Geometrically non-linear transverse vibrations of C-S-S-S and C-S-C-S rectangular plates

This paper is concerned with a new improved formulation of the theoretical model previously developed by Benamar et al. based on Hamilton's principle and spectral analysis, for the geometrically non-linear vibrations of thin structures. The problem is reduced to a non-linear algebraic system, the solution of which leads to determination of the amplitude-dependent fundamental non-linear mode shapes, the frequency parameters, and the non-linear stress distributions. The cases of C-S-C-S and C-S-S-S rectangular plates are examined, and the results obtained are in a good qualitative and quantitative agreement with the previous available works, based on various methods. In order to obtain explicit analytical solutions for the first non-linear mode shapes of C-S-C-S RP² and C-S-S-S RP, which are expected to be very useful in engineering applications and in further analytical developments, the improved version of the semi-analytical model developed by El Kadiri et al. For beams and fully clamped rectangular plates, has been slightly modified, and adapted to the above cases, leading to explicit expressions for the higher basic function contributions, which are shown to be in a good agreement with the iterative solutions, for maximum non-dimensional vibration amplitude values up to 0.75 and 0.6 for the first non-linear mode shapes of C-S-C-S RP and C-S-S-S RP, respectively.     

Similarities and Differences of the Active Sites in Basic and Advanced MgCl2‐Supported Ziegler‐Natta Propylene Polymerization Catalysts

Though preparation procedures of heterogeneous Ziegler‐Natta catalysts for propylene polymerization are sophisticated, it is uncertain whether the nature of the active sites is similar or different for different preparation procedures. In this study, the effects of preparation procedures on the nature of the active sites were investigated by stopped‐flow polymerization in combination with microstructure analysis of polymers. Both basic and advanced types of catalysts showed the same two kinds of isospecific active site, which indicated little influence of the preparation method on the active site structure. On the contrary, the ratios of the two kinds of isospecific sites were not the same, resulting in variation of average polymer properties.

     

A high order moving boundary treatment for compressible inviscid flows

We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax–Wendroff procedure proposed in [17] for conservation laws in static geometries. This procedure helps us obtain normal spatial derivatives at inflow boundaries from Lagrangian time derivatives and tangential derivatives by repeated use of the Euler equations. Together with high order extrapolation at outflow boundaries, we can impose accurate values of ghost points near the boundaries by a Taylor expansion. To maintain high order accuracy in time, we need some special time matching technique at the two intermediate Runge–Kutta stages. Numerical examples in one and two dimensions show that our boundary treatment is high order accurate for problems with smooth solutions. Our method also performs well for problems involving interactions between shocks and moving rigid bodies.     

The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids

Novel limiters based on the weighted average procedure are developed for finite volume methods solving multi-dimensional hyperbolic conservation laws on unstructured grids. The development of these limiters is inspired by the biased averaging procedure of Choi and Liu [10]. The remarkable features of the present limiters are the new biased functions and the weighted average procedure, which enable the present limiter to capture strong shock waves and achieve excellent convergence for steady state computations. The mechanism of the developed limiters for eliminating spurious oscillations in the vicinity of discontinuities is revealed by studying the asymptotic behavior of the limiters. Numerical experiments for a variety of test cases are presented to demonstrate the superior performance of the proposed limiters.     

居民生活碳排放抽样调查方案设计:以青海省为例

调查方案设计是居民生活碳排放调查及数据分析的基础和保证.以大量文献和作者在居民生活碳排放调查中的实践经验为基础,立足调查方案的科学性和实践操作的可行性,以青海省为例,从居民生活碳排放调查的统计量选取、抽样框的构建、抽样方法的选择和样本量的确定、调查方案实施的详细步骤4方面综述性归纳了一套居民生活碳排放调查方案设计的方法,以期为居民生活碳排放研究提供参考.     

A parametric successive underestimation method for convex multiplicative programming problems

This paper addresses itself to the algorithm for minimizing the product of two nonnegative convex functions over a convex set. It is shown that the global minimum of this nonconvex problem can be obtained by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in a higher dimensional space and to apply a branch-and-bound algorithm using an underestimating function. Computational results indicate that our algorithm is efficient when the objective function is the product of a linear and a quadratic functions and the constraints are linear. An extension of our algorithm for minimizing the sum of a convex function and a product of two convex functions is also discussed.     

An inverse design approach for magnetic lenses operated under infinite magnification condition

A theoretical-computational investigation has been carried out to describe a synthesis optimization procedure of asymmetrical magnetic lenses with the aid of numerical analysis methods. Where a certain mathematical form for the electron beam is proposed to be a target function. This function has several optimization parameters where the influence of each of them, when the other ones kept fixed, is investigated. Results have clearly shown that some of the optimization parameters have a considerable effect on the first order properties, third order aberrations and the reconstructed polepieces. While the others have no significant influence on these physical and geometrical properties. Furthermore, the results obviously show that there is an excellent ability for producing a conventional magnetic field for the double polepieces lenses.     

Investigation of distribution of beryllium, nickel and vanadium in subsoil of Csepel-Island

In order to investigate the long-term effect of the Százhalombatta power plant on the environment of the Csepel-Island subsoil samples were collected in 55 points within 200 km². Using a microwave-assisted extraction procedure, Be, Ni and V were extracted from the soil samples by aqua regia and the metal concentrations were determined by inductively coupled plasma mass spectrometry (ICP-MS). The analytical results were evaluated by chemometric methods and interpreted considering the main mineral constituents of the subsoil.     

Asymptotic expansions of the Robbins-Monro process

Assume that the function values f(x) of an unknown regression function f: ℝ → ℝ can be observed with some random error V. To estimate the zero ϑ of f, Robbins and Monro suggested to run the recursion X _n+1 = X _n − a/n Y _n with Y _n = f(X _n ) − V _n . Under regularity assumptions, the normalized Robbins-Monro process, given by (X _n+1 − ϑ)/√Var(X _n+1, is asymptotically standard normal. In this paper Edgeworth expansions are presented which provide approximations of the distribution function up to an error of order o(1/√n) or even o(1/n). As corollaries asymptotic confidence intervals for the unknown parameter ϑ are obtained with coverage probability errors of order O(1/n). Further results concern Cornish-Fisher expansions of the quantile function, an Edgeworth correction of the distribution function and a stochastic expansion in terms of a bivariate polynomial in 1/√n and a standard normal random variable. The proofs of this paper heavily rely on recently published results on Edgeworth expansions for approximations of the Robbins-Monro process.