In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
We discuss the concepts, research methods, and infrastructure of watershed science. A watershed is a basic unit and possesses all of the complexities of the land surface system, thereby making it the best unit for pra...We discuss the concepts, research methods, and infrastructure of watershed science. A watershed is a basic unit and possesses all of the complexities of the land surface system, thereby making it the best unit for practicing Earth system science. Watershed science is an Earth system science practiced on a watershed scale, and it has developed rapidly over the previous two decades. The goal of watershed science is to understand and predict the behavior of complex watershed systems and support the sustainable development of watersheds. However, watershed science confronts the difficulties of understanding complex systems, achieving scale transformation, and simulating the co-evolution of the human-nature system. These difficulties are fundamentally methodological challenges. Therefore, we discuss the research methods of watershed science, which include the self-organized complex system method, the upscaling method dominated by statistical mechanics, Darwinian approaches based on selection and evolutionary principles, hydro-economic and eco-economic methods that emphasize the human-nature system co-evolution, and meta-synthesis for addressing unstructured problems. These approaches together can create a bridge between holism and reductionism and work as a group of operational methods to combine hard and soft integrations and capture all aspects of both natural and human systems. These methods will contribute to the maturation of watershed science and to a methodology that can be used throughout land-surface systems science.展开更多
Power system restoration has attracted more attention and made great progress recently. Research progress of the power system restoration from 2006 to 2016 is reviewed in this paper, including black-start, network rec...Power system restoration has attracted more attention and made great progress recently. Research progress of the power system restoration from 2006 to 2016 is reviewed in this paper, including black-start, network reconfiguration and load restoration. Some emerging methods and key techniques are also discussed in the context of the integration of variable renewable energy and development of the smart grid. There is a long way to go to achieve automatic self-healing in bulk power systems because of its extreme complexity. However, rapidly developing artificial intelligence technology will eventually enable the step-by-step dynamic decision-making based on the situation awareness of supervisory control and data acquisition systems(SCADA) and wide area measurement systems(WAMS) in the near future.展开更多
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
基金supported by Prof.Chen Fahurepresented by this paper was funded by the Major Research Plan of the National Natural Science Foundation of China(Grant Nos.91225302,91425303)the Cross-disciplinary Collaborative Teams Program for Science,Technology,and Innovation of the Chinese Academy of Sciences
文摘We discuss the concepts, research methods, and infrastructure of watershed science. A watershed is a basic unit and possesses all of the complexities of the land surface system, thereby making it the best unit for practicing Earth system science. Watershed science is an Earth system science practiced on a watershed scale, and it has developed rapidly over the previous two decades. The goal of watershed science is to understand and predict the behavior of complex watershed systems and support the sustainable development of watersheds. However, watershed science confronts the difficulties of understanding complex systems, achieving scale transformation, and simulating the co-evolution of the human-nature system. These difficulties are fundamentally methodological challenges. Therefore, we discuss the research methods of watershed science, which include the self-organized complex system method, the upscaling method dominated by statistical mechanics, Darwinian approaches based on selection and evolutionary principles, hydro-economic and eco-economic methods that emphasize the human-nature system co-evolution, and meta-synthesis for addressing unstructured problems. These approaches together can create a bridge between holism and reductionism and work as a group of operational methods to combine hard and soft integrations and capture all aspects of both natural and human systems. These methods will contribute to the maturation of watershed science and to a methodology that can be used throughout land-surface systems science.
基金supported by National Basic Research Program of China(973 Program)(No.2012CB215101)
文摘Power system restoration has attracted more attention and made great progress recently. Research progress of the power system restoration from 2006 to 2016 is reviewed in this paper, including black-start, network reconfiguration and load restoration. Some emerging methods and key techniques are also discussed in the context of the integration of variable renewable energy and development of the smart grid. There is a long way to go to achieve automatic self-healing in bulk power systems because of its extreme complexity. However, rapidly developing artificial intelligence technology will eventually enable the step-by-step dynamic decision-making based on the situation awareness of supervisory control and data acquisition systems(SCADA) and wide area measurement systems(WAMS) in the near future.
