Complex formation in solutions of oppositely charged polyelectrolytes at different polyion compositions and salt content

The formation of complexes in solutions containing positively charged polyions (polycations) and a variable amount of negatively charged polyions (polyanions) has been investigated by Monte Carlo simulations. The polyions were described as flexible chains of charged hard spheres interacting through a screened Coulomb potential. The systems were analyzed in terms of cluster compositions, structure factors, and radial distribution functions. At 50% charge equivalence or less, complexes involving two polycations and one polyanion were frequent, while closer to charge equivalence, larger clusters were formed. Small and neutral complexes dominated the solution at charge equivalence in a monodisperse system, while larger clusters again dominated the solution when the polyions were made polydisperse. The cluster composition and solution structure were also examined as functions of added salt by varying the electrostatic screening length. The observed formation of clusters could be rationalized by a few simple rules.

A Monte Carlo study of solutions of oppositely charged polyelectrolytes

The formation of complexes appearing in solutions containing oppositely charged polyelectrolytes has been investigated by Monte Carlo simulations using two different models. The polyions are described as flexible chains of 20 connected charged hard spheres immersed in a homogenous dielectric background representing water. The small ions are either explicitly included or their effect described by using a screened Coulomb potential. The simulated solutions contained 10 positively charged polyions with 0, 2, or 5 negatively charged polyions and the respective counterions. Two different linear charge densities were considered, and structure factors, radial distribution functions, and polyion extensions were determined. A redistribution of positively charged polyions involving strong complexes formed between the oppositely charged polyions appeared as the number of negatively charged polyions was increased. The nature of the complexes was found to depend on the linear charge density of the chains. The simplified model involving the screened Coulomb potential gave qualitatively similar results as the model with explicit small ions. Finally, owing to the complex formation, the sampling in configurational space is nontrivial, and the efficiency of different trial moves was examined.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Predicting long-term growth in students' mathematics achievement: the unique contributions of motivation and cognitive strategies

This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long-term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.

Bacillus subtilis natto: a non-toxic source of poly-γ-glutamic acid that could be used as a cryoprotectant for probiotic bacteria

It is common practice to freeze dry probiotic bacteria to improve their shelf life. However, the freeze drying process itself can be detrimental to their viability. The viability of probiotics could be maintained if they are administered within a microbially produced biodegradable polymer - poly-γ-glutamic acid (γ-PGA) - matrix. Although the antifreeze activity of γ-PGA is well known, it has not been used for maintaining the viability of probiotic bacteria during freeze drying. The aim of this study was to test the effect of γ-PGA (produced by B. subtilis natto ATCC 15245) on the viability of probiotic bacteria during freeze drying and to test the toxigenic potential of B. subtilis natto. 10% γ-PGA was found to protect Lactobacillus paracasei significantly better than 10% sucrose, whereas it showed comparable cryoprotectant activity to sucrose when it was used to protect Bifidobacterium breve and Bifidobacterium longum. Although γ-PGA is known to be non-toxic, it is crucial to ascertain the toxigenic potential of its source, B. subtilis natto. Presence of six genes that are known to encode for toxins were investigated: three component hemolysin (hbl D/A), three component non-haemolytic enterotoxin (nheB), B. cereus enterotoxin T (bceT), enterotoxin FM (entFM), sphingomyelinase (sph) and phosphatidylcholine-specific phospholipase (piplc). From our investigations, none of these six genes were present in B. subtilis natto. Moreover, haemolytic and lecithinase activities were found to be absent. Our work contributes a biodegradable polymer from a non-toxic source for the cryoprotection of probiotic bacteria, thus improving their survival during the manufacturing process.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

Linear and non-linear transmission of equity return volatility: evidence from the US, Japan and Australia

This paper models the transmission of shocks between the US, Japanese and Australian equity markets. Tests for the existence of linear and non-linear transmission of volatility across the markets are performed using parametric and non-parametric techniques. In particular the size and sign of return innovations are important factors in determining the degree of spillovers in volatility. It is found that a multivariate asymmetric GARCH formulation can explain almost all of the non-linear causality between markets. These results have important implications for the construction of models and forecasts of international equity returns.

A stated preference valuation of the non-market benefits of pollination services in the UK

Using a choice experiment survey this study examines the UK public's willingness to pay to conserve insect pollinators in relation to the levels of two pollination service benefits: maintaining local produce supplies and the aesthetic benefits of diverse wildflower assemblages. Willingness to pay was estimated using a Bayesian mixed logit with two contrasting controls for attribute non-attendance, exclusion and shrinkage. The results suggest that the UK public have an extremely strong preference to avoid a status quo scenario where pollinator populations and pollination services decline. Total willingness to pay was high and did not significantly vary between the two pollination service outputs, producing a conservative total of £379M over a sample of the tax-paying population of the UK, equivalent to £13.4 per UK taxpayer. Using a basic production function approach, the marginal value of pollination services to these attributes is also extrapolated. The study discusses the implications of these findings and directions for related future research into the non-market value of pollination and other ecosystem services.

Modelling the rheology of anisotropic particles adsorbed on a two-dimensional fluid interface

We present a general approach based on nonequilibrium thermodynamics for bridging the gap between a well-defined microscopic model and the macroscopic rheology of particle-stabilised interfaces. Our approach is illustrated by starting with a microscopic model of hard ellipsoids confined to a planar surface, which is intended to simply represent a particle-stabilised fluid–fluid interface. More complex microscopic models can be readily handled using the methods outlined in this paper. From the aforementioned microscopic starting point, we obtain the macroscopic, constitutive equations using a combination of systematic coarse-graining, computer experiments and Hamiltonian dynamics. Exemplary numerical solutions of the constitutive equations are given for a variety of experimentally relevant flow situations to explore the rheological behaviour of our model. In particular, we calculate the shear and dilatational moduli of the interface over a wide range of surface coverages, ranging from the dilute isotropic regime, to the concentrated nematic regime.

Morphology of polymer networks formed in the chiral and non chiral phases of an anti-ferroelectric liquid crystal

We introduced photo-polymer networks into the various liquid crystalline phases of the antiferroelectric liquid crystal AS612 and studied the effects of these networks by measuring the temperature dependence of the Bragg wavelengths selectively reflected. After polymerization, the decrease in Bragg wavelengths with respect to the original values is consistent with a shorter helical pitch due to polymer network shrinkage. Also, by removing the liquid crystalline material, we are able to image the residual polymer network using scanning electron microscopy and polarized light microscopy. The polymer strands are a few microns thick and the networks show both chiral and non-chiral features.