Some theorems in asymptotic analysis

Basing ourselves on the analysis of magnitude of order, we strictly prove fundamental lemmas for asymptotic integral, including the cases of infinite region. Then a general formula for asymptotic expansion of integrals is given. Finally, we derive a sufficient condition for an ordinary differential equation to possess a solution of the Frobenius series type at finite irregular singularities or branching points.

High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Naive asymptotic expansion of the water wave generated by a slowly moving body

It is pointed out that the naive asymptotic expansion does not satisfy all the body boundary condition. A nonhomogeneous body boundary condition is obtained from this expansion. It is this condition that the additional wave term must satisfy. Moreover, because of this condition, the wave term must appear. It is pointed out that the zeroth approximation in the naive asymptotic expansion has weak singularity and the singularities become still stronger in the subsequent approximations.

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

The asymptotic near-tip solution for mode-iii crack in steady growth in power hardening media

Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.

The effect of strain softening in the matrix material during void growth

Furthermore, the compressed flow driven by the piston is discussed. The consistent solution of gasdynamical equations including solar gravity is obtained for the unsteady and two-dimensional configuration, which is applied to the region between the piston and shock wave. This solution may satisfy the jump conditions of shock wave, which separates the region of compressed flow and quiet corona.

Interface cracking and particulate size effect in particle-reinforced metal-matrix composites

The mechanical behaviors of the ceramic particle-reinforced metal matrix composites are modeled based on the conventional theory of mechanism-based strain gradient plasticity presented by Huang et al. Two cases of interface features with and without the effects of interface cracking will be analyzed, respectively. Through comparing the result based on the interface cracking model with experimental result, the effectiveness of the present model can be evaluated. Simultaneously, the length parameters included in the strain gradient plasticity theory can be obtained.

High-Strength Composite Fibers: Realizing True Potential of Carbon Nanotubes in Polymer Matrix through Continuous Reticulate Architecture and Molecular Level Couplings

Carbon nanotubes have unprecedented mechanical properties as defect-free nanoscale building blocks, but their potential has not been fully realized in composite materials due to weakness at the interfaces. Here we demonstrate that through load-transfer-favored three-dimensional architecture and molecular level couplings with polymer chains, true potential of CNTs can be realized in composites as Initially envisioned. Composite fibers with reticulate nanotube architectures show order of magnitude improvement in strength compared to randomly dispersed short CNT reinforced composites reported before. The molecular level couplings between nanotubes and polymer chains results in drastic differences in the properties of thermoset and thermoplastic composite fibers, which indicate that conventional macroscopic composite theory falls to explain the overall hybrid behavior at nanoscale.

Experimental Study Of Multi-Hole Cooling For Integrally-Woven, Ceramic Matrix Composite Walls For Gas Turbine Applications

In this paper, multi-hole cooling is studied for an oxide/oxide ceramic specimen with normal injection holes and for a SiC/SiC ceramic specimen with oblique injection holes. A special purpose heat transfer tunnel was designed and built, which can provide a wide range of Reynolds numbers (10(5)similar to 10(7)) and a large temperature ratio of the primary flow to the coolant (up to 2.5). Cooling effectiveness determined by the measured surface temperature for the two types of ceramic specimens is investigated. It is found that the multi-hole cooling system for both specimens has a high cooling efficiency and it is higher for the SiC/SiC specimen than for the oxide/oxide specimen. Effects on the cooling effectiveness of parameters including blowing ratio, Reynolds number and temperature ratio, are studied. In addition, profiles of the mean velocity and temperature above the cooling surface are measured to provide further understanding of the cooling process. Duplication of the key parameters for multi-hole cooling, for a representative combustor flow condition (without radiation effects), is achieved with parameter scaling and the results show the high efficiency of multi-hole cooling for the oblique hole, SiC/SiC specimen. (C) 2008 Elsevier Ltd. All rights reserved.

Synthesis Of Plastic Zr-Based Bulk Metallic Glass Matrix Composites By The Copper-Mould Suction Casting And The Bridgman Solidification

Zr-based bulk metallic glass matrix composites with the composition of Zr56.2Ti13.8Nb5.0Cu6.9Ni5.6Be12.(5) were synthesized by the copper-mould suction casting and the Bridgman solidification. The composite, containing a well-developed flowery beta-Zr dendritic phase, was obtained by the Bridgman solidification with the withdrawal velocity of 0.8 mm/s and the temperature gradient of 45 K/mm, and the ultimate strength of 2050 MPa and fracture plastic strain of 14.6% of the composite were achieved, which was mainly interpreted by the homogeneous dispersion of bcc beta-Zr phase in the glass matrix. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

MODIFIED ENGAGEMENT METHOD FOR MATRIX OPERATION

We describe a modified engagement method for matrix operation based on a two-dimensional crossed-ring interconnection network, Our method incorporates fewer steps than that reported by Bocker et al. [Appl. Opt. 22, 804 (1983)], and its performance is found to be the most efficient (minimum steps) in comparison with other systolic and/or engagement methods for matrix operation. Thus, it may be helpful for other optical and electronic implementations of matrix operations. One compact optoelectronic integrity approach for implementing the modified engagement method is briefly described. (C) 1995 Optical Society of America