A posteriori error analysis of an augmented fully-mixed formulation for the stationary Boussinesq model

In this paper we undertake an a posteriori error analysis along with its adaptive computation of a new augmented fully-mixed finite element method that we have recently proposed to numerically simulate heat driven flows in the Boussinesq approximation setting. Our approach incorporates as additional unknowns a modified pseudostress tensor field and an auxiliary vector field in the fluid and heat equations, respectively, which possibilitates the elimination of the pressure. This unknown, however, can be easily recovered by a postprocessing formula. In turn, redundant Galerkin terms are included into the weak formulation to ensure well-posedness. In this way, the resulting variational formulation is a four-field augmented scheme, whose Galerkin discretization allows a Raviart–Thomas approximation for the auxiliary unknowns and a Lagrange approximation for the velocity and the temperature. In the present work, we propose a reliable and efficient, fully-local and computable, residual-based a posteriori error estimator in two and three dimensions for the aforementioned method. Standard arguments based on duality techniques, stable Helmholtz decompositions, and well-known results from previous works, are the main underlying tools used in our methodology. Several numerical experiments illustrate the properties of the estimator and further validate the expected behavior of the associated adaptive algorithm.     

Hierarchically CdS Decorated 1D ZnO Nanorods‐2D Graphene Hybrids: Low Temperature Synthesis and Enhanced Photocatalytic Performance

A simple, low‐temperature synthesis approach is reported for planting CdS‐sensitized 1D ZnO nanorod arrays on the 2D graphene (GR) sheet to obtain the ternary hierarchical nanostructures, during which graphene oxide (GO) as the precursor of GR acts as a flexible substrate for the formation of ZnO nanorod arrays. The hierarchical CdS‐1D ZnO‐2D GR hybrids can serve as an efficient visible‐light‐driven photocatalyst for selective organic transformations. The fast electron transport of 1D ZnO nanorods, the well‐known electronic conductivity of 2D GR, the intense visible‐light absorption of CdS, the unique hierarchical structure, and the matched energy levels of CdS, ZnO and GR efficiently boost the photogenerated charge carriers separation and transfer across the interfacial domain of hierarchical CdS‐1D ZnO‐2D GR hybrids under visible light irradiation via three‐level electron transfer process. Furthermore, the superior reusability of ternary hybrids is achieved by controlling the reaction parameters, i.e., using visible light irradiation and holes scavenger to prevent ZnO and CdS from photocorrosion. This work demonstrates a facile way of fabricating hierarchical CdS‐1D ZnO‐2D GR hybrids in a controlled manner and highlights a promising scope of adopting integrative photosensitization and co‐catalyst strategy to design more efficient semiconductor‐based composite photocatalysts toward solar energy capture and conversion.     

Application of Piecewise Hierarchical Linear Growth Modeling to the Study of Continuity in Behavioral Development of Baboons (Papio hamadryas).

In behavioral science, developmental discontinuities are thought to arise when the association between an outcome measure and the underlying process changes over time. Sudden changes in behavior across time are often taken to indicate that a reorganization in the outcome-process relationship may have occurred. The authors proposed in this article the use of piecewise hierarchical linear growth modeling as a statistical methodology to search for discontinuities in behavioral development and illustrated its possibilities by applying 2-piece hierarchical linear models to the study of developmental trajectories of baboon (Papio hamadryas) mothers' behavior during their infants' 1st year of life. The authors provided empirical evidence that piecewise growth modeling can be used to determine whether abrupt changes in development trajectories are tied to changes in the underlying process. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mother-infant relationships in baboons (Papio hamadryas): Predictors of differences and discontinuities in developmental pathways.

This study uses hierarchical linear regression modeling to analyze sources of variation in the developmental pathways of mother-infant relationships and to search for behavioral discontinuities. The data come from 23 mother-infant dyads of baboons (Papio hamadryas), whose interactions were recorded longitudinally during the infants' 1st year of life. The infant's sex and the mother's age and reproductive experience accounted for part of the variation observed in the developmental pathways of 11 of 20 behavioral measures analyzed; however, some of them did so only in some periods but not in others. The authors proposed that this can reflect the occurrence of reorganizations or discontinuities in the mother-infant relationship that can be related to important life events such as the mother's resumption of sexual activity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A posteriori error analysis of an augmented mixed-primal formulation for the stationary Boussinesq model

In an earlier work of us, a new mixed finite element scheme was developed for the Boussinesq model describing natural convection. Our methodology consisted of a fixed-point strategy for the variational problem that resulted after introducing a modified pseudostress tensor and the normal component of the temperature gradient as auxiliary unknowns in the corresponding Navier-Stokes and advection-diffusion equations defining the model, respectively, along with the incorporation of parameterized redundant Galerkin terms. The well-posedness of both the continuous and discrete settings, the convergence of the associated Galerkin scheme, as well as a priori error estimates of optimal order were stated there. In this work we complement the numerical analysis of our aforementioned augmented mixed-primal method by carrying out a corresponding a posteriori error estimation in two and three dimensions. Standard arguments relying on duality techniques, and suitable Helmholtz decompositions are used to derive a global error indicator and to show its reliability. A globally efficiency property with respect to the natural norm is further proved via usual localization techniques of bubble functions. Finally, an adaptive algorithm based on a reliable, fully local and computable a posteriori error estimator induced by the aforementioned one is proposed, and its performance and effectiveness are illustrated through a few numerical examples in two dimensions.     

An augmented fully-mixed finite element method for the stationary Boussinesq problem

In this paper we propose and analyze a new fully-mixed finite element method for the stationary Boussinesq problem. More precisely, we reformulate a previous primal-mixed scheme for the respective model by holding the same modified pseudostress tensor depending on the pressure, and the diffusive and convective terms of the Navier–Stokes equations for the fluid; and in contrast, we now introduce a new auxiliary vector unknown involving the temperature, its gradient and the velocity for the heat equation. As a consequence, a mixed approach is carried out in heat as well as fluid equation, and differently from the previous scheme, no boundary unknowns are needed, which leads to an improvement of the method from both the theoretical and computational point of view. In fact, the pressure is eliminated and as a result the unknowns are given by the aforementioned auxiliary variables, the velocity and the temperature of the fluid. In addition, for reasons of suitable regularity conditions, the scheme is augmented by using the constitutive and equilibrium equations, and the Dirichlet boundary conditions. Then, the resulting formulation is rewritten as a fixed point problem and its well-posedness is guaranteed by the classical Banach theorem combined with the Lax–Milgram theorem. As for the associated Galerkin scheme, the Brouwer and the Banach fixed point theorems are utilized to establish existence and uniqueness of discrete solution, respectively. In particular, Raviart–Thomas spaces of order k for the auxiliary unknowns and continuous piecewise polynomials of degree \(\le k +1\) for the velocity and the temperature become feasible choices. Finally, we derive optimal a priori error estimates and provide several numerical results illustrating the good performance of the scheme and confirming the theoretical rates of convergence.     

Resolution of pattern recognition problems using a hybrid Genetic/Random Neural Network learning algorithm

Gelenbe has proposed a neural network, called a Random Neural Network, which calculates the probability of activation of the neurons in the network. In this paper, we propose to solve the patterns recognition problem using a hybrid Genetic/Random Neural Network learning algorithm. The hybrid algorithm trains the Random Neural Network by integrating a genetic algorithm with the gradient descent rule-based learning algorithm of the Random Neural Network. This hybrid learning algorithm optimises the Random Neural Network on the basis of its topology and its weights distribution. We apply the hybrid Genetic/Random Neural Network learning algorithm to two pattern recognition problems. The first one recognises or categorises alphabetic characters, and the second recognises geometric figures. We show that this model can efficiently work as associative memory. We can recognise pattern arbitrary images with this algorithm, but the processing time increases rapidly.     

Complex defects in the oxidation of uranium

Thermogravimetric studies of the oxidation of uranium in oxygen, water vapor, and air water vapor atmospheres have suggested that the oxidation process is controlled by oxygen interstitial/vacancy defect clusters. An interstitial-rich cluster of the Willis type 2(O _i ^a V _iO _i ^b )] has been postulated to control the oxidation of uranium in oxygen, water vapor, and the initial stage in air-water vapor, while a vacancy-rich defect cluster was proposed for the final oxidation stage in air-water vapor. Electron paramagnetic studies of uranium oxides have shown that the vacancy-rich defect displays a strong EPR resonance with a g value of 2.06, and the interstitial defect does not display a paramagnetic resonance. These measurements confirm directly the defect states inferred from kinetic studies. This paper is based on a presentation made at the “Stephen R. Shatynski Memorial Symposium on Surfaces and Interfaces” held at the 114th annual AIME meeting in New York, February 24-28, 1985, under the auspices of the ASM-MSD Thermodynamic Activity Committee.     

Effects of tensile stress on microstructural change of eutectoid Zn-AI alloy

Microstructural changes and phase transformations of eutectoid Zn-Al-based alloy ZnA120.2Cul.8 (wt pct) were studied under tensile stress by using X-ray diffraction and scanning electron microscopy (SEM) techniques. It was found that the lamellar microstructure of the heat-treated eutectoid Zn-Albased alloy changed partially into a spheroidized structure at the rupture part of the specimen after tensile testing, while the lamellar structure at the bulk part of the specimen remained stable in the original state. The X-ray diffraction identification results showed that two phase transformations,i.e., decomposition of metastable phase η′_T and a four-phase transformation, α+ ε → T + η, occurred during tensile testing. It was concluded that the tensile stress affected not only microstructural change but also phase transformation of the alloy. The SEM observation on the etched specimen showed clearly the morphology of the microstructural change.