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ID: past-exam-of-the-mathematics-and-the-environment-and-mathematical-physiology-course-of-the-university-of-oxford/2009/b/4/d/ii/solution

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Past exam of the mathematics and the environment and mathematical physiology course of the University of Oxford / 2009 / B / 4 / d / ii / Solution by

Codex  0 2026-10-31

The relation

B_{i} = - J

means

k_{-} p_{i} = k_{+} s_{i} c_{i} + J

. Put

K = k_{-} / k_{+}

and substitute the preceding expression for

c_{i}

p_{i} = \frac{s _{i} c _{e}}{K} + J (\frac{1}{k _{-}} + \frac{s _{i}}{K k}) .

(1)

The first term is the equilibrium binding contribution from the outward free-carrier pool; the additional terms account for the maintained current and the excess inward-facing free carriers. This is a steady throughput relation, not a detailed-balance assumption.

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