## 5.2 Definition and flux models

In order to display the motion process of a singular object, it is enough to assert that its position is variable (eventually, continuous) depending on time, and the ratio between the position variation and the time interval which is necessary for this variation (density of the variation’s temporal distribution) represents the intensity of this motion process (velocity magnitude). But, if we are dealing with the motion of some spatial distributions of material objects, their motion issue is not simple any more, the introduction of a new term being required - that is the flux - which in the present paper is defined as the simultaneous motion of a set of objects, namely, a distributed motion (or a motion distribution).

Based on the facts presented in the previous chapter, few correlations may be established, because since we are talking about motion, we already know which is the variable attribute - spatial position of the mobile object. With only a single variable attribute20, the result is that the motion process is a specific process. Since there are many objects which are in motion (a spatial distribution of objects with a simultaneous existence) within this process, we are dealing with a collective process.

Definition 5.2.1 The collective and specific motion (transfer, transport, displacement) process of some spatial distribution of objects or processes is called flux.

As we have noticed in chapter 3, an object means an invariant distribution (against its inner reference system) of a collection of properties. In order to initiate a motion of an attribute (amount - according to the mathematic language) we must have a motion of an object which is the holder of that property. Even in case when we are dealing with an information transfer (abstract objects), we are about to see in the following chapters that this also means the transfer of some objects, namely, material information support systems (ISS). The following section which is focused on the flux model according to the mathematic version (virtual), shall let aside the real property’s support (the carrier object), because this is the operation mode in mathematics. In chapter 2, we have seen that the distributions are divided in two categories - virtual and realizable - that is why the flux’s mathematical models shall be divided according to the same classification.

20 Although we have asserted that the motion consist in translations and rotations, only the translations are important in case of the flux model, because only them are involved in a translation process.