| Abstract: |
| I will present an overview of discrete-to-continuum limit passages of nonlocally interacting particles where the unknowns are the positions of the particles in a one-dimensional domain. Such particle systems can be used as models for dislocations in metals, cellular aggregation, granular media, pedestrian movement, opinion formation and predator--prey models.
The interesting common feature of these results is that numerical simulations show striking agreements between the particle systems and the related continuum models. However, any rigorous result beyond $\Gamma$-convergence of the particle interaction energy in the many-particle limit calls for novel mathematical ideas. |
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