On the homotopy groups of the self-equivalences of linear spheres

Peer reviewed

On the homotopy groups of the self-equivalences of linear spheres

Peer reviewed

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

Fast and robust stereo object recognition for spheres

The paper presents a fast and robust stereo object recognition method. The method is currently unable to identify the rotation of objects. This makes it very good at locating spheres which are rotationally independent. Approximate methods for located non-spherical objects have been developed. Fundamental to the method is that the correspondence problem is solved using information about the dimensions of the object being located. This is in contrast to previous stereo object recognition systems where the scene is first reconstructed by point matching techniques. The method is suitable for real-time application on low-power devices.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Globally networked public spheres? The Australian media reaction to WikiLeaks

The global release of 250,000 US Embassy diplomatic cables to selected media sites worldwide through the WikiLeaks website, was arguably the major global media event of 2010. As well as the implications of the content of the cables for international politics and diplomacy, the actions of WikiLeaks and its controversial editor-in-chief, the Australian Julian Assange, bring together a range of arguments about how the media, news and journalism are being transformed in the 21st century. This paper will focus on the reactions of Australian online news media sites to the release of the diplomatic cables by WikiLeaks, including both the online sites of established news outlets such as The Australian, Sydney Morning Herald and The Age, the ABC’s The Drum site, and online-only sites such as Crikey, New Matilda and On Line Opinion. The study focuses on opinion and commentary rather than straight news reportage, and analysis is framed around three issues: WikiLeaks and international diplomacy; implications of WikiLeaks for journalism; and WikiLeaks and democracy, including debates about the organisation and the ethics of its own practice. It also whether a “WikiLeaks Effect” has wider implications for how journalism is conducted in the future, particularly the method of ‘redaction’ of large amounts of computational data.

Inverse expression states of the BRN2 and MITF transcription factors in melanoma spheres and tumour xenografts regulate the NOTCH pathway

The use of adherent monolayer cultures have produced many insights into melanoma cell growth and differentiation, but often novel therapeutics demonstrated to act on these cells are not active in vivo. It is imperative that new methods of growing melanoma cells that reflect growth in vivo are investigated. To this end, a range of human melanoma cell lines passaged as adherent cultures or induced to form melanoma spheres (melanospheres) in stem cell media have been studied to compare cellular characteristics and protein expression. Melanoma spheres and tumours grown from cell lines as mouse xenografts had increased heterogeneity when compared with adherent cells and 3D-spheroids in agar (aggregates). Furthermore, cells within the melanoma spheres and mouse xenografts each displayed a high level of reciprocal BRN2 or MITF expression, which matched more closely the pattern seen in human melanoma tumours in situ, rather than the propensity for co-expression of these important melanocytic transcription factors seen in adherent cells and 3D-spheroids. Notably, when the levels of the BRN2 and MITF proteins were each independently repressed using siRNA treatment of adherent melanoma cells, members of the NOTCH pathway responded by decreasing or increasing expression, respectively. This links BRN2 as an activator, and conversely, MITF as a repressor of the NOTCH pathway in melanoma cells. Loss of the BRN2-MITF axis in antisense-ablated cell lines decreased the melanoma sphere-forming capability, cell adhesion during 3D-spheroid formation and invasion through a collagen matrix. Combined, this evidence suggests that the melanoma sphere-culture system induces subpopulations of cells that may more accurately portray the in vivo disease, than the growth as adherent melanoma cells.

Reduced electron recombination of dye-sensitized solar cells based on TiO 2 spheres consisting of ultrathin nanosheets with [001] facet exposed

An anatase TiO 2 material with hierarchically structured spheres consisting of ultrathin nanosheets with 100% of the [001] facet exposed was employed to fabricate dye-sensitized solar cells (DSC s). Investigation of the electron transport and back reaction of the DSCs by electrochemical impedance spectroscopy showed that the spheres had a threefold lower electron recombination rate compared to the conventional TiO 2 nanoparticles. In contrast, the effective electron diffusion coefficient, D n, was not sensitive to the variation of the TiO 2 morphology. The TiO 2 spheres showed the same Dn as that of the nanoparticles. The influence of TiCl 4 post-treatment on the conduction band of the TiO 2 spheres and on the kinetics of electron transport and back reactions was also investigated. It was found that the TiCl 4 post-treatment caused a downward shift of the TiO 2 conduction band edge by 30 meV. Meanwhile, a fourfold increase of the effective electron lifetime of the DSC was also observed after TiCl4 treatment. The synergistic effect of the variation of the TiO 2 conduction band and the electron recombination determined the open-circuit voltage of the DSC. © 2012 Wang et al.

The music of the spheres

This article describes a method for making a spectroscope from scrap materials, i.e. a fragment of compact disc, a cardboard box, a tube and a digital camera to record the spectrum. An image processing program such as ImageJ can be used to calculate the wavelength of emission and absorption lines from the digital photograph. Multiple images of a spectrum can be stacked to reduce random noise, enabling spectra of faint objects to be obtained. Some basic experiments are described, such as viewing the spectrum produced by various types of lamp and the Sun. © 2012 IOP Publishing Ltd.

Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Comparative study of photocatalytic performance of titanium oxide spheres assembled by nanorods, nanoplates and nanosheets

TiO2 spheres assembled by nanorods, nanoplates and nanosheets were fabricated by facile hydrothermal/solvothermal methods. The three samples were thoroughly characterised by scanning electron microscopy, X-ray diffraction, the Brunauer–Emmett–Teller method and UV spectroscopy. The surface area of spheres assembled by nanosheets was 83.9 m2g–1, which is larger than that obtained for nanorods (10.8 m2g–1) and nanoplates (6.31 m2g–1). Their photocatalytic performance was evaluated in terms of the decomposition rate of methyl orange in these three samples under UV irradiation. The best photoactivity was observed in the samples constructed from nanosheets.

Protein loaded mesoporous silica spheres as a controlled delivery platform

Background The adsorption of bovine serum albumin (BSA) onto mesoporous silica spheres (MPS) synthesized from silica colloids was studied employing real time in situ measurements. The stabilities of the BSA at different pH values, their isoelectric points and zeta potentials were determined in order to probe the interactions between the protein and the mesoporous silica. Results The pore size of MPS was designed for protein, and this, coupled with an in depth understanding of the physico-chemical characteristics of the protein and MPS has yielded a better binding capacity and delivery profile. The adsorption isotherm at pH 4.2 fitted the Langmuir model and displayed the highest adsorption capacity (71.43 mg mL-1 MPS). Furthermore, the delivery rates of BSA from the MPS under physiological conditions were shown to be dependent on the ionic strength of the buffer and protein loading concentration. Conclusion Economics and scale-up considerations of mesoporous material synthesized via destabilization of colloids by electrolyte indicate the scaleability and commercial viability of this technology as a delivery platform for biopharmaceutical applications.

Mesoporous silica spheres from colloids

A novel method has been developed to synthesize mesoporous silica spheres using commercial silica colloids (SNOWTEX) as precursors and electrolytes (ammonium nitrate and sodium chloride) as destabilizers. Crosslinked polyacrylamide hydrogel was used as a temporary barrier to obtain dispersible spherical mesoporous silica particles. The influences of synthesis conditions including solution composition and calcination temperature on the formation of the mesoporous silica particles were systematically investigated. The structure and morphology of the mesoporous silica particles were characterized via scanning electron microscopy (SEM) and N2 sorption technique. Mesoporous silica particles with particle diameters ranging from 0.5 to 1.6 μm were produced whilst the BET surface area was in the range of 31-123 m2 g-1. Their pore size could be adjusted from 14.1 to 28.8 nm by increasing the starting particle diameter from 20-30 nm up to 70-100 nm. A simple and cost effective method is reported that should open up new opportunities for the synthesis of scalable host materials with controllable structures.

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function psi(t) decays much faster than t(-3/2) obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity-driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of psi(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.