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This study reports the findings of a questionnaire survey about clergy experiences of isolation and solutions to it in a rural diocese which is embedding within its structures opportunities to enhance the care and efficacy of its ministers. Two thirds of the 87 participants felt isolated to some extent, while one third did not feel isolated at all. Significantly higher scores of isolation were recorded by: stipendiary clergy (compared with self-supporting clergy); clergy working alone (compared with clergy working in teams); and clergy working in multi-parish contexts (compared with clergy working elsewhere). Existing support structures are explored, as well as new opportunities for mutual support: 79% of participants reported being supported by other clergy; and 53% found deanery chapter a support. Nearly 30% were supported by a cell group or other small group. Several participants suggested that opportunities for informal fellowship at deanery chapter could be a solution to their isolation. However, there are dangers that diocesan interventions to solve the problem of isolation may be perceived as yet another ‘initiative’ or present as one more among multiple overwhelmings. [ABSTRACT FROM AUTHOR]

Abstract  In 2000 Bezdek asked which plane convex bodies have the property that whenever an annulus, consisting of the body less a sufficiently small scaled copy of itself, is covered by strips, the sum of the widths of the strips must still be at least the minimal width of the body. We characterise the polygons for which this is so. [ABSTRACT FROM AUTHOR]

Magnetic skyrmions are promising candidates as information carriers in logic or storage devices thanks to their robustness, guaranteed by the topological protection, and their nanometric size. Currently, little is known about the influence of parameters such as disorder, defects, or external stimuli on the long-range spatial distribution and temporal evolution of the skyrmion lattice. Here, using a large (7.3 x 7.3 µm²) single-crystal nanoslice (150 nm thick) of Cu2OSeO3, we image up to 70,000 skyrmions by means of cryo-Lorentz transmission electron microscopy as a function of the applied magnetic field. The emergence of the skyrmion lattice from the helimagnetic phase is monitored, revealing the existence of a glassy skyrmion phase at the phase transition field, where patches of an octagonally distorted skyrmion lattice are also discovered. In the skyrmion phase, dislocations are shown to cause the emergence and switching between domains with different lattice orientations, and the temporal fluctuation of these domains is filmed. These results demonstrate the importance of direct-space and real-time imaging of skyrmion domains for addressing both their long-range topology and stability. [ABSTRACT FROM AUTHOR]