Creating a school programme to cater for learner diversity: A school administrator’s journey and dialogue with an academic

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Double solid twistor spaces: the case of arbitrary signature

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of 'double solid type' on 3CP^2, projective models of present twistor spaces have a natural structure of double covering of a CP^2-bundle over CP^1. We explicitly give a defining polynomial of the branch divisor of the double covering whose restriction to fibers are degree four. If n>3 these are new twistor spaces, to the best of the author's knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from math.DG/0701278, the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was "Explicit construction of new Moishezon twistor spaces, II".

Glasses in hard spheres with short-range attraction

We report a detailed experimental study of the structure and dynamics of glassy states in hard spheres with short-range attraction. The system is a suspension of nearly-hard-sphere colloidal particles and non-adsorbing linear polymer which induces a depletion attraction between the particles. Observation of crystallization reveals a re-entrant glass transition. Static light scattering shows a continuous change in the static structure factors upon increasing attraction. Dynamic light scattering results, which cover 11 orders of magnitude in time, are consistent with the existence of two distinct kinds of glasses, those dominated by inter-particle repulsion and caging, and those dominated by attraction. Samples close to the `A3 point' predicted by mode coupling theory for such systems show very slow, logarithmic dynamics.Comment: 22 pages, 18 figure

A cluster mode-coupling approach to weak gelation in attractive colloids

Mode-coupling theory (MCT) predicts arrest of colloids in terms of their volume fraction, and the range and depth of the interparticle attraction. We discuss how effective values of these parameters evolve under cluster aggregation. We argue that weak gelation in colloids can be idealized as a two-stage ergodicity breaking: first at short scales (approximated by the bare MCT) and then at larger scales (governed by MCT applied to clusters). The competition between arrest and phase separation is considered in relation to recent experiments. We predict a long-lived `semi-ergodic' phase of mobile clusters, showing logarithmic relaxation close to the gel line.Comment: 4 pages, 3 figure

Rejecting another pains the self: The impact of perceived future rejection

The current investigation examined whether people would experience a higher level of pain after rejecting another person, especially for those high in evaluative concern, through increased perceptions of future rejection. Three experiments provide converging support to these predictions. After reliving a past rejecting experience (Experiments 1 and 2) and concurrently rejecting another person (Experiment 3), the source of rejection experienced a higher level of pain than participants in the control conditions. We also found that evaluative concern, either primed (Experiment 2) or measured (Experiment 3) moderated the above effect, such that this effect was only observed among participants high in evaluative concern, but not among those low in evaluative concern. Moreover, perceived future rejection mediated the moderating effect of evaluative concern and rejecting another person on the levels of pain that people experience (Experiment 3). These findings contribute to the literature by showing a mechanism explaining why rejecting another person pains the self and who are more susceptible to this influence.postprin

Scaling of dynamics with the range of interaction in short-range attractive colloids

We numerically study the dependence of the dynamics on the range of interaction $\Delta$ for the short-range square well potential. We find that, for small $\Delta$, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive glass line and the liquid-gas line does not depend on $\Delta$. This proves that in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.Comment: 4 pages, 4 figure

Hawking radiation in different coordinate settings: Complex paths approach

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semiclassical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation as far as these coordinates are concerned.Comment: 18 pages, 2 figures, Uses IOP style file; final version; accepted in Class. Quant. Gra

Entanglement transformation between sets of bipartite pure quantum states using local operations

Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient conditions on the existence of such a transformation. We also provide efficient algorithms that can quickly rule out the possibility of transforming a set of initial states to a set of final states.Comment: 19 pages, 1 figure, minor revision, to appear in J.Math.Phy