A novel particle tracking algorithm using polar coordinate system similarity

A new algorithm using polar coordinate system similarity （PCSS） for tracking particle in particle tracking velocimetry （PTV） is proposed. The essence of the algorithm is to consider simultaneously the changes of the distance and angle of surrounding particles relative to the object particle. Monte Carlo simulations of a solid body rotational flow and a parallel shearing flow are used to investigate flows measurable by PCSS and the influences of experimental parameters on the implementation of the new algorithm. The results indicate that the PCSS algorithm can be applied to flows subjected to strong rotation and is not sensitive to experimental parameters in comparison with the conventional binary image cross-correlation （BICC） algorithm. Finally, PCSS is applied to images of a real experiment.

One-Dimensional Optimal System and Similarity Reductions of Wu–Zhang Equation

The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.

Principle of nonlinear chemical fingerprint by using dissipative components in samples as well as calculation and evaluation of similarity

Under the conditions of constant temperature and pressure,different influences of samples with different chemical components on the mechanism of nonlinear chemical reaction will cause different changes of the potential-time relationship curve of the nonlinear chemical reaction system.Using it as the character,and using the B-Z nonlinear chemical system to use acetone and substrates in samples as main dissipative substances qua an example,the principle of nonlinear chemical fingerprint has been researched and discussed in detail.At the same time,the general method for calculating the system similarity about nonlinear chemical fingerprint was also put forward,and similarities of nonlinear chemistry fingerprints of different batches of Guhan Yangshengjing and 18 sorts of other samples were calculated by Euclidean distance,correlation coefficient,included angle cosine and system similarity,at the same time,the various similarities were analyzed.The results showed that,both of correlation coefficient and included angle cosine are unable to be used as the criterion for quantitatively evaluating the similarity of nonlinear chemistry fingerprint;as non-parametric similarity,Euclidean distance can accurately reflect the feature differences in the fingerprints,but as parametric similarity,sometimes,Euclidean distance can not accurately reflect the relative extent of characteristic difference in the nonlinear chemical fingerprints;system similarity can most truthfully reflect the characteristic difference in the nonlinear chemical fingerprints,and is the best evaluating method among the four ones.Therefore,system similarity can be used to quantitatively calculate the similar extent between the nonlinear chemical fingerprints.An economical,simple and convenient,easy pushing and effective method for identifying and evaluating complicated samples has successfully been put forward.