arXiv subjects

Diana C. S. Bello

Publications and source records attributed to Diana C. S. Bello.

3 recordsLinked to original sources

arXiv2025

Spectrum of the Laplacian in waveguide shaped surfaces

Let $-Δ_{\cal S}$ be the Laplace operator in ${\cal S} \subset \mathbb{R}^3$ on a waveguide shaped surfaces, i.e., ${\cal S}$ is built by translating a closed curve in a constant direction along an unbounded spatial curve. Under the condition that the tangent vector of the reference curve admits a finite limit at infinity, we find the essential spectrum of $-Δ_{\cal S}$ and discuss conditions under which discrete eigenvalues emerge. Furthermore, we analyze the Laplacian in the case of a broken sheared waveguide shaped surface.

math-ph↗

arXiv2025

A note on twisted, straight, and sheared waveguide

In this work, we analyze the Dirichlet Laplacian $-Δ_Ω^D$ in an unbounded waveguide $Ω\subset \mathbb R^3$, where the cross-section is translated in a constant direction and rotated along a spatial line. We focus on the effects of twisting on the spectrum, discussing conditions under which discrete eigenvalues emerge. Our results highlight the interplay between geometry and spectral properties, showing that shearing can induce a richer spectral structure even in straight waveguides.

math-ph↗

arXiv2022

Spectral analysis in broken sheared waveguides

Let $Ω\subset \mathbb R^3$ be a broken sheared waveguide, i.e., it is built by translating a cross-section in a constant direction along a broken line in $\mathbb R^3$. We prove that the discrete spectrum of the Dirichlet Laplacian operator in $Ω$ is non-empty and finite. Furthermore, we show a particular geometry for $Ω$ which implies that the total multiplicity of the discrete spectrum is equals 1.

math.SP↗