Efficient shock capturing for isentropic flows using arithmetic averaging

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two-dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two-dimensional dam-break problem and the approximate solution compares well with those given by other authors.

An efficient numerical method for compressible flows of a real gas using arithmetic averaging

An efficient numerical method is presented for the solution of the Euler equations governing the compressible flow of a real gas. The scheme is based on the approximate solution of a specially constructed set of linearised Riemann problems. An average of the flow variables across the interface between cells is required, and this is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual square root averaging. The scheme is applied to a test problem for five different equations of state.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Estimating mean exposures from censored data: exposure to benzene in the Australian petroleum industry

A retrospective assessment of exposure to benzene was carried out for a nested case control study of lympho-haematopoietic cancers, including leukaemia, in the Australian petroleum industry. Each job or task in the industry was assigned a Base Estimate (BE) of exposure derived from task-based personal exposure assessments carried out by the company occupational hygienists. The BEs corresponded to the estimated arithmetic mean exposure to benzene for each job or task and were used in a deterministic algorithm to estimate the exposure of subjects in the study. Nearly all of the data sets underlying the BEs were found to contain some values below the limit of detection (LOD) of the sampling and analytical methods and some were very heavily censored; up to 95% of the data were below the LOD in some data sets. It was necessary, therefore, to use a method of calculating the arithmetic mean exposures that took into account the censored data. Three different methods were employed in an attempt to select the most appropriate method for the particular data in the study. A common method is to replace the missing (censored) values with half the detection limit. This method has been recommended for data sets where much of the data are below the limit of detection or where the data are highly skewed; with a geometric standard deviation of 3 or more. Another method, involving replacing the censored data with the limit of detection divided by the square root of 2, has been recommended when relatively few data are below the detection limit or where data are not highly skewed. A third method that was examined is Cohen's method. This involves mathematical extrapolation of the left-hand tail of the distribution, based on the distribution of the uncensored data, and calculation of the maximum likelihood estimate of the arithmetic mean. When these three methods were applied to the data in this study it was found that the first two simple methods give similar results in most cases. Cohen's method on the other hand, gave results that were generally, but not always, higher than simpler methods and in some cases gave extremely high and even implausible estimates of the mean. It appears that if the data deviate substantially from a simple log-normal distribution, particularly if high outliers are present, then Cohen's method produces erratic and unreliable estimates. After examining these results, and both the distributions and proportions of censored data, it was decided that the half limit of detection method was most suitable in this particular study.

Some Mean-Value Theorems of the Cauchy Type

2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05

Comparison of scoring systems for invasive pests using ROC analysis and Monte Carlo simulation

Different international plant protection organisations advocate different schemes for conducting pest risk assessments. Most of these schemes use structured questionnaire in which experts are asked to score several items using an ordinal scale. The scores are then combined using a range of procedures, such as simple arithmetic mean, weighted averages, multiplication of scores, and cumulative sums. The most useful schemes will correctly identify harmful pests and identify ones that are not. As the quality of a pest risk assessment can depend on the characteristics of the scoring system used by the risk assessors (i.e., on the number of points of the scale and on the method used for combining the component scores), it is important to assess and compare the performance of different scoring systems. In this article, we proposed a new method for assessing scoring systems. Its principle is to simulate virtual data using a stochastic model and, then, to estimate sensitivity and specificity values from these data for different scoring systems. The interest of our approach was illustrated in a case study where several scoring systems were compared. Data for this analysis were generated using a probabilistic model describing the pest introduction process. The generated data were then used to simulate the outcome of scoring systems and to assess the accuracy of the decisions about positive and negative introduction. The results showed that ordinal scales with at most 5 or 6 points were sufficient and that the multiplication-based scoring systems performed better than their sum-based counterparts. The proposed method could be used in the future to assess a great diversity of scoring systems.

Population variation in biomonitoring data for persistent organic pollutants (POPs) : an examination of multiple population-based datasets for application to Australian pooled biomonitoring data

Background Australian national biomonitoring for persistent organic pollutants (POPs) relies upon age-specific pooled serum samples to characterize central tendencies of concentrations but does not provide estimates of upper bound concentrations. This analysis compares population variation from biomonitoring datasets from the US, Canada, Germany, Spain, and Belgium to identify and test patterns potentially useful for estimating population upper bound reference values for the Australian population. Methods Arithmetic means and the ratio of the 95th percentile to the arithmetic mean (P95:mean) were assessed by survey for defined age subgroups for three polychlorinated biphenyls (PCBs 138, 153, and 180), hexachlorobenzene (HCB), p,p-dichlorodiphenyldichloroethylene (DDE), 2,2′,4,4′ tetrabrominated diphenylether (PBDE 47), perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS). Results Arithmetic mean concentrations of each analyte varied widely across surveys and age groups. However, P95:mean ratios differed to a limited extent, with no systematic variation across ages. The average P95:mean ratios were 2.2 for the three PCBs and HCB; 3.0 for DDE; 2.0 and 2.3 for PFOA and PFOS, respectively. The P95:mean ratio for PBDE 47 was more variable among age groups, ranging from 2.7 to 4.8. The average P95:mean ratios accurately estimated age group-specific P95s in the Flemish Environmental Health Survey II and were used to estimate the P95s for the Australian population by age group from the pooled biomonitoring data. Conclusions Similar population variation patterns for POPs were observed across multiple surveys, even when absolute concentrations differed widely. These patterns can be used to estimate population upper bounds when only pooled sampling data are available.

Exposure to bioaerosols in the school environment in Brisbane, Australia

Introduction: Exposure to bioaerosols in indoor environments has been linked to various adverse health effects, such as airway disorders and upper respiratory tract symptoms. The aim of this study was to assess exposure to bioaerosols in the school environment in Brisbane, Australia. Methods: Culturable fungi and endotoxin measurements were conducted in six schools between October 2010 and May 2011. Culturable fungi (2 indoor air and 1-2 outdoor air samples per school) were assessed using a Biotest RCS High Flow Air Sampler, with a flow rate of either 50L/min or 20L/min. A rose pengar agar was used for recovery, which was incubated prior to counting and partial identification. Endotoxins were sampled (8h, 2L/min) using SKC glass fibre filters (4 indoor air samples per school) and analysed using an endpoint chromogenic LAL assay. Results: The arithmetic mean for fungi concentration in indoor and outdoor air was 710 cfu/m3(125- 1900 cfu/m3) and 524 cfu/m3 (140-1250 cfu/m3), respectively. The most frequently isolated fungal genus from the outdoor air was Cladosporium (over 40 %), followed by isolated Penicillium (21%) and Aspergillus (12%). The percent of Penicillium, Cladosporium and Aspergillus in indoor air samples was 32%, 32% and 8%, respectively. The aritmetic mean of endotoxin concentration was 0.59 EU/m3 (0-2,2 EU/m3). Discussion: The results of the current study are in agreement with previously reported studies, in that airborne fungi and endotoxin concentrations varied extensively, and were mostly dependent on climatic conditions. In addition, the indoor air mycoflora largely reflected the fungal flora present in the outdoor air, with Cladosporium being the most common in both outdoor and indoor (with Penicillium) air. In indoor air, unusually high endotoxin levels, over 1 EU/m3, were detected at 2 schools. Although these schools were not affected by the recent Brisbane floods, persistent rain prior to and during the study perios could explain the results.

Analysis of volatility transmissions in integrated and interconnected markets: The case of the Iberian and French markets

This paper models the mean and volatility spillovers of prices within the integrated Iberian and the interconnected Spanish and French electricity markets. Using the constant (CCC) and dynamic conditional correlation (DCC) bivariate models with three different specifications of the univariate variance processes, we study the extent to which increasing interconnection and harmonization in regulation have favoured price convergence. The data consist of daily prices calculated as the arithmetic mean of the hourly prices over a span from July 1st 2007 until February 29th 2012. The DCC model in which the variances of the univariate processes are specified with a VARMA(1,1) fits the data best for the integrated MIBEL whereas a CCC model with a GARCH(1,1) specification for the univariate variance processes is selected to model the price series in Spain and France. Results show that there are significant mean and volatility spillovers in the MIBEL, indicating strong interdependence between the two markets, while there is a weaker evidence of integration between the Spanish and French markets. We provide new evidence that the EU target of achieving a single electricity market largely depends on increasing trade between countries and homogeneous rules of market functioning.

Composição florística e estrutura da comunidade arbustivo-arbórea de um trecho de floresta submontana na vertente sudeste do Parque Estadual da Ilha Grande, Angra dos Reis / RJ

O estudo objetivou avaliar a composição florística e estrutural dos componentes arbustivo-arbóreo da Floresta Ombrófila Densa submontana em diferentes estágios de regeneração natural, na vertente sudeste do Parque Estadual da Ilha Grande/RJ. Para o inventário florístico foram realizadas coletas assistemáticas em diferentes trechos nessa vertente. A complementação da lista de espécies foi feita a partir, da consulta às exsicatas dos herbários do Rio de Janeiro (FCAB, GUA, HB, HRJ, R, RB, RBR, RFA, RFFP e RUSU) e do inventário fitossociológico. Foi verificado o status de conservação das espécies inventariadas para a Flora Brasileira. Para o inventário fitossociológico foram estabelecidas 34 parcelas amostrais, totalizando 1,02 ha de área amostrada. Todos os indivíduos arbustivo-arbóreos com DAP ≥ 5 cm foram registrados e, após identificação, foram depositados no Herbário da Universidade do Estado do Rio de Janeiro (HRJ). O pacote estatístico FITOPAC 2.1. foi utilizado para a análise dos dados. A similaridade entre o remanescente investigado neste estudo e as outras quatorze áreas distintas do Rio de Janeiro, da própria Ilha Grande ou não, foi avaliada, utilizando-se o coeficiente de Similaridade de Sorensen; pelo critério de agrupamento por ligação média não ponderada (UPGMA) e pelo método de autorreamostragem para a estrutura de grupos; utilizados os programas PAST v1.34 e Multiv 2.4. A partir do levantamento em herbários e dos inventários florístico e fitossociológico realizados neste trabalho, foram analisados 3.470 registros, sendo 1.778 do levantamento de herbários, 1.536 do levantamento fitossociológico e 156 do inventário florístico. Esses registros corresponderam a 606 espécies ou morfo-espécies de Angiospermas e uma de Pteridófita. Os resultados obtidos revelaram a existência de 22 espécies ameaçadas de extinção para a Flora do Brasil. Dentre, as quais, sete são exclusivas da amostragem fitossociológica: Abarema cochliacarpos (Gomes) Barneby & J.W. Grimes, Chrysophyllum flexuosum Mart., Ficus pulchella Schott ex Spreng., Macrotorus utriculatus Perkins, Myrceugenia myrcioides (Cambess.) O.Berg, Rudgea interrupta Benth e Urbanodendron bahiense (Meisn.) Rohwer. No estudo fitossociológico, inventariou-se 1.536 indivíduos de 217 espécies, subordinadas a 53 famílias. O índice de diversidade de Shannon (H) calculado foi de 4,702 nats/ind e equabilidade (J) de 0,874. As 10 famílias com maior riqueza foram: Myrtaceae (31 spp.), Rubiaceae (21), Fabaceae (17), Lauraceae (12), Euphorbiaceae (11), Monimiaceae (8), Melastomataceae (7), Sapindaceae (7), Sapotaceae (6) e Annonaceae (6). Os 10 maiores Valores de Importância das espécies foram para Chrysophyllum flexuosum (3,43%), Lamanonia ternata Vell. (3,40%), Hyeronima alchorneoides Allemão (2,83%), Actinostemon verticillatus (Klotzsch) Baill. (2,55%), Psychotria brasiliensis Vell. (2,55%), Eriotheca pentaphylla (Vell.) A. Robyns (2,28%), Guatteria australis A. St.-Hil. (2,12%), Mabea brasiliensis Müll. Arg. (2,04%), Miconia prasina (Sw.) DC. (1,89%) e Rustia formosa (Cham. & Schltdl. ex DC.) Klotzsch (1,82%). Amostraram-se 27% de espécies representadas por apenas um indivíduo. As análises florísticas avaliadas a partir do Índice de Similaridade de Sorensen indicaram como principais variáveis para a formação dos blocos, os diferentes valores de diversidade para as áreas e a distribuição fitogeográfica das espécies. Os resultados obtidos junto aos dados dos grupos ecológicos, para os indivíduos da fitossociologia, indicaram maior percentual de indivíduos secundários tardios amostrados. Conclui-se que a área de estudo é uma floresta secundária em estágio intermediário de regeneração, com grande riqueza de espécies, muitas das quais de relevante importância ecológica.

A modeling approach to identify optimal habitat and suitable fishing grounds for neon flying squid (Ommastrephes bartramii) in the Northwest Pacific Ocean

We developed a habitat suitability index (HSI) model to understand and identify the optimal habitat and potential fishing grounds for neon f lying squid (Ommastrephes bartramii) in the Northwest Pacific Ocean. Remote sensing data, including sea surface temperature, sea surface salinity, sea surface height, and chlorophyll-a concentrations, as well as fishery data from Chinese mainland squid f leets in the main fishing ground (150–165°E longitude) from August to October, from 1999 to 2004, were used. The HSI model was validated by using fishery data from 2005. The arithmetic mean modeling with three of the environmental variables—sea surface temperature, sea surface height anomaly, and chlorophyll- a concentrations—was defined as the most parsimonious HSI model. In 2005, monthly HSI values >0.6 coincided with productive fishing grounds and high fishing effort from August to October. This result implies that the model can reliably predict potential f ishing grounds for O. bartramii. Because spatially explicit fisheries and environmental data are becoming readily available, it is feasible to develop a dynamic, near real-time habitat model for improving the process of identifying potential fishing areas for and optimal habitats of neon flying squid.

Consensus on homogeneous manifolds

The present paper considers distributed consensus algorithms for agents evolving on a connected compact homogeneous (CCH) manifold. The agents track no external reference and communicate their relative state according to an interconnection graph. The paper first formalizes the consensus problem for synchronization (i.e. maximizing the consensus) and balancing (i.e. minimizing the consensus); it thereby introduces the induced arithmetic mean, an easily computable mean position on CCH manifolds. Then it proposes and analyzes various consensus algorithms on manifolds: natural gradient algorithms which reach local consensus equilibria; an adaptation using auxiliary variables for almost-global synchronization or balancing; and a stochastic gossip setting for global synchronization. It closes by investigating the dependence of synchronization properties on the attraction function between interacting agents on the circle. The theory is also illustrated on SO(n) and on the Grassmann manifolds. ©2009 IEEE.

Consensus optimization on manifolds

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO (n) and the Grassmann manifold Grass (p, n) are treated as original examples. A link is also drawn with the many existing results on the circle. © 2009 Society for Industrial and Applied Mathematics.

Phylogenetic relationships among Trichodinidae (Ciliophora : Peritricha) derived from the characteristic values of denticles

The phylogenetic relationships among trichodinids remain obscure. As an important diagnostic marker, the morphology of the denticles in the adhesive disc as well as the adoral spiral has been widely used in generic discrimination and species identification of trichodinids. We studied the characters of denticles of the ten genera of Trichodinidae and the sole genus Urceolaria of Urceolariidae by using a quantitative method. The characteristic values were used to generate Manhattan distance, on which the dendrogram was based to construct with the Unweighted Paired Group Method using the Arithmetic mean (UPGMA). The investigations show that all the genera of the family Trichodinidae were clearly separate from the outgroup Urceolaria, and within the Trichodinidae: (i) Dipartiella grouped with Trichodinella and Tripartiella and lay in the closest position to the outgroup with a low dissimilarity, suggesting Dipartiella might be the most primitive genus in the family; (ii) Hemitrichodina clustered in a single clad and lay in the farthest position to the outgroup with the highest dissimilarity, indicating that it might be the most advanced genus; and (iii) the other 6 genera, Trichodina, Paratrichodina, Semitrichodina, Vauchomia, Pallitrichodina and Trichodoxa clustered in a big clad with very low dissimilarity, showing that they are closely related to each other. We discuss the evolutionary trend of the denticle and conclude that the denticles of the adhesive disc should be an apomorphic feature of the trichodinids and their changes could reflect the evolutionary tendencies of these ciliates.

Polydispersity of ethylene sequence length in metallocene ethylene/alpha-olefin copolymers. I. Characterized by thermal-fractionation technique

In this article, the polydispersity of the ethylene sequence length (ESL) in ethylene/alpha-olefin copolymers was studied by atomic force microscopy (AFM) and the thermal-fractionation technique. The crystal morphology observation by AFM showed that morphology changed gradually with decreasing average ESL from complete lamellae over shorter and more curved lamellae to a granular-like morphology, and the mixed morphology was observed after stepwise crystallization from phase-separated melt. This result indicated that the ethylene sequence with different lengths crystallized into a crystalline phase with a different size and stability at the copolymer systems. The thermal-fractionation technique was used to characterize the polydispersity of ESL. Three of the following statistical terms were introduced to describe the distribution of ESL and the lamellar thickness: the arithmetic mean (L) over bar (n), the weight mean (L) over bar (w), and the broadness index I = (L) over bar (w)/(L) over bar (n). It was concluded that the polydispersity of ESL could be quantitatively characterized by the thermal-fractionation technique. The effects of temperature range, temperature-dependent specific heat capacity C-p of copolymer, and the molecular weight on the results of thermal fractionation were discussed,