Motivated by the potential of atomically thin magnets towards achieving tunable high-frequency magnonics, we detail spin-wave dispersion bilayer ${\mathrm{CrI}}_{3}$. We demonstrate that magnonic behavior strongly depends on its stacking configuration and interlayer magnetic ordering, where a topological band gap opens in caused Dzyaloshinskii-Moriya Kitaev interactions, classifying ${\mathrm{C...

‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $mathbb{Z}_2$‎, ‎it has many base systems and some of the base systems can also be restricted to its sub algebras‎. ‎On the contrary‎, ‎in ...

The structural description of disordered systems has been a longstanding challenge in physical science. We propose an atomic cluster alignment method to reveal the development of three-dimensional topological ordering in a metallic liquid as it undercools to form a glass. By analyzing molecular dynamic (MD) simulation trajectories of a Cu(64.5)Zr(35.5) alloy, we show that medium-range order (MR...

Topological defects easily form in liquid crystals (LCs) as a result of frustrations in spatially dependent anisotropic molecular ordering, and have been regarded as promising tools for facilitating manipulation of relatively large non-LC materials such as colloids. However, it remains unclear whether low-molecular-weight (LMW) impurities that do not aggregate or self-assemble in bulk LCs becau...

We study central configurations lying on a common circle in the Newtonian four-body problem. Using topological argument we prove that there is at most one co-circular configuration for each cyclic ordering of masses circle.

Bogdan and Kolumbán [3] gave sufficient conditions for closedness of the solution map defined on the set of parameters. They considered the parametric equilibrium problems governed by topological pseudomonotone maps depending on a parameter. In this paper we generalize this result for parametric vector equilibrium problems with trifunctions. Let X and Y be Hausdorff topological spaces and P , t...

Let I (:z: ,y ,z) be a homogeneous polynomial With. rational coefficients. Let C, be the real projective curve defined by ! = 0" and suppos~ that C/ is nonsingular. It is well known that C/ is essentially a finite collection of disjoint circles, all except possibly one of which lie in th~ projective plane Rp2 in such a way as to have both an interior (homeomorphic to a disk), and an exterior (h...