Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [ Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multirelaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling.     

2ω1ω激光驱动的类氖锗19.6 nm X光激光

 类氖离子的X光激光理论研究可以为类镍X光激光提供有益启示。设计了一系列瞬态电子碰撞激发类氖锗19.6 nm X光激光的实验,采用2ω1ω泵浦方式,即预脉冲采用倍频钕玻璃激光,主脉冲采用基频,用新开发的瞬态电子碰撞激发类氖锗的系列程序进行了模拟,并与1ω1ω驱动的情况进行了比较。模拟表明, 2ω1ω泵浦方案使类氖锗19.6 nm Ｘ光激光的小信号增益系数增大为1ω1ω方案的1.6倍,增益区也转移到了更高的电子密度区,是获得更短波长X光激光的一种有效方法。     

农民健康需求中的逆向选择效应:来自辽宁省新农合的证据

使用辽宁省统计局2008年"城乡居民医疗保障与健康"调查数据,重点围绕逆向选择效应,考察了农村居民的健康需求和参合意愿影响因素.研究发现,拥有保险者健康状况不佳的概率更高,表明新农合存在明显的逆向选择效应.收入、医疗服务可及性、信息认知程度、教育水平等因素对健康需求具有显著的正向影响.参合行为和参合意愿的影响因素差异较大,努力促使有参合意愿者转变成实际的参与者,提高居民收入和医疗服务可及性是制度改进的关键.     

An Improved Linearity-Preserving Cell-Centered Scheme for Nonlinear Diffusion Problems on General Meshes

In this paper, we suggest a new vertex interpolation algorithm to improve an existing cell-centered finite volume scheme for nonlinear diffusion problems on general meshes. The new vertex interpolation algorithm is derived by applying a special limit procedure to the well-known MPFA-O method. Since the MPFA-O method for 3D cases has been addressed in some studies, the new vertex interpolation algorithm can be extended to 3D cases naturally. More interesting is that the solvability of the corresponding local system is proved under some assumptions. Additionally, we modify the edge flux approximation by an edge-based discretization of diffusion coefficient, and thus the improved scheme is free of the so-called numerical heat-barrier issue suffered by many existing cell-centered or hybrid schemes. The final scheme allows arbitrary continuous or discontinuous diffusion coefficients and can be applicable to arbitrary star-shaped polygonal meshes. A second-order convergence rate for the approximate solution and a first-order accuracy for the flux are observed in numerical experiments. In the comparative experiments with some existing vertex interpolation algorithms, the new algorithm shows obvious improvement on highly distorted meshes.     

UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OF DIVERGENCE TYPE

The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2~(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.     

基于非结构化模糊决策方法的设备采购方案评价

为解决设备采购方案评价中存在的多目标决策问题以及弥补运用层次分析法(AHP法)和多因素价值理论(效用理论)解决此类问题的某些局限性，提出了运用非结构化模糊决策方法(NSFDM)进行设备采购方案评价。在论述了NSFDM的原理和步骤之后，以某项目空调系统采购为例，着重分析了NSFDM在设备采购方案评价中的应用。结果表明：相对于AHP法，NSFDM在建立层次结构模型时同一层次比较因素的数目可以超过9个，且判断矩阵易于通过一致性检验，因而NSFDM是解决设备采购方案评价和其它类似的复杂多目标决策问题的一种有效方法。     

Numerical simulation of a class of fractional subdiffusion equations via the alternating direction implicit method

In this article, a new numerical technique is proposed for solving the two‐dimensional time fractional subdiffusion equation with nonhomogeneous terms. After a transformation of the original problem, standard central difference approximation is used for the spatial discretization. For the time step, a new fractional alternating direction implicit (FADI) scheme based on the L₁ approximation is considered. This FADI scheme is constructed by adding a small term, so it is different from standard FADI methods. The solvability, unconditional stability and H¹ norm convergence are proved. Finally, numerical examples show the effectiveness and accuracy of our proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 531–547, 2016     

Two unconditionally stable and convergent difference schemes with the extrapolation method for the one‐dimensional distributed‐order differential equations

The Grünwald formula is used to solve the one‐dimensional distributed‐order differential equations. Two difference schemes are derived. It is proved that the schemes are unconditionally stable and convergent with the convergence orders and in maximum norm, respectively, where and are step sizes in time, space and distributed order. The extrapolation method is applied to improve the approximate accuracy to the orders and respectively. An illustrative numerical example is given to confirm the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 591–615, 2016     

Antidiffusive Lagrangian‐remap schemes for models of polydisperse sedimentation

One‐dimensional models of gravity‐driven sedimentation of polydisperse suspensions with particles that belong to N size classes give rise to systems of N strongly coupled, nonlinear first‐order conservation laws for the local solids volume fractions. As the eigenvalues and eigenvectors of the flux Jacobian have no closed algebraic form, characteristic‐wise numerical schemes for these models become involved. Alternative simple schemes for this model directly utilize the velocity functions and are based on splitting the system of conservation laws into two different first‐order quasi‐linear systems, which are solved successively for each time iteration, namely, the Lagrangian and remap steps (so‐called Lagrangian‐remap [LR] schemes). This approach was advanced in (Bürger, Chalons, and Villada, SIAM J Sci Comput 35 (2013), B1341–B1368) for a multiclass Lighthill–Whitham‐Richards traffic model with nonnegative velocities. By incorporating recent antidiffusive techniques for transport equations a new version of these Lagrangian‐antidiffusive remap (L‐AR) schemes for the polydisperse sedimentation model is constructed. These L‐AR schemes are supported by a partial analysis for N = 1. They are total variation diminishing under a suitable CFL condition and therefore converge to a weak solution. Numerical examples illustrate that these schemes, including a more accurate version based on MUSCL extrapolation, are competitive in accuracy and efficiency with several existing schemes. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1109–1136, 2016     

Conservative compact finite difference scheme for the coupled Schrödinger–Boussinesq equation

In this article, two conserved compact finite difference schemes for solving the nonlinear coupled Schrödinger–Boussinesq equation are proposed. The conservative property, existence, convergence, and stability of the difference solutions are theoretically analyzed. The numerical results are reported to demonstrate the accuracy and efficiency of the methods and to confirm our theoretical analysis. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1667–1688, 2016