arXiv subjects

Sebastián Domínguez

Publications and source records attributed to Sebastián Domínguez.

4 recordsLinked to original sources

arXiv2021

The evolution of the COVID-19 pandemic in Chile during 2020: a data perspective

The COVID-19 pandemic has had a great impact in most countries worldwide, in particular impacting Chile greatly to become one of the worst hit countries in the world, despite its low population compared to other affected countries around the world. In this study we report the evolution of the COVID-19 pandemic and the spread of the SARS-CoV-2 virus in Chile since the first positive case was announced on March 3, 2020, and until November 30, 2020. We provide a detailed description of the data provided by the Chilean Ministry of Science per administrative region on the number of new cases, tests per capita, and deaths in the country.

q-bio.PE↗

arXiv2020

Steklov eigenvalues for the Lamé operator in linear elasticity

In this paper we study Steklov eigenvalues for the Lamé operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement. To establish the existence of a countable spectrum for this problem, we present an extension of Korn's inequality. We also show that a proposed conforming Galerkin scheme provides convergent approximations to the true eigenvalues. A standard finite element method is used to conduct numerical experiments on 2D and 3D domains to support our theoretical findings.

math.AP↗

arXiv2019

Korn's inequality and Jones eigenpairs

In this paper we show that Korn's inequality \cite{ref:korn1906} holds for vector fields with a zero normal or tangential trace on a subset (of positive measure) of the boundary of Lipschitz domains. We further show that the validity of this inequality depends on the geometry of this subset of the boundary. We then consider the {\it Jones eigenvalue problem} which consists of the usual traction eigenvalue problem for the Lamé operator for linear elasticity coupled with a zero normal trace of the displacement on a non-empty part of the boundary. Here we extend previous works in the literature to show the Jones eigenpairs exist on a broad variety of domains even when the normal trace of the displacement is constrained only on a subset of the boundary. We further show that one can have eigenpairs of a modified eigenproblem in which the constraint on the normal trace on a subset of the boundary is replaced by one on the tangential trace.

math.AP↗

arXiv2019

Revisiting the Jones eigenproblem in fluid-structure interaction

The Jones eigenvalue problem first described by D.S. Jones in 1983 concerns unusual modes in bounded elastic bodies: time-harmonic displacements whose tractions and normal components are both identically zero on the boundary. This problem is usually associated with a lack of unique solvability for certain models of fluid-structure interaction. The boundary conditions in this problem appear, at first glance, to rule out {\it any} non-trivial modes unless the domain possesses significant geometric symmetries. Indeed, Jones modes were shown to not be possible in most $C^\infty$ domains (see article by T. Hargé 1990). However, we should in this paper that while the existence of Jones modes sensitively depends on the domain geometry, such modes {\it do} exist in a broad class of domains. This paper presents the first detailed theoretical and computational investigation of this eigenvalue problem in Lipschitz domains. We also analytically demonstrate Jones modes on some simple geometries.

math.NA↗