The combined effect of periodic water impoundment and seasonal natural flood events has created a 30 m high water-level fluctuation zone(WLFZ) around the Three Gorges Reservoir(TGR), China, forming a unique eco-landsc...The combined effect of periodic water impoundment and seasonal natural flood events has created a 30 m high water-level fluctuation zone(WLFZ) around the Three Gorges Reservoir(TGR), China, forming a unique eco-landscape. Siltation, eutrophication, enrichment of heavy metals, and methane emissions in the WLFZ have been widely associated with sediment and soil particles generated from the upstream catchment or upland slopes. However, little attention has been paid to the complexity of sediment particle-size distributions in the WLFZ. In the present study, core samples(from a 345 cm thick sediment core from the base of the WLFZ), slope transect surface samples(across/up a WLFZ slope), and along-river/longitudinal surface samples(from the reservoir reaches) were collected. Laser granulometry and a volume-based fractal model were used to reveal the characteristics of sediment particle-size distributions. Results indicate that the alternation of coarse and fine particles in the sedimentary core profile is represented as a fluctuation of low and high values of fractal dimension(D), ranging from 2.59 to 2.77. On the WLFZ slope transect, surface sediment particles coarsen with increasing elevation, sand content increases from 3.3% to 78.5%, and D decreases from 2.76 to 2.53. Longitudinally, surface sediments demonstrate a downstream-fining trend, and D increases gradually downstream. D is significantly positively correlated with the fine particle content. We conclude that D is a useful measure for evaluating sediment particle-size distribution.展开更多
Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brown...Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.展开更多
Urban spatial expansion characteristics are the responses of urbanization acts on the geographical space. Analyzing the characteristics can reveal the process of urban expansion and mechanism which is one of useful me...Urban spatial expansion characteristics are the responses of urbanization acts on the geographical space. Analyzing the characteristics can reveal the process of urban expansion and mechanism which is one of useful methods to find out the sustainable land use strategy balancing development and protection. In this paper, two main methods have been deployed in analyzing the spatial expansion characteristics of rapid urbanization region. One is the expansion index method and the other is fractal dimension method. And the results show that town-level urban sprawl has increased in a non-linear way since 1985, and even the increments of the urban expansion intensity are fluctuated. Morphology transformation from scatter to concentration is common phenomenon in the process of urbanization in the towns. From the morphology point of view, downtowns are more homogenous than towns with less variation. The concentration is the leading development trend in downtowns. And the more distance from the downtown is, the more spatial pattern morphology will be observed. These characteristics indicate that macro-scale policies of economic development and land use management have great impacts on the formation and characteristics of spatial patterns of urban dynamic patterns.展开更多
The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower...The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.展开更多
基金funded by the National Natural Science Foundation of China (Grant nos. 41771320, 41771321, and 41571278)the Opening Project of Chongqing Key Laboratory of Earth Surface Processes and Environmental Remote Sensing in the Three Gorges Reservoir Area (Grant no. DBGC201801)the Sichuan Science and Technology Program (Grant no. 2018SZ0132)
文摘The combined effect of periodic water impoundment and seasonal natural flood events has created a 30 m high water-level fluctuation zone(WLFZ) around the Three Gorges Reservoir(TGR), China, forming a unique eco-landscape. Siltation, eutrophication, enrichment of heavy metals, and methane emissions in the WLFZ have been widely associated with sediment and soil particles generated from the upstream catchment or upland slopes. However, little attention has been paid to the complexity of sediment particle-size distributions in the WLFZ. In the present study, core samples(from a 345 cm thick sediment core from the base of the WLFZ), slope transect surface samples(across/up a WLFZ slope), and along-river/longitudinal surface samples(from the reservoir reaches) were collected. Laser granulometry and a volume-based fractal model were used to reveal the characteristics of sediment particle-size distributions. Results indicate that the alternation of coarse and fine particles in the sedimentary core profile is represented as a fluctuation of low and high values of fractal dimension(D), ranging from 2.59 to 2.77. On the WLFZ slope transect, surface sediment particles coarsen with increasing elevation, sand content increases from 3.3% to 78.5%, and D decreases from 2.76 to 2.53. Longitudinally, surface sediments demonstrate a downstream-fining trend, and D increases gradually downstream. D is significantly positively correlated with the fine particle content. We conclude that D is a useful measure for evaluating sediment particle-size distribution.
基金supported by National Natural Science Foundation of China (Grant No.10721091)
文摘Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.
文摘Urban spatial expansion characteristics are the responses of urbanization acts on the geographical space. Analyzing the characteristics can reveal the process of urban expansion and mechanism which is one of useful methods to find out the sustainable land use strategy balancing development and protection. In this paper, two main methods have been deployed in analyzing the spatial expansion characteristics of rapid urbanization region. One is the expansion index method and the other is fractal dimension method. And the results show that town-level urban sprawl has increased in a non-linear way since 1985, and even the increments of the urban expansion intensity are fluctuated. Morphology transformation from scatter to concentration is common phenomenon in the process of urbanization in the towns. From the morphology point of view, downtowns are more homogenous than towns with less variation. The concentration is the leading development trend in downtowns. And the more distance from the downtown is, the more spatial pattern morphology will be observed. These characteristics indicate that macro-scale policies of economic development and land use management have great impacts on the formation and characteristics of spatial patterns of urban dynamic patterns.
基金Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6100663)
文摘The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.
