Shear-free perfect fluids with a γ-law equation of state

 We investigate all shear-free perfect fluid solutions of the Einstein field equations where the pressure and energy density satisfy a (Formula presented.)-law equation of state with (Formula presented.). We prove that such a fluid is either non rotating or non expanding. As a consequence, it follows by combining our result with those of Collins and Wainwright that any such shear-free perfect fluid which models either an expand universe or a collapsing star must in fact be a Friedmann–Robertson–Walker spacetime.

Shear-free perfect fluids with a solenoidal magnetic curvature

We investigate shear-free perfect fluid solutions of the Einstein field equations where the fluid pressure satisfies a barotropic equation of state and the spatial divergence of the magnetic part of the Weyl tensor is zero. We prove, with the exception of certain quite restricted special cases within the class of solutions in which there exists a Killing vector aligned with the vorticity and for which the magnitude of the vorticity ω is not a function of the matter density μ alone, that such a fluid is either non-rotating or non-expanding. In the restricted cases the equation of state must satisfy an over-determined differential system.

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.

Enhancement of aerobic granulation by zero-valent iron in sequencing batch airlift reactor

This study elucidates the enhancement of aerobic granulation by zero-valent iron (ZVI). A reactor augmented with ZVI had a start-up time of aerobic granulation (43 days) that was notably less than that for a reactor without augmentation (64 days). The former reactor also had better removal efficiencies for chemical oxygen demand and ammonium. Moreover, the mature granules augmented with ZVI had better physical characteristics and produced more extracellular polymeric substances (especially of protein). Three-dimensional-excitation emission matrix fluorescence showed that ZVI enhanced organic material diversity. Additionally, ZVI enhanced the diversity of the microbial community. Fe(2+) dissolution from ZVI helped reduce the start-up time of aerobic granulation and increased the extracellular polymeric substance content. Conclusively, the use of ZVI effectively enhanced aerobic granulation.

Characterization of the extracellular polymeric substances and microbial community of aerobic granulation sludge exposed to cefalexin

This study characterizes the extracellular polymeric substances and bacterial community composition of aerobic granules exposed to cefalexin (CLX). The presence of CLX potentially decreases granular stabilities, resulting in a lowered granule diameter. Chemical oxygen demand and NH4+-N removal efficiencies were slightly decreased and the denitrification process was inhibited with CLX addition. Extracellular polymeric substance contents were significantly increased in aerobic granules exposed to CLX. The shifts of fluorescence intensities and peak locations in 3D-EEM fluorescence spectra indicated changes of EPS components. High-throughput sequencing analysis showed aerobic granules with CLX addition in synthetic wastewater had superior diversity of microbial species, and this was the reason that the level and components of EPS changed. The species richness for bacteria was increased from 341 to 352, which was revealed by Chao1. The Shannon index of diversity rose slightly from 3.59 to 3.73 with CLX addition. The abundance of Proteobacteria significantly decreased, while the abundance of Bacteroidetes and Chloroflexi underwent a highly significant increase in aerobic granules exposed to CLX.

Molecular dynamics simulations of highly concentrated salt solutions : structural and transport effects in polymer electrolytes

Structural, thermodynamic and transport properties have been calculated in concentrated non-aqueous NaI solutions using molecular dynamics simulations. Although the solvent has been represented by a simplistic Stockmayer fluid (spherical particles with point dipoles), the general trends observed are still a useful indication of the behavior of real non-aqueous electrolyte systems. Results indicate that in low dielectric media, significant ion pairing and clustering occurs. Contact ion pairs become more prominent at higher temperatures, independent of the dielectric strength of the solvent. Thermodynamic analysis shows that this temperature behavior is predominantly entropically driven. Calculation of ionic diffusivities and conductivities in the NaI/ether system confirms the clustered nature of the salt, with the conductivities significantly lower than those predicted from the Nernst-Einstein relation. In systems where the solvent-ion interactions increase relative to ion-ion interactions (lower charge or higher solvent dipole moment), less clustering is observed and the transport properties indicate independent motion of the ions, with higher calculated conductivities. The solvent in this system is the most mobile species, in comparison with the polymer electrolytes where the solvent is practically immobile.

On the concept of ionicity in ionic liquids

Ionic liquids are liquids comprised totally of ions. However, not all of the ions present appear to be available to participate in conduction processes, to a degree that is dependent on the nature of the ionic liquid and its structure. There is much interest in quantifying and understanding this ‘degree of ionicity’ phenomenon. In this paper we present transport data for a range of ionic liquids and evaluate the data firstly in terms of the Walden plot as an approximate and readily accessible approach to estimating ionicity. An adjusted Walden plot that makes explicit allowance for differences in ion sizes is shown to be an improvement to this approach for the series of ionic liquids described. In some cases, where diffusion measurements are possible, it is feasible to directly quantify ionicity via the Nernst–Einstein equation, confirming the validity of the adjusted Walden plot approach. Some of the ionic liquids studied exhibit ionicity values very close to ideal; this is discussed in terms of a model of a highly associated liquid in which the ion correlations have similar impact on both the diffusive and conductive motions. Ionicity, as defined, is thus a useful measure of adherence to the Nernst–Einstein equation, but is not necessarily a measure of ion availability in the chemical sense.

Highly concentrated salt solutions : molecular dynamics simulations of structure and transport

Molecular dynamics (MD) simulations in NaI solutions, where the solvent has been represented by the Stockmayer fluid, were performed as a function of temperature, salt concentration, and solvent dipole strength. At higher temperatures contact ion pairs become more prevalent, regardless of solvent strength. An examination of the temperature dependence of the potential of mean force demonstrates the entropic nature of this effect. The transport properties calculated in the simulations are dependent on the balance between solvent dielectric constant and ion charge. In systems with a large solvent dipole moment, the ions appear to be independently mobile, and deviations from Nernst–Einstein behavior are small. In systems of smaller solvent dipole moment or greater ion charge, the ions form clusters, and large deviations from Nernst–Einstein behavior are observed.

Simulations of structure and transport in polymer electrolytes

Simulations implementing both Monte Carlo (MC) and molecular dynamics (MD) techniques were used to explore various aspects of polymer electrolytes. Evidence is presented to support the conclusion that collective behavior of ions determines much of the behavior of these complex materials. Simple theories attributing ion transport to either single ions or clusters of three ions are inadequate to explain ion transport behavior; in particular, the Nernst-Einstein relation commonly used to discuss polymer electrolytes is almost certainly quantitatively inappropriate for these materials.

Ion clustering in molecular dynamics simulations of sodium iodide solutions

Model systems of sodium iodide dissolved in dimethyl ether or 1,2-dimethoxyethane (glyme) were studied in order to investigate the structural and dynamic properties of ionic solutions in small and polymeric ethers. Full molecular dynamics simulations were performed at a range of different salt concentrations. An algorithm was designed which assigns ions to clusters and then calculates all the terms which contribute to ionic conductivity. In dilute solutions, free ions are the most common ionic species, followed by ion pairs. As the concentration increases, pairs become the most common species, with significant concentrations of clusters with 3 through 6 ions. Changing the solvent from dimethyl ether to glyme significantly decreases the ion clustering due to the chelate effect in which the two oxygens on a solvent stabilize an associated cation. The conductivity in stable systems is shown to be primarily the result of the movement of free ions and the relative movement of ions within neutral pairs. The Nernst-Einstein relation, commonly used in the discussion of polymer electrolytes, is shown to be inadequate to quantitatively describe conductivity in the model systems.

Physical and electrochemical properties of thioether-functionalized ionic liquids

The preparation and characterization of a series of ionic liquids based on S-alkyl thiolonium, S-alkyl thiotetrazolium, or S-alkyl thiobenzolium cations coupled with bis(trifluoromethanesulfonyl)amide, trifluoromethanesulfonate, alkyl phosphate, chloride, and hexafluorophosphate anions are reported. All are liquid at room temperature, except the chloride salt, which has a melting point of 92 °C. The electrochemical characteristics of this class of ionic liquid have been determined by cyclic voltammetry. Potential windows of the ionic liquids have been obtained at glassy carbon, platinum, and gold electrodes and found to be the largest at glassy carbon, but are limited by oxidation of the thioether-functionalized cation. The voltammetry of IUPAC reference potential scale systems, ferrocene/ferrocenium, cobaltocenium/cobaltocene, and decamethylferrocene/decamethylferrocenium have been evaluated, with the last being most widely applicable. Nonadditivity of Faradaic current is found in the voltammograms of decamethylferrocene in the presence of ferrocene and cobaltocenium. Diffusion coefficient, viscosity, ionic conductivity, double layer capacitance, and other physical properties have also been measured. The dependence of the diffusion coefficient vs viscosity follows the Stokes−Einstein relationship. The properties of the ionic liquids are compared with the related imidazolium family of ionic liquids.

Comparisons of sidewall correction of bed shear stress in open-channel flows

When investigating sediment transport in laboratory open-channel flows, it is often necessary to remove sidewall effects for computing effective bed shear stress. Previous sidewall correction methods are subject to some assumptions that have not been completely verified, and different values of the bed shear stress may be obtained depending on the approach used in making sidewall corrections. This study provides a quantitative assessment of the existing correction procedures by comparing them to a new sidewall correction model proposed in this study. The latter was derived based on the shear stress function and equivalent roughness size for both rigid and mobile bed conditions, which were obtained directly from experimental measurements. The comparisons show that the Einstein correction formula and the Vanoni and Brooks method generally predict relatively lower and higher bed shear stresses, respectively, while the Williams’ empirical function leads to more scatter. This study also demonstrates that the widely used Vanoni and Brooks approach can be well approximated by a simple formula derived based on the Blasius resistance function. The sidewall effects, when removed in the different ways, would consequently affect the presentation of the bedload function. Experimental results of bedload transport, when plotted as the dimensionless transport rate against the dimensionless shear stress with the latter being corrected using the present model, exhibit less scatter than those associated with the previous procedures.

Development and characterization of the 2,4,6-trichlorophenol (2,4,6-TCP) aerobic degrading granules in sequencing batch airlift reactor

2,4,6-trichlorophenol (2,4,6-TCP) aerobic degrading granules were successfully developed in the sequencing batch airlift reactor. The key strategy used in cultivation of the granules was dosing glucose and acetate as co-substrates. After granulation, average concentrations of 2,4,6-TCP and COD in the effluent were less than 8mgL-1 and 59mgL-1, respectively. The removal efficiencies of 2,4,6-TCP and COD were above 93% and 90%, respectively. The specific degradation rate of 2,4,6-TCP peaked at 61mg 2,4,6-TCP gVSS-1h-1 when inoculated at the concentration of 400mgL-1. The extracellular polymeric substance (EPS) contents of the 2,4,6-TCP aerobic degrading granules were decreased compared with the contents in seed sludge. Two peaks attributed to the protein-like fluorophores were identified by three-dimensional excitation emission matrix (EEM) fluorescence spectra. The decrease of fluorescence parameters, e.g., peak locations, intensities, indicated quenching effect of 2,4,6-TCP on the EPS fluorescence. Meanwhile, the shift of peak position indicated chemical changes of the EPS.

Global, regional, and national incidence and mortality for HIV, tuberculosis, and malaria during 1990-2013: a systematic analysis for the Global Burden of Disease Study 2013

BACKGROUND: The Millennium Declaration in 2000 brought special global attention to HIV, tuberculosis, and malaria through the formulation of Millennium Development Goal (MDG) 6. The Global Burden of Disease 2013 study provides a consistent and comprehensive approach to disease estimation for between 1990 and 2013, and an opportunity to assess whether accelerated progress has occured since the Millennium Declaration. METHODS: To estimate incidence and mortality for HIV, we used the UNAIDS Spectrum model appropriately modified based on a systematic review of available studies of mortality with and without antiretroviral therapy (ART). For concentrated epidemics, we calibrated Spectrum models to fit vital registration data corrected for misclassification of HIV deaths. In generalised epidemics, we minimised a loss function to select epidemic curves most consistent with prevalence data and demographic data for all-cause mortality. We analysed counterfactual scenarios for HIV to assess years of life saved through prevention of mother-to-child transmission (PMTCT) and ART. For tuberculosis, we analysed vital registration and verbal autopsy data to estimate mortality using cause of death ensemble modelling. We analysed data for corrected case-notifications, expert opinions on the case-detection rate, prevalence surveys, and estimated cause-specific mortality using Bayesian meta-regression to generate consistent trends in all parameters. We analysed malaria mortality and incidence using an updated cause of death database, a systematic analysis of verbal autopsy validation studies for malaria, and recent studies (2010-13) of incidence, drug resistance, and coverage of insecticide-treated bednets. FINDINGS: Globally in 2013, there were 1·8 million new HIV infections (95% uncertainty interval 1·7 million to 2·1 million), 29·2 million prevalent HIV cases (28·1 to 31·7), and 1·3 million HIV deaths (1·3 to 1·5). At the peak of the epidemic in 2005, HIV caused 1·7 million deaths (1·6 million to 1·9 million). Concentrated epidemics in Latin America and eastern Europe are substantially smaller than previously estimated. Through interventions including PMTCT and ART, 19·1 million life-years (16·6 million to 21·5 million) have been saved, 70·3% (65·4 to 76·1) in developing countries. From 2000 to 2011, the ratio of development assistance for health for HIV to years of life saved through intervention was US$4498 in developing countries. Including in HIV-positive individuals, all-form tuberculosis incidence was 7·5 million (7·4 million to 7·7 million), prevalence was 11·9 million (11·6 million to 12·2 million), and number of deaths was 1·4 million (1·3 million to 1·5 million) in 2013. In the same year and in only individuals who were HIV-negative, all-form tuberculosis incidence was 7·1 million (6·9 million to 7·3 million), prevalence was 11·2 million (10·8 million to 11·6 million), and number of deaths was 1·3 million (1·2 million to 1·4 million). Annualised rates of change (ARC) for incidence, prevalence, and death became negative after 2000. Tuberculosis in HIV-negative individuals disproportionately occurs in men and boys (versus women and girls); 64·0% of cases (63·6 to 64·3) and 64·7% of deaths (60·8 to 70·3). Globally, malaria cases and deaths grew rapidly from 1990 reaching a peak of 232 million cases (143 million to 387 million) in 2003 and 1·2 million deaths (1·1 million to 1·4 million) in 2004. Since 2004, child deaths from malaria in sub-Saharan Africa have decreased by 31·5% (15·7 to 44·1). Outside of Africa, malaria mortality has been steadily decreasing since 1990. INTERPRETATION: Our estimates of the number of people living with HIV are 18·7% smaller than UNAIDS's estimates in 2012. The number of people living with malaria is larger than estimated by WHO. The number of people living with HIV, tuberculosis, or malaria have all decreased since 2000. At the global level, upward trends for malaria and HIV deaths have been reversed and declines in tuberculosis deaths have accelerated. 101 countries (74 of which are developing) still have increasing HIV incidence. Substantial progress since the Millennium Declaration is an encouraging sign of the effect of global action. FUNDING: Bill & Melinda Gates Foundation.

Global, regional, and national levels and causes of maternal mortality during 1990-2013: a systematic analysis for the Global Burden of Disease Study 2013

BACKGROUND: The fifth Millennium Development Goal (MDG 5) established the goal of a 75% reduction in the maternal mortality ratio (MMR; number of maternal deaths per 100,000 livebirths) between 1990 and 2015. We aimed to measure levels and track trends in maternal mortality, the key causes contributing to maternal death, and timing of maternal death with respect to delivery. METHODS: We used robust statistical methods including the Cause of Death Ensemble model (CODEm) to analyse a database of data for 7065 site-years and estimate the number of maternal deaths from all causes in 188 countries between 1990 and 2013. We estimated the number of pregnancy-related deaths caused by HIV on the basis of a systematic review of the relative risk of dying during pregnancy for HIV-positive women compared with HIV-negative women. We also estimated the fraction of these deaths aggravated by pregnancy on the basis of a systematic review. To estimate the numbers of maternal deaths due to nine different causes, we identified 61 sources from a systematic review and 943 site-years of vital registration data. We also did a systematic review of reports about the timing of maternal death, identifying 142 sources to use in our analysis. We developed estimates for each country for 1990-2013 using Bayesian meta-regression. We estimated 95% uncertainty intervals (UIs) for all values. FINDINGS: 292,982 (95% UI 261,017-327,792) maternal deaths occurred in 2013, compared with 376,034 (343,483-407,574) in 1990. The global annual rate of change in the MMR was -0·3% (-1·1 to 0·6) from 1990 to 2003, and -2·7% (-3·9 to -1·5) from 2003 to 2013, with evidence of continued acceleration. MMRs reduced consistently in south, east, and southeast Asia between 1990 and 2013, but maternal deaths increased in much of sub-Saharan Africa during the 1990s. 2070 (1290-2866) maternal deaths were related to HIV in 2013, 0·4% (0·2-0·6) of the global total. MMR was highest in the oldest age groups in both 1990 and 2013. In 2013, most deaths occurred intrapartum or postpartum. Causes varied by region and between 1990 and 2013. We recorded substantial variation in the MMR by country in 2013, from 956·8 (685·1-1262·8) in South Sudan to 2·4 (1·6-3·6) in Iceland. INTERPRETATION: Global rates of change suggest that only 16 countries will achieve the MDG 5 target by 2015. Accelerated reductions since the Millennium Declaration in 2000 coincide with increased development assistance for maternal, newborn, and child health. Setting of targets and associated interventions for after 2015 will need careful consideration of regions that are making slow progress, such as west and central Africa. FUNDING: Bill & Melinda Gates Foundation.