Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

双轴压缩下颗粒物质剪切带的形成与发展

本文采用离散元方法,研究了双轴压缩的颗粒体系在刚性边界约束下,局部剪切带的形成和发展过程,注重分析了细观的体积分数、配位数、颗粒旋转角度等参数以及力链结构形态的演变.并从颗粒体系jamming 相图中J点附近的边壁压强和配位数随体积分数的标度规律出发,分析了剪切带内外的体积分数和配位数的变化.结果表明:剪切带形成于颗粒体系的塑性变形开始阶段,此时体系发生剪胀,颗粒体积分数减小,颗粒体系抵抗旋转的能力降低,开始出现细小剪切带,随着轴向应变的继续,细小剪切带发生连接,最终导致贯穿性优势剪切带形成 关键词： 颗粒物质 力链 双轴压缩 剪切带     

次近邻相互作用对Heisenberg XX链纠缠影响的研究

研究了存在次近邻相互作用(耦合)时Heisenberg XX链的纠缠特性. 结果表明对近邻格点, 随着耦合常数J的变化, 次近邻相互作用的存在可能使其纠缠度增大或者减小; 而对次近邻格点, 引进次近邻相互作用却可以产生纠缠, 并且使其随着|J|的增大而增大. 近邻格点间纠缠存在的临界温度T_c随着J的增大而降低, 次近邻格点间纠缠存在的临界温度T_c随着|J|的增大而升高. 此外对纠缠W态的制备, 次近邻相互作用的存在还使得三量子位情形时W态产生的时刻改变, 而对于四量子位情形却没有影响.     

Role of ligands in the formation, phase stabilization, structural and magnetic properties of α-Fe2O3 nanoparticles

The electrochemical synthesis of alpha Fe₂O₃ nanoparticles was performed using quaternary ammonium salts viz. TPAB, TBAB and TOAB in an organic medium by optimizing current density and molar concentration of the ligand. The role of ligands in the formation of α phase, structure and magnetic properties was investigated in details. The effect of increasing chain length on the particle size confirmed that as the chain length increases from propyl to octyl, the particle size decreases. X-ray diffraction spectra of as prepared samples and TEM analysis confirmed the amorphous nature of iron oxide. TEM showed beads of iron oxide joined together with a size distribution in the range of 6–30 nm. The Mossbauer studies also support this observation that for the lowest particle size, the line width is broader which successively reduces with increase in particle size. Iron oxide capped with TOAB indicated superparamagnetic nature at room temperature. The resultant internal magnetic field of 506 mm/s due to hyperfine splitting clearly established the formation of α-Fe₂O₃ The infrared spectroscopy and pH measurements revealed the binding of tetra alkyl ligand with iron oxide. The IR spectra and the increase in basicity of as prepared samples confirmed the formation of hydrated iron oxide. Above 800°C the spectra indicated only iron oxide. Surface area obtained by BET method was 205 m²/g.     

关于二级相变中热力学物理量突变的分析与自旋链模拟

理论上对二级相变中热容、体膨胀系数、等温压缩系数三个热力学物理量的变化进行了分析,进而使用自旋链模型的基态能量和von Neumann熵随模型参数变化的突变行为对二级相变中这三个物理量的变化所引起的系统序变进行模拟,得到二级相变中热容、体膨胀系数、等温压缩系数的变化是由于系统内部微观上发生关联序变的结果。     

Spin transport in a chain of polygonal quantum rings with Dresselhaus spin-orbit coupling

Using a transfer matrix method, we investigate spin transport through a chain of polygonal rings with Dresselhaus spin-orbit coupling(DSOC). The spin conductance is dependent on the number of sides in the polygons. When DSOC is considered in a chain which also has Rashba spin-orbit coupling(RSOC) of the same magnitude, the total conductance is the same as that for the same chain with no SOC. However, when the two types of SOC have different values, there results a unique anisotropic conductance.     

1H NMR研究β-环糊精与环氧氯丙烷共聚物的反应机理和分子链结构

β-环糊精(cyclodcxtrin)与环氧氯丙烷(Epichlorohydrin)一个系列的共聚物获得,¹H NMR以D₂O或DMSO-d₆为溶剂的测定,其谱峰被归属.共聚合反应机理为以羟基和环氧基为活性中心的亲核取代.当环氧氯丙烷:β-环糊精=n ≤ 3时,聚合物分子链呈现以β-环糊精母体为中心的线状或低枝化状链结构;当n ≥ 5时,分子链出现交联网络结构.n越大(n ≤ 12),分子量越急剧增加,其交联度也越大.     

Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach

This paper deals with the consensus problem for heterogeneous multi-agent systems. Different from most existing consensus protocols, we consider the consensus seeking of two types of agents, namely, active agents and passive agents. The objective is to directly control the active agents such that the states of all the agents would achieve consensus. In order to obtain a computational approach, we subtly introduce an appropriate Markov chain to cast the heterogeneous systems into a unified framework. Such a framework is helpful for tackling the constraints from passive agents. Furthermore, a sufficient and necessary condition is established to guarantee the consensus in heterogeneous multi-agent systems. Finally, simulation results are provided to verify the theoretical analysis and the effectiveness of the proposed protocol.     

Variational Formulation of the Schrödinger Field

The variational formulation of the Schrödinger field was investigated and the applicability of the chain method was analyzed. Using Batalin-Fradkin-Tyutin formalism a gauge invariant theory was constructed.     

用于质子交换膜材料的侧链型磺化聚芳醚酮砜的光谱分析

采用直接缩聚的方法,通过调整氨基单体用量,合成出了系列带有不同氨基含量的聚芳醚酮砜(Am-PAEKS)聚合物,在聚合物侧链上进行后磺化接枝制备出了系列不同磺化度的侧链型磺化聚芳醚酮砜(S-SPAEKS),并且通过调整磺酸基团含量来控制聚合物的磺化度。通过红外光谱(FTIR)和氢核磁谱(1HNMR),对所合成的单体及其聚合物的结构进行了表征,S-SPAEKS红外光谱在1 239和1 060 cm-1处出现了磺酸基团中OSO的特征吸收峰,氢核磁谱中1.64 ppm处出现了处于烷基链中间位置的两个氢(—CH₂—CH₂—)化学位移,证明得到了S-SPAEKS聚合物。经热失重分析发现,聚合物中磺酸基团的脱落温度都高于240 ℃,聚合物主链降解温度都高于450 ℃。研究表明,该系列聚合物具有良好的热性能,可以用作质子交换膜材料。