MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Mass-Selection in Alignment Models with Non-Deterministic Effects
Ivano Primi, Angela Stevens and Juan J.L. VelazquezAbstract
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.
- Received:
- 30.03.07
- Published:
- 30.03.07
- MSC Codes:
- 45K05, 47H10, 65M06, 65M12
- Keywords:
- Mass selection, alignment, integro-differential equations, fix point arguments