Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Fine tuning in quintessence models with exponential potentials

We explore regions of parameter space in a simple exponential model of the form V = V0 e-λ(Q/Mp) that are allowed by observational constraints. We find that the level of fine tuning in these models is not different from more sophisticated models of dark energy. We study a transient regime where the parameter λ has to be less than √3 and the fixed point ΩQ = 1 has not been reached. All values of the parameter λ that lead to this transient regime are permitted. We also point out that this model can accelerate the universe today even for λ > √2, leading to a halt of the present acceleration of the universe in the future thus avoiding the horizon problem. We conclude that this model can not be discarded by current observations. © SISSA/ISAS 2002.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of autocorrelated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Piggery pond sludge as a nitrogen source for crops. 1. Mineral N supply estimated from laboratory incubations and field application of stockpiled and wet sludge

Piggery pond sludge (PPS) was applied, as-collected (Wet PPS) and following stockpiling for 12 months (Stockpiled PPS), to a sandy Sodosol and clay Vertosol at sites on the Darling Downs of Queensland. Laboratory measures of N availability were carried out on unamended and PPS-amended soils to investigate their value in estimating supplementary N needs of crops in Australia's northern grains region. Cumulative net N mineralised from the long-term (30 weeks) leached aerobic incubation was described by a first-order single exponential model. The mineralisation rate constant (0.057/week) was not significantly different between Control and PPS treatments or across soil types, when the amounts of initial mineral N applied in PPS treatments were excluded. Potentially mineralisable N (No) was significantly increased by the application of Wet PPS, and increased with increasing rate of application. Application of Wet PPS significantly increased the total amount of inorganic N leached compared with the Control treatments. Mineral N applied in Wet PPS contributed as much to the total mineral N status of the soil as did that which mineralised over time from organic N. Rates of C02 evolution during 30 weeks of aerobic leached incubation indicated that the Stockpiled PPS was more stabilised (19-28% of applied organic C mineralised) than the WetPPS (35-58% of applied organic C mineralised), due to higher lignin content in the former. Net nitrate-N produced following 12 weeks of aerobic non-leached incubation was highly correlated with net nitrate-N leached during 12 weeks of aerobic incubation (R^2 = 0.96), although it was <60% of the latter in both sandy and clayey soils. Anaerobically mineralisable N determined by waterlogged incubation of laboratory PPS-amended soil samples increased with increasing application rate of Wet PPS. Anaerobically minemlisable N from field-moist soil was well correlated with net N mineralised during 30 weeks of aerobic leached incubation (R^2 =0.90 sandy soil; R^2=0.93 clay soil). In the clay soil, the amount of mineral N produced from all the laboratory incubations was significantly correlated with field-measured nitrate-N in the soil profile (0-1.5 m depth) after 9 months of weed-free fallow following PPS application. In contrast, only anaerobic mineralisable N was significantly correlated with field nitrate-N in the sandy soil. Anaerobic incubation would, therefore, be suitable as a rapid practical test to estimate potentially mineralisable N following applications of different PPS materials in the field.

Seasonal changes in pasture quality and diet selection and their relationship with liveweight gain of steers grazing tropical grass and grass-legume pastures in northern Australia.

The variation in liveweight gain in grazing beef cattle as influenced by pasture type, season and year effects has important economic implications for mixed crop-livestock systems and the ability to better predict such variation would benefit beef producers by providing a guide for decision making. To identify key determinants of liveweight change of Brahman-cross steers grazing subtropical pastures, measurements of pasture quality and quantity, and diet quality in parallel with liveweight were made over two consecutive grazing seasons (48 and 46 weeks, respectively), on mixed Clitoria ternatea/grass, Stylosanthes seabrana/grass and grass swards (grass being a mixture of Bothriochloa insculpta cv. Bisset, Dichanthium sericeum and Panicum maximum var. trichoglume cv. Petrie). Steers grazing the legume-based pastures had the highest growth rate and gained between 64 and 142 kg more than those grazing the grass pastures in under 12 months. Using an exponential model, green leaf mass, green leaf %, adjusted green leaf % (adjusted for inedible woody legume stems), faecal near infrared reflectance spectroscopy predictions of diet crude protein and diet dry matter digestibility, accounted for 77, 74, 80, 63 and 60%, respectively, of the variation in daily weight gain when data were pooled across pasture types and grazing seasons. The standard error of the regressions indicated that 95% prediction intervals were large (+/- 0.42-0.64 kg/head.day) suggesting that derived regression relationships have limited practical application for accurately estimating growth rate. In this study, animal factors, especially compensatory growth effects, appeared to have a major influence on growth rate in relation to pasture and diet attributes. It was concluded that predictions of growth rate based only on pasture or diet attributes are unlikely to be accurate or reliable. Nevertheless, key pasture attributes such as green leaf mass and green leaf% provide a robust indication of what proportion of the potential growth rate of the grazing animals can be achieved.

Consistently replicating locus linked to migraine on 10q22-q23

Here, we present the results of two genome-wide scans in two diverse populations in which a consistent use of recently introduced migraine-phenotyping methods detects and replicates a locus on 10q22-q23, with an additional independent replication. No genetic variants have been convincingly established in migraine, and although several loci have been reported, none of them has been consistently replicated. We employed the three known migraine-phenotyping methods (clinical end diagnosis, latent-class analysis, and trait-component analysis) with robust multiple testing correction in a large sample set of 1675 individuals from 210 migraine families from Finland and Australia. Genome-wide multipoint linkage analysis that used the Kong and Cox exponential model in Finns detected a locus on 10q22-q23 with highly significant evidence of linkage (LOD 7.68 at 103 cM in female-specific analysis). The Australian sample showed a LOD score of 3.50 at the same locus (100 cM), as did the independent Finnish replication study (LOD score 2.41, at 102 cM). In addition, four previously reported loci on 8q21, 14q21, 18q12, and Xp21 were also replicated. A shared-segment analysis of 10q22-q23 linked Finnish families identified a 1.6-9.5 cM segment, centered on 101 cM, which shows in-family homology in 95% of affected Finns. This region was further studied with 1323 SNPs. Although no significant association was observed, four regions warranting follow-up studies were identified. These results support the use of symptomology-based phenotyping in migraine and suggest that the 10q22-q23 locus probably contains one or more migraine susceptibility variants.