SCRATA's practical approach to vibration-white finger in foundries : A. Champion, (17 pages, 7 figures, 17 references)

Linearized, quasi-static, fluid force coefficient data obtained from wind tunnel tests are used in an analysis of the fluidelastic stability of a double row of flexible circular cylinders subject to a cross-flow. Although the analysis is quasi-static, frequency dependent terms are obtained in the aerodynamic stiffness and damping matrices; the origin of these terms is twofold: firstly, because of the time lag between flow leaving an upstream row and arriving at a downstream row, which becomes important at low values of the non-dimensional flow velocity $\text{U}\text{fd}$; secondly, because of retardation of the flow approaching the cylinder, which is particularly important when small displacements of the cylinder result in large changes in the fluid force coefficients. This analysis is used to investigate the effects of a number of parameters on the critical flow velocity and the theoretical results are compared with those available in the literature. In general, agreement between theory and experiment is reasonably good, indicating the validity of this analysis.     

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Two-dimensional (2D) photonic band gaps (PBG) structure fabricated from anisotropic dielectric is studied by solving Maxwell's equations with use of plane-wave expansion method. Numerical simulations show that absolute photonic band gaps can be substantially improved in two dimensional square and triangular lattices of cylinders by introducing anisotropy in material dielectricity. Owing to different refractive indices for electromagnetic waves with E- and H-polarization, the quasi-independent adjustment of band gaps for the E- and H-polarization modes can be implemented by uniaxial crystals with their extraordinary axis parallel to the cylinders. Large absolute band gaps can be created for uniaxial cylinders in air with a positive anisotropy. In the case of air holes in background uniaxial dielectric with even a weak negative anisotropy, the absolute band gap can be increased 2-3 times. Large absolute band gap can also be obtained in other complex configurations of uniaxial and biaxial materials and this enables a full exploitation of potential utilization for anisotropic materials available in nature. Such a mechanism of band gap adjustment should open up a new scope for designing band gaps in 2D PBG structures. Received 26 January 1999     

Analysis of Radiation Phenomena in a Wedge Ended Dielectric Slab Waveguide

Radiation phenomena observed in a wedge shape ended dielectric slab waveguide are analyzed using mode matching technique. The case of transverse electric polarization (TE) being parallel to dielectric slab waveguide is assumed. In order to describe the fields in the wedge region, a stack of dielectric plates is assumed and in each layer the fields are expanded in terms of the mixed spectrum of guided and radiated modes. A similar expansion is used in the constant thickness slab waveguide while in free space medium a continuous-radiation mode expansion is used. Then a mode matching approach is applied, incorporating the orthogonality properties of mixed spectrum modes, in order to compute the wave fields inside the dielectric slab waveguide and wedge medium. Mode matching is achieved by discretizing the continuous radiation mode spectrum leading into a numerically stable solution provided a sufficient large number of points are used to convert integrals into finite summations. Numerical computations are carried out for various wedge geometries and shapes including linear and exponential profiles.     

Molecular ordering of Fluoro-Nematogen in a dielectric medium at phase-transition temperature: a statistical–mechanical approach based on computer simulation

A molecular-ordering study of p-phenylene-4-methoxy benzoyl 4-trifluoromethylbenzoate (FLUORO) in a dielectric medium (benzene) has been carried out on the basis of statistical mechanics and computer simulation. The atomic net charge and atomic dipole moment at each atomic centre has been evaluated using the CNDO/2 method. The modified Rayleigh–Schrodinger perturbation theory with multicentered–multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while ‘6-exp’ potential function has been assumed for the short-range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium at the phase-transition temperature (506?K), using the MB-formula. The flexibility of various interacting configurations was studied in terms of variation of probability due to departure from the most probable configuration. It has been observed that in dielectric medium the energies/probabilities are redistributed, and there is considerable rise in the probability of interaction, although the order of preference remains the same. The results are discussed in the light of experimental observations.     

ANALYSIS OF PARTICLE-PARTICLE FORCES IN ELECTRORHEOLOGICAL FLUIDS

The Rayleigh identity, based on a multipole expansion theory, is extended to analyse the forces between particles in an electrorheological system. The shear modulus for chains of particles arrayed on a square lattice is calculated. It is found that the modulus increases linearly with the ratio of dielectric constants of the dispersed particles to that of the continuous phase; as the ratio becomes larger, contrary to the expectations from a simple dipole approximation, the modulus would saturate. In the case of conducting particles, the modulus varies with the frequency of the applied field. In a limiting case of perfectly conducting particles, the conductivity is also considered. It is found that the particle-particle forces are extremely sensitive to their separations from each other.     

A faster aggregation for 3D fast evanescent wave solvers using rotations

A novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented. The new method calculates the six plane wave radiation patterns from a multipole expansion (aggregation) and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns. It is faster than the direct approach for multipole orders larger than one, and becomes six times faster for large multipole orders. The method relies on a connection between the discretizations of the six integral representations, and on the fact that the Wigner D-matrices become diagonal for rotations around the z-axis. The proposed technique can also be extended to the vectorial case in two different ways, one of which is very similar to the scalar case. The other method relies on a Beltrami decomposition of the fields and is faster than the direct approach for any multipole order. This decomposition is also not limited to evanescent wave solvers, but can be used in any vectorial multilevel fast multipole algorithm.     

Discussion of the He-He interaction energy in the average energy approximation

Using the Unsöld average energy method a double perturbation theory expression for the interaction energy through second order is obtained which includes intra-atomic correction terms arising from the use of trial wavefunctions to represent the non-interacting molecules. These formal expressions are applied to the ground state He-He interaction and results for the interaction energy are obtained that compare favourably with recent semiempirical and ab initio calculations. The Unsöld calculations are used to investigate approximations that have been introduced into the average energy calculation by other workers, and as a model for discussing the relative importance of second-order charge overlap and exchange effects and the convergence of the multipole treatment of the interaction energy for this typical non-bonded interaction. The results illustrate the importance of knowing as many terms as possible in the R ^-1 expansion of the energy. Finally a portion of this work required the recalculation of the He-He repulsive energy obtained by using the Eckart wavefunction to represent the helium atom. The resultant energy is approximately 25 per cent lower than that previously obtained using this wavefunction for most values of R.     

Form-factor representation and multipole expansion of the retarded interatomic dispersion energy

Dispersion-relation methods are used to derive a form-factor representation for the retarded dispersion energy of two hydrogen atoms that are described by relativistic electron theory. By expressing the electromagnetic form factors in terms of atomic transition matrix elements the complete multipole expansion of the interatomic dispersion energy is obtained. The long-range asymptotic limit of the successive multipole interactions is given explicitly.     

涂覆石墨烯的非对称并行电介质纳米线波导的模式特性分析

采用多级展开方法,对涂覆石墨烯的非对称并行电介质纳米线波导的模式特性进行了分析.首先对这种波导中的表面等离子模式进行分类,然后对七种低阶模式的有效折射率和传播长度随工作频率、几何结构参数和石墨烯费米能的依赖关系进行详细的分析.结果表明,通过改变工作频率、几何结构参数和石墨烯的费米能,可以在较大范围内调节模式的特性.与有限元法进行的对比表明,基于多级方法的半解析结果与有限元法的数值结果非常符合.研究结果可为涂覆石墨烯的非对称并行电介质纳米线的设计和制作提供一定的理论基础.     

The texture problem in Mössbauer spectroscopy

The theory of preferred orientation determination (crystallographic- or spintexture) by Mössbauer effect is presented for the case of unpolarized and polarized source radiation. The maximum information one can get out from Mössbauer measurements for the case of dipole radiation (M1) are nine expansion coefficients of the texture distribution expanded in a series of spherical harmonics. These coefficients can be obtained by a fitting procedure of the experimentally determined line intensity ratios in an absorption spectrum with rotated source and absorber. The general theory is applied for M1 radiation (Fe⁵⁷) and the cases of pure Zeeman or quadrupole splitting of source and absorber. Extension to higher multipole radiation can be easily done. Some graphs of possible textures are shown.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Lagrangian dynamics of spinning particles and polarized media in general relativity

The general form of the Lagrangian equations of motion is derived for a spinning particle having arbitrary multipole structure in arbitrary external fields. It is then shown how these equations, together with the complete system of field equations can be recovered from a fourdimensional action integral representing a polarized dustlike medium interacting with an arbitrary set of fields. These general results are then specialized to the case of Einstein-Maxwell fields in order to obtain the general-relativistic extension of Lorentz's dielectric theory.     

The quark-antiquark potential of SU(2) lattice gauge theory in 2+1 dimensions

Within the framework of a hamiltonian formulation of SU($\text{N}$) lattice gauge theory in two spatial dimensions we develop a weak coupling expansion in the static quark-antiquark sector. For SU(2) the quark-antiquark potential is calculated to fourth order. Moreover we extend the former calculation of the energy gap in the gauge invariant sector to general SU($\text{N}$) and extrapolate to the infinite lattice limit from large lattices. Due to the infrared divergence of the weak coupling expansion on infinite lattices the quark-antiquark potential contains a term diverging logarithmically with the lattice expansion. Hence the expansion has to be interpreted as a pseudo-perturbation expansion in the sense of Symanzik.     

System of two dielectric cylinders involving charge sources: I. Calculation of the electric field

The electric field of two dielectric straight circular cylinders containing line charges on their axes is investigated. The cylindrical bodies in question are parallel and touch each other from the exterior. They have different dielectric permittivities, charges, and radii. Also, they are surrounded by an arbitrary dielectric medium. An analytic solution to the respective boundary-value problem is given, and the most important particular cases are analyzed. Special features of the electric field in the region around the contact of the dielectric cylinders are studied versus the permittivity of the material used and the relationship between electric charges.     

High-frequency Franz-Keldysh effect on excitons

When the effective characteristic electro-optic energy ?|Λ_H|, which is obtained by including the electron-hole interaction in the solid, is very large compared to ?ω of the modulating electric field, the line shapes of the field-induced change of dielectric function are the same as those of Franz-Keldysh effect. However, in the low-field and high-frequency limit Δ∈₂(Ω, $\text{E}$ is nearly proportional to the first derivative of the unperturbed dielectric function. It is different from the low-field and low-frequency limit case where Δ∈₂(Ω, $\text{E}$) is proportional to the third derivative of the unperturbed dielectric function.     

Electric multipole interaction of pairs in solids: Ce in LaCl3

The electric multipole interaction (EMI) is studied in general for the case of two rare earth (RE) ions interacting in host crystals possessing C_3h symmetry at the ion sites. The particular case of Ce³⁺ substituted for La³⁺ in LaCl₃ is used as an example. The splitting of two degenerate levels of such a system is studied as an application of elementary group theory, and a notation is proposed for the resulting levels. The angular dependence of the splitting due to the first term of the EMI, namely, the electric quadrupole-quadrupole interaction (EQQ), is obtained for one of the levels of the system under consideration. The ground quartet is studied for the nearest neighbor configuration (nn), and all of the multipoles in the expansion for EMI are kept. The shielding effects, which are very important in this problem, are assumed to depend on one parameter. This makes possible the study of the variation of the splittings with respect to such a parameter. The importance of terms beyond the quadrupole is brought out.     

Electrical tuning of photonic crystals infilled with liquid crystals

In this paper we perform a complete study of electrical tuning in liquid crystal-infilled two-dimensional (2D) photonic crystals (PCs). The nematic liquid crystal (NLC) is characterized by a full range of bulk and surface elastic parameters. An essentially DC tuning field is applied in the axial direction. By minimizing the total (elastic plus electromagnetic) free energy, the configuration of the NLC directors, as a function of radial distance, is obtained. Three possible configurations are considered: escaped radial, planar radial, and axial. It is found that, in general, the escaped radial configuration is the preferred one. However, for sufficiently large applied fields, a phase transition occurs to the axial configuration. For example, in the case of the NLC 5CB, this transition is realized at about 14 V/μm provided that the cylinder radius is greater than about 50 nm. The configuration of the NLC directors determines the dielectric tensor as function of radial distance and this, in turn, leads to the eigenvalue equation for the PC. We present two such equations: one exact and the other approximate. The exact eigenvalue equation is based on the full anisotropy of the dielectric tensor and does not result in the usual separation of normal modes in a 2D PC. The approximate eigenvalue equation is derived from the average (over the cylinder cross-section) dielectric tensor and leads to modes that are polarized in the directions either parallel (E-mode) or perpendicular (H-mode) to the cylinders. Our calculations of the photonic band structure, by both methods, show that the approximate calculation works very well for the 5CB NLC cylinders in a silicon oxide (silica) host. This allows us to introduce the terminology quasi-E and quasi-H polarizations. We show how the partial photonic band gap in the [1 0 0] direction for these polarizations can be tuned and even completely closed. This behavior could be applied to the design of versatile, tunable polarization filters.