4,139 research outputs found
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
Knotted Defects in Nematic Liquid Crystals
We show that the number of distinct topological states associated to a given
knotted defect, , in a nematic liquid crystal is equal to the determinant of
the link . We give an interpretation of these states, demonstrate how they
may be identified in experiments and describe the consequences for material
behaviour and interactions between multiple knots. We show that stable knots
can be created in a bulk cholesteric and illustrate the topology by classifying
a simulated Hopf link. In addition we give a topological heuristic for the
resolution of strand crossings in defect coarsening processes which allows us
to distinguish topological classes of a given link and to make predictions
about defect crossings in nematic liquid crystals.Comment: 10 pages, 4 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:
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 . 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 â 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. Ă© 2007 IEEE
FARM LEVEL IRRIGATION TECHNOLOGY DECISIONS OVER TIME
A time-series cross-sectional model of irrigation technology choice is developed for an irrigation district in California's Central Valley to show how changes in the relative price of irrigation water and variations in water supply over time influence the choice of irrigation system. Results indicate changes in crop mix and variations in water supply are at least as important as price in determining the choice of irrigation system.Farm Management,
THE IMPORTANCE OF TARIFF STRUCTURE IN CONSERVATION PRICING
Resource /Energy Economics and Policy,
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