Multilevel Structures Abstracted From Creatures And Their Growth Kinematics

One of the common features of creatures is the multilevel structure. And the harmonious growth is one reason warranting creatures’ regular life. During the whole growth process, one sub-stage is the proportional growth stage. An interesting question may be asked: How multilevel structure of creature grows in this growth stage. To answer this problem, the ideas of the combination of the growth of multilevel structures in creatures, the fractal geometry and the kinematics in mechainis are adopted to study the growth kinematics of multilevel structures abstracted from creatures universally in this paper.Based on the viewpoint of proportional growth and kinematics, concepts of proportional movement and proportional movement mode are defined. The universality of the proportional movement mode is confirmed. The definition of proportional movement transformation groups is presented. Based on the proportional movement mode and proportional movement transformation groups, the existence of two independent self-similar ratios in multilevel structures is verified. The sufficient and necessary condition for the multilevel structures with self-similarity is revealed. Besides, the result that two identical self-similar ratios must exist in regular fractal sets is proved.Under the proportional movement transformation groups, the growth kinematics of N-segment line is explored(including topological evolution and coordinate evolution). In topological evolution part, the movement transformation law of the vacant space of N-segment line is regarded, and by means of the concept of gap, the condition that N-segment line can grow to infinite level structure is obtained at the first time. The influence of topological invariant N to topological evolution of N-segment line is exposed. In coordinate evolution part, this paper focuses on the entity part of N-segment line. The algebraic expression of coordinates in N-segment line is derived for the first time. The corresponding relationship between codes and coordinates of line segments is obtained.Following the research approach in growth kinematics of N-segment line, the growth kinematics of N-segment regular polygon is explored. By means of proportional movement transformation vectors, proprotional movement transformation groups are reconstructed. Under proprotional movement transformation groups, the topological evolution law and the coordinate evolution law of N-segment regular polygon are obtained.From the viewpoint of fractal geometry, an explanation for the size scale effect in multilevel structures is provided. Based on the conserved evolution mode of multilevel structures, the uncertainty of the macroscopic density of such structures is confirmed. By means of conservation mode, abnormal density phenomena of nanoparticle materials are explained from the geometric viewpoint. The following proposition is suggested: The size scale effect in multilevel structures is essentially a sort of geometric effect due to the mismatch of space measurement and space form.Two applications of multilevel structures in different disciplines are introduced. One is the controlling of the surface buckling wrinkles by fractal structures in the material system of film/substrate structures. The other is the decrease of eddy losses of surfaces of metal medium during the electromagnetic coupling energy transmission process by fractal structures. These applications confirm the following fact: The fractal geometrization idea can provide original solutions to the manufacture of soft micro-nano components with high-precision and the increase of the electromagnetic coupling energy transmission effect of metal medium.