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We have made a further approximation here. In our stability analysis we use the steady state solution to the dendrite problem. For the wedge and for the channel there are two solutions for each surface tension corresponding to different finger widths. In the wedge, the solution with the smaller width is the stable one, and the opposite is true in the channel. However, for the question of finger competition, we think it does not matter which solution one looks at, since the two solutions differ only in their local tip structure. Finger competition is a more global question
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We have made a further approximation here. In our stability analysis we use the steady state solution to the dendrite problem. For the wedge and for the channel there are two solutions for each surface tension corresponding to different finger widths. In the wedge, the solution with the smaller width is the stable one, and the opposite is true in the channel. However, for the question of finger competition, we think it does not matter which solution one looks at, since the two solutions differ only in their local tip structure. Finger competition is a more global question.
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