Related papers: Self-energy of dislocations and dislocation pileup…
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 propose a discrete lattice model of the energy of dislocations in three-dimensional crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic interatomic interactions, elastic deformations and discrete…
In this study, we examine a double nonlinear porous medium equation subject to a novel nonlinearity condition within a bounded domain. First, we introduce the blow-up solution for the problem under consideration for the negative initial…
Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the…
The dislocation structures appearing in highly mis-oriented soft/hard grain pairs in near-alpha titanium alloy Ti6242Si were examined with and without the application of load holds (dwell) during fatigue. Dislocation pile-up in a soft grain…
We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First we obtain the local equilibrium…
We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the corresponding continuum…
To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge…
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…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior…
A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and…
We investigate a suspension bridge model described by a nonlinear plate equation incorporating internal fractional damping and infinite memory effects. The system also includes a nonlinear source term that may induce instability. Using…
We consider a spatially distributed demand for electrical vehicle recharging, that must be covered by a fixed set of charging stations. Arriving EVs receive feedback on transport times to each station, and waiting times at congested ones,…
We investigate bound state solutions of the 2D Schr\"odinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. The knowledge of these states could be useful for understanding a wide variety…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends…
The paper suggests a new stochastic model for energy producing, dispatching, and storing in the multi-battery setting that takes into account the topology of the system of the links between the batteries, the transmission and storage…
In the present work, we propose a novel model coupling phase-field, dislocation density based plasticity and damage. The dislocation density governing equations are constructed based on evolutions of mobile and immobile dislocations.…
We study the critical points of Coulomb energy considered as a function on configuration spaces associated with certain geometric constraints. Two settings of such kind are discussed in some detail. The first setting arises by considering…