  The Strukov model was the phenomenological model that accompanied the
announcement of the first recognised physical instantiation of the memristor
and, as such, it has been widely used. This model described the motion of a
boundary, $w$, between two types of inter-converting material,
$R_{\mathrm{off}}$ and $R_{\mathrm{on}}$, seemingly under a uniform field
across the entire device. In fact, what was intended was a field with a
discontinuity at $w$, that was uniform between $0<x<w$. In this paper we show
that the discontinuity is required for the Strukov model derivation to be
completed, and thus the derivation as given does not describe a situation with
a uniform field across the entire device. The discontinuity can be described as
a Heaviside function, $H$, located on $w$, for which there are three common
single-valued approximations for $H(w)$. The Strukov model as intended includes
an approximation for the Heaviside function (the field is taken to be the same
as that across the $R_{\mathrm{on}}$ part of the device). We compare
approximations and give solutions. We then extend the description of the field
to a more-realistic continuously varying sigmoidal transition between two
uniform fields and demonstrate that the centro-symmetric approximation model
(taking the field as being the average of the fields across $R_{\mathrm{on}}$
and $R_{\mathrm{off}}$) is a better single-point model of that situation: the
other two approximations over or underestimate the field.
