Drs. Hussaini, Cogan, and Oates are active in using cutting edge mathematics in fields where quantification and theory is limited. Dr. Cogan has active collaborations with two biological labs and one chemistry lab at FSU. Each of these projects was developed to use mathematical theory to provide theoretical insight into experimental design, treatment and physical, biological and chemical processes. One project focuses on a complex ecological system of multiple bacterial species and a pathogen. A second project is aimed at understanding the developing symbiosis between plant root nodules and invading bacteria that fix nitrogen for the plant to adsorb. The spatial locations of the bacteria appear to be key to the effectiveness of nitrogen fixation, and hence related to artificial nitrogen fertilizer development, but there is currently little understanding of the dynamics of the bacterial localization and our mathematical framework will lead to insight into key processes that can lead more efficient plant growth.

The final example relates to the chemical origin of life that is thought to occur in deep ocean vents. Here the chemical reaction simultaneously alters the physical environment via sedimentation leading to highly complex patterning that require theoretical understanding to predict the chemical processes.

Dr. Oates has a long history of working with Dr. Hussaini on applying mathematical theories to engineering applications. This includes previous DARPA and AFOSR projects on fluid-structure interactions of photomechanical flapping insect wings, a program on fractional calculus to understand advanced functional materials, and the most recent work on the uncertainty quantification and global sensitivity analysis of near term quantum computing hardware. Three different post doctorate researchers have been co-mentored on this research.