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Applying The Power Of Math

New Faculty Expand Department's Cross-Disciplinary Efforts

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Four new faculty members with the Mathematics Department in Dedman College – Thomas Hagstrom, Alejandro Aceves, Brandilyn Stigler and Daniel Reynolds – are expected to build on the department’s strengths and help it expand cross-disciplinary efforts. Math faculty are working with SMU colleagues in the Mechanical Engineering, Electrical Engineering and Chemistry Departments. Applied mathematics is helping researchers across disciplines solve questions that range in scale from the vastness of the cosmos down to the cellular level, says professor and former department chair Peter K. Moore, who recently was named dean ad interim of Dedman College of Humanities and Sciences. “Mathematical modeling, simulation and analysis can lead to greater efficiency in interdisciplinary projects by indicating which direct experiments are likely to provide the most useful results.”

The Highs And Lows Of Wave Propagation
Professor Thomas Hagstrom, who holds a Ph.D. from the California Institute of Technology and comes to SMU from the University of New Mexico, specializes in using computational science – mathematics that harnesses the power of computers – to devise the most efficient methods of solving partial differential equations for wave propagation. The equations have applications in a variety of cross-disciplinary settings including acoustics, seismics, electrical engineering and astrophysics. Just like waves in the ocean, sound waves in the field of acoustics and electromagnetic waves such as radar are made up of peaks and valleys that are described by their wavelength, which is the distance between successive peaks, he says. “When you look at something or listen to something, the peaks and troughs of those waves are carrying the information to your eyes, ears or, in the case of radar, to a machine that augments your own senses.” Hagstrom’s greatest success has been in developing algorithms – instructions for solving complex programs – that limit the size of the sampling region in models of so-called wave-scattering problems. For instance, if an airplane is the object of interest, his algorithms can maximize the efficiency of simulating a radar system by curbing the computation to the airplane, rather than sampling everywhere in the sky, he explains. In addition to teaching a graduate course that focuses on applying computational methods to wave propagation phenomena, Hagstrom taught a Calculus I course last fall. “I haven’t taught any students below senior level in more than 12 years,” he says, describing the opportunity as one of the unique aspects of teaching at SMU. “One unfortunate trend at a lot of state universities has been to cover much of the lower level teaching with either lecturers or adjunct faculty, whereas at SMU, senior faculty teach those classes.”

Laser Lightning Rods
Professor Alejandro Aceves also came to SMU from the University of New Mexico, where he served as chair of the mathematics department. His specialty is nonlinear optics and lasers: the science of the visible and nearvisible spectrum of light at energy levels so large they distort the propagating medium – the medium through which the energy travels, such as the atmosphere. Aceves is continuing one project with University of New Mexico experimental physicist Jean Claude Diels on ultraviolet (UV) laser beams as they travel over great distances through the atmosphere. The project may someday lead to laser sensors that identify explosives at a distance, says Aceves, who earned his Ph.D. from University of Arizona.

Another application of this research would use high-energy laser pulses as a conduit to collect and channel lightning, basically improving on Benjamin Franklin’s lightning rod. “Lightning is a random effect because you don’t know where it’s going to hit. There is always a danger of it hitting in the wrong place, like a house or where individuals are standing,” he says. “If you send one of these lasers into the atmosphere it acts like a channel, so now the lightning will propagate where the channel travels.”