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Mathematicians tackle challenging real-world problems

This is the first article in our series on Faculty Research Impact. The mathematics faculty are involved in world class research that is deep in mathematical innovation, broad and diverse in its application, and collaborative, interdisciplinary and international in its nature. This series of articles will focus on the impact that our faculty research is producing and showcase our disciplinary and interdisciplinary strengths in mathematical research.

Never heard of Methane Hydrates? Professor Malgo Peszynska says that might be good news. In a recent article that was published in the premier news publication in applied mathematics, SIAM NEWS, Professor Peszynska talks about her international collaborative research on Methane Hydrates.

Methane hydrate is an ice-like crystalline substance and is considered a “smoking gun” in environmental and (paleo-) climate studies, since dissociation of hydrate can dramatically increase the amount of methane in the atmosphere. They are a significant drilling hazard, e.g., they contributed to the Deepwater Horizon explosion and oil spill. Researchers also study the presence of hydrates due to their impact on slope stability of submarine formations. If you haven’t yet heard about methane hydrate, it has likely not caused any recent high-profile disasters, good news indeed!

A diagram with lots of text inside and outside a circle. The center of the circle has three molecules. The text inside the circle reads: "Applications, Data, Math, and Computing." There is smaller text that reads "Geophysics, oceanography, experiments, reservoir engineering, simulation, algorithms, analysis, modeling, observations, experiments." On the outside of the circle, there is more text relating to the inside of the circle.

Interdisciplinary objectives and multiple scales in gas hydrate studies and modeling. The molecules pictured in the middle include water (H20), methane (CH4), and carbon dioxide (CO2); Image credit: Malgorzata Peszynska.

Dr. Peszynska says, “the overarching challenge in studying hydrates is arguably not just the complexity of the problem itself, but rather the ability to simplify and extract subproblems so as to move forward and make progress without compromising the results. For applied and computational mathematicians, the process of translating the hydrate model so it can fit into a mathematical framework amenable to analysis and simulation can be very rewarding. However, it requires vigilance from all participants of the interdisciplinary team, since the problem has many mathematical and computational sensitivities. Progressing from basin to production timescales, or from sediment depths to the scale of microcracks and gas chimneys, requires collaborations and resources across several fields. Observations and data are needed, so modeling can at least be guided even if validation is impossible.”

This research, funded by the National Science Foundation (NSF), has involved many of our mathematics graduate students including Joe Umhoefer, Choah Shin, and former students Tim Costa, Patricia Medina, and Ken Kennedy, as well as students outside mathematics such as Wei-Li Hong from CEOAS. Originally started in collaboration with CEAOS professors Marta Torres and Anne Trehu, the project involved many other Mathematics and CEOAS faculty including Ralph Showalter, Nathan Gibson, and Justin Webster.

Understanding Random Distrubances in Populations: How can we construct a mathematical framework to understand how population-reducing events of varying frequency and intensity, like fires, floods, storms and droughts, can affect a species’ ability to survive? Mathematics Professor Patrick De Leenheer's collaborative work identifies “critical growth thresholds” for species subjected to random events that immediately and substantially impact the species’ population levels. The research was motivated in part to try to predict the effects of global climate change which may alter the characteristics of these events.

De Leenheer said, “Our main goal was to analyze when these models predict population extinction or persistence. We identified specific ecological and disturbance parameter combinations for which threshold values can be determined such that when these thresholds are crossed, the system’s extinction or persistence behavior changes fundamentally. That’s a key feature of these models. They provide precise conditions for which the mortality rate due to the frequency and magnitude of episodic disturbances exceeds the natural, net growth rate of a population. The thresholds mark a boundary between a persisting population of fluctuating size and one that becomes extinct at an exponentially fast rate.”

A graph that depicts a decreasing population model.

A set of 28 empirical, steady-state pdfs, each obtained from running the discrete model for 10 million disturbance events. Image Credit: Patrick De Leenheer.

The research provides a framework for biologists and other life scientists to better understand how a particular system behaves when it gets disturbed in ways that aren’t predictable, or are predictable only in certain terms.

Dr. De Leenheer’s work was funded by the NSF, and was featured in OSU News and research communications. Collaborators included Edward Waymire, professor emeritus of mathematics at Oregon State, and Scott Peckham, an OSU alumnus who is a geophysicist at the University of Colorado.

How can mathematics help tackle a destructive Plant virus? Associate Professor Vrushali Bokil’s international team of mathematical and biology collaborators came up with a mathematical model to understand the spread of maize lethal necrosis in Kenya and strategies for its control. OSU Alumna Carrie Manore (Mathematics, PhD 2011), who was Dr. Bokil’s advisee, was a part of the research team. Dr. Manore is now a staff scientist at Los Alamos National Laboratory.

The research was conducted at the NSF funded National Institute for Mathematical and Biological Synthesis (NIMBioS), as part of a working group on Multiscale Vectored Plant Diseases, and is now published in the journal Phytopathology. The paper is in the top 5% of all research outputs scored by Altmetric. This work can not only help improve our understanding of maize lethal necrosis but could also help inform the management and control of other destructive plant diseases caused by combinations of pathogens.

The study focuses on maize lethal necrosis disease in Kenya where crop losses are particularly high. Infected corn plants die prematurely or are frequently barren, drastically reducing the yield. Most of the nation's maize supply comes from small to medium-size farms, which are less able to withstand threats to their food production than large resource-rich farms.

A maize plants with a virus.

Maize lethal necrosis. Image courtesy of NIMBioS.

The study found that a combination of rotating crops, controlling insects, and using virus-free purchased seed provides the best disease control, but such a management strategy is usually only available to large commercial maize farms with sufficient resources to afford agrochemicals and purchased seed. Resource-poor farmers, with smaller holdings, who rely primarily on crop rotation and removing diseased plants, can only achieve a more limited control, the study found. For both types of farmer, synchronized management over large areas would be needed to provide long-term, sustainable control. The results emphasize the value of mathematical modeling in informing management of an emerging disease especially when epidemiological information is sparse.

"Mathematical modeling can play an important role in integrating what biological information is available with reasonable assumptions on what is missing to give at least a first indication of the potential effectiveness of disease control options. Modeling can also indicate and help prioritize some key research questions that need to be addressed in seeking long-term sustainable control options," Dr. Bokil and her co-authors write.