Related papers: Snaking without subcriticality: grain boundaries a…
While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework…
This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are…
We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…
A grain boundary which separates domains with different orientation along the c-axis is analyzed. The coupling of two parallel superconducting planes whose order parameters are rotated leads to interesting properties which are expected to…
We consider surface states in semiconductors with inverted-band structures, such as $\alpha$-Sn and HgTe. The main interest is the interplay of the effect of a strain of an arbitrary sign and that of the sample finite size. We consider, in…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
A continuum grain boundary model is developed that uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a 1-D grain array. The model uses a continuum…
Topological edge states in gaps of non-Hermitian systems are robust due to topological protection. Using the non-Hermitian Floquet Su-Schrieffer-Heeger model, we show that this robustness can break down: edge states may be suppressed by…
We show that the gapless boundary signatures - namely, chiral/helical hinge modes or localized zero modes - of three-dimensional higher-order topological insulators and superconductors with inversion symmetry can be gapped without symmetry…
The conditions for both the stability and the breakdown of the topological classification of gapped ground states of noninteracting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions are given for any…
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Topological semimetals exhibit protected band crossings in momentum space, accompanied by corresponding surface states. Non-Hermitian Hamiltonians introduce geometry-sensitive features that dissolve this bulk-boundary correspondence…
We consider non-colliding Brownian bridges starting from two points and returning to the same position. These positions are chosen such that, in the limit of large number of bridges, the two families of bridges just touch each other forming…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
Topological semimetals exhibit band crossings near the Fermi energy, which are protected by the nontrivial topological character of the wave functions. In many cases, these topological band degeneracies give rise to exotic surface states…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…
The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general…