An improved model of partition curve based on accumulation normal distribution function

Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.

Edge detection and mathematic fitting for corneal surface with Matlab software

AIM：To select the optimal edge detection methods to identify the corneal surface,and compare three fitting curve equations with Matlab software. METHODS：Fifteen subjects were recruited. The corneal images from optical coherence tomography（OCT）were imported into Matlab software. Five edge detection methods（Canny,Log,Prewitt,Roberts,Sobel）were used to identify the corneal surface. Then two manual identifying methods（ginput and getpts）were applied to identify the edge coordinates respectively. The differences among these methods were compared. Binomial curve（y=Ax2＋Bx＋C）,Polynomial curve [p（x）=p1xn＋p2x（n-1）＋....＋pnx＋pn＋1] and Conic section（Ax2＋Bxy＋Cy2＋Dx＋Ey＋F=0）were used for curve fitting the corneal surface respectively. The relative merits among three fitting curves were analyzed. Finally,the eccentricity（e）obtained by corneal topography and conic section were compared with paired t-test. RESULTS：Five edge detection algorithms all had continuous coordinates which indicated the edge of the corneal surface. The ordinates of manual identifying were close to the inside of the actual edges. Binomial curve was greatly affected by tilt angle. Polynomial curve was lack of geometrical properties and unstable. Conic section could calculate the tilted symmetry axis,eccentricity,circle center,etc. There were no significant differences between ＇e＇ values by corneal topography and conic section（t=0.9143,P=0.3760 〉0.05）.CONCLUSION：It is feasible to simulate the corneal surface with mathematical curve with Matlab software. Edge detection has better repeatability and higher efficiency. The manual identifying approach is an indispensable complement for detection. Polynomial and conic section are both the alternative methods for corneal curve fitting. Conic curve was the optimal choice based on the specific geometrical properties.

Effect of tempering temperature on strain hardening exponent and flow stress curve of 1000MPa grade steel for construction machinery

To study the effect of tempering temperature on strain hardening exponent and flow stress curve,one kind of 1000 MPa grade low carbon bainitic steel for construction machinery was designed,and the standard uniaxial tensile tests were conducted at room temperature.A new flow stress model,which could predict the flow behavior of the tested steels at different tempering temperatures more efficiently,was established.The relationship between mobile dislocation density and strain hardening exponent was discussed based on the dislocation-stress relation.Arrhenius equation and an inverse proportional function were adopted to describe the mobile dislocation,and two mathematical models were established to describe the relationship between tempering temperature and strain hardening exponent.Nonlinear regression analysis was applied to the Arrhenius type model,hence,the activation energy was determined to be 37.6kJ/mol.Moreover,the square of correlation coefficient was 0.985,which indicated a high reliability between the fitted curve and experimental data.By comparison with the Arrhenius type curve,the general trend of the inverse proportional fitting curve was coincided with the experimental data points except of some fitting errors.Thus,the Arrhenius type model can be adopted to predict the strain hardening exponent at different tempering temperatures.