Related papers: Unveiling Topological Modes on Curved Surfaces

The description of free surface flows can often be simplified to thin film (or lubrication) equations, when the slopes of the liquid-gas interface are small. Here we present a long wavelength theory that remains fully quantitative for steep…

To investigate the topological structure of Morse functions on the projective plane we use the Reeb graphs. We describe it properties and prove that it is a complete topological invariant of simple Morse function on $\mathbb{R} P^2$. We…

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the…

This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a…

We prove existence and multiplicity of periodic motions for the forced 2-body problem under conditions of topological character. In the different cases, the lower bounds obtained for the number of solutions are related to the winding number…

We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…

Given two closed curves in a surface, we propose an algorithm to detect whether they are of the same type or not.

This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…

In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…

Propagation of the surface waves on the interface between an uniaxial hyperbolic material and an isotopical topological insulator is studied. The cases of the anisotropy axes is normal to interface or one is coplanar to interface are…

Topological aspects of surface states in semiconductors are studied by an adiabatic deformation which connects a realistic system and a decoupled covalent-bond model. Two topological invariants are focused. One is a quantized Berry phase,…

We study the topological properties of a kagome plasmonic metasurface, modelled with a coupled dipole method which naturally includes retarded long range interactions. We demonstrate the system supports an obstructed atomic limit phase…

This study proposes the topology optimization method for moving rigid bodies subjected to forces from fluid flow, such as sails and turbines, with an unsteady time-dependent formulation. Unlike existing topology optimization frameworks in…

We demonstrate applications of topological characteristics of oil and gas reservoirs considered as three-dimensional bodies to geological modeling.

The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…

Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for Purcell…