The postulated stochastic independence of the nucleation events make them Poisson distributed.[20] As a result
This well-known result can be demonstrated in two ways:
1. By considering how is changed when there is a change
in
,
which is readily integrated to give
2. Alternatively we can use the Poisson distribution for finding n
events when the expectation is
Evaluated at this gives
which can be
identified
with
.
Equation (2.10) combined with equation (2.6), or when
appropriate (2.7) or (2.8), are the basic
equations of this paper.
When and
are constant, equation (2.6) may be
replaced with equation (2.9), which is identical to the
classical JMAK results for any dimension. In 3 dimensions this result
is