Related papers: Point defects in two-dimensional colloidal crystal…
Vacancies are prevalent point defects in crystals, but their thermal responses are elusive. Herein, we formulate a simple theoretical model to shed light on the vacancy evolution during heating. Vibrational excitations are thoroughly…
We present a new definition of defects which is based on a Riemannian formulation of incompatible elasticity. Defects are viewed as local deviations of the material's reference metric field, $\bar{\mathfrak{g}}$, from a Euclidian metric.…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
In order to predict the long-term effects of irradiation on the material properties of tungsten, a continuum approach to simulating the interactions of dislocation loops, which arise from radiation damage, is proposed. Continuum models of…
Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement…
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that…
A direct formulation of linear elasticity of cell complexes based on discrete exterior calculus is presented. The primary unknown are displacements, represented by primal vector-valued 0-cochain. Displacement differences and internal forces…
During plastic deformation of crystalline materials, point defects such as vacancies and interstitials are generated by jogs on moving dislocations. A detailed model for jog formation and transport during plastic deformation was developed…
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect…
The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries, occurs when the lattice configuration loses stability, that is, when an eigenvalue of the Hessian of the lattice energy functional becomes…
We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of…
The evolution of point defect concentrations under irradiation is controlled by their diffusion properties, and by their formation and elimination mechanisms. The latter include the mutual recombination of vacancies and interstitials, and…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
We study the interplay between an isostructural critical point and dislocation mediated two-dimensional melting, using a combination of Landau and continuum elasticity theory. If dislocations are excluded, coupling to the elastic degrees of…
We calculate mean square deviations for crystals in one and two dimensions. For the two dimensional lattices, we consider several distinct geometries (i.e. square, triangular, and honeycomb), and we find the same essential phenomena for…