We examine the inverse problem of locating and describing an internal point defect in a one-dimensional rod $\Omega$ by controlling the heat inputs and measuring the subsequent temperatures at the boundary of $\Omega$. We use a variation of the forward heat equation to model heat flow through $\Omega$, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.

Author Bio

I participated in Rose-Hulman's REU in the summer before my junioryear. I have always been interested in physics-based mathematics. I am currently a math/psychology double-major at Eckerd College in St. Pete, FL. Iguess I like studying behavior, especially change, in both a qualitative andquantitative fashion. My other hobbies are art, writing poetry, and dreaming.Sometimes my mind drifts and falls into abstraction, but math can always bring meback to reality (unless, of course, it is abstract algebra).

I am currently a senior at MIT, both in the mathematics and science, technology, and society (STS) departments. This work was done in the summer of 2002 REU program at the Rose-Hulman Institute of Technology, under the excellent supervision of Prof. Kurt Bryan. In mathematics, I am generally interested in nonlinear dynamics. In STS, I am interested in the social construction of risk. When not doing math or working on my senior thesis, I can be found working on MITs literary magazine and planning social events for the MIT Class of 2003.