Speaker
Description
The study of collective dynamics has attracted growing interest across multiple scientific fields due to its ability to describe self-organization and its broad range of applications. Many natural systems, including cell dynamics, display global patterns arising from local and nonlocal interactions. A distinctive feature of collective cell migration is its dependence not only on mechanical interactions but also on chemical signaling, which drives cells toward higher concentrations of specific substances \cite{bretti2021estimation}. Modeling such phenomena through mathematical models and numerical approaches has become increasingly important, enabling the development of in silico models to study complex processes. However, microscopic models of cell migration are computationally expensive, especially when dealing with large numbers of cells in high-dimensional settings.
In this talk we investigate a multidimensional pressureless nonlocal Euler-type model with chemotaxis, derived from hybrid ODE-PDE microscopic dynamics \cite{natalini2023mean}. The goal is to explore the role of nonlocal mechanical interactions, such as attraction-repulsion effects, and the extension to multi-population models \cite{menci2023microscopic, menci2026numerical}. Beyond the assumptions under which the limit has been rigorously derived, the validity of the macroscopic model and its agreement with the microscopic dynamics is assessed in more general scenarios. Finally, parameter estimation is performed to identify optimal values and enable comparisons with the underlying microscopic dynamics.
This is a joint work with Marta Menci (Universit`a Campus Bio-Medico di Roma) and Roberto Natalini (IAC-CNR).
Bibliography
@article{bretti2021estimation,
title={Estimation algorithm for a hybrid PDE--ODE model inspired by immunocompetent cancer-on-chip experiment},
author={Bretti, Gabriella and De Ninno, Adele and Natalini, Roberto and Peri, Daniele and Roselli, Nicole},
journal={Axioms},
volume={10},
number={4},
pages={243},
year={2021},
publisher={MDPI}
}
@article{menci2023microscopic,
title={Microscopic, kinetic and hydrodynamic hybrid models of collective motions with chemotaxis: a numerical study},
author={Menci, Marta and Natalini, Roberto and Paul, Thierry},
journal={Mathematics and Mechanics of Complex Systems},
volume={12},
number={1},
pages={47--83},
year={2023},
publisher={Mathematical Sciences Publishers}
}
@article{menci2026numerical,
title={Numerical Study on a Multidimensional Pressureless Euler-Type Model with Nonlocal Interactions and Chemotaxis for Collective Cell Migration},
author={Menci, Marta and Natalini, Roberto and Tenna, Tommaso},
journal={Multiscale Modeling \& Simulation},
volume={24},
number={1},
pages={267--289},
year={2026},
publisher={SIAM}
}
@article{natalini2023mean,
title={The Mean-Field limit for hybrid models of collective motions with chemotaxis},
author={Natalini, Roberto and Paul, Thierry},
journal={SIAM Journal on Mathematical Analysis},
volume={55},
number={2},
pages={900--928},
year={2023},
publisher={SIAM}
}
