An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Hydrogen adsorption on boron doped graphene: an ab initio study

(i) The electronic and structural properties of boron doped graphene sheets, and (ii) the chemisorption processes of hydrogen adatoms on the boron doped graphene sheets have been examined by ab initio total energy calculations. In (i) we find that the structural deformations are very localized around the boron substitutional sites, and in accordance with previous studies (Endo et al 2001 J. Appl. Phys. 90 5670) there is an increase of the electronic density of states near the Fermi level. Our simulated scanning tunneling microscope (STM) images, for occupied states, indicate the formation of bright (triangular) spots lying on the substitutional boron (center) and nearest-neighbor carbon (edge) sites. Those STM images are attributed to the increase of the density of states within an energy interval of 0.5 eV below the Fermi level. For a boron concentration of similar to 2.4%, we find that two boron atoms lying on the opposite sites of the same hexagonal ring (B1-B2 configuration) represents the energetically most stable configuration, which is in contrast with previous theoretical findings. Having determined the energetically most stable configuration for substitutional boron atoms on graphene sheets, we next considered the hydrogen adsorption process as a function of the boron concentration, (ii). Our calculated binding energies indicate that the C-H bonds are strengthened near boron substitutional sites. Indeed, the binding energy of hydrogen adatoms forming a dimer-like structure on the boron doped B1-B2 graphene sheet is higher than the binding energy of an isolated H(2) molecule. Since the formation of the H dimer-like structure may represent the initial stage of the hydrogen clustering process on graphene sheets, we can infer that the formation of H clusters is quite likely not only on clean graphene sheets, which is in consonance with previous studies (Hornekaer et al 2006 Phys. Rev. Lett. 97 186102), but also on B1-B2 boron doped graphene sheets. However, for a low concentration of boron atoms, the formation of H dimer structures is not expected to occur near a single substitutional boron site. That is, the formation (or not) of H clusters on graphene sheets can be tuned by the concentration of substitutional boron atoms.

Disorder-based graphene spintronics

The use of the spin of the electron as the ultimate logic bit-in what has been dubbed spintronics-can lead to a novel way of thinking about information flow. At the same time single-layer graphene has been the subject of intense research due to its potential application in nanoscale electronics. While defects can significantly alter the electronic properties of nanoscopic systems, the lack of control can lead to seemingly deleterious effects arising from the random arrangement of such impurities. Here we demonstrate, using ab initio density functional theory and non-equilibrium Green`s functions calculations, that it is possible to obtain perfect spin selectivity in doped graphene nanoribbons to produce a perfect spin filter. We show that initially unpolarized electrons entering the system give rise to 100% polarization of the current due to random disorder. This effect is explained in terms of different localization lengths for each spin channel which leads to a new mechanism for the spin filtering effect that is disorder-driven.

Size effects on silver nanoparticles` properties

In this work a systematic study of the dependence of the structural, electronic, and vibrational properties on nanoparticle size is performed. Based on our total energy calculations we identified three characteristic regimes associated with the nanoparticle`s dimensions: (i) below 1.5 nm (100 atoms) where remarkable molecular aspects are observed; (ii) between 1.5 and 2.0 nm (100 and 300 atoms) where the molecular behavior is influenced by the inner core crystal properties; and (iii) above 2.0 nm (more than 300 atoms) where the crystal properties are preponderant. In all considered regimes the nanoparticle`s surface modulates its properties. This modulation decreases with the increasing of the nanoparticle`s size.

Single-step chemical synthesis of ferrite hollow nanospheres

We report a single-step chemical synthesis of iron oxide hollow nanospheres with 9.3 nm in diameter. The sample presents a narrow particle diameter distribution and chemical homogeneity. The hollow nature of the particles is confirmed by HRTEM and HAADF STEM analysis. Electron and x-ray diffraction show that the outer material component is constituted by 2 nm ferrite crystals. Mossbauer data provide further evidence for the formation of iron oxide with high structural disorder, magnetically ordered at 4.2 K and superparamagnetism at room temperature. An unusual magnetic behavior under an applied field is reported, which can be explained by the large fraction of atoms existing at both inner and outer surfaces.

Oxygen-mediated electron transport through hybrid silicon-organic interfaces

We investigate from first principles the electronic and transport properties of hybrid organic/silicon interfaces of relevance to molecular electronics. We focus on conjugated molecules bonded to hydrogenated Si through hydroxyl or thiol groups. The electronic structure of the systems is addressed within density functional theory, and the electron transport across the interface is directly evaluated within the Landauer approach. The microscopic effects of molecule-substrate bonding on the transport efficiency are explicitly analyzed, and the oxygen-bonded interface is identified as a candidate system when preferential hole transfer is needed.

Directed self-assembly of quantum structures by nanomechanical stamping using probe tips

We demonstrate that nanomechanically stamped substrates can be used as templates to pattern and direct the self-assembly of epitaxial quantum structures such as quantum dots. Diamond probe tips are used to indent or stamp the surface of GaAs( 100) to create nanoscale volumes of dislocation-mediated deformation, which alter the growth surface strain. These strained sites act to bias nucleation, hence allowing for selective growth of InAs quantum dots. Patterns of quantum dots are observed to form above the underlying nanostamped template. The strain state of the patterned structures is characterized by micro-Raman spectroscopy. The potential of using nanoprobe tips as a quantum dot nanofabrication technology are discussed.

Spin-polarization effects in homogeneous and non-homogeneous diluted magnetic semiconductor heterostructures

Spin polarization is a key characteristic in developing spintronic devices. Diluted magnetic heterostructures (DMH), where subsequent layers of conventional and diluted magnetic semiconductors (DMS) are alternate, are one of the possible ways to obtain it. Si being the basis of modern electronics, Si or other group-IV DMH can be used to build spintronic devices directly integrated with conventional ones. In this work we study the physical properties and the spin-polarization effects of p-type DMH based in group-IV semiconductors (Si, Ge, SiGe, and SiC), by performing self-consistent (k) over right arrow . (p) over right arrow calculations in the local spin density approximation. We show that high spin polarization can be maintained in these structures below certain values of the carrier concentrations. Full spin polarization is attained in the low carrier concentration regime for carrier concentrations in the DMS layer up to similar to 2.0 x 10(19) cm(-3) for Si and up to similar to 6.0 x 10(19) cm(-3) for SiC. Partial, but still important spin polarization can be achieved for all studied group-IV DMH, with the exception of Ge for carrier concentrations up to 6.0 x 10(19) cm(-3). The role played by the effective masses and the energy splitting of the spin-orbit split-off hole bands is also discussed throughout the paper.

Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.

Degradation and adsorption of AZO RR239 dye in aqueous solution by nanoscale zerovalent iron particles immobilized on sawdust

Carra sawdust pretrated with formaldehyde was used to adsorb RR239 (reactive azo dye) at varying pH and zerovalent iron (ZVI) dosage. Modeling of kinetic results shows that sorption process is best described by the pseudo-second-order model. Batch experiments suggest that the decolorization efficiency was strongly enhanced with the presence of ZVI and low solution pH. The kinetics of dye sorption by mixed sorbent (5 g of sawdust and 180 mg of ZVI) at pH 2.0 was rapid, reaching more than 90% of the total discoloration in three minutes.

Effects of hydroxyl group distribution on the reactivity, stability and optical properties of fullerenols

We investigate the impact of hydroxyl groups on the properties of C(60)(OH)(n) systems, with n = 1, 2, 3, 4, 8, 10, 16, 18, 24, 32 and 36 by means of first-principles density functional theory calculations. A detailed analysis from the local density of states has shown that adsorbed OH groups can induce dangling bonds in specific carbon atoms around the adsorption site. This increases the tendency to form polyhydroxylated fullerenes (fullerenols). The structural stability is analyzed in terms of the calculated formation enthalpy of each species. Also, a careful examination of the electron density of states for different fullerenols shows the possibility of synthesizing single molecules with tunable optical properties.