Motility of active fluid drops on surfaces

Drops of active liquid crystal have recently shown the ability to self-propel, which was associated with topological defects in the orientation of active filaments [Sanchez {\em et al.}, Nature {\bf 491}, 431 (2013)]. Here, we study the onset and different aspects of motility of a three-dimensional drop of active fluid on a planar surface. We analyse theoretically how motility is affected by orientation profiles with defects of various types and locations, by the shape of the drop, and by surface friction at the substrate. In the scope of a thin drop approximation, we derive exact expressions for the flow in the drop that is generated by a given orientation profile. The flow has a natural decomposition into terms that depend entirely on the geometrical properties of the orientation profile, i.e. its bend and splay, and a term coupling the orientation to the shape of the drop. We find that asymmetric splay or bend generates a directed bulk flow and enables the drop to move, with maximal speeds achieved when the splay or bend is induced by a topological defect in the interior of the drop. In motile drops the direction and speed of self-propulsion is controlled by friction at the substrate.Comment: 11 pages, 8 figure

The many-body reciprocal theorem and swimmer hydrodynamics

We present a reinterpretation and extension of the reciprocal theorem for swimmers, extending its application from the motion of a single swimmer in an unbounded domain to the general setting, giving results for both swimmer interactions and general hydrodynamics. We illustrate the method for a squirmer near a planar surface, recovering standard literature results and extending them to a general squirming set, to motion in the presence of a ciliated surface, and expressions for the flow field throughout the domain. Finally, we present exact results for the hydrodynamics in two dimensions which shed light on the near-field behaviour.Comment: 6 pages, 6 figure

Umbilic Lines in Orientational Order

Three-dimensional orientational order in systems whose ground states possess non-zero, chiral gradients typically exhibits line-like structures or defects: $\lambda$ lines in cholesterics or Skyrmion tubes in ferromagnets for example. Here we show that such lines can be identified as a set of natural geometric singularities in a unit vector field, the generalisation of the umbilic points of a surface. We characterise these lines in terms of the natural vector bundles that the order defines and show that they give a way to localise and identify Skyrmion distortions in chiral materials -- in particular that they supply a natural representative of the Poincar\'{e} dual of the cocycle describing the topology. Their global structure leads to the definition of a self-linking number and helicity integral which relates the linking of umbilic lines to the Hopf invariant of the texture.Comment: 14 pages, 9 figure

Maxwell's Theory of Solid Angle and the Construction of Knotted Fields

We provide a systematic description of the solid angle function as a means of constructing a knotted field for any curve or link in $\mathbb{R}^3$. This is a purely geometric construction in which all of the properties of the entire knotted field derive from the geometry of the curve, and from projective and spherical geometry. We emphasise a fundamental homotopy formula as unifying different formulae for computing the solid angle. The solid angle induces a natural framing of the curve, which we show is related to its writhe and use to characterise the local structure in a neighborhood of the knot. Finally, we discuss computational implementation of the formulae derived, with C code provided, and give illustrations for how the solid angle may be used to give explicit constructions of knotted scroll waves in excitable media and knotted director fields around disclination lines in nematic liquid crystals.Comment: 20 pages, 9 figure

TRUTH – A Conversation between P F Strawson and Gareth Evans (1973)

This is a transcript of a conversation between P F Strawson and Gareth Evans in 1973, filmed for The Open University. Under the title 'Truth', Strawson and Evans discuss the question as to whether the distinction between genuinely fact-stating uses of language and other uses can be grounded on a theory of truth, especially a 'thin' notion of truth in the tradition of F P Ramsey

Exploring the Trade-offs Between Incentives for Distributed Generation Developers and DNOs

Regulators are aiming to incentivize developers and Distribution Network Operators to connect distributed generation (DG) to improve network environmental performance and efficiency. A key question is whether these incentives will encourage both parties to connect DG. Here, multiobjective optimal power flow is used to simulate how the parties' incentives affect their choice of DG capacity within the limits of the existing network. Using current U.K. incentives as a basis, this paper explores the costs, benefits and tradeoffs associated with DG in terms of connection, losses and, in a simple fashion, network deferral. © 2007 IEEE

THE IMPORTANCE OF TARIFF STRUCTURE IN CONSERVATION PRICING

Resource /Energy Economics and Policy,

Scarring, Habituation and Social Exclusion: Work Histories in Secure and Insecure Employment

This paper analyses the impact of unemployment experiences on the life satisfaction of Australian workers in casual and permanent employment. Using panel data techniques, it was found that male permanent workers were scarred by previous unemployment. This contrasted with casual workers who seem habituated to the e¤ects of past unemployment. Social norming e¤ects were evident for permanent workers, unemployment scarred deeper when it was less of a general norm, this was not the case for casual workers. Social psychology research suggests that disadvantaged groups tend to prefer intragroup or intertemporal comparisons. Casual workers. habituation to past unemployment and lack of social norming could contribute to the process of social exclusion.