Related papers: Long time behavior of dynamic solution to Peierls-…
We study the relaxation times for a parabolic differential equation whose solution represents the atom dislocation in a crystal. The equation that we consider comprises the classical Peierls-Nabarro model as a particular case, and it allows…
In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core structure. We focus on the static and dynamic PN models of an…
We study the existence and uniqueness of solutions to the vector field Peierls-Nabarro model for curved dislocations in a transversely isotropic medium. Under suitable assumptions for the misfit potential on the slip plane, we reduce the 3D…
We study the well-posedness of the vector-field Peierls-Nabarro model for curved dislocations with a double well potential and a bi-states limit at far field. Using the Dirichlet to Neumann map, the 3D Peierls-Nabarro model is reduced to a…
The theory of the dislocation motion in the periodic potential relief of the crystal lattice (the Peierls-Nabarro barriers) is reviewed. On the basis of the kink mechanism the temperature dependence of the flow stress is described for a…
This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic L\'{e}vy operator of order 1 and a potential depending periodically on…
High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high…
We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in a plane. Both a continuous energy with linear growth depending on a measure which characterizes the macroscopic dislocation density and a nonlocal…
Non-singular dislocation continuum theories are studied. A comparison between Peierls-Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses,…
In this paper, we prove the convergence from the atomistic model to the Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex lattice. We show that the displacement field of the dislocation solution of the PN model…
We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schr\"odinger model with saturable on-site nonlinearity. A numerical constrained…
The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the `glide' and `climb' type, by means of Mura's eigenstrains method. These…
Plasticity of metals is the emergent phenomenon of many crystal defects (dislocations) which interact and move on microscopic time and length scales. Two of the commonly used models to describe such dislocation dynamics are the…
We reexamine two essential issues within the Peierls-Nabarro model which are critical in obtaining accurate values for the Peierls stress. The first issue is related to the sampling scheme of the misfit energy across the glide plane and the…
In this paper we investigate two types of relaxation processes quantitatively in the context of small data global-in-time solutions for compressible one-velocity multi-fluid models. First, we justify the pressure-relaxation limit from a…
A new semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls-Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve the desired…
Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability…
We consider a nonlocal reaction-diffusion equation that physically arises from the classical Peierls-Nabarro model for dislocations in crystalline structures. Our initial configuration corresponds to multiple slip loop dislocations in…
A novel semidiscrete Peierls-Nabarro model is introduced which can be used to study dislocation spreading at more than one slip planes, such as dislocation cross-slip and junctions. The strength of the model, when combined with ab initio…
We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian whose solution represents the atom dislocation in a crystal. The equation comprises the evolutive version of the classical…