The local geometry of compact homogeneous Lorentz spaces

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding Lie algebra contains a direct summand isomorphic to the two-dimensional special linear algebra or to a twisted Heisenberg algebra, Zeghib also described the geometric structure of the manifolds. Using these results, we investigate the local geometry of compact homogeneous Lorentz spaces whose isometry groups have non-compact connected components. It turns out that they all are reductive. We investigate the isotropy representation and curvatures. In particular, we obtain that any Ricci-flat compact homogeneous Lorentz space is flat or has compact isometry group.     

On quantum symmetries of compact metric spaces

An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. In this study, we show that an isometric action in this sense has the following additional property: the corresponding action on the algebra of continuous functions on $X$ by the convolution semigroup of probability measures on the quantum group contracts Lipschitz constants. In other words, it is isometric in another sense due to Li, Quaegebeur, and Sabbe, which partially answers a question posed by Goswami. We also introduce other possible notions of isometric quantum actions in terms of the Wasserstein $p$-distances between probability measures on $X$ for $p\ge 1$, which are used extensively in optimal transportation. Indeed, all of these definitions of quantum isometry belong to a hierarchy of implications, where the two described above lie at the extreme ends of the hierarchy. We conjecture that they are all equivalent.     

用声波速度确定骨组织弹性参数

本文用超声方法确定密质骨的弹性特征,其基本原理是基于弹性波理论中的Christoffel方程。本文应用液浸、声波穿透技术,对牛胫骨样品中一些特殊入射方向的声波速度进行了测试,利用固体中沿任意方向的弹性波传播速度与材料的弹性系数间的关系,通过计算机编程反演出具有六方晶体对称结构的密质骨组织的5个独立弹性常数。结果与相关文献中其它方法所得结果一致。     

Hadrons in compact stars

We discuss β-equilibrated and charge neutral matter involving hyperons and {ie817-1} condensates within relativistic models. It is observed that populations of baryons are strongly affected by the presence of antikaon condensates. Also, the equation of state including {ie817-2} condensates becomes softer resulting in a smaller maximum mass neutron star     

Volumes of compact manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some parameters, set up a metric, which induces a volume element, and perform the integration for the adequate range of the parameters; in most cases our manifolds will be either spheres or (twisted) products of spheres, or quotients of spheres (homogeneous spaces).Our results should be useful in several physical instances, as instanton calculations, propagators in curved spaces, sigma models, geometric scattering in homogeneous manifolds, density matrices for entangled states, etc. Some flag manifolds have also appeared recently as exceptional holonomy manifolds; the volumes of compact Einstein manifolds appear in string theory.     

Optimized prefactored compact schemes

The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and dissipation errors. In this paper we describe a strategy for developing high-order accurate prefactored compact schemes, requiring very small stencil support. These schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes. The prefactorization strategy splits the central implicit schemes into forward and backward biased operators. Using Fourier analysis, we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components. This ensures that when the forward and backward stencils are added, the original central compact scheme is recovered. To extend the resolution characteristic of the schemes, an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh. The resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth- and eighth-order compact schemes making them more suitable for high-resolution numerical simulations in gas dynamics and computational aeroacoustics. The efficiency, accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems.     

Nanotaper for compact mode conversion

We propose and demonstrate an efficient coupler for compact mode conversion between a fiber and a submicrometer waveguide. The coupler is composed of high-index-contrast materials and is based on a short taper with a nanometer-sized tip. We show that the micrometer-long silicon-on-insulator-based nanotaper coupler is able to efficiently convert both the mode field profile and the effective index, with a total length as short as 40 microm. We measure an enhancement of the coupling efficiency between an optical fiber and a waveguide by 1 order of magnitude due to the coupler.     

The Finslerian compact star model

We construct a toy model for compact stars based on the Finslerian structure of spacetime. By assuming a particular mass function, we find an exact solution of the Finsler–Einstein field equations with an anisotropic matter distribution. The solutions are revealed to be physically interesting and pertinent for the explanation of compact stars.     

Eye-safe compact scanning LIDAR technology

A 1.5-μm eye-safe, 3-D scanning, and compact Mie LIght Detection and Ranging (LIDAR) is presented. The transmitter of the LIDAR is based on a KTA optical parameter oscillator (OPO) resonator. For detecting return signals, an InGaAs APD is used. The all solid-state OPO laser transmitter has the feature of small volume and lightweight, which allows a 165-lb compact eye-safe scanning LIDAR to be constructed. A system simulation using our own model was conducted to direct the system development. A method to solve the problem with small active area APD detectors was developed and described. The preliminary field-test measurement results indicated that the LIDAR has the capability to detect aerosols and clouds in lower atmospheres up to three dimensions.     

Spatially compact space-times that shrink

A criterion is given under which essential singularities occur in any space-time having compact spacelike slices whose size (measured by a parallelly propagated frame) shrinks to zero, and where there is a timelike congruence with incomplete curves.     

Molecular and compact four-quark states

We study charmonium (c(c)n(n)), bottomonium (b(b)n(n)) and exotic (cc(n)(n) and bb(n)(n)) four-quark states by means of a standard non-relativistic quark potential model. We look for possible bound states. Among them we are able to distinguish between meson-meson molecules and compact four-quark states.     

紧凑重频PFN-Marx脉冲发生器

研制了一台紧凑重频脉冲形成网络(PFN)-Marx脉冲发生器,由PFN-Marx发生器、脉冲充电单元、重频触发单元等组成。PFN-Marx发生器模块采用全电感隔离,直径为480 mm,长度为700 mm。脉冲充电单元采用中储电容加脉冲变压器方法,单次充电可以满足10次输出。重频触发单元采用变压器和磁开关一体化设计的全固态Marx发生器技术,输出电压大于50 kV,前沿小于100 ns。脉冲发生器早期输出电参数为单次10 GW,脉冲宽度100 ns,前沿10 ns,阻抗40 。重频工作时输出功率7 GW,频率5 Hz。后期调整后电参数更改为单次10 GW,脉冲宽度70 ns,前沿10 ns,阻抗50 。重复频率工作时稳定输出功率8 GW,频率10 Hz,单串10个脉冲。初步的应用研究中,利用改进后的平台,在5 GW条件下驱动磁控管获得了S波段约1 GW的微波输出。     

Continuous melting of compact polymers

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by Flory in 1956 [Proc. R. Soc. London A 234, 60 (1956)]]. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition and compute exact values of critical exponents at the transition point.     

Molecular and compact four-quark states

We study charmonium （ccnn）,bottomonium （b bnn） and exotic （ccnn and bbnn） four-quark states by means of a standard non-relativistic quark potential model.We look for possible bound states.Among them we are able to distinguish between meson-meson molecules and compact four-quark states.     

Spectral subspaces for compact actions

We study spectral subspaces under the action of compact groups on Banach spaces, with particular reference to operator algebras.