Topology and electronic structure of nanotube junctions of tetrapod shape

We propose a series of carbon nanostructures in the shape of tetrapod as a kind of three-dimensional junction for carbon nanotubes. The tetrapod junctions are such open networks that are made of sp² carbon atoms only, have negative Gaussian curvature, and connect four nanotubes together. We define the structure of standard tetrapod junctions, the simplest one, that have 12 heptagons other than hexagons and have the T_d symmetry.Our tight-binding energy-band calculations for the standard tetrapod junctions of smaller sizes show that their electronic property mainly depends on one particular topological factor: the junctions having a carbon atom in the center of each triangular face of tetrahedron exhibit metallic band structure while the junctions having a benzene ring in the center of the faces are semiconductors. We also find that tetrapod junctions connecting (6,0) nanotubes exhibit a flat band near the Fermi energy in a particular momentum region. The origin of the flat band states can be figured out from the wavefunction distribution. We also show the possibility to extend the standard tetrapod junctions to some non-standard ones that can connect nanotubes of different kinds and/or radii.     

翅片长度对纵向翅片扁管换热器换热性能的影响

纵向翅片扁管换热器是一种新型换热器。气体沿扁管轴向方向流动,与管内介质的流动路径平行,可强化传热,减少气侧阻力,不易积灰结垢,维护方便。利用数值模拟方法,以纵向翅片扁管换热器为研究对象,分析翅片长度对换热性能的影响,对换热器的翅片长度进行优化。研究表明,不同进口风速对应不同的有效纵向翅片长度。随着进口风速的增大,翅片的有效长度越大。     

A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients

This paper is devoted to the analysis of measure-valued solutions to a nonlinear structured population model given in the form of a nonlocal first-order hyperbolic problem on R⁺. We show global existence and Lipschitz continuity with respect to the model ingredients. In distinction to previous studies, where the L¹ norm was used, we apply the flat metric, similar to the Wasserstein W₁ distance. We argue that analysis using this metric, in addition to mathematical advantages, is consistent with intuitive understanding of empirical data. Lipschitz continuous dependence with respect to the model coefficients and initial data and the uniqueness of the weak solutions are shown under the assumption on the Lipschitz continuity of the kinetic functions. The proof of this result is based on the duality formula and the Gronwall-type argument.     

Flat orbits and kernels of irreducible representations of the group algebra of a completely solvable Lie group

We show that the kernel of an irreducible unitary representation π of the group algebra L¹(G) of a completely solvable Lie group G is given by the functions, whose abelian Fourier transform vanish on the Kirillov orbit Oπ of π if and only if this orbit Oπ is flat. This is a generalization of a result obtained before for nilpotent Lie groups.     

基于光子晶体光纤四波混频效应的波长转换研究

研究了光子晶体光纤中的四波混频效应及其波长转换.采用长度为25 m的高非线性色散平坦光子晶体光纤,当泵浦功率为19.8 dBm时,得到100 nm的转换带宽和－20 dB的最大转换效率.实验结果表明,当信号功率低于四波混频阈值时,两路不同波长的信号同时输入产生的四波混频效应互不影响.     

Flat RF coils in static field gradient nuclear magnetic resonance

The use of flat RF coils allows considerable gains in the sensitivity of static field gradient (SFG) nuclear magnetic resonance (NMR) experiments. In this article, this effect is studied theoretically as well as experimentally. Additionally, the flat coil geometry has been studied theoretically depending on magnetic field gradient, pulse sequence and amplifier power. Moreover, detecting the signal directly from the free induction decay (FID) turned out to be quite attractive for STRAFI-like microimaging experiments, especially when using flat coils. In addition to wound rectangular flat coils also spiral flat coils have been developed which can be manufactured by photolithography from printed circuit boards.     

Flux modulated flat band engineering in square-kagomé ladder network

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagomé ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical boundary created by the site with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.     

Numerical study of flow-induced oscillations of two rigid plates elastically hinged at the two ends of a stationary plate in a cross-flow

The flow-induced oscillation (FIO) of bluff bodies is commonly encountered in the fluid structure interaction (FSI) problems. In this study, we use an unstructured moving grid strategy and simulate the FIO of two rigid plates, which are elastically hinged at the two ends of a fixed flat plate in a cross-flow. We use a hybrid finite-element-volume (FEV) method in an arbitrary Lagrangian–Eulerian (ALE) framework to study FIO of the two hinged plates. The current simulations are carried out for wide ranges of flow Reynolds number (50–175), spring stiffness coefficient, and the two hinged plates' moment of inertia magnitudes. The influences of these parameters are investigated on the magnitudes of maximum deflection angle, the amplitude of oscillation, the total lift and drag coefficients, and so on. The study is also carried out in the transition period to describe the in-phase and out-of-phase angular oscillations occurring for the two elastically hinged plates with respect to each other. After the transition period, the two hinged plates eventually arrive to a similar periodic oscillation; however, with some phase lags. We find that the achieved phase lag is equal to the phase lag between the two pairs of flow vortices, which are alternatively shed into the flow from the upper and lower hinged plates. Similar to past FIO problems, the current model also exhibits two important lock-in and phase-switch FSI phenomena; however, in angular directions. There is a phase jump of approximately 170° between the aerodynamic lift coefficient and angular oscillations of hinged plates, which nearly occurs in the middle of lock-in region. Indeed, our literature review shows that this is the first time to report the phase-switch phenomenon in angular oscillations of three-element bluff bodies in a FSI problem.     

特征模对环的刻划

设Ｒ是一个环，Ｍ是一个左Ｒ摸，Ｍ＊＝ＨｏｍＺ（Ｍ，Ｑ／Ｚ）为Ｍ的特征模．Ｒ．Ｒ．Ｃｏｌｂｙ和Ｔ．Ｊ．Ｃｈｏａｔｈａｎ等人利用特征模对ＩＦ环、凝聚环、Ｎｏｅｔｈｅｒ环、Ａｒｔｉｎ环作出了一些非常好的刻划．本文利用特征模对更为广泛的一些环作出了较有意义的刻划．     

Solution of a flat elliptical crack in an electrostrictive solid

Based on the assumption that the elastic strain of electrostrictive materials is a higher-order small quantity, this paper studies the 3D problem of an infinite electrostrictive solid with a flat elliptical crack which is electrically permeable. According to existing solutions of similar problems in pure elastic materials, with the displacement function method, we first derived explicit expression for displacement potential function and obtained stress field near the crack and open displacement of crack surface. Then, the general solution for the stress intensity factor was derived, and the corresponding solutions were also presented for a penny-shaped crack and a permeable line-crack as two special cases of the present problem. Finally, numerical results were given to discuss the effect of environment at infinity and electric field inside the crack on the stress-intensity factors.