Wulff shape emergence in graphene

DOI10.1142/S0218202516500536zbMath1355.82073OpenAlexW2514662701MaRDI QIDQ2833260

Paolo Piovano, Ulisse Stefanelli, Elisa Davoli

Publication date: 17 November 2016

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202516500536

zbMATH Keywords

nanostructures and nanoparticlesatomic physicslattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Mathematics Subject Classification ID

Atomic physics (81V45) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of nanostructures and nanoparticles (82D80)

Related Items (18)

Microscopical justification of solid-state wetting and dewetting ⋮ Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities ⋮ Stable carbon configurations ⋮ Microscopical justification of the Winterbottom problem for well-separated lattices ⋮ The double-bubble problem on the square lattice ⋮ Emergence of Wulff-crystals from atomistic systems on the FCC and HCP lattices ⋮ A proof of finite crystallization via stratification ⋮ Ripples in graphene: a variational approach ⋮ Maximal fluctuations around the Wulff shape for edge-isoperimetric sets in \({\mathbb{Z}}^d \): a sharp scaling law ⋮ Sharp \(N^{3/4}\) law for the minimizers of the edge-isoperimetric problem on the triangular lattice ⋮ Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule ⋮ Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy ⋮ Graphene ground states ⋮ Finite Crystallization and Wulff shape emergence for ionic compounds in the square lattice ⋮ Crystallization in the hexagonal lattice for ionic dimers ⋮ The Geometry of $C_{60}$: A Rigorous Approach via Molecular Mechanics ⋮ \(N^{3/4}\) law in the cubic lattice ⋮ Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings

Cites Work

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• Some numerical estimations of energy levels on a model for a graphene ribbon in a magnetic field
• Transient analysis of single-layered graphene sheet using the KP-Ritz method and nonlocal elasticity theory
• Carbon-nanotube geometries: analytical and numerical results
• Crystallization for a Brenner-like potential
• Sharp \(N^{3/4}\) law for the minimizers of the edge-isoperimetric problem on the triangular lattice
• The crystallization conjecture: a review
• Ground states of the 2D sticky disc model: fine properties and \(N^{3/4}\) law for the deviation from the asymptotic Wulff shape
• Analysis of models for quantum transport of electrons in graphene layers
• On the low lying spectrum of the magnetic Schrödinger operator with kagome periodicity
• Finite crystallization in the square lattice

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