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.     

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.     

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.     

New developments and directions in the area of elastomers and rubberlike elasticity

There are number of important developments in the area of elastomeric polymers, including (i) network chains of controlled stiffness, (ii) model elastomers (including dangling-chain networks), (iii) fluorosiloxane elastomers, (iv) new thermoplastic elastomers, (v) other new elastomers, (v) bimodal network chain-length distributions, (vi) cross linking in solution or in a state of deformation, and (vii) gel collapse. Interesting elastomeric composites include those with (i) in-situ generated ceramic-like particles, (ii) ellipsoidal fillers, (iii) clay-like layered fillers, (iv) polyhedral oligomeric silsesquioxane (POSS) particles, (v) porous fillers, (vi) elastomeric domains modifying ceramics, and (vii) controlled interfaces. New characterization techniques are being developed for elastomers, and there have been new developments in elasticity theory and in elastomer processing. Some examples of societal aspects of relevance are (i) synthesis of elastomers in environmentally-friendly solvents, (ii) biosynthesis, (iii), recyclability, (iv) improved adhesion to tire cords, and (v) better barrier properties in anti-terrorism clothing. Educational topics include curriculum development, and mobile laboratories for elastomer experiments and demonstrations.     

Exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling is present on an equal footing, is studied within the tunable extended coherent states. The eigenvalues and eigenstates are therefore obtained exactly. Surprisingly, the entanglement entropy in the ground-state is found to jump suddenly with the coupling strength. The first-order quantum phase transition can be detected by level crossing of the ground state and the first excited state, which is however lacking in the original linear quantum Rabi model. Performing the first-order approximation in the present theory, we can derive closed-form analytical results for the ground-state. Interestingly, it agrees well with the exact solutions up to the ultra-strong coupling regime in a wide range of model parameters. The spectral collapses when the absolute value of the nonlinear coupling strength approaches to twice the cavity frequency is observed with the help of new solutions in the limits.