This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉...This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator.展开更多
A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and...A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and noncircular slip surfaces associated with their minimum safety factors.The slope safety factors of circular and noncircular critical slip surfaces were calculated by the simplified Bishop method and an improved Morgenstern-Price method which can be conveniently programmed,respectively.Comparisons with other methods were made which indicate the high efficiency and accuracy of the HGA approach.The HGA approach was used to calculate one case example and the results demonstrated its applicability to practical engineering.展开更多
设图 G 是简单连通图,从 Vizing 定理可知:Δ(G)≤x′(G)≤Δ(G)+1,其中Δ(G)表示图 G 的最大顶点次,x(G)是图 G 的边色数.若 x′(G)=Δ(G),则称 G 为第一类图,并简记为 G∈C^1;否则称 G 为第二类图并简记为 G∈C^2;本文的目的在于讨论...设图 G 是简单连通图,从 Vizing 定理可知:Δ(G)≤x′(G)≤Δ(G)+1,其中Δ(G)表示图 G 的最大顶点次,x(G)是图 G 的边色数.若 x′(G)=Δ(G),则称 G 为第一类图,并简记为 G∈C^1;否则称 G 为第二类图并简记为 G∈C^2;本文的目的在于讨论边色数分类问题.展开更多
Water plays a crucial role in the melting of Earth's mantle. Mantle magmatisms mostly occur at plate boundaries(including subduction zones and mid-ocean ridges) and in some intraplate regions with thermal anomaly....Water plays a crucial role in the melting of Earth's mantle. Mantle magmatisms mostly occur at plate boundaries(including subduction zones and mid-ocean ridges) and in some intraplate regions with thermal anomaly. At oceanic subduction zones, water released by the subducted slab may induce melting of the overlying mantle wedge or even the slab itself, giving rise to arc magmatism, or may evolve into a supercritical fluid. The physicochemical conditions for the formation of slab melt and supercritical fluid are still under debate. At mid-ocean ridges and intraplate hot zones, water and CO_2 cause melting of the upwelling mantle to occur at greater depths and in greater extents. Low degree melting of the mantle may occur at boundaries between Earth's internal spheres, including the lithosphere-asthenosphere boundary(LAB), the upper mantletransition zone boundary, and the transition zone-lower mantle boundary, usually attributed to contrasting water storage capacity across the boundary. The origin for the stimulating effect of water on melting lies in that water as an incompatible component has a strong tendency to be enriched in the melt(i.e., with a mineral-melt partition coefficient much smaller than unity), thereby lowering the Gibbs free energy of the melt. The partitioning of water between melt and mantle minerals such as olivine, pyroxenes and garnet has been investigated extensively, but the effects of hydration on the density and transport properties of silicate melts require further assessments by experimental and computational approaches.展开更多
Experimental research has long shown that forced-convective heat transfer in wall-bounded turbulent flows of fluids in the supercritical thermodynamic state is not accurately predicted by correlations that have been d...Experimental research has long shown that forced-convective heat transfer in wall-bounded turbulent flows of fluids in the supercritical thermodynamic state is not accurately predicted by correlations that have been developed for single-phase fluids in the subcritical thermodynamic state. In the present computational study, the statistical properties of turbulent flow as well as the development of coherent flow structures in a zero-pressuregradient flat-plate boundary layer are investigated in the absence of body forces, where the working fluid is in the supercritical thermodynamic state. The simulated boundary layers are developed to a friction Reynolds number of 250 for two heat-flux to mass-flux ratios corresponding to cases where normal heat transfer and improved heat transfer are observed. In the case where improved heat transfer is observed, spanwise spacing of the near-wall coherent flow structures is reduced due to a relatively less stable flow environment resulting from the lower magnitudes of the wall-normal viscosity-gradient profile.展开更多
In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical noz...In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical nozzle. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.展开更多
This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nire...This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.展开更多
In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the ...In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.展开更多
The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number,initial c...The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number,initial condition,intersection angle,length of the wedge edges,and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow,then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow,the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°,a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow,although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability,the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment,providing a possible explanation for the hysteresis phenomenon in the experiment.展开更多
基金Supported by the National Natural Science Foundation of China（10171032） Supported by the Guangdong Provincial Natural Science Foundation of China（011606）
文摘This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator.
基金Project(50878082)supported by the National Natural Science Foundation of ChinaProject(2012C21058)supported by the Public Welfare Technology Application Research of Zhejiang Province,China
文摘A local improvement procedure based on tabu search(TS) was incorporated into a basic genetic algorithm(GA) and a global optimal algorithm,i.e.,hybrid genetic algorithm(HGA) approach was used to search the circular and noncircular slip surfaces associated with their minimum safety factors.The slope safety factors of circular and noncircular critical slip surfaces were calculated by the simplified Bishop method and an improved Morgenstern-Price method which can be conveniently programmed,respectively.Comparisons with other methods were made which indicate the high efficiency and accuracy of the HGA approach.The HGA approach was used to calculate one case example and the results demonstrated its applicability to practical engineering.
文摘设图 G 是简单连通图,从 Vizing 定理可知:Δ(G)≤x′(G)≤Δ(G)+1,其中Δ(G)表示图 G 的最大顶点次,x(G)是图 G 的边色数.若 x′(G)=Δ(G),则称 G 为第一类图,并简记为 G∈C^1;否则称 G 为第二类图并简记为 G∈C^2;本文的目的在于讨论边色数分类问题.
基金supported by the National Natural Science Foundation of China(Grant Nos.41590622&41473058)the 111 Project of Ministry of Education,China+1 种基金the Fundamental Research Funds for the Central Universities of Chinathe Recruitment Program of Global Experts(Thousand Talents),China
文摘Water plays a crucial role in the melting of Earth's mantle. Mantle magmatisms mostly occur at plate boundaries(including subduction zones and mid-ocean ridges) and in some intraplate regions with thermal anomaly. At oceanic subduction zones, water released by the subducted slab may induce melting of the overlying mantle wedge or even the slab itself, giving rise to arc magmatism, or may evolve into a supercritical fluid. The physicochemical conditions for the formation of slab melt and supercritical fluid are still under debate. At mid-ocean ridges and intraplate hot zones, water and CO_2 cause melting of the upwelling mantle to occur at greater depths and in greater extents. Low degree melting of the mantle may occur at boundaries between Earth's internal spheres, including the lithosphere-asthenosphere boundary(LAB), the upper mantletransition zone boundary, and the transition zone-lower mantle boundary, usually attributed to contrasting water storage capacity across the boundary. The origin for the stimulating effect of water on melting lies in that water as an incompatible component has a strong tendency to be enriched in the melt(i.e., with a mineral-melt partition coefficient much smaller than unity), thereby lowering the Gibbs free energy of the melt. The partitioning of water between melt and mantle minerals such as olivine, pyroxenes and garnet has been investigated extensively, but the effects of hydration on the density and transport properties of silicate melts require further assessments by experimental and computational approaches.
基金Funding by the Government of Ontario and Atomic Energy of Canada Limited (AECL)
文摘Experimental research has long shown that forced-convective heat transfer in wall-bounded turbulent flows of fluids in the supercritical thermodynamic state is not accurately predicted by correlations that have been developed for single-phase fluids in the subcritical thermodynamic state. In the present computational study, the statistical properties of turbulent flow as well as the development of coherent flow structures in a zero-pressuregradient flat-plate boundary layer are investigated in the absence of body forces, where the working fluid is in the supercritical thermodynamic state. The simulated boundary layers are developed to a friction Reynolds number of 250 for two heat-flux to mass-flux ratios corresponding to cases where normal heat transfer and improved heat transfer are observed. In the case where improved heat transfer is observed, spanwise spacing of the near-wall coherent flow structures is reduced due to a relatively less stable flow environment resulting from the lower magnitudes of the wall-normal viscosity-gradient profile.
文摘In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical nozzle. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.
文摘This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.
基金supported by the National Natural Science Foundation of China(Grant No. 10972116)
文摘In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.
基金supported by the National Basic Research Program (973) of China (No. 2006CB705400)the National Natural Science Foundation of China (Nos. 10602051 and 50735004)
文摘The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number,initial condition,intersection angle,length of the wedge edges,and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow,then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow,the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°,a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow,although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability,the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment,providing a possible explanation for the hysteresis phenomenon in the experiment.
