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In this paper, the correlation dimension, which describes chaotic motion, is used to analyze the time series of silicon single crystal diameter. It is furthermore used to extract the dynamics characteristics of silicon single crystal dislocation. However, the correlation dimension is difficult to realize automatic calculation. This paper proposes a new automatic calculation method for the correlation dimension based on fuzzy C regression model (FCRM) algorithm. In this method, FCRM algorithm is used to identify the correlation integral curve of the scale-free zone. The correlation integral curve slope of the scale-free zone is the correlation dimension. The proposed method is investigated through both simulation and experimentation. Both demonstrate that the proposed automatic calculation method of the correlation dimension has higher computation precision and efficiency, and can effectively extract the dynamics characteristics of silicon single crystal dislocation.

In order to achieve a real-time and visual observation of multi-plane images,a method using light-emitting materials is proposed.A 3D object can be divided into a series of 2D slices along the optical axis.With an efficient and fast 3D Gerchberg-Saxton algorithm,a computer-generated phase hologram is obtained and a numerical reconstruction is carried out on the computer.The process of 3D Gerchberg-Saxton algorithm is expounded,and the experiment for reconstruction and visualization of multi-plane images based on LC-SLM is conducted.With the grey level-phase curve of the LC-SLM,the computer-generated phase hologram is converted to gray-scale hologram,which is loaded to the LC-SLM to reconstruct the 3D light fields.The fluorescence characteristic of quantum dot materials is used to achieve the visualization of the light fields.Experimental results show that the optical reconstruction is in good agreement with numerical simulation.This technique is applicable in medicine,military,3D display,micromachining and micro-technology.

In this paper we combine stable noise with bistable stochastic resonance to investigate the parameter-induced stochastic resonance in the high-and low-frequency (both for multi-frequency) weak signal detection with different stable noise, and explore the action laws between the stability index (0 2) and skewness parameter (-1 1) of stable noise, and the resonance system parameters a, b on the resonant output effect. Results show that for different distribution of stable noise, the high- and low-frequency weak signal detection can be realized by tuning the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with or . Moreover, while detecting the high- and low-frequency weak signal, the action laws of the resonant output effect which are affected by or are the same. These results will contribute to realize a reasonable selection of parameter-induced stochastic resonance system parameters under stable noise, and lay the foundation for a practical engineering application of multi-frequency weak signal detection based on the stochastic resonance.