多组态Dirac-Fock方法与准相对论组态相互作用方法的比较研究

利用多组态Dirac-Fock(MCDF)方法与准相对论组态相互作用方法,分别详细计算了低Z、中Z和高Z原子(离子)各个壳层上电子的束缚能、平均轨道半径、总束缚能、激发能、精细结构能级以及类Ne等电子系列离子的2p53s 1,3P1-2p6 1S0跃迁能,并且对这两种方法的结果进行了数值比较.     

A massively parallel multi-block hybrid compact–WENO scheme for compressible flows

A new multi-block hybrid compact–WENO finite-difference method for the massively parallel computation of compressible flows is presented. In contrast to earlier methods, our approach breaks the global dependence of compact methods by using explicit finite-difference methods at block interfaces and is fully conservative. The resulting method is fifth- and sixth-order accurate for the convective and diffusive fluxes, respectively. The impact of the explicit interface treatment on the stability and accuracy of the multi-block method is quantified for the advection and diffusion equations. Numerical errors increase slightly as the number of blocks is increased. It is also found that the maximum allowable time steps increase with the number of blocks. The method demonstrates excellent scalability on up to 1264 processors.     

A second order virtual node method for elliptic problems with interfaces and irregular domains

We present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities or on irregular domains, handling both cases with the same approach. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes and a Lagrange multiplier approach is used to enforce jump conditions and Dirichlet boundary conditions. Our combination of these two aspects yields a symmetric positive definite discretization. In the general case, we obtain the standard 5-point stencil away from the interface. For the specific case of interface problems with continuous coefficients, we present a discontinuity removal technique that admits use of the standard 5-point finite difference stencil everywhere in the domain. Numerical experiments indicate second order accuracy in L^∞.     

Review of Fluorescence Suppression Techniques in Raman Spectroscopy

Abstract

Raman spectroscopy is an important and powerful technique for analyzing the chemical composition of biological or nonbiological samples in many fields. A serious challenge frequently encountered in Raman measurements arises from the existence of the concurrent fluorescence background. The fluorescence intensity is normally several orders of magnitude larger than the Raman scattering signal, especially in biological samples. Such fluorescence background must be suppressed in order to obtain accurate Raman spectra. Several different techniques have been explored for this purpose. These techniques could be generally grouped into time-domain, frequency-domain, wavelength-domain, and computational methods in addition to various Raman enhancement techniques and other unconventional methods. This review briefly describes the fundamental principles of each group of methods, reports the most recent advances, and makes comparison across those major categories of techniques in terms of cost and performance in a hope to guide interested readers to select proper methods for specific applications.     

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319–338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC–WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.     

Multigrid algorithms for high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations on unstructured meshes. The algorithms are based on coupling both p- and h-multigrid (ph-multigrid) methods which are used in nonlinear or linear forms, and either directly as solvers or as preconditioners to a Newton–Krylov method.The performance of the algorithms are examined in solving the laminar flow over an airfoil configuration. It is shown that the choice of the cycling strategy is crucial in achieving efficient and scalable solvers. For the multigrid solvers, while the order-independent convergence rate is obtained with a proper cycle type, the mesh-independent performance is achieved only if the coarsest problem is solved to a sufficient accuracy. On the other hand, the multigrid preconditioned Newton–GMRES solver appears to be insensitive to this condition and mesh-independent convergence is achieved under the desirable condition that the coarsest problem is solved using a fixed number of multigrid cycles regardless of the size of the problem.It is concluded that the Newton–GMRES solver with the multigrid preconditioning yields the most efficient and robust algorithm among those studied.     

Feynman's approach to quantum mechanics: Trajectories,commutation relations and uncertainty principle

Summary In this paper the meaning of trajectory for a quantum-mechanical particle is discussed, starting from the path integral expression of the propagator. By a direct method the trajectories mostly contributing to the total amplitude are found, but it seems impossible to interpret them as paths in the physical space-time; on the contrary, the position-momentum commutation relations directly follow. Moreover, we show that the Heisenberg uncertaint principle can be obtained from the path integral approach. In order to give a better understanding of the characteristic quantum-mechanical features and of the difference from the classical problems, the diffusion equation for a Brownian particle is considered in the first part of the paper. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

High-order compact finite-difference methods on general overset grids

This work investigates the coupling of a very high-order finite-difference algorithm for the solution of conservation laws on general curvilinear meshes with overset-grid techniques originally developed to address complex geometric configurations. The solver portion of the algorithm is based on Padé-type compact finite-differences of up to sixth-order, with up to 10th-order filters employed to remove spurious waves generated by grid non-uniformities, boundary conditions and flow non-linearities. The overset-grid approach is utilized as both a domain-decomposition paradigm for implementation of the algorithm on massively parallel machines and as a means for handling geometric complexity in the computational domain. Two key features have been implemented in the current work; the ability of the high-order algorithm to accommodate holes cut in grids by the overset-grid approach, and the use of high-order interpolation at non-coincident grid overlaps. Several high-order/high-accuracy interpolation methods were considered, and a high-order, explicit, non-optimized Lagrangian method was found to be the most accurate and robust for this application. Several two-dimensional benchmark problems were examined to validate the interpolation methods and the overall algorithm. These included grid-to-grid interpolation of analytic test functions, the inviscid convection of a vortex, laminar flow over single- and double-cylinder configurations, and the scattering of acoustic waves from one- and three-cylinder configurations. The employment of the overset-grid techniques, coupled with high-order interpolation at overset boundaries, was found to be an effective way of employing the high-order algorithm for more complex geometries than was previously possible.     

A comparison of high-order time integrators for thermal convection in rotating spherical shells

A numerical study of several time integration methods for solving the three-dimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The codes are validated with a known benchmark, and their efficiency is studied. The results show that the use of high-order methods, especially those with time step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.