GHP: a maple package for performing calculations in the Geroch-Held-Penrose formalism

We present a new symbolic algebra package, written for Maple, for performing computations in the Geroch-Held-Penrose formalism. We demonstrate the essential features and capabilities of our package by investigating Petrov-D vacuum solutions of Einstein's field equations.

Algebraically special coplanar shear-free perfect fluids in general relativity

We investigate all algebraically special, not conformally flat, shear-free, isentropic (p(w), w + p ≠ 0), perfect fluid solutions of Einstein's field equations. We show, using the GHP formalism, that if the repeated principle null direction of the Weyl tensor is coplanar with the fluid's 4-velocity and vorticity vector (assumed nonzero), then the fluid's expansion must vanish.

Baby, it`s you : international capital discovers the under threes

Well-established international entertainment firms such as Disney and Fisher-Price are joining new start-up firms such as Baby Einstein to create a 'Baby' market of products (including toys, games and videos) specifically targeted at children aged 0-3 years. Despite its novelty, the 'Baby' market mirrors older markets that these firms have created around other demographic groups (e.g. older children, adolescents and adults) - it redefines its target demographic group around specific commodities and promotes its redefinition as 'common sense'. The 'Baby' firms redefine babies solely as early learners whose potential to learn can be released by these firms' brand-name 'educational' or 'developmental' products. Many adults buy these products because they accept the firms' redefinition of babies, but other adults ignore the firms' promotional messages and buy the products to give themselves some time apart from their babies. The 'Baby' market is significant for children and adults because it changes young children's relationships with adults and because it subordinates local cultural differences to a children's culture that purports to be 'global' but has, in reality, extremely narrow foundations in class, race and gender.

Micro-credit programs and land distribution: a note

"Micro-credit" has come to refer to a popular extension strategy---usually in the agricultural sector---whereby a government or NGO extends credit at favorable rates to poorer borrowers, with repayment being supported by some kind of mortgage on the borrower's social capital. In the commonest case, eligibility is determined by the borrower's wealth, as indexed by his/her landholding. This note shows that, with an imperfect land market, the response to such a program will be to fragment landholdings which are smaller than a certain threshold, while larger holdings remain unaffected. Thus the pattern of landholding will tend to become more polarized.

Picturing Australian history: visual texts in nonfiction for children

Time is one of the most prominent themes in the relatively young genre of children's literature, for the young, like adults, want to know about the past. The historical novel of the West grew out of Romanticism, with its exploration of the inner world of feeling, and it grew to full vigor in the era of imperialism and the exploration of the physical world. From the end of the 18th century, children's books flourished, partly in response to these cultural and political influences. After Darwin, Freud, and Einstein, literary works began to grapple with skepticism about the nature of time itself. This book explores how children's writers have presented the theme and concept of time past. While the book looks primarily at literature of the 19th and 20th centuries, it considers a broad range of historical material treated in works from that period. Included are discussions of such topics as Joan of Arc in children's literature, the legacy of Robinson Crusoe, colonial and postcolonial children's literature, the Holocaust, and the supernatural. International in scope, the volume examines history and collective memory in Portuguese children's fiction, Australian history in picture books, Norwegian children's literature, and literary treatments of the great Irish famine. So too, the expert contributors are from diverse countries and backgrounds.

Partners in crime : collusive corruption and search

This paper analyzes corruption as a collusive act which requires the participation of two willing partners. An agent intending to engage in a corrupt act must search for a like-minded partner. When many people in the economy are corrupt, such a search is more likely to be fruitful. Thus when an agent engages in a search, he raises the net benefit of searching for other similar agents in the economy, creating an externality. This introduces a non-convexity in the model, which consequently has multiple equilibria. The economy can be in stable equilibrium with a high or low level of corruption.

Starting from the high-corruption equilibrium, a sufficient increase in vigilance triggers a negative cascade, leading the economy to a new equilibrium in which no agent finds it profitable to search for corrupt partners. The no-corruption equilibrium continues to be stable if vigilance is then relaxed. This suggests that the correct way to deal with corruption is to launch a ``big push'' with large amounts of resources. Once the level of corruption declines, these resources can be withdrawn.

Purely magnetic spacetimes in general relativity

Given the deep links between Maxwell's equations and General Relativity, it is natural to ask whether there exist solutions of the field equations which are purely magnetic, like Dirac's magnetic monopole. The thesis succeeds in producing two entirely new families of purely magnetic solutions.

Shear-free perfect fluids with a solenoidal magnetic curvature

We investigate shear-free perfect fluid solutions of the Einstein field equations where the fluid pressure satisfies a barotropic equation of state and the spatial divergence of the magnetic part of the Weyl tensor is zero. We prove, with the exception of certain quite restricted special cases within the class of solutions in which there exists a Killing vector aligned with the vorticity and for which the magnitude of the vorticity ω is not a function of the matter density μ alone, that such a fluid is either non-rotating or non-expanding. In the restricted cases the equation of state must satisfy an over-determined differential system.

Room temperature fast-ion conduction in imidazolium halide salts

Fast-ion conduction has been observed in the iodide and bromide salts of 1-methyl-3-ethylimidazolium at ambient temperatures. The melting point of these two compounds is above 350 K and even at 273 K the ionic conductivity in the solid-state is greater than 10⁻³S cm⁻¹. Cation diffusion coefficients have been measured using fringe field gradient and/or pulse field gradient ¹H NMR techniques, which indicated cation diffusion coefficients of the order of 10⁻¹⁰ m² s⁻¹ in the solid-state. Remarkably, these values are up to an order of magnitude higher than the cation diffusion coefficient in the supercooled liquid at 293 K. The activation energy for diffusion in the solid-state is extremely small, as is typical of solid-state fast-ion conductors and indicates a change in transport mechanism from the melt to the crystal. The inability to detect an ¹²⁷I signal together with the modelling of the conductivity using the Nernst–Einstein equation suggests that the solid-state conduction is primarily due to cation diffusion. The solid-state fast-ion conduction is most likely related to vacancy diffusion along the cation layers in the crystal. The temperature dependence of the NMR signal intensity indicates that the number of mobile species is increasing with increasing temperature with an activation energy of approximately 20–30 kJ mol⁻¹.

Molecular dynamics simulations of highly concentrated salt solutions : structural and transport effects in polymer electrolytes

Structural, thermodynamic and transport properties have been calculated in concentrated non-aqueous NaI solutions using molecular dynamics simulations. Although the solvent has been represented by a simplistic Stockmayer fluid (spherical particles with point dipoles), the general trends observed are still a useful indication of the behavior of real non-aqueous electrolyte systems. Results indicate that in low dielectric media, significant ion pairing and clustering occurs. Contact ion pairs become more prominent at higher temperatures, independent of the dielectric strength of the solvent. Thermodynamic analysis shows that this temperature behavior is predominantly entropically driven. Calculation of ionic diffusivities and conductivities in the NaI/ether system confirms the clustered nature of the salt, with the conductivities significantly lower than those predicted from the Nernst-Einstein relation. In systems where the solvent-ion interactions increase relative to ion-ion interactions (lower charge or higher solvent dipole moment), less clustering is observed and the transport properties indicate independent motion of the ions, with higher calculated conductivities. The solvent in this system is the most mobile species, in comparison with the polymer electrolytes where the solvent is practically immobile.

On the concept of ionicity in ionic liquids

Ionic liquids are liquids comprised totally of ions. However, not all of the ions present appear to be available to participate in conduction processes, to a degree that is dependent on the nature of the ionic liquid and its structure. There is much interest in quantifying and understanding this ‘degree of ionicity’ phenomenon. In this paper we present transport data for a range of ionic liquids and evaluate the data firstly in terms of the Walden plot as an approximate and readily accessible approach to estimating ionicity. An adjusted Walden plot that makes explicit allowance for differences in ion sizes is shown to be an improvement to this approach for the series of ionic liquids described. In some cases, where diffusion measurements are possible, it is feasible to directly quantify ionicity via the Nernst–Einstein equation, confirming the validity of the adjusted Walden plot approach. Some of the ionic liquids studied exhibit ionicity values very close to ideal; this is discussed in terms of a model of a highly associated liquid in which the ion correlations have similar impact on both the diffusive and conductive motions. Ionicity, as defined, is thus a useful measure of adherence to the Nernst–Einstein equation, but is not necessarily a measure of ion availability in the chemical sense.

Highly concentrated salt solutions : molecular dynamics simulations of structure and transport

Molecular dynamics (MD) simulations in NaI solutions, where the solvent has been represented by the Stockmayer fluid, were performed as a function of temperature, salt concentration, and solvent dipole strength. At higher temperatures contact ion pairs become more prevalent, regardless of solvent strength. An examination of the temperature dependence of the potential of mean force demonstrates the entropic nature of this effect. The transport properties calculated in the simulations are dependent on the balance between solvent dielectric constant and ion charge. In systems with a large solvent dipole moment, the ions appear to be independently mobile, and deviations from Nernst–Einstein behavior are small. In systems of smaller solvent dipole moment or greater ion charge, the ions form clusters, and large deviations from Nernst–Einstein behavior are observed.

Simulations of structure and transport in polymer electrolytes

Simulations implementing both Monte Carlo (MC) and molecular dynamics (MD) techniques were used to explore various aspects of polymer electrolytes. Evidence is presented to support the conclusion that collective behavior of ions determines much of the behavior of these complex materials. Simple theories attributing ion transport to either single ions or clusters of three ions are inadequate to explain ion transport behavior; in particular, the Nernst-Einstein relation commonly used to discuss polymer electrolytes is almost certainly quantitatively inappropriate for these materials.

Ion clustering in molecular dynamics simulations of sodium iodide solutions

Model systems of sodium iodide dissolved in dimethyl ether or 1,2-dimethoxyethane (glyme) were studied in order to investigate the structural and dynamic properties of ionic solutions in small and polymeric ethers. Full molecular dynamics simulations were performed at a range of different salt concentrations. An algorithm was designed which assigns ions to clusters and then calculates all the terms which contribute to ionic conductivity. In dilute solutions, free ions are the most common ionic species, followed by ion pairs. As the concentration increases, pairs become the most common species, with significant concentrations of clusters with 3 through 6 ions. Changing the solvent from dimethyl ether to glyme significantly decreases the ion clustering due to the chelate effect in which the two oxygens on a solvent stabilize an associated cation. The conductivity in stable systems is shown to be primarily the result of the movement of free ions and the relative movement of ions within neutral pairs. The Nernst-Einstein relation, commonly used in the discussion of polymer electrolytes, is shown to be inadequate to quantitatively describe conductivity in the model systems.