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Also well studied is the limit when $L$ is fixed, and $A \\to \\infty$. In this case the solution equilibrates along stream lines.\n  In this paper, we show that if \\textit{both} $A \\to \\infty$ and $L \\to \\infty$, then a transition between the homogenization and averaging regimes occurs at $A \\approx L^4$. 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