Dielectric resonances in three-dimensional binary disordered media

Powdered solids often present very specific properties due to their granular nature. Such powders are often obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. In a very natural way, these systems are modeled by regular lattices, whose sites or bonds are randomly chosen with given probabilities. It is known that the electrical and optical properties of random bi-dimensional (2D) networks are well described by their conductance's poles (resonances) and residues (amplitudes). The numerical implementation of a spectral method gave the spectral density, the AC conductivity, the multi-fractal properties of the moments for the local electric field (or currents), and spectrum of resonances characteristic of some small clusters (animals). This work extends the spectral method to the three-dimensional (3D) case where the problem is more complicated because the duality property and the corresponding symmetries are broken. As in the 2D-case, the two significant parameters are the ratio of the complex conductances and of both phases, and the probability p (resp. 1-p) of (resp. ). All the resonances lie on the negative real h-axis, i.e. for pure non resistive networks in the AC case. For a static (DC) system, only the value h=0 (corresponding to a binary system with finite and , or and finite) can give a resonance. Some applications are proposed, in particular the ability for small clusters (animals with one, two or three bonds) to present a singular response for well identified frequencies of the incident electromagnetic field. Received 24 March 1999     

From 2D hyperbolic forests to 3D Euclidean entangled thickets

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra- and octa-continuous forms. Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts. Received 10 December 1999     

The Box counting Dimension of Invariant Sets for Iterated Function Systems

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SOME PROBLEMS OF THE TIME DISCRETE HOPFIELD NEURAL NETWORK SYSTEM

如果一个Hopfield神经网络系统(以下简记为HNNS)是时间离散、状态连续的,就称之为时间离散的HNNS(以下简记为TD-HNNS).对这种系统,如果在它的算子的作用下,状态的能量函数具有固定的增、减趋势,那么就称之为单向的TD-HNNS.本文讨论并给出了这种模型的一系列性质,如运动轨迹的稳定性、收敛性和稳定解的唯一性等,并由此给出了它在优化计算中的一系列应用.     

应用灰色模型GM（1,1）预测期货走向

本文试图应用灰色模型ＧＭ（１,１）分析期货走向,通过具体例子显示,应用这种模型能有效地预测期货走向     

核磁共振碳谱研究:烷烃化学位移和(CSS)与分子路径指数矢量(VPM)

系统研究了核磁共振碳谱和化学位移规律及其定量构谱关系(QSSR).本文研究了一组十元素分子路径指数矢量VPM,并发现它与烷烃化学位移和CCS有良好线性相关性.采用多元线性回归进行准确估计与预测,结果优良.     

Localization and dephasing driven by magnetic fluctuations in low carrier density colossal magnetoresistance materials

Localization and dephasing of conduction electrons in a low carrier density ferromagnet due to scattering on magnetic fluctuations is considered. We claim the existence of the “mobility edge”, which separates the states with fast diffusion and the states with slow diffusion; the latter is determined by the dephasing time. When the “mobility edge” crosses the Fermi energy a large and sharp change of conductivity is observed. The theory provides an explanation for the observed temperature dependence of conductivity in ferromagnetic semiconductors and manganite pyrochlores. Received 17 January 1999 and Received in final form 12 March 1999     

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Two-dimensional (2D) photonic band gaps (PBG) structure fabricated from anisotropic dielectric is studied by solving Maxwell's equations with use of plane-wave expansion method. Numerical simulations show that absolute photonic band gaps can be substantially improved in two dimensional square and triangular lattices of cylinders by introducing anisotropy in material dielectricity. Owing to different refractive indices for electromagnetic waves with E- and H-polarization, the quasi-independent adjustment of band gaps for the E- and H-polarization modes can be implemented by uniaxial crystals with their extraordinary axis parallel to the cylinders. Large absolute band gaps can be created for uniaxial cylinders in air with a positive anisotropy. In the case of air holes in background uniaxial dielectric with even a weak negative anisotropy, the absolute band gap can be increased 2-3 times. Large absolute band gap can also be obtained in other complex configurations of uniaxial and biaxial materials and this enables a full exploitation of potential utilization for anisotropic materials available in nature. Such a mechanism of band gap adjustment should open up a new scope for designing band gaps in 2D PBG structures. Received 26 January 1999     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998