# $$\varGamma $$Γ-Convergence of the Heitmann–Radin Sticky Disc Energy to the Crystalline Perimeter

@article{Luca2019varGammaO, title={\$\$\varGamma \$\$$\Gamma$-Convergence of the Heitmann–Radin Sticky Disc Energy to the Crystalline Perimeter}, author={Lucia De Luca and Matteo Novaga and Marcello Ponsiglione}, journal={Journal of Nonlinear Science}, year={2019}, pages={1-27} }

We consider low-energy configurations for the Heitmann–Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann–Radin potential by subtracting the minimal energy per particle, i.e. the so-called kissing number. For configurations whose energy scales like the perimeter, we prove a compactness result which shows the emergence of polycrystalline structures: The empirical measure converges to a set of finite perimeter, while a microscopic…

## 8 Citations

Emergence of Rigid Polycrystals from Atomistic Systems with Heitmann–Radin Sticky Disk Energy

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1
/
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∈
(
0…

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We analyse integral representation and Γ -convergence properties of functionals defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition whose…

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. The meeting focused on the last advances in particle systems. The talks covered a broad range of topics, ranging from questions in crystallization and atomistic systems to mesoscopic models of…

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- Mathematics
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In this paper we introduce a model for hard spheres interacting through attractive Riesz type potentials, and we study its thermodynamic limit. We show that the tail energy enforces optimal packing…

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