Persistence of the Thomas–Fermi approximation for ground states of the Gross–Pitaevskii equation supported by the nonlinear confinement

We justify the Thomas–Fermi approximation for the stationary Gross–Pitaevskii equation with the repulsive nonlinear confinement, which was recently introduced in physics literature. The method is based on the resolvent estimates and the fixed-point iterations. The results cover the case of the algebraically growing nonlinear confinement.     

On the Thomas Equation for the Ion-Exchange Operations

The Thomas equation is an interesting subject in physical sciences. In this paper, we analytically solve the Thomas equation. The transformation obtained hereby is more general than the Thomas-Rosales transformation.     

Parameter-free H(div) preconditioning for a mixed finite element formulation of diffusion problems

^** Email: c.powell{at}manchester.ac.uk Mixed finite element formulations of generalised diffusion problemsyield linear systems with ill-conditioned, symmetric and indefinitecoefficient matrices. Preconditioners with optimal work complexitythat do not rely on artificial parameters are essential. Weimplement lowest order Raviart–Thomas elements and analysepractical issues associated with so-called ‘H(div) preconditioning’.Properties of the exact scheme are discussed in Powell &Silvester (2003, SIAM J. Matrix Anal. Appl., 25, 718–738).We extend the discussion, here, to practical implementation,the components of which are any available multilevel solverfor a weighted H(div) operator and a pressure mass matrix. Anew bound is established for the eigenvalue spectrum of thepreconditioned system matrix and extensive numerical resultsare presented.     

Thomas Rotation and Thomas Precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. A straightforward derivation of the Fermi–Walker equation is also given. Besides the simplicity of calculations the absolute treatment of spacetime allows us to make a clear conceptual distinction between the phenomena of Thomas rotation and Thomas precession.Supported by Hungarian research fund OTKA-T048489.Supported by Hungarian research funds OTKA-T047276, F049457, T049301.     

圣咏《愤怒的日子》的特征与运用

《愤怒的日子》是托马斯(Thomas of Celano)所作的诗,主题纯朴,音调平稳。众多作品以不同的形式引用《愤怒的日子》,以象征宗教、讽刺、死亡等特定的形象,可见这是一支独一无二、亘古流传的"歌"。     

《土生子》中主人公别格悲剧命运的心理原因分析——别格·托马斯的本我、自我与超我的矛盾

从分析《土生子》主人公别格的心理着手,揭示别格悲剧形成的原因。认为在别格身上体现出自我、本我与超我的冲突的心理刻画与描写与弗洛伊德的心理分析学说有异曲同工之妙。从人格结构理论这一新的角度诠释别格的内心冲突与矛盾及其成因,能更深入揭示小说主题。     

Kernel‐based vector field reconstruction in computational fluid dynamic models

Kernel‐based reconstruction methods are applied to obtain highly accurate approximations of local vector fields from normal components assigned at the edges of a computational mesh. The theoretical background of kernel‐based reconstructions for vector‐valued functions is first reviewed, before the reconstruction method is adapted to the specific requirements of relevant applications in computational fluid dynamics. To this end, important computational aspects concerning the design of the reconstruction scheme like the selection of suitable stencils are explained in detail. Extensive numerical examples and comparisons concerning hydrodynamic models show that the proposed kernel‐based reconstruction improves the accuracy of standard finite element discretizations, including Raviart–Thomas (RT) elements, quite significantly, while retaining discrete conservation properties of important physical quantities, such as mass, vorticity, or potential enstrophy. Copyright © 2010 John Wiley & Sons, Ltd.