基于哈密顿体系的平面无限解析元

在有限元法中,无限域的问题不便于处理求解。但无限域往往可以由规则的无限外域再加上有限的局部域组成。将无限域问题中的有限局部域用有限元法处理,在规则的无限外域中建立极坐标系,将规则无限域问题导向哈密顿体系,利用本征向量展开的方法,推导出一种新的半解析无限解析元,其刚度阵是精确的。该单元可用常规方法作为一个超级有限单元与有限的局部域连接。数值计算结果表明,该单元具有精度高,应用方便,数据处理非常简单的特点。对无限域问题的数值求解有重要意义。该方法可推广到三维无限域问题中。     

Unified Theory of Fundamental Interactions

Based on local gauge invariance, four different kinds of fundamental interactions in nature are unified in a theory which has SU(3)C( )SU SU(2)L( )U(1)( )s Gravitational Gauge Group gauge symmetry. In this approach,gravitational field, like electromagnetic field, intermediate gauge field, and gluon field, is represented by gauge potential.Four kinds of fundamental interactions are formulated in the similar manner, and therefore can be unified in a direct or semi-direct product group. The model discussed in this paper is a renormalizable quantum model and can be regarded as an extension of the standard model to gravitational interactions, so it can be used to study quantum effects of gravitational interactions.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

向列相液晶沿面到垂面排列转变的分子场理论

以摩擦基板间的液晶薄层为研究对象,用分子场理论研究了向列相液晶分子排列转变行为.分子质心固定在简单立方晶格的格点上.液晶由极性分子构成,与基板相接触的一层分子同时受到色散和极性两类表面作用.通过自洽的数值计算,获得3种相图,清楚地展示了摩擦基板间向列相出现的从高温沿面到低温垂面排列的转变;获得实现这类转变所需要的两类表面作用的参数范围.结果表明:基板的摩擦会改变基板表面色散作用,但不会影响基板表面极性作用;表面极性相互作用能引起基板间向列相液晶发生沿面到垂面排列转变.     

P同位素的质子滴线核研究

研究了在相对论平均场近似下P同位素的滴线核的性质,首先在理论上探讨了25P作为P的滴线核存在的可能性及其可能具有的质子晕结构,然后给出了在兰州放射性束流装置上25P的实验鉴别结果. Great progress was made on the study of P isotope both in theory and in experiments, but the final conclusion about the dripline of P isotope has not been made. In this article the properties of P isotope was studied in the frame work of relativistic mean field (RMF). First the probability of 25P as the dripline nuclei of P isotope and the proton halo structure of 25P was discussed, and then the RIBLL experiental result of 25P is presented.     

Classical and quantum wormholes with tachyon field

The wormhole equations are presented in the presence of tachyon field. Specializing at some values of ω(the ratio of pressure to energy density), we find a family of classical and quantum wormhole solutions.     

Collapse and revival of a single—Cooper—pair box in a single—mode quantized field

We study the quantum dynamics of a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We demonstrate that under weak damping of the quantized field, the collapse-revival phenomena can exist in this system, and the oscillations of the collapse and revival depend sensitively on the initial state of the single-mode quantized field and the damping rate κ. We also demonstrate that this system can show the beats phenomena.     

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrödinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.     

Elastic analysis of a mode II crack in a decagonal quasi—crystal

The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.     

A design of novel type superconducting magnet for super—high field functional magnetic resonance imaging by using the harmonic analysis method of magnetic vector potentials

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_m/B₀ in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.