Coronavirus-fighting theories deploying resistance, microwaves have roots in centuries-old fundamentals of resonance, mathematics professor says

The week before spring break at Norwich University, I was teaching my differential equations class about solutions to linear differential equations and I was teaching my calculus class about related rates, an application of the chain rule of differentiation. These topics have existed for many years, dating back to the 17th and 18th centuries from the minds of Isaac Newton, Gottfried Leibniz and Leonhard Euler, to name a few. In the year 2020, it may seem outdated and irrelevant to have students learn such “old-fashioned” mathematics. Indeed, we are teaching our students to solve mathematical problems whose solutions can be obtained by our current-day calculators, apps and software.

I am often asked why this is so. Why not teach students an overview and leave the details to the machines? Because this knowledge and experience is the basis of innovation in our modern world. New discoveries in mathematics, engineering, and the sciences come from a deep understanding of the foundations, especially mathematical foundations, and deep understanding comes from doing.

A group of Taiwanese researchers has reported the ability to inactivate influenza A viruses using microwaves with power low enough to not harm humans.

As a mathematics educator, it is important that I give context to the mathematical foundations, provide evidence of its worthiness, try to spark curiosity and motivate students. For these purposes, I find that examples of current-day innovations are important. Our current-day coronavirus pandemic provides at least one such example.

In differential equations we study spring-mass systems as an application of linear differential equations. (A spring-mass system is one in which a spring is suspended from a beam and a mass hangs from the end of the spring.) They are simple systems that provide context to develop a clear understanding of solutions to linear differential equations. We analyze how the up-and-down movement of the mass depends on the mass, the spring, the initial displacement and velocity of the mass, any resistance and any external forces that move the beam.

One such combination, in which an external force moves the beam up and down at the same frequency intrinsic to the given spring and mass, leads to *resonance*. If there is no resistance, the matching frequency causes the vibrations of the mass to continuously increase in amplitude, presumably until the spring breaks. With resistance, the vibrations of the mass increase in amplitude until the effect of resistance becomes dominant and damps the vibrations. Today, researchers are looking to apply this resonance-type phenomenon to inactive viruses in public areas.

**Viruses and microwaves**

Person-to-person spread of viruses occurs through droplets, airborne transmission and surface transmission. Cleaning and disinfecting common spaces in energy-efficient, cost-effective and timely ways is a priority. It has been known since the 1980s that viruses can absorb ultrasonic energy. It has been hypothesized that viruses may be inactivated by absorbing ultrasonic energy at their so-called resonant frequency. Now, researchers are studying the interaction of microwaves with viruses.

The idea is that spherical viruses have intrinsic vibrational modes that can be excited by the energy absorbed from microwaves. By exciting these resonance vibrations, the virus becomes inactive. A group of Taiwanese researchers has reported observing the inactivation of influenza A viruses using such a mechanism. Most significantly, the group reported the ability to inactivate influenza A viruses using low-power microwaves, with power low enough to not harm humans (as determined by the Institute of Electrical and Electronics Engineers safety standard). Thus, this group claims it has found the first feasible mechanism to inactivate airborne viruses in the open, without adversely affecting the public. Perhaps we have a future in which “virus antennas” are ubiquitous in our grocery stores, libraries and schools.

A look at the research articles reveals that this idea of coupling electromagnetic waves to acoustical vibrations requires more knowledge than a simple spring-mass system. We need to know more mathematics, some engineering and physics and some biology. This research builds upon previous work, which has research ideas that come from yet others’ previous work, and so on.

Yet, all of these works are variations on the fundamental idea of resonance, noted by Galileo over 300 years ago and now taught to our students at Norwich. My students, our next generation of innovators, will call upon these old-fashioned mathematical concepts to solve our modern-day problems.

*Dr. Natalie Cartwright is an assistant professor of mathematics at Norwich University.*

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