A linear potential and phonons in sodium

A simple form for the pseudo-potential is suggested for metallic sodium to investigate its properties. The computed values of the phonon frequencies in symmetry directions established an excellent accord with the measurements. A calculation of binding energy, compressibility and the elastic constants also highlighted the success of the proposed simple model- potential.     

Linear potential and phonons in calcium and strontium

The success recently achieved by the linear form of electron-ion pseudopotential in the case of alkalies, Al and Pb has led to further apply it to the bivalent metals, Ca and Sr, for the calculation of phonon propagation along the three symmetry directions. The results obtained compare well with the value based on the more sophisticated formulations of Animalu and Moriarty. The reliability of these results is confirmed through an excellent reproduction of the experimental binding energy and compressibility. A succesful prediction of elastic constants further highlights the usefulness of the present simple approach.     

新型八边形谐振环金属线复合周期结构左手材料奇异性质研究

通过实验及仿真研究了基于C环的新型八边形开口谐振环金属线复合周期结构左手材料.以金属铜八边形谐振环(SRRs)为基本单元的周期结构负磁导率材料,与闭口环(CSRRs)结果对比发现八边形谐振环能产生很好的谐振效果即能产生负磁导率;复合结构仿真结果显示,八边形谐振环金属线复合结构实现负折射具有可行性.设计、制作并实验和仿真研究了两种尺寸的八边形谐振环金属线复合周期结构左手材料,实验结果显示,分别在9.8—15GHz和9.5—15GHz出现良好负折射效应,表明小尺寸材料负折射频段较宽但整体能量透过率较小.通过与尺寸相近的传统C环样品实验对比发现八边形样品损耗较大,但其负折射区域能量分布比例较大,具有一定的优越性.该研究对新型周期结构左手材料的研究、设计和研制具有重要的科学意义,在国防、通信等领域也具有广阔的应用前景.     

Isobaric expansion coefficient and isothermal compressibility for a finite-size ideal Fermi gas system

Due to quantum size effects (QSEs), the isobaric thermal expansion coefficient and isothermal compressibility well defined for macroscopic systems are invalid for finite-size systems. The two parameters are redefined and calculated for a finite-size ideal Fermi gas confined in a rectangular container. It is found that the isobaric thermal expansion coefficient and isothermal compressibility are generally anisotropic, i.e., they are generally different in different directions. Moreover, it is found the thermal expansion coefficient may be negative in some directions under the condition that the pressures in all directions are kept constant.     

The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case

We show how averaging defines an Ehresmann connection whose holonomy is the classical adiabatic angles which Hannay defined for families of completely integrable systems. The averaging formula we obtain for the connection only requires that the family of Hamiltonians has a continuous symmetry group. This allows us to extend the notion of the Hannay angles to families of non-integrable systems with symmetry. We state three geometric axioms satisfied by the connection. These axioms uniquely determine the connection, thus enabling us to find new formulas for the connection and its curvature. Two examples are given.     

Negative linear compressibility of generic rotating rigid triangles

The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed.It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility(NLC), that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features(i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them) and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.     

On a new hyperchaotic system

A new hyperchaotic system is presented, which has two large positive and one small negative Lyapunov exponent over a large range of parameters. As a consequence, system orbits strongly expand in some directions but rapidly shrink in some other directions. These strong expansions and shrinking lead the system orbits to be more disordered and random. Bifurcation and Poincaré-map analyses further show that the system has very rich bifurcations in different directions and extremely complicated dynamics overall. Spectral analysis shows that the system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.     

On the phonon frequencies of copper in off symmetry directions

A previously proposed five parameter phenomenological screened shell model for the lattice dynamics of cubic metals is applied to compute the phonon frequencies of copper in the off-symmetry directions. The theoretical results are compared with the experimental findings for the first time. It has been pointed out that a model which gives excellent results in the symmetry directions may not necessarily reproduce similar results in the off-symmetry directions.     

Optical tug-of-war tweezers:shaping light for dynamic control of bacterial cells(Invited Paper)

We design and demonstrate new types of optical tweezers with lateral pulling forces that allow full control of biological samples with complex geometric shapes.With appropriate beam shaping,the dual tug-of-war tweezers effectively hold and stretch elongated biological objects of different sizes,and the triangular tug-of-war tweezers with threefold rotational symmetry steadily hold asymmetric objects in the plane of observation and exert stretching forces along three directions.We successfully apply these tweezers to manipulate microparticles and bacterial cells in aqueous media.     

Stochastic least-action principle for the incompressible Navier-Stokes equation

We formulate a stochastic least-action principle for solutions of the incompressible Navier-Stokes equation, which formally reduces to Hamilton’s principle for the incompressible Euler solutions in the case of zero viscosity. We use this principle to give a new derivation of a stochastic Kelvin Theorem for the Navier-Stokes equation, recently established by Constantin and Iyer, which shows that this stochastic conservation law arises from particle-relabelling symmetry of the action. We discuss issues of irreversibility, energy dissipation, and the inviscid limit of Navier-Stokes solutions in the framework of the stochastic variational principle. In particular, we discuss the connection of the stochastic Kelvin Theorem with our previous “martingale hypothesis” for fluid circulations in turbulent solutions of the incompressible Euler equations.     

广义Birkhoff系统的Birkhoff对称性与守恒量

研究广义Birkhoff系统的Birkhoff对称性问题,并给出此情形下相应的守恒量.将力学系统的等效Lagrange函数的一个定理推广到广义Birkhoff系统,证明了在一定条件下与两组动力学函数B,R_μ,Λ_μ和B,R_μ,Λ_μ分别给出的广义Birkhoff方程相关联的矩阵Λ 关键词： 广义Birkhoff系统 Birkhoff对称性 守恒量 矩阵迹     

A pure geometric approach to stellar structure

The present work represents a step in dealing with stellar structure using a pure geometric approach. Geometric field theory is used to construct a model for a spherically symmetric configuration. In this case, two solutions have been obtained for the field equations. The first represents an interior solution which may be considered as a pure geometric one in the sense that the tensor describing the material distributions is not a phenomenological object, but a part of the geometric structure used. A general equation of state for a perfect fluid, is obtained from, and not imposed on, the model. The second solution gives rise to Schwarzschild exterior field in its isotropic form. The two solutions are matched, at a certain boundary, to evaluate the constants of integration. The interior solution obtained shows that there are different zones characterizing the configuration: a central radiation dominant zone, a probable convection zone as a physical interpretation of the singularity of the model, and a corona like zone. The model may represent a type of main sequence stars. The present work shows that Einstein’s geometerization scheme can be extended to gain more physical information within material distribution, with some advantages.     

Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry

Given a finite dimensional C ^*-Hopf algebra H and its dual Ĥ we construct the infinite crossed product and study its superselection sectors in the framework of algebraic quantum field theory. is the observable algebra of a generalized quantum spin chain with H-order and Ĥ-disorder symmetries, where by a duality transformation the role of order and disorder may also appear interchanged. If is a group algebra then becomes an ordinary G-spin model. We classify all DHR-sectors of – relative to some Haag dual vacuum representation – and prove that their symmetry is described by the Drinfeld double . To achieve this we construct localized coactions and use a certain compressibility property to prove that they are universal amplimorphisms on . In this way the double can be recovered from the observable algebra as a universal cosymmetry. Received: 4 September 1995\,/\,Accepted: 3 December 1996     

A Gallavotti-Cohen-Evans-Morriss Like Symmetry for a Class of Markov Jump Processes

We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but it concerns a different functional of the stochastic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where time-integrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to time-reversal if stochastic trajectories are grouped appropriately.     

Influence analysis of symmetry on capsule in six-cylinder-port hohlraum

We have investigated the flux symmetry on the capsule in a six-cylinder-port hohlraum for improving the design of the hohlraum. The influence factors of drive symmetry on the capsule in the hohlraum are studied, including laser power,laser beams arrangement, hohlraum geometric parameters, plasma condition, capsule convergence, etc. The x-ray radiation flux distribution on the capsule is obtained based on the three-dimensional view factor model. In the six-cylinder-port hohlraum, the main drive asymmetry is the C40 mode asymmetry. When the C40 mode asymmetry approaches zero, the drive symmetry on the capsule is optimal. Our results demonstrate that in order to have a high flux symmetry on the capsule in the laser main-pulse stage, more negative initial C40 modes are needed, which can be realized by adjusting the hohlraum geometry parameters. The hohlraum with column length L_H = 4.81 mm has an optimal symmetry in the laser main-pulse stage.     

Static perfect fluids with Pant-Sah equations of state

We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein’s equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and “rediscovered” by Rosquist and by the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically realistic for suitable parameter ranges. The equations of state can be characterized geometrically by the property that the 3-metric on the static slices, rescaled conformally with the fourth power of any linear function of the norm of the static Killing vector, has constant scalar curvature. This local property does not require spherical symmetry; in fact it simplifies the proof of spherical symmetry of asymptotically flat solutions which we recall here for the Pant-Sah equations of state. We also consider a model in Newtonian theory with analogous geometric and physical properties, together with a proof of spherical symmetry of the asymptotically flat solutions. Supported by grants FIS2006-05319 (Ministerio de Educación y Tecnología) and SA010C0 (Junta de Castillia y León).     

Negative-refractive bicrystal with broken symmetry produces asymmetric electromagnetic fields in guided-wave heterostructures

Heterostructure arrangements of uniaxial bicrystals have been discovered to produce electromagnetic fields with asymmetric distributions in guide wave structures. The property behind this remarkable phenomenon is the broken crystalline symmetry which allows the new physics to be seen in unsymmetric distributions. Here the theory behind this phenomenon is presented, numerical calculations are performed using an ab initio anisotropic Green's function approach, and the results provided at 10 GHz for a realistic crystal system with nominal permittivity of 5. Asymmetric distributions seen here are one facet of the broken symmetry property which generates negative refraction for impinging waves on a bicrystal.     

基于对称特征相似性的图像识别算法研究

研究了一类微小生物——线虫的图像识别算法。首先对图像进行边缘检测、二值化和去除干扰点等操作,得到线虫的身体轮廓线;然后利用其身体的对称特征,通过比较相邻线段的相似性实现对线虫的识别及对干扰的区分。实验结果表明,此算法优于骨架法、面积法等典型图像识别方法,对线虫的检测和定位具有很高的准确度和快速性,并可应用于其它具有对称特性的微小生物的图像识别。     

Correlation of atomic cluster symmetry and glass-forming ability of metallic glass

Local structures play a crucial role in glass formation and properties. In addition to topological short-range order, the geometric property of site symmetry is another important but less known characteristic of local structures. It is shown that the observed sharp increase of glass forming ability of Ce70-xAl10Cu20Cox upon Co addition is correlated with a dramatic increase of Al site symmetry, as reflected by decreasing quadrupole frequency measured by 27Al NMR. The result is consistent with the structure model of Al-centered icosahedral clusters as the predominant structural building blocks.