Gated variable resistors were manufactured by depositing epitaxial heterostructures of doped $\ce{La2CuO_{4+$\delta$}}$ and $\ce{SrTiO3}$ layers. Their conductance change as function of write current $I$ and write time $t$ followed a simple empirical law of the form $\Delta G/G = C I^A t^B$. This behavior is in agreement with ionic transport that accelerates exponentially with electrical field strength.
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The following article appeared in J. Appl. Phys. 111, 056101 (2012) and may be found at http://dx.doi.org/10.1063/1.3691599