Living systems are full of astonishing diversity and complexity of life.Despite differences in the length scales and cognitive abilities of these systems,collective motion of large groups of individuals can emerge.It ...Living systems are full of astonishing diversity and complexity of life.Despite differences in the length scales and cognitive abilities of these systems,collective motion of large groups of individuals can emerge.It is of great importance to seek for the fundamental principles of collective motion,such as phase transitions and their natures.Via an eigen microstate approach,we have found a discontinuous transition of density and a continuous transition of velocity in the Vicsek models of collective motion,which are identified by the finite-size scaling form of order-parameter.At strong noise,living systems behave like gas.With the decrease of noise,the interactions between the particles of a living system become stronger and make them come closer.The living system experiences then a discontinuous gas-liquid like transition of density.The even stronger interactions at smaller noise make the velocity directions of the particles become ordered and there is a continuous phase transition of collective motion in addition.展开更多
We propose a renormalization group(RG)theory of eigen microstates,which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations.A microstate in the ensemble...We propose a renormalization group(RG)theory of eigen microstates,which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations.A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues.Under the renormalization of a factor b,the largest eigenvalueσ1 has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relationσb1=bβ/νσ1,whereβandνare the critical exponents of order parameter and correlation length,respectively.With the Ising model in different dimensions,it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class.Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian,which is the foundation of Wilson’s RG theory and is absent for most complex systems.展开更多
The concept of smart city gives an excellent resolution to construct and develop modern cities, and also demands infrastructure construction. How to build a safe, stable, and highly efficient public transportation sys...The concept of smart city gives an excellent resolution to construct and develop modern cities, and also demands infrastructure construction. How to build a safe, stable, and highly efficient public transportation system becomes an important topic in the process of city construction. In this work, we study the structural and robustness properties of transportation networks and their sub-networks. We introduce a complementary network model to study the relevance and complementarity between bus network and subway network. Our numerical results show that the mutual supplement of networks can improve the network robustness. This conclusion provides a theoretical basis for the construction of public traffic networks, and it also supports reasonable operation of managing smart cities.展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities,China(Grant No.2019XD-A10)the National Natural Science Foundation of China(Grant No.71731002)。
文摘Living systems are full of astonishing diversity and complexity of life.Despite differences in the length scales and cognitive abilities of these systems,collective motion of large groups of individuals can emerge.It is of great importance to seek for the fundamental principles of collective motion,such as phase transitions and their natures.Via an eigen microstate approach,we have found a discontinuous transition of density and a continuous transition of velocity in the Vicsek models of collective motion,which are identified by the finite-size scaling form of order-parameter.At strong noise,living systems behave like gas.With the decrease of noise,the interactions between the particles of a living system become stronger and make them come closer.The living system experiences then a discontinuous gas-liquid like transition of density.The even stronger interactions at smaller noise make the velocity directions of the particles become ordered and there is a continuous phase transition of collective motion in addition.
基金supported by the National Natural Science Foundation of China(Grant No.12135003)。
文摘We propose a renormalization group(RG)theory of eigen microstates,which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations.A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues.Under the renormalization of a factor b,the largest eigenvalueσ1 has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relationσb1=bβ/νσ1,whereβandνare the critical exponents of order parameter and correlation length,respectively.With the Ising model in different dimensions,it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class.Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian,which is the foundation of Wilson’s RG theory and is absent for most complex systems.
基金Project supported by the Major Projects of the China National Social Science Fund(Grant No.11&ZD154)
文摘The concept of smart city gives an excellent resolution to construct and develop modern cities, and also demands infrastructure construction. How to build a safe, stable, and highly efficient public transportation system becomes an important topic in the process of city construction. In this work, we study the structural and robustness properties of transportation networks and their sub-networks. We introduce a complementary network model to study the relevance and complementarity between bus network and subway network. Our numerical results show that the mutual supplement of networks can improve the network robustness. This conclusion provides a theoretical basis for the construction of public traffic networks, and it also supports reasonable operation of managing smart cities.
