Studying the topology of infrastructure communication networks(e.g., the Internet) has become a means to understand and develop complex systems. Therefore, investigating the evolution of Internet network topology migh...Studying the topology of infrastructure communication networks(e.g., the Internet) has become a means to understand and develop complex systems. Therefore, investigating the evolution of Internet network topology might elucidate disciplines governing the dynamic process of complex systems. It may also contribute to a more intelligent communication network framework based on its autonomous behavior. In this paper, the Internet Autonomous Systems(ASes) topology from 1998 to 2013 was studied by deconstructing and analysing topological entities on three different scales(i.e., nodes,edges and 3 network components: single-edge component M1, binary component M2 and triangle component M3). The results indicate that: a) 95% of the Internet edges are internal edges(as opposed to external and boundary edges); b) the Internet network consists mainly of internal components, particularly M2 internal components; c) in most cases, a node initially connects with multiple nodes to form an M2 component to take part in the network; d) the Internet network evolves to lower entropy. Furthermore, we find that, as a complex system, the evolution of the Internet exhibits a behavioral series,which is similar to the biological phenomena concerned with the study on metabolism and replication. To the best of our knowledge, this is the first study of the evolution of the Internet network through analysis of dynamic features of its nodes,edges and components, and therefore our study represents an innovative approach to the subject.展开更多
2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization...2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.展开更多
For a discrete system, the idea that the orbit’s topological structure possesses three levels is proposed and the notions of the quasi-weakly almost periodic point and the minimal covering of a topological semi-conju...For a discrete system, the idea that the orbit’s topological structure possesses three levels is proposed and the notions of the quasi-weakly almost periodic point and the minimal covering of a topological semi-conjugacy are introduced. The relationship between the three levels and the recurrence of points and some properties kept under the topological semi-conjugacy is also discussed.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61671142)
文摘Studying the topology of infrastructure communication networks(e.g., the Internet) has become a means to understand and develop complex systems. Therefore, investigating the evolution of Internet network topology might elucidate disciplines governing the dynamic process of complex systems. It may also contribute to a more intelligent communication network framework based on its autonomous behavior. In this paper, the Internet Autonomous Systems(ASes) topology from 1998 to 2013 was studied by deconstructing and analysing topological entities on three different scales(i.e., nodes,edges and 3 network components: single-edge component M1, binary component M2 and triangle component M3). The results indicate that: a) 95% of the Internet edges are internal edges(as opposed to external and boundary edges); b) the Internet network consists mainly of internal components, particularly M2 internal components; c) in most cases, a node initially connects with multiple nodes to form an M2 component to take part in the network; d) the Internet network evolves to lower entropy. Furthermore, we find that, as a complex system, the evolution of the Internet exhibits a behavioral series,which is similar to the biological phenomena concerned with the study on metabolism and replication. To the best of our knowledge, this is the first study of the evolution of the Internet network through analysis of dynamic features of its nodes,edges and components, and therefore our study represents an innovative approach to the subject.
文摘2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.
基金the Foundation of Guangdong Province and the Foundation of Advanced Research Zhongshan University
文摘For a discrete system, the idea that the orbit’s topological structure possesses three levels is proposed and the notions of the quasi-weakly almost periodic point and the minimal covering of a topological semi-conjugacy are introduced. The relationship between the three levels and the recurrence of points and some properties kept under the topological semi-conjugacy is also discussed.
