Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole

The generalized 2D problem of icosahedral quasicrystals containing an elliptic hole is considered by using the extended Stroh formalism.The closed-form solutions for the displacements and stresses are obtained under general loading conditions.The solution of the Griffith crack problem as a special case of the results is also observed.The stress intensity factor and strain energy release rate are given.The effect of the phonon–phason coupling elastic constant on the mechanical behavior is also discussed.     

Elliptic hole in octagonal quasicrystals

The stress potential function theory for plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method (Lekhnitskii method) for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.     

Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading

Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode {\rm II} Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.     

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.     

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 Dugdale–Barenblatt model for a strip with a semi-infinite crack embedded in decagonal quasicrystals

The present study is to determine the solution of a strip with a semi-infinite crack embedded in decagonal quasicrystals, which transforms a physically and mathematically daunting problem. Then cohesive forces are incorporated into a plastic strip in the elastic body for nonlinear deformation. By superposing the two linear elastic fields, one is evaluated with internal loadings and the other with cohesive forces, the problem is treated in Dugdale-Barenblatt manner. A simple but yet rigorous version of the complex analysis theory is employed here, which involves conformal mapping technique. The analytical approach leads to the establishment of a few equations, which allows the exact calculation of the size of cohesive force zone and the most important physical quantity in crack theory: stress intensity factor. The analytical results of the present study may be used as the basis of fracture theory of decagonal quasicrystals.     

Multiple slow light bands in photonic crystal coupled resonator optical waveguides constructed with a portion of photonic quasicrystals

Coupled resonator optical waveguides (CROWs) in complex two-dimensional (2D) photonic crystals (PCs) constructed with a portion of 12-fold photonic quasicrystals (PQs) are proposed. We show that enhanced transmission and slow light can be simultaneously achieved in such waveguides as well as general CROWs. Moreover, due to higher degree of flexibility and tunability of PQs for defect mode properties compared to conventional periodic PCs, multiple slow light bands can be flexibly obtained in CROWs constructed with complex 2D PCs. Our results may lead to the development of a variety of novel ultracompact devices for photonic integrated circuits.     

散射计资料对台风海平面气压场的反演和定位的新方法研究

文章首先利用QuikSCAT散射计获取的海面风场资料,利用华盛顿大学行星边界层(UWPBL)模式对台风海平面气压场进行反演(称为直接反演),并对其强度进行了分析;然后对获取的海面风场,采用变分方法对风场进行分解,分解出无旋和有旋风场,对分解出的有旋风场,再利用UWPBL模式对魔羯台风的海平面气压场进行了反演,对所得结果与通常直接反演、NCEP海平面气压场及台风报文资料进行一一对比,结果表明:新的反演定位的方法对台风海平面气压场中心气压的定位精度有了进一步的提高,此种定位的方法为散射计资料在台风中的实际应用开辟了一条新的思路. 关键词： 散射计风场 变分方法 台风 海平面气压场     

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.     

Elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity existing in orthotropic media under uniform tension at infinity

This paper presents an analytical solution for the elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity embedded in the orthotropic matrix under tension at infinity and inclined at any angle. The conformal transformation and complex function method for the anisotropic elastic material were used to determine the strain energies in the inhomogeneity and matrix, which were expressed by four undetermined coefficients characterizing the equilibrium boundary of the inhomogeneity due to the acting eigenstrains and external load. The use of the principle of the minimum potential energy led to analytical expressions for these coefficients and thus generated a closed-form solution for the elastic strain/stress fields. The resulting stress field in the inhomogeneity was examined and verified by checking the continuity conditions for the normal and shear stresses on the interior boundary of the matrix. Supported by the Program for New Century Excellent Talents in Universities (NCET) of the Ministry of Education of China (Grant No. NCET-04-0373) and the Program for Shanghai Pujiang Talents (Grant No. 05PJ14092)     

Large Amplitude Solitary Waves in a Fluid-Filled Elastic Tube

By using the potential method to a fluid filled elastic tube, we obtained a solitary wave solution. Comparedwith reductive perturbation method, this method can be used for larger amplitude solitary waves. The result is inagreement with that of small amplitude approximation from reductive perturbation method when the amplitude is smallenough.     

Elastic medium confined in a column versus the Janssen experiment

We compute the stresses in an elastic medium confined in a vertical column, when the material is at the Coulomb threshold everywhere at the walls. Simulations are performed in 2 dimensions using a spring lattice, and in 3 dimensions, using the Finite Element Method. The results are compared to the Janssen model and to experimental results for a granular material. The necessity to consider elastic anisotropy to render qualitatively the experimental findings is discussed.     

Large Amplitude Solitary Waves in a Fluid－Filled Elastic Tube

By usign the potential method to a fluid filled elastic tube, we obtained a solitary wave solution.Compared with recluetive perturbation method, this method can be used for larger amplitude solitary waves. The result is in agreement with that of small amplitude approximation from reduetive perturbation method when the amplitude is small enough.     

Evolution of massive scalar fields in the spacetime of a tense brane black hole

In the spacetime of a d-dimensional static tense brane black hole we elaborate the mechanism by which massive scalar fields decay. The metric of a six-dimensional black hole pierced by a topological defect is especially interesting. It corresponds to a black hole residing on a tensional 3-brane embedded in a six-dimensional spacetime, and this solution has gained importance due to the planned accelerator experiments. It happened that the intermediate asymptotic behaviour of the fields in question was determined by an oscillatory inverse power-law. We confirm our investigations by numerical calculations for five- and six-dimensional cases. It turned out that the greater the brane tension is, the faster massive scalar field decay in the considered spacetimes.     

Diffraction of stochastic electromagnetic fields by a hole in a thin film with real optical properties

The classical Kirchhoff theory of diffraction is extended to the case of real optical properties of a screen and its finite thickness. A spectral power density of diffracted electromagnetic fields by a hole in a thin film with real optical properties was calculated. The problem was solved by use of the vector Green theorems and related Green function of the boundary value problem. A spectral and spatial selectivity of the considered system was demonstrated. Diffracted patterns were calculated for the coherent and incoherent incident fields in case of holes array in a screen of perfect conductivity.     

光学薄膜样品的温度场和形变场分析

通过积分变换理论上求解了光学薄膜样品在脉冲或方波调制激励光作用下的热传导方程和热弹方程,从而获得了样品在瞬态和稳态情况下对应的温度场和形变场.为验证所求解,将理论解析解的计算机模拟结果与有限元的分析结果在时域和空间域进行了比较,两结果获得了较好的一致性;同时讨论了温度,热变形随激励光的调制频率、光斑半径等参数的变化.讨论了此模型在测量光学薄膜样品吸收损耗和表面热变形中的应用. 关键词： 温度场 形变场 表面热透镜 有限元     

Structure of 6He in the frame of a cluster model

A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, <'6>He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data.     

Structure of ^6He in the frame of a cluster model

A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, ⁶He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data.