Related papers: Snaking without subcriticality: grain boundaries a…

We study the vibrational spectrum of a constrained classical ring. Due to the presence of 2-order exceptional points, a topologically trivial band at the infinity can make the vibrational band topologically nontrivial. The symmetry, which…

Topological boundary states exhibit distinctive properties, including unidirectional propagation and noise robustness, which hold significant potential for advancing the performance of quantum science and technology. Here, we demonstrate…

Amplitude equations are used to describe the onset of instability in wide classes of partial differential equations (PDEs). One goal of the field is to determine simple universal/generic PDEs, to which many other classes of equations can be…

The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~$\R^3$, i.e. nonlocal minimal surfaces with a graphical structure. We establish that at any boundary points at which the trace from inside…

The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case…

Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…

We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…

Band structures of metamaterials described by a nonlinear eigenvalue problem are beyond the existing topological band theory. In this paper, we analyze non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we elucidate…

Defects between gapped boundaries provide a possible physical realization of projective non-abelian braid statistics. A notable example is the projective Majorana/parafermion braid statistics of boundary defects in fractional quantum…

We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed with the…

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

This study delves into the complex mechanisms of defect production and accumulation in nanocrystalline tungsten under irradiation, with a particular focus on the interplay between grain boundaries and free surfaces. Through molecular…

Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum criticality admit sigma model descriptions in…

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…

The dynamical mechanisms underlying the grain evolution and growth are of fundamental importance in controlling the structural properties of large-scale polycrystalline materials, but the effects of lattice ordering and distinct atomic…

Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work however, we show that signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest…

The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that…

We consider localized states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localized states is made possible by…

Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…