The Crystallization of Poly (3-dodecyltbiophene) in an Oriented Solidification Environment

Poly (3-alkylthiophenes) (P3ATs) have made up of a family of conductive polymerswhich are soluble, fusible and processable, since the introduction of flexible alkyl sidechains"'. It is generally accepted that P3ATs can form similar layered structures. inwhich the thiophene rings possess planarity and the side chains act as spacers'-'. Whenthe number. of 'carbon atoms of alkyl side chains is more than 10, some orderlyarrangements will occur for side chains betWeen the' layers'. It has been w…     

On Percolation with Fibers or Layers

We consider site percolation on Z ^d, directed edges going from any sZ ^d to s+A ₁,..., s+A _n, where A ₁,..., A _n are the same for all sites and at least two of them are noncollinear. A site is closed if it belongs to p+Block, where p is a point in a Poisson distribution in R ^dZ ^d with a density and Block={sL: |s|M}+{sR ^d: |s|}, where L is a linear subspace of R ^d, |·| is the Euclidean norm, =max(|A ₁|,..., |A _n|) and M is a parameter. We study the behavior of *, the critical value, and P _closed*, corresponding critical percentage of closed sites, when M. Denote R ^d/L the factor space. Call two nonzero vectors U, V codirected if U=kV, where k>0. Theorem. If there are A _i and A _j whose projections to R ^d/L are not codirected, then *1/M ^dim(L) and P _closed* remains separated both from 0 and 1 when M. If projections of all A ₁,..., A _n to R ^d/L are codirected, then *1/M ^dim(L)+1 and P _closed*1/M when M.     

基于面向对象技术的多媒体CAI素材库系统

建立实用、高效的多媒体ＣＡＩ素材库是高效率、高质量开发ＣＡＩ软件的基础和关键．本文从数据模型、面向对象分析和存储模式三方面入手,提出一种支撑ＣＡＩ制作工具的素材库体系结构,并讨论该体系结构的特性和进一步研究的问题．     

A tunable reentrant resonator with transverse orientation of electric field for in vivo EPR spectroscopy

There has been a need for development of microwave resonator designs optimized to provide high sensitivity and high stability for EPR spectroscopy and imaging measurements of in vivo systems. The design and construction of a novel reentrant resonator with transversely oriented electric field (TERR) and rectangular sample opening cross section for EPR spectroscopy and imaging of in vivo biological samples, such as the whole body of mice and rats, is described. This design with its transversely oriented capacitive element enables wide and simple setting of the center frequency by trimming the dimensions of the capacitive plate over the range 100-900 MHz with unloaded Q values of approximately 1100 at 750 MHz, while the mechanical adjustment mechanism allows smooth continuous frequency tuning in the range +/-50 MHz. This orientation of the capacitive element limits the electric field based loss of resonator Q observed with large lossy samples, and it facilitates the use of capacitive coupling. Both microwave performance data and EPR measurements of aqueous samples demonstrate high sensitivity and stability of the design, which make it well suited for in vivo applications.     

Convection-enhanced diffusion for random flows

We analyze the effective diffusivity of a passive scalar in a two-dimensional, steady, incompressible random flow that has mean zero and a stationary stream function. We show that in the limit of small diffusivity or large Peclet number, with convection dominating, there is substantial enhancement of the effective diffusivity. Our analysis is based on some new variational principles for convection diffusion problems and on some facts from continuum percolation theory, some of which are widely believed to be correct but have not been proved yet. We show in detail how the variational principles convert information about the geometry of the level lines of the random stream function into properties of the effective diffusivity and substantiate the result of Isichenko and Kalda that the effective diffusivity behaves likeɛ ^3/13 when the molecular diffusivityɛ is small, assuming some percolation-theoretic facts. We also analyze the effective diffusivity for a special class of convective flows, random cellular flows, where the facts from percolation theory are well established and their use in the variational principles is more direct than for general random flows.     

压力对聚苯胺导电性的影响

 导电高聚物聚苯胺薄膜经过定向拉伸后，其有序度、电导及跃迁势垒都发生了很大变化。本文研究了准静水压力对定向拉伸前后，聚苯胺薄膜电学性质的影响。发现未定向拉伸的聚苯胺薄膜的电导随压力单调增加，跃迁势垒T₀随压力单调减少，而定向拉伸后的聚苯胺薄膜则在0.47 GPa出现电导的极大值，在0.35~0.71 GPa之间出现T₀的极小值，这个异常行为与聚乙炔、聚噻吩等导电高聚物均不相同。     

Spectra of Some Interesting Combinatorial Matrices Related to Oriented Spanning Trees on a Directed Graph

The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H _n ) follows, where H _n stands for the complete directed graph on n vertices without loops.     

On a multiscale continuous percolation model with unbounded defects

We study the multiscale (fractal) percolation in dimension greater than or equal to 2, where the model at each level is the Poisson Boolean model [[, ]]. Also, the random radius is supposed to be unbounded. We prove that if the rate of Poisson field is less than some critical value, then by choosing the scaling parameter large enough one can assure that there is no multiscale percolation. Another result of this paper is that if the expectation of ^2d is finite, then the expectation of the size of the cluster raised to the power is also finite for small , which is a generalization of one of the results of [8].1 Partially supported by FAPESP (97/12826–6, 02/02984–3) and CNPq (300676/00–0)2 Partially supported by FAPESP (00/11462–5, 02/03012–5)     

The Percolation Transition for the Zero-Temperature Stochastic Ising Model on the Hexagonal Lattice

On the planar hexagonal lattice , we analyze the Markov process whose state (t), in , updates each site v asynchronously in continuous time t0, so that _v (t) agrees with a majority of its (three) neighbors. The initial _v (0)'s are i.i.d. with P[ _v (0)=+1]=p[0,1]. We study, both rigorously and by Monte Carlo simulation, the existence and nature of the percolation transition as t and p1/2. Denoting by ⁺(t,p) the expected size of the plus cluster containing the origin, we (1) prove that ⁺(,1/2)= and (2) study numerically critical exponents associated with the divergence of ⁺(,p) as p1/2. A detailed finite-size scaling analysis suggests that the exponents and of this t= (dependent) percolation model have the same values, 4/3 and 43/18, as standard two-dimensional independent percolation. We also present numerical evidence that the rate at which (t)() as t is exponential.     

On Crossing Event Formulas in Critical Two-Dimensional Percolation

Several formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for the expected number of crossing clusters. It is shown that for lattices where conformal invariance holds, they simplify when the spatial domain is taken to be the interior of an equilateral triangle. The two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry. This suggests that rigorous proofs of Watts's formula and Cardy's new formula will be easiest to construct if the underlying lattice is triangular. The simplification in a triangular domain of Schramm's bulk Cardy's formula is also studied.