An element-based displacement preconditioner for linear elasticity problems

Finite element analysis of problems in structural and geotechnical engineering results in linear systems where the unknowns are displacements and rotations at nodes. Although the solution of these systems can be carried out using either direct or iterative methods, in practice the matrices involved are usually very large and sparse (particularly for 3D problems) so an iterative approach is often advantageous in terms of both computational time and memory requirements. This memory saving can be further enhanced if the method used does not require assembly of the full coefficient matrix during the solution procedure. One disadvantage of iterative methods is the need to apply preconditioning to improve convergence. In this paper, we review a range of established element-based preconditioning methods for linear elastic problems and compare their performance with a new method based on preconditioning with element displacement components. This new method appears to offer a significant improvement in performance.     

Identification of the adverse effect of nitrate on the phosphate release rate and improvement of EBPR process models.

The adverse effect of nitrate on the phosphate release rate in the anaerobic phase was observed and was hardly explainable with conventional EBPR process models. Four possible mechanisms were proposed including substrate competition, reduced fermentation, parallel reaction and sequential reaction. Batch experiments were designed and conducted to identify the dominant mechanism. Results showed that the sequential reaction was the only possible mechanism where only denitrification occurred if any nitrate existed in the anaerobic phase. Then the phosphate release following after the nitrate was completely removed. Nitrate inhibition effect was added into the PHA storage rate to incorporate the sequential reaction in the conventional ASM3 plus EAWAG bio-P module (ASM3 + P). Nitrate inhibition coefficient, K(I,NO,PAO) was found to be as low as 0.05 mg/L. This correlated well with experimental observation where no also meant that the anaerobic compartment of a continuous flow reactor could be seriously affected by the residual nitrate contained in the sludge recycle flow. This phenomenon caused overestimation of the phosphate uptake rate and consequently underestimation of PO4(3-) -P concentration. This problem was resolved by incorporation of a nitrate inhibition term in the ASM3 + P for more accurate simulation of the EBPR process.     

Design of a retention tank: comparison of stormwater quality models with various levels of complexity.

Stormwater quality simulation models are useful tools for the design and management of sewer systems. Modelling results are highly sensitive to experimental data used for calibration. This sensitivity is examined for three modelling approaches of various complexities (site mean concentration approach, event mean concentration approach and build-up, washoff and transport modelling approach) applied to a typical case study (design of a dry detention tank), accounting for the variability of calibration data and their effect on simulation results. Calibrated models with different calibration data sets were used to simulate 3 years of rainfall with different retention tank specific volumes. Annual pollutant load interception efficiencies were determined. Simulations results revealed (i) that there is no advantage in using the EMC model compared to the SMC model and (ii) that the BWT model resulted in higher design ratios than those given by the SMC/hydraulic approach. For both EMC and BWT models, using an increasing number n of events for calibration leads to narrower confidence intervals for the design ratios. It is crucial for design ratios to account for successive storm events in chronological order and to account for the maximum allowable flow to be transferred to the downstream WWTP.     

The Applied Mathematics and Computer Science Schism

Isolating applied mathematics from computer science harms the profession and those who depend on it.     

Structure and electrical characteristics of Ce4+-doped Ba2In2O5

The In-site of Ba₂In₂O₅ with Brownmillerite structure was partially substituted for Ce⁴⁺ ions in order to examine the doping effect on the order-disorder transition. Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.1, 0.2, 0.3, 0.5, 1.0, and 1.5) were prepared by solid state reaction. X-Ray diffraction analyses of these powder samples demonstrated that Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.1 and 0.2) possesses Brownmillerite structure. With increasing content of Ce⁴⁺ ion the crystal system of Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.3, 0.5, and 1.0) changed to cubic perovskite structure above the order-disorder transition temperature of Ba₂In₂O₅. Arrhenius plots of the electrical conductivities of Ba₂In_{2 – x} Ce _x O_{5 + x/2} (x = 0.2, 0.3, and 1.0) exhibited no discontinuity. These compounds had high transference numbers of oxide ion above 973 k.     

Thaumasite––direct, woodfordite and other possible formation routes

Two main formation routes for thaumasite exist below 15 °C. One is the direct route from C–S–H reacting with appropriate carbonate, sulfate, Ca²⁺ ions and excess water. The other route is the woodfordite route from ettringite reacting with C–S–H, carbonate, Ca²⁺ ions and excess water, in which thaumasite arises through the intermediate formation of the solid solution woodfordite. The woodfordite route for thaumasite formation appears to be relatively quicker (although still slow) than the direct route, presumably because with the former the ettringite already has the octahedral [M(OH)₆] units that can facilitate the critical change from [Al(OH)₆]³⁻ to [Si(OH)₆]²⁻ groupings. Both routes are mutually dependent on each other. The presence of magnesium salts can modify the path to thaumasite formation. High pressure might be able to stabilise [Si(OH)₆]²⁻ groupings and allow thaumasite to become formed above 15 °C. This possibility is discussed.     

State of polarization changes: Classification and measurement

We propose a standardization procedure that provides a convenient, quantitative and reproducible laboratory-based method for measuring the state of polarization (SOP) fluctuations produced by polarization varying devices. This method is based on the SOP distributions generated by commercial polarization scramblers. We show that these devices generate distributions of the maximum change of the SOP (in a given sample time) that follow Rayleigh statistics, which scale linearly with scrambling frequency and the sample time. We use this procedure to measure the SOP fluctuations in a short length of coiled fiber subject to mechanical perturbations.     

Oligo(ethylene oxide) side‐chain steric screening effects on conductimetric properties of grafted poly(4‐vinylpyridinium) salts in aqueous solutions

A set of poly[N‐oligo(ethylene oxide)yl 4‐vinylpyridinium tosylate] (P4VOEOOTs) has been prepared by spontaneous polymerization of 4‐vinylpyridine. This method gives a grafted polyelectrolyte having a positive charge on every backbone pyridinic moiety. The P4VP15Ts, P4VP164Ts, P4VP350Ts and P4VP750Ts aqueous solution conductivities were determined in the concentration range from 6 × 10^?4 to 10^?2 M at 25 °C. The variation of the conductivity versus concentration of the investigated system exhibits typical polyelectrolyte behaviour. The polyelectrolyte mobility was found to be dependent on the oligo(ethylene oxide) (OEO) side‐chain length. Manning's rod‐like model fails to describe these results. A simple steric effect is proposed to explain the influence of the OEO length. Copyright © 2003 Society of Chemical Industry     

Effects of surface charge, micro-bubble size and particle size on removal efficiency of electro-flotation.

Flotation is a water treatment alternative to sedimentation, and uses small bubbles to remove low-density particles from potable water and wastewater. The effect of zeta potential, bubble size and particle size on removal efficiency of the electro-flotation process was investigated because previous model-simulations indicated that these attributes are critical for high collision efficiency between micro-bubbles and particles. Solutions containing Al3+ as the metal ion were subjected to various conditions. The zeta potentials of bubbles and particles were similar under identical conditions, and their charges were influenced by metal ion concentration and pH. Maximum removal efficiency was 98 and 12% in the presence and absence of flocculation, respectively. Removal efficiency was higher when particle size was similar to bubble size. These results agree with modelling simulations and indicate that collision efficiency is greater when the zeta potential of one is negative and that of the other is positive and when their sizes are similar.     

Unresolved controversies concerning psychopathy: Implications for clinical and forensic decision making.

At some point in their careers, clinicians who work or consult in forensic and correctional settings will almost certainly encounter individuals who exhibit psychopathic personality features. Because of the widespread use of this disorder to inform legal and clinical decision making, psychologists should be exceedingly familiar with the relevant research literature on this topic before venturing into these settings. This article reviews the empirical bases of several clinically relevant claims and assertions regarding psychopathy and concludes that many areas of research are decidedly more equivocal in their findings than is commonly perceived. Although there is much to be gained by assessing psychopathy in various contexts, clinicians need to be cautious about drawing overzealous and empirically questionable conclusions about an important disorder that also has great potential for abuse. (PsycINFO Database Record (c) 2010 APA, all rights reserved)