High order asymptotic field for plane stress crack problem

This paper presents an exact analysis for high order asymptotic field of the plane stress crack problem. It has been shown that the second order asymptotic field is not an independent eigen field and should be matched with the elastic strain term of the first order asymptotic field. The second order stress field ahead of the crack tip is quite small compared with the first order stress field. The stress field ahead of crack tip is characterized by the HRR field. Hence the J integral can be used as a criterion for crack initiation.

The plane problem of collinear rigid lines under arbitrary loads

The elastic plane problem of collinear rigid lines under arbitrary loads is dealt with. Applying the Riemann-Schwarz symmetry principle integrated with the analysis of the singularity of complex stress functions, the general formulation is presented, and the closed-form solutions to several problems of practical importance are given, which include some published results as the special cases. Lastly the stress distribution in the immediate vicinity of the rigid line end is examined.

Plane strain problem of growing crack for a perfectly plastic solid

In this paper, fundamental equations of the plane strain problem based on the 3-dimensional plastic flow theory are presented for a perfectly-plastic solid The complete governing equations for the growing crack problem are developed. The formulae for determining the velocity field are derived.The asymptotic equation consists of the premise equation and the zero-order governing equation. It is proved that the Prandtl centered-fan sector satisfies asymptotic equation but does not meet the needs of hlgher-order governing equations.

Complete solution of the columbus problem for large-disturbance cases

The Columbus problem has been rigorously solved by Lyapunov's direct approach to the continuous system in gencral cases of large disturbance and the theory has proved to be in strict consistency with Kelvin's experiments.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.

Relaxed purifying selection of rhodopsin gene within a Chinese endemic cavefish genus Sinocyclocheilus (Pisces: Cypriniformes)

The cyprinid fish genus Sinocyclocheilus, as the most cavefish rich genus, includes many species showing striking adaptation to caves and convergent reduction or even loss of eyes and pigmentation. RH1 is responsible for dim vision. In order to explore the evolution of RH1 gene in this genus, we sequenced the complete gene from 28 individuals of 16 representative species of Sinocyclocheilus, with cave and surface species included. Phylogenetic analyses supported the monophyly of Sinocyclocheilus and polyphyly of the cave species. Codon models implemented in PAML were used to infer the evolution of RH1. We found that Sinocyclocheilus had a significantly higher evolutionary rate for amino acids than other cyprinid fishes compared, which might be the result of relaxation of purifying selection and could be ascribed to cave habit of this genus. In contrast to previous hypotheses, both cave and surface lineages exhibited a similar rate of molecular evolution, so the RH1 of cave species may still be functional, although these species were highly adapted to cave environment. Two amino acid substitutions (D83G and E122V) that were not reported before were found, which may be useful for site-directed mutagenesis in the future.

A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Growth and magnetic properties of zincblende CrSb epilayers on relaxed and strained (In, Ga)As buffers

Zincblende CrSb (zb-CrSb) layers with room-temperature ferromagnetism have been grown on relaxed and strained (In,Ga)As buffer layers epitaxially prepared on (001) GaAs substrates by molecular-beam epitaxy. The structural characterizations of CrSb layers fabricated under the two cases are studied by using synchrotron grazing incidence x-ray diffraction (GID). The results of GID experiments indicate that no sign of second phase exists in all the zb-CrSb layers. Superconducting quantum interference device measurements demonstrate that the thickness of zb-CrSb layers grown on both relaxed and strained (In,Ga)As buffer layers can be increased to similar to 12 monolayers (similar to 3.6nm), compared to similar to 3 monolayers (similar to 1nm) on GaAs directly.

Effect of low-temperature SiGe interlayer on the growth of relaxed SiGe

A low-temperature Si0.8Ge0.2 (LT-Si0.8Ge0.2) interlayer was grown at 500 degrees C to improve the relaxed Si0.8Ge0.2 surface and reduce the dislocation density in it, which was confirmed by the change of reflective high-energy electron diffraction (RHEED) pattern from spotty to streaky and etch pits counts. For the same extent of strain; the threading dislocation density was reduced from 8 x 10(7) cm(-2) in the latter to 2 x 10(6) cm(-2) in the former. (C) 2000 Elsevier Science B.V. All rights reserved.

Relaxed GexSi1-x layer formation with reduced dislocation density grown by ultrahigh vacuum chemical vapor deposition

A new alternative method to grow the relaxed Ge0.24Si0.76 layer with a reduced dislocation density by ultrahigh vacuum chemical vapor deposition is reported in this paper. A 1000-Angstrom Ge0.24Si0.76 layer was first grown on a Si(100) substrate. Then a 500-Angstrom Si layer and a subsequent 5000-Angstrom Ge0.24Si0.76 overlayer followed. All these three layers were grown at 600 degrees C. After being removed from the growth system to air, the sample was first annealed at 850 degrees C for 30 min, and then was investigated by cross-sectional transmission electron microscopy and Rutherford backscattering spectroscopy. It is shown that the 5000-Angstrom Ge0.24Si0.76 thick over layer is perfect, and most of the threading dislocations are located in the embedded thin Si layer and the lower 1000-Angstrom Ge0.24Si0.76 layer. The relaxation ratio of the over layer is deduced to be 0.8 from Raman spectroscopy.