Mathematical theory for topological photonic materials in one dimension

Topological superconducting phases in one dimension

Topological phases of fermions in one dimension

In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the time-reversal-invariant Majorana chain (BDI symmetry class). While the band classification yields an integer topological index k, it is known that phases characterized by values of k in the same equivalence class...

Mathematical Theory of Plasticity for Frictional Materials

We consider the extension of the classical mathematical theory of plasticity to frictional materials. It is shown that the apparently nonassociated plastic flow characteristics often observed in such materials can be accounted for by models that are variational in structure. In addition, the theory predicts a number of new terms and functional relationships that appear to have particular releva...

Photonic Materials and Devices

Our recent advances in solid-state optoelectronic materials and devices will be reviewed. In the area of glass optics, fabrication of novel microstructured and multi-core fibers and their use in realizing single mode lasers will be summarized. In organic and plastic optics, photorefractive polymers for 3D display applications and nonlinear optical polymers for high speed modulators in RF photon...

Dimension theory and fuzzy topological spaces

J.M. Aarts introduced and studied a new dimension function, Hind, in 1975 and obtained several results on this function. In this paper, a new local inductive dimension function called local huge inductive dimension function denoted by locHind is introduced and studied. Furthermore, an effort is made to introduce and study dimension functions for fuzzy topological spaces. It has been possible to...