Design Element Concept of squeeze casting process

Design sensitivity analysis and the application of Design Element Concept have been explored. Exploration has focused on expressed sensitivity with respect to material property and shape of the coolant channel. The Design Element Concept has been applied to the die domain, since the design elements can be considered as a direct mapping of the blocks that make up a die. Analytical methods such as Direct Differentiation Method (DDM) and Adjoint Variable Method (AVM) have been employed in calculating the design element sensitivities. All the calculated design element sensitivities were verified with the Finite Difference Method and the results showed close agreement. From the design element sensitivities distribution in the die, the results show that convergence can be observed as more design elements are employed.     

X-ray scattering from warm dense iron

We have carried out X-ray scattering experiments on iron foil samples that have been compressed and heated using laser-driven shocks created with the VULCAN laser system at the Rutherford-Appleton Laboratory. This is the highest Z element studied in such experiments so far and the first time scattering from warm dense iron has been reported. Because of the importance of iron in telluric planets, the work is relevant to studies of warm dense matter in planetary interiors. We report scattering results as well as shock breakout results that, in conjunction with hydrodynamic simulations, suggest the target has been compressed to a molten state at several 100 GPa pressure. Initial comparison with modelling suggests more work is needed to understand the structure factor of warm dense iron.     

An Extension of the Stefan-Type Solution Method Applicable to Multi-component,Multi-phase 1D Systems

We present an extension of the Stefan-type solution method applicable to multi-component, multi-phase 1D porous flows, and illustrate the method by applying it to phase separation dynamics in an NaCl–\(\hbox {H}_2\hbox {O}\)-saturated hydrothermal heat pipe. For this example, three mathematical models are constructed. The first two models concern the rate of progression of two interfaces, one separating brine from two-phase fluid and another separating two-phase fluid from single-phase liquid at seawater salinity. The brine layer model shows that the layer may reach quasi-steady-state thickness even while the salt content of the layer continues to increase; the two-phase layer model shows how variable heat flux at the top of the layer leads to departure from the linear growth rate predicted by a simpler model. The third model concerns the temperature profile in the entire column. The governing advection–diffusion equation has highly variable coefficients, with no negligible terms in it in the region of parameter space considered. We present a method to solve this type of equation by constructing a propagator and a corresponding Green’s function. Finally, we show how to use the developed framework to test the internal consistency of numerical simulations, again using the 1D heat pipe as an example.     

Structure and properties of the aluminum borates Al(BO2)n and Al(BO2)n(-), (n = 1-4)

The geometrical and electronic structures of Al(BO(2))(n) and Al(BO(2))(n)(-) (n = 1-4) clusters are computed at different levels of theory including density functional theory (DFT), hybrid DFT, double-hybrid DFT, and second-order perturbation theory. All aluminum borates are found to be quite stable toward the BO(2) and BO(2)(-) loss in the neutral and anion series, respectively. Al(BO(2))(4) belongs to the class of hyperhalogens composed of smaller superhalogens, and should possess a large adiabatic electron affinity (EA(ad)) larger than that of its superhalogen building block BO(2). Indeed, the aluminum tetraborate possesses the EA(ad) of 5.6 eV, which, however, is smaller than the EA(ad) of 7.8 eV of the AlF(4) supehalogen despite BO(2) is more electronegative than F. The EA(ad) decrease in Al(BO(2))(4) is due to the higher thermodynamic stability of Al(BO(2))(4) compared to that of AlF(4). Because of its high EA and thermodynamic stability, Al(BO(2))(4) should be capable of forming salts with electropositive counter ions. We optimized KAl(BO(2))(4) as corresponding to a unit cell of a hypothetical KAl(BO(2))(4) salt and found that specific energy and energy density of such a salt are competitive with those of trinitrotoluol (TNT).     

Fenchel decomposition for stochastic mixed-integer programming

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establish finite convergence for binary first-stage. Second, we derive FD cuts based on the second-stage variables only and use an idea from disjunctive programming to lift the cuts to the higher dimension space including the first-stage variables. We then devise an alternative algorithm (FD-L algorithm) based on the lifted FD cuts. Finally, we report on computational results based on several test instances from the literature involving the special structure of knapsack problems with nonnegative left-hand side coefficients. The results are promising and show that both algorithms can outperform a standard direct solver and a disjunctive decomposition algorithm on large-scale instances. Furthermore, the FD-L algorithm provides better performance than the FD algorithm in general. Since Fenchel cuts can be computationally expensive in general and are best suited for problems with special structure, both algorithms exploit the special structure of the test instances by reducing the size of the cut generation problems based on the number of nonzero components in the non-integer solution that needs to be cut off.     

Preparation for Practice: Elementary Preservice Teachers Learning and Using Scientific Classroom Discourse Community Instructional Strategies

Despite historical national efforts to improve elementary science education, science instruction continues to be marginalized, varying by state. This study was designed to address the ongoing challenge of educating elementary preservice teachers (PSTs) to teach science. Elementary PSTs are one of the science education community's major links to schools and science education reform. However, they often lack a strong background in science, knowledge of effective science teaching strategies, and consequently have low confidence and self‐efficacy. This investigation explored the initial learning of elementary PSTs using an interdisciplinary model of a scientific classroom discourse community during a science methods course. Findings post‐methods course suggested that the PSTs gained confidence in how to teach inquiry‐based elementary science and recognized inquiry‐based science as an effective means for engaging student learning. Additionally, PSTs embraced the interdisciplinary model as one that benefits students' learning and effectively uses limited time in a school day.     

Appollonius Revisited: Supporting Spheres for Sundered Systems

When C is a ball in and S is the sphere , we say that S supports a convex body B if S intersects B and either (then S is a far support) or the interior of C is disjoint from B (then S is a near support). The focus here is on common supports for a system of d+1 bodies in such that for each way of selecting a point from each member of , the selected points are affinely independent and hence form the vertex-set of a d-simplex. The main result asserts that if is an arbitrary partition of , then there exists a unique Euclidean sphere that is simultaneously a near support for each member of and a far support for each member of . Received August 2, 1995, and in revised form November 30, 1995.     

An extension of the simplex algorithm for semi-infinite linear programming

We present a primal method for the solution of the semi-infinite linear programming problem with constraint index setS. We begin with a detailed treatment of the case whenS is a closed line interval in . A characterization of the extreme points of the feasible set is given, together with a purification algorithm which constructs an extreme point from any initial feasible solution. The set of points inS where the constraints are active is crucial to the development we give. In the non-degenerate case, the descent step for the new algorithm takes one of two forms: either an active point is dropped, or an active point is perturbed to the left or right. We also discuss the form of the algorithm when the extreme point solution is degenerate, and in the general case when the constraint index set lies in ^p . The method has associated with it some numerical difficulties which are at present unresolved. Hence it is primarily of interest in the theoretical context of infinite-dimensional extensions of the simplex algorithm.     

The Oscillation of Elliptic Systems

Foliated differential forms were introduced in [7], [9], to study the cohomology on a RIEMANNian foliated manifold with coefficients in the sheaf of germs of foliated differential forms. In this paper the notion of DE RHAM like current of the type (p, q) is defined for a RIEMANNian foliated manifold and some properties of various differential operators acting on the spaces of currents are given. In particular, special DE RHAM like currents are considered namely the foliated ones. It turns out that the space of foliated p-forms is dense in the space of foliated p-currents with the usual topology. We get certain results concerning the cohomology on a RIEMANNian foliated manifold with coefficients in the sheaf of germs of foliated currents.     

On the regularizing properties of the GMRES method

Summary. The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. However, little is known about the behavior of this method when it is applied to the solution of nonsymmetric linear ill-posed problems with a right-hand side that is contaminated by errors. We show that when the associated error-free right-hand side lies in a finite-dimensional Krylov subspace, the GMRES method is a regularization method. The iterations are terminated by a stopping rule based on the discrepancy principle. Received November 10, 2000 / Revised version received April 11, 2001 / Published online October 17, 2001