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We analyze transmission electron microscopy (TEM) images of self-assembled quasicrystals, composed of binary systems of nanoparticles. We use an automated procedure that identifies the positions of dislocations and determines their…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation…
We present a variational framework for studying screw dislocations subject to antiplane shear. Using a classical model developed by Cermelli and Gurtin, methods of Calculus of Variations are exploited to prove existence of solutions, and to…
We experimentally and numerically examine stress-dependent electrical transport in granular materials to elucidate the origins of their universal dielectric response. The ac responses of granular systems under varied compressive loadings…
In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. This model describes the evolution of phase transitions…
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…
In this paper a family of non-autonomous scalar parabolic PDEs over a general compact and connected flow is considered. The existence or not of a neighbourhood of zero where the problems are linear has an influence on the methods used and…
In recent years there has been renewed interest in the behavior of dislocations in crystals that exhibit strong atomic scale disorder, as typical of compositionally complex single phase alloys. The behavior of dislocations in such crystals…
As fundamental one-dimensional defects, screw dislocations profoundly reshape the energy landscape and carrier dynamics of crystalline materials. By restoring the exact algebra of the screw dislocation group, we unveil the latent symmetry…
Predicting the strength of materials requires considering various length and time scales, striking a balance between accuracy and efficiency. Peierls stress measures material strength by evaluating dislocation resistance to plastic flow,…
A phenomenological model of the Landau type forms the basis for a study of elastic distortions near the spin-Peierls transition $T_c$ in $CuGeO_3$. The atomic displacements proposed by Hirota {\it et al.} [Phys. Rev. Lett. {\bf 73}, 736…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We…
We develop a unified Cartan geometric framework where dislocations and disclinations correspond to torsion and curvature of the material coframe connection, respectively, and phase defects emerge as U(1) vortices. This single action…
In this paper a we derive by means of $\Gamma$-convergence a macroscopic strain-gradient plasticity from a semi-discrete model for dislocations in an infinite cylindrical crystal. In contrast to existing work, we consider an energy with…
We consider a nonlocal semi-linear parabolic equation on a connected exterior domain of the form $\mathbb{R}^N\setminus K$, where $K\subset\mathbb{R}^N$ is a compact "obstacle". The model we study is motivated by applications in biology and…
Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk.…
A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous collocation-based discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of the…
Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum…