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| 1 | Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions显示文摘我们由使用 L 的同等值分解与流入边界条件在一个围住的、一个维的空间领域上学习静止 Wigner 方程。Barletti 和 P. F。Zweifel [运输理论统计员。Phys, 2001, 30 (4-6 ) :507-520 ] 。分解减少一半范围,二点的边界价值问题进二 decoupled 平部分的起始的价值问题和奇怪的部分。没有在零速度附近使用截止近似,我们证明为平部分的起始的价值问题是提出得好的。为奇怪的部分,我们由分析片刻系统在奇怪的 L 2-space 证明解决方案的唯一。一个例子被提供看那怎么使用分析与流入边界条件获得静止 Wigner 方程的答案。 | Ruo LI Tiao LU Zhangpeng SUN | 2017 | Frontiers of Mathematics in China2017，12，4： | 4 |
| 2 | Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport显示文摘A new adaptive cell average spectral element method(SEM)is proposed to solve the time-dependent Wigner equation for transport in quantum devices.The proposed cell average SEM allows adaptive non-uniform meshes in phase spaces to reduce the high-dimensional computational cost of Wigner functions while preserving exactly the mass conservation for the numerical solutions.The key feature of the proposed method is an analytical relation between the cell averages of the Wigner function in the k-space(local electron density for finite range velocity)and the point values of the distribution,resulting in fast transforms between the local electron density and local fluxes of the discretized Wigner equation via the fast sine and cosine transforms.Numerical results with the proposed method are provided to demonstrate its high accuracy,conservation,convergence and a reduction of the cost using adaptive meshes. | Sihong Shao Tiao Lu Wei Cai | 2011 | Communications in Computational Physics2011，9，3： | 2 |
| 3 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-kappa B activity显示文摘 | Tiao M M Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 4 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-kappaB activity显示文摘 | Tiao MM Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 5 | Cross-tolerance of recipientderived transforming growth factor-beta dendritic cells显示文摘 | Tiao MM Lu L Huang LT | 2007 | Transplant Proc2007，39，1： | 1 |
| 6 | Application of recipient derived dendritic cells to induce donor-specific T-cell hyporesponsivehess 显示文摘 | Tiao MM Lu L Tao R etal | 2004 | Transplant Proc2004，36，5： | 1 |
| 7 | Discontinuous Galerkin methods for dispersive and lossy Maxwells equations and PML boundary conditions显示文摘 | Lu Tiao Zhang Pngwen Cai Wei | 2004 | Journal of Computational Physics2004，200，2： | 1 |
| 8 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic ceils deficient in NF-kappaB activity显示文摘 | Tiao MM Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 9 | Application of recipient - derived dendritic cells to induce donor- specific T- cell hyporesponsiveness显示文摘 | Tiao MM Lu L Tao R | 2004 | Transplant Pro2004，36，5： | 1 |
| 10 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-κB activity显示文摘 | Tiao M M Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 11 | 查看详情显示文摘 | Tiao MM Lu L Tao R | | 0，，： | 1 |
| 12 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-kappaB activity显示文摘 | Tiao M M Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 13 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-kappaB activity显示文摘 | TIAO MM LU L TAO R | 2005 | Ann Surg2005，241，3： | 1 |
| 14 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-kappaB activity显示文摘 | Tiao MM Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 15 | Discontinuous Galerkin Time-Domain Method for GPR Simulation in Dispersive Media显示文摘 | LU TIAO CAI WEI ZHANG PING-WEN | 2005 | IEEE Transactions on Geoscience and Remote Sensing2005，43，1： | 1 |
| 16 | Discontinu- ous galerkin time-domain method for GPR simulation in dispersive media显示文摘 | LU Tiao CAI Wei ZHANG Ping-wen | 2005 | IEEE Transactions on Geo science and Remote Sensing2005，43，1： | 1 |
| 17 | Prolongation of cardiac allograft survival by systemic administration of immature recipient dendritic cells deficient in NF-kappaB activity显示文摘 | Tiao MM Lu L Tao R | 2005 | Ann Surg2005，241，3： | 1 |
| 18 | A HYBRID EXPLICIT-IMPLICIT SCHEME FOR THE TIME-DEPENDENT WIGNER EQUATION显示文摘This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value problem.An explicit-implicit time-splitting scheme is used for time integration and the second-order upwind finite difference scheme is used to dis-cretize the advection term.The consistence error and the stability of the full discretization are analyzed.A Fourier spectral method is used to approximate the pseudo-differential operator term and the corresponding error is studied in detail.The final convergence result shows clearly how the regularity of the solution affects the convergence order of the pro-posed scheme.N umerical results are presented for confirming the sharpness of the analysis.The scattering effects of a Gaussian wave packet tunneling through a Gaussian potential barrier are investigated.The evolution of the density function shows that a larger portion of the wave is reflected when the height and the width of the barrier increase.Mathematics subject classification:65M06,65M70. | Haiyan Jiang Tiao Lu Xu Yin | 2021 | Journal of Computational Mathematics2021，39，1： | 0 |
| 19 | Numerical Validation for High Order Hyperbolic Moment System of Wigner Equation显示文摘A globally hyperbolic moment system upto arbitrary order for the Wigner equation was derived in[6].For numerically solving the high order hyperbolic moment system therein,we in this paper develop a preliminary numerical method for this system following the NRxx method recently proposed in[8],to validate the moment system of the Wigner equation.The method developed can keep both mass and momentum conserved,and the variation of the total energy under control though it is not strictly conservative.We systematically study the numerical convergence of the solution to the moment system both in the size of spatial mesh and in the order of the moment expansion,and the convergence of the numerical solution of the moment system to the numerical solution of the Wigner equation using the discrete velocity method.The numerical results indicate that the high order moment system in[6]is a valid model for the Wigner equation,and the proposed numerical method for the moment system is quite promising to carry out the simulation of the Wigner equation. | Ruo Li Tiao Lu Yanli Wang Wenqi Yao | 2014 | Communications in Computational Physics2014，15，3： | 0 |
| 20 | SINGULARITY-FREE NUMERICAL SCHEME FOR THE STATIONARY WIGNER EQUATION显示文摘For the stationary Wigner equation with inflow boundary conditions, the numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the fact that the solution of the stationary Wigner equation is subject to an integral constraint, we prove that the Wigner equation can be written into a form with a bounded operator B[V]. which is equivalent to the operatorA[V]=θ[V]/v in the original Wigner equation under some conditions. Then the discrete operators discretizing B[V] are proved to be uniformly bounded with respect to the mesh size. Basted on the thcoretical findings, a singularity-free numerical incthod is proposed. Numerical results are provided to show our improved numerical scheme performs much better in numerical convergence than the original scheme based on discretizing A[V]. | Tiao Lu Zhangpeng Sun | 2019 | Journal of Computational Mathematics2019，37，2： | 0 |
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