Related papers: Crystal dislocations with different orientations a…

Molecular static simulations have been performed to study the interaction between a single dislocation and a substitutional Al solute atom in a pure crystal of Ni. When the Al solute is situated at intermediate distance from the slip plane,…

We investigate the diffusion of a grain boundary in a crystalline material. We consider in particular the case of a regularly spaced low-angle grain boundary schematized as an array of dislocations that interact with each other through…

The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…

In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a…

We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the solution. Our system describes an approximate model of the…

We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a one-dimensional system of a parabolic equation and a first order Hamilton-Jacobi equation that are coupled together. We…

We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…

We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are…

The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the…

The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…

A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…

Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…

This chapter reviews the different methodological aspects of the ab ini-tio modeling of dislocations. Such simulations are now frequently used to study the dislocation core, i.e. the region in the immediate vicinity of the line defect where…

This work unravels the atomic details of the interaction of solute atoms with nanoscale crystalline defects. The complexity of this phenomenon is elucidated through detailed atom probe tomographic investigations on epitaxially-strained,…

The universality class of the avalanche behavior in plastically deforming crystalline and amorphous systems has been commonly discussed, despite the fact that the microscopic defect character in each of these systems is different. In…

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and…

We propose a numerical model to study the viscoplastic deformation of ice single crystals. We consider long-range elastic interactions among dislocations, the possibility of mutual annihilation, and a multiplication mechanism representing…

Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of…

Defects play a key role in deciding the mechanisms and kinetics of phase transformations. In this paper, we show how dislocations influence phase separation in alloys with miscibility gap. Specifically, depending on the ratio of pipe…