Coxeter Transformation and Quasiquivers

Mathematical Notes -     

化整为零:聚合物/粘土纳米复合材料的微观结构和阻隔性能

在聚合物基体中掺入少量的层状硅酸盐所制备的聚合物／粘土纳米复合材料，其阻隔性能明显地优于纯聚合物及其传统的复合材料。实验及分析结果表明，聚合物／粘土纳米复合材料的微观结构和阻隔性能主要受控于粘土剥离后的径厚比．一简单的重整化群模型被用来评估粘土几何因素（诸如径厚比、取向、剥离程度等）对聚合物／粘土纳米复合材料阻隔性能的影响，所得到的逾渗阈值及最佳粘土含量与实验结果吻合。     

Charge transport properties in carbon black/polymer composites

The charge transport properties of polymer matrix–carbon black composites are investigated in this study. Direct current conductivity is examined with varying parameters: the temperature and the conductive filler content. Conductivity data are analyzed by means of percolation theory, and both percolation threshold and critical exponent are determined at each of the examined temperatures. The temperature dependence of conductivity and the agreement of experimental results with the variable range hopping model reveal hopping conduction as the predominant transport mechanism, below and in the vicinity of the critical concentration of carbon black particles. At higher concentrations, the contribution of hopping transport to the overall conductivity is reduced and a balance between hopping and conduction via geometrical contact occurs. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2535–2545, 2007     

Optical Diffractive Memories: Angular Selectivity and Diffraction Efficiency in Dichromated Gelatin

Two thousand images of resolution 512×512 pixels as a regular matrix pattern of 10×10 elements are stored, where each element is angularly multiplexed 20 times in a 25 μm thickness of dichromated gelatin emulsion without cross-talk effect. The surface area of the matrix is 1 cm². We show good concordance of the angular selectivity between the experimental result and theory. The diffraction efficiency of each 20 multiplexed images is measured and has nearly the same value. Examples of reconstructed images for multiple applications are given, for example, storage of 160,000 images on a 3′1/2 floppy disc format, which is about 100 min of black and white film. Application can be made to automobile cartography and storage of X-ray images as well as weather forecast images. Colored diffractive images are also possible and are illustrated.     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

二维渗流相关长度ξ(p)的幂估计(英文)

相关长度ξ(p)是渗流理论中最重要的一个量。本文对它给出了一个幂估计     

Cardy's formula for some dependent percolation models

We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice  (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice 𝕋 with flips when a site disagrees with six, five and sometimes four of its six neighbors. Received: 24 December 2001     

Cu-MgF2复合纳米金属陶瓷薄膜的电导特性研究

用射频磁控共溅射法制备了Cu体积分数分别为 10 % ,15 % ,2 0 %和 3 0 %的Cu MgF2 复合金属陶瓷薄膜 .用x射线衍射、x射线光电子能谱和变温四引线技术对薄膜的微结构、组分及电导特性进行了测试分析 .微结构分析表明 :制备的Cu MgF2 复合薄膜由fcc Cu晶态纳米微粒镶嵌于主要为非晶态的MgF2 陶瓷基体中构成 ,Cu晶粒的平均晶粒尺寸随组分增加从 11 9nm增至 17 8nm .5 0— 3 0 0K温度范围内的电导测试结果表明 :当Cu体积分数qM 由 15 %增加到 2 0 %时 ,Cu MgF2 复合薄膜的电阻减小了 8个量级 ,得出制备的复合薄膜渗透阈qCM 应处于 15 %和 2 0 %之间 .qM 在 10 %和 15 %之间的薄膜呈介质导电状态 ,而在 2 0 %和 3 0 %之间的薄膜则呈金属导电状态 .从理论上讨论了复合薄膜中杂质电导和本征电导的激活能及其对电导的贡献 ,并讨论了Cu MgF2 复合纳米金属陶瓷薄膜的渗透阈 ,得到了和实验一致的结果     

Structural morphology of poly(styrene)-poly(butyl acrylate) polymer-polymer composites studied by dynamic mechanical measurements

The emulsion polymerization process allows production of polymer particles with different structural morphologies. Films obtained after coalescence keep some memory of this morphology, but large modifications can occur during coalescence. In the present case, one of the polymers, polystyrene (PS), exhibits a glass temperature (Tg) much higher than the filmification temperature (close to room temperature), while the other one, poly(butyl acrylate) (PBA), has a much lowerTg. Furthermore, it is well known that dynamic mechanical measurements can be very helpful in providing information on the morphology of polymer materials, i.e., on geometrical and topological arrangement of homopolymer domains. At first, this method was used for comparison of two types of films: i) the first one obtained from structured-core (PS)-shell (PBA) particles, ii) the second one obtained from a blend of homopolymer particles (PS and PBA). It appears that the expected core-shell particles lost their geometric structure in the second film. Second, comparison of the predicted dynamic modulus and experimental data shows that i) strong interactions exist between PS nodules unless their coalescence has occured, leading to an abnormally high modulus at room temperature, ii) after achieving their coalescence, PS forms a more or less continuous phase. Both phenomena strongly depend on the particle size and their respective volume fractions.     

Size dependence of self-diffusion in the hard-square lattice gas

A striking size dependence of the mean-square displacement of diffusing particles in the two-dimensional lattice gas of hard squares has been observed by Monte Carlo simulation. It is shown that the size effect is due to the formation of a stable cage structure in small lattices when the particle concentration is high. The formation of cages is governed by a new type of percolation problem related to bootstrap percolation.