C3

The electrochemical processes in electrolytic cells are the basis for modern energy technology such as batteries. Electrolytic cells consist of an electrolyte (an salt dissolved in solution), two electrodes, and a battery. The Poisson–Nernst–Planck equations are the simplest mathematical model of steady state ionic transport in an electrolytic cell. We find the matched asymptotic solutions for the ionic concentrations and electric potential inside the electrolytic cell with mass conservation and known flux boundary conditions. The mass conservation condition necessitates solving for a higher order solution in the outer region. Our results provide insight into the behaviour of an electrochemical system with a known voltage and current, which are both experimentally measurable quantities.

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We present Gromov's celebrated reconstruction theorem in Lorentzian geometry and show two applications. First, we introduce several notions of convergence of (isomorphism classes of) normalized bounded Lorentzian metric measure spaces, for which we describe several fundamental properties. Second, we state a version within the spacetime reconstruction problem from quantum gravity. Partly in collaboration with Clemens Sämann (University of Vienna).

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