A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades <-1 to >9) were separated, and each fraction was analysed for its chemical composition. The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø <8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar). To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend. Key words: sediment, geochemistry, grain size, regression, step function

A bagging-based correction for the mixture model estimator of population size

Estimation of a population size by means of capture-recapture techniques is an important problem occurring in many areas of life and social sciences. We consider the frequencies of frequencies situation, where a count variable is used to summarize how often a unit has been identified in the target population of interest. The distribution of this count variable is zero-truncated since zero identifications do not occur in the sample. As an application we consider the surveillance of scrapie in Great Britain. In this case study holdings with scrapie that are not identified (zero counts) do not enter the surveillance database. The count variable of interest is the number of scrapie cases per holding. For count distributions a common model is the Poisson distribution and, to adjust for potential heterogeneity, a discrete mixture of Poisson distributions is used. Mixtures of Poissons usually provide an excellent fit as will be demonstrated in the application of interest. However, as it has been recently demonstrated, mixtures also suffer under the so-called boundary problem, resulting in overestimation of population size. It is suggested here to select the mixture model on the basis of the Bayesian Information Criterion. This strategy is further refined by employing a bagging procedure leading to a series of estimates of population size. Using the median of this series, highly influential size estimates are avoided. In limited simulation studies it is shown that the procedure leads to estimates with remarkable small bias.

Can carbon surface oxidation shift the pore size distribution curve calculated from Ar, N(2) and CO(2) adsorption isotherms? Simulation results for a realistic carbon model

Using the virtual porous carbon model proposed by Harris et al, we study the effect of carbon surface oxidation on the pore size distribution (PSD) curve determined from simulated Ar, N(2) and CO(2) isotherms. It is assumed that surface oxidation is not destructive for the carbon skeleton, and that all pores are accessible for studied molecules (i.e., only the effect of the change of surface chemical composition is studied). The results obtained show two important things, i.e., oxidation of the carbon surface very slightly changes the absolute porosity (calculated from the geometric method of Bhattacharya and Gubbins (BG)); however, PSD curves calculated from simulated isotherms are to a greater or lesser extent affected by the presence of surface oxides. The most reliable results are obtained from Ar adsorption data. Not only is adsorption of this adsorbate practically independent from the presence of surface oxides, but, more importantly, for this molecule one can apply the slit-like model of pores as the first approach to recover the average pore diameter of a real carbon structure. For nitrogen, the effect of carbon surface chemical composition is observed due to the quadrupole moment of this molecule, and this effect shifts the PSD curves compared to Ar. The largest differences are seen for CO2, and it is clearly demonstrated that the PSD curves obtained from adsorption isotherms of this molecule contain artificial peaks and the average pore diameter is strongly influenced by the presence of electrostatic adsorbate-adsorbate as well as adsorbate-adsorbent interactions.

Aircraft observations and model simulations of concentration and particle size distribution in the Eyjafjallajökull volcanic ash cloud

The Eyjafjallajökull volcano in Iceland emitted a cloud of ash into the atmosphere during April and May 2010. Over the UK the ash cloud was observed by the FAAM BAe-146 Atmospheric Research Aircraft which was equipped with in-situ probes measuring the concentration of volcanic ash carried by particles of varying sizes. The UK Met Office Numerical Atmospheric-dispersion Modelling Environment (NAME) has been used to simulate the evolution of the ash cloud emitted by the Eyjafjallajökull volcano during the period 4–18 May 2010. In the NAME simulations the processes controlling the evolution of the concentration and particle size distribution include sedimentation and deposition of particles, horizontal dispersion and vertical wind shear. For travel times between 24 and 72 h, a 1/t relationship describes the evolution of the concentration at the centre of the ash cloud and the particle size distribution remains fairly constant. Although NAME does not represent the effects of microphysical processes, it can capture the observed decrease in concentration with travel time in this period. This suggests that, for this eruption, microphysical processes play a small role in determining the evolution of the distal ash cloud. Quantitative comparison with observations shows that NAME can simulate the observed column-integrated mass if around 4% of the total emitted mass is assumed to be transported as far as the UK by small particles (< 30 μm diameter). NAME can also simulate the observed particle size distribution if a distal particle size distribution that contains a large fraction of < 10 μm diameter particles is used, consistent with the idea that phraetomagmatic volcanoes, such as Eyjafjallajökull, emit very fine particles.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Excitations and finite-size properties of an integrable supersymmetric electronic model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of platelet-rich plasma on bone healing of autogenous bone grafts in critical-size defects

AimThis study histologically analysed the effect of autogenous platelet-rich plasma (PRP), prepared according to a new semiautomatic system, on healing of autogenous bone (AB) grafts placed in surgically created critical-size defects (CSD) in rabbit calvaria.Material and MethodsSixty rabbits were divided into three groups: C, AB and AB/PRP. A CSD was created in the calvarium of each animal. In Group C (control), the defect was filled by blood clot only. In Group AB (autogenous bone graft), the defect was filled with particulate autogenous bone. In Group AB/PRP (autogenous bone graft with platelet-rich plasma), it was filled with particulate autogenous bone combined with PRP. All groups were divided into subgroups (n=10) and euthanized at 4 or 12 weeks post-operatively. Histometric and histologic analyses were performed. Data were statistically analysed (anova, t-test, p < 0.05).ResultsGroup C presented significantly less bone formation compared with Group AB and AB/PRP in both periods of analysis (p < 0.001). At 4 weeks, Group AB/PRP showed a statistically greater amount of bone formation than Group AB (64.44 +/- 15.0% versus 46.88 +/- 14.15%; p=0.0181). At 12 weeks, no statistically significant differences were observed between Groups AB and AB/PRP (75.0 +/- 8.11% versus 77.90 +/- 8.13%; p > 0.05). It is notable that the amount of new bone formation in Group AB/PRP at 4 weeks was similar to that of Group AB at 12 weeks (p > 0.05).ConclusionWithin its limitation, the present study has indicated that (i) AB and AB/PRP significantly improved bone formation and (ii) a beneficial effect of PRP was limited to an initial healing period of 4 weeks.

Vortices in superconductors with a columnar defect: Finite size effects

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it is considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated. (c) 2005 Elsevier B.V. All rights reserved.

Thirring model with jump defect

The purpose of our work is to extend the formulation of classical affine Toda Models in the presence of jump defects to pure fermionic Thirring model. As a first attempt we construct the Lagrangian of the Grassmanian Thirring model with jump defect (of Backlund type) and present its conserved modified momentum and energy expressions giving a first indication of its integra-bility. Copyright © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

Effects of LLLT in combination with bisphosphonate on bone healing in critical size defects: A histological and histometric study in rat calvaria

The purpose of this study was to analyze histologically the effect of low-level laser therapy (LLLT) in combination with bisphosphonate on bone healing in surgically created critical size defects (CSD) in rat calvaria. One hundred Wistar female rats sham operated (sham) and ovariectomized (Ovx) were maintained untreated for 1 month to allow for the development of osteopenia in the Ovx animals. A CSD was made in the calvarium of each rat, and the animals were divided into five groups according to following treatments: (1) sham rats (control), (2) Ovx rats, (3) Ovx rats treated with LLLT, (4) Ovx rats treated with bisphosphonate, and (5) Ovx rats treated with bisphosphonate and LLLT. Groups 4 and 5 were irrigated with 1 ml of bisphosphonate, and groups 3 and 5 were submitted to LLLT (GaAlAs), 660 nm, 24 J, and 0.4285 W/cm2 on the CSD. Ten animals of each treatment were killed at 30 and 60 days. Histomorphometric assessments, using image analysis software, and histological analyses were performed. No defect was completely regenerated with the bone. Histometrically, it can be observed that groups 3 (37.49 ± 1.94%, 43.11 ± 2.39%) and 5 (35.05 ± 1.57%, 41.07 ± 1.89%) showed a significant bone neoformation when compared to groups 1 (16.81 ± 1.57%, 27.54 ± 1.49%), 2 (11.68 ± 0.98%, 22.51 ± 1.05%), and 4 (14.62 ± 1.70%, 25.67 ± 1.41%) in all experimental periods (P < 0.05). It was possible to conclude that the LLLT associated or not with bisphosphonate treatment was effective for stimulating bone formation in CSD in the calvaria of rats submitted to ovariectomy. © 2012 Springer-Verlag London Ltd.

Improving methods in gap ecology: Revisiting size and shape distributions using a model selection approach

Questions: We assess gap size and shape distributions, two important descriptors of the forest disturbance regime, by asking: which statistical model best describes gap size distribution; can simple geometric forms adequately describe gap shape; does gap size or shape vary with forest type, gap age or the method used for gap delimitation; and how similar are the studied forests and other tropical and temperate forests? Location: Southeastern Atlantic Forest, Brazil. Methods: Analysing over 150 gaps in two distinct forest types (seasonal and rain forests), a model selection framework was used to select appropriate probability distributions and functions to describe gap size and gap shape. The first was described using univariate probability distributions, whereas the latter was assessed based on the gap area-perimeter relationship. Comparisons of gap size and shape between sites, as well as size and age classes were then made based on the likelihood of models having different assumptions for the values of their parameters. Results: The log-normal distribution was the best descriptor of gap size distribution, independently of the forest type or gap delimitation method. Because gaps became more irregular as they increased in size, all geometric forms (triangle, rectangle and ellipse) were poor descriptors of gap shape. Only when small and large gaps (> 100 or 400m2 depending on the delimitation method) were treated separately did the rectangle and isosceles triangle become accurate predictors of gap shape. Ellipsoidal shapes were poor descriptors. At both sites, gaps were at least 50% longer than they were wide, a finding with important implications for gap microclimate (e.g. light entrance regime) and, consequently, for gap regeneration. Conclusions: In addition to more appropriate descriptions of gap size and shape, the model selection framework used here efficiently provided a means by which to compare the patterns of two different types of forest. With this framework we were able to recommend the log-normal parameters μ and σ for future comparisons of gap size distribution, and to propose possible mechanisms related to random rates of gap expansion and closure. We also showed that gap shape varied highly and that no single geometric form was able to predict the shape of all gaps, the ellipse in particular should no longer be used as a standard gap shape. © 2012 International Association for Vegetation Science.

The influence of floc size and hydraulic detention time on the performance of a dissolved air flotation (DAF) pilot unit in the light of a mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Analysis of Lattice Size, Energy Density and Denaturation for a One-Dimensional DNA Model

There are several mechanical models to describe the DNA phenomenology. In this work the DNA denaturation is stu- died under thermodynamical and dynamical point of view using the well known Peyrard-Bishop model. The thermody-namics analysis using the transfer integral operator method is briefly reviewed. In particular, the lattice size is discussed and a conjecture about the minimum energy to denaturation is proposed. In terms of the dynamical aspects of the model, the equations of motion for the system are integrated and the results determine the energy density where the denatura- tion occurs. The behavior of the lattice near the phase transition is analyzed. The relation between the thermodynamical and dynamical results is discussed.

Potential of Bioactive Glass Particles of Different Size Ranges to Affect Bone Formation in Interproximal Periodontal Defects in Dogs

Background: The aim of this study was to compare the potential of bioactive glass particles of different size ranges to affect bone formation in periodontal defects, using the guided tissue regeneration model in dogs. Methods: In six dogs, 2-wall intrabony periodontal defects were surgically created and chronified on the mesial surfaces of mandibular third premolars and first molars bilaterally. After 1 month, each defect was randomly assigned to treatment with bioabsorbable membrane in association with bioactive glass with particle sizes between 300 and 355 mu m (group 1) or between 90 and 710 mu m (group 2), membrane alone (group 3), or negative control (group 4). The dogs were sacrificed 12 weeks after surgeries, and histomorphometric measurements were made of the areas of newly formed bone, new mineralized bone, and bioactive glass particle remnants. Results: With regard to the area of bioactive glass particle remnants, there was a statistically significant difference between groups 1 and 2, favoring group 1. There were greater areas of mineralized bone in groups 1 and 2 compared to groups 3 and 4 (P<0.05). Conclusion: The bioactive glass particles of small size range underwent faster resorption and substitution by new bone than the larger particles, and the use of bioactive glass particles favored the formation of mineralized bone. J Periodontol 2009;80:808-815.