In the section 5.2.2.2, we have seen
that the support of a realizable spatial 3D distribution may be based
on two elements: the volume quantum and the volume element. In case
of the ensemble motion of the distribution, its inner T reference (if
this reference however exist, precisely in case of some S or L-type
relations between the distribution’s elements), with the
position vector
against an outer T reference, it shall have a translation motion with
the velocity
,
motion which shall be evenly transmitted to all the distribution
elements. In such conditions, the stockpile quantum given by the
relation 5.2.2.2.1, with the external position
,
would be moved with the velocity
,
resulting a *flux quantum*:

(5.2.2.4.1)

Because the flux quanta represents the motion of a 3D DP, on which the quantum is evenly distributed, otherwise speaking, the motion of a realizable “material point”, the vector is also called flux quantum vector (FQV) in this paper, and it is the realizable version of FDV from the virtual model.

If it is taken into account the motion
of an elementary quantity given by the relation 5.2.2.2.2, we shall
have an *elementary flux*:

(5.2.2.4.2)

Comment
5.2.2.4.1: Within the relations 5.2.2.4.1 and 5.2.2.4.2, there is a
series of states S_{0}(t) (samples of the spatial positions
of a distribution element 5.2.2.1 or 5.2.2.2), taken at the moments
,
which *t*_{0} is the moment of the flux
initiation. The sampling interval (period) is *dt*, so that the
velocity (temporal density of the motion process) could be considered
constant on its duration.

**Attention! **Within the relations
5.2.2.4.1 and 5.2.2.4.2, the objects
and
,
although they have the same temporal reference *t*_{k},
they do not have a simultaneous existence but, as it is mentioned in
annex X.6, their support temporal ranges are adjacent but also
disjoint. For
,
the moment *t*_{k} is included in the support
range, whereas for
,
the moment *t*_{k} is not included, that is a
right asymptotic boundary.

The main feature of both types of flux
elements is that the FDV distributions are even on their support
elements. In case of the vectorial distributions, the
technico-scientific literature uses the term of *resultant vector,
*an abstract object which is substituted to a set of vectors
through a single one, with a significant decrease of the information
amount which needs to be processed. In case of the vector
equipartitions, the resultant vector shall be a vector with the same
direction with the represented vectors, and the modulus shall be
equal to the sum (integral) of all these vectors. As regards the
relations 5.2.2.4.1 and 5.2.2.4.2, the vectors
and
are even those vectors coming from the integration along the volume
quantum or along the elementary volume of FDV. The application point
of these resultant vectors is the inner T reference of the elementary
object.

Similar with the case of the flux virtual model, the objectual model has also two study methods of flux :

Study on the motion of a single object involved in flux (Lagrange method);

Study on the global spatial distribution of the vector field at a certain

*t*_{k}moment (Euler method).

The distributions 5.2.2.4.1 and
5.2.2.4.2, are distributions with temporal support of the spatial
position of inner T reference of a spatial distribution element
belonging to the amount *M*. Therefore, these are *Lagrange
distributions*, trajectory of a single elementary object set in
motion. Just like in the virtual model, this kind of pathway is a
flux line (or a flow line). The set of all the flux quanta
or of the elementary fluxes
existing at a single *t*_{k} moment makes-up an
overall state of the flux of amount *M *at that moment, that is
a vector field which was called an *Euler distribution*.

Copyright © 2006-2011 Aurel Rusu. All rights reserved.