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Pontifical Catholic University of Rio de Janeiro

1. JOAO MARCOS BREIA JUCA. [en] INVISIBILITY CLOAK AS AN INVERSE PROBLEM IN ELECTROMAGNETISM AND HOMOGENIZATION TECHNIQUES.

Degree: 2016, Pontifical Catholic University of Rio de Janeiro

[pt] Invisibilidade sempre mexeu com a imaginação de crianças e adultos. Quem nunca imaginou ser capaz de tornar-se invisível em certas ocasiões? Recentemente essa ideia da ficção científica tomou forma na vida real, e um dos objetivos do presente texto é explicar de uma maneira acessível as principais ideias físicas e matemáticas por trás do conceito de invisibilidade. Pedimos do leitor somente uma modesta familiaridade com Cálculo Vetorial, Séries de Fourier e Álgebra Linear. O objetivo da capa de invisibilidade é tornar um objeto não detectável por meio de energia eletromagnética. A capa é fisicamente realizada por um metamaterial especialmente projetado para redirecionar certas ondas eletromagnéticas irradiadas sobre o objeto. Nesta exposição, usaremos como exemplo a tomografia de impedância elétrica (TIE) como método de detecção e explicaremos como criar uma capa invisível à TIE. Cabe ressaltar que o processamento de imagem através da TIE diz respeito a um problema inverso e, no contexto das equações diferenciais, esse problema envolve, a partir de determinadas simplificações, a equação de Laplace com condições de contorno. Despretensiosamente, optamos pelo caso bidimensional para facilitar a exposição das idéias principais, embora todos os nossos resultados possam ser generalizados em 3 dimensões.

[en] Invisibility has always instigated children and adult s imagination. Who never thought of occasionally being able to turn yourself invisible? Recently, this science fiction idea has taken shape in real life, and one of the objectives of this text is explain the main physical and mathematical ideas behind the invisibility concept, on a comprehensible way. We only require the reader has a modest familiarity with Vectorial Calculus, Fourier Series and Linear Algebra. Invisibility cloak aims to turn an object imperceptible to electromagnetic energy detection. The cloak is made of an especially projected metamaterial that redirects certain electromagnetic waves irradiated over the object. Here we will take as an example electrical impedance tomography (EIT) as a detection method and we will explain how to create an invisible cloak for EIT. It is worth mentioning that image processing through EIT is an inverse problem. Thereby, in the context of differential equations, this problem involves a few simplifications in the Laplace s problem with contours conditions. Unpretentiously, we chose the two-dimensional case to simplify the exposition of the main ideas, although all of our results may be generalized in three-dimensional case.

Advisors/Committee Members: ALEX LUCIO RIBEIRO CASTRO.

Subjects/Keywords: [pt] PROBLEMA INVERSO; [en] INVERSE PROBLEM; [pt] METAMATERIAL; [en] METAMATERIAL; [pt] CAMUFLAGEM; [en] CLOAKING; [pt] TOMOGRAFIA DE IMPEDANCIA ELETRICA; [en] TOMOGRAFIA DE IMPEDANCIA ELETRICAELECTRICAL IMPEDANCE TOMOGRAPHY; [pt] EQUACAO DE LAPLACE; [en] LAPLACE S EQUATION

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

JUCA, J. M. B. (2016). [en] INVISIBILITY CLOAK AS AN INVERSE PROBLEM IN ELECTROMAGNETISM AND HOMOGENIZATION TECHNIQUES. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25619

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

JUCA, JOAO MARCOS BREIA. “[en] INVISIBILITY CLOAK AS AN INVERSE PROBLEM IN ELECTROMAGNETISM AND HOMOGENIZATION TECHNIQUES.” 2016. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed December 16, 2019. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25619.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

JUCA, JOAO MARCOS BREIA. “[en] INVISIBILITY CLOAK AS AN INVERSE PROBLEM IN ELECTROMAGNETISM AND HOMOGENIZATION TECHNIQUES.” 2016. Web. 16 Dec 2019.

Vancouver:

JUCA JMB. [en] INVISIBILITY CLOAK AS AN INVERSE PROBLEM IN ELECTROMAGNETISM AND HOMOGENIZATION TECHNIQUES. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2016. [cited 2019 Dec 16]. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25619.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

JUCA JMB. [en] INVISIBILITY CLOAK AS AN INVERSE PROBLEM IN ELECTROMAGNETISM AND HOMOGENIZATION TECHNIQUES. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2016. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25619

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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