High-spin states in 128I

The high-spin states in 128I have been studied by using in-beam γ-ray spectroscopy with the 124Sn(7Li,3n)128I reaction at beam energies of 25, 28 and 42 MeV. A new level scheme including 20 new levels and 27 new γ-transitions for 128I has been established preliminarily.     

A compact finite difference method for solving Burgers' equation

In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

A weighted-integral based scheme

A weighted-integral based scheme (WIBS) and a weighted essentially non-oscillatory (WENO)-WIBS are constructed, where the integral of the unknown function with a set of linearly independent test functions are recorded on every cell. The time evolutions of these recordings are computed with TVD Runge–Kutta method. At the boundary of every two cells, the function values are interpolated from the recordings of the neighboring cells to calculate flux and volumetric integral in the weak form.     

Some basic problems in numerically simulating effective properties and local fields of composite materials

It is pointed out that to numerically estimate the effective properties and local fields of matrix-inclusion composites, a commonly adopted method is accompanied with some serious draw-backs. We call this method the nominal loading scheme (NLS), which considers the actual inclusion distribution inside a finite domain, Ω say, treats the external domain of Ω to be of the pure matrix material, and imposes the actural traction, σ^∞ say on the remote boundary. It thus gives rise to the following basic problems: (i) Can NLS be improved remarkably just by adjusting σ^∞? (ii) What is the relationship between the size of Ω and the scale of inclusions? (iii) Which choice is better in calculating the effective properties, the whole domain Ω or an appropriately selected sub-domain of Ω? Targeting these problems, the equivalent loading scheme (ELS) and equivalent matrix scheme (EMS) are proposed. It is theoretically analyzed that both ELS and EMS can be used to precisely simulating the effective properties and local fields of matrix-inclusion composities, and both ELS and EMS are self-approved. As an application, ELS combined with a so-called pseudo-dislocations method is used to evaluate the effective properties and local fields of two-dimensional two-phase composites with close-packed circular inclusions, or randomly distributed circular inclusions, or randomly distributed microcracks. The results show that substituting the remore traction σ^∞ with the effective stress field σ^ɛ suggested by IDD scheme is a simple and effective method, and the estimation of the effective properties and local fields is very close to the accurate solution. The present work is supported by the National Natural Science Foundation of China (No. 19525207).     

The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations

The weakly dissipative version of the Kolmogorov-Arnold-Moser theory deals with the dynamics of systems that are a weakly dissipative perturbation of Hamiltonian systems. In the framework of this approach, both regular (asymptotically stable (unstable) periodic motions) and stochastic (Arnold’s web) dynamic properties are combined in the phase space. In this case, computer calculations are considerably simplified for the regular dynamics, which makes it possible to estimate physical parameters for stochastic components. A simple example of this approach is presented.     

High order compact solution of the one‐space‐dimensional linear hyperbolic equation

In this article, we introduce a high‐order accurate method for solving one‐space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high‐order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one‐space‐dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, 3 .© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme

In this paper we continue systematic study of the dimension estimate of the global attractors for the chemotaxis-growth system and its finite-element approximations. Utilizing a conservative upwind finite-element scheme we managed significantly to improve dimension estimates with respect to the chemotactic parameter.     

An unstructured/structured multi‐layer hybrid grid method and its application

A multi‐layer hybrid grid method is constructed to simulate complex flow field around 2‐D and 3‐D configuration. The method combines Cartesian grids with structured grids and triangular meshes to provide great flexibility in discretizing a domain. We generate the body‐fitted structured grids near the wall surface and the Cartesian grids for the far field. In addition, we regard the triangular meshes as an adhesive to link each grid part. Coupled with a tree data structure, the Cartesian grid is generated automatically through a cell‐cutting algorithm. The grid merging methodology is discussed, which can smooth hybrid grids and improve the quality of the grids. A cell‐centred finite volume flow solver has been developed in combination with a dual‐time stepping scheme. The flow solver supports arbitrary control volume cells. Both inviscid and viscous flows are computed by solving the Euler and Navier–Stokes equations. The above methods and algorithms have been validated on some test cases. Computed results are presented and compared with experimental data. Copyright © 2006 John Wiley & Sons, Ltd.     

On incidence between strata of the Hilbert scheme of points on $$\mathbb{P}^{2}$$

The Hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated Hilbert series. In general, the precise inclusion relation between the closures of the strata is still unknown. Guerimand, Ph.D Thesis, Universite’de Nice, 2002 studied this problem for strata whose Hilbert series are as close as possible. Preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata. In this paper we present a new approach, based on deformation theory, to Guerimand’s result. This allows us to show that the technical condition is not necessary. Michel Van den Bergh is a director of research at the FWO.     

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.