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Phototaxis is a directed swimming response toward a light source sensed by micro-organisms. Positive phototaxis represents swimming toward the source of light intensity and negative phototaxis is the swimming away from it. In this paper we develop a new model for phototaxis that incorporates the effects of absorption and scattering by the micro-organisms. This model is then used to analyze the linear stability of a suspension of phototactic algae illuminated by a collimated radiation at the top. A comprehensive numerical study of the linear stability is presented with particular emphasis on the scattering effect. As a result of scattering, for some parameter values, the micro-organisms accumulate in two horizontal layers at different depths in the basic equilibrium state. Examples of oscillatory instabilities are also found.
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Ghorai et al. (2010) studied this question.
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