This paper is concerned with the blow-up solutions of the Gross-Pitaevskii equation. Using the concentration compact principle and the variational characterization of the corresponding ground state, we obtain the limi...This paper is concerned with the blow-up solutions of the Gross-Pitaevskii equation. Using the concentration compact principle and the variational characterization of the corresponding ground state, we obtain the limiting profile of blow-up solutions with critical mass in the corresponding weighted energy space. Moreover, we extend this result to small super-critical mass case by the variational methods and scaling technique.展开更多
To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media, we derived conservation equations using the first-order perturbation approach and assuming stationary fluc...To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media, we derived conservation equations using the first-order perturbation approach and assuming stationary fluctuation fields of velocity and concentration. The concentration variance equation, similar to the mean concentration equation, consists of convection and dispersion terms with the mean water velocity and macrodispersivity. In addition, there is a production term in the concentration variance e-quation. The concentration variance production is quadratically proportional to the mean concentration gradient with a coefficient Qij , defined as the concentration variance productivity , which is the difference between the macrodispersivity Aij and the local dispersivity aij multiplied by a four-rank tensor. The macrodispersivity and the local dispersivity, respectively, result in the creation and dissipation of the concentration variance. The concentration variance is produced if the concentration gradient exists. For t→∞, Qij→0 , which indicates that the creation and dissipation of the concentration variance are balanced at large travel time. We solve the variance equation numerically along with the mean e-quation using Aij, Qij, and the effective solute velocity v . The variance productivity increases with the decrease in transverse local dispersivity and is not sensitive to longitudinal local dispersivity. The maximum concentration variance occurs near the maximum mean concentration gradient.展开更多
We assessed the influence of Yb^3+ and Er34 dopant concentration on the relative spectral distribution, quantum yield (Фuc), and decay kinetics of the upconversion luminescence (UCL) and particle brightness (BUC) for...We assessed the influence of Yb^3+ and Er34 dopant concentration on the relative spectral distribution, quantum yield (Фuc), and decay kinetics of the upconversion luminescence (UCL) and particle brightness (BUC) for similarly sized (33 nm) oleate-capped p-NaYF4:Yb3t,Er^3+ upconversion (UC) nanoparticles (UCNPs) in toluene at broadly varied excitation power densities (F). This included an Yb^3+ series where the Yb^3+ concentration was varied between 11%—21% for a constant Er^3+ concentration of 3%, and an Er^3+ series, where the Er^3+ concentration was varied between 1%-4% for a constant Yb^3+ concentration of 14%. The results were fitted with a coupled rate equation model utilizing the UCL data and decay kinetics of the green and red Er34 emission and the Yb34 luminescence at 980 nm. An increasing Yb34 concentration favors a pronounced triphotonic population of 4F9/2 at high P by an enhanced back energy transfer (BET) from the 4G11/2 level. Simultaneously, the Yb^3+-controlled UCNPs absorption cross section overcompensates for the reduction in Фuc with increasing Yb^3+ concentration at high P, resulting in an increase in Sue. Additionally, our results show that an increase in Yb34 and a decrease in Er^3+ concentration enhance the color tuning range by P. These findings will pave the road to a deeper understanding of the energy transfer processes and their contribution to efficient UCL, as well as still debated trends in green-to-red intensity ratios of UCNPs at different P.展开更多
We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of...We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.展开更多
The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The...The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10771151)Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 2006A068)
文摘This paper is concerned with the blow-up solutions of the Gross-Pitaevskii equation. Using the concentration compact principle and the variational characterization of the corresponding ground state, we obtain the limiting profile of blow-up solutions with critical mass in the corresponding weighted energy space. Moreover, we extend this result to small super-critical mass case by the variational methods and scaling technique.
基金NNSF of China and NSF-EPSCoR of University of Wyoming,USA
文摘To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media, we derived conservation equations using the first-order perturbation approach and assuming stationary fluctuation fields of velocity and concentration. The concentration variance equation, similar to the mean concentration equation, consists of convection and dispersion terms with the mean water velocity and macrodispersivity. In addition, there is a production term in the concentration variance e-quation. The concentration variance production is quadratically proportional to the mean concentration gradient with a coefficient Qij , defined as the concentration variance productivity , which is the difference between the macrodispersivity Aij and the local dispersivity aij multiplied by a four-rank tensor. The macrodispersivity and the local dispersivity, respectively, result in the creation and dissipation of the concentration variance. The concentration variance is produced if the concentration gradient exists. For t→∞, Qij→0 , which indicates that the creation and dissipation of the concentration variance are balanced at large travel time. We solve the variance equation numerically along with the mean e-quation using Aij, Qij, and the effective solute velocity v . The variance productivity increases with the decrease in transverse local dispersivity and is not sensitive to longitudinal local dispersivity. The maximum concentration variance occurs near the maximum mean concentration gradient.
文摘We assessed the influence of Yb^3+ and Er34 dopant concentration on the relative spectral distribution, quantum yield (Фuc), and decay kinetics of the upconversion luminescence (UCL) and particle brightness (BUC) for similarly sized (33 nm) oleate-capped p-NaYF4:Yb3t,Er^3+ upconversion (UC) nanoparticles (UCNPs) in toluene at broadly varied excitation power densities (F). This included an Yb^3+ series where the Yb^3+ concentration was varied between 11%—21% for a constant Er^3+ concentration of 3%, and an Er^3+ series, where the Er^3+ concentration was varied between 1%-4% for a constant Yb^3+ concentration of 14%. The results were fitted with a coupled rate equation model utilizing the UCL data and decay kinetics of the green and red Er34 emission and the Yb34 luminescence at 980 nm. An increasing Yb34 concentration favors a pronounced triphotonic population of 4F9/2 at high P by an enhanced back energy transfer (BET) from the 4G11/2 level. Simultaneously, the Yb^3+-controlled UCNPs absorption cross section overcompensates for the reduction in Фuc with increasing Yb^3+ concentration at high P, resulting in an increase in Sue. Additionally, our results show that an increase in Yb34 and a decrease in Er^3+ concentration enhance the color tuning range by P. These findings will pave the road to a deeper understanding of the energy transfer processes and their contribution to efficient UCL, as well as still debated trends in green-to-red intensity ratios of UCNPs at different P.
基金Supported by CAS-KJCX3-SYW-S03,Grant Fondecyt No. 1050613Scientific Research Fund for Youth of Hubei Provincial Education Department(Q20083401)
文摘We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in R^N . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.
文摘The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.
