def test_log(self):
a = pybamm.InputParameter("a")
fun = pybamm.log(a)
self.assertEqual(fun.evaluate(inputs={"a": 3}), np.log(3))
h = 0.0000001
self.assertAlmostEqual(
fun.diff(a).evaluate(inputs={"a": 3}),
(
pybamm.log(pybamm.Scalar(3 + h)).evaluate()
- fun.evaluate(inputs={"a": 3})
)
/ h,
places=5,
)
# Base 10
fun = pybamm.log10(a)
self.assertEqual(fun.evaluate(inputs={"a": 3}), np.log10(3))
h = 0.0000001
self.assertAlmostEqual(
fun.diff(a).evaluate(inputs={"a": 3}),
(
pybamm.log10(pybamm.Scalar(3 + h)).evaluate()
- fun.evaluate(inputs={"a": 3})
)
/ h,
places=5,
)
def lead_dioxide_ocp_Bode1977(m):
"""
Dimensional open-circuit voltage in the positive (lead-dioxide) electrode [V],
from [1]_, as a function of the molar mass m [mol.kg-1].
References
----------
.. [1] H Bode. Lead-acid batteries. John Wiley and Sons, Inc., New York, NY, 1977.
"""
U = (
1.628
+ 0.074 * log10(m)
+ 0.033 * log10(m) ** 2
+ 0.043 * log10(m) ** 3
+ 0.022 * log10(m) ** 4
)
return U
def lead_ocp_Bode1977(m):
"""
Dimensional open-circuit voltage in the negative (lead) electrode [V], from [1]_,
as a function of the molar mass m [mol.kg-1].
References
----------
.. [1] H Bode. Lead-acid batteries. John Wiley and Sons, Inc., New York, NY, 1977.
"""
U = (
-0.294
- 0.074 * log10(m)
- 0.030 * log10(m) ** 2
- 0.031 * log10(m) ** 3
- 0.012 * log10(m) ** 4
)
return U