In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to ...In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect.展开更多
The temperature-dependent Gilbert damping in Co2FeAl thin film grown on a Pb(Mg1/3Nb2/3)O3-30%PbTiO3 substrate is investigated by the systematic measurement of physical property measurement system(PPMS) on a series of...The temperature-dependent Gilbert damping in Co2FeAl thin film grown on a Pb(Mg1/3Nb2/3)O3-30%PbTiO3 substrate is investigated by the systematic measurement of physical property measurement system(PPMS) on a series of samples with different substrate temperatures. Varying the substrate temperatures from 350℃ to 500℃, the B2 ordering degrees of Co2FeAl thin films increase, which can lead the Gilbert damping to decrease, indicated by the field-sweep in-plane PPMS measurements. In addition, the measurement result of PPMS demonstrates that the Gilbert damping decreases first with measurement temperature decreasing down to about 150 K, then increases at a measurement temperature of ~ 50 K, and decreases again with the measurement temperature decreasing. There are two independent damping manners, namely bulk damping and surface damping, which contribute to the Gilbert damping. Moreover, the observed peak of Gilbert damping at ~ 50 K can be attributed to the spin re-orientation transition at the Co2FeAl surface, which is similar to the result of the effective magnetization as a function of measurement temperature. The result presents the evidence for further studying the Gilbert damping in Co2FeAl thin film.展开更多
文摘In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure of the distance between original high order Bézier curve and degree-reduced curve. The other part represents the second derivative of degree-reduced curve. We tackle two kinds of conditions which are position vector constraint and tangent vector constraint respectively. The explicit representations of unknown points are presented. Some examples are illustrated to show the influence of the differential terms to approximation and smoothness effect.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51671099,11974149,and 51901163)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35).
文摘The temperature-dependent Gilbert damping in Co2FeAl thin film grown on a Pb(Mg1/3Nb2/3)O3-30%PbTiO3 substrate is investigated by the systematic measurement of physical property measurement system(PPMS) on a series of samples with different substrate temperatures. Varying the substrate temperatures from 350℃ to 500℃, the B2 ordering degrees of Co2FeAl thin films increase, which can lead the Gilbert damping to decrease, indicated by the field-sweep in-plane PPMS measurements. In addition, the measurement result of PPMS demonstrates that the Gilbert damping decreases first with measurement temperature decreasing down to about 150 K, then increases at a measurement temperature of ~ 50 K, and decreases again with the measurement temperature decreasing. There are two independent damping manners, namely bulk damping and surface damping, which contribute to the Gilbert damping. Moreover, the observed peak of Gilbert damping at ~ 50 K can be attributed to the spin re-orientation transition at the Co2FeAl surface, which is similar to the result of the effective magnetization as a function of measurement temperature. The result presents the evidence for further studying the Gilbert damping in Co2FeAl thin film.
