Seminari dell’Istituto per le Applicazioni del Calcolo del Cnr: “AIM: Artificial Intelligence and Mathematics, fundamentals and beyond”, https://sites.google.com/view/aimseminars/home
Il prossimo si terrà Giovedì 15 aprile 2021, ore 14:30
Speaker: Lucia De Luca
Titolo Crystallization results for pairwise interaction energies in two dimensions
Abstract I will discuss some recent crystallization results for pairwise interaction energies of systems of particles in the plane. I will focus on the so-called Heitmann-Radin (HR) sticky disc potential that in its classic form is defined by V(r)=+infty for r<1, V(r)=-1 for , V(r) elsewhere. For the classic HR functional it has been proven that minimizing configurations are subsets of the triangular lattice. First, I will show how this result extends in a suitable sense to the class of quasi-minimizers. Furthermore, I will enrich the classic HR model in order to deal with vectorial crystallization problems arising in mathematical biology. Specifically, associating a vectorial orientation to each particle of the configuration and enforcing threshold criteria for the interactions between particles, I will show that minimizing configurations exhibit the so-called diamond formation (typical in fish schooling).
Il seminario si terrà sul Canale Youtube di Cnr-IAC a questo link: https://www.youtube.com/watch?v=XGuyvTINi_A
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