Some recent results on 2D crystallization for sticky disc models and generalizations for systems of oriented particles

DOI10.1007/978-3-031-04496-0_17zbMath1498.82033OpenAlexW4312805915MaRDI QIDQ2080568

Publication date: 9 October 2022

Full work available at URL: https://doi.org/10.1007/978-3-031-04496-0_17

Crystalline structure (74E15) Statistical mechanics of crystals (82D25) Planar graphs; geometric and topological aspects of graph theory (05C10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Uses Software

Boids

Cites Work

Unnamed Item
Unnamed Item
Face-centered cubic crystallization of atomistic configurations
Sharp \(N^{3/4}\) law for the minimizers of the edge-isoperimetric problem on the triangular lattice
A proof of crystallization in two dimensions
The crystallization conjecture: a review
Crystallization in two dimensions and a discrete Gauss-Bonnet theorem
Crystallization in carbon nanostructures
Packing twelve spherical caps to maximize tangencies
Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy
Crystallization to the square lattice for a two-body potential
Distribution of cracks in a chain of atoms at low temperature
Vectorial crystallization problems and collective behavior
Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities
Surface energy and boundary layers for a chain of atoms at low temperature
\(\mathit\Gamma\)-convergence of the Heitmann-Radin sticky disc energy to the crystalline perimeter
\(N^{3/4}\) law in the cubic lattice
Classification of particle numbers with unique Heitmann-Radin minimizer
Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape
Ground states of the 2D sticky disc model: fine properties and \(N^{3/4}\) law for the deviation from the asymptotic Wulff shape
A uniqueness proof for the Wulff Theorem
Emergent Behavior in Flocks
Finite crystallization in the square lattice

This page was built for publication: Some recent results on 2D crystallization for sticky disc models and generalizations for systems of oriented particles