Sol–Gel-Derived Corrosion-Protection Coatings

There is a current need for alternative coatings that can provide corrosion resistance to metals or alloy surfaces due to the environmental hazards posed by conventional coatings. Herein, we report on novel organically-modified sol–gel coatings for the protection of metal and alloy surfaces. The basic concept of chemical conversion of metal surfaces is based on deposition of a hydrophobic, nonporous sol–gel barrier layer for surface protection and corrosion prevention. The properties of these organosilica coatings can be tuned by varying the composition of precursors. The evaluation of hydrophobicity, adhesive strength, and anticorrosion properties of organically-modified sol–gel derived coatings suggests their potential utility as technologically-compatible alternatives to conventional coatings.     

Nanostructured Ion-Selective MCM-48 Membranes

Templated MCM-48 silica was prepared using CTAB as surfactant. The MCM-48 powders and thin films were characterized by different techniques. MCM-48 layers were deposited on macroporous α-alumina supports and silicon nitride microsieves. The water permeability of MCM-48 was compared with the permeability of conventional mesoporous γ-alumina membranes. The applicability of MCM-48 as ion-selective electric field-driven switchable interconnect for microfluidic devices was demonstrated.     

Electro-optic pulse response of ferroelectric liquid crystals

The electro-optic response of ferroelectric smectic C* liquid crystals has been studied. Anomalous switching behaviour of such materials which possess a negative dielectric anisotropy has been reported. These materials show a minimum in response time at a sufficiently high field. We present results showing the dependency of this minimum upon spontaneous polarisation and the effect of AC bias. Calculations based upon the equation of motion of the director around the cone are presented which describe this effect and its dependence on the relative magnitudes of the spontaneous polarization and dielectric anisotropy of the material. Good agreement with the experimental results is found.     

New efficient numerical procedures for solving stochastic variational problems with a priori maximum pointwise error estimates

In a previous paper we gave a new formulation and derived the Euler equations and other necessary conditions to solve strong, pathwise, stochastic variational problems with trajectories driven by Brownian motion. Thus, unlike current methods which minimize the control over deterministic functionals (the expected value), we find the control which gives the critical point solution of random functionals of a Brownian path and then, if we choose, find the expected value.This increase in information is balanced by the fact that our methods are anticipative while current methods are not. However, our methods are more directly connected to the theory and meaningful examples of deterministic variational theory and provide better means of solution for free and constrained problems. In addition, examples indicate that there are methods to obtain nonanticipative solutions from our equations although the anticipative optimal cost function has smaller expected value.In this paper we give new, efficient numerical methods to find the solution of these problems in the quadratic case. Of interest is that our numerical solution has a maximal, a priori, pointwise error of O(h3/2) where h is the node size. We believe our results are unique for any theory of stochastic control and that our methods of proof involve new and sophisticated ideas for strong solutions which extend previous deterministic results by the first author where the error was O(h²).We note that, although our solutions are given in terms of stochastic differential equations, we are not using the now standard numerical methods for stochastic differential equations. Instead we find an approximation to the critical point solution of the variational problem using relations derived from setting to zero the directional derivative of the cost functional in the direction of simple test functions.Our results are even more significant than they first appear because we can reformulate stochastic control problems or constrained calculus of variations problems in the unconstrained, stochastic calculus of variations formulation of this paper. This will allow us to find efficient and accurate numerical solutions for general constrained, stochastic optimization problems. This is not yet being done, even in the deterministic case, except by the first author.     

Navigating Schooled Numeracies: Explanations for Low Achievement,in Mathematics of UK Children From Low SES Background

The intention of the research reported here was to seek explanations for low achievement in school mathematics, as conventionally assessed, that derive from broad understandings of mathematics as social. Such a broad social perspective can provide explanations for low achievement, which could lead to different understandings and hence to different teaching approaches. This study centered on 5- to 8-year-old children from a White working-class area in England. Data were collected during visits to the children in school, in their homes, and in the broader community over a 3-year period. Parents, teachers, and other professionals in the broad school context were interviewed, and data were also collected from school documents and policy statements. Interpretations of these data in terms of ways of understanding children's achievements in school mathematics are put forward. The potential effects of these factors on low schooled numeracy attainment are discussed, together with some possible strategic implications for practice and policy.