Related papers: Emergence of rigid Polycrystals from atomistic Sys…
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the `sticky disk' interaction potential models the…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…
The calculation of the discrete atomistic energy of a crystal near the continuum limit encounters difficulties caused by the geometric discrepancy between the continuum region occupied by the body, and the discrete collection of lattice…
In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…
We study the behavior of atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
We design, fabricate and test heterogeneous architected polycrystals, composed of hard plastomers and soft elastomers, which thus show outstanding mechanical resilience and energy dissipation simultaneously. Grain boundaries that separate…
We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a line of fixed atoms. The rescaled model…
Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Non-equilibrium filling, through random…
Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list…
The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…
We consider a system of $N$ hard spheres sitting on the nodes of either the $\mathrm{FCC}$ or $\mathrm{HCP}$ lattice and interacting via a sticky-disk potential. As $N$ tends to infinity (continuum limit), assuming the interaction energy…
In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from…