A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin (DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48: 708-733, 2010) for an elliptic obstacle problem. Using a key property of DG methods, we perform the analysis in a general framework. The error estimator we have obtained for DG methods is comparable with the estimator for the conforming Galerkin (CG) finite element method. In the analysis, we construct a non-linear smoothing function mapping DG finite element space to CG finite element space and use it as a key tool. The error estimator consists of a discrete Lagrange multiplier associated with the obstacle constraint. It is shown for non-over-penalized DG methods that the discrete Lagrange multiplier is uniformly stable on non-uniform meshes. Finally, numerical results demonstrating the performance of the error estimator are presented.

Effect of pH on structural and magnetic properties of nanocrystalline Y3Fe5O12 by aqueous co-precipitation method

The Y3Fe5O12 (YIG) nanopowders were synthesised at different pH using co-precipitation method. The effect of pH on the phase formation of YIG is characterised using XRD, TEM, FTIR and TG/DTA. From the Scherer formula, the particle sizes of the powders were found to be 13, 19 and 28 nm for pH=10, 11 and 12 respectively. It is found that as the pH of the solution increase the particle size is also increases. It is also clear from the TG/DTA curves that as the pH is increasing the weight losses were found to be small. The nanopowders were sintered at 600, 700, 800 and 900 degrees C for 5 h using conventional sintering method. The phase formation is completed at 800 degrees C/5 h which is correlated with TG/DTA. The average grain size of the samples is found to be similar to 161 nm. The high values of M-s=23 emu g(-1) and H-c=22 Oe were recorded for the sample sintered at 900 degrees C.

Role of pH controlled DNA secondary structures in the reversible dispersion/precipitation and separation of metallic and semiconducting single-walled carbon nanotubes

Single-stranded DNA (ss-DNA) oligomers (dA(20), d(C(3)TA(2))(3)C-3] or dT(20)) are able to disperse single-walled carbon nanotubes (SWNTs) in water at pH 7 through non-covalent wrapping on the nanotube surface. At lower pH, an alteration of the DNA secondary structure leads to precipitation of the SWNTs from the dispersion. The structural change of dA(20) takes place from the single-stranded to the A-motif form at pH 3.5 while in case of d(C(3)TA(2))(3)C-3] the change occurs from the single-stranded to the i-motif form at pH 5. Due to this structural change, the DNA is no longer able to bind the nanotube and hence the SWNT precipitates from its well-dispersed state. However, this could be reversed on restoring the pH to 7, where the DNA again relaxes in the single-stranded form. In this way the dispersion and precipitation process could be repeated over and over again. Variable temperature UV-Vis-NIR and CD spectroscopy studies showed that the DNA-SWNT complexes were thermally stable even at similar to 90 degrees C at pH 7. Broadband NIR laser (1064 nm) irradiation also demonstrated the stability of the DNA-SWNT complex against local heating introduced through excitation of the carbon nanotubes. Electrophoretic mobility shift assay confirmed the formation of a stable DNA-SWNT complex at pH 7 and also the generation of DNA secondary structures (A/i-motif) upon acidification. The interactions of ss-DNA with SWNTs cause debundling of the nanotubes from its assembly. Selective affinity of the semiconducting SWNTs towards DNA than the metallic ones enables separation of the two as evident from spectroscopic as well as electrical conductivity studies.

Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity

In this article, we analyse several discontinuous Galerkin (DG) methods for the Stokes problem under minimal regularity on the solution. We assume that the velocity u belongs to H-0(1)(Omega)](d) and the pressure p is an element of L-0(2)(Omega). First, we analyse standard DG methods assuming that the right-hand side f belongs to H-1(Omega) boolean AND L-1(Omega)](d). A DG method that is well defined for f belonging to H-1(Omega)](d) is then investigated. The methods under study include stabilized DG methods using equal-order spaces and inf-sup stable ones where the pressure space is one polynomial degree less than the velocity space.

CONVERGENCE ANALYSIS OF THE LOWEST ORDER WEAKLY PENALIZED ADAPTIVE DISCONTINUOUS GALERKIN METHODS

In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm which guides to the convergence of adaptive discontinuous Galerkin methods.

Laboratory Studies on Stabilization of an Expansive Soil by Lime Precipitation Technique

Lime stabilization prevails to be the most widely adopted in situ stabilization method for controlling the swell-shrink potentials of expansive soils despite construction difficulties and its ineffectiveness in certain conditions. In addition to the in situ stabilization methods presently practiced, it is theoretically possible to facilitate in situ precipitation of lime in soil by successive permeation of calcium chloride (CaCl2 ) and sodium hydroxide (NaOH) solutions into the expansive soil. In this laboratory investigation, an attempt is made to study the precipitation of lime in soil by successive mixing of CaCl2 and NaOH solutions with the expansive soil in two different sequences.Experimental results indicated that in situ precipitation of lime in soil by sequential mixing of CaCl2 and NaOH solutions with expansive soil developed strong lime-modification and soil-lime pozzolanic reactions. The lime-modification reactions together with the poorly de- veloped cementation products controlled the swelling potential, reduced the plasticity index, and increased the unconfined compressive strength of the expansive clay cured for 24 h. Comparatively, both lime-modification reactions and well-developed crystalline cementation products (formed by lime-soil pozzolanic reactions) contributed to the marked increase in the unconfined compressive strength of the ex-pansive soil that was cured for 7–21 days. Results also show that the sequential mixing of expansive soil with CaCl2 solution followed by NaOH solution is more effective than mixing expansive soil with NaOH solution followed by CaCl2 solution. DOI: 10.1061/(ASCE)MT .1943-5533.0000483. © 2012 American Society of Civil Engineers.

Comparison of structural and luminescence properties of Dy2O3 nanopowders synthesized by co-precipitation and green combustion routes

Dysprosium oxide (Dy2O3) nanopowders were prepared by co-precipitation (CP) and eco-friendly green combustion (GC) routes. SEM micrographs prepared by CP route show smooth rods with various lengths and diameters while, GC route show porous, agglomerated particles. The results were further confirmed by TEM. Thermoluminescence (TL) responses of the nanopowder prepared by both the routes were studied using gamma-rays. A well resolved glow peak at 353 degrees C along with less intense peak at 183 degrees C was observed in GC route while, in CP a single glow peak at 364 degrees C was observed. The kinetic parameters were estimated using Chen's glow peak route. Photoluminescence (PL) of Dy2O3 shows peaks at 481, 577,666 and 756 nm which were attributed to Dy3+ transitions of F-4(9/2)-H-6(15/2), H-6(11/2), H-6(11/2) and H-6(9/2), respectively. Color co-ordinate values were located in the white region as a result the product may be useful for the fabrication of WLED'S. (C) 2014 Elsevier Ltd. All rights reserved.

Influence of source concentration on structural and optical properties of SnO2 nanoparticles prepared by chemical precipitation method

In present work, a systematic study has been carried out to understand the influence of source concentration on structural and optical properties of the SnO2 nanoparticles. SnO2 nanoparticles have been prepared by using chemical precipitation method at room temperature with aqueous ammonia as a stabilizing agent. X-ray diffraction analysis reveals that SnO2 nanoparticles exhibit tetragonal structure and the particle size is in range of 4.9-7.6 nm. High resolution transmission electron microscopic image shows that all the particles are nearly spherical in nature and particle size lies in range of 4.6-7 nm. Compositional analysis indicates the presence of Sn and O in samples. Blue shift has been observed in optical absorption spectra due to quantum confinement and the bandgap is in range of 4-4.16 eV. The origin of photoluminescence in SnO2 is found to be due to recombination of electrons in singly occupied oxygen vacancies with photo-excited holes in valance band.

Development and Evaluation of Statistical Downscaling Models for Monthly Precipitation

Several statistical downscaling models have been developed in the past couple of decades to assess the hydrologic impacts of climate change by projecting the station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs). This paper presents and compares different statistical downscaling models that use multiple linear regression (MLR), positive coefficient regression (PCR), stepwise regression (SR), and support vector machine (SVM) techniques for estimating monthly rainfall amounts in the state of Florida. Mean sea level pressure, air temperature, geopotential height, specific humidity, U wind, and V wind are used as the explanatory variables/predictors in the downscaling models. Data for these variables are obtained from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis dataset and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled Global Climate Model, version 3 (CGCM3) GCM simulations. The principal component analysis (PCA) and fuzzy c-means clustering method (FCM) are used as part of downscaling model to reduce the dimensionality of the dataset and identify the clusters in the data, respectively. Evaluation of the performances of the models using different error and statistical measures indicates that the SVM-based model performed better than all the other models in reproducing most monthly rainfall statistics at 18 sites. Output from the third-generation CGCM3 GCM for the A1B scenario was used for future projections. For the projection period 2001-10, MLR was used to relate variables at the GCM and NCEP grid scales. Use of MLR in linking the predictor variables at the GCM and NCEP grid scales yielded better reproduction of monthly rainfall statistics at most of the stations (12 out of 18) compared to those by spatial interpolation technique used in earlier studies.

Precipitation response of the magnesium alloy WE43 in strained and unstrained conditions

The precipitation behavior of the magnesium alloy WE43 (Mg-4%Y-2.3%Nd-0.5%Zr) has been studied in strained and unstrained conditions using Transmission Electron Microscopy (TEM). Ageing treatments were carried out at three temperatures, namely 210 degrees C, 230 degrees C and 260 degrees C. The precipitation sequence during static aging of solution treated (ST) samples has been identified as ST —> beta'' —> beta' followed by the formation of beta(1) and equilibrium beta precipitates form after very long ageing periods. Dynamic precipitation was observed during high temperature deformation, leading to the formation of beta' and intermediate beta(1) precipitates. The strained samples, when further heat treated, resulted in the transformation of beta(1) into beta equilibrium precipitates. The sequence of dynamic precipitation is ST —> beta(1) —> beta and ST —> beta'. (C) 2014 Elsevier B.V. All rights reserved.

Performance evaluation of AR4 Climate Models in simulating daily precipitation over the Indian region using skill scores

The ability of Coupled General Circulation Models (CGCMs) participating in the Intergovernmental Panel for Climate Change's fourth assessment report (IPCC AR4) for the 20th century climate (20C3M scenario) to simulate the daily precipitation over the Indian region is explored. The skill is evaluated on a 2.5A degrees x 2.5A degrees grid square compared with the Indian Meteorological Department's (IMD) gridded dataset, and every GCM is ranked for each of these grids based on its skill score. Skill scores (SSs) are estimated from the probability density functions (PDFs) obtained from observed IMD datasets and GCM simulations. The methodology takes into account (high) extreme precipitation events simulated by GCMs. The results are analyzed and presented for three categories and six zones. The three categories are the monsoon season (JJASO - June to October), non-monsoon season (JFMAMND - January to May, November, December) and for the entire year (''Annual''). The six precipitation zones are peninsular, west central, northwest, northeast, central northeast India, and the hilly region. Sensitivity analysis was performed for three spatial scales, 2.5A degrees grid square, zones, and all of India, in the three categories. The models were ranked based on the SS. The category JFMAMND had a higher SS than the JJASO category. The northwest zone had higher SSs, whereas the peninsular and hilly regions had lower SS. No single GCM can be identified as the best for all categories and zones. Some models consistently outperformed the model ensemble, and one model had particularly poor performance. Results show that most models underestimated the daily precipitation rates in the 0-1 mm/day range and overestimated it in the 1-15 mm/day range.

Effects of large-scale deforestation on precipitation in the monsoon regions: Remote versus local effects

In this paper, using idealized climate model simulations, we investigate the biogeophysical effects of large-scale deforestation on monsoon regions. We find that the remote forcing from large-scale deforestation in the northern middle and high latitudes shifts the Intertropical Convergence Zone southward. This results in a significant decrease in precipitation in the Northern Hemisphere monsoon regions (East Asia, North America, North Africa, and South Asia) and moderate precipitation increases in the Southern Hemisphere monsoon regions (South Africa, South America, and Australia). The magnitude of the monsoonal precipitation changes depends on the location of deforestation, with remote effects showing a larger influence than local effects. The South Asian Monsoon region is affected the most, with 18% decline in precipitation over India. Our results indicate that any comprehensive assessment of afforestation/reforestation as climate change mitigation strategies should carefully evaluate the remote effects on monsoonal precipitation alongside the large local impacts on temperatures.

Microstructure and Crystallographic Texture Evolution During the Friction-Stir Processing of a Precipitation-Hardenable Aluminum Alloy

Friction-stir processing (FSP) has been proven as a successful method for the grain refinement of high-strength aluminum alloys. The most important attributes of this process are the fine-grain microstructure and characteristic texture, which impart suitable properties in the as-processed material. In the current work, FSP of the precipitation-hardenable aluminum alloy 2219 has been carried out and the consequent evolution of microstructure and texture has been studied. The as-processed materials were characterized using electron back-scattered diffraction, x-ray diffraction, and electron probe microanalysis. Onion-ring formation was observed in the nugget zone, which has been found to be related to the precipitation response and crystallographic texture of the alloy. Texture development in the alloy has been attributed to the combined effect of shear deformation and dynamic recrystallization. The texture was found heterogeneous even within the nugget zone. A microtexture analysis revealed the dominance of shear texture components, with C component at the top of nugget zone and the B and A(2)* components in the middle and bottom. The bulk texture measurement in the nugget zone revealed a dominant C component. The development of a weaker texture along with the presence of some large particles in the nugget zone indicates particle-stimulated nucleation as the dominant nucleation mechanism during FSP. Grain growth follows the Burke and Turnbull mechanism and geometrical coalescence.

Probable maximum precipitation estimation for catchments in Mahanadi river basin

Probable maximum precipitation (PMP) is a theoretical concept that is widely used by hydrologists to arrive at estimates for probable maximum flood (PMF) that find use in planning, design and risk assessment of high-hazard hydrological structures such as flood control dams upstream of populated areas. The PMP represents the greatest depth of precipitation for a given duration that is meteorologically possible for a watershed or an area at a particular time of year, with no allowance made for long-term climatic trends. Various methods are in use for estimation of PMP over a target location corresponding to different durations. Moisture maximization method and Hershfield method are two widely used methods. The former method maximizes the observed storms assuming that the atmospheric moisture would rise up to a very high value estimated based on the maximum daily dew point temperature. On the other hand, the latter method is a statistical method based on a general frequency equation given by Chow. The present study provides one-day PMP estimates and PMP maps for Mahanadi river basin based on the aforementioned methods. There is a need for such estimates and maps, as the river basin is prone to frequent floods. Utility of the constructed PMP maps in computing PMP for various catchments in the river basin is demonstrated. The PMP estimates can eventually be used to arrive at PMF estimates for those catchments. (C) 2015 The Authors. Published by Elsevier B.V.

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.