6.4 Types of distributed systems

We have seen in section 5.2.2.3 that the material fluxes, as collective conveyance processes of a set of objects, can be divided in three basic classes S, L and G, according to the type of the relations deployed between the inner spatial references of the objects and the spatial global reference of the set.

It is worth reminding that these relation types are:

1. S-type relations - If the relations between the inner T and R references of the constitutive objects are invariant during the motion, both between the proximity objects and against the homologue common T and R reference, the entire distribution of the amount M shall move just as a solid (rigid) body. In this case, there is a global (which is internal within the set) T and R reference with the positions defined against an external RS, and the variation of this position represents the overall motion of the set’s spatial distribution. One may notice that within S-type relations, the inner free motions of the complex object’s elements, either T or R, are forbidden.

2. L-type relations - If only the relations between the inner T references of the neighbouring elements are maintained invariant (the elements remain adjacent, permanently connected during the motion, but they are able to rotate freely), the entire distribution shall be moving just as a finite liquid quantity which preserves its volume, but it is not able to preserve its shape (inner distribution of the elements’spatial position). In this case, there is only one common T reference (the mass-center for a liquid portion) whose motion against an outer T reference is the overall motion of the complex object.

3. G-type relations - If there is no invariant relation between the inner T and R references of the components and the common T and R reference of the distribution, those particular elements do not make-up a complex object any longer, each of these elements moving freely, just as the molecules of a gas. In case of G-type relations, any kind of inner motion is allowed and there is no interrelation between the T and R motions.

The possibility of relative translation motions within the pairs of proximity elements, as we are about to see later on, is strictly connected to the temporal distribution of the interaction intensity. As for a DS whose elements are permanently related (the inner spatial domains are always adjacent), their free translation is excluded (there are translation motions, but they are not free and are generated as a result of the continuous action exerted by a system of forces). The possibility of the rotation motions also depends (in case of some permanent interactions) on the unevenness of the spatial distribution of the interaction intensity against the inner RS of each DS element. The uneven is the distribution (more anisotropic), the less possible is the rotation of the elements one another. If this distribution is even (isotropic), there are no favourite bonding directions, and the elements will be able to rotate freely and autonomously against their neighbors.

According to these specifications made in case of the distributed systems, two of the criteria - (an)isotropy and time distribution of the interaction intensity - allow their classification in the following types:

1. S-type systems (with their representative element, that is the solids), characterized by:

• permanent interaction;

• increased anisotropy of the interaction intensity (which leads to the drastic limitation of the changes produced in the elements position, both T and R). In case of this DS type, there are only S-type relations between its elements.

1. L-type systems (with their representative element, that is the liquids), characterized by:

• permanent interaction;

• interaction intensity (determined against the inner RS of DS’s elements or of a group of elements) is quasi-isotropic (the position change by means of indefinite rotation is allowed, at least at the level of elements subset). In case of this DS type, there are L-type relations, either at the element level, or at the elements subset.

2. G-type systems (with their representative element, that is the gases) characterized by:

• non-permanent interaction (most of the times, the elements are isolated each other, the interaction with the rest of the medium is insignificant, the only type of interaction is represented by the collisions which occur only on very short time intervals);

• interaction’s intensity is isotropic (the parameters of the interaction generated by means of collision do not have a preferential direction). In case of this type of DS, only G-type relations occur between their elements.

The non-permanent interaction which is specific to G media allows the introduction of the free system concept, considered to be the system whose interactions with other systems are negligible (for certain periods of time). This fact makes that the pathway covered during the time when the system is isolated to be called free pathway. The free pathway (or free path) notion is real only in case of this type of medium (the volume restraint by means of compression is made only based on the reduction of the free pathway and not through the modification of the interaction intensity, resulting therefore the high compressibility of these media).

Few remarks regarding the above-mentioned classification may be pointed out:

1. The systems with permanent interaction (S and L-types) do not allow the free inner translation, thus resulting their very low compressibility degree; the existence of this continuous interaction, inclusively for the elements placed at the system periphery makes that these DS to have a defined bounding surface (as area and form for S-type media and only as area for L-type media) against the outside medium, and accordingly, a proper defined volume.

2. The systems with an isotropic distribution of the interaction intensity against the inner R reference of the elements allow the elements rotation. As we are about to see on another occasion, the systems with anisotropic features of the interaction at a short distance are able to make-up an isotropic medium (or quasi-isotropic), if the conditions for the elements rotation are created (for example, by increasing the space between the elements over the working radius of the anisotropy, that is a situation which occurs, for instance, during the flow phase of the materials subjected to the stretching force, or as a result of the thermal dilatation).

Comment 6.4.1: It is the moment to make a specification regarding the (an)isotropy term. One aspect must be clearly understood: so far, in this chapter, the discussion was only about the isotropy or anisotropy of the spatial distribution of a single attribute, that is: the intensity of the bilateral interaction between the elements of a DS (in case of a NM, between its atoms or molecules). We are not talking about the isotropy or anisotropy of other properties, such as the mass density, refractive index, photon transparency etc., all of these were mentioned because of an error found in the technical papers, namely, the case of glass which is also called “undercooled and frozen liquids”²5. The fact that the above-mentioned macroscopic properties deploy an isotropic distribution inside the glass, similarly with the liquids, does not mean that at the molecular level, the distribution of the interaction intensity between the glass molecules is not highly anisotropic (with preferential bonding directions), by hindering in this way the molecules rotation one to another, which gives the non-deformable character of this material.

It is important to notice that, within the media which have a prohibited free translation, the translation motion is however possible, not under a free form, but rather through the modulation of the interaction intensity, that is the forced translation (such as the vibratory one). The same thing is also valid in case of the rotation motion.

The classification into S, L or G systems is universal. As we are about to see further on, the category of S-type of systems shall also include, besides solids, also the bio-systems, artificial material systems, information support systems (therefore, the abstract systems) etc. The category of L-type systems may also include the media of the conduction electrons from metals, the plasma structures (their ionized fraction), dry grained media etc. Besides the non-ionized gases, the G-type systems also comprise an extremely significant DS segment - which is represented by the bio-populations (organismal media or the ones made-up from independent cells) - in which the meaning of concepts such as “free” and “freedom” remains the above-mentioned one.

As regards the maintenance capacity of DS without additional external barriers (which shall be analyzed later on in this paper), this time involving the interaction sense, DS are divided in:

1. DS with self-maintenance, which consists of only the S-type DS, with attractive interactions known as S_A, the only systems which are self-maintained without external barriers;

2. DS with forced maintenance, which can be also divided in:

• Systems with permanent attraction interaction, but insufficient for maintaining the system without the addition of an external barrier. These systems are a fraction of L-type of media which are called L_A-type media with the representative element found in the common liquids (which are maintained in a liquid phase, at a specific temperature, only under the conditions of air pressure caused by the gravitation field - natural barrier - or also under pressure inside a solid precinct - that is the natural or artificial barrier).

• Systems with permanent but repulsive interactions (either remote repulsion or only at the contact between elements), which consist of S media with repulsive interactions called S_R²6 and the rest of L-type media, known as L_R (the surface layers of the grained material deposits, dry powders, sand, gravel, but also the medium of the conduction electrons existing in metals, etc).

• Systems with non-permanent interactions, G-type DS.

So far, we have focused on the maintenance of the natural abiotic systems, but we have to mention that the issue of media maintenance has the same approach as in the case of the biotic systems. For example, the tissues or the organisms are S_A-type of media (they are therefore self-maintained as long as they are alive), whereas the human populations (for example) are an ensemble of G-type media (with forced maintenance); these populations cannot be preserved without some barriers:

1. natural barriers (gravitation field, relief forms, food and energy resources etc.);

2. artificial barriers:

• the administration’s barriers (the frontiers well guarded);

• the informational barriers (language, traditions, religions etc.).

The artificial barriers are provided by a centralized system - state’s authority - which maintains all the social media (population’s constitutive media) by means of its powerful interaction).

The S-type systems can also be divided according to the number and the position of the elements which make-up the proximity of an element considered as a reference:

1. one-dimensional S systems (series type), in which the proximity oriented in a certain direction is made-up from a single element (linear molecules, written or spoken information support systems, so on);

2. two-dimensional S systems, in which the proximity is made-up from elements with positions included in a plane which is parallel with the tangent plane through the reference element (the outer surfaces of the solid bodies, the organisms’ epidermis, 2D images etc);

3. three-dimensional S systems, comprise all the other S systems.

The classifications made so far have taken into consideration that the elements of the above-described systems have an non-altered (complete) structure. If some of the elements from DS structure are partly decomposed, we shall be dealing with a partly dissociated system, the system’s dissociation degree being in proportion to the number of the decomposed elements as compared with the total number of the elements belonging to the system (medium). This category comprises for example, plasma structures, ionic solutions, bio-populations made-up from families of sexual individuals, among which other mature individuals who are not joining to a family are also introduced, so on.

Comment 6.4.2: The “dissociation” term suggests the reverse operation of the association, that is the breaking-out (decomposition) of a system. Through dissociation, the system may lose one or more of its elements (as compared to the complete model configuration), until the entire decomposition of the system. The currently used meaning for this word is limited to the description on the dismemberment of some particular systems (such as the atoms, molecules), but it can be also used for the decomposition of other systems which show charge attributes, such as the families of the sexual bio-systems. In case of the dissociated systems, the interaction of the fragments coming from the dissociated system is much different than the one of the non-dissociated system. As we are about to notice further on, this aspect is specific mainly to the systems characterized by charge interaction. As a result of the intensity and duration modification of the interactions, the dissociation may lead to the modification of the medium type as compared to a non-dissociated medium. For example, the ionized gases (plasmas) are not G media any longer, because the interaction of the ionized molecules is permanent (as long as the ionization lasts), therefore, there is no free pathway except the one for the non-ionized molecules.

If the systems which belong to a DS are all of the same kind, we may consider that particular medium as a pure one. The purity concept is gradual (measurable), rarely noticed at the abiotic media, but more frequent at the biotic and artificial media.

Comment 6.4.3: If according to the usual language, the purity concept is mostly used in relation to the natural media (pure crystals, liquids or gases etc.), this does not mean that it cannot be used for the characterization of other media made-up from a single type of elements. For example, a bacterial culture made-up from the division of the same cell type under sterile conditions is genetically speaking a pure medium (if no mutations are interfering). There is also the term of ethnic purity for the social media.

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INDEX

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