Abstract
Many recently published research papers examine the representation of nanostructures and biomimetic materials, especially using mathematical methods. For this purpose, it is important that the mathematical method is simple and powerful. Theory of fractals, artificial neural networks and graph theory are most commonly used in such papers. These methods are useful tools for applying mathematics in nanostructures, especially given the diversity of the methods, as well as their compatibility and complementarity. The purpose of this paper is to provide an overview of existing results in the field of electrochemical and magnetic nanostructures parameter modeling by applying the three methods that are “easy to use”: theory of fractals, artificial neural networks and graph theory. We also give some new conclusions about applicability, advantages and disadvantages in various different circumstances.
Highlights
The application of fractal nature analysis on electro-ceramic materials’ micro-structure characterization opens a variety of new frontiers for higher-level microelectronic devices and integrations, especially if the approach is scientific and inspired by self-similarities that exist in nature
The shape, size and structure of grains and pores, or other aspects of a ceramic material’s micro-structure morphology, influence its intergranular physical properties, such as dielectric, ferroelectric and magnetic properties. This is important for the design of electro-ceramic materials with desired features
Especially regarding the determination and prediction of dielectric properties at the nano level by applying fractal nature analysis, we introduced two other practical and useful methods: artificial neural networks and graph theory
Summary
The development of new and advanced technologies for micro-electronic complex devices, as well as their further miniaturization and integrations, becomes more and more interesting every day for industry as well as for scientific research teams. Micro-structure is illustrated today, itnew is4.one ofis the most expansive research fields and there are various procedure in the characterization of materials’ Electronic miadvanced prognosis of microstructural property possible [10]aiming This is an a fractal method of property structural material reconstruction, to croscopy methods enable obtaining micro-graphs, regardless of resolution and magnifiThe new procedure in the characterization of materials’. Modification of the ceramic alters these properties, and it is often employed to enhance these properties The application of this type of fractal analysis for the determination of dielectric properties at the grain boundary level for samples obtained with different sintering conditions and modifying agents will enable researchers to build more efficient materials for higher-level microelectronic devices and integrations
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