  There are three theoretical models which purport to relate
experimentally-measurable or fabrication-controllable device properties to the
memristor's operation: 1. Strukov et al's phenomenological model; 2. Georgiou
et al's Bernoulli rewrite of that phenomenological model; 3. Gale's
memory-conservation model. They differ in their prediction of the effect on
memristance of changing the electrode size and factors that affect the
hysteresis. Using a batch of TiO$_2$ sol-gel memristors fabricated with
different top electrode widths we test and compare these three theories. It was
found that, contrary to model 2's prediction, the `dimensionless lumped
parameter', $\beta$, did not correlate to any measure of the hysteresis.
Contrary to model 1, memristance was found to be dependent on the three spatial
dimensions of the TiO$_2$ layer, as was predicted by model 3. Model 3 was found
to fit the change in resistance value with electrode size. Simulations using
model 3 and experimentally derived values for contact resistance gave
hysteresis values that were linearly related to (and only one order of
magnitude out) from the experimentally-measured values. Memristor hysteresis
was found to be related to the ON state resistance and thus the electrode size
(as those two are related). These results offer a verification of the
memory-conservation theory of memristance and its association of the vacancy
magnetic flux with the missing magnetic flux in memristor theory. This is the
first paper to experimentally test various theories pertaining to the operation
of memristor devices.
