A Stochastic Model of Crystallization in an Emulsion - Laboratoire de ...

the rst one is to use | w w | instead of w w in the computing (see gure 11),
n+1 n n+1 n
Figure 11: With | w w |
n+1 n
the second one is to consider that wn+1 wn
has a positive mean (instead of 0,
see gure 12).
That is, to introduce a derive vector to the Wiener process i.e. to consider the equation
instead of
∂ϕ
∂t
∂w
= (1 ϕ) J( u) + b( u, ϕ)( cte + ) , in
∂t
∂ϕ
∂t
= (1 ϕ) J( u) + b( u, ϕ)
∂w
, in .
∂t
Figure 12: With positive mean
The shapes of the temperature curves are the same as the experimental one (cf. gure 10).
But, we do not prove any mathematical results for this stochastic context.
An other way to take into account this phenomenon is to modify the deterministic model by
introducing some convection terms, in the above equation, for example. To our knowledge, such a
model does not actually exist.
28