Stability of pargasite during ultrahigh-temperature metamorphism:A consequence of titanium and REE partitioning

Orthopyroxene-clinopyroxene-plagioclase needles and symplectite along the cleavage planes and grain boundaries of fluorine-bearing titanian-ferroan pargasite from the Highland Complex, Sri Lanka, are interpreted as evidence for dehydration melting at ultrahigh-temperature conditions. High Ti (up to 0.4 pfu) and F (XF up to 0.56) content in pargasite extends its stability to higher temperatures, and the composition indicates the dehydration melting reaction may take place at ultrahigh-temperatures (~950 °C) at a pressure around 10 kbar, close to peak metamorphic conditions. The increase of Ti content close to the grain boundaries and cleavage planes in pargasite indicates titanium partitioning from the melt during dehydration melting enhanced the stability of the mineral toward ultrahigh-temperature conditions. The REE content in the pargasite shows a similar behavior to that of titanium. The cores with no breakdown assemblage consist of low and flat REE concentrations with respect to the high and Eu-depleted rim. Clinopyroxene in symplectite and needle-shaped lamellae within the pargasite porphyroblasts have similar REE patterns with slightly low-concentrations relative to that of pargasite. In the breakdown assemblage, LREEs are partitioned mainly into plagioclase while the HREEs are partitioned into orthopyroxene. The REE enrichment in the pargasite rims signals their relative partitioning between pargasite rims and melt. Modeling of the partitioning of Ti and REEs associated with pargasite breakdown demonstrates that its stability is greatly enhanced at UHT conditions. This investigation implies that the stability of hydrous minerals such as amphibole can be extended to UHT conditions, and expands our knowledge of metamorphism in the lower crust.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Grain boundary strengthening in strongly textured magnesium produced by hot rolling

The grain size dependence of the yield stress in hot rolled 99.87 pct magnesium sheets and rods was measured in the temperature range 77 K to 420 K. Hot rolling produced strong basal textures and, for a given grain size, the hot rolled material has a higher strength than extruded material. The yield strength-grain size relation in the above temperature range follows the Hall-Petch equation, and the temperature dependencies of the Hall-Petch constants σ0 and k are in support of the theory of Armstrong for hcp metals that the intercept σ0 is related to the critical resolved shear stress (CRSS) for basal slip (easy slip) and the slope k is related to the CRSS for prismatic slip (difficult slip) occurring near the grain boundaries. In the hot rolled magnesium, σ0 is larger and k is smaller than in extruded material, observations which are shown to result from strong unfavorable basal and favorable 1010 textures, respectively. Texture affects the Hall-Petch constants through its effect on the orientation factors relating them to the CRSS for the individual slip systems controlling them.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

CFD Analysis of conjugate natural convection in a vertical annulus

Conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. A parametric study is performed by varying the Grashof number, aspect ratio, and the solid-to-fluid thermal conductivity ratio over wide ranges with the Prandtl number fixed at 0.7. Results are presented for the variation of several quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number, and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The average Nusselt number from the conjugate analysis is found to be between the Nusselt numbers of the isothermal and the isoflux cases. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. Correlations are presented for the Nusselt number and the dimensionless temperatures of interest in terms of the parameters of the problem.

Load Transfer from a Smooth Elastic Pin to a Large Sheet

The plane problem of load transfer from an elastic interference or clearance fit pin to a large elastic sheet with a perfectly smooth interface is solved. As the load on the pin is monotonically increased, the pin-hole interface is in partial contact above certain critical load in interference fit and throughout the loading range in clearance fit.Such situations result in mixed boundary-value problems with moving boundaries and the arc of contact varies nonlinearly with applied load. These problems are analyzed by an inverse technique in which the arcs of contact/separation are prescribed and the causative loads are evaluated. A direct method of analysis is adopted using biharmonic polar trigonometric stress functions and a simple collocation method for satisfying the boundary conditions. A unified analytical formulation is achieved for interference and clearance fits. The solutions for the linear problem of push fits are inherent in the unified analysis. Numerical results highlighting the effects of pin and sheet elasticity parameters are presented.

Thermoelectric Properties of Co4Sb12 Skutterudite Materials with Partial In Filling and Excess In Additions

The properties of Co4Sb12 with various In additions were studied. X-ray diffraction revealed the presence of the pure δ-phase of In0.16Co4Sb12, whereas impurity phases (γ-CoSb2 and InSb) appeared for x = 0.25, 0.40, 0.80, and 1.20. The homogeneity and morphology of the samples were observed by Seebeck microprobe and scanning electron microscopy, respectively. All the quenched ingots from which the studied samples were cut were inhomogeneous in the axial direction. The temperature dependence of the Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ) was measured from room temperature up to 673 K. The Seebeck coefficient of all In-added Co4Sb12 materials was negative. When the filler concentration increases, the Seebeck coefficient decreases. The samples with In additions above the filling limit (x = 0.22) show an even lower Seebeck coefficient due to the formation of secondary phases: InSb and CoSb2. The temperature variation of the electrical conductivity is semiconductor-like. The thermal conductivity of all the samples decreases with temperature. The central region of the In0.4Co4Sb12 ingot shows the lowest thermal conductivity, probably due to the combined effect of (a) rattling due to maximum filling and (b) the presence of a small amount of fine-dispersed secondary phases at the grain boundaries. Thus, regardless of the non-single-phase morphology, a promising ZT (S 2 σT/κ) value of 0.96 at 673 K has been obtained with an In addition above the filling limit.

On the Kelvin-Helmholtz instability of structured plasma layers in the magnetosphere

The hydromagnetic Kelvin-Helmholtz (K-H) instability problem is studied for a three-layered system analytically by arriving at the marginal instability condition. As the magnetic field directions are taken to vary in the three regions, both the angle and finite thickness effects are seen on the instability criterion. When the relative flow speed of the plasmas on the two sides of the interfaces separating the inner and the surrounding layers is U < Uc, where Uc is the critical speed, the system is stable both for symmetric and asymmetric perturbations. However, unlike the case of the interface bounded by two semiinfinite media, Uc is no longer the minimum critical speed above which the system will be unstable for all wavenumbers; another critical speed U* > Uc is introduced due to the finiteness of the system. When Uc < U < U*, the instability can set in either through the symmetric or asymmetric mode, depending on the ratio of the plasma parameters and angle between the magnetic field directions across the boundaries. The instability arises for a finite range of wavenumbers, thus giving rise to the upper and lower cut-off frequencies for the spectra of hydromagnetic surface waves generated by the K-H instability mechanism. When U > U*, both the modes are unstable for short wavelengths. The results are finally used to explain some observational features of the dependence of hydromagnetic energy spectra in the magnetosphere on the interplanetary parameters.

Combined Use of Solid of Revolution, Thin Shell, and Interphase Elements for Analysis of Cylindrical Shells

Near the boundaries of shells, thin shell theories cannot always provide a satisfactory description of the kinematic situation. This imposes severe limitations on simulating the boundary conditions in theoretical shell models. Here an attempt is made to overcome the above limitation. Three-dimensional theory of elasticity is used near boundaries, while thin shell theory covers the major part of the shell away from the boundaries. Both regions are connected by means of an “interphase element.” This method is used to study typical static stress and natural vibration problems

Robustness of the partitions in grouping multi-item inventories

A recent work obtained closed-form solutions to the.problem of optimally grouping a multi-item inventory into subgroups with a common order cycle per group, when the distribution by value of the inventory could be described by a Pareto function. This paper studies the sensitivity of the optimal subgroup boundaries so obtained. Closed-form expressions have been developed to find intervals for the subgroup boundaries for any given level of suboptimality. Graphs have been provided to aid the user in selecting a cost-effective level of aggregation and choosing appropriate subgroup boundaries for a whole range of inventory distributions. The results of sensitivity analyses demonstrate the availability of flexibility in the partition boundaries and the cost-effectiveness of any stock control system through three groups, and thus also provide a theoretical support to the intuitive ABC system of classifying the items.