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fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 1d85f14 fe49880 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 | import marimo
__generated_with = "0.12.5"
app = marimo.App(width="medium")
@app.cell
def _():
import marimo as mo
import numpy as np
import matplotlib.pyplot as plt
from typing import Dict
from numpy.typing import NDArray
conc_a = mo.ui.text(value="0.2",label="$[\mathrm{A}]_0$")
conc_b = mo.ui.text(value="0.1",label="$[\mathrm{B}]_0$")
keq = mo.ui.text(value="12",label="$K_{eq}$")
step = mo.ui.slider(steps=np.logspace(-8,0,90),label="$\delta c$",show_value=True)
tol = mo.ui.slider(steps=np.logspace(-8,0,90),label="Convergence Threshold",show_value=True)
mo.md(
f"""
##**Initial conditions**
{conc_a} {conc_b} {keq}\n
##**Chemical Equilibrium Solver Parameters**
{step} {tol}
"""
)
return Dict, NDArray, conc_a, conc_b, keq, mo, np, plt, step, tol
@app.cell
def _(np):
def compute_Q(conc,stoich):
Q = 1
for c in conc:
Q *= conc[c]**stoich[c]
return Q
def compute_force(conc,stoich,pkeq):
Q = compute_Q(conc,stoich)
return -np.log10(Q) - pkeq
def update_concentrations(conc,stoich,force,dc):
for c in conc:
conc[c] += dc*stoich[c]*force
return conc
def solve_analytic(conc,keq):
"""
(b+x) / (a-2x)**2 = c
"""
a = conc["A"]
b = conc["B"]
c = keq
x0 = (-np.sqrt(8*a*c + 16*b*c + 1) + 4*a*c + 1)/(8*c)
x1 = (np.sqrt(8*a*c + 16*b*c + 1) + 4*a*c + 1)/(8*c)
return x0,x1
return compute_Q, compute_force, solve_analytic, update_concentrations
@app.cell
def _(
Dict,
NDArray,
compute_Q,
compute_force,
conc_a,
conc_b,
keq,
mo,
np,
plt,
solve_analytic,
step,
tol,
update_concentrations,
):
conc = {
"A": float(conc_a.value),
"B": float(conc_b.value),
}
stoich = {
"A":-2,
"B":1,
}
pkeq = -np.log10(float(keq.value))
dc = float(step.value)
rtol = float(tol.value)
# print(conc,np.log10(compute_Q(conc,stoich)),pkeq)
initial = mo.md(
f"""
##**Initial conditions**
$Q$ = {compute_Q(conc,stoich):.4e}
Initial force = {compute_force(conc, stoich, pkeq):.4e}
"""
)
def solve_equilibrium(
initial_conc: Dict[str, float],
stoichiometry: Dict[str, float],
pK_eq: float,
dc: float,
rtol: float = 1e-5,
max_iterations: int = 10
) -> NDArray:
"""
Solves chemical equilibrium equations using an iterative approach.
Args:
initial_conc: Dictionary of initial concentrations for each species
stoichiometry: Dictionary of stoichiometric coefficients
pK_eq: Negative log of equilibrium constant
dc: Concentration step size for iterations
rtol: Relative tolerance for convergence
max_iterations: Maximum number of iterations before stopping
Returns:
NDArray: Array with columns [iteration, conc_A, conc_B, force]
"""
# Initialize arrays to store results
iterations = np.zeros(max_iterations + 1)
conc_A = np.zeros(max_iterations + 1)
conc_B = np.zeros(max_iterations + 1)
forces = np.zeros(max_iterations + 1)
# Set initial values
conc = initial_conc.copy()
force_0 = compute_force(conc, stoichiometry, pK_eq)
conc_A[0] = conc['A']
conc_B[0] = conc['B']
forces[0] = force_0
# Iterate until convergence or max iterations
for i in range(max_iterations):
# Update values
conc = update_concentrations(conc, stoichiometry, forces[i], dc)
force = compute_force(conc, stoichiometry, pK_eq)
# if force*forces[i] < 0:
# dc /=2
pQ = -np.log10(compute_Q(conc, stoichiometry))
# Store results
iterations[i + 1] = i + 1
conc_A[i + 1] = conc['A']
conc_B[i + 1] = conc['B']
forces[i + 1] = force
# Check convergence
# if np.isclose(pQ, pK_eq, rtol=rtol):
if np.abs(force) < rtol:
# Trim unused array space if converged early
return np.column_stack([
iterations[:i + 2],
conc_A[:i + 2],
conc_B[:i + 2],
forces[:i + 2]
])
# Return all iterations if no convergence
return np.column_stack([iterations, conc_A, conc_B, forces])
def plot(data,labels=None,refs=None,log=False,axes=None):
ncols = data.shape[1]
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
plt.figure(figsize=(4,4))
for i in range(0,ncols-1):
plt.plot(data[:,0],data[:,i+1],label=labels[i],color=colors[i])
if refs is not None:
for i in range(len(refs)):
plt.axhline(refs[i],linestyle='dashed',label=labels[i]+"$_{exact}$",color=colors[i])
if axes is not None:
plt.xlabel(axes[0])
plt.ylabel(axes[1])
if log:
plt.yscale("log")
plt.legend()
return plt.gca()
data = solve_equilibrium(conc,stoich,pkeq,dc,rtol,max_iterations=1000)
final_conc = {"A":data[-1,1] , "B":data[-1,2]}
roots = solve_analytic(conc,float(keq.value))
analytic_solution = [ data[0,1] + stoich["A"]*roots[0] , data[0,2] + stoich["B"]*roots[0] ]
plot_c = plot(data[:,0:3],labels=["[A]","[B]"],refs=analytic_solution,axes=["Cycles","Concentration"])
plot_f = plot(
np.column_stack([data[:,0],np.abs(data[:,3])]),
labels=["Force"],refs=[rtol],log=True,axes=["Cycles","Force"])
final = mo.md(
f"""
##**Final conditions**
$[A]_f$ = {final_conc["A"]:.4e}
$[B]_f$ = {final_conc["B"]:.4e}
$Q$ = {compute_Q(final_conc,stoich):.4e}
$K_{{eq}}$ = {float(keq.value):.4e} \n
Final force = {compute_force(final_conc,stoich,pkeq):.4e}
Force threshold = {float(tol.value):.4e}
"""
)
mo.vstack([initial,final,
mo.hstack([plot_c,plot_f])
])
return (
analytic_solution,
conc,
data,
dc,
final,
final_conc,
initial,
pkeq,
plot,
plot_c,
plot_f,
roots,
rtol,
solve_equilibrium,
stoich,
)
if __name__ == "__main__":
app.run()
|