Project Overview

The Mathematics of Invisibility

Faculty Sponsor

Silvia Jimenez Bolanos (sjimenez@colgate.edu)

Department(s)

Mathematics

Abstract

The goal of cloaking is to render an object invisible to detection from electromagnetic energy by surrounding the object with a specially engineered “metamaterial” that redirects electromagnetic waves around the object.  The main objective of the summer project is for the student(s) to understand the essential mathematical ideas behind cloaking.  The main tools to be used are vector calculus, Fourier series, differential equations, and linear algebra. The student(s) will go through a series of exercises to show how to cloak an object against detection from impedance tomography, though the mathematical ideas apply to much more general forms of imaging. The expected outcome of the project will be for the student(s) to generalize these ideas to more general forms of imaging.

Student Qualifications

The student must have completed (or have knowledge of the material covered in) the following courses: Calculus I, Calculus II, Calculus III, Linear Algebra and Ordinary Differential Equations.

Number of Student Researchers

2 students

Project Length

8 weeks

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If you have questions, please contact Karyn Belanger (kgbelanger@colgate.edu).