We investigate the role of the interparticle-interaction strength in the distribution of two species of atoms inside a condensate. We focus upon the study of systems for which the minima of the trapping potentials for the species are displaced from each other by a distance that is small compared to the size of the total condensate. We show that in a small range of the interparticle-interaction strength the distribution of species undergoes dramatic changes, and exhibits a variety of different features. We demonstrate that this behavior can be easily understood in terms of the Thomas-Fermi approximation. This effect may be useful in experimentally determining the values of the scattering lengths.
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