Related papers: On new surface-localized transmission eigenmodes
In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse…
We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In…
The Neumann--Poincar\'e operator defined on a smooth surface has a sequence of eigenvalues converging to zero, and the single layer potentials of the corresponding eigenfunctions, called plasmons, decay to zero, i.e., are localized on the…
We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under…
A theory of surface electromagnetic waves in gradient media exhibiting arbitrary surface gradients of dielectric permittivity and magnetic permeability has been developed. Novel low-loss propagating surface wave solutions have been found in…
Van der Waals (vdW) heterostructures, which are produced by the precise assemblies of varieties of two-dimensional (2D) materials, have demonstrated many novel properties and functionalities. Here we report a nano-plasmonic study of vdW…
Self-supervised representation learning techniques utilize large datasets without semantic annotations to learn meaningful, universal features that can be conveniently transferred to solve a wide variety of downstream supervised tasks. In…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
This article addresses the microlocalization of eigenfunctions for the semiclassical Schr\"odinger operator $-h^2\Delta+V$ on closed Riemann surfaces with real bounded potentials. Our primary aim is to establish quantitative bounds on the…
It is an open problem in general to prove that there exists a sequence of $\Delta_g$-eigenfunctions $\phi_{j_k}$ on a Riemannian manifold $(M, g)$ for which the number $N(\phi_{j_k}) $ of nodal domains tends to infinity with the eigenvalue.…
Let $\Omega\subset\mathbb{R}^{n}$ be a smooth bounded domain and $m\in C(\overline{\Omega})$ be a sign-changing weight function. For $1<p<\infty$, consider the eigenvalue problem $$ \left\{ \begin{array} [c]{ll} -\Delta_{p}u=\lambda…
Enhanced transmissions through a gold film with arrays of subwavelength holes are theoretically studied, employing the rigid full vectorial three dimensional finite difference time domain method. Influence of air-holes shape to the…
In this paper we study the theory of self translating solitons of the mean curvature flow of immersed surfaces in the product space $\mathbb{H}^2\times\mathbb{R}$. We relate this theory to the one of manifolds with density, and exploit this…
We propose and analyze an efficient spectral-Galerkin approximation for the Maxwell transmission eigenvalue problem in spherical geometry. Using a vector spherical harmonic expansion, we reduce the problem to a sequence of equivalent…
We studied electromagnetic wave propagation in a system that is periodic in both space and time, namely a discrete 2D transmission line (TL) with capacitors modulated in tandem externally. Kirchhoff's laws lead to an eigenvalue equation…
A local permittivity model is proposed to accurately characterize spatial dispersion in non-local wire-medium (WM) structures with arbitrary terminations. A closed-form expression for the local thickness-dependent permittivity is derived…
We consider the chemotaxis model \begin{align*} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v), \\ v_t = \Delta v - vw, \\ w_t = -\delta w + u \end{cases} \end{align*} in smooth, bounded domains $\Omega \subset \mathbb R^n$, $n…
After the surface theory of M\"obius geometry, this study concerns a pair of conformally immersed surfaces in $n$-sphere. Two new invariants $\theta$ and $\rho$ associated with them are introduced as well as the notion of touch and…
In this paper, the propagation of water surface waves over one-dimensional periodic and random bottoms is investigated by the transfer matrix method. For the periodic bottoms, the band structure is calculated, and the results are compared…
We introduce the longitudinal and transverse static surface modes and use them to solve the full-wave electromagnetic scattering problem from penetrable objects. The longitudinal static modes are the eigenmodes with zero surface curl of the…