Computer Physics Reports最新文献

Analytic derivative methods have made a great impact in quantum chemistry in recent years,considerably extending the range of chemical systems which can be studied accurately.This review summarises these methods and discusses various computational aspects of their implementation in the context of the CADPAC quantum chemistry program. The discussion covers the analytic evaluation of first and seconds derivatives of SCF energies,as well as those of more accurate correlated techniques. Computational aspects include vectorisation and the influence of memory size.

The complex flow situations that regularly develop in a two-dimensional vortical flow h ave tradionally, indeed almost exclusively, been studied using Eulerian numerical methods, particularly spectral methods. These Eulerian methods have done remarkably well at modelling low to moderate Reynolds number flows.However, at the very high Reynolds numbers typical of geophysical flows, Eulerain methods run into difficulties, not the least of which is sufficient spatial resolutions. On the other hand, Lagrangian methods are and contour dynamics methods, are inherently inviscid. It would appear, therefore, that Lagrangian mehtods ideally suited for the modelling of flows at very high Reynolds numbers. Yet in practice, Lagrangian methods have themselves been limited by the frequent, extraordinary increase in the spatial complexity of inviscid flows. As a consequence, Lagrangian methods have been restricted to relatively simple flows which remain simple. Recently, an extension of contour dynamics, “contour surgery”, has enabled the modelling of complex inviscid flows in wholly Lagrangian terms, This extension overcomes the buildup of small-scale structure by truncating, in physical space, the modelled range of scales. The results of this truncation, or “surgery”, is to make feasible the computation of flows having a range of scales spanning four to five orders of magnitude, or one to two orders of magnitude greater than ever considered by Eulerian-Lagrangian methods. This paper discusses the history of contour dynamis which led to contour surgery, gives details of the contour surgery algorithm for planar, cylindrical, spherical, and quasi-geostrophic flow, presents new results obtained with high-resolutions calculations, including the first every comparison between contour surgery and a traditional pseudo- spectral method, and outlines some outstanding problems facing dynamics/ surgery.

The linear algebraic method (LAM) for the scattering of electrons from atoms and molecules is described with particular emphasis on the techniques used to perform numerical calculations on real systems. We begin with a detailed discussion of scattering from a simple, one-dimensional, non-local potential, move to more complicated multichannel problems, and conclude with some examples. Throughout the discussion we stress the strong interplay between the basic theory and the numerical methods developed by the authors to treat the algebraic equations.

The computational techniques of sensitivity analysis in molecular scattering and inverse scattering problems are discussed. Emphasis is placed on the computation of functional sensitivity densities (functional derivatives) of the dynamical observables with respect to an arbitrary variation in the interaction potential. In the case of quantum mechanics, these sensitivity densities are completely determined by the scattering wave functions. Thus, it is shown that scattering wave functions may be used not only to yield the traditional dynamical observables but also the sensitivity of these observables to detailed features in the interaction potential. In the case of classical dynamical calculations, functional sensitivity analysis requires a solution of an additional set of sensitivity differential equations. These equations may require special treatment due to the singular nature of the trajectory functional sensitivities as well as the high sensitivity associated with long-lived trajectories. The functional sensitivity densities provide a means to extract maximal information from dynamical calculations. Furthermore, the sensitivity densities may be employed to establish an iterative procedure for reconstruction of the fundamental underlying interaction potential from experimentally measured dynamical observables.