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Mass-Selection in Alignment Models with Non-Deterministic Effects
Ivano Primi, Angela Stevens and Juan J.L. Velazquez
In this paper we consider an integro-differential equation model for alignment of oriented bundles of cells or filaments which includes non-deterministic effects. The reorientation of the aligning bundles of cells is described by a non-trivial probability distribution. In a paper from K. Kang, B. Perthame, A. Stevens and J.J.L. Velazquez it was shown that the long time behavior of a related deterministic model aligns the bundles into two opposite directions, but the masses are not balanced. Here we show that the probabilistic effects result in a selection of masses, namely exactly balanced for two opposite directions or accumulation into one direction only.