b/examples/ReproducableCode/ValidationSimplifiedSystem.py
@@ -22,7 +22,6 @@ del sys.path[0]
# Further imports
import matplotlib.pyplot as plt
import numpy as np
-import pandas as pd
# Define the parameters and boundary conditions
phi_left = 4.0
@@ -36,59 +35,11 @@ Lambda2 = 8.553e-6
a2 = 7.5412e-4
solvation = 15
number_cells = 1024#*4
-refinement_style = 'log'
+refinement_style = 'hard_log'
rtol = 1e-8
-# # Incompressible
-# K = 'incompressible'
-
-# # solve the complete system
-# y_A_4eq, y_C_4eq, phi_4eq, p_4eq, x_4eq = solve_System_4eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=solvation, relax_param=0.05, refinement_style='hard_log', return_type='Vector', max_iter=1_000, rtol=rtol)
-
-# # solve the simplified system
-# y_A_2eq, y_C_2eq, phi_2eq, p_2eq, x_2eq = solve_System_2eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=solvation, relax_param=0.05, refinement_style='hard_log', return_type='Vector', max_iter=1_000, rtol=rtol)
-
-# # Evaluate the difference
-# plt.figure()
-# # plt.plot(x_4eq, y_A_4eq, label='y_A_4eq')
-# # plt.plot(x_2eq, y_A_2eq, label='y_A_2eq')
-# plt.plot(x_4eq, y_A_4eq - y_A_2eq, label='y_A_4eq - y_A_2eq')
-# plt.grid()
-# plt.xlim(0, 0.05)
-# plt.legend()
-# plt.show()
-
-# plt.figure()
-# # plt.plot(x_4eq, y_C_4eq, label='y_C_4eq')
-# # plt.plot(x_2eq, y_C_2eq, label='y_C_2eq')
-# plt.plot(x_4eq, y_C_4eq - y_C_2eq, label='y_C_4eq - y_C_2eq')
-# plt.grid()
-# plt.xlim(0, 0.05)
-# plt.legend()
-# plt.show()
-
-# plt.figure()
-# # plt.plot(x_4eq, phi_4eq, label='phi_4eq')
-# # plt.plot(x_2eq, phi_2eq, label='phi_2eq')
-# plt.plot(x_4eq, phi_4eq - phi_2eq, label='phi_4eq - phi_2eq')
-# plt.grid()
-# plt.xlim(0, 0.05)
-# plt.legend()
-# plt.show()
-
-# plt.figure()
-# # plt.plot(x_4eq, p_4eq, label='p_4eq')
-# # plt.plot(x_2eq, p_2eq, label='p_2eq')
-# plt.plot(x_4eq, p_4eq - p_2eq, label='p_4eq - p_2eq')
-# plt.grid()
-# plt.xlim(0, 0.05)
-# plt.legend()
-# plt.show()
-
-
-
-# Compressible
-K = 10_000
+# Incompressible
+K = 'incompressible'
# solve the complete system
y_A_4eq, y_C_4eq, phi_4eq, p_4eq, x_4eq = solve_System_4eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=solvation, relax_param=0.05, refinement_style='hard_log', return_type='Vector', max_iter=1_000, rtol=rtol)
@@ -98,20 +49,20 @@ y_A_2eq, y_C_2eq, phi_2eq, p_2eq, x_2eq = solve_System_2eq(phi_left, phi_right,
# Evaluate the difference
plt.figure()
-plt.plot(x_4eq, y_A_4eq, label='y_A_4eq')
-plt.plot(x_2eq, y_A_2eq, label='y_A_2eq')
-# plt.plot(x_4eq, y_A_4eq - y_A_2eq, label='y_A_4eq - y_A_2eq')
+# plt.plot(x_4eq, y_A_4eq, label='y_A_4eq')
+# plt.plot(x_2eq, y_A_2eq, label='y_A_2eq')
+plt.plot(x_4eq, y_A_4eq - y_A_2eq, label='y_A_4eq - y_A_2eq')
plt.grid()
-plt.xlim(0, 0.1)
+plt.xlim(0, 0.05)
plt.legend()
plt.show()
plt.figure()
-plt.plot(x_4eq, y_C_4eq, label='y_C_4eq')
-plt.plot(x_2eq, y_C_2eq, label='y_C_2eq')
-# plt.plot(x_4eq, y_C_4eq - y_C_2eq, label='y_C_4eq - y_C_2eq')
+# plt.plot(x_4eq, y_C_4eq, label='y_C_4eq')
+# plt.plot(x_2eq, y_C_2eq, label='y_C_2eq')
+plt.plot(x_4eq, y_C_4eq - y_C_2eq, label='y_C_4eq - y_C_2eq')
plt.grid()
-plt.xlim(0, 0.1)
+plt.xlim(0, 0.05)
plt.legend()
plt.show()
@@ -120,7 +71,7 @@ plt.figure()
# plt.plot(x_2eq, phi_2eq, label='phi_2eq')
plt.plot(x_4eq, phi_4eq - phi_2eq, label='phi_4eq - phi_2eq')
plt.grid()
-plt.xlim(0, 0.1)
+plt.xlim(0, 0.05)
plt.legend()
plt.show()
@@ -129,6 +80,54 @@ plt.figure()
# plt.plot(x_2eq, p_2eq, label='p_2eq')
plt.plot(x_4eq, p_4eq - p_2eq, label='p_4eq - p_2eq')
plt.grid()
-plt.xlim(0, 0.1)
+plt.xlim(0, 0.05)
plt.legend()
-plt.show()
\ No newline at end of file
+plt.show()
+
+
+
+# # Compressible
+# K = 10_000
+
+# # solve the complete system
+# y_A_4eq, y_C_4eq, phi_4eq, p_4eq, x_4eq = solve_System_4eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=solvation, relax_param=0.05, refinement_style='hard_log', return_type='Vector', max_iter=1_000, rtol=rtol)
+
+# # solve the simplified system
+# y_A_2eq, y_C_2eq, phi_2eq, p_2eq, x_2eq = solve_System_2eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=solvation, relax_param=0.05, refinement_style='hard_log', return_type='Vector', max_iter=1_000, rtol=rtol)
+
+# # Evaluate the difference
+# plt.figure()
+# plt.plot(x_4eq, y_A_4eq, label='y_A_4eq')
+# plt.plot(x_2eq, y_A_2eq, label='y_A_2eq')
+# # plt.plot(x_4eq, y_A_4eq - y_A_2eq, label='y_A_4eq - y_A_2eq')
+# plt.grid()
+# plt.xlim(0, 0.1)
+# plt.legend()
+# plt.show()
+
+# plt.figure()
+# plt.plot(x_4eq, y_C_4eq, label='y_C_4eq')
+# plt.plot(x_2eq, y_C_2eq, label='y_C_2eq')
+# # plt.plot(x_4eq, y_C_4eq - y_C_2eq, label='y_C_4eq - y_C_2eq')
+# plt.grid()
+# plt.xlim(0, 0.1)
+# plt.legend()
+# plt.show()
+
+# plt.figure()
+# # plt.plot(x_4eq, phi_4eq, label='phi_4eq')
+# # plt.plot(x_2eq, phi_2eq, label='phi_2eq')
+# plt.plot(x_4eq, phi_4eq - phi_2eq, label='phi_4eq - phi_2eq')
+# plt.grid()
+# plt.xlim(0, 0.1)
+# plt.legend()
+# plt.show()
+
+# plt.figure()
+# # plt.plot(x_4eq, p_4eq, label='p_4eq')
+# # plt.plot(x_2eq, p_2eq, label='p_2eq')
+# plt.plot(x_4eq, p_4eq - p_2eq, label='p_4eq - p_2eq')
+# plt.grid()
+# plt.xlim(0, 0.1)
+# plt.legend()
+# plt.show()
\ No newline at end of file
diff --git a/src/Helper_DoubleLayerCapacity.py b/src/Helper_DoubleLayerCapacity.py
index 77149453f1646d83950c3add8b5c16eb56ab010e..6fa7ab41a37ab09a4f46e03bb961c83ac4e137e2 100644
--- a/src/Helper_DoubleLayerCapacity.py
+++ b/src/Helper_DoubleLayerCapacity.py
@@ -4,6 +4,7 @@ Jan.Habscheid@rwth-aachen.de
'''
import numpy as np
+from scipy.optimize import fixed_point, fsolve
# Helper functions
@@ -157,66 +158,51 @@ def Q_DL_dimless_ana(y_A_R:float, y_C_R:float, y_N_R:float, z_A:float, z_C:float
# Assume E_p = p_R = 0
D_A = y_A_R / (np.exp(-(solvation+1)*a2*p_R-z_A*phi_R))
D_C = y_C_R / (np.exp(-(solvation+1)*a2*p_R-z_C*phi_R))
- D_N = y_N_R / (np.exp(-(solvation+1)*a2*p_R-z_N*phi_R))
-
- D_tilde_A = np.log(D_A)
- D_tilde_C = np.log(D_C)
- D_tilde_N = np.log(D_N)
-
- CLambda_L = - z_A * phi_L + D_tilde_A - z_C * phi_L + D_tilde_C - z_N * phi_L + D_tilde_N
- CLambda_R = - z_A * phi_R + D_tilde_A - z_C * phi_R + D_tilde_C - z_N * phi_R + D_tilde_N
-
- Lambda = np.sqrt(Lambda2)
- a = np.sqrt(a2)
-
- N = 3
-
- Q_DL = Lambda * a * (np.sqrt(-CLambda_L/(-(N-1)*(solvation+1)-1)) - np.sqrt(-CLambda_R/(-(N-1)*(solvation+1)-1)))
-
- # CLambda_L = np.log(D_A * np.exp(-z_A * phi_L) + D_C * np.exp(-z_C * phi_L) + D_N * np.exp(-z_N * phi_L))
- # CLambda_R = np.log(D_A * np.exp(-z_A * phi_R) + D_C * np.exp(-z_C * phi_R) + D_N * np.exp(-z_N * phi_R))
-
+ D_N = y_N_R / (np.exp(-a2*p_R))
+
+ Q_DL = []
+ dx_phi_L = 0
+ for phi_L_ in phi_L:
+ def func(p_L):
+ # A_Term = D_A * np.exp(-z_A*phi_L)
+ A_Term = D_A * np.exp(-(solvation+1)*a2*p_L-z_A*phi_L_)
+ C_Term = D_C * np.exp(-(solvation+1)*a2*p_L-z_C*phi_L_)
+ N_Term = D_N * np.exp(-a2*p_L)
+
+ return (A_Term + C_Term + N_Term) - 1
+ p_L = fsolve(func, dx_phi_L)
+ dx_phi_L = np.sqrt(p_L - E_p) * np.sqrt(2*a2/Lambda2)
+ Q_DL_ = Lambda2 * dx_phi_L
+ Q_DL.append(Q_DL_)
+ Q_DL = np.array(Q_DL)
+
+ # def func_L(p_L):
+ # CLambda = D_A * np.exp(-z_A * phi_L - solvation*a2*p_L) + D_C * np.exp(-z_C * phi_L - solvation*a2*p_L) + D_N
+ # return np.log(CLambda)/a2
+
+ # p_L = fixed_point(func_L, 0, maxiter=5_000)
# Lambda = np.sqrt(Lambda2)
- # Q_DL = (phi_L-phi_R) / np.abs(phi_L-phi_R) * Lambda * np.sqrt(2) * (np.sqrt(CLambda_L/(solvation+1) - E_p * a2) - np.sqrt(CLambda_R/(solvation+1) - E_p * a2))
- else:
- C_A = y_A_R / ((K + p_R - 1)**(-(solvation+1)*a2*K)*np.exp(-z_A*phi_R))
- C_C = y_C_R / ((K + p_R - 1)**(-(solvation+1)*a2*K)*np.exp(-z_C*phi_R))
- C_N = y_N_R / ((K + p_R - 1)**(-(solvation+1)*a2*K)*np.exp(-z_N*phi_R))
-
- # # Lambda_tilda_L = C_A * np.exp(-z_A*phi_L) + C_C * np.exp(-z_C*phi_L) + C_N * np.exp(-z_N*phi_L)
- # # Lambda_tilda_R = C_A * np.exp(-z_A*phi_R) + C_C * np.exp(-z_C*phi_R) + C_N * np.exp(-z_N*phi_R)
-
- # # # Lambda_hat_L = np.exp(np.log(Lambda_tilda_L) / (a2 * K))
- # # # Lambda_hat_R = np.exp(np.log(Lambda_tilda_R) / (a2 * K))
-
- # # dx_Phi_L = np.sqrt(2 * a2/Lambda2 * (1 - K - E_p + Lambda_hat_L))
- # # dx_Phi_R = np.sqrt(2 * a2/Lambda2 * (1 - K - E_p + Lambda_hat_R))
-
- # # Q_DL = Lambda2 * (dx_Phi_L - dx_Phi_R)
-
- # Lambda_tilde_L = C_A * np.exp(-z_A*phi_L) + C_C * np.exp(-z_C*phi_L) + C_N * np.exp(-z_N*phi_L)
- # Lambda_tilde_R = C_A * np.exp(-z_A*phi_R) + C_C * np.exp(-z_C*phi_R) + C_N * np.exp(-z_N*phi_R)
-
- # Lambda_hat_L = (1/Lambda_tilde_L)**(-1/((solvation+1)*a2*K))
- # Lambda_hat_R = (1/Lambda_tilde_R)**(-1/((solvation+1)*a2*K))
-
# a = np.sqrt(a2)
- # Lambda = np.sqrt(Lambda2)
- # K_tilde = 1 - K + E_p
+ # Q_DL = np.sqrt(2) * Lambda * a * np.sqrt(p_L - E_p)
- # Q_DL = Lambda * a * np.sqrt(2) * (np.sqrt(Lambda_hat_L - K_tilde) - np.sqrt(Lambda_hat_R - K_tilde))
+ # ! ToDo: Implement full analytical for solvation == 0
+
+ else:
+ C_A = y_A_R / ((K + p_R - 1)**(-1*a2*K)*np.exp(-z_A*phi_R))
+ C_C = y_C_R / ((K + p_R - 1)**(-1*a2*K)*np.exp(-z_C*phi_R))
+ C_N = y_N_R / ((K + p_R - 1)**(-1*a2*K)*np.exp(-z_N*phi_R))
- Lambda_L = C_A * np.exp(-z_A*phi_L) + C_C * np.exp(-z_C*phi_L) + C_N * np.exp(-z_N*phi_L)
- Lambda_R = C_A * np.exp(-z_A*phi_R) + C_C * np.exp(-z_C*phi_R) + C_N * np.exp(-z_N*phi_R)
+ CLambda_L = C_A * np.exp(-z_A*phi_L) + C_C * np.exp(-z_C*phi_L) + C_N
+ # CLambda_R = C_A * np.exp(-z_A*phi_R) + C_C * np.exp(-z_C*phi_R) + C_N
- B = -a2 * K
- A = 1/2 * Lambda2/a2
- K_tilde = K + E_p - 1
+ Left = np.sqrt((1/CLambda_L)**(-1/(a2*K)) + 1 - K - E_p)
+ # Right = np.sqrt((1/CLambda_R)**(-1/(a2*K)) + 1 - K - E_p)
- dx_Phi_L = (np.power(1/Lambda_L, B) - K_tilde) / A
- dx_Phi_R = (np.power(1/Lambda_R, B) - K_tilde) / A
+ Lambda = np.sqrt(Lambda2)
+ a = np.sqrt(a2)
- Q_DL = Lambda2 * (dx_Phi_L - dx_Phi_R)
+ Q_DL = Lambda * a * np.sqrt(2) * (Left)# - Right)
+
return Q_DL
def Q_DL_dim_ana(y_A_R:float, y_C_R:float, y_N_R:float, z_A:float, z_C:float, phi_L:float, phi_R:float, p_R:float, K:str|float, Lambda2:float, a2:float, nR_m:float, e0:float, LR:float, solvation:float) -> float:
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