A continuum model for brittle nanowires derived from an atomistic description by -convergence

B Schmidt, J Zeman - Calculus of Variations and Partial Differential …, 2023 - Springer
Starting from a particle system with short-range interactions, we derive a continuum model
for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional …

The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling

A Bach, M Cicalese, L Kreutz, G Orlando - Calculus of Variations and …, 2021 - Springer
We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the
two-dimensional triangular lattice. The system is fully frustrated and displays two families of …

Microscopical justification of the Winterbottom problem for well-separated lattices

P Piovano, I Velčić - Nonlinear Analysis, 2023 - Elsevier
We consider the discrete atomistic setting introduced in Piovano and Velčić (2022) to
microscopically justify the continuum model related to the Winterbottom problem, ie, the …

Distribution of cracks in a chain of atoms at low temperature

S Jansen, W König, B Schmidt, F Theil - Annales Henri Poincaré, 2021 - Springer
We consider a one-dimensional classical many-body system with interaction potential of
Lennard–Jones type in the thermodynamic limit at low temperature 1/β∈(0,∞). The ground …

A Proof of Finite Crystallization via Stratification

M Friedrich, L Kreutz - Journal of Statistical Physics, 2023 - Springer
We devise a new technique to prove two-dimensional crystallization results in the square
lattice for finite particle systems. We apply this strategy to energy minimizers of …

Attractive Riesz potentials acting on hard spheres

A Kubin, M Ponsiglione - Nonlinearity, 2021 - iopscience.iop.org
Attractive Riesz potentials acting on hard spheres Page 1 Nonlinearity PAPER Attractive Riesz
potentials acting on hard spheres To cite this article: A Kubin and M Ponsiglione 2021 …

Emergence of Wulff-Crystals from atomistic systems on the FCC and HCP lattices

M Cicalese, L Kreutz, GP Leonardi - Communications in Mathematical …, 2023 - Springer
We consider a system of N hard spheres sitting on the nodes of either the FCC or HCP
lattice and interacting via a sticky-disk potential. As N tends to infinity (continuum limit) …

A proof of finite crystallization via stratification

L Kreutz, M Friedrich - arxiv preprint arxiv:2209.14880, 2022 - arxiv.org
We devise a new technique to prove two-dimensional crystallization results in the square
lattice for finite particle systems. We apply this strategy to energy minimizers of …

Some Recent Results on 2D Crystallization for Sticky Disc Models and Generalizations for Systems of Oriented Particles

LD Luca - Research in Mathematics of Materials Science, 2022 - Springer
We review some recent results on crystallization in two dimensions for pairwise interaction
energies adopting a variational approach. We discuss the behavior of minimizers and quasi …

A variational approach to nonlocal interactions: discrete-to-continuum analysis, ground states and geometric evolutions

A Kubin - 2021 - iris.uniroma1.it
This thesis deals with variational models for systems governed by nonlocal interactions. In
particular, we analyze systems of hard spheres governed by attractive Riesz potentials …