Peierls-Nabarro model of interfacial misfit dislocation: An analytic solution

We propose a method to treat the interfacial misfit dislocation array following the original Peierls-Nabarro's ideas. A simple and exact analytic solution is derived in the extended Peierls-Nabarro's model, and this solution reflects the core structure and the energy of misfit dislocation, which depend on misfit and bond strength. We also find that only with beta < 0.2 the structure of interface can be represented by an array of singular Volterra dislocations, which conforms to those of atomic simulation. Interfacial energy and adhesive work can be estimated by inputting ab initio calculation data into the model, and this shows the method can provide a correlation between the ab initio calculations and elastic continuum theory.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Effects of forced solution flow on lysozyme crystal growth

In order to study quantitatively the effects of forced solution on crystal growth, we designed a new set of experimental equipment, in particular, a microchannel mixer was used as crystallization container so that the consumption of protein samples was much reduced and thus an exact syringe pump could be used for precise control of the flow rates. Since the mixer’s section was designed to be rectangular, the solution velocity in its center was steady and constant, and thus repeatable experiments were facilitated. Experimental results showed that the effects of forced solution on protein crystal growth were different under different levels of supersaturation, and new results were obtained for cases of high supersaturation. When the supersaturation is σ = 2.3, with increasing flow rates the growth rates of the lysozyme crystal’s (110) face hardly change when the flow rates are lower than 1300 μm/s, and decrease quickly afterwards. When the flow rate reaches 2000 μm/s, the crystal nearly ceases to grow. When the supersaturation is σ = 2.7, with increasing flow rates the (110) face growth rates increase at the beginning then reach the maximum values at 1700 μm/s – 1900 μm/s and decrease afterwards, approaching zero or so when the flow rate reaches 12000 μm/s. The higher the supersaturation, the larger the flow rate at which the crystal ceases to grow. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Effects of the orientation of microgravity on the concentration distribution in crystallization from solution

A quasi-steady state growth and dissolution in a 2-D rectangular enclosure is numerically investigated. This paper is an extension to indicate the effects of the orientation of gravity on the concentration field in crystallization from solution under microgravity, especially on the lateral non-uniformity of concentration distribution at the growth surface. The thermal and solute convection are included in this model.

Optical Diagnostic and Modeling Solution Growth Process of Sodium Chlorate Crystals

Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous sodium chlorate crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

Concentration distribution in solution crystal growth: effect of moving interface conditions

The linear diffusion-reaction theory with finite interface kinetics is employed to describe the dissolution and the growth processes. The results show that it is imperative to consider the effect of the moving interfaces on the concentration distribution at the growth interface for some cases. For small aspect ratio and small gravity magnitude, the dissolution and the growth interfaces must be treated as the moving boundaries within an angle range of 0 degrees < gamma < 50 degrees in this work. For large aspect ratio or large gravity magnitude, the effect of the moving interfaces on the concentration distribution at the growth interface can be neglected except for gamma < - 50 degrees.

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

Localized Solid-State Amorphization at Grain Boundaries in a Nanocrystalline Al Solid Solution Subjected to Surface Mechanical Attrition

Using high-resolution electron microscopy, localized solid-state amorphization (SSA) was observed in a nanocrystalline (NC) Al solid solution (weight per cent 4.2 Cu, 0.3 Mn, the rest being Al) subjected to a surface mechanical attrition treatment. It was found that the deformation-induced SSA may occur at the grain boundary (GB) where either the high density dislocations or dislocation complexes are present. It is suggested that lattice instability due to elastic distortion within the dislocation core region plays a significant role in the initiation of the localized SSA at defective sites. Meanwhile, the GB of severely deformed NC grains exhibits a continuously varying atomic structure in such a way that while most of the GB is ordered but reveals corrugated configurations, localized amorphization may occur along the same GB.

Static Study of Cantilever Beam stiction under Electrostatic Force Influence

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beamsolutions of the loads with different distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation offers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length offers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The effects of dielectric layer thickness and electrostatic voltage on the cantilever beamstiction are studied.The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

The mechanical properties of an aluminum alloy by plasma-based ion implantation and solution-aging treatment

The age-strengthening 2024 aluminum alloy was modified by a combination of plasma-based ion implantation (PBII) and solution-aging treatments. The depth profiles of the implanted layer were investigated by X-ray photoelectron spectroscopy (XPS). The structure was studied by glancing angle X-ray diffraction (GXRD). The variation of microhardness with the indenting depth was measured by a nanoindenter. The wear test was carried on with a pin-on-disk wear tester. The results revealed that when the aluminum alloys were implanted with nitrogen at the solution temperature, then quenched in the vacuum chamber followed by an artificial aging treatment for an appropriate time, the amount of AIN precipitates by the combined treatment were more than that of the specimen implanted at ambient temperature. Optimum surface mechanical properties were obtained. The surface hardness was increased and the weight loss in a wear test decreased too.

A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

Studying Aggregate in Lysozyme Solution by Atomic Force Microscope

The aggregates in lysozyme solution with different NaCl concentration were investigated by Atomic Force Microscope (AFM). The AFM images show that there exist lysozyme monomers, n-mers and clusters in lysozyme solution when the conditions are not suitable for crystal growth. In favorable conditions for crystal growth, the lysozyme clusters disappear and almost only monomers exist in solution.