Topological structure of the many vortices solution in Jackiw-Pi model

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw-Pi model. We obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Psi-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw-Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.

Study on reactive extrusion processes of block copolymer

The anionic copolymerization process of styrene-buradiene (S/B) block copolymer in a closely intermeshing co-rotating twin screw extruder with butyl-lithium initiator was studied. According to the anionic copolymerization mechanism and the reactive extrusion characteristics, the mathematical models of monomer conversion, average molecular weight and fluid viscosity during the anionic copolymerization of S/B were constructed, and then the reactive extrusion process was simulated by means of the finite volume method and the uncoupled semi-implicit iterative algorithm. Finally, the influence of the feeding mixture composition on conversion was discussed. The simulated results were nearly in agreement with the experimental results.

Numerical simulation of reactive extrusion processes of PA6

To analyze the complicated relationships among the variables during the reactive extrusion process of polyamide 6 (PA6), and then control the chemical reaction and the material structures, the process of continuous polymerization of caprolactam into PA6 in a closely intermeshing co-rotating twin screw extruder was simulated by means of the finite volume method, and the influences of three key processing parameters on the reactive extrusion process were discussed. The simulated results of an example were in good agreement with the experimental results.

Self-assembly of crystalline-coil diblock copolymer in solvents with varying selectivity: From spinodal-like aggregates to spheres, cylinders, and lamellae

We have investigated systematically the morphology of thin films spin-coated from solutions of a semicrystalline diblock copolymer, poly(L-lactic acid)-block-polystyrene (PLLA-b-PS), in solvents with varying selectivity. In neutral solvents (chloroform and tetrahydrofuran (THF)), a spinodal-like pattern was obtained and the pattern boundary was sharpened by diluting the solution. Meanwhile, loose spherical associates, together with larger aggregates composed of these associates by unimer bridges, formed partly due to crystallization of the PLLA blocks in relatively concentrated solutions. In slightly PS-selective solvent (e.g., benzene), both loose and compact spherical micelles were obtained, depending on the polymer concentration, coexisting with unimers. When enhancing the selectivity with mixed solvents, for example, mixing the neutral solvent and the slightly selective solvent with a highly PS-selective solvent, CS2, loose assemblies (nanorods in CS2/THF mixtures and polydisperse aggregates in CS2/benzene mixtures) and well-developed lamellar micelles were obtained.

Separation of thorium(IV) and extracting rare earths from sulfuric and phosphoric acid solutions by solvent extraction method

The bastnasite of Baotou (China) was roasted in concentrated sulfuric acid at 250-300 degreesC and the calcined products were leached by water. Almost all rare earths (RE) were moved into solutions in trivalent along with some radioactive impurity thorium(IV) (Th(IV))which accounts for 0.4% of RE and other impurities such as Fe(III), Ca, F, P, etc. Through fractional extraction (seven stages for extraction and nine for scrubbing), the mass ratio of Th(IV) and RE (ThO2/REO) in solution has decreased to 5 x 10(-6). The purity of ThO2 product recovered from organic phase is above 99%. The iron(III) in solutions can be removed in the form of precipitation by adding some magnesia into the solutions. Then RE can be concentrated by solvent extraction with 2-ethylhexyl phosphinic acid 2-ethylhexylester (P-507). The results of fractional extraction show that the concentration of total RE in aqueous solutions stripped by hydrochloric acid is over 200 g REO/I with the yield of RE above 99%. Individual RE can be attained by solvent extraction with P507 in the following process.

STUDIES OF ELECTROCHEMICAL CATALYTIC REDUCTION REACTIONS OF TETRAPHENYLPORPHINATOCOBALT 1,2-DIBROMOETHANE AND 1,2-DICHLOROETHANE SYSTEMS IN NONAQUEOUS MEDIA

Electrochemical catalytic reactions of tetraphenylporphinatocobalt were studied in DMF and EtCl2 solutions in the presence of 1,2-dibromoethane and 1, 2-dichloroethane utilizing cyclic voltammetry, thin-layer electrochemistry, in situ UV-visible spectroel

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

海相碳酸盐－稀土元素共沉淀过程中的分异作用研究

本文主要运用稳定加液－反应系统对海水中方解石和文石形成时稀土元素的共沉淀现象进行了分析，研究了稀土元素在固-液体系中的迁移、转化和分配。进而在对其定量描述的前提下，研究了稀土元素共沉淀对各种反应条件的响应，并对共沉淀行为的机制进行了探讨。 本实验首先运用pH测试、高精度滴定分析等手段测定了实验中的一些基本参数，如[H+]、碱度和[Ca2+]，根据计算结果获得了各碳酸体系要素，并以此为基础建立了5℃、15℃和25℃及pCO2=0.003atm下海水中方解石或文石的沉淀动力学方程。实验结果表明： 1）在各条件下，方解石或文石的沉淀速率（R）和其在海水中过饱和度（Ω）存在很好的线性相关性，即海相碳酸盐的沉淀动力学方程可以通过下面的基本表达式来表示：LogR=k*Log(Ω-1)+b ； 2）过高的稀土元素浓度会对文石或方解石的沉淀产生抑制作用，进而对共沉淀过程中YREEs的分异和分馏产生一定的影响。相比方解石而言，文石的沉淀动力学过程承受稀土元素的干扰能力更强； 3）不同温度下得到的方解石或文石各自的沉淀动力学方程存在明显的差异，表明这一过程受热力学因素控制。相对于方解石而言，温度对文石的沉淀动力学的影响更为显著。 与前人研究不同的是，本实验中YREEs的浓度设定在非常低的范围内，从而避免了过高浓度YREEs对方解石或文石沉淀动力学过程的干扰。在最终的反应液中，各种实验条件非常接近自然环境。有关稀土元素的共沉淀行为主要得出以下定性或定量化结论： 1）YREEs在随方解石或文石的共沉淀过程中，均发生了强烈的分异作用。在方解石实验中，稀土元素的分异系数分布曲线呈凸状分布；而在文石实验中，稀土元素的分异系数随原子序数的增加逐渐减小，遵循镧系收缩的规律。总的来说，稀土元素，尤其轻稀土元素在文石中的分异作用要强于方解石。 2）无论是方解石还是文石，沉淀速率对YREEs的分异作用都有着明显的影响。在方解石中，YREEs的分异系数随沉淀速率的增加呈一致性递减趋势；而在文石中，其分异系数对文石沉淀速率有着截然不同的响应：轻稀土元素（La, Ce, Nd, Sm, Eu, Gd）的分异系数随文石沉淀速率的增加而下降，而重稀土元素（Ho, Y, Tm, Yb , Lu）的分异系数则随文石沉淀速率的增加呈上升趋势。 3）在方解石中YREEs的分异系数之间存在非常好的相互关系，表明这些元素是以成比例的方式参与共沉淀。整个谱系呈现中等强度的分馏，MREE相对于LREE和HREE要更为富集；在文石中由于沉淀速率的作用不同，只有Y、Ho、Yb、Lu等元素的分异系数之间有较好的相互关系。YREEs出现了差异性的强烈分馏，在新生成沉淀中轻稀土元素相对于重稀土元素强烈富集。 4）YREEs在溶液中和碳酸盐晶体表面的碳酸根配位形式对YREEs在共沉淀过程中的分异作用极为重要，YREEs在碳酸盐晶体表面的吸附是整个谱系发生分馏效应的关键环节。对于文石来讲，晶体中有效YREE离子和Ca离子半价大小之间的相近程度是其分馏效应的关键因素；而对于方解石来说，YREEs在方解石晶格中的安置就是其分馏效应的关键控制因子，但在晶格安置中起到关键作用的是YREEs和方解石中O原子之间离子键M-O的键长，而非离子半径。 5）综合YREEs在方解石中的分异作用和分馏效应，我们认为M2(CO3)3-CaCO3和MNa(CO3)2-CaCO3是最为可能的两种固体溶液形成模式。 最为重要的是，对比我们的实验结果与前人在灰岩、叠层石、微生物成因碳酸盐等方解石质载体中的研究成果，两者之间出现了非常好的一致性。我们认为方解石质载体将是重建古海水中稀土元素相关信息的重要工具。相比之下，文石质载体不适合作为类似的载体。

地震波传播模拟的边界元―体积元积分方程法及其近似求解

To improve the efficiency of boundary-volume integral equation technique, this paper is involved in the approximate solutions of boundary-volume integral equation technique. Firstly, based on different interpretations of the self-interaction and extrapolation operators of the resulting boundary integral equation matrix, two different hybrid BEM+Born series modeling schemes are formulated and validated through comparisons with the full-waveform BE numerical solutions for wave propagation simulation in a semicircular alluvial valley and a complex fault model respectively. Numerical experiments indicate that both the BEM+Born series modeling schemes are suitable for complex geological structures and significantly improve computational efficiency especially for the cases of high frequencies and multisource seismic survey. Then boundary-volume integral equation technique is illuminated in detail and verified by modeling wave propagation in complex media. Furthermore, the first-order and second-order Born approximate solutions for the volume-scattering waves are studied and quantified by numerical simulation in different random medium models. Finally, preconditioning generalized minimal residual method is applied to solve boundary-volume integral equation and compared with Gaussian elimination method. Numerical experiments indicate this method makes the calculations more efficient.

Formalizing Triggers: A Learning Model for Finite Spaces

In a recent seminal paper, Gibson and Wexler (1993) take important steps to formalizing the notion of language learning in a (finite) space whose grammars are characterized by a finite number of parameters. They introduce the Triggering Learning Algorithm (TLA) and show that even in finite space convergence may be a problem due to local maxima. In this paper we explicitly formalize learning in finite parameter space as a Markov structure whose states are parameter settings. We show that this captures the dynamics of TLA completely and allows us to explicitly compute the rates of convergence for TLA and other variants of TLA e.g. random walk. Also included in the paper are a corrected version of GW's central convergence proof, a list of "problem states" in addition to local maxima, and batch and PAC-style learning bounds for the model.

Moisture conditions in timber cladding: field trial data for Sitka spruce.

Exposure trials on timber cladding are valuable for informing facade designers. This paper describes a trial using Sitka spruce (Picea sitchensis). Sitka spruce is the only UK-grown timber available in sufficient volume to supply the growing cladding market, but its suitability is unclear. Data indicated that the moisture content range in timber cladding was wider than generally accepted. The minimum of around 10% moisture content appeared to be similar for all details tested. The maximum was influenced by construction detailing but was around 30%. From a theoretical standpoint, the range, and rate, of moisture content fluctuation observed meant that the commonly quoted average value was largely irrelevant. The mode was a more representative statistic; most of the data were skewed towards the wood's fibre saturation point. Sitka spruce is, therefore, at risk of fungal decay and is only suitable as external cladding in the UK if treated with preservative

Reinventing the Matter of Britain: Undermining the State in Jacobean Masques

Archer, Jayne, Berry, Philippa, 'Reinventing the Matter of Britain: Undermining the State in Jacobean Masques', In: British Identities and English Renaissance Literature, David J. Baker and Willy Maley (eds),(Cambridge: Cambridge University Press), pp.119-134, 2002 RAE2008

Credit and Debt in medieval England, c.1180-c.1350

Schofield, Phillipp, and N. J. Mayhew, eds., Credit and Debt in medieval England, c.1180-c.1350 (Oxford: Oxbow Books, 2002), pp.x+164 RAE2008

PROPAGATION OF SONIC BOOMS THROUGH A REAL, STRATIFIED ATMOSPHERE

Sonic boom propagation in a quiet) stratified) lossy atmosphere is the subject of this dissertation. Two questions are considered in detail: (1) Does waveform freezing occur? (2) Are sonic booms shocks in steady state? Both assumptions have been invoked in the past to predict sonic boom waveforms at the ground. A very general form of the Burgers equation is derived and used as the model for the problem. The derivation begins with the basic conservation equations. The effects of nonlinearity) attenuation and dispersion due to multiple relaxations) viscosity) and heat conduction) geometrical spreading) and stratification of the medium are included. When the absorption and dispersion terms are neglected) an analytical solution is available. The analytical solution is used to answer the first question. Geometrical spreading and stratification of the medium are found to slow down the nonlinear distortion of finite-amplitude waves. In certain cases the distortion reaches an absolute limit) a phenomenon called waveform freezing. Judging by the maturity of the distortion mechanism, sonic booms generated by aircraft at 18 km altitude are not frozen when they reach the ground. On the other hand, judging by the approach of the waveform to its asymptotic shape, N waves generated by aircraft at 18 km altitude are frozen when they reach the ground. To answer the second question we solve the full Burgers equation and for this purpose develop a new computer code, THOR. The code is based on an algorithm by Lee and Hamilton (J. Acoust. Soc. Am. 97, 906-917, 1995) and has the novel feature that all its calculations are done in the time domain, including absorption and dispersion. Results from the code compare very well with analytical solutions. In a NASA exercise to compare sonic boom computer programs, THOR gave results that agree well with those of other participants and ran faster. We show that sonic booms are not steady state waves because they travel through a varying medium, suffer spreading, and fail to approximate step shocks closely enough. Although developed to predict sonic boom propagation, THOR can solve other problems for which the extended Burgers equation is a good propagation model.

A Characterization of First-Order Definable Subsets on Classes of Finite Total Orders

We give an explicit and easy-to-verify characterization for subsets in finite total orders (infinitely many of them in general) to be uniformly definable by a first-order formula. From this characterization we derive immediately that Beth's definability theorem does not hold in any class of finite total orders, as well as that McColm's first conjecture is true for all classes of finite total orders. Another consequence is a natural 0-1 law for definable subsets on finite total orders expressed as a statement about the possible densities of first-order definable subsets.