In this paper,effective Eulerian algorithms are introduced for the computation of the forwardfinite time Lyapunov exponent(FTLE)of smoothflowfields.The advantages of the proposed algorithms mainly manifest in two aspe...In this paper,effective Eulerian algorithms are introduced for the computation of the forwardfinite time Lyapunov exponent(FTLE)of smoothflowfields.The advantages of the proposed algorithms mainly manifest in two aspects.First,previous Eulerian approaches for computing the FTLEfield are improved so that the Jacobian of theflow map can be obtained by directly solving a corresponding system of partial differential equations,rather than by implementing certainfinite difference upon theflow map,which can significantly improve the accuracy of the numerical solution especially near the FTLE ridges.Second,in the proposed algorithms,all computations are done on thefly,that is,all required partial differential equations are solved forward in time,which is practically more natural.The new algorithms still maintain the optimal computational complexity as well as the second order accuracy.Numerical examples demonstrate the effectiveness of the proposed algorithms.展开更多
In this paper the concept of first boundary condition （i）（i = 0, 1, 2,…, n） is proposed based on [1], the existence of two times spline interpolant under first boundary condition is proved using constructivity me...In this paper the concept of first boundary condition （i）（i = 0, 1, 2,…, n） is proposed based on [1], the existence of two times spline interpolant under first boundary condition is proved using constructivity method and the uniqueness of the two times spline interpolant under first boundary condition（n） is proved too.展开更多
We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then...We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.展开更多
Grain growth kinetics of austenite in a hypoeutectoid steel（containing carbon of 0.35%）at 920 ℃ and in a hypereutectoid steel（containing carbon of 1%）at 980 ℃ for holding time ranging from 1 h to 6 h was investi...Grain growth kinetics of austenite in a hypoeutectoid steel（containing carbon of 0.35%）at 920 ℃ and in a hypereutectoid steel（containing carbon of 1%）at 980 ℃ for holding time ranging from 1 h to 6 h was investigated.The hypoeutectoid steel exhibited normal grain growth without solute drag hindrance with a time exponent（0.51）close to the theoretical value（0.5）.However,the grain growth of austenite in the hypereutectoid steel held up to 3 h was extremely slow,characterizing by a low value of time exponent（0.08）.Thereafter,a breakaway occurred and the grain growth in the hypereutectoid steel held from 3 h to 6 h progressed normally with a time exponent（0.52）close to the theoretical value（0.5）.展开更多
基金supported by the National Natural Science Foundation of China(12071409)the Natural Science Foundation of Jiangsu Province(BK20211293).
文摘In this paper,effective Eulerian algorithms are introduced for the computation of the forwardfinite time Lyapunov exponent(FTLE)of smoothflowfields.The advantages of the proposed algorithms mainly manifest in two aspects.First,previous Eulerian approaches for computing the FTLEfield are improved so that the Jacobian of theflow map can be obtained by directly solving a corresponding system of partial differential equations,rather than by implementing certainfinite difference upon theflow map,which can significantly improve the accuracy of the numerical solution especially near the FTLE ridges.Second,in the proposed algorithms,all computations are done on thefly,that is,all required partial differential equations are solved forward in time,which is practically more natural.The new algorithms still maintain the optimal computational complexity as well as the second order accuracy.Numerical examples demonstrate the effectiveness of the proposed algorithms.
文摘In this paper the concept of first boundary condition （i）（i = 0, 1, 2,…, n） is proposed based on [1], the existence of two times spline interpolant under first boundary condition is proved using constructivity method and the uniqueness of the two times spline interpolant under first boundary condition（n） is proved too.
文摘We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.
文摘Grain growth kinetics of austenite in a hypoeutectoid steel（containing carbon of 0.35%）at 920 ℃ and in a hypereutectoid steel（containing carbon of 1%）at 980 ℃ for holding time ranging from 1 h to 6 h was investigated.The hypoeutectoid steel exhibited normal grain growth without solute drag hindrance with a time exponent（0.51）close to the theoretical value（0.5）.However,the grain growth of austenite in the hypereutectoid steel held up to 3 h was extremely slow,characterizing by a low value of time exponent（0.08）.Thereafter,a breakaway occurred and the grain growth in the hypereutectoid steel held from 3 h to 6 h progressed normally with a time exponent（0.52）close to the theoretical value（0.5）.
