Development and assessment of coupled wave theory of axial propagation in thin-film helicoidal bianisotropic media. Part 1: Reflectances and transmittances

Abstract

The coupled wave theory (CWT) for axial propagation of light in dielectric thin-film helicoidal bianisotropic media is presented and compared with the full electromagnetic analysis (FEMA). Two sets of formulas are developed for the location and bandwidth of the wavelength regime wherein the circular Bragg phenomenon is exhibited. Multi-layer structures are also analysed using the CWT, the location of the spectral hole in a class of threelayer structures being determined analytically. Absorption and dispersion effects are considered.     

Image Intensity at the Edge of a Straight Edge Object

Abstract

We consider the value of the intensity image at the geometrical position of a general, flat, straight edge object. We adopt a Fourier optical transfer function approach and obtain, rigorously, analytic expressions for the cases of coherent, incoherent and equal aperture, partially coherent imaging. Aberration-free, circular pupils are considered and the analytic results are found to agree with earlier numerical calculations. We also obtain expressions for the intensity gradient at the edge.     

Focusing of axially symmetric flattened Gaussian beams

Abstract

We study the three-dimensional field distribution of a focused axially symmetric flattened Gaussian beam. In particular, exact closed-form expressions for the intensity along the optical axis and at the focal plane are provided, together with a comparison between our results and those pertinent to the case of a converging spherical wave diffracted by a hard-edge circular aperture. Some hints for future investigations are also given.     

Explicit analysis for the ground-support interaction of a circular tunnel excavation in anisotropic stress fields

ABSTRACT

The convergence-confinement method (CCM) applied to a circular tunnel drilled through the ground under, initially, an anisotropic stress condition is investigated in this paper by employing the explicit procedure for implementing the analytical solution for executable calculations that can be directly estimated using a simple computational spreadsheet. The solutions of ground-support interaction in the final equilibrium state are solved with, in the elastic state, the simultaneous equations between the support confining curve (SCC) and the ground reaction curve (GRC) and using the Newton recursion method for finding roots in the plastic state. The influence factor of ground reaction, the apparent shear modulus of the ground, the apparent stiffness of the support and the interaction curve (IC) were especially examined in this study to consider the influence of locations around the tunnel in anisotropic stress fields. The validity of the developed explicit procedure for analytical solution was verified by numerical analysis to study the effects of in-situ stress ratio on the stress path, SCC and GRC at the intrados of the tunnel. The comparison of results obtained between the proposed explicit analysis (EAM) and the numerical analysis (FEM) was found to be consistent in elastic and elastic-perfectly plastic media.     

Prediction of Young’s modulus and Poisson ratio for foamed metals using octahedron model

Abstract

The present paper deals with the mathematical–physical expression of Young’s modulus and Poisson ratio of foamed metals. As it is known that, Young’s modulus and Poisson ratio are two basic mechanical parameters of engineering materials. Foamed metal is a class of excellent engineering materials with dual attributes of structural and functional characteristics; therefore, these two parameters are investigated for these materials, and the relevant mathematical–physical expressions are derived from the ‘octahedron model’ of porous materials in the present paper. The results show that the apparent Young’s modulus displays a quite complicated mathematical relationship to porosity of the porous body, and the apparent Poisson ratio is just a characteristic of the material constant almost not relative to porosity of the foamed metal.     

The focal shift in converging waves

Abstract

The focal shift effect in converging spherical waves diffracted by circular apertures is analysed, based on a geometrical interpretation of the mathematical expressions taken from scalar wave theory. The approach leads to a quasi-exact formula for the axial complex amplitude without the need for calculating any integral. The procedures can naturally be extended to image-forming instruments and an application to a single-lens system is also presented.     

On the applicability of Stoney’s formula for calculating the mechanical stresses in thick films and coatings

The most accurate expressions for determining stresses in coatings, for example, in aluminum nitride on molybdenum, are derived. The stress curve has a characteristic shape, and for this reason it is proposed that the entire system be called a “z system.” It is shown that Stoney’s formula is of limited applicability, over-or underestimating the true values of the stresses. Pis’ma Zh. Tekh. Fiz. 23, 32–36 (September 26, 1997)     

Misalignment Sensitivity of Stable Resonators in Multimode Operation

Abstract

The sensitivity of the output power of stable resonators in multimode operation to mirror tilt was investigated both theoretically and experimentally. It is shown that the decrease of power is only caused by the decreasing mode volume inside the active medium. A simple geometrical model including the refractive power of the medium is used to derive expressions for the tilt angles at which the power has decreased by 10%. Experiments were performed with pulsed Nd : YAG lasers, the results showing good agreement with the theoretical predictions.     

Note on eddy formation for stokes flows in circular cavities

Abstract

In this note, a simple model of a circular cavity with two arcs rotated in opposite directions on the boundary is employed to demonstrate flow patterns of recirculation. A particular streamline “cutting” the domain into two separating eddies is formed as a circular arc. When the rotating angular speed of the arc is proportional to the length of the arc, the streamline degenerates to a straight line.     

Asymptotic Coupling Coefficients of Well-separated Single-mode Optical Waveguides

Abstract

Simple general formulae for the coupling coefficients of the fundamental modes on well-separated parallel optical waveguides are derived. The calculation merely requires accurate knowledge of the propagation constants and core fields of the modes on the individual waveguides, while the far-from-core fields need not be known. Results for coupled circular fibres are identical with the asymptotic expansions of previously derived exact coupling coefficients. Analytical expressions for the coupling coefficients between the fundamental modes on identical weakly guiding channel waveguides are obtained.     

Static and cyclic creep behaviour of SiC whisker reinforced aluminium composite

Abstract

Static and cyclic creep tests were carried out in tension at 573–673 K on a 20 vol.-%SiC whisker reinforced aluminium (Al/SiC_w ) composite. The Al/SiC_w composite exhibited an apparent stress exponent of 18·1–19·0 at 573–673 K and an apparent activation energy of 325 kJ mol^-1 for static creep, whereas an apparent stress exponent of 19·6 at 623 K and an apparent activation energy of 376 kJ mol^-1 were observed for cyclic creep. A cyclic creep retardation (CCR) behaviour was observed for the Al/SiC_w composite. The steady state creep rate for cyclic creep was three orders of magnitude lower than that for static creep. Furthermore, the steady state creep rates of the composite tended to decrease continuously with increasing percentage unloading amount. The static creep data of the Al/SiC_w composite were rationalised by the substructure invariant model with a true stress exponent of 8 together with a threshold stress. The CCR behaviour can be explained by the storage of anelastic strain delaying non-recoverable creep during the onload cycles.     

Amorphous nanoparticle complex of perphenazine and dextran sulfate as a new solubility enhancement strategy of antipsychotic perphenazine

Objective: The objective of this study is to develop a new solubility enhancement strategy of antipsychotic drug – perphenazine (PPZ) – in the form of its amorphous nanoparticle complex (or nanoplex) with polyelectrolyte dextran sulfate (DXT).

Significance: Poor bioavailability of PPZ necessitated the development of fast-dissolving PPZ formulations regardless of delivery routes. Existing fast-dissolving formulations, however, exhibited low PPZ payload. The high-payload PPZ-DXT nanoplex represents an attractive fast-dissolving formulation, as dissolution rate is known to be proportional to payload.

Methods: The nanoplex was prepared by electrostatically driven complexation between PPZ and DXT in a simple process that involved only ambient mixing of PPZ and DXT solutions. We investigated the effects of key variables in drug-polyelectrolyte complexation (i.e. pH and charge ratio R_DXT/PPZ) on the physical characteristics and preparation efficiency of the nanoplex produced. Subsequently, we characterized the colloidal and amorphous state stabilities, dissolution enhancement, and supersaturation generation of the nanoplex prepared at the optimal condition.

Results: The physical characteristics of nanoplex were governed by R_DXT/PPZ, while the preparation efficiency was governed by the preparation pH. Nanoplex having size of ≈80?nm, zeta potential of ≈(-) 60?mV, and payload of ≈70% (w/w) were prepared at nearly 90% PPZ utilization rate and ≈60% yield. The nanoplex exhibited superior dissolution than native PPZ in simulated intestinal juice, resulting in high and prolonged apparent solubility with good storage stabilities.

Conclusions: The simple yet efficient preparation, excellent physical characteristics, fast dissolution, and high apparent solubility exhibited by the PPZ-DXT nanoplex established its potential as a new bioavailability enhancement strategy of PPZ.     

Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real‐part dual BEM

It has been found recently that the multiple reciprocity method (MRM) (Chen and Wong. Engng. Anal. Boundary Elements 1997; 20 (1):25–33; Chen. Processings of the Fourth World Congress on Computational Mechanics, Onate E, Idelsohn SR (eds). Argentina, 1998; 106; Chen and Wong. J. Sound Vibration 1998; 217 (1): 75–95.) or real‐part BEM (Liou, Chen and Chen. J. Chinese Inst. Civil Hydraulics 1999; 11 (2):299–310 (in Chinese)). results in spurious eigenvalues for eigenproblems if only the singular (UT) or hypersingular (LM) integral equation is used. In this paper, a circular cavity is considered as a demonstrative example for an analytical study. Based on the framework of the real‐part dual BEM, the true and spurious eigenvalues can be separated by using singular value decomposition (SVD). To understand why spurious eigenvalues occur, analytical derivation by discretizing the circular boundary into a finite degree‐of‐freedom system is employed, resulting in circulants for influence matrices. Based on the properties of the circulants, we find that the singular integral equation of the real‐part BEM for a circular domain results in spurious eigenvalues which are the zeros of the Bessel functions of the second kind, Y (kρ), while the hypersingular integral equation of the real‐part BEM results in spurious eigenvalues which are the zeros of the derivative of the Bessel functions of the second kind, Y_n′(kρ). It is found that spurious eigenvalues exist in the real‐part BEM, and that they depend on the integral representation one uses (singular or hypersingular; single layer or double layer) no matter what the given types of boundary conditions for the interior problem are. Furthermore, spurious modes are proved to be trivial in the circular cavity through analytical derivations. Numerically, they appear to have the same nodal lines of the true modes after normalization with respect to a very small nonzero value. Two examples with a circular domain, including the Neumann and Dirichlet problems, are presented. The numerical results for true and spurious eigensolutions match very well with the theoretical prediction. Copyright © 2000 John Wiley & Sons, Ltd.     

Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Exact mathematical expressions for the intrinsic electromagnetic (EM) cross–sections (i.e. extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous non–absorptive medium are derived. The multipole expansion method in cylindrical coordinates and the translational addition theorem, applicable to any range of frequencies or particle sizes are used. An effective EM field, incident on the probed cylinder is defined first, which includes the initial and re-scattered field from the second cylinder. It is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross–sections. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies per unit-length for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross–sections.     

A simple practical analytic design method for multiloop‐controlled PWM switching regulators

Abstract

In this paper, a simple practical analytic method is proposed for designing multiloop‐controlled pulse width modulation (PWM) switching regulators. First, an equivalent single loop gain is presented and an approximate optimal set of closed‐loop poles is suggested according to the given specification such that the familiar design concept of a single‐loop second order system can be applied directly. In particular, closed form expressions of the feedback gains and the unknown parameters of the standard implemented circuit are derived. This renders the implementation problem surprisingly simple. Finally, some experimental results are also presented to demonstrate the effectiveness of the proposed method.     

Calculation of Nonlinear Waves Guided by Optical Fibres Using the Resonance Technique

Abstract

A recently developed, simple, and easily programmable method based on a resonance technique for the analysis of nonlinear guided modes for planar geometry has been extended to include fibre configurations. We consider here nonlinear media of the general type (non-Kerr media) including the more complicated but realistic case of saturable media. In the present paper, as an example of the proposed methodology, the following configuration is treated: a circular optical fibre consisting of a linear core bounded by a nonlinear cladding medium. The numerical results obtained by the method, correspond to the ‘weak guidance’ approximation, including both field distribution and power calculations.     

Requirements for the Production of Microtablets: Suitability of Direct-Compression Excipients Estimated from Powder Characteristics and Flow Rates

Abstract

Eleven direct-compression excipients, namely 3 microcrystalline celluloses, 4 lactoses, 4 co-processed excipients, and 4 mixtures of lactoses with Avicel PHI02 SCG were evaluated for possible use in micro tableting. Powder-technological parameters, namely particle size distributions, true and apparent densities, densification behaviour, and mass flow rates from a funnel through very narrow orifices, were determined.

Flow rates required on modern high-speed rotary tableting machines were calculated.

Flow rates may be estimated even for very narrow orifices, and such studies aid in selection of suitable excipients.

Mainly spray-dried lactose preparations with certain, definite upper limits in size distribution, seem to comply with the prerequisites for the production of micro tablets.     

Model for grain boundary sliding and its relevance to optimal structural superplasticity

Abstract

he conclusions reached based on a grain/interphase boundary sliding controlled flow model for optimal structural superplasticity are verified using experimental data from three aluminium alloy systems. Isostructural strain rate–stress relationships could be calculated very accurately using five experimentally determined, physically meaningful constants (three of which could also be calculated from theory; two fully and one partially). The true activation energy for the rate controlling boundary sliding process, the variations of the internal stress distribution arising from sliding, the stress function that is proportional to the measured isostructural isothermal strain rate, and the apparent viscosity, were calculated. It is suggested that the basic units of microscopic boundary sliding in the three aluminium alloys examined have a common structure.

MST/3077