Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings

A two-dimensional (2-D) probabilistic model, previously developed for the prediction of microstructure formation in solidification processes, is applied to thin section superalloy precision castings. Based upon an assumption of uniform temperature across the section of the plate, the model takes into account the heterogeneous nucleation which might occur at the mold wall and in the bulk of the liquid. The location and crystallographic orientation of newly nucleated grains are chosen randomly among a large number of sites and equiprobable orientation classes, respectively. The growth of the dendritic grains is modeled by using a cellular automaton technique and by considering the growth kinetics of the dendrite tips. The computed 2-D grain structures are compared with micrographie cross sections of specimens of various thicknesses. It is shown that the 2-D approach is able to predict the transition from columnar to equiaxed grains. However, in a transverse section, the grain morphology within the columnar zone differs from that of the experimental micrographs. For this reason, a three-dimensional (3-D) extension of this model is proposed, in which the modeling of the grain growth is simplified. It assumes that each dendritic grain is an octaedron whose half-diagonals, corresponding to the <100> crystallographic orientations of the grain, are simply given by the integral, from the time of nucleation to that of observation, of the velocity of the dendrite tips. All the liquid cells falling within a given octaedron solidify with the same crystallographic orientation of the parent nucleus. It is shown that the grain structures computed with this 3-D model are much closer to the experimental micrographie cross sections.     

Counterfactual reasoning by (means of) defaults

We show how defaults can be used for counterfactual reasoning. We use a framework of modal logic to reason about both defaults and counterfactuals, in which one can express certainties, possibilities, actualities and (preferred or practical) beliefs in a distinct manner. Firstly, we discuss some properties of our approach in relation to other approaches in the literature.     

Small sub-Riemannian balls onR 3

This paper deals with sub-Riemannian metrics onR ³ in the contact case. We study the singularities of the exponential mapping in the neighborhood of its pole. This is in stark contrast with the Riemannian case where this situation never occurs.     

Runge-Kutta pairs for periodic initial value problems

We study the relative merits of the phase-lag property of Runge-Kutta pairs and we propose new explicit embedded pairs for the numerical solution of first order differential systems with periodical solution. We analyze two families of 5(4) paris and one family of 6(5) pairs with respect to the attainable phase-lag order. From each family we choose a pair with the highest achievable phase-lag order, optimized with respect to a measure of the magnitude of its truncation error coefficients. The new 5(4) algebraic order pairs are of phase-lag order 8(4) and 8(6) and they are both non-dissipative, while the 6(5) pair is dissipative and of phase-lag order 10(6). The new pairs exhibit an improved performance, in comparison with other currently known general and special purpose methods, when they are applied to semidiscretized hyperbolic equations and problems describing free and weakly forced oscillations.     

Bound-to-continuum GaInAs-AlAsSb quantum cascade lasers with reduced electric injection power density

Short-wavelength (/spl lambda/<4 /spl mu/m) GaInAs-AlAsSb quantum cascade (QC) lasers have been demonstrated using a "bound-to-continuum" design for the purpose of reducing the electric injection power density. As a result, we have reduced the low-temperature electric injection power density of the lasers by 40%, compared to that of GaInAs-AlAsSb QC lasers emitting at the same wavelength but adopting a triple-quantum-well design. The lasers in the present report can operate up to room temperature (300 K) in pulsed mode, emitting at short-wavelength /spl lambda//spl sim/3.7-3.9 /spl mu/m.     

Analysis of various Nigerian foodstuffs for crude protein and mineral contents by neutron activation

Various Nigerian foodstuffs were analysed for crude protein and some important nutrient minerals, Ca, Fe, K and P, using the neutron activation technique. The protein content of the staple foods, cassava and its products, cocoyam, yam, rice and plantains, varies from about 1% to 12·8%, while the grains, maize, guinea corn and millet, as well as African breadfruit seeds and some popular vegetables, have a relatively high protein content. Corrections for the relevant reaction interferences in nitrogen determination were carried out. The precision of the sample analyses varied in the range ± 2·1 to ± 6·3%.     

Application of controlled and electrical discharge assisted mechanical alloying for the synthesis of nanocrystalline MgB2 superconducting compound

In this paper we present the results of our efforts to synthesize the nanocrystalline MgB₂ superconducting compound from elemental Mg and B powders by combination of controlled mechanical pre-alloying in a magneto-mill Uni-Ball-Mill 5 under shearing mode followed by electrical discharge (ED) assisted mechanical alloying (MA). There is no conclusive evidence of MgB₂ formation in the Mg-2B mixture using crystalline boron after controlled mechanical alloying (CMA) under protective argon or helium atmosphere as well as subsequent ED assisted alloying. There seems to be some XRD evidence of the strongest (1 0 1) MgB₂ peak presence in the Mg-2B mixture processed using both crystalline and amorphous boron after CMA under hydrogen as well as subsequent ED assisted alloying but this evidence is rather ambiguous. We postulate here that it is highly likely that a certain critical Mg nanograin size must be achieved before a successful reaction to form nanocrystalline MgB₂ is going to be completed. Following recent report by Gümbel et al. [Appl. Phys. Lett. 80 (2002) 2725] this critical value can be roughly estimated at 15 nm or less. Calculations of the Mg nanograin size in the present work show that only three Mg-2B powders ball milled under hydrogen meet this critical nanograin size criterion for the Mg phase. However, a massive formation of the β-MgH₂ hydride in these powders consumes the available Mg in the reaction with hydrogen which may leave inadequate concentration of Mg to form MgB₂ even though the nanograin size of Mg is sufficiently refined, say below 15 nm.     

The finite element solution of laminar combined convection from a horizontal cylinder

The purpose of this investigation is to study the flow and heat-transfer characteristics of laminar combined convection from an isothermal cylinder. The full Navier-Stokes and energy equations are solved by a finite element method. The variations of surface shear stress, pressure and Nusselt number are obtained over the whole cylinder surface including the zone beyond the separation point. The predicted values of the average Nusselt number as well as the angle of separation, and the results of the pressure distribution and the local Nusselt number are compared with the available experimental correlations and previous numerical investigations. The agreement is satisfactory.     

亲电性有机硒试剂的反应及其在天然物合成中的应用

简要综述了有机硒试剂的亲电加成和取代反应,从分子中消去硒基团的方法及其在天然物合成中的应用。