Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Exploring the learning potential of an artificial life simulation

CULTURE is an Artificial Life simulation that aims to provide primary school children with opportunities to become actively engaged in the high-order thinking processes of problem solving and critical thinking. A preliminary evaluation of CULTURE has found that it offers the freedom for children to take part in process-oriented learning experiences. Through providing children with opportunities to make inferences, validate results, explain discoveries and analyse situations, CULTURE encourages the development of high-order thinking skills. The evaluation found that CULTURE allows users to autonomously explore the important scientific concepts of life and living, and energy and change within a software environment that children find enjoyable and easy to use.

Expression of Heparan Sulphate N-deacetylase/N-sulphotransferase by Vascular Smooth Muscle Cells

Heparan sulphate is an important mediator in determining vascular smooth muscle cell (SMC) phenotype. The sulphation pattern of the heparan sulphate chains is critical to their function. We have examined the initial step in the biosynthesis of the sulphated domains mediated by the enzyme heparan sulphate N-deacetylase/N-sulphotransferase (NDST). Rabbit aortic SMC in primary culture exhibited NDST enzyme activity and expressed NDST-1 in their Golgi apparatus, with maximal expression in SMC 2 days after dispersal in primary culture confirmed by Western blot analysis. Endothelial cells, macrophages and fibroblasts expressed NDST-1 but had generally less intense staining than SMC, although SMC expression decreased with culture. The uninjured rat aorta also showed widespread expression of NDST-1. After balloon de-endothelialisation, NDST-1 could not be detected in SMC of the neointima in the early stages of neointimal formation, but was re-expressed at later time points (after 12 weeks). In human coronary arteries, SMC of the media and the diffuse intimal thickening expressed NDST-1, while SMC in the atherosclerotic plaque were negative for NDST-1. We conclude that SMC may regulate their heparan sulphate sulphation at the level of expression of the enzyme heparan sulphate NDST in a manner related to their phenotypic state.