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 t...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.展开更多
In actual engineering, processing of big data sometimes requires building of mass physical models, while processing of physical model requires relevant math model, thus producing mass multivariate polynomials, the eff...In actual engineering, processing of big data sometimes requires building of mass physical models, while processing of physical model requires relevant math model, thus producing mass multivariate polynomials, the effective reduction of which is a difficult problem at present. A novel algorithm is proposed to achieve the approximation factorization of complex coefficient multivariate polynomial in light of characteristics of multivariate polynomials. At first, the multivariate polynomial is reduced to be the binary polynomial, then the approximation factorization of binary polynomial can produce irreducible duality factor, at last, the irreducible duality factor is restored to the irreducible multiple factor. As a unit root is cyclic, selecting the unit root as the reduced factor can ensure the coefficient does not expand in a reduction process. Chinese remainder theorem is adopted in the corresponding reduction process, which brought down the calculation complexity. The algorithm is based on approximation factorization of binary polynomial and calculation of approximation Greatest Common Divisor, GCD. The algorithm can solve the reduction of multivariate polynomials in massive math models, which can obtain effectively null point of multivariate polynomials, providing a new approach for further analysis and explanation of physical models. The experiment result shows that the irreducible factors from this method get close to the real factors with high efficiency.展开更多
基金supported by the National Natural Science Foundation of China(50206019)
文摘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.
文摘In actual engineering, processing of big data sometimes requires building of mass physical models, while processing of physical model requires relevant math model, thus producing mass multivariate polynomials, the effective reduction of which is a difficult problem at present. A novel algorithm is proposed to achieve the approximation factorization of complex coefficient multivariate polynomial in light of characteristics of multivariate polynomials. At first, the multivariate polynomial is reduced to be the binary polynomial, then the approximation factorization of binary polynomial can produce irreducible duality factor, at last, the irreducible duality factor is restored to the irreducible multiple factor. As a unit root is cyclic, selecting the unit root as the reduced factor can ensure the coefficient does not expand in a reduction process. Chinese remainder theorem is adopted in the corresponding reduction process, which brought down the calculation complexity. The algorithm is based on approximation factorization of binary polynomial and calculation of approximation Greatest Common Divisor, GCD. The algorithm can solve the reduction of multivariate polynomials in massive math models, which can obtain effectively null point of multivariate polynomials, providing a new approach for further analysis and explanation of physical models. The experiment result shows that the irreducible factors from this method get close to the real factors with high efficiency.
