This paper is a continuation work of[26]and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow.We assume the initial dens...This paper is a continuation work of[26]and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow.We assume the initial densityρ0=η11Ω0+η21Ω0^c,where(η1,η2)is any pair of positive constants andΩ0 is a bounded,simply connected domain with W^k+2,p(R^2)boundary regularity.We prove that for any positive time t,the density functionρ(t)=η11Ω(t)+η21Ω(t)^c,and the domainΩ(t)preserves the W^k+2,p-boundary regularity.展开更多
Roads are conspicuous components in a river landscape;however,their impacts on river landscape patterns and ecological processes have not been systematically studied at the watershed scale.In this paper,the Lancang Ri...Roads are conspicuous components in a river landscape;however,their impacts on river landscape patterns and ecological processes have not been systematically studied at the watershed scale.In this paper,the Lancang River Valley in Yunnan Province,China was selected as a case to study road lateral disconnection and crossing impacts and identify river-road network interaction.This study was primarily focused on the road impacts on soil erosion intensity and patch density by using GIS analysis at different scales and explored their distribution with terrain factors.The results showed that river density revealed spatial autocorrelation although both of the roads and rivers were distributed unevenly in the valley.The lateral road(road curvature≥1.1)proportion correlated with soil erosion intensity(p 0.01)at the small sub-basin scale.Soil erosion intensity decreased with increasing lateral road buffer width.Light erosion generally accounted for a large proportion of the erosion in the lateral road buffer zones(1.0–4.0 km),while higher class lateral roads imposed greater impacts on soil erosion than lower class roads,which primarily had a moderate erosion level.In addition,the results of road-river intersection density indicated that road crossing impacts were significantly correlated with patch density at the small sub-basin scale.Topography factor(percent of slope>25°in each sub-basin had a close relationship with the ratio of total length of road line with curvature value≥1.1 to the total number of intersections.The correlation(p 0.01)between road impacts and terrain factor revealed that topography affected the road impact distribution in the Lancang River Valley.展开更多
基金MCM for the hospitality and the financial supportsupported by SFB 1060+2 种基金Universitat Bonn during the last part of the workpartially supported by NSF of China under Grants Nos.11371347 and 11688101innovation grant from National Center for Mathematics and Interdisciplinary Sciences
文摘This paper is a continuation work of[26]and studies the propagation of the high-order boundary regularities of the two-dimensional density patch for viscous inhomogeneous incompressible flow.We assume the initial densityρ0=η11Ω0+η21Ω0^c,where(η1,η2)is any pair of positive constants andΩ0 is a bounded,simply connected domain with W^k+2,p(R^2)boundary regularity.We prove that for any positive time t,the density functionρ(t)=η11Ω(t)+η21Ω(t)^c,and the domainΩ(t)preserves the W^k+2,p-boundary regularity.
基金Under the auspices of Nonprofit Environment Protection Specific Project of China(No.201209029-4)National Natural Science Foundation of China(No.50939001)
文摘Roads are conspicuous components in a river landscape;however,their impacts on river landscape patterns and ecological processes have not been systematically studied at the watershed scale.In this paper,the Lancang River Valley in Yunnan Province,China was selected as a case to study road lateral disconnection and crossing impacts and identify river-road network interaction.This study was primarily focused on the road impacts on soil erosion intensity and patch density by using GIS analysis at different scales and explored their distribution with terrain factors.The results showed that river density revealed spatial autocorrelation although both of the roads and rivers were distributed unevenly in the valley.The lateral road(road curvature≥1.1)proportion correlated with soil erosion intensity(p 0.01)at the small sub-basin scale.Soil erosion intensity decreased with increasing lateral road buffer width.Light erosion generally accounted for a large proportion of the erosion in the lateral road buffer zones(1.0–4.0 km),while higher class lateral roads imposed greater impacts on soil erosion than lower class roads,which primarily had a moderate erosion level.In addition,the results of road-river intersection density indicated that road crossing impacts were significantly correlated with patch density at the small sub-basin scale.Topography factor(percent of slope>25°in each sub-basin had a close relationship with the ratio of total length of road line with curvature value≥1.1 to the total number of intersections.The correlation(p 0.01)between road impacts and terrain factor revealed that topography affected the road impact distribution in the Lancang River Valley.
