The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to ± or there are eigenvalues converging to those of the torus. This is shown to be true in general for collapsing circle bundles with totally geodesic fibers. Using the Hopf fibration we use this fact to compute the Dirac eigenvalues on complex projective space including the multiplicities.Finally, we show that there are 1-parameter families of Riemannian nilmanifolds such that the Laplacian on functions and the Dirac operator for certain spin structures have constant spectrum while the Laplacian on 1-forms and the Dirac operator for the other spin structures have nonconstant spectrum. The marked length spectrum is also constant for these families.     

Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.     

原位微区同步辐射X射线荧光和近边吸收谱研究铅耐受细菌吸附-转化铅机理

为了从微观水平研究细菌生物吸附及转化铅机理,利用原位微区同步辐射X射线荧光(μ-SRXRF)及X射线吸收近边结构谱( XANES)研究云南兰坪铅锌矿区农田土壤样品中筛选的铅耐受性细菌吸附铅的分布特征及铅形态转化规律。土壤中具有铅耐受性的菌株主要为Arthrobacter sp.属(节杆菌属),采用μ-SRXRF对其吸附铅的含量进行快速简单直接分析,部分细菌吸附铅的含量高达5925μg/g,富集系数达14.8。XANES结果表明,细菌吸附 Pb 后存在形态为 PbS、(C17 H35 COO)2Pb 和 Pb5(PO4)3Cl 分别占58.0％,22.2％和19.8％,与培养基本身以有机态为主的Pb形态有明显差异,表明培养基中铅被细菌吸附后有向硫化物转化的趋势,这为研究重金属生物有效性的影响因素提供了实验参考。     

Relaxation Oscillation Enhancement and Coherence Collapse in Semiconductor Lasers with Optical Feedback

The dynamic characteristics of a semiconductor laser with optical feedback are strongly dependent on the injection current and the reflectivity and position of the external feedback reflector. We investigated the relaxation oscillation enhancement and coherence collapse state of the laser oscillation based on the laser rate equations. It is well known that laser output power jumps with increase of the injection current due to external mode transition. But here for the first we time demonstrate the existence of a chaotic scenario within successive laser power jumps. The results calculated by numerical simulations based on the rate equations are compared with those of the experiments and good coincidence between them is found.     

锚杆支护的神经网络设计系统及其应用

本文简要地概括了锚杆支护设计理论存在的局限性。强调锚杆支护理论应用必须考虑地下工程的类型。为此,作者将地下工程划分为3类,指出每一类地下工程特性及其支护设计应遵循的准则,第3类采场巷道工程的锚杆支护设计应以工程类比和设计经验为主;并介绍了作者已经开发的锚杆支护神经网络设计系统。     

流体动力润滑油膜破裂的热力学失稳机理

分析了流体动力学润滑过程中的热量传递及对润滑剂流变特性的影响,得出了流体动力润滑油膜发生热力学失稳的条件,建立了描述润滑剂温度非牛顿效应的本构方程数值计算结果表明,由于温度的影响,流体动力润滑油膜存在最大承载能力;在临界状态,微小的扰动将会引起油膜失稳而丧失承载能力。初步揭示了流体动力学力润滑膜破失效的内在力学机制。     

Particle scattering factor of pearl necklace chains

The particle scattering behaviour of a pearl necklace chain is derived. The chain is composed of sphere-like pearls, separated by rod-like segments of fixed length, which have no angular restrictions. By calculating several series of model scattering curves, the important structural features are retrieved. The model is believed to be useful in interpreting intermediate structures of collapsing macromolecules or polyelectrolytes. A first application to a shrinking polyelectrolyte coil generated by molecular dynamic simulations (Limbach and Holm, J.Phys.Chem. 2003) is presented and used to discuss the potentials and limits of the model.     

基于整体易损性的猫头型输电塔抗倒塌能力分析

作为输电线路的主要组成部分,输电塔结构对地震作用非常敏感。本文以中国输电线路中常采用的猫头型输电塔结构为例,开展了输电塔结构整体抗地震倒塌能力分析。以某一实际单回路3个不同高度的直线塔为研究对象,基于OpenSees平台建立输电塔结构三维有限元模型,定义4个倒塌极限状态依据,选取20条远场地震动记录,采用增量动力分析(IDA)方法,得到4个倒塌极限状态依据下输电塔结构的倒塌点,进一步获得输电塔结构的倒塌易损性曲线及其潜在失效杆件,并评估其在不同水平设计地震作用下的倒塌裕度比。研究结果表明,猫头型输电塔的地震损伤主要集中在塔头位置;随着塔体高度的增高,猫头型输电塔抗地震倒塌能力减弱;猫头型输电塔在巨震作用下存在一定的倒塌风险。     

Solvent‐ and counterion‐specific swelling behavior of poly(acrylic acid) gels

The collapse of alkali metal poly(acrylate) (PAAM) gels was investigated for various water/organic solvent mixture systems: methanol (MeOH), ethanol (EtOH), 2‐propanol (2PrOH), t‐butanol (tBuOH), dimethyl sulfoxide (DMSO), acetonitrile (AcN), acetone, tetrahydrofuran (THF), and dioxane. In order to ascertain the counterion specificity in the swelling behavior, four kinds of alkali metal counterions were used: Li⁺, Na⁺, K⁺, and Cs⁺. Remarkable solvent and counterion specificities were observed for every counterion species and every solvent system, respectively. For example, in aqueous EtOH the dielectric constants (D_cr) at which collapse occurred were in the order PAACs < PAALi < PAAK < PAANa. On the other hand, the D_cr at which PAALi gel collapsed increased in the order tBuOH < dioxane < THF < MeOH < 2PrOH < EtOH < acetone < AcN < DMSO, where the D_cr ranged from about 39 to about 67. This was in contrast to our previous observation for a partially quaternized poly(4‐vinyl pyridine) (P4VP) gel, which collapsed in a much narrower D_cr region in similar mixed solvents. The present solvent‐ and counterion‐specific collapses are discussed on the basis of solvent properties such as the dielectric constant and Gutmann's donor number and acceptor number of a pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2791–2800, 2000     

Coil‐Globule Collapse in Flexible Macromolecules

The transition of a solvated flexible macromolecular chain from random coil behavior in the θ‐state to a globular compact form in the collapsed state has been the subject of extensive theoretical and experimental studies. Most of the coil‐globule transition studies of macromolecules have concentrated on the prototypical polystyrene‐cyclohexane system. However, chain contractions reported in this system have been around 75% of those in the unperturbed θ‐state. This relatively small decrease in size does not satisfy the criterion for a densely packed, collapsed globule. Experimentally, the collapse from a coil to a true compact globular state has now been established for two flexible macromolecules: poly(N‐isopropylacrylamide) in water and poly(methyl methacrylate) in various solvents. In this contribution, we review recent theoretical studies covering phenomenological and Langevin models as well as computer simulations. In addition, we outline recent experimental studies of the coil‐globule transition of various flexible polymers, copolymers, and polyelectrolytes.

Expansion factor, αequation/tex2gif-stack-1.gif, versus temperature for NaPSS in 4.17 M aqueous NaCl solution. (•): NaPSS‐1, (○): NaPSS‐2.