Relationship between grain boundary diffusion in nanocrystals and amorphous microstructure

The effects of microstructure on diffusion behaviors of Ni in Zr₄₈Cu₃₆Ag₈Al₈ alloy were investigated by transmission electron microscope and secondary ion mass spectrum. The temperature dependence of Ni diffusivities in Zr₄₈Cu₃₆Ag₈Al₈ alloy with different states (metallic glass, nanocrystals and coarse crystals) has been measured in the temperature range of 693–723 K. The results show that diffusion behavior is microstructure dependence, and the relations between the microstructure and diffusion are discussed. The activity energy of the grain boundary diffusion in nanocrystals calculated by the Suzuoka solution is about 1.433 eV/atom. It is equivalent with that of metallic glass, which is attributed to the similar microstructure between the two. Copyright © 2016 John Wiley & Sons, Ltd.     

BEM for simulation of a 2D elastic body with randomly distributed circular inclusions

Based on our 2D BEM software THBEM2 which can be applied to the simulation of an elastic body with randomly distributed identical circular holes, a scheme of BEM for the simulation of elastic bodies with randomly distributed circular inclusions is proposed. The numerical examples given show that the boundary element method is more accurate and more effective than the finite element method for such a problem. The scheme presented can also be successfully used to estimate the effective elastic properties of composite materials. Project supported by the National Natural Science Foundation of China (No. 19772025).     

Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

An explicitly solvable kinetic model for semiconductors

We consider a simple model for the electron Boltzmann equation in a semiconductor and show that specific boundary value problems can be explicitly solved. Cases of both homogeneous and inhomogeneous electric fields are considered.     

A perturbation solution for bacterial growth and bioremediation in a porous medium with bio-clogging

We investigate a flow problem of relevance in bioremediation and develop a mathematical model for transport of contamination by groundwater and the spreading, confinement, and remediation of chemical waste. The model is based on the fluid mass and momentum balance equations and simultaneous transport and consumption of the pollutant (hydrocarbon) and nutrient (oxygen). Particular emphasis is placed on the study of processes involving the full coupling of reaction, transport and mechanical effects. Dimensional analysis and asymptotic reduction are used to simplify the governing equations, which are then solved numerically.     

The elastostatic three-dimensional boundary element method: analytical integration for linear isoparametric triangular elements

In this paper an analytical integration scheme is described that is designed to reduce the errors resulting from the numerical evaluation of integrals with singular integrands. The analytical scheme can be applied to linear triangular elements for use in elastostatic problems and is particularly useful for predicting distortion, to high accuracy, close to surfaces. It is demonstrated that although the analytical scheme takes longer computationally than the usual quadrature approach it is quicker when element subdivision is required to achieve reasonable accuracy. Numerical tests are performed on a simple test problem to demonstrate the advantages of the analytical approach, which is shown to be orders of magnitude more accurate than standard quadrature techniques.     

Fatigue Crack Nucleation at Σ3(1 1 2) Boundary in a Ferritic Stainless Steel

The effect of a geometrical relationship between a grain boundary (GB) plane and a tensile axis on intergranular fatigue cracking along 3(1 1 2) twin boundaries has been investigated in Fe-30%Cr alloy crystals. Fatigue experiments were carried out on the three kinds of the specimens containing the 3(1 1 2) twin boundary. It was found that the fatigue cracking behavior was sensitive to the geometry of the GB plane. In a specimen where both the GB plane and a slip vector lying in the GB plane in adjacent grains are inclined to the tensile axis at 45°, the fatigue cracks were nucleated preferentially along the twin boundary at a stress amplitude of 170 MPa. The specimen with the GB plane normal to the tensile axis showed that the fatigue crack was initiated from a slip band formed within a constituent grain at a stress amplitude of 300 MPa. When the GB plane was inclined to the tensile axis but the slip vector lying in the GB plane was normal to the tensile axis, development of additional slips formed perpendicular to the GB plane were observed at a specific site of the GB. Initiation of intergranular fatigue cracks at the site was recognized at a stress amplitude of 250 MPa. It can be suggested that the GB plane normal to the tensile axis provides the highest fatigue performance among them. The difference in the cracking property among these specimens could be understood in terms of the effective Schmid factor derived from elastically incompatible stress.     

Linking-Preserving Perturbations of Symmetric Functionals

We consider paths of functionals starting with one which is invariant under the action of an arbitrary group of symmetries. We give conditions for the existence of an unbounded sequence of critical values of the non-symmetric functional at the end of the path in terms of the growth of the critical values of the symmetric one. We apply this to obtain a multiplicity result for a system of elliptic equations whose symmetries are perturbed by a linear term and a non-homogeneous boundary condition.     

On the zeros ofζ (1)(s) — a (on the zeros of a class of a generalized Dirichlet series — XVII)

Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forl≥l _o =l _o(a) (l _o being a large constant). In particular for the precise results on the zeros ofζ ⁽¹⁾ (s) —a (a any complex constant andl≥l _o) see Theorems 1 and 2 of the introduction.