# Mathematical Biology Seminar - Harry Dudley

**Harry Dudley, Department of Applied Mathematics, University of Colorado Boulder**

*Differential-Algebraic Equation Models of Microbial Electrolysis Cells*

Microbial electrolysis cells (MECs) are an emerging technology that employs microorganisms to recover energy from organic waste in the form of hydrogen. MECs consist of two types of microbes. In these devices, bacteria on the electroactive anode

biofilm oxidize (in)organic substrate and transfer electrons to generate electrical current and release protons (H+). A small voltage (0.2−0.8 V) is needed to overcome the thermodynamic barrier, which is much lower than traditional water electrolysis (1.8–3.5 V). Hydrogen is produced via a reduction reaction as protons in solution react with electrons at the cathode. Methanogenic archaea reduce the efficiency of the system by consuming the substrate to make methane. The outcome of competition between electroactive

bacteria and methanogens determines current and hydrogen production.

In this talk, we discuss previous work on sensitivity and bifurcation analysis of differential-algebraic equation (DAE) models of microbial electrolysis, current work on global stability analysis using LaSalle’s invariance principle, and provide a basis for future work on model selection with numerical analysis of the effect of various solvers. In different models, either Sotomayor’s theorem for transcritical bifurcations or LaSalle’s invariance principle can be used to determine when the stable equilibria exhibits competitive exclusion or coexistence with the outcome determined by particular model parameters. We also propose a framework for investigating novel MEC models that could be used to better represent current and hydrogen production. A statistical model for inter- and intra-substrate variability will be used to account for differences in the current density data within and between substrates. Assumptions on distributions for the random effects will be examined and modified appropriately to best represent MEC current data. A model selection criterion will be used to rank relative information loss among proposed MEC models. Since model selection criteria involve approximations of the maximum likelihood, we will evaluate of the effects of numerical schemes on the discrepancy between model and data. This framework will be used to further development of MEC modeling.

Tuesday, November 6, 2018 at 2:00pm to 3:00pm

Engineering Center, ECCR 257

1111 Engineering Drive, Boulder, CO 80309

- Event Type
- Interests
- Audience
- College, School & Unit

- Group
- Applied Mathematics
- Subscribe
- Google Calendar iCal Outlook