# Doctoral Students Apply Passion for Mathematics to Nuclear Research, Cosmology, and Microscopy

Kasey Bray always finds beauty in the difficulty and struggle of problem solving. A fourth-year doctoral student in mathematics at the University of Kentucky, she understands it’s not a passion often shared by others.

“Mathematics is simultaneously stigmatized and esteemed, yet it is overwhelmingly perceived as inaccessible in our culture,” Bray said. “A career as a mathematician affords the opportunity to address such contradictory connotations.”

For those outside the field, mathematics research can be hard to visualize. “We don’t wear coats or goggles, nor tinker with beakers and fancy machines in a lab, and the language we use can sound foreign, if not like straight gibberish,” Bray noted.

The NSF MSGI program—administered through the DOE’s Oak Ridge Institute for Science and Education—provides research opportunities for mathematical sciences doctoral students to participate in internships at national laboratories, industries, and other facilities. NSF MSGI seeks to provide hands-on experience for the use of mathematics in a nonacademic setting.

During her internship, Bray contributed research on the nation’s nuclear stockpile to advance scientific understanding of special nuclear materials and enhance national security.

“As an average American, in an increasingly tense political climate, I find it comforting to know there are competent and trustworthy scientists studying and understanding the nation’s nuclear stockpile in an effort to keep us all safe,” Bray said. “Understanding these aging weapons is imperative to our ability to handle them responsibly.”

Under the mentorship of Aaron Luttman and Marylesa Howard of the Signal Processing and Applied Mathematics group at the NNSS, Bray studied field experiments designed to help scientists observe the behavior of plutonium and other nuclear materials when subjected to extreme temperature, pressure, and shocks.

Scientists can study nuclear material properties by observing how these materials break up into ejected particles. Measuring the size distribution of the cloud of ejected particles can provide valuable insight. The world’s fastest high-resolution camera cannot capture the necessary information, so researchers must utilize light-scattering methods to make such measurements. Specifically, scientists shine lasers through the cloud of ejected particles and then use specialized probes to measure the intensity of light scattered off of the particulates.

“When gathered and analyzed appropriately, the measurements yield information about the particle size distribution at a given moment in time,” Bray explained. “The current setup, however, is ill- defined, leaving us with questions like ‘What wavelength of laser light should be used? How many lasers are necessary? At what angles should the measurements be taken?’ My research sought to answer these questions.”

Bray used tools from linear algebra to analyze data capture methods that would produce the most reliable results. By the end of the internship, she had proposed and tested an approach that could be replicated in future experiments.

“My favorite part about the NSF MSGI program was the environment of collaboration and support for the advancement of colleagues’ projects and careers. There was an air of overall excitement within the group in a ‘Let’s talk about all the cool stuff we’re doing’ kind of way,” Bray said. “I entered this internship in the hopes of fulfilling curiosity about the role of math in an industry setting. Undeniably, this expectation was satisfied, and the skills I gained will be advantageous regardless of where my career takes me.”

Steven Reeves also had the opportunity to propel his love for science through the MSGI Program.

Reeves has been captivated by science since he was a child, when he borrowed conceptual physics books from his older brothers. He read and reread *The Universe in a Nutshell* by Stephen Hawking because of his fascination with galaxies, the universe, and beyond.

Now pursuing a doctoral degree in applied mathematics and statistics at the University of California, Santa Cruz, Reeves was assigned to Lawrence Berkeley National Laboratory for the internship, and joined the Center for Computational Science and Engineering under the mentorship of Ann Almgren.

For 10 weeks, Reeves was tasked with adapting an existing cosmology simulation code, called Nyx, to use magnetohydrodynamics – the study of matter moving in an electromagnetic field. Nyx is a computer code used in scientific exploration; it specializes in cosmological flows where dark matter and gas interact gravitationally. The addition of magnetohydrodynamics would include magnetic field interactions with gas.

Scientists turn to simulations when they want to study an area of science that is too expensive or impossible to observe with current technology. Theories regarding the formation of the universe suggest that a weak primordial magnetic field formed after the Big Bang, which was then strengthened by gravitational collapse. The current cosmology simulation code accounts for density, momentum, and energy, but requires the addition of magnetic fields acting in each direction. By adding magnetic fields to Nyx, researchers can run simulations and test whether these theories may be true.

“The more we understand the universe the more we can do in it,” Reeves reflected. “I loved my time at the lab. The best part of the program was being able to work alongside some of the best people in my field on problems that I find truly interesting.”

Reeves, who primarily studies computational fluid dynamics as related to astrophysics, appreciated the opportunity to apply his interests in a meaningful way. “I feel like my elementary school self is catching up to me with his Stephen Hawking book, telling me to look at the pretty figures,” he remarked. His interest in mathematics and the greater universe continues on.

Dania Sheaib has also long understood the value of mathematics in everyday life. Since high school, she has been fascinated by the ability to justify the world from a scientific point of view. When she discovered that mathematics can be used to answer physical, biological, and medical questions, she knew that mathematics was the field for her.

A doctoral student at the University of Oklahoma, Sheaib was excited to learn about the MSGI program. “While studying pure mathematics, you dive into so much theory that sometimes your vision becomes blurry about how it all should come together and serve other areas of science,” she said. “The [MSGI] program takes students from pure mathematics backgrounds and introduces them to how they can use that knowledge to solve real-world problems. It seemed like the perfect opportunity.”

Sheaib was assigned to Argonne National Laboratory where she was mentored by Mark Hereld. She focused on developing and applying mathematical methods to compute three-dimensional (3-D) representations of data. Sheaib collaborated with other researchers to assist in the development of a high-resolution, high-speed, 3-D microscope to study biological systems at the molecular and cellular level.

To study such small objects, a technique called multifocal plane microscopy (MFM) is used. The two-dimensional (2-D) MFM image measures the sample in several focal planes at once. To reconstruct the 3-D structure of objects in these images—such as bacteria—an optimal mathematical model is found to account for the 2-D image content. The model attempts to distinguish between 3-D structures and background noise, but the model’s accuracy must be evaluated to ensure the quality of the technique and images produced.

To assess the model’s accuracy, Sheaib and her colleagues utilized an algorithm called two-step iterative shrinkage/thresholding (TwIST) to test how the model performs in ideal noiseless situations and in cases of significant noise interferences. Their findings revealed ways to speed up the processing of image reconstruction without compromising the accuracy of 3-D images. They also demonstrated the need to reevaluate the mathematical model that helps distinguish background noise.

All these observations help improve the MFM imaging technique. Detailed, precise images of molecular and cellular systems are needed by biologists and other scientists who study bacteria and biological fluids that can cause human, animal, and plant diseases.

Sheaib appreciated the opportunity to conduct research and participate in activities such as seminars, workshops, and student talks. She gained a new understanding of what research is possible in mathematics and what a career would be like at a national lab.

“This unique experience has broadened my horizons and allowed me to discover other career options I might enjoy. Now I know that I want to work in the area of applied mathematics, and I have some ideas for future research projects,” Sheaib said. “This would not have been possible without the great impact the internship had on my career. I loved the experience and all it had to offer.”

To find out more about these experiences and further opportunities in STEM, visit the ORISE website. ORISE supports the DOE and other federal agencies’ missions to strengthen the nation’s science education and research initiatives. ORISE is managed for the DOE by Oak Ridge Associated Universities. Applications are now open for the NSF’s 2018 MSGI Program.