On a class of preconditioners for solving the Helmholtz equation

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called “shifted Laplace” preconditioners of the form Δφ−k²φ with . Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR.     

Mean curvature flows and isotopy of maps between spheres

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area‐decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc.     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

Vibrational spectrum of uridine obtained by means of nonresonant-background-free CARS spectroscopy

Received: 18 June 1996/Revised version: 3 January 1997     

一种漂移室定位子性能反常现象的研究

研究了一种漂移室定位子性能的反常现象,它关系到定位子的使用寿命．着重测量了暗电流和随机噪声与时间、高压及温度的关系.     

Double-diffusive convection for a heated cylinder submerged in a salt-stratified fluid layer

Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra _T , and the buoyancy ratio, R _ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder are the latter. The increase in Ra _T reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio. For the same Ra _T , the increase of R _ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number are between the pure conduction and natural convection modes and the variation is due to the evolution of layers. Received on 13 September 1996     

Time-harmonic response of a vertical crack in plates

A technique for the characterization of an interior crack perpendicular to the surface of the plates is presented. A time-harmonic line load is applied on the upper surface of the plate. The scattered displacement field is calculated by using the strip element method. It is found that there are additional superimposed oscillations in the curve of the absolute values of the displacement in the region between the load and the crack. The mean value of the peaks of the additional oscillations increases with the crack length, and is less dependent on the distance from the load to the crack. The crack position is determined from the displacement distribution curve and the crack length is determined from the mean value of the peaks of the additional oscillations. Approximate polynomial formula of degree four for predicting the length of interior vertical cracks in isotropic homogeneous plates is also proposed. Numerical examples are given to demonstrate the present technique.