Editor’s note: This commentary, written by Assistant Professor Eric Stachura, is published as part of an annual sponsorship of Global Atlanta by Kennesaw State University’s Division of Global Affairs.
Mathematical modeling sounds intimidating and complicated, but also vague. What does it really mean, and more importantly, what does it mean for the world?
According to the Society of Industrial and Applied Mathematics, the process involves using mathematics to represent, analyze, make predictions or otherwise provide insight into real-world phenomena.
Any student who has banged their head on a desk while wrestling with an equation has grasped the need to connect theoretical thinking to solving real-world problems.
It’s easy to get lost in entire courses or abstract disciplines related to math (and some of us do), but at its core there exists a more utilitarian function of our discipline, and mine in particular: Mathematical modeling teaches us how to make assumptions, test predictions, come up with formulas and analyze and assess the solutions.
From COVID to Cell Phones
Modeling entails a particularly useful set of skills today, in light of the current pandemic, for it permits policy makers to foresee the consequences of decisions, as well as educate all of us on the nature of the pandemic and what we can do about it.
But not all mathematicians are epidemiological modelers, and there is a myriad of other big questions toward which we can aim our academic ammunition.
In the modern world, there may be no more vital infrastructure than that of telecommunications, and Swedish companies like Ericsson are world leaders, particularly in the hardware that relays 5G mobile signals, promising exponential increases in mobile Internet speed.
But as many know, questions linger about deployment: particularly how radiofrequency signals will behave in the built environment.
Last June, I was part of a collaborative research project along with Elena Cherkaev (University of Utah) and Niklas Wellander (FOI Sweden) charged with implementing mathematical modeling to ultimately help improve modern communication systems.
Funded in part by an American-Scandinavian Foundation grant, I went to Linköping, Sweden, southwest of the capital in Stockholm, with the particular goal of studying Passive Intermodulation (PIM) from a rigorous mathematical perspective.
PIM occurs when multiple signals are active in a passive device (such as a cable) that exhibits a nonlinear response. Frequently, PIM occurs as a result of multiple cell phone providers sharing certain paths in wireless networks. To the everyday user on their cell phone, this can manifest as decreased data speed or even dropped calls.
The focus of our research is the relationship between PIM, temperature effects and rough surfaces. In particular, taking into account the heat generated by radio-frequency signals, we are working to understand how surfaces with sharp corners or angles affect signal integrity.
While the research is ongoing, the impact is clear: understanding the effects of geometry (such as buildings in a large urban environment) on signal integrity is important for the development of improved cellular networks. What we find will affect everyone: From the drivers of future autonomous vehicles to the companies relying on 5G technology to track their products, as well as patients enjoying newly enabled telemedicine sessions.
Indeed, the state of Georgia has already been involved in 5G innovation: the Marine Corps Logistics Base in Albany was selected by the Department of Defense as a testing ground for 5G-enabled warehouses.
To unlock the advantages of these and other technologies, we will need to continue to drive new and collaborative thinking around their usage — perhaps even breaking out a mathematical model every now and then for problems that don’t seem like they can be solved on paper.
About the author:
Dr. Eric Stachura has a B.S. and Ph.D. in Mathematics from the University of Illinois at Chicago and Temple University, respectively. He is currently an Assistant Professor of Mathematics at Kennesaw State University in Atlanta. His research interests include problems at the interface of mathematics and physics, in particular nonlinear electromagnetics and geometric optics. During his studies, he has spent two significant periods abroad studying and conducting research: one at the Eidgenossiche Technische Hochschule (ETH) in Zurich, Switzerland, and one at the Instituto de Ciencias Matematicas (ICMAT) in Madrid, Spain.
In addition to his research, he is interested in innovative teaching techniques. As part of the Silver’19 cohort of the Mathematical Association of America’s Project NExT, he has incorporated numerous active learning strategies into his classes.