Even though a large number of large-scale arch dams with height larger than 200 m have been built in the world, the transient groundwater flow behaviors and the seepage control effects in the dam foundations under dif...Even though a large number of large-scale arch dams with height larger than 200 m have been built in the world, the transient groundwater flow behaviors and the seepage control effects in the dam foundations under difficult geological conditions are rarely reported. This paper presents a case study on the transient groundwater flow behaviors in the rock foundation of Jinping I double-curvature arch dam, the world＇s highest dam of this type to date that has been completed. Taking into account the geological settings at the site, an inverse modeling technique utilizing the time series measurements of both hydraulic head and discharge was adopted to back-calculate the permeability of the foundation rocks,which effectively improves the uniqueness and reliability of the inverse modeling results. The transient seepage flow in the dam foundation during the reservoir impounding was then modeled with a parabolic variational inequality（PVI） method. The distribution of pore water pressure, the amount of leakage, and the performance of the seepage control system in the dam foundation during the entire impounding process were finally illustrated with the numerical results.展开更多
By using the nice behavior of the Hawking mass of the slices of a weak solution of inverse mean curvature flow in three-dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow ...By using the nice behavior of the Hawking mass of the slices of a weak solution of inverse mean curvature flow in three-dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean curvature flow in asymptotically hyperbolic manifolds. As an application, we prove that the limit of the Hawking mass of the slices of a weak solution of inverse mean curvature flow with any connected C^(2)-smooth surface as initial data in asymptotically anti-de Sitter-Schwarzschild manifolds with positive mass is greater than or equal to the total mass, which is completely different from the situation in the asymptotically flat case.展开更多
We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smoo...We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smooth,symmetric,strictly increasing and 1-homogeneous function of the principal curvatures of the evolving hypersurfaces.We show that the curvature pinching ratio of the evolving hypersurface is controlled by its initial value,and prove the long time existence and convergence of the flows.No second derivatives conditions are required on F.展开更多
In this paper,we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold.We give C^(0),C^(1),C^(2) estimates of the flow.Using these fac...In this paper,we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold.We give C^(0),C^(1),C^(2) estimates of the flow.Using these facts,we prove that the solution exists for all time and the principal curvatures converge to 1 polynomially fast.展开更多
基金financially supported through NSERC Discovery Grant(RGPIN/4994-2014)
文摘Even though a large number of large-scale arch dams with height larger than 200 m have been built in the world, the transient groundwater flow behaviors and the seepage control effects in the dam foundations under difficult geological conditions are rarely reported. This paper presents a case study on the transient groundwater flow behaviors in the rock foundation of Jinping I double-curvature arch dam, the world＇s highest dam of this type to date that has been completed. Taking into account the geological settings at the site, an inverse modeling technique utilizing the time series measurements of both hydraulic head and discharge was adopted to back-calculate the permeability of the foundation rocks,which effectively improves the uniqueness and reliability of the inverse modeling results. The transient seepage flow in the dam foundation during the reservoir impounding was then modeled with a parabolic variational inequality（PVI） method. The distribution of pore water pressure, the amount of leakage, and the performance of the seepage control system in the dam foundation during the entire impounding process were finally illustrated with the numerical results.
基金supported by National Natural Science Foundation of China(Grant Nos.11671015 and 11731001)。
文摘By using the nice behavior of the Hawking mass of the slices of a weak solution of inverse mean curvature flow in three-dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean curvature flow in asymptotically hyperbolic manifolds. As an application, we prove that the limit of the Hawking mass of the slices of a weak solution of inverse mean curvature flow with any connected C^(2)-smooth surface as initial data in asymptotically anti-de Sitter-Schwarzschild manifolds with positive mass is greater than or equal to the total mass, which is completely different from the situation in the asymptotically flat case.
基金Supported by the National Key R and D Program of China(Grant No.2020YFA0713100)National Natural Science Foundation of China(Grant Nos.11971244 and 11871283)+1 种基金Natural Science Foundation of Tianjin,China(Grant No.19JCQNJC14300)Research(Grant No.KY0010000052)from University of Science and Technology of China。
文摘We consider the inverse curvature flows of smooth,closed and strictly convex rotation hypersurfaces in space forms M_(κ)^(n+1)with speed function given by F^(-α),whereα∈(0,1]forκ=0,-1,α=1 forκ=1 and F is a smooth,symmetric,strictly increasing and 1-homogeneous function of the principal curvatures of the evolving hypersurfaces.We show that the curvature pinching ratio of the evolving hypersurface is controlled by its initial value,and prove the long time existence and convergence of the flows.No second derivatives conditions are required on F.
基金supported by National Natural Science Foundation of China(Grant No.11831005)a collaboration project funded by National Natural Science Foundation of China and the Research Foundation Flanders(Grant No.11961131001)。
文摘In this paper,we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold.We give C^(0),C^(1),C^(2) estimates of the flow.Using these facts,we prove that the solution exists for all time and the principal curvatures converge to 1 polynomially fast.
