2024 Student Essay Contest: Grades 9-12 Honorable Mention

“Mathematics at Mach Speed: Tulin Kaman’s Soaring Journey in Safeguarding Skies and Transforming Cancer Treatment”

by: Annie Katz (The Leffell School)

Interviewee: Tulin Kaman (University of Arkansas)

Did you know mathematics could safeguard our airspace? Meet Tulin Kaman, a computational applied mathematics professor at the University of Arkansas and a testament to unwavering dedication. Her real-life applications, a collaborative effort with engineers and scientists, showcase not only her mathematical prowess but a fervent commitment to push boundaries. In her latest study, she uses statistical models to understand the relationship between force and deformation under different simulated collisions between an aircraft and an unmanned aerial vehicle, like a drone. This model has promising future applications including regulatory guidelines and structural enhancements for safer skies. Her persistent drive propels breakthroughs in computational efficiency as this model is 103 times faster than the traditional method called Finite Element Analysis, condensing 28 hours of previous computational time to milliseconds. While her math will keep everyone safer in the sky, it also fuels excitement for speed, echoing the sentiment of “I feel the need, the need for speed” from Top Gun.

Ever wonder if Top Gun Maverick’s speed could be achieved in real life? Well, Kaman collaborated with Stanford University on scramjets, which are unmanned jets designed to reach Mach 7, 7x the speed of sound (not quite Top Gun Maverick Mach 10 but still supersonic!). She developed models and simulations for turbulent combustion within the scramjet. Kaman explained that simulations involve harnessing the inherent power of nature, enabling predictions and observations of mixing and combustion behavior. Studying the complex reactions that occur when injecting air and hydrogen into the scramjet, she gained insights into turbulent combustion processes for efficient, high-speed propulsion systems. Additionally, she applies her models beyond aviation, infusing them into the medical field.

Kaman’s work illustrates that numbers can transform into crucial tools, as her simulations can be used to advance cancer treatment technologies. She engaged in a project involving the design of a cyclotron – a machine designed to accelerate and store high-energy particle beams. A laser-like beam is injected into the cyclotron through electrodes, guiding particles to a specific energy level. Her mathematical models, integrated into the simulation code, accurately predict the behavior of the ion beams. Thanks to her efforts, controlling the energy levels of accelerated particles is closer to reality, which will facilitate targeting cancer cells while minimizing damage to healthy tissues.

What do these three case studies have in common? The answer is modeling and simulations of physical phenomena to understand and analyze the behaviors and dynamics of highly random and unpredictable systems. By understanding these mechanisms, it can lead to better predictions and control of unstable processes. Kaman finds turbulence fascinating – it is everywhere in nature – in the swirling of the morning coffee, in the movement of clouds, or in the explosion of stars, one is observing turbulence mixing.

Another common denominator that emerges is Tulin Kaman is a polymath like Nikola Tesla – a chemist, engineer, and physicist all woven into the intricate fabric of mathematical expertise. Her expertise extends beyond the conventional disciplinary boundaries, as she not only comprehends the “why” but adeptly integrates mathematics into other fields. Kaman emphasizes the versatility of a robust mathematical foundation, asserting its applicability in diverse fields, including chemistry. Her expertise is sought beyond math conferences; she is invited to speak at an engineering conference to discuss dynamical systems – observation in motion akin to sprint math problems.

While not quite a pint-sized prodigy tackling Calculus, her fascination with math was ignited at age 5! Even as a child, she had a clear vision of her future – she wanted to be a math professor. She credits her mom for instilling in her a love of math by making it fun. One cherished memory involves a game where Player A asked Player B to pick a number and perform various mathematical operations– add 5, multiply by 3, and more. Player B undertakes the reverse calculations to deduce the original number. Today, Kaman extends her math passion and spirit of gaming by welcoming girls ages 7 to 14 to her campus. In a symbolic parallel to the cinematic journey of Barbie overcoming indoctrination, girls smash the “math is hard” or “math is not for girls” narratives. They build ziplines for Barbie dolls, calculating the shortest distance. They also run experiments with small explosions, teaching units and proper measurements. She encourages her female students to pursue Ph.D. studies, providing guidance to overcome potential psychological challenges as the lone female in a room. She advises: “Being unique is good…trust yourself, work hard and you will get what you want always.”

Diving into new challenges, Kaman represented Team USA at the 2023 Underwater Hockey World Championship in Australia. Balancing her professional commitments, parenthood, faculty advisory role, collaborative research, and active participation in mathematical societies, she also tackled the challenge of finding time for exercise. She excels in a sport demanding the combined skillsets of Wayne Gretzky and Michael Phelps, nurtured by childhood water activities in Turkey: summer swimming and spearfishing. In Switzerland, she discovered underwater hockey, where she honed her breath-holding skills. Kaman applies her mathematical mindset to make strategic predictions during play. Analyzing body positions, puck trajectories, and leveraging math to optimize energy consumption, she strategically positions herself, predicting game dynamics based on teammates’ underwater stamina and unique skills.

Kaman advocates for persistence: “Whatever you do, love it. Have an interest. But give it three chances…Give it a second and third chance and see if you like it or not. Never quit easy. You might not solve the problem on the first try, try to approach it in different ways. Be persistent and see that math is actually everywhere.” Professor Kaman is not just a mathematician; she exemplifies the transformative influence of mathematics on our world. Whether facing the unpredictable gust of wind in a race or experimenting with colors and textures in an art class, her guidance on persistence and the ubiquity of math serves as a compass for making the most of life’s endeavors.