The rigidity of infinite graphs

A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and 1<p<\infty. Generalisations are obtained for the Laman and Henneberg combinatorial characterisations of generic infinitesimal rigidity for finite graphs in the Euclidean plane. Also Tay's multi-graph characterisation of the rigidity of generic finite body-bar frameworks in d-dimensional Euclidean space is generalised to the non-Euclidean l^p norms and to countably infinite graphs. For all dimensions and norms it is shown that a generically rigid countable simple graph is the direct limit of an inclusion tower of finite graphs for which the inclusions satisfy a relative rigidity property. For d>2 a countable graph which is rigid for generic placements in R^d may fail the stronger property of sequential rigidity, while for d=2 the equivalence with sequential rigidity is obtained from the generalised Laman characterisations. Applications are given to the flexibility of non-Euclidean convex polyhedra and to the infinitesimal and continuous rigidity of compact infinitely-faceted simplicial polytopes.Comment: 51 page

Strain-Modified RKKY Interaction in Carbon Nanotubes

For low-dimensional metallic structures, such as nanotubes, the exchange coupling between localized magnetic dopants is predicted to decay slowly with separation. The long-range character of this interaction plays a significant role in determining the magnetic order of the system. It has previously been shown that the interaction range depends on the conformation of the magnetic dopants in both graphene and nanotubes. Here we examine the RKKY interaction in carbon nanotubes in the presence of uniaxial strain for a range of different impurity configurations. We show that strain is capable of amplifying or attenuating the RKKY interaction, significantly increasing certain interaction ranges, and acting as a switch: effectively turning on or off the interaction. We argue that uniaxial strain can be employed to significantly manipulate magnetic interactions in carbon nanotubes, allowing an interplay between mechanical and magnetic properties in future spintronic devices. We also examine the dimensional relationship between graphene and nanotubes with regards to the decay rate of the RKKY interaction.Comment: 7 pages, 6 figures, submitte

Seasonal Occurrence of the Sod Webworm Moths (Lepidoptera: Crambidae) of Ohio

While nearly 100 species of sod webworms are known to occur in North America, the species complex and seasonal occurrence of these moths has been documented in relatively few states. For Ohio, there is little published record of the sod webworm species complex, and the seasonal occurrence of only a few economically important species has been documented. Using black light traps, sod web worm adult flight activity was monitored over the course of three to five years at four different locations throughout Ohio. In this paper we report the seasonal occurrence of sod web worms species captured at these locations. These data provide a historical benchmark of sod web­worm species diversity, local abundance, and seasonal occurrence in Ohio

Reflexivity of the translation-dilation algebras on L^2(R)

The hyperbolic algebra A_h, studied recently by Katavolos and Power, is the weak star closed operator algebra on L^2(R) generated by H^\infty(R), as multiplication operators, and by the dilation operators V_t, t \geq 0, given by V_t f(x) = e^{t/2} f(e^t x). We show that A_h is a reflexive operator algebra and that the four dimensional manifold Lat A_h (with the natural topology) is the reflexive hull of a natural two dimensional subspace.Comment: 10 pages, no figures To appear in the International Journal of Mathematic

Antenna pattern shaping, sensing, and steering study Final report

Design of steerable satellite antenna with beam pattern sensing syste

Crop residue conservation during fallow and erosion risk in west central Saskatchewan

Non-Peer ReviewedSummerfallow is considered to be a necessary practice to replenish soil moisture reserves in much of west central Saskatchewan. Unfortunately, this practice has been largely responsible for severe erosion in the past. Recently many farmers have attempted to keep more crop residue on the soil surface, by using herbicides and wide blade cultivators to control weeds during the fallow period. Much of the increase in these practices has been due to assistance programs provided by PFRA, Saskatchewan Agriculture (e.g., Save Our Soils (SOS) program), Ducks Unlimited and other organizations. This paper looks at the effectiveness of these projects in mainta1n1ng crop residue to minimize erosion. Included are evaluations of weed control, costs, subsequent crop yields and farmer perceptions. Results of a crop residue survey are also presented. This survey provides a good comparison with the project fields. It also enables one to forecast erosion potential for the following winter, spring, and summer seasons. While the paper focuses mainly on 1988 activities, it should be noted that similar work was done in 1986-87

On the effects of mass and momentum transfer from droplets impacting on steady two-dimensional rimming flow in a horizontal cylinder

Motivated by applications in aero-engines, steady two-dimensional thin-filmflow on the inside of a circular cylinder is studied when the filmsurface is subject to mass and momentum transfer from impacting droplets. Asymptotic analysis is used systematically to identify distinguished limits that incorporate these transfer effects at leading order and to provide a new mathematical model. Applying both analytical and numerical approaches to the model, a set of stable steady, two-dimensional solutions that fit within the rational framework is determined. A number of these solutions feature steep fronts and associated recirculating pools, which are undesirable in an aeroengine since oil may be stripped away from the steep fronts when there is a core flow external to the film, and recirculation may lead to oil degradation. The model, however, provides a means of investigating whether the formation of the steep fronts on the filmsurface and of internal recirculation pools can be delayed, or inhibited altogether, by designing jets to deliver prescribed distributions of oil droplets or by the judicious siting of oil sinks. Moreover, by studying pathlines, oil-residence times can be predicted and systems optimized

Conquering the great divide: Rural mothers of children with chronic health conditions accessing specialist medical care for their children

© 2019 Australian College of Nursing Ltd Background: Globally, the number of children with chronic health conditions (CHCs) is increasing and mothers are mostly responsible for their care. Aim: Few studies have focused on rural mothers and their experiences of sourcing health care for their children who have CHCs. The purpose of this study was to explore these experiences. Method: Using a phenomenological approach, semi-structured interviews were conducted in early 2018. The Consolidated criteria for Reporting Qualitative research (COREQ) guidelines were followed. Sixteen rural mothers were interviewed regarding their experiences of accessing health care to provide optimal management of their children's CHC. Findings: Thematic analysis of resulting data revealed the overarching theme ‘Conquering the great divide’. From this overarching theme, four themes emerged. This paper focuses on the first theme, ‘Heading to the big smoke: access’. Discussion: Rural mothers felt challenged accessing health care for their children in the major cities whilst also maintaining routine family life back home. Conclusion: Understanding these rural women's experiences could assist health care professionals to develop strategies to facilitate rural mothers accessing services for their children with a CHC