| Wednesday, 20.03.2024 | |
| Type | seminar in the framework of the PDE Afternoon |
| Time | 14:00 - 14:45 |
| Place | University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, Vienna (map) |
| Room | HS 2, ground floor - how to get there |
| Speaker | (Kyoto University, Japan) |
| Title | Position-based dynamics: convergence theory and applications to agent-based models |
| Abstract | In this talk, I will present our new convergence proof for a numerical method called position-based dynamics (PBD) [1]. PBD is a method for particle simulations with non-overlap conditions, which has widespread use in computer graphics (games, animation), but little attention in math. Mathematically speaking, the method integrates differential equations with inequality constraints (differential inclusions) by applying a splitting method to a sum of non-smooth potentials. Our convergence theory relies on variational analysis: In particular, we use a new bound for alternating projections and introduce a new notion of numerical consistency based on scalarly upper semicontinuity. Finally, I will showcase some applications in developmental biology [2-3]. The first application developed during my PhD in Vienna uses PBD for answering equations about the initiation of cell migration in the neural tube (epithelial-to-mesenchymal transition). The second application is an ongoing project for modelling limb morphogenesis with a hybrid model which mixes an agent-based model with reaction-diffusion equations to explain symmetry breaking and self-organisation of mesenchymal cells. [1] S. Plunder, S. Merino-Aceituno, Convergence proof for first-order position-based dynamics: An efficient scheme for inequality constrained ODEs. (2023) arxiv. [2] S. Plunder, C. Danesin, B. Glise, M. A. Ferreira, S. Merino-Aceituno, E. Theveneau, Modelling variability and heterogeneity of EMT scenarios highlights nuclear positioning and protrusions as main drivers of extrusion. (2023) bioRxiv. [3] E. Despin-Guitard, S. Plunder, N. Mathiah, E. Theveneau, I. Migeotte Occurrence of non-apical mitoses at the primitive streak, induced by relaxation of actomyosin and acceleration of the cell cycle, contributes to cell delamination during mouse gastrulation. (2024) bioRxiv. |
| Notes | This event takes place in hybrid form (in person and online on Zoom). Slides and additional materials are available on the Moodle service of the University of Vienna. If you want to participate, please write an email to matteo.tommasini@univie.ac.at. Further details are available at this link. |
| Attachment | link |
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