11 citations · 34 across the 19 of their papers we have counts for
20 papers
The charge dependent hard-sphere model: Polycrystals as low-energy configurations
Leonard Kreutz, Timo Ziereis
We investigate the emergence of rigid polycrystalline structures in atomistic ionic particle systems as low-energy configurations. The interaction between particles of opposite cha…
Emergence of rigid Polycrystals from atomistic Systems with general Interactions
Leonard Kreutz, Timo Ziereis
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being loca…
Crystallization in the Winterbottom shape and sharp fluctuation laws
Manuel Friedrich, Leonard Kreutz, Ulisse Stefanelli
We address finite crystallization in two dimensions in the presence of a flat crystalline substrate. Particles interact through short-range two- and three-body potentials favoring…
Derivation of Kirchhoff-type plate theories for elastic materials with voids
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featur…
Energy concentration in a two-dimensional magnetic skyrmion model: variational analysis of lattice and continuum theories
Luca Briani, Marco Cicalese, Leonard Kreutz
We investigate the formation of singularities in a baby Skyrme type energy model, which describes magnetic solitons in two-dimensional ferromagnetic systems. In presence of a diver…
Derivation of effective theories for thin 3D nonlinearly elastic rods with voids
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of -convergence. Hereby, we generalize the results of the purely elastic setting […
A proof of finite crystallization via stratification
Leonard Kreutz, Manuel Friedrich
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 configu…
Emergence of Wulff-Crystals from atomistic systems on the FCC and HCP lattices
Marco Cicalese, Leonard Kreutz, Gian Paolo Leonardi
We consider a system of hard spheres sitting on the nodes of either the or lattice and interacting via a sticky-disk potential. As tends to in…
From atomistic systems to linearized continuum models for elastic materials with voids
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discre…
Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We present a quantitative geometric rigidity estimate in dimensions generalizing the celebrated result by Friesecke, James, and Müller to the setting of variable domains. L…
Crystallinity of the homogenized energy density of periodic lattice systems
Antonin Chambolle, Leonard Kreutz
We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the eff…
The antiferromagnetic XY model on the triangular lattice: topological singularities
Annika Bach, Marco Cicalese, Leonard Kreutz +1
We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice in the vortex regime. Within this regime, the spin…
Emergence of rigid Polycrystals from atomistic Systems with Heitmann-Radin sticky disk energy
Manuel Friedrich, Leonard Kreutz, Bernd Schmidt
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energ…
The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling
Annika Bach, Marco Cicalese, Leonard Kreutz +1
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 fa…
Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice
Manuel Friedrich, Leonard Kreutz
We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of conf…
Microscopic validation of a variational model of epitaxially strained crystalline film
Leonard Kreutz, Paolo Piovano
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by -convergence. The discrete model here introduced…
Crystallization in the hexagonal lattice for ionic dimers
Manuel Friedrich, Leonard Kreutz
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-range…
A homogenization result for weak membrane energies
Leonard Kreutz
We prove a -convergence result for space dependent weak membrane energies, that is for 'truncated quadratic potentials', that are quadratic below some threshold (depending on th…
An integral-representation result for continuum limits of discrete energies with multi-body interactions
Andrea Braides, Leonard Kreutz
We prove a compactness and integral-representation theorem for sequences of families of lattice energies describing atomistic interactions defined on lattices with vanishing lattic…
Optimal design of mixtures of ferromagnetic interactions
Andrea Braides, Leonard Kreutz
We provide a general framework for the optimal design of surface energies on networks. We prove sharp bounds for the homogenization of discrete systems describing mixtures of ferro…