Simulation of non-stationary electrodiffusion processes in charged membranes by the network approach

Single techniques of network approach have been used to obtain the numerical solution for a boundary value problem involving the Nernst-Planck and Poisson equations system. A network model has been proposed for a particular physical situation, namely, ionic transport in charged membranes including the Donnan equilibrium relations at the membrane/solution interfaces. With this network model and using the electrical circuit simulation program PSPICE, the ionic concentration profiles as well as electric potentials and ionic fluxes have been simulated as a function of time for the ternary systems HClKCl and NaClKCl.     

Two Algorithms for Computing the Randles–Sevcik Function from Electrochemistry

We derive two expansions of the Randles–Sevcik function : an asymptotic expansion of for x and its Taylor expansion at any x ₀ . These expansions are accompanied by error bounds for the remainder at any order of the approximation.     

Mathematical homogenization and stochastic modeling of energy storage systems

Mathematical homogenization theory as a multiscale modeling strategy for deriving macroscopic models is gaining relevance in modeling electrochemical energy storage systems (ESSs) for its ability to capture the detailed microstructural properties of a material. Stochastic modeling, on the other hand, captures molecular fluctuations and uncertainties associated with ESSs. In this short review, modeling ESSs using both tools is presented. Integrating mathematical homogenization theory and stochastic modeling provides an effective tool for deriving macroscopic models that accurately predict various macroscopic behavior and electrochemical properties of ESSs to enable optimization and manufacturing of high performance ESSs.