Related papers: Emergence of rigid Polycrystals from atomistic Sys…
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the…
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to…
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group…
In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the $\Gamma$-limit of a family of discrete energies driven by a sequence of independent and…
Microstructural changes in solids, driven by energy flows, do not develop in a static continuous space, such as the space considered in conventional plasticity models. The applied forces create an evolving internal energy landscape, which…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some…
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…
While diffusion in crystalline solids is quantitatively understood through defect-mediated atomic hops, no comparable quantitative framework exists for glasses. In these systems, the origin of large diffusion activation energies remains…
We derive a microscopic theory of glassy dynamics based on the transport of voids by micro-string motions, each of which involves particles arranged in a line hopping simultaneously displacing one another. Disorder is modeled by a random…
When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that…
In this paper we present two atomistic models for the energy of a one-dimensional elastic crystal. We assume that the macroscopic displacement equals the microscopic one. The energy of the first model is given by a two-body interaction…
In this paper we analyze a two-dimensional discrete model of nearest-neighbour Lennard-Jones interactions under the microscopical constraint that points on a lattice triangle maintain their order. This can be understood as a microscopical…
We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the…
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…
We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the…