We selected a dark coniferous forest ecosystem of Gongga Mountain in the upper reaches of the Yangtze River as our research area to study the preferential flow and solute preferential transport by adding the tracers K...We selected a dark coniferous forest ecosystem of Gongga Mountain in the upper reaches of the Yangtze River as our research area to study the preferential flow and solute preferential transport by adding the tracers KNO3 and KBr to the self-made soil column equipment in different ways to examine density and volume changes of inflows and outflows of a mass input （impulse input） and a stable, well-distributed input （step input））. The results showed that this dark coniferous forest ecosystem of Gongga Mountain is a typical area of preferential flow and solute preferential transport, a process that can be classified into five parts. A great amount of solute was transported at high speed as the result of preferential flow in the soil and caused the density of the solute in both deep water and in groundwater to rise rapidly, which definitely increased pollution in the deep soil layer.展开更多
The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the ave...The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.展开更多
This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, w...This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.展开更多
基金the financial support provided by the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060022006)National Natural Sciences Foundation of China (Grant No. 30471379)
文摘We selected a dark coniferous forest ecosystem of Gongga Mountain in the upper reaches of the Yangtze River as our research area to study the preferential flow and solute preferential transport by adding the tracers KNO3 and KBr to the self-made soil column equipment in different ways to examine density and volume changes of inflows and outflows of a mass input （impulse input） and a stable, well-distributed input （step input））. The results showed that this dark coniferous forest ecosystem of Gongga Mountain is a typical area of preferential flow and solute preferential transport, a process that can be classified into five parts. A great amount of solute was transported at high speed as the result of preferential flow in the soil and caused the density of the solute in both deep water and in groundwater to rise rapidly, which definitely increased pollution in the deep soil layer.
文摘The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.
文摘This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.
