The energy crisis has aroused widespread concern, and the reform of energy structure is imminent. In the future,the energy structure will be dominated by the solar energy and other renewable energy sources. The solar ...The energy crisis has aroused widespread concern, and the reform of energy structure is imminent. In the future,the energy structure will be dominated by the solar energy and other renewable energy sources. The solar concentrating technology as a promising method has been widely studied for collecting solar energy. However, the previous solar concentrating technologies suffer from some drawbacks, such as low focusing efficiency and large concentrating size. The Luneburg lens with highly efficient aberration-free focusing provides a new route for solar/energy concentrator. In this work, we designed a plane focal surface Luneburg lens(PFSLL) by transformation optics(TO). The PFSLL provides a relatively high focusing efficiency and concentration ratio of collection of energy. At the same time, it circumvents the disadvantage of curve surface of the classical Luneburg lens in device integration. Based on the reciprocity of electromagnetic waves, the PFSLL can also be applied to the antenna field to achieve broadband wide-angle scanning and highly directional radiation.展开更多
In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space.It is a generalization of the previous results of regular spacelike curves,since singula...In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space.It is a generalization of the previous results of regular spacelike curves,since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike components.Meanwhile,we show a new geometric invariant to characterise singularities of the focal surface.Then,the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.展开更多
We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that ...We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the...展开更多
基金Project supported by the National Key Research and Development Program of China (Grant No. 2020YFA0710100)the National Natural Science Foundation of China (Grant Nos. 92050102 and 11874311)+1 种基金the Shenzhen Science and Technology Program (Grant No. JCYJ20210324121610028)the Fundamental Research Funds for the Central Universities (Grant Nos. 20720220033 and 20720200074)。
文摘The energy crisis has aroused widespread concern, and the reform of energy structure is imminent. In the future,the energy structure will be dominated by the solar energy and other renewable energy sources. The solar concentrating technology as a promising method has been widely studied for collecting solar energy. However, the previous solar concentrating technologies suffer from some drawbacks, such as low focusing efficiency and large concentrating size. The Luneburg lens with highly efficient aberration-free focusing provides a new route for solar/energy concentrator. In this work, we designed a plane focal surface Luneburg lens(PFSLL) by transformation optics(TO). The PFSLL provides a relatively high focusing efficiency and concentration ratio of collection of energy. At the same time, it circumvents the disadvantage of curve surface of the classical Luneburg lens in device integration. Based on the reciprocity of electromagnetic waves, the PFSLL can also be applied to the antenna field to achieve broadband wide-angle scanning and highly directional radiation.
基金Supported by National Natural Science Foundation of China(Grant No.11671070)。
文摘In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space.It is a generalization of the previous results of regular spacelike curves,since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike components.Meanwhile,we show a new geometric invariant to characterise singularities of the focal surface.Then,the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.
基金Specialized Research Fund for the Doctoral Program of Higher Education (No.20050141011)
文摘We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the...