The Farnum Lab
Edward Farnum, PhD
Dr. Ted Farnum is an assistant professor of Applied Mathematics at NJCSTM. Dr. Farnum’s research interests are in differential equations, mathematical physics, asymptotic analysis and numerical methods and scientific computing. He combines all these approaches to models in nonlinear optical science. In particular, he is interested in constructing and analyzing nonlinear wave models for ultra-short pulse propagation, which may be especially useful in all optical computing and improved fiber optic communications. His teaching interests have a similar applied and computational flavor.
His courses feature mathematical modeling, scientific computation, asymptotic analysis and spectral methods. Dr. Farnum received his Ph.D. in Applied Mathematics from the University of Washington in 2005.
Current Research Focus - Dynamical Systems & Wave Propagation
Dynamical Systems is a branch of mathematics which uses differential equations to describe the evolution of a system over time. These equations are often nonlinear, and can lead to unexpected or chaotic results. Nonlinear wave equations govern the behavior of a wide variety of phenomena in physics and engineering, including tsunami formation, ultra-short fiber-optical communications, laser mode-locking, and Bose-Einstein Condensates. Improved understanding of these nonlinear wave systems can impact areas as diverse as advanced tidal wave warnings and high precision biological spectroscopy. The purpose of this research stream is to develop and analyze nonlinear wave models for ultra-short optical pulses. Presently, mode-locked lasers can generate pulses exceeding the bounds predicted by standard models. New mathematical models are needed to guide engineers, and to help determine a feasible range of physical parameters for construction and operation of ultra-fast optical devices.
Students in this stream will learn numerical and computational methods for optimization, root-finding, partial differential equations, spectral analysis, and linear stability analysis. This research stream is appropriate for students with interests in applied mathematics, physics, computational science, engineering, differential equations, and numerical analysis. Familiarity with any of the above fields will be beneficial. Students considering this research stream should have two semesters of calculus and some programming experience. Some background in linear algebra and differential equations is desirable but not required. Exceptions will be considered based on an interview with the instructor and approval of the Dean
Microbes and Microbiomes
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