Several Classes Of Fractal Behavior And Control In Engineering Technology

Fractal geometry theory plays an important role in the nonlinear field. It has been widely applied to the engineering technical fields, such as high polymer chemi-cal industry production, oil drilling, thin-film material preparation, heat transfer and dissipation. On the one hand, there are many dynamics behaviors far from equilib-rium in the field of engineering technology, for instance, diffusion of dust particle aggregation, water drive oil viscous fingering, conductor of heat transmission, early growth of thin film materials. In these processes, we also can observe many com-plex and irregular growth phenomena. Thus, we can understand related physical phenomena and fractal growth mechanism by fractal theory to conduct quantitative characterization to its complex graphics, and to use the obtained conclusion. Howev-er, in the real and complex environment, the process of fractal diffusion aggregation will be affected by many other external factors like the change of magnetic field, thermal conductivity change with temperature, current change, so that the fractal growth morphology is complicated and difficult to be predicted. As a result, pre-diction and control of the fractal growth morphology bring about a new problem of important and realistic application value. Regretfully, most of the present work-s still focused on changing different parameter values of computer simulation and experimental research. In particular, there are few quantitative relationships starting from the mechanism of mathematical to analyze in the process of growth and related researches to carry out the fractal growth form and the directional region control.On the other hand, self-similarity is an important characteristic of fractal struc-ture. Compared with traditional periodic photonic crystals, fractal photonic crystals have unique properties and advantages. Therefore, it is an important subject in prac-tical application to implement the fractal theory to the field of photonic crystals and to study optical fractal behavior of fractal photonic crystals.The fractal behavior is extremely common in the field of engineering technol- ogy. In this paper, several classes of fractal behavior and control in engineering technology are studied. The main contents involved are as follows.1. Diffusion limited aggregation of magnetic particles with exponential func-tion interactionOn the basis of magnetic diffusion limited aggregation (MDLA) model, two spin states of magnetic particles are introduced. Assuming that the magnetic interac-tion force between the particles decays exponentially with their distance, the Monte Carlo method is used to simulate the dynamic behavior of cluster fractal growth for different physical parameters in three-dimensional space. And the cluster morphol-ogy, fractal dimension and magnetic susceptibility of the MDLA are analyzed with respect to the range factor a and the coupling energy βC. The obtained conclusion provides a reference for studying the fractal growth mechanism of magnetic particles and many others.2. Environmental disturbance control of thermal fractal diffusion growthAccording to the structure characteristics of thin plates composed of tightly compressed heterogeneous layers and space body, a nonlinear dynamical model is presented to study the fractal growth of thermal diffusion in the thin plates and space body under the disturbance of changeable environment. The model can be applied to predicate and control the thermal fractal diffusion of tightly compressed hetero-geneous layers of thin plates and space body. The quantitative relationship between the growth probability and the disturbance item can be obtained according to the corresponding nonlinear dynamical model, thus predicting the influence of different source item on fractal growth. When nonlinear disturbance is expressed as polyno-mial function and exponential function, the effectiveness of the diffusion control of thermal fractal growth was illustrated, providing a reference method for rational se-lection of control parameters and regions. Moreover, the simulation results show that the smaller η, the more powerfully the environmental interference item performing control action on thermal diffusion aggregation. As a consequence, the study will be helpful and significant to understand the physical mechanism of fractal growth as well as the application in the other fields of engineering technology.3. Directional region control of the thermal fractal diffusion in three-dimensional spaceA directional region control (DRC) model was presented of thermal diffusion fractal growth with active thermal diffusion in three-dimensional space. When the nonlinear interference and the internal thermal source items are generalized function-s, the relationship between the particle aggregation probability and the interference items can be obtained using the norm theory of functional analysis. The aggregation form of particles in different regions can be predicted. When the nonlinear inter-ference in the model are expressed as a trigonometric function and its composite function, the simulation shows that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.4. Optical properties of one-dimensional quasi-periodic fractal photonic crystalsThe optical properties of one-dimensional quasi-periodic fractal photonic crys-tals were analyzed. In particular, the anomalous optical properties of heterostruc-tures composed of a highly-absorptive metal film and a truncated Fibonacci fractal photonic crystal were theoretically investigated. It is found that one or multiple highly reflected peaks, even enhanced transmission narrowband can be realized in the near-complete absorption broadband, where the photonic crystals are selected with various Fibonacci sequences or a given sequence as the basic unit. These prop-erties are significant to design important reflection or transmission optical devices in the visible and near infrared ranges.