Discretization of the solutions to Poisson’s equation

Sharp estimates (in the power scale) are obtained for the discretization error in the solutions to Poisson’s equation whose right-hand side belongs to a Korobov class. Compared to the well-known Korobov estimate, the order is almost doubled and has an ultimate value in the power scale.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

电子回旋共振放电的电离特性PIC/MCC模拟(Ⅰ)——物理模型与理论方法

采用粒子模拟与蒙特卡罗相结合(PIC/MCC)的方法对电子回旋共振(ECR)放电中的电离过程进行了模拟，其中带电粒子与微波的相互作用由PIC方法的电磁模型描述，粒子间的碰撞过程由MCC方法描述.考虑的碰撞类型有电子与中性粒子的弹性、激发、电离碰撞，离子与中性粒子的弹性、电荷交换碰撞，碰撞截面均依赖于能量而变化.阐述了理论分析的过程，为数值模拟ECR放电奠定了基础. 关键词： 电子回旋共振放电 粒子模拟 蒙特卡罗 电离     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Correlation between the Mechanical Properties and the Amount of Desorbed Water for Composites Based on Low-Density Polyethylene and Linen Yarn Production Waste

The effect of the amount of desorbed water on the mechanical properties of composites based on low-density polyethylene and linen yarn production waste (LW) is analyzed by statistical methods. It is shown that the amount of absorbed water decreases during the desorption process at room temperature both for specimens modified and unmodified with diphenylmethane diisocyanate (DIC.) The most sensitive to the action of water is the elastic modulus, which decreases considerably under the effect of water and is fully restored in the desorption process. The tensile strain also increases with the amount of absorbed water. It is found that the elastic modulus of the unmodified composite correlates linearly with the amount of desorbed water. Between the amount of desorbed water and the tensile strain, as well the specific work of deformation, a negative linear correlation is revealed. After water desorption, all strength and deformation characteristics of both the modified and unmodified composites are fully recovered.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 515–524, July–August, 2005.     

Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality.     

An AFM, XPS and electrochemical study of molecular electroactive monolayers formed by wet chemistry functionalization of H-terminated Si(1 0 0) with vinylferrocene

Molecular electroactive monolayers have been produced from vinylferrocene (VFC) via light-assisted surface anchoring to H-terminated n- and p-Si(1 0 0) wafers prepared via wet chemistry, in a controlled atmosphere. The resulting Si-C bound hybrids have been characterized by means of XPS and AFM. Their performance as semiconductor functionalized electrodes and their surface composition have been followed by combining electrochemical and XPS measurements on the same samples, before and after use in an electrochemical cell. White-light photoactivated anchoring at short (1 h) exposure times has resulted in a mild route, with a very limited impact on the initial quality of the silicon substrate. In fact, the functionalized Si surface results negligibly oxidized, and the C/Fe atomic ratio is close to the value expected for the pure molecular species. The VFC/Si hybrids can be described as (η⁵-C₅H₅)Fe²⁺(η⁵-C₅H₄)-CH₂-CH₂-Si species, on the basis of XPS results. Electrochemical methods have been applied in order to investigate the role played by a robust, covalent Si-C anchoring mode towards substrate-molecule electronic communication, a crucial issue for a perspective development of molecular electronics devices. The response found from cyclic voltammograms for p-Si(1 0 0) functionalized electrodes, run in the dark and under illumination, has shown that the electron transfer is not limited by the number of charge carriers, confirming the occurrence of electron transfer via the Si valence band. The hybrids have shown a noticeable electrochemical stability and reversibility under cyclic voltammetry (cv), and the trend in peak current intensity vs. the scan rate was linear. The molecule-Si bond is preserved even after thousands of voltammetric cycles, although the surface coverage, evaluated from cv and XPS, decreases in the same sequence. An increasingly larger surface concentration of Fe³⁺ at the expenses of Fe²⁺ redox centers has been found at increasing number of cv’s, experimentally associated with the growth of silicon oxide. Surface SiO⁻ groups from deprotonated silanol termination, induced by the electrochemical treatments, are proposed as the associated counterions for the Fe³⁺ species. They could be responsible for the observed decrease in the electron transfer rate constant with electrode ageing.     

Decreasing the Displacements of a Composite Saddle-Shaped Cable Roof

The structural possibilities of decreasing the compliance of a composite saddle-shaped cable roof having a compliant support contour are investigated. The use of a supporting contour consisting of cables joined together with tie-bars is considered as a structural method enabling one to decrease the compliance of the roof. Each cable of the support has its own initial flexure. The method is most efficient from the viewpoint of material consumption per unit of covered area relative to the increasing rigidity and prestress level of the cable net.The efficiency of the method was evaluated by a numerical experiment, which was carried out for a composite saddle-shaped cable roof 50 × 50 m in the plan. The roof was formed by two orthogonal cable groups joined with a compliant supporting contour. A hybrid composite cable based on a carbon-fiber-reinforced plastic, a glass-fiber-reinforced plastic, and steel was considered as a material for the cable net in combination with steel. The material consumption and the maximum vertical displacement of the cable net in relation to the initial geometrical characteristics of the supporting contour were obtained. A possibility of decreasing the maximum vertical displacements of the roof by 8% was established.     

束晕-混沌的复杂性理论与控制方法及其应用前景

本文系统论述涉及强流加速器等强流离子束装置中产生的束晕-混沌的复杂性理论与控制方法及其应用前景。强流离子束在核材料生产与增殖、洁净核能、放射性废物嬗变、放射性药物生产、重离子聚变、高能物理、核科学与工程、国防与民用工业和医疗等许多方面都有极其重要的应用潜力和诱人的发展前景。尤其是，近年来强流加速器驱动的放射性洁净核能系统是国内外关注的热门课题，因为它比常规核电更安全、更干净、更便宜。但是，强流离子束形成的束晕-混沌的复杂性现象已引起了国内外广泛关注，需要加以抑制、控制和消除这类现象，解决这一难题已经成为强流离子束应用中的关键问题之一。目前不仅必须深入研究这类束晕-混沌的复杂特性及其产生的物理机制，而且需要研究如何实现对束晕-混沌的有效控制，并寻求和发展其新理论、新方法和新技术。这就向强流离子束物理和非线性-复杂性科学及其技术提出了一系列极富挑战性的新课题。本文结合国内外的研究概况，根据我们多年来的研究成果，特别是我们首创性地提出了一些束晕-混沌的有效控制方法，它们包括：非线性反馈控制法，小波反馈控制法，变结构控制法，延迟反馈控制法，参数自适应控制法等，进行重点的介绍。对上述课题当前的主要进展及相关问题进行系统的总结和比较全面综述的评论。最后，指出该领域今后的研究方向，以推动这个崭新领域的深入研究和应用发展。     

Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating Solutions

New explicit, zero dissipative, hybrid Numerov type methods are presented in this paper. We derive these methods using an alternative which avoids the use of costly high accuracy interpolatory nodes. We only need the Taylor expansion at some internal points then. The method is of sixth algebraic order at a cost of seven stages per step while their phase lag order is fourteen. The zero dissipation condition is satisfied, so the methods possess an non empty interval of periodicity. Numerical results over some well known problems in physics and mechanics indicate the superiority of the new method.