Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. The...Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. These opposite signed layers, formed by shock induced baroclinic deposition of vorticity, "ind" and are strongly affected by secondary reflected shocks and vortex interactions. In our visiometric mode of working, we quantify several of these processes and introduce time epochs to discuss the emerging phenomena and normalizations to scale (collapse) the data at M =1.5 and 2.0. This versatile configuration, easily obtained in the laboratory, allows us to study the formation, evolution and reacceleration of VPs and stratified turbulence and mixing.展开更多
In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the inhomogeneous Schrdinger flow for maps from a compact Riemannian manifold M with dim(M)≤3 into a compact Khler mani...In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the inhomogeneous Schrdinger flow for maps from a compact Riemannian manifold M with dim(M)≤3 into a compact Khler manifold(N, J)with nonpositive Riemannian sectional curvature展开更多
Results concerning existence, uniqueness and local regularity of Inhomogeneous Schrodinger flow from TR^d into S2, are presented by using the difference method,where TR^d=R^d/（R.Z）^d.
Stabilizing the interface wave of the molten aluminum(metal)-electrolyte(bath)is beneficial to shorten the anode-cathode distance(ACD)which is critical to the energy saving.A coupled mathematical model was developed t...Stabilizing the interface wave of the molten aluminum(metal)-electrolyte(bath)is beneficial to shorten the anode-cathode distance(ACD)which is critical to the energy saving.A coupled mathematical model was developed to study the impact of the novel cathode protrusion on the molten fluid motion as well as the metal-bath interface deformation.The molten fluid motion in the aluminum reduction ceils is under the combined effect of the electro-magnetic forces(EMFs)and the gas bubbles generated at the anode.A transient inhomogeneous three-phase model(metal-bath-gas bubble)was established in order to calculate more accurate.The results indicate that the metal-bath interface deformation can be reduced significantly by the novel cathode protrusion which is beneficial to the electric energy saving.Besides,The EMFs decreases as a result of the optimizing of the magnetic field due to the novel cathode convex which is an important driving force for the deformation of the interface.In addition,large vortex in the metal flow field is break up into the small vortex by the cathode protrusion and then dissipated due to the viscous force and the hindering effect of the cathode protrusion.The quantity of the vortex as well as the strength of the vortex reduces significantly in the reduction cell with novel cathode protrusion.展开更多
文摘Vortex double layers (VDLs) and vortex projectiles (VPs) are the essential coherent structures which emerge in the shock excited (s/f/s) planar parallel "curtain" simulations of a 2D shock tube with PPM. These opposite signed layers, formed by shock induced baroclinic deposition of vorticity, "ind" and are strongly affected by secondary reflected shocks and vortex interactions. In our visiometric mode of working, we quantify several of these processes and introduce time epochs to discuss the emerging phenomena and normalizations to scale (collapse) the data at M =1.5 and 2.0. This versatile configuration, easily obtained in the laboratory, allows us to study the formation, evolution and reacceleration of VPs and stratified turbulence and mixing.
基金Partially Supported by National University of Singapore Academic Research Fund Grant RP3982718the Natural Science Foundation of China: 19701034 (the third author)
文摘In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the inhomogeneous Schrdinger flow for maps from a compact Riemannian manifold M with dim(M)≤3 into a compact Khler manifold(N, J)with nonpositive Riemannian sectional curvature
文摘Results concerning existence, uniqueness and local regularity of Inhomogeneous Schrodinger flow from TR^d into S2, are presented by using the difference method,where TR^d=R^d/（R.Z）^d.
基金Item Sponsored by the National Natural Science Foundation of China[NO.50934005 and NO.50904014]
文摘Stabilizing the interface wave of the molten aluminum(metal)-electrolyte(bath)is beneficial to shorten the anode-cathode distance(ACD)which is critical to the energy saving.A coupled mathematical model was developed to study the impact of the novel cathode protrusion on the molten fluid motion as well as the metal-bath interface deformation.The molten fluid motion in the aluminum reduction ceils is under the combined effect of the electro-magnetic forces(EMFs)and the gas bubbles generated at the anode.A transient inhomogeneous three-phase model(metal-bath-gas bubble)was established in order to calculate more accurate.The results indicate that the metal-bath interface deformation can be reduced significantly by the novel cathode protrusion which is beneficial to the electric energy saving.Besides,The EMFs decreases as a result of the optimizing of the magnetic field due to the novel cathode convex which is an important driving force for the deformation of the interface.In addition,large vortex in the metal flow field is break up into the small vortex by the cathode protrusion and then dissipated due to the viscous force and the hindering effect of the cathode protrusion.The quantity of the vortex as well as the strength of the vortex reduces significantly in the reduction cell with novel cathode protrusion.
