Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1802.06326

Sensitivity and Bifurcation Analysis of a DAE Model for a Microbial Electrolysis Cell

Harry J. Dudley·Lu Lu·Zhiyong Jason Ren·David M. Bortz
View original source ↗Read source document ↗Export metadata ↓

Abstract

Microbial electrolysis cells (MECs) are a promising new technology for producing hydrogen cheaply, efficiently, and sustainably. However, to scale up this technology, we need a better understanding of the processes in the devices. In this effort, we present a differential-algebraic equation (DAE) model of a microbial electrolysis cell with an algebraic constraint on current. We then perform sensitivity and bifurcation analysis for the DAE system. The model can be applied either to batch-cycle MECs or to continuous-flow MECs. We conduct differential-algebraic sensitivity analysis after fitting simulations to current density data for a batch-cycle MEC. The sensitivity analysis suggests which parameters have the greatest influence on the current density at particular times during the experiment. In particular, growth and consumption parameters for exoelectrogenic bacteria have a strong effect prior to the peak current density. An alternative strategy to maximizing peak current density is maintaining a long term stable equilibrium with non-zero current density in a continuous-flow MEC. We characterize the minimum dilution rate required for a stable nonzero current equilibrium and demonstrate transcritical bifurcations in the dilution rate parameter that exchange stability between several curves of equilibria. Specifically, increasing the dilution rate transitions the system through three regimes where the stable equilibrium exhibits (i) competitive exclusion by methanogens, (ii) coexistence, and (iii) competitive exclusion by exolectrogens. Positive long term current production is only feasible in the final two regimes. These results suggest how to modify system parameters to increase peak current density in a batch-cycle MEC or to increase the long term current density equilibrium value in a continuous-flow MEC.

Explore related subjects

math.DSq-bio.OT

Keep this discovery

BibTeXRIS

Harry J. Dudley, Lu Lu, Zhiyong Jason Ren, David M. Bortz. 2018-02-18. Sensitivity and Bifurcation Analysis of a DAE Model for a Microbial Electrolysis Cell. https://arxiv.org/abs/1802.06326

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗