Studies on the Adsorption of Asymmetrical Triblock Copolymers by Scheutjens-Fleer Theory and Monte Carlo Simulation

The adsorption of asymmetrical triblock copolymers from a non-selective solvent on solid surface has been studied by using Scheutjens-Fleer mean-field theory and Monte Carlo simulation method on lattice model. The main aim of this paper is to provide detailed computer simulation data, taking A8-kB20Ak as a key example, to study the influence of the structure of copolymer on adsorption behavior and make a comparison between MC and SF results. The simulated results show that the size distribution of various configurations and density-profile are dependent on molecular structure and adsorption energy. The molecular structure will lead to diversity of adsorption behavior. This discrepancy between different structures would be enlarged for the surface coverage and adsorption amount with increasing of the adsorption energy. The surface coverage and the adsorption amount as well as the bound fraction will become larger as symmetry of the molecular structure becomes gradually worse. The adsorption layer becomes thicker with increasing of symmetry of the molecule when adsorption energy is smaller but it becomes thinner when adsorption energy is higher. It is shown that SF theory can reproduce the adsorption behavior of asymmetrical triblock copolymers. However, systematic discrepancy between the theory and simulation still exists.The approximations inherited in the mean-filed theory such as random mixing and the allowance of direct back folding may be responsible for those deviations.     

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Carousels,Zindler curves and the floating body problem

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

An approach to deciding the observational equivalence of Algol-like languages

We prove that the observational equivalence of third-order finitary (i.e. recursion-free) Idealized Algol (IA) is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function f_M. Given any such f_M, we construct a real-time deterministic pushdown automaton (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable.     

The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.     

非饱和土本构关系的混合物理论(Ⅱ)--线性本构方程和场方程

通过对非饱和土非线性本构方程和场方程的线性化，推导出了非饱和土的线性本构方程和场方程，把线性方程表示为与Biot饱和多孔介质方程相似的形式；证明了Darcy定律对非饱和土的适用性；说明了Biot饱和多孔介质方程是这些线性方程的特征。所有这些都表明用混合理论处理非饱和土本构问题的正确性。     

基于粗糙集理论的知识约简及应用实例

在保持分类能力不变的前提下 ,通过利用粗糙集理论中的知识约简方法 ,在保护知识库分类不变的条件下 ,删除其中不相关或不重要的知识 ,从而导出问题的决策 .利用基于决策表的粗糙集模型算法 ,实例分析如何数字化表示决策表 ,并对其进行属性约简和属性值的约简 ,从而提取决策规则 .     

脉冲充磁的超导圆盘的电流密度和俘获场分布的研究

本从第一性原理出发，计算了充磁线圈产生的磁场，脉冲充磁的超导圆盘中的感应电流密度和俘获场分布．以超导体中的电流运动方程为基础，通过磁通动力学方程E=Ec(J/Jc)^n和物质方程B=μ0H表示超导圆盘的超导特性．计算表明第一个脉冲充磁电流的峰值和磁通蠕动指数对于超导圆盘中的感应电流分布非常重要．同时研究了充磁电流的宽度，波形，第二个充磁电流的峰值和充磁线圈的形状对于俘获场的影响．计算表明不断减小脉冲充磁电流峰值的反复充磁可以保持超导圆盘中的感应电流密度的平台在一确定水平．     

Electromagnetic energy flow near nanoparticles—I: single spheres

The electromagnetic (EM) energy flow near single spheres is investigated by applying Mie theory. From the patterns of the energy flow, the absorption and the scattering of light can be understood in the microscopic point of view. In the absorption profiles of metallic particles, most absorbed energy is consumed on the surface of the particles, which indicates that the resonance of surface plasmon is different from that of the bulk plasmon. Two mechanisms to enhanced local EM field are also distinguished. One is the surface plasmon resonance, and another one is the intensified energy flow.