On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Materials processing under microgravity conditions using drop tubes

Drop tube provides a low-cost alternative to study the influence of microgravity in materials processing. In the present paper, the current status of the drop tubes and associated experiments on materials processing are reviewed. Emphasis is placed on the advantages and limitations of these studies. It is pointed out that despite size limitation, large opportunities exist to study the fundamental aspects of the influence of gravity in materials processing.

Role of bacterial growth conditions and adhesion in the bioleaching of chalcopyrite by Thiobacillus ferrooxidans

The role of growth conditions and adhesion of Thiobacillus ferrooxidans on the leaching of chalcopyrite was investigated. Thiobacillus ferrooxidans grown on sulfur, thiosulfate and ferrous ion substrates was used in this comparative study. Growth on sulfur, a solid substrate, requires bacterial adhesion unlike that required in the presence of soluble thiosulfate and ferrous ion in a mineral-salts medium. Solid substrate-grown cells showed higher rates of leaching than those grown in liquid media. An initial lag period noticed during leaching by solution-grown cells was absent when solid substrate-grown cells were used. Such a behavior is attributed to the presence of an inducible proteinaceous cell-surface appendage on the sulfur-grown cells. This appendage aids in bacterial adhesion onto the mineral surfaces. Such an appendage is absent in solution-grown cells, as substantiated by electrophoretic measurements. The importance of bacterial adhesion and the direct mechanism in leaching by Thiobacillus ferrooxidans are demonstrated.

Structural variants of hyperbranched polyesters

Hyperbranched polyesters based on 3,5-dihydroxybenzoic acid and its derivatives were prepared by self-condensation of the corresponding ester under standard trans-esterification conditions. The spacer segment length that connects the branching points was systematically varied by starting from the appropriate ethyl 3,5-bis(omega-hydroxyoligo(ethyleneoxy))benzoate. The thermal properties of the hyperbranched polyesters were studied using DSC, and they have been compared with those of the linear analogues prepared from the corresponding p-hydroxybenzoic acid derivatives and also with the molecularly ''kinked'' analogues prepared from the meta isomers. These hyperbranched polyesters were also terminally functionalized by using a potentially mesogenic 4-butoxybiphenylcarboxylic acid derivative in an attempt to prepare novel hyperbranched liquid crystalline polyesters. This was achieved by copolymerization of the AB(2) monomer with the mesogenic A-type capping unit. These polymers were found to be amorphous and did not exhibit any liquid crystalline phases, probably due to the random distribution of the mesogenic segments on the polymer framework, making it difficult to both crystallize and form mesophases.

Stability analysis of stochastically parametered nonconservative columns

Nonconservatively loaded columns. which have stochastically distributed material property values and stochastic loadings in space are considered. Young's modulus and mass density are treated to constitute random fields. The support stiffness coefficient and tip follower load are considered to be random variables. The fluctuations of external and distributed loadings are considered to constitute a random field. The variational formulation is adopted to get the differential equation and boundary conditions. The non self-adjoint operators are used at the boundary of the regularity domain. The statistics of vibration frequencies and modes are obtained using the standard perturbation method, by treating the fluctuations to be stochastic perturbations. Linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed. Bounds for the statistics of vibration frequencies are obtained. The critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought. Then, the frequency equation is employed to transform the eigenvalue statistics to critical load statistics. Specialization of the general procedure to Beck, Leipholz and Pfluger columns is carried out. For Pfluger column, nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics.

Stability of stochastic Leipholz column with stochastic loading

The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.

Link Conditions for Simplifying Meshes with Embedded Structures

Interactive visualization applications benefit from simplification techniques that generate good-quality coarse meshes from high-resolution meshes that represent the domain. These meshes often contain interesting substructures, called embedded structures, and it is desirable to preserve the topology of the embedded structures during simplification, in addition to preserving the topology of the domain. This paper describes a proof that link conditions, proposed earlier, are sufficient to ensure that edge contractions preserve the topology of the embedded structures and the domain. Excluding two specific configurations, the link conditions are also shown to be necessary for topology preservation. Repeated application of edge contraction on an extended complex produces a coarser representation of the domain and the embedded structures. An extension of the quadric error metric is used to schedule edge contractions, resulting in a good-quality coarse mesh that closely approximates the input domain and the embedded structures.

Interannual variations of Indian summer monsoon in a GCM: External conditions versus internal feedbacks

The potential predictability of the Indian summer monsoon due to slowly varying sea surface temperature (SST) forcing is examined. Factors responsible for limiting the predictability are also investigated. Three multiyear simulations with the R30 version of the Geophysical Fluid Dynamics Laboratory's climate model are carried out for this purpose, The mean monsoon simulated by this model is realistic including the mean summer precipitation over the Indian continent. The interannual variability of the large-scale component of the monsoon such as the "monsoon shear index" and its teleconnection with Pacific SST is well simulated by the model in a 15-yr integration with observed SST as boundary condition. On regional scales, the skill in simulating the interannual variability of precipitation over the Indian continent by the model is rather modest and its simultaneous correlation with eastern Pacific SST is negative but poor as observed. The poor predictability of precipitation over the Indian region in the model is related to the fact that contribution to the interannual variability over this region due to slow SST variations [El Nino-Southern Oscillation (ENSO) related] is comparable to those due to regional-scale fluctuations unrelated to ENSO SST. The physical mechanism through which ENSO SST tend to produce reduction in precipitation over the Indian continent is also elucidated. A measure of internal variability of the model summer monsoon is obtained from a 20-yr integration of the same model with fixed annual cycle SST as boundary conditions but with predicted soil moisture and snow cover. A comparison of summer monsoon indexes between this run and the observed SST run shows that the internal oscillations can account for a large fraction of the simulated monsoon variability. The regional-scale oscillations in the observed SST run seems to arise from these internal oscillations. It is discovered that most of the interannual internal variability is due to an internal quasi-biennial oscillation (QBO) of the model atmosphere. Such a QBO is also found in the author's third 18-yr simulation in which fixed annual cycle of SST as well as soil moisture and snow cover are prescribed. This shows that the model QBO is not due to land-surface-atmosphere interaction. It is proposed that the model QBO arises due to an interaction between nonlinear intraseasonal oscillations and the annual cycle. Spatial structure of the QBO and its role in limiting the predictability of the Indian summer monsoon is discussed.

Stereospecific and regioselective catalytic epoxidation of alkenes by a novel ruthenium(II) complex under aerobic conditions

Epoxidation of alkenes by molecular oxygen is effected in high yields by catalysis of RuCl2(biox)(2) using isobutyraldehyde as the co-reductant: the reaction is stereospecific and regioselective.

Studies on the variations in compression strengths of graphite powders bearing glass-epoxy composites exposed to humid conditions

The moisture absorption and changes in compression strengths in glass-epoxy (G-E composites without and with discrete quantities of graphite powders introduced into the resin mix prior to its spreading on specific glass fabric (layers) during the lay-up (stacking) sequence forms the subject matter of this report. The results point to higher moisture absorption for graphite bearing specimens. The strengths of graphite-free coupons show a continuous decrease, while the filler bearing ones show an initial rise followed by a drop for larger exposure times. Scanning Fractographic features were examined for an understanding of the process. The observations were explained invoking the effect of matrix plasticizing and the role of interfacial regions.

Algal Photosynthetic Dynamics in Urban Lakes under Stress Conditions

Urban lakes form vital ecosystems supporting livelihood with social, economic and aesthetic benefits that are essential for quality life. This depends on the biotic and abiotic components in an ecosystem. The structure of an ecosystem forms a decisive factor in sustaining its functional abilities which include nutrient cycling, oxygen production, etc. A community assemblage of primary producers (algae) plays a crucial role in maintaining the balance as they form the base of energy pyramid in the ecosystem. Algae assimilate carbon in the environment via photosynthetic activities and releases oxygen for the next level of biotic elements in an ecosystem. Besides these, algal cells rich in protein serve as food and feed, used as manure and for production of biofuels. Understanding algal photosynthetic dynamics helps in assessing the level of dissolved oxygen (DO), food (fish, etc.), waste assimilation, etc. Algal chlorophyll content, algal biomass, primary productivity and algal photosynthetic quotient are some of the parameters that help in assessing the status of urban lakes. Chlorophyll content gives a measure of the growth, spread and quantity of algae. Unplanned rapid urbanization in Bangalore in recent times has resulted in either disappearance of lake ecosystems or deteriorated the lake water quality impairing the ecological processes. This paper computes algal growth, community structure, primary productivity and composition for three major lakes (T G Halli, Bellandur and Varthur lakes) under contrast levels of anthropogenic influences.

The prop-2-ynyloxy carbonyl function (POC): A new amino-protecting group removable from sulfur-containing peptides by ultrasonic irradiation with tetrathiomolybdate under mild and neutral conditions

The prop-2-ynyloxy carbonyl function (POC) which can be cleaved under mild and neutral conditions in the presence of benzyltriethylammonium tetrathiomolybdate has been developed as a new protecting group for amines. (C) 1999 Elsevier Science Ltd. All rights reserved.