回归法与作图法求解实验方程之比较

以测约利弹簧秤劲度系数为例对回归法与作图法求解实验方程作了比较，并建议在高校实验教学中推广用回归法处理数据。     

The connection between general observers and Lanczos potential

We present some algorithms to find the explicit form of the Lanczos potential in an arbitrary geometry.     

经验正交函数与广义数值环境模式重构声速剖面的比较

本文利用Argo资料对经验正交函数(EOF)和GDEM模式拟合声速剖面的效果进行了比较。结果表明,两种方法都能较好地重构局地声速剖面。EOF方法的拟合精度与选取的EOF阶数有关,阶数越高,精度越高;GDEM模式的拟合精度介于EOF的前5阶到前10阶之间。EOF易受到样本数量和采样深度的限制,难以提供完整的声速剖面;而GDEM模式能够将剖面扩展到更深的深度,与仅有上层海洋采样数据的声速剖面相比,结合深海水团的信息可使拟合结果达到更高的精度。     

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 comparison between analytic and numerical methods for modelling automotive dissipative silencers with mean flow

Identifying an appropriate method for modelling automotive dissipative silencers normally requires one to choose between analytic and numerical methods. It is common in the literature to justify the choice of an analytic method based on the assumption that equivalent numerical techniques are more computationally expensive. The validity of this assumption is investigated here, and the relative speed and accuracy of two analytic methods are compared to two numerical methods for a uniform dissipative silencer that contains a bulk reacting porous material separated from a mean gas flow by a perforated pipe. The numerical methods are developed here with a view to speeding up transmission loss computation, and are based on a mode matching scheme and a hybrid finite element method. The results presented demonstrate excellent agreement between the analytic and numerical models provided a sufficient number of propagating acoustic modes are retained. However, the numerical mode matching method is shown to be the fastest method, significantly outperforming an equivalent analytic technique. Moreover, the hybrid finite element method is demonstrated to be as fast as the analytic technique. Accordingly, both numerical techniques deliver fast and accurate predictions and are capable of outperforming equivalent analytic methods for automotive dissipative silencers.     

Fitting models to correlated data III: A comparison between residual analysis and other methods

Applications of the χ² test, the F test, the Durbin-Watson d test, and the f (or Sign) test, to examples of correlated data treatment, show important drawbacks with the d test and (apparently) with the f test. An analytical approach based on residual analysis suggests an improvement in their use that leads to better results at lowest order; it also points out a distinction between goodness-of-fit tests, as the f test, and goodness-of-modeling tests, as the χ² and F tests. The residual analysis method is applied to the same examples; it looks faster, simpler, and often more accurate than the classical ones.     

A Lanczos Potential for Plane Gravitational Waves

We exhibit explicitly a Lanczos generator for the conformal tensor associated with plane gravitational waves.     

A comparison study between the saturation-recovery-T1 and CASL MRI methods for quantitative CBF imaging

The saturation-recovery (SR)-T₁ MRI method for quantitatively imaging cerebral blood flow (CBF) change (ΔCBF) concurrently with the blood oxygenation level dependence (BOLD) alteration has been recently developed and validated by simultaneous measurement of relative CBF change using laser Doppler flowmetry (LDF) in rats at 9.4T. In this study, ΔCBF induced by mildly transient hypercapnia and measured by the SR-T₁ MRI method was rigorously compared with an established perfusion MRI method—continuous arterial spin labeling (CASL) approach in normal and preclinical middle cerebral artery occlusion (MCAo) rat models. The results show an excellent agreement between ΔCBF values measured with these two imaging methods. Moreover, the intrinsic longitudinal relaxation rate (R₁^int) was experimentally determined in vivo in normal rat brains at 9.4T by comparing two independent measures of the apparent longitudinal relaxation rate (R₁^app) and CBF measured by the CSAL approach across a wide range of perfusion. In turn, the R₁^int constant can be employed to calculate the CBF value based on the R₁^app measurement in healthy brain. This comparison study validates the fundamental relationship for linking brain tissue water R₁^app and cerebral perfusion, demonstrates the feasibility of imaging and quantifying both CBF and its change using the SR-T₁ MRI method in vivo.     

Higher-order quadrature-based moment methods for kinetic equations

Kinetic equations containing terms for spatial transport, body forces, and particle–particle collisions occur in many applications (e.g., rarefied gases, dilute granular gases, fluid-particle flows). The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. A useful alternative is to reformulate the problem in terms of the moments of the velocity distribution function. Closure of the moment equations is challenging for flows sufficiently far away from the Maxwellian limit. In previous work, a quadrature-based third-order moment closure was derived for approximating solutions to the kinetic equation for arbitrary Knudsen number. A key component of quadrature-based closures is the moment-inversion algorithm used to find the non-negative weights and velocity abscissas. Here, a robust inversion procedure is proposed for three-component velocity moments up to ninth order. By reconstructing the velocity distribution function, the spatial fluxes in the moment equations are treated using a kinetic-based finite-volume solver. Because the quadrature-based moment method employs the moment transport equations directly instead of a discretized form of the kinetic equation, the mass, momentum and energy are conserved for arbitrary Knudsen and Mach numbers. The computational algorithm is tested for the Riemann shock problem and, for increasing Knudsen numbers (i.e. larger deviations from the Maxwellian limit), the accuracy of the moment closure is shown to be determined by the discrete representation of the spatial fluxes.     

Dynamic formulation of the moment and the recursion methods

The dynamic equations at the basis of the recursion method and of the moment method are discussed using the projection techniques borrowed from statistical mechanics. A local orbital is regarded as the system of interest and the rest of the crystal takes the place of a highly non-Markovian reservoir. A rewarding aspect of the formalism is an improved relation between the chain parameters of the recursion method and the moments. It is speculated that the concepts of random forces and their dynamics could be of help in determining the asymptotic behaviour of the chain variables.     

Lanczos Spintensor and GHP Formalism

This work shows how the equations which relate the Lanczos potential K _ijr to the conformal tensor C _abpq, can be structured in a simple form when written in terms of the formalism proposed by Geroch-Held-Penrose. As working examples, we present the immediate construction of K _ijk for any spacetime with Petrov type O, N or III. Our findings are in good agreement with already published results, which indicates a relationship between the spin coefficients and the Lanczos spintensor onto the canonical tetrad.     

On the relation between the connected-moments expansion and the Lanczos variational scheme

Summary The recently introduced Connected-Moments Expansion (CMX) is compared to a variational Lanczos scheme for estimating ground-state energies of many-body systems. A systematic approach is given for three quantum-mechanical systems: harmonic oscillator, anharmonic oscillator and the Kondo model. A second-order analysis is given in terms of particular ratios of moments of the Hamiltonian.     

A direct comparison between volume and surface tracking methods with a boundary-fitted coordinate transformation and third-order upwinding

A Volume Tracking (VT) and a Front Tracking (FT) algorithm are implemented and compared for locating the interface between two immiscible, incompressible, Newtonian fluids in a tube with a periodically varying, circular cross-section. Initially, the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube (core fluid) and the other one surrounds it (annular fluid). A constant pressure gradient sets them in motion. With both VT and FT, a boundary-fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry. The surface tension force is approximated using the continuous surface force method. All terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one-sided forward finite differences in time. In each time step, the incompressibility condition is enforced by a transformed Poisson equation, which is linear in pressure. This equation is solved by either direct LU decomposition or a Multigrid iterative solver. When the two fluids have the same density, the former method is about 3.5 times faster, but when they do not, the Multigrid solver is as much as 10 times faster than the LU decomposition. When the interface does not break and the Reynolds number remains small, the accuracy and rates of convergence of VT and FT are comparable. The well-known failure of centered finite differences arises as the Reynolds number increases and leads to non-physical oscillations in the interface and failure of both methods to converge with mesh refinement. These problems are resolved and computations with Reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third-order upwind differences using Lagrangian Polynomials. When the volume of the core fluid or the Weber number decrease, increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid, the FT method converges faster with mesh refinement than the VT method and upwinding may be required. Finally, examining the generation of spurious currents around a stationary “bubble” in the tube for Ohnesorge numbers between 0.1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when VT is applied, whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when FT is applied.     

A direct comparison between volume and surface tracking methods with a boundary-fitted coordinate transformation and third-order upwinding

A Volume Tracking (VT) and a Front Tracking (FT) algorithm are implemented and compared for locating the interface between two immiscible, incompressible, Newtonian fluids in a tube with a periodically varying, circular cross-section. Initially, the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube (core fluid) and the other one surrounds it (annular fluid). A constant pressure gradient sets them in motion. With both VT and FT, a boundary-fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry. The surface tension force is approximated using the continuous surface force method. All terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one-sided forward finite differences in time. In each time step, the incompressibility condition is enforced by a transformed Poisson equation, which is linear in pressure. This equation is solved by either direct LU decomposition or a Multigrid iterative solver. When the two fluids have the same density, the former method is about 3.5 times faster, but when they do not, the Multigrid solver is as much as 10 times faster than the LU decomposition. When the interface does not break and the Reynolds number remains small, the accuracy and rates of convergence of VT and FT are comparable. The well-known failure of centered finite differences arises as the Reynolds number increases and leads to non-physical oscillations in the interface and failure of both methods to converge with mesh refinement. These problems are resolved and computations with Reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third-order upwind differences using Lagrangian Polynomials. When the volume of the core fluid or the Weber number decrease, increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid, the FT method converges faster with mesh refinement than the VT method and upwinding may be required. Finally, examining the generation of spurious currents around a stationary “bubble” in the tube for Ohnesorge numbers between 0.1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when VT is applied, whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when FT is applied.     

Realizable high-order finite-volume schemes for quadrature-based moment methods

Dilute gas–particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle–particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently, a quadrature-based moment method was derived for approximating solutions to kinetic equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from the moments. The moment-inversion algorithm does not work if the moments are non-realizable, which might lead to negative weights. It has been recently shown [14] that realizability is guaranteed only with the 1st-order finite-volume scheme that has an inherent problem of excessive numerical diffusion. The use of high-order finite-volume schemes may lead to non-realizable moments. In the present work, realizability of the finite-volume schemes in both space and time is discussed for the 1st time. A generalized idea for developing realizable high-order finite-volume schemes for quadrature-based moment methods is presented. These finite-volume schemes give remarkable improvement in the solutions for a certain class of problems. It is also shown that the standard Runge–Kutta time-integration schemes do not guarantee realizability. However, realizability can be guaranteed if strong stability-preserving (SSP) Runge–Kutta schemes are used. Numerical results are presented on both Cartesian and triangular meshes.     

原子结构的几种处理方法及其比较

主要论述了处理原子结构问题中常见的几种处理方法,着重论述了全实加关联的理论方法,对这几种方法进行了比较,并总结出它们在处理原子结构问题中的优点和缺陷.