General description

The world that we experience emerges from many underlying small-scale ‘worlds’: we know that there are atoms, molecules, cells,…, a rich variety of small scale objects that compose the world we live in. One cannot fully understand the world that we experience without understanding what is going on in the underlying, small-scale, ‘invisible’ layers of our world. Science has made huge steps into understanding the different layers of reality, however, is this enough to understand how things work? Unfortunately not, we also need to understand how the large-scale layers emerge from the underlying ones: how do cells self-organise into tissue and this one into organs?, how do pedestrians form spontaneously lanes?, why gullies have particular erosion patterns?, how do termites manage to build their huge nests without a boss putting order in the group? Linking scales is very hard to do experimentally, but we, humans, are gifted with a very powerful tool: abstract thinking!, and hence, mathematics. Mathematics gives the key to linking our layers of knowledge.

In this project we wonder: which are the mechanical factors producing metastasis? Cancerous cells are unfortunately not rare in the human body. However, only in few cases they manage to produce tumours. We want to understand how, from a few bunch of individual cells going wrong, a whole tissue-like cluster can emerge, leading to metastasis. Another question that we look at is how tissue, particularly, fat tissue, is generated. Understanding what can go wrong in the underlying cell dynamics can explain the diseases that we observe.

But this is not all, we also look at other type of natural systems, like collective motion observed in birds flocking or pedestrian dynamics. For example, we investigate micro-swimmers and their group dynamics, like the case of spermatozoa: believe it or not, fertility, at its early stages at least, is a team effort!

Team members

Apart from Sara Merino-Aceituno (PI, University of Vienna) and Christian Schmeiser (proponent, University of Vienna) the full list team members can be found here.

Collaborators

• Pedro Aceves Sanchez (University of South Carolina) – mathematician.

• Christa Bücker (Max Perutz Lab, University of Vienna) - biologist.

• Pierre Degond (Imperial College University of London) – mathematician.

• Marina Amado Ferreira (University of Helsinki) – mathematician.

• Shotaro Otsuka (Max Perutz Lab, Vienna) - biologist.

• Diane Peurichard (INRIA Paris) – mathematician.

• Christian Schmeiser (University of Vienna) – mathematician.

• Eric Theveneau (University of Toulouse) – biologist.

Publications and preprints by team members:

1. Pierre Degond, Amic Frouvelle, Sara Merino-Aceituno, Ariane Trescases "Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies", arXiv (2022).

2. Steffen Plunder, Markus Burkard, Ulrich Lauer, Sascha Venturelli, and Luigi Marongiu. "Determination of phage load and administration time in simulated occurrences of antibacterial treatments." Frontiers in Medicine: 3231.

3. Vincent Calvez, Hélène Hivert, and Havva Yoldaş. "Concentration in Lotka-Volterra parabolic equations: an asymptotic-preserving scheme." arXiv preprint arXiv:2204.04146 (2022).

4. Steffen Plunder, Bend Simeon. "The mean-field limit for particle systems with uniform full-rank constraints" arXiv preprint (2022).

5. Havva Yoldaş. "On quantitative hypocoercivity estimates based on Harris-type theorems." arXiv preprint arXiv:2203.00096 (2022).

6. Romain Ducasse, Filippo Santambrogio, Havva Yoldaş. "A cross-diffusion system obtained via (convex) relaxation in the JKO scheme." arXiv preprint arXiv:2111.13764 (2021).

7. Marc Briant, Antoine Diez, Sara Merino-Aceituno, Cauchy theory and mean-field limit for general Vicsek models in collective dynamics, (2022).

8. Pierre Degond, Sara Merino-Aceituno, Nematic alignment of self-propelled particles in the macroscopic regime, accepted at Math. Models Methods Appl. Sci., (2019).

9. Degond, Pierre, Sara Merino-Aceituno, Fabien Vergnet, and Hui Yu. “Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles.” Journal of Mathematical Fluid Mechanics 21, no. 1 (2019): 6.

10. Pierre Degond, Antoine Diez, Amic Frouvelle, Sara Merino-Aceituno (2019) “Phase transitions and macroscopic limits in a BGK model of body-attitude coordination“

11. Pierre Degond, Sara Merino-Aceituno (2019) “Nematic alignment of self-propelled particles in the macroscopic regime”

12. Sophie Hecht, Gantas Perez-Mockus, Dominik Schienstock, Carles Recasens-Alvarez, Sara Merino-Aceituno, Pierre Degond, Jean-Paul Vincent (2019) “Mechanical constraints to cell cycle progression in a pseudostratified epithelium”

13. Antoine Diez (2019) “Propagation of chaos and moderate interaction for a piecewisedeterministic system of geometrically enriched particles”.

Press articles

• Claudia Wytrzens explains her research! (in German)