This paper proposes the advection-diffusion equation for modeling the bipolar memristor. The model identifies limiters to switching speed, reproduces general experimental results including those relating temperature dependence of    $I$   –   $V$    curves, and abstracts the contemporary dual variable resistor model. The model also reveals implicit complex resistors that cause the fleeting negative resistance characteristic in the memristor, as observed by Chua. Elegant closed-form solutions with remarkable scope are produced even under simplified modeling conditions. Numerical methods verify the closed form model. The proposed model uniquely derives all memristive behavior from a single governing advection-diffusion equation and bridges the vacancy and circuit domain abstractions.
['Isaac Abraham']
An Advection-Diffusion Model for the Vacancy Migration Memristor