Interatomic distances and atomic valences in NaZn_(13)

The crystal structure of NaZn_(13) and of several homologous compounds AB_(13) was reported by Ketelaar and by Zintl & Hauke to be based on space group O_h^6-Fm3c, with 8 :Na in 8(a): ¼, ¼:, ¼; ... ; 8 Zn_I in 8(b): 0, 0, 0; .... ; and 96 Zn_(II) in 96(i): 0, y, z; ... . Approximate values were reported for the parameters a_0, y, and z; for NaZn_(13) Zintl & Hauke reported 12.27 Å, 0.178, and 0.122 for these three parameters. Each Zn_I is surrounded by twelve Zn_(II) at the vertices of a nearly regular icosahedron, and each Na by twenty-four Zn_(II) at the vertices of a snub cube. Our interest in the structure was largely concerned with the valences of the two different kinds of Zn atoms, it being presumptive that Zn_I has a larger valence than Zn_(II) because its icosahedral coordination requires it to be smaller than Zn_(II). Lines on new powder photographs of NaZn_(13) were measured and the intensities were estimated visually with as much precision as possible. Least-squares treatments were employed in order to obtain the best possible values for the three parameters; the values obtained are a_0 = 12.2836 ± 0.0003Å, y = 0.1806 ± 0.0003, and z = 0.1192 ± 0.0003. The uncertainties given are calculated standard deviations. Analysis of the interatomic distances yields a selfconsistent interpretation in which Zn_I is assumed to be quinquevalent and Zn_(II) quadrivalent, while Na may have a valence of unity or one as high as 1¼, the excess over unity being suggested by the interatomic distances and being, if real, presumably a consequence of electron transfer. A valence electron number of approximately 432 per unit cell is obtained, which is in good agreement with the value 428.48 predicted on the basis of a filled Brillouin polyhedron defined by the forms {444}, {640}, and {800}

An Approximation to Miscible Fluid Flows in Porous Media With Point Sources and Sinks by an Eulerian-Lagrangian Localized Adjoint Method and Mixed Finite Element Methods

We develop an Eulerian–Lagrangian localized adjoint method (ELLAM)-mixed finite element method (MFEM) solution technique for accurate numerical simulation of coupled systems of partial differential equations (PDEs), which describe complex fluid flow processes in porous media. An ELLAM, which was shown previously to outperform many widely used methods in the context of linear convection-diffusion PDEs, is presented to solve the transport equation for concentration. Since accurate fluid velocities are crucial in numerical simulations, an MFEM is used to solve the pressure equation for the pressure and Darcy velocity. This minimizes the numerical difficulties occurring in standard methods for approximating velocities caused by differentiation of the pressure and then multiplication by rough coefficients. The ELLAM-MFEM solution technique significantly reduces temporal errors, symmetrizes the governing transport equation, eliminates nonphysical oscillation and/or excessive numerical dispersion in many simulators, conserves mass, and treats boundary conditions accurately. Numerical experiments show that the ELLAM-MFEM solution technique simulates miscible displacements of incompressible fluid flows in porous media accurately with fairly coarse spatial grids and very large time steps, which are one or two orders of magnitude larger than the time steps used in many methods. Moreover, the ELLAM-MFEM solution technique can treat large mobility ratios, discontinuous permeabilities and porosities, anisotropic dispersion in tensor form, and point sources and sinks

An Ellam Scheme for Advection-Diffusion Equations in Two Dimensions

We develop an Eulerian{Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme

As Time Goes by: Understanding Child and Family Factors Shaping Behavioral Outcomes After Traumatic Brain Injury

Objective: To model pre-injury child and family factors associated with the trajectory of internalizing and externalizing behavior problems across the first 3 years in children with pediatric traumatic brain injury (TBI) relative to children with orthopedic injuries (OI). Parent-reported emotional symptoms and conduct problems were expected to have unique and shared predictors. We hypothesized that TBI, female sex, greater pre-injury executive dysfunction, adjustment problems, lower income, and family dysfunction would be associated with less favorable outcomes. Methods: In a prospective longitudinal cohort study, we examined the level of behavior problems at 12 months after injury and rate of change from pre-injury to 12 months and from 12 to 36 months in children ages 4–15 years with mild to severe TBI relative to children with OI. A structural equation model framework incorporated injury characteristics, child demographic variables, as well as pre-injury child reserve and family attributes. Internalizing and externalizing behavior problems were indexed using the parent-rated Emotional Symptoms and Conduct Problems scales from the Strengths and Difficulties questionnaire. Results: The analysis cohort of 534 children [64% boys, M (SD) 8.8 (4.3) years of age] included 395 with mild to severe TBI and 139 with OI. Behavior ratings were higher after TBI than OI but did not differ by TBI severity. TBI, higher pre-injury executive dysfunction, and lower income predicted the level and trajectory of both Emotional Symptoms and Conduct Problems at 12 months. Female sex and poorer family functioning were vulnerability factors associated with greater increase and change in Emotional Symptoms by 12 months after injury; unique predictors of Conduct Problems included younger age and prior emotional/behavioral problems. Across the long-term follow-up from 12 to 36 months, Emotional Symptoms increased significantly and Conduct Problems stabilized. TBI was not a significant predictor of change during the chronic stage of recovery. Conclusions: After TBI, Emotional Symptoms and Conduct Problem scores were elevated, had different trajectories of change, increased or stayed elevated from 12 to 36 months after TBI, and did not return to pre-injury levels across the 3 year follow-up. These findings highlight the importance of addressing behavioral problems after TBI across an extended time frame