The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the perfo...The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the performance function is given under various kinds of slice methods, even under various shapes of slice partition, beyond the traditional vertical slice method. A simple example shows explicitly the relationship of four commonly used slice methods in the slope reliability analysis. It is also found that the results of the reliability analysis are basically consistent with those of the stability analysis based on Sarma′s method.展开更多
On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict ...On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.展开更多
Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Sc...Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S 〉 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.展开更多
This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (P...This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.展开更多
On-chip microsupercapacitors （MSCs） compatible with on-chip geometries of integrated circuits can be used either as a separate power supply in microelectronic devices or as an energy storage or energy receptor acces...On-chip microsupercapacitors （MSCs） compatible with on-chip geometries of integrated circuits can be used either as a separate power supply in microelectronic devices or as an energy storage or energy receptor accessory unit. In this work, we report the fabrication of flexible two-dimensional Ni（OH）2 nanoplates-based MSCs, which achieved a specific capacitance of 8.80 F/cm^3 at the scan rates of 100 mV/s, losing only 0.20% of its original value after 10,000 charge/discharge cycles. Besides, the MSCs reached an energy density of 0.59 mWh/cm^3 and a power density up to 1.80 W/cm^3, which is comparable to traditional carbon-based devices. The flexible MSCs exhibited good electrochemical stability when subjected to bending at various conditions, illustrating the promising application as electrodes for wearable energy storage.展开更多
Two-dimensional(2D) molybdenum disulfide(MoS2 ) holds significant promise as an energy storage material, whereas the exfoliation of MoS2 into few-layer from natural molybdenites remains a challenge. An efficient elect...Two-dimensional(2D) molybdenum disulfide(MoS2 ) holds significant promise as an energy storage material, whereas the exfoliation of MoS2 into few-layer from natural molybdenites remains a challenge. An efficient electrochemical strategy was proposed for the preparation of fewlayer MoS2 through cationic intercalation. Few-layer MoS2 without the impurity phases was obtained with high yield through Raman mapping analysis, and the intermediate(TBA+)xMoS2x- was captured by in-situ Raman. Note that the charge transport kinetics of the exfoliated few-layer MoS2 was further enhanced by the introduction of graphene, which could efficiently enhance the Na+diffusion mobility, alleviate the volume change of MoS2 and stabilize the reaction products. Commendably, the exfoliated MoS2 /graphene hybrid shows a reversible specific capacity of 642.8 mA h g-1 at 0.1 A g-1, superior rate performance(447.8 and 361.9 mA h g-1 at 1 and 5 A g-1, respectively) and remarkable long-cycle stability with 328.7 mA h g-1 at 1 A g-1 after 1000 cycles for sodium-ion batteries(SIBs). Therefore, this efficient electrochemical exfoliation method can be driven to prepare other few-layer 2D materials for SIBs.展开更多
In this paper, we introduce a multi-material arbitrary Lagrangian and Eulerian method for the hydrodynamic radiative multi-group diffusion model in 2D cylindrical coordinates. The basic idea in the construction of the...In this paper, we introduce a multi-material arbitrary Lagrangian and Eulerian method for the hydrodynamic radiative multi-group diffusion model in 2D cylindrical coordinates. The basic idea in the construction of the method is the following： In the Lagrangian step, a closure model of radiation-hydrodynamics is used to give the states of equations for materials in mixed cells. In the mesh rezoning step, we couple the rezoning principle with the Lagrangian interface tracking method and an Eulerian interface capturing scheme to compute interfaces sharply according to their deformation and to keep cells in good geometric quality. In the interface reconstruction step, a dual-material Moment-of-Fluid method is introduced to obtain the unique interface in mixed ceils. In the remapping step, a conservative remapping algorithm of conserved quantities is presented. A munber of numerical tests are carried out and the numerical results show that the new method can simulate instabilities in complex fluid field under large deformation, and are accurate and robust.展开更多
The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is construc...The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is constructed and investigated. Absolute stability regarding space and time steps of scheme is shown. The convergence statement for the constructed scheme is proved. Rate of convergence is given. Various numerical experiments are carried out and results of some of them are considered in this paper. Comparison of numerical experiments with the results of the theoretical investigation is given too.展开更多
文摘The reliability analysis, based on the reliability index method, of two dimensional slopes is generalized by taking Sarma′s acceleration as the performance function. That is to say, a general expression of the performance function is given under various kinds of slice methods, even under various shapes of slice partition, beyond the traditional vertical slice method. A simple example shows explicitly the relationship of four commonly used slice methods in the slope reliability analysis. It is also found that the results of the reliability analysis are basically consistent with those of the stability analysis based on Sarma′s method.
基金Supported by the National Natural Science Foundation of China(11172205,11372219,51176137)
文摘On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.
基金Supported by the National Natural Science Foundation of China under Grant No. 11175158the Natural Science Foundation ofZhejiang Province of China under Grant No. LY12A04001
文摘Applying the similarity transformation, we construct the exact vortex solutions for topological charge S≥1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrodinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S 〉 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.
基金supported by Shandong Provincial Natural Science Foundation (Grant No. Y2008A19)supported by Research Reward for Excellent Young Scientists from Shandong Province(Grant No. 2007BS01020) +1 种基金supported by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministrysupported by National Natural Science Foundation of China (Grant No. 11071244)
文摘This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （No. 61377033）.
文摘On-chip microsupercapacitors （MSCs） compatible with on-chip geometries of integrated circuits can be used either as a separate power supply in microelectronic devices or as an energy storage or energy receptor accessory unit. In this work, we report the fabrication of flexible two-dimensional Ni（OH）2 nanoplates-based MSCs, which achieved a specific capacitance of 8.80 F/cm^3 at the scan rates of 100 mV/s, losing only 0.20% of its original value after 10,000 charge/discharge cycles. Besides, the MSCs reached an energy density of 0.59 mWh/cm^3 and a power density up to 1.80 W/cm^3, which is comparable to traditional carbon-based devices. The flexible MSCs exhibited good electrochemical stability when subjected to bending at various conditions, illustrating the promising application as electrodes for wearable energy storage.
基金supported by the National Natural Science Foundation of China (51622406, 21673298, and 21473258)the National Key Research and Development Program of China (2017YFB0102000 and 2018YFB0104200)the Project of Innovation Driven Plan in Central South University (2017CX004 and 2018CX005)。
文摘Two-dimensional(2D) molybdenum disulfide(MoS2 ) holds significant promise as an energy storage material, whereas the exfoliation of MoS2 into few-layer from natural molybdenites remains a challenge. An efficient electrochemical strategy was proposed for the preparation of fewlayer MoS2 through cationic intercalation. Few-layer MoS2 without the impurity phases was obtained with high yield through Raman mapping analysis, and the intermediate(TBA+)xMoS2x- was captured by in-situ Raman. Note that the charge transport kinetics of the exfoliated few-layer MoS2 was further enhanced by the introduction of graphene, which could efficiently enhance the Na+diffusion mobility, alleviate the volume change of MoS2 and stabilize the reaction products. Commendably, the exfoliated MoS2 /graphene hybrid shows a reversible specific capacity of 642.8 mA h g-1 at 0.1 A g-1, superior rate performance(447.8 and 361.9 mA h g-1 at 1 and 5 A g-1, respectively) and remarkable long-cycle stability with 328.7 mA h g-1 at 1 A g-1 after 1000 cycles for sodium-ion batteries(SIBs). Therefore, this efficient electrochemical exfoliation method can be driven to prepare other few-layer 2D materials for SIBs.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11371065, 11126134, 11401033, 91130002 and 91330205)the China Academy of Engineering Physics Project (Grant Nos.2012A0202010 and 2015B0202035)+2 种基金the National High Technology Research and Development Program of China (Grant No. 2012AA01A303)the Foundation of Science and Technology Computation Physics Laboratorythe National Hi-Tech Inertial Confinement Fusion Committee of China
文摘In this paper, we introduce a multi-material arbitrary Lagrangian and Eulerian method for the hydrodynamic radiative multi-group diffusion model in 2D cylindrical coordinates. The basic idea in the construction of the method is the following： In the Lagrangian step, a closure model of radiation-hydrodynamics is used to give the states of equations for materials in mixed cells. In the mesh rezoning step, we couple the rezoning principle with the Lagrangian interface tracking method and an Eulerian interface capturing scheme to compute interfaces sharply according to their deformation and to keep cells in good geometric quality. In the interface reconstruction step, a dual-material Moment-of-Fluid method is introduced to obtain the unique interface in mixed ceils. In the remapping step, a conservative remapping algorithm of conserved quantities is presented. A munber of numerical tests are carried out and the numerical results show that the new method can simulate instabilities in complex fluid field under large deformation, and are accurate and robust.
文摘The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is constructed and investigated. Absolute stability regarding space and time steps of scheme is shown. The convergence statement for the constructed scheme is proved. Rate of convergence is given. Various numerical experiments are carried out and results of some of them are considered in this paper. Comparison of numerical experiments with the results of the theoretical investigation is given too.
