Related papers: A variational model for dislocations at semi-coher…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…
This paper introduces for the first time the concepts of non-coherent interfaces and microstructure-driven interface forces in the framework of micromorphic elasticity. It is shown that such concepts are of paramount importance when…
We study energy transport in a system of two dimensional conformal field theories exchanging energy across a non-conformal interface involving a localised scalar operator, using holographic duality. By imposing the sourceless boundary…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model…
The elastic energy of a bending-resistant interface depends both on its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The…
A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys…
A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material…
The static and dynamic properties of a Cosserat-type lattice interface of finite thickness are studied, so that both displacements and rotational degrees of freedom are taken into account. The model allows considering interfaces with a…
Interface migration in microstructures is mediated by the motion of line defects with step and dislocation character, i.e., disconnections. We propose a continuum model for arbitrarily-curved grain boundaries or heterophase interfaces…
Using first principles, classical potentials, and elasticity theory, we investigated the structure of a semiconductor/semiconductor interface with a high lattice mismatch, SiC/Si(001). Among several tested possible configurations, a…
Friction is a major source of energy loss in mechanical devices. This energy loss may be minimized by creating interfaces with extremely reduced friction, i.e. superlubricity. Conventional wisdom holds that incommensurate interface…
We consider a simplified physics of the could interface where condensation, evaporation and radiation are neglected and momentum, thermal energy and water vapor transport is represented in terms of the Boussinesq model coupled to a passive…
We have developed different network approaches to complex patterns of frictional interfaces (contact areas developments). Here, we analyze the dynamics of static friction. We found, under the correlation measure, the fraction of triangles…
The elastic energy functional of a system of discrete dislocation lines is well known from dislocation theory. In this paper we demonstrate how the discrete functional can be used to systematically derive approximations which express the…
Interface free energy is the contribution to the free energy of a system due to the presence of an interface separating two coexisting phases at equilibrium. It is also called surface tension. The content of the paper is 1) the definition…
We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as…
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…
In this study we try to answer the qustion : What happens when explicit constraints are introduced such that the low energy, long wavelength modes of a system are unavailable ? This question has assumed some importance in recent years due…
Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…