This paper presents a new method for simulating the evolution of a gully head in a loess catchment with cellular automata(CA) based on the Fisher discriminant. The experimental site is an indoor loess catchment that w...This paper presents a new method for simulating the evolution of a gully head in a loess catchment with cellular automata(CA) based on the Fisher discriminant. The experimental site is an indoor loess catchment that was constructed in a fixed-intensity rainfall erosion test facility. Nine high-resolution digital elevation model(DEM) data sets were gathered by close range photogrammetry during different phases of the experiment. To simulate the evolution of the catchment gully head, we assumed the following. First, the 5th and 6th DEM data sets were used as a data source for acquiring the location of the catchment gully head and for obtaining spatial variables with GIS spatial analysis tools. Second, the Fisher discriminant was used to calculate the weight of the spatial variables to determine the transition probabilities. Third, CA model was structured to simulate the evolution of the gully head by iterative looping. The status of the cell in the CA models was dynamically updated at the end of each loop to obtain realistic results. Finally, the nearest neighbor, G-function, K-function, Moran′s I and fractal indexes were used to evaluate the model results. Overall, the CA model can be used to simulate the evolution of a loess gully head. The experiment demonstrated the advantages of the CA model which can simulate the dynamic evolution of gully head evolution in a catchment.展开更多
The mesoscopic modeling developed rapidly in the past three decades is a promising tool for predicting and understanding the microstructure evolution at grain scale.In this paper,the recent development of mesoscopic m...The mesoscopic modeling developed rapidly in the past three decades is a promising tool for predicting and understanding the microstructure evolution at grain scale.In this paper,the recent development of mesoscopic modeling and its application to microstructure evolution in steels is reviewed.Firstly,some representative computational models are briefly introduced,e.g.,the phase field model,the cellular automaton model and the Monte Carlo model.Then,the emphasis is put on the application of mesoscopic modeling of the complex features of microstructure evolution,including solidification,solid-state phase transformation,recrystallization and grain growth.Finally,some issues in the present mesoscopic modeling and its perspective are discussed.展开更多
In this paper,we study a long-range percolation model on the lattice Z d with multi-type vertices and directed edges.Each vertex x ∈ Z d is independently assigned a non-negative weight Wx and a type ψx,where(Wx) x∈...In this paper,we study a long-range percolation model on the lattice Z d with multi-type vertices and directed edges.Each vertex x ∈ Z d is independently assigned a non-negative weight Wx and a type ψx,where(Wx) x∈Z d are i.i.d.random variables,and(ψx) x∈Z d are also i.i.d.Conditionally on weights and types,and given λ,α > 0,the edges are independent and the probability that there is a directed edge from x to y is given by pxy = 1 exp(λφψ x ψ y WxWy /| x-y | α),where φij 's are entries from a type matrix Φ.We show that,when the tail of the distribution of Wx is regularly varying with exponent τ-1,the tails of the out/in-degree distributions are both regularly varying with exponent γ = α(τ-1) /d.We formulate conditions under which there exist critical values λ WCC c ∈(0,∞) and λ SCC c ∈(0,∞) such that an infinite weak component and an infinite strong component emerge,respectively,when λ exceeds them.A phase transition is established for the shortest path lengths of directed and undirected edges in the infinite component at the point γ = 2,where the out/in-degrees switch from having finite to infinite variances.The random graph model studied here features some structures of multi-type vertices and directed edges which appear naturally in many real-world networks,such as the SNS networks and computer communication networks.展开更多
基金National Natural Science Foundation of China(No.41171320,41101349)National Innovation and Entrepreneurship Program(No.201210319025)
文摘This paper presents a new method for simulating the evolution of a gully head in a loess catchment with cellular automata(CA) based on the Fisher discriminant. The experimental site is an indoor loess catchment that was constructed in a fixed-intensity rainfall erosion test facility. Nine high-resolution digital elevation model(DEM) data sets were gathered by close range photogrammetry during different phases of the experiment. To simulate the evolution of the catchment gully head, we assumed the following. First, the 5th and 6th DEM data sets were used as a data source for acquiring the location of the catchment gully head and for obtaining spatial variables with GIS spatial analysis tools. Second, the Fisher discriminant was used to calculate the weight of the spatial variables to determine the transition probabilities. Third, CA model was structured to simulate the evolution of the gully head by iterative looping. The status of the cell in the CA models was dynamically updated at the end of each loop to obtain realistic results. Finally, the nearest neighbor, G-function, K-function, Moran′s I and fractal indexes were used to evaluate the model results. Overall, the CA model can be used to simulate the evolution of a loess gully head. The experiment demonstrated the advantages of the CA model which can simulate the dynamic evolution of gully head evolution in a catchment.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50871109 and 51001096)
文摘The mesoscopic modeling developed rapidly in the past three decades is a promising tool for predicting and understanding the microstructure evolution at grain scale.In this paper,the recent development of mesoscopic modeling and its application to microstructure evolution in steels is reviewed.Firstly,some representative computational models are briefly introduced,e.g.,the phase field model,the cellular automaton model and the Monte Carlo model.Then,the emphasis is put on the application of mesoscopic modeling of the complex features of microstructure evolution,including solidification,solid-state phase transformation,recrystallization and grain growth.Finally,some issues in the present mesoscopic modeling and its perspective are discussed.
文摘In this paper,we study a long-range percolation model on the lattice Z d with multi-type vertices and directed edges.Each vertex x ∈ Z d is independently assigned a non-negative weight Wx and a type ψx,where(Wx) x∈Z d are i.i.d.random variables,and(ψx) x∈Z d are also i.i.d.Conditionally on weights and types,and given λ,α > 0,the edges are independent and the probability that there is a directed edge from x to y is given by pxy = 1 exp(λφψ x ψ y WxWy /| x-y | α),where φij 's are entries from a type matrix Φ.We show that,when the tail of the distribution of Wx is regularly varying with exponent τ-1,the tails of the out/in-degree distributions are both regularly varying with exponent γ = α(τ-1) /d.We formulate conditions under which there exist critical values λ WCC c ∈(0,∞) and λ SCC c ∈(0,∞) such that an infinite weak component and an infinite strong component emerge,respectively,when λ exceeds them.A phase transition is established for the shortest path lengths of directed and undirected edges in the infinite component at the point γ = 2,where the out/in-degrees switch from having finite to infinite variances.The random graph model studied here features some structures of multi-type vertices and directed edges which appear naturally in many real-world networks,such as the SNS networks and computer communication networks.
