A novel scale-flee network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving ...A novel scale-flee network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P(d) is 2m^2m1^-3(d-m1 + 1)^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P(k) is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.展开更多
Long waves such as tsunamis can be trapped by islands due to wave refraction,and these trapped waves will cause huge damage even in the sheltered shoreline of the island.That all waves propagating into the topography ...Long waves such as tsunamis can be trapped by islands due to wave refraction,and these trapped waves will cause huge damage even in the sheltered shoreline of the island.That all waves propagating into the topography and finally reaching the coastline are called perfect trapped modes,while any waves escaping from the topography are called leaky modes.Whether these long waves can be trapped is dependent on the depth profile of the island.This paper presents analytic solutions of the ray path for waves propagating into the circular island with power function profiles.Wave height distributions over the island are further investigated based on the principia that crowded rays correspond to large wave height and sparse rays correspond to small wave height.The trapped mechanism for water waves over the island is revealed based on their ray paths.Furthermore,the perfectly trapped criterion is derived,that is,when the slope gradient at the topography toe is greater than twice the ratio of the water depth to the radial distances,all wave rays propagating on the island will finally reach the coastline,and the waves are perfectly trapped.展开更多
Aims It is important to explore the underlying mechanisms that cause triphasic species–area relationship(triphasic SAR)across different scales in order to understand the spatial patterns of biodiversity.Methods Inste...Aims It is important to explore the underlying mechanisms that cause triphasic species–area relationship(triphasic SAR)across different scales in order to understand the spatial patterns of biodiversity.Methods Instead of theory establishment or field data derivation,I adopted a data simulation method that used the power function of SAR to fit log-normal distribution of species abundance.Important Findings The results showed that one-step sampling caused biphasic SAR and n-step sampling could cause 2n-phasic SAR.Practical two-step sampling produced triphasic SAR due to the Preston and Pan effects in large areas.Furthermore,before exploring biological or ecological mechanisms for the nature phenomenon,we should identify or exclude potential mathematical,statistical or sampling reasons.展开更多
Nuclear decay is investigated by the view of network science and the relationship of nuclear decay among different radionuclide can be mapped to a network topology directly.The network includes 1410 nodes and 1275 edg...Nuclear decay is investigated by the view of network science and the relationship of nuclear decay among different radionuclide can be mapped to a network topology directly.The network includes 1410 nodes and 1275 edges.The average degree of the network of nuclear decay is about 1.8,the cumulative degree distribution still meets the typical power-law distribution,and the corresponding exponent is about 4.1.Not considering their dynamic behavior,the fitting parameters of the nuclear decay network are obtained according to the LUHNM theory proposed by our group before.Their cumulated degree distributions of the nuclear decay network match well.The idea and method may provide a new way to study some other problems of nuclear physics.展开更多
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-retu...The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.展开更多
基金Projects(60504027,60573123) supported by the National Natural Science Foundation of ChinaProject(20060401037) supported by the National Postdoctor Science Foundation of ChinaProject(X106866) supported by the Natural Science Foundation of Zhejiang Province,China
文摘A novel scale-flee network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P(d) is 2m^2m1^-3(d-m1 + 1)^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P(k) is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.
基金supported by the National Key Research and Development Program of China(No.2016YFC 1402800)the National Science Fund for Distinguished Young Scholars(No.51425901)+1 种基金the National Natural Science Foundation of China(No.51579090)Innovation Project of Colleges and Universities in Jiangsu Province(No.2015B41814)
文摘Long waves such as tsunamis can be trapped by islands due to wave refraction,and these trapped waves will cause huge damage even in the sheltered shoreline of the island.That all waves propagating into the topography and finally reaching the coastline are called perfect trapped modes,while any waves escaping from the topography are called leaky modes.Whether these long waves can be trapped is dependent on the depth profile of the island.This paper presents analytic solutions of the ray path for waves propagating into the circular island with power function profiles.Wave height distributions over the island are further investigated based on the principia that crowded rays correspond to large wave height and sparse rays correspond to small wave height.The trapped mechanism for water waves over the island is revealed based on their ray paths.Furthermore,the perfectly trapped criterion is derived,that is,when the slope gradient at the topography toe is greater than twice the ratio of the water depth to the radial distances,all wave rays propagating on the island will finally reach the coastline,and the waves are perfectly trapped.
基金The work was supported by the National Key R&D Program of China(2018YFF0214905 and 2016YFC1200802).
文摘Aims It is important to explore the underlying mechanisms that cause triphasic species–area relationship(triphasic SAR)across different scales in order to understand the spatial patterns of biodiversity.Methods Instead of theory establishment or field data derivation,I adopted a data simulation method that used the power function of SAR to fit log-normal distribution of species abundance.Important Findings The results showed that one-step sampling caused biphasic SAR and n-step sampling could cause 2n-phasic SAR.Practical two-step sampling produced triphasic SAR due to the Preston and Pan effects in large areas.Furthermore,before exploring biological or ecological mechanisms for the nature phenomenon,we should identify or exclude potential mathematical,statistical or sampling reasons.
基金Supported by National Natural Science Foundation of China under Grant Nos. 60874087 and 61174151
文摘Nuclear decay is investigated by the view of network science and the relationship of nuclear decay among different radionuclide can be mapped to a network topology directly.The network includes 1410 nodes and 1275 edges.The average degree of the network of nuclear decay is about 1.8,the cumulative degree distribution still meets the typical power-law distribution,and the corresponding exponent is about 4.1.Not considering their dynamic behavior,the fitting parameters of the nuclear decay network are obtained according to the LUHNM theory proposed by our group before.Their cumulated degree distributions of the nuclear decay network match well.The idea and method may provide a new way to study some other problems of nuclear physics.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos.10635020 and 10775057by the Ministry of Education of China under Grant Nos.306022,IRT0624by the Programme of Introducing Talents of Discipline to Universities under Grant No.B08033
文摘The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.