Self-Formation, Development and Reproduction of the Artificial Planar Systems-Reference-Cited by-同舟云学术

Self-Formation, Development and Reproduction of the Artificial Planar Systems

Published:2004-04 Issue: Volume:97-98 Page:391-443
ISSN:1662-9779
Container-title:Solid State Phenomena
language:
Short-container-title:SSP

Author:

Janušonis Stepas¹,Janušonienė Vida

Affiliation:

1. Institute of Lithuanian Scientific Society

Publisher

Trans Tech Publications, Ltd.

Subject

Condensed Matter Physics,General Materials Science,Atomic and Molecular Physics, and Optics

Link

https://www.scientific.net/SSP.97-98.391.pdf

Reference286 articles.

1. M. Apter 5. 3. 1. Closed Topological System. The systems discussed above interact with certain sequences of external systems, i. e. a formation takes place in the systems open for information. In the case of the system open for topology the topology is transferred in consecutive order from external systems to a forming system. In case of the system open for parameter, the figures of the initial system go through a series of transformations partly caused by a sequence of external systems, excluding topology, partly - by changing structure of the forming systems: by configuration and arrangement of figures. Examination of the system closed for topology and parameter will be accomplished hereinafter. The system closed for information is not closed from the point of view of thermodynamics. It may be open for energy and/or substances, however an energy and substance are derived in a chaotic state with no structure in space and in time. As it has been discussed, a closed topological system does not interact with a medium or external systems in the examined interval of time. There we have a non-equilibrium system. On the other hand an examination of completely non-equilibrium systems has no practical sense as discussed above. We are interested in non-equilibrium systems, that are in equilibrium state in the initial phase and carry themselves to equilibrium state after having progressed to the point of given complexity. Thus what interests us most is an investigation including putting out from equilibrium state, an evolution process and the resting to equilibrium state. Thus we introduce the new useful concepts. A closed equilibrium topological system in the non-interacting medium is further called as an elementary system. The elementary system can obtain a very different structure. The system, including two equilibrium elementary systems in distance of radius R<� of neighbourhood of a Euclidean point and obtaining an non-equilibrium state is further referred to the initial system. The initial system can be realised when two elementary systems come into contact and form a non-equilibrium system. As a rule there are two kinds of elementary systems. One of them includes topology on the plane while the other one can include a set of homogeneous planes with different parameters. We will call an evolution of a closed system followed by increase of its complexity we will call development [101, 126, 118]. This concept shows a principle analogous to the evolution of the closed topological systems with development of living beings from germ (seed-corn, egg, embryo). We will go into different kinds of development systems. It is a pity that we are able to examine only random cases of the development results of which confirm rather the fact of existence of such systems rather than its detail examination. The undetermined class and general laws of development of such systems remain. No doubt the research cases are chosen not by chance. They are defined by the already known technological achievements [101, 126, 118] and by analogous with living nature. 5. 3. 2. Development of Single Topological System. Development of the topological system occurs as an evolution of the initial system followed by increase of its complexity when an object interacts with another object. Localisation of interactions in space and time are controlled by evolutionary object itself. Evolution continues on at finite interval of time. Therefore a system must be equilibrium before and retain after evolution. Title of Publication (to be inserted by the publisher) Let us have a topological space including a set of parameters P = {0, 1, .., 7}. (5. 27) Let us assume that there are two different elementary systems in the topological space (Fig. 5. 9., a, b).

2. [1] [1] [1] [0] [0] [0] [0] [0] [0] [3] 3 A a b c.

3. [2] [2] Fig. 5. 9. Elementary systems in topological space a - elementary system including a figure; b - elementary system without figure; c - initial system. S= {0}{(A1, 2)(\A1, 1)}{0}, (5. 28) K = {0}{3}{0}. (5. 29) The matrix (Matrix 5. 30) of interactions is given by: Matrix 5. 30. 0000 0101 0202 0303 0404 0505 0606 0707 1010 1111 1212 1313 2020 2121 2222 2324 424 2526 2626 2727 3030 3131 3242 3333 3435* 3737 4040 4242 4353* 4444 4545 4647* 4747 5050 5262 5454 5555 5656 6060 6262 6363 6474* 6565 6666 6767 7070 7272 7373 7474 7676 7777 Let us remind you of an asterisk that marks the self-stopping interaction in distance R between Euclidean points juxtaposed to interaction parameters. Let us assume that elementary systems S and K draw closer to each other in distance R<� and the initial system arises as shown on figure (Fig. 5. 9, c). Thus we have merging of two elementary systems of different kinds (Eq. 5. 28, Eq. 5. 29), causing a formation of the initial system G: G = S � K = {0}{(A1, 2)(\A1, 1)}{3}{0}. (5. 31) Title of Publication (to be inserted by the publisher) Owing to the Euclidean points with parameters 2 and 3 which get into the same neighbourhoods, and interaction 2324 the initial system will take out of equilibrium: the figure A1 with parameter 4 arises on the plane {3} (Fig. 5. 10).

4. 0 0 0 0.

5. [3] [2] 1 2 1 2.