Optimal unstirred state of a passive scalar

This work was supported by Leverhulme Trust grant PRG-2017-169.Given a passive tracer distribution, what is the simplest unstirred pattern that may be reached under incompressible advection? This question is partially motivated by recent studies of three-dimensional (3-D) magnetic reconnection, in which the patterns of a topological invariant called the field line helicity greatly simplify until reaching a relaxed state. We test two approaches: a variational method with minimal constraints, and a magnetic relaxation scheme where the velocity is determined explicitly by the pattern of. Both methods achieve similar convergence for simple test cases. However, the magnetic relaxation method guarantees a monotonic decrease in the Dirichlet seminorm of, and is numerically more robust. We therefore apply the latter method to two complex mixed patterns modelled on the field line helicity of 3-D magnetic braids. The unstirring separates into a small number of large-scale regions determined by the initial topology, which is well preserved during the computation. Interestingly, the velocity field is found to have the same large-scale topology as. Similarity to the simplification found empirically in 3-D magnetic reconnection simulations supports the idea that advection is an important principle for field line helicity evolution.Publisher PDFPeer reviewe

Evolution of field line helicity in magnetic relaxation

This work was facilitated by Leverhulme Trust under Grant No. PRG-2017–169, with additional support from Science and Technology Facilities Council (UK) under consortium Grants Nos. ST/N000714, ST/N000781, and ST/S000321.Plasma relaxation in the presence of an initially braided magnetic field can lead to self-organization into relaxed states that retain non-trivial magnetic structure. These relaxed states may be in conflict with the linear force-free fields predicted by the classical Taylor theory, and remain to be fully understood. Here, we study how the individual field line helicities evolve during such a relaxation, and show that they provide new insights into the relaxation process. The line helicities are computed for numerical resistive-magnetohydrodynamic simulations of a relaxing braided magnetic field with line-tied boundary conditions, where the relaxed state is known to be non-Taylor. First, our computations confirm recent analytical predictions that line helicity will be predominantly redistributed within the domain, rather than annihilated. Second, we show that self-organization into a relaxed state with two discrete flux tubes may be predicted from the initial line helicity distribution. Third, for this set of line-tied simulations we observe that the sub-structure within each of the final tubes is a state of uniform line helicity. This uniformization of line helicity is consistent with Taylor theory applied to each tube individually. However, it is striking that the line helicity becomes significantly more uniform than the force-free parameter.Publisher PDFPeer reviewe

Taking research to members of the public

In 2006, with funding from the Engineering and Physical Sciences Research Council (£30k), we built a themed exhibit with the Sensation Science Centre in Dundee. In the main part of the exhibit, which was kitted out as a ‘police station’, a visitor would see a video of a man pretending to commit a crime and construct a composite of his face using a simplified version of our EvoFIT facial-composite system. Visitors were asked, using written and spoken prompts, to select faces from an array of alternatives, with selected items being ‘bred’ together, to allow a composite to be ‘evolved’. The exhibit then presented a picture of the man’s face alongside the evolved composite, example composites created by previous visitors and an average (‘morphed’) composite from the last four visitors. The exhibit took about five minutes for a user to complete and was accompanied by a ‘Research Lab’, a station which explained more of the underlying science: themes around evolution, computer-based generation of faces, forensic use of composites, etc. We expected the exhibit to last five years but, partly due to the robustness of the hardware, it remains today and is still popular

On Samuelson Submanifolds in Four Space

The object of study in this talk is a general class of submanifolds of R^4. The motivation for this work was the derivation of the following equation which answered a question posed by the distinguished economist P.A. Samuelson

Absorption of tricarballylic acid from the rumen of sheep and cattle fed forages containing trans-aconitic acid

Some forages accumulate high concentrations (<5% of dry matter) of trans-aconitate, and this acid has been implicated in Mg chelation and the occurrence of grass tetany in ruminants. In vitro experiments have indicated that rumen microorganisms convert trans-aconitate to tricarballylate. The feeding studies described here were conducted to demonstrate absorption of tricarballylate by ruminant animals fed diets similar to those producing grass tetany. When sheep were switched from a diet containing alfalfa (lucerne) (Medicago sativa L.) hay (no detectable trans-aconitate) to wheat (Triticum aestivum L.) and rye (Secale cereale L.) forage containing 1:52 and 1:37% trans-aconitate, respectively, there was a rapid increase in blood plasma tricarballylate. Trans-aconitate was not detected in the plasma. At 16 h after feeding, plasma tricarballylate concentrations were 0.58±0.08 and 0.48±0.21 mm in sheep fed the wheat and rye forage, respectively. Tricarballylate concentrations remained relatively constant for the remaining 60 h of the experiment. Cattle were fed rye forage one week later, and the concentration of trans-aconitate in the forage had dropped to 0.83% of the dry matter. Once again there was a rapid appearance of tricarballylate in plasma, but the maximum concentration was 0.31±0.05 mm (t=27 h). When the cattle were removed from the rye forage, there was a linear decline in tricarballylate and none was detected 24 h later. The studies indicated that trans-aconitate is converted to tricarballylate in the rumen and that tricarballylate rather than trans-aconitate is absorbed

Dilution effects on magnesium efflux from the rumen

Factors affecting magnesium absorption from the rumen are integrally involved in grass tetany because most of the absorbed Mg passes through the rumen wall. Recent work has shown that ruminal Mg absorption occurs by a sodium-linked active transport following saturation kinetics. The dilution effects on Mg absorption were evaluated by a dynamic simulation of Mg flow in the rumen. As several factors in the rumen influence Mg availability, a simple rumen submodel was developed to predict rumen parameters (fiber content, microbial mass, liquid dilution rate, particulate passage rate) for different conditions. Cation-exchange capacity of fiber and the microbial mass as well as insoluble Mg complex formation reduce the available Mg pool for absorption in the model. Preliminary results for 500 kg cattle grazing crested wheatgrass (DMI = 1.2 % BW / day), indicate that efficiency of magnesium absorption from the rumen was greatly affected by liquid dilution rate. Without considering insoluble Mg precipitate formation, the efficiency of Mg absorption from the rumen ranged from .41 to .31 as the rumen liquid fractional passage rate varied from .08/h to .14/h. Factors affecting the rumen liquid dilution rate include rumen water holding capacity, saliva secretion, rumen osmolarity, and water intake from drinking and eating. Kinetic factors may be responsible for the poor efficiency of absorption of Mg under conditions when rumen liquid dilution rates are high

An automated high-throughput system for phenotypic screening of chemical libraries on C. elegans and parasitic nematodes

Parasitic nematodes infect hundreds of millions of people and farmed livestock. Further, plant parasitic nematodes result in major crop damage. The pipeline of therapeutic compounds is limited and parasite resistance to the existing anthelmintic compounds is a global threat. We have developed an INVertebrate Automated Phenotyping Platform (INVAPP) for high-throughput, plate-based chemical screening, and an algorithm (Paragon) which allows screening for compounds that have an effect on motility and development of parasitic worms. We have validated its utility by determining the efficacy of a panel of known anthelmintics against model and parasitic nematodes: Caenorhabditis elegans, Haemonchus contortus, Teladorsagia circumcincta, and Trichuris muris. We then applied the system to screen the Pathogen Box chemical library in a blinded fashion and identified compounds already known to have anthelmintic or anti-parasitic activity, including tolfenpyrad, auranofin, and mebendazole; and 14 compounds previously undescribed as anthelmintics, including benzoxaborole and isoxazole chemotypes. This system offers an effective, high-throughput system for the discovery of novel anthelmintics

Persistence of the efficacy of copper oxide wire particles against Haemonchus contortus in grazing South African goats

A study was conducted to examine the duration of anthelmintic effect of copper oxide wire particles (COWP) in grazing goats, as data for the persistence of efficacy of COWP in this host species is limited. Forty-eight indigenous male goats were infected naturally by grazing them on Haemonchus contortus-infected pasture. When the faecal egg count (FEC) in the goats was 3179 ± 540 eggs per gram of faeces (mean ± standard error), half the animals were treated with 4 g COWP (day 0; mean live weight = 25.5 ± 0.8 kg). Eight treated (COWP) and eight non-treated (CONTROL) goats were removed from the pasture on each of days 7, 28 and 56, maintained for 27 or 29 days in concrete pens and then humanely slaughtered for nematode recovery. Mean liver copper levels were in the high range in the goats removed from pasture at day 7 (treated: 191 ± 19.7 ppm; untreated: 120 ± 19.7 ppm; P = 0.022), but had dropped to normal levels at days 28 and 56. The mean H. contortus burdens of the treated versus the non-treated goats were, respectively, 184 ± 48 and 645 ± 152 for the goats removed from pasture at day 7 (71% reduction; P = 0.004), 207 ± 42 and 331 ± 156 at day 28 (37% reduction; P = 0.945) and 336 ± 89 and 225 ± 53 at day 56 (−49% reduction; P = 0.665). Weekly monitoring of FECs after treatment until slaughter indicated that the COWP-treated goats had lower FECs than the controls, the treatment main effect being significant at days 7, 28 and 56 (P < 0.01). The day main effect and the treatment × day interaction were only significant for the goats removed from pasture at day 28 (P ≤ 0.001). Packed cell volumes increased during the course of the experiment (day, P < 0.001), but the treatment main effect was significant only for the goats removed from pasture at day 28 (CONTROL 28 d, 28.65 ± 0.52% < COWP 28 d, 31.31 ± 0.52%; P < 0.001). No differences in live weight between groups were considered to be of any practical significance. The study indicated that persistence of efficacy of COWP is limited in goats, extending at most to 28 days after treatment. However, repeated COWP administration at three-month intervals may be safe, given that liver copper levels return to normal two to three months after COWP treatment