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Creating New Knowledge
Creating New Knowledge

Complex Systems, Complex Challenges

The research of Mary Silber, engineering sciences and applied mathematics, has taken her in many directions that may initially seem unrelated: from understanding the mechanisms behind exotic surface wave patterns on fluids to modeling biological processes within cells, to searching for tipping points associated with climate change. This wide range of applications for fundamental mathematical concepts is what drew her to a career in applied mathematics, and that career has been sustained by the enriching collaborations required by highly interdisciplinary research.

Mathematical models of complex nonlinear phenomena present inescapable challenges. Typically the models cannot be solved exactly. Even in using a computer to explore such phenomena, scientists often confront insurmountable challenges because of disparities in spatial and temporal scales that prevent a fall and appropriate resolution. There is always some uncertainty in their model parameters, and there may be some inherent chaos associated with the process they aim to model. What questions can we meaningfully ask of such a mathematical model? A goal of Silber's research is to develop mathematics that helps identify robust and universal qualitative phenomena associated with nonlinear dynamical systems.

Earth's climate is a perfect example of a complex system where these challenges apply. As part of an NSF-funded network of mathematicians and climate scientists, Silber is investigating the mathematical problems posed by climate change. One of her key interests is in identifying tipping-point mechanisms for Earth's climate and ecosystems. Can we anticipate when this complex system is driven to the brink of an abrupt transition? She is currently focusing on this general question through investigations of the melting of Arctic sea ice and of spatial patterning that accompanies a transition to desertification in models of semi-arid ecosystems. These projects fit well with 2013's designation as Mathematics of Planet Earth Year.

This article originally appeared in the Office for Research 2012 Annual Report.

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