As it was already mentioned in paragraph 5.2, a flux is a transport process of a distributed amount, each element of this flux drawing a pathway which is called the flux line (or flow line). According to the virtual model, this pathway is a continuous curve, and according to the systemic model, it is a concatenation of right-oriented (vectors) segments which represent a series of concatenated SEP.

The spatial configuration of the flow lines allows the classification of fluxes in two categories, which will serve only as asymptotic (virtual) bench-marks for the real fluxes.

**Definition
5.3.1:** The flux at which __all__ the flow lines are open
curves is named a **totally open flux.**

The amount which is transported by these fluxes cannot be localized in space. The totally open flux is able to transfer an amount from an object to another, provided that at least a part from these flow lines to intersect the area of the receiving object.

Comment
5.3.1: The word *localized* used in this paper means the
definition of the spatial position of an object or of an amount which
belongs to an object. Mathematically speaking, the position of an
object is given by the position vector of that object against an
external RS. The precise localization of the object requires that
this vector to be invariant. But for the objects which are in motion
(such as the fluxes), it is obviously that this vector vary
continuously. In this case, we are dealing with a global definition
of the __domain__ in which the position variation of objects takes
place and this global definition is possible if only the objects in
motion are kept inside a known space with a definite position, as we
are about to see next.

**Definition
5.3.2:** The flux at which __all__ the flow lines are closed
curves, confined inside a closed area Σ is named a **totally
closed flux**.

The closed fluxes
are also known as *storage* fluxes. For these fluxes, a closed
area Σ may exist and this area contains all the flux lines
inside it. This area confines a volume *V*, in which the entire
scalar quantity *M* shall be found, this quantity representing
the conveyance attribute of the closed flux. Based on the assumption
that its position is determined in relation to a reference system,
the area Σ allows the localization of amount *M *even if,
in the inside, it is the object of a flux. Thus, as regards the
outside section of area Σ, it might be stated that the volume *V
*contains the amount *M* (but with a higher degree of
non-determination than in the absence of the closed flux, without
mentioning the inner static distribution of the amount *M*). The
closed fluxes are the only method of localization and storage of some
amounts which are able to exist only as fluxes (found to be in a
continuous motion, such as, for instance, the photons).

A closed flux
arises (is generated) as a result of a *closure process*, which
means the forcing of the flux’s flow lines for their
confinement only within a closed area Σ, and this closure can
be done by using different means which shall be minutely described in
the following chapters, but which are only listed in the present
chapter:

Reflexion (special case - elastic collisions);

Refraction;

Rotation.

Comment 5.3.2: The closure of a flux is made, as it was already depicted, through the modification of the direction of the transfer rate so that the flow lines to become closed pathways in a confined volume. As we are about to see in the following chapters, the boundary surface of a medium does not allow the entire flux passing over; therefore, there will always be fractions of the initial flux which shall return into the origin medium (the reflected fluxes), otherwise speaking, this flux section shall be kept closed in this medium. As for the propagation fluxes, the same process of modification of the flux direction caused by the unevenness of the propagation medium’s parameters can lead to the propagation by curved flux lines which can be confined in a limited and definite volume. The closure through rotation is the most notorious closure method, knowing that any system which moves is equivalent with a flux; if a body has a known volume and it spins around a defined axis, all the pathways of the constitutive elements shall be curves confined in a definite volume, with the center in a point along this axis.

The totally closed
or totally open fluxes are flux virtual models (theoretical,
mathematical, ideal), most of the real fluxes being only partly open
or closed, therefore, a certain flux is associated to a certain
*closure degree* (complementary with the aperture one), that is
a degree which represents the fraction of the closed flux lines from
the total number of flux lines).

Comment 5.3.3: An eloquent example for displaying the closure degree of a flux is the case of a fluid which flows through a pipeline, in which case two types of flow exist: laminar and turbulent. The laminar flow in which the flux lines are theoretically maintained parallel is an example of a totally open flux, with a null closure degree. As for the turbulent flow, most of the flux lines are locally closed (the vortex phenomenon occurs), but there is an overall motion of all the swirls, an open flux, that is the common component of all the vortex vector fields, motion which determines the effective fluid flow through the pipeline. If a fluid fills a steady pot, any inner motion of the fluid (convective or turbulent) will represent a totally closed flux inside the pot volume.

The fluxes can also
be divided in two groups according to a previous-mentioned parameter,
called *effective area* (or section) (see definition 5.2.1.2).
To not be mistaken with the capture cross section from the nuclear
physics field, although they are interrelated notions.

**Definition
5.3.3.:** The flux with a constant effective section across its
entire pathway is named **isotom** **flux** (synonym
**corpuscular flux**).

The flux which
outlines the translation motion of an EP, AT, of a missile, of an AB
(for example, of a planet within a PS) as well as of an isolated
photon, all of these being examples of isotom fluxes. All the other
fluxes (non-corpuscular) make-up the class of fluxes with *variable
effective section* (divergent or convergent fluxes depending on
the sign of the effective section variation - plus or minus - on the
covered distance unit).

If the Euler
distribution of FDV is temporally invariant, we are dealing with
*stationary* fluxes, otherwise, they will be *non-stationary*
(time-variable).

From the point of
view of the object which is involved in the flux and based on the
process type, the fluxes can also be divided in *displacement*
fluxes and *propagation* fluxes.

**Definition
5.3.4: **The flux which carries material __objects__ along its
entire pathway is named **displacement flux**.

The displacement fluxes carry material systems (abiotic, biotic or artificial) from one spatial location to another. The running water, wind, sea streams, people, goods and migratory animal flows, etc. are only few examples of displacement fluxes.

**Definition
5.3.5: **The flux which carries __local state variations__ of a
set of objects is named **propagation flux**.

The propagation fluxes carry local
state modulations (mainly symmetrical variations around a reference
value), the motion processes of the inner reference of the objects
involved within the flux are cyclical (reversible) and strictly local
processes. According to the above-mentioned facts, we may assert that
the propagation fluxes __carry processes__. Within a propagation
process, the elements with an altered state are not always the same
but they are different every time. We shall return to the propagation
process in the next chapter, after the medium’s definition
shall be presented. These flux types are also abstract (ideal)
models, the real fluxes containing components of both models in
various ratios. Any propagation also involves a low local
displacement (that is a local displacement flux), and the
displacement fluxes imply state variations between the objects which
are set in motion (which are therefore local propagation processes).

The equipartition of some vectors means
an even spatial distribution of the application points and an
evenness of the direction and modules of these vectors. Otherwise
speaking, the *direction *and the *module* are __common__
attributes on the set of the vectors distributed on the flux element,
whereas *the positions of the application points *are __specific__
(differential, disjoint) attributes of each vector.

**Definition
5.3.6: **The flux with null specific components of FDV modules and
directions (all vectors have the same module and the same direction)
is named **totally coherent flux**.

The totally
coherent fluxes are therefore fluxes with FDV equipartition, the
pathways of the application points (flux lines) are in this case
clusters of parallel straight (or curved) lines. This flux type
occurs only as an abstract model, the real fluxes might be only
*partly coherent*. An example of this kind of flux is the
elementary flux which was previously presented. The opposite
situation is when FDV set of the flux has a *null common component.*

**Definition
5.3.7: **The flux with a null common component of FDV set is named
**totally stochastic flux**.

Comment
5.3.4: The fact that the totally stochastic flux has a null common
component of FDV set (or FQV), this means that there is no __global__
motion (conveyance) process, which might lead the reader to the
conclusion that there is no flux (namely, motion). Indeed, an overall
flux does not exist, but a space-temporal distribution of the motion
processes of the stochastic flux elements exist, therefore, there is
also a flux (but a special type of flux with a null coherent
component of the FDV set). The same fact (lack of an overall
displacement of the flux elements) makes that the totally stochastic
flux to be a __totally closed flux__.

The Euler distribution of a totally
stochastic flux is a *totally chaotic* distribution (see par.
2.3). Neither this type of flux can really exist (it is also an ideal
model), the real fluxes being only partly stochastic or otherwise
speaking, for each real stochastic flux, there is an associated level
of analysis (decomposition into domains) for which the common
component of the flux elements set is no longer null (there is a
local coherency, at the level of spatial or temporal domain).

Comment 5.3.5: For instance, in a gas where there is a partly coherent molecule flux (a flow) oriented in a given direction. If this flux would be entirely coherent, this means that no interaction would be able to exist on the direction normal on flow direction, so, the static pressure into the flow would be null. This is not allowed by the external flux molecules (not involved into the flux) which are ready to occupy the section with null static pressure, and they shall restrict the flux’s coherency degree up to a value which is always subunitary.

Although the real
fluxes are neither totally coherent nor totally stochastic, the two
basic flux types are very important for the objectual philosophy. We
have seen that the inner T reference of a compound object is unique
and common to all the object’s elements. The result is that the
motion of this reference is evenly submitted to all of these
components, which means that the inner T references of the components
shall basically have the same motion (with the same modulus and
direction), therefore, we are dealing with a totally coherent flux.
This means that if a totally coherent real flux cannot occur in a
medium, we might have in exchange __totally coherent components__
(abstract) of these fluxes.

We shall see further on that not only T* *component of an isotom
flux belongs to this category but also other components with
invariant direction (for example, the normal and tangent component on
a boundary surface or the components which are settled based on the
directions of the axes of reference). We shall also notice that a
coherent component of a real flux cannot simply vanish just like
that, but as a result of an interaction process with a boundary
surface, this component __may turn into__ a stochastic one. There
is also the reverse process of the transformation of a stochastic
flux into a coherent flux (more exactly, into a flux with a totally
coherent component), but this is also conditioned by the presence of
a boundary surface.

Comment 5.3.6: For example, in case of the collision of a ball with a wall, the initial kinetic flux (impulse) is the totally coherent T component of the set made-up from the molecules of the ball’s membrane and the molecules of its inner pressure gas, all of them moving with the common translation velocity. At the moment of collision, there is a temporal interval in which the ball is deformed by the impact with the wall, but it does not move (the coherent component of normal translation at the wall is null). What has happened to the coherent flux? It’s simple! The initial coherent flux has turned into a stochastic flux (with a null coherent component), namely, into pressure and heat, and after that, very short temporal interval of immobility, the reverse process of turning the stochastic flux again into a coherent flux, but with an opposite direction (the ball reflection on the wall) to be initiated.

Therefore, we shall
be dealing in the following sections with totally coherent or totally
stochastic __components of a flux__, but these will be presented
in a brief version, which means that a flux with a totally coherent
component is referred to as a flux with a coherent component, a
partly coherent flux, or coherent flux component. The same procedure
is applied to the stochastic fluxes.

Comment
5.3.7: The concept of *coherency *has a broader meaning in this
paper than the term used in the regular scientific language, and it
is closely-connected to the notion mentioned in chapter 3, that is a
*common component* of a set of objects. According to the
definition of the totally coherent flux, the result was that, in case
of the translation fluxes, if the directions and FDV modulus are the
same (therefore, they are common on the vectors set), that particular
flux is therefore totally coherent. However, the same coherency issue
is valid for the rotation fluxes, but the difference is that, in this
case, FDV directions cannot be invariant any longer, the modules also
depend on the radius of gyration, but, the sense and the angular
speed can be invariant. Therefore, the fluxes’ coherency
criteria are different due to the motion type, but in case there are
common components of SEP, there are also __coherency degrees.__

It is very important to be understood that a flux such as the stochastic one, contains a distributed motion of some objects within itself, but this motion is not perceptible from the outside of the space occupied by this flux, in the absence of a global, external component of the motion. This fact (inexistence of an apparent common motion) does not also mean the inexistence of the elementary fluxes, therefore, of the objects’ inner motion.

Comment
5.3.8: A classic example of this kind of flux is the chaotic motion
of the molecules of a pressure gas inside a gas cylinder with a
steady position, motion which obviously does not have a common
component since the gas cylinder is motionless. The attribute which
strictly depends on the intensity of the stochastic kinetic flux of
the gas molecules is the pressure of the gas from the inside,
pressure transmitted to the cylinder’s wall, where it causes a
stretching effort of the cylinder casing material (another stochastic
flux, but this time, it belongs to the cylinder casing’s
atoms). As long as the intensity of the kinetic stochastic flux from
the casing is under the breaking point of the cylinder material, the
two fluxes (the stochastic one of the gas and the other stochastic
flux of the casing atoms) will be in equilibrium on the bounding
surface. When this limit is exceeded, the casing medium breaks, the
equilibrium vanishes and the fractions of the cylinder walls will
move together with the gas molecules towards quaquaversal directions
(flux with a coherent component - the motion sense) as compared to
the former position of the cylinder. None of these visible motions
could not have been generated if the stochastic flux, __occult but
persevering__, of the gas molecules would not have existed.

We are about to see
in the following chapters that the introduction of these two basic
concepts, of *stochastic* and *coherent flux,* allows us to
have a new approach on notions, such as the equilibrium between
forces, or the energy classification in the two components - kinetic
and potential.

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