HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

Thus, using Proposition 1 we get,
dN l
= (a 21 − N l )a 22
dt
dN u
+ N l a 22 = a 21 a 22
dt
N l (t) = a 21 + N 0 e −a 22t
lim
t→+∞ N l (t) = a 21
To summarize the bounds,
a 21 + N 0 e −a 22
≤ N(t) ≤ γ N +
(N 0 − γ N
)
e −a 22t
When t → ∞ we obtain,
∴ a 21 = 31 ≤ N(t) ≤ ∞ (28)
Nitrate then has constant lower bound, which implies that the concentration will
never go below a 21 for this particular model structure. This make us re-iterate that
these models are very sensitive to parameter selection process. As mentioned above
Iron as the same equation structures, thus using the same analysis we found Iron as
follows:
[
] [
dF
dt = Da 17
+
(a 8 12.0107)
[
P
−
(a 8 12.0107)
]
E T H2 O
(a 23 − F )a
max
− E T H2 O(t)
24
E T H2 O max
− E T H2 O min
[
]
(1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t)
]
Thus,
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