Papers by Keyword: Topological Space

Abstract: Eight-dimensional topological space providing an object evolution in time, including causes of evolution is presented. Part of Euclidean space separated by any close surface from complementary space, where any Euclidean point of space is juxtaposed with parameter, is being felt as an object. Coplanar approximation of flat planar devices is based on the flat, homogeneous, isotropic planar object and chaotic medium. The new, more general approximation of the topological space by equidistant surfaces, suitable for spatial planar objects, is presented. Selfformation of spatial objects (homogeneous, non-homogeneous, anisotropic), medium (chaotic, chaotic oriented, homogeneous oriented, structural) based on non-homeomorpheous mapping in peculiar points and evolution irreversibility, is discussed.

Abstract: Self-formation concept as a generalization of the huge number of technologies in microelectronics was defined. Self-formation as irreversible evolution, causing self-increasing of an object complexity, is presented. Differential equation method allows description of evolution of any figures contour. Numerical model of self-formation in essence is a cellular automata of the second kind. Neither analytical nor numerical models did not involve causes of contour evolution. However causes of evolution are hidden in interactions of parameters which approximate an object and ambient materials. On the basis of above-mentioned factors, the right-dimensional topological space was created. It is the Cartesian product of the eight sets, including three Euclidean space axes, four parameter axes (defining parameters of the Euclidean points and interaction matrix) and time axis. Self-formation is a result of non-homogeneous mapping sequence in time. On the other hand non-homeomorpheous mapping indicates irreversibility of an evolution. Evolution is irreversible in time if only the object either contains the peculiar points or they arise under evolution. Therefore an interaction, defining the figure evolution out-side, does not return the object to initial state after its diversion inside and can implicate the complexity increasing. The new self-formation technologies for electron devices and integrated circuits manufacturing were carried out. Topological approach allows analysis and synthesis of real world structures, known in the areas of microelectronics, nanotechnology, photovoltaics and fuel cell technology, possibly in living world (genes, cells, organs, organism) as well. Problems remaining to be investigated are presented.