Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples

Extremely narrow spectrum of GRB110920A: further evidence for localised, subphotospheric dissipation

Much evidence points towards that the photosphere in the relativistic outflow in GRBs plays an important role in shaping the observed MeV spectrum. However, it is unclear whether the spectrum is fully produced by the photosphere or whether a substantial part of the spectrum is added by processes far above the photosphere. Here we make a detailed study of the $\gamma-$ray emission from single pulse GRB110920A which has a spectrum that becomes extremely narrow towards the end of the burst. We show that the emission can be interpreted as Comptonisation of thermal photons by cold electrons in an unmagnetised outflow at an optical depth of $\tau \sim 20$. The electrons receive their energy by a local dissipation occurring close to the saturation radius. The main spectral component of GRB110920A and its evolution is thus, in this interpretation, fully explained by the emission from the photosphere including localised dissipation at high optical depths.Comment: 14 pages, 11 figures, accepted to MNRA

Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $\ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.Comment: 18 pages, 3 figure

Arboreal methodologies: Getting lost to explore the potential of the non-innocence of ‘nature’

This paper recounts a workshop that took place in a polytunnel in a forest school in Sligo, North-West Ireland on a cold day in early-December. The event sought to materialise ‘arboreal methodologies’ (Osgood, 2019; Osgood & Odegard, 2022; Osgood & Axelsson, 2023) which are characterised by the enactment of feminist posthumanist praxis to engage in world-making (Haraway, 2008) intended to unsettle recognisable tropes of biophilia that have come to frame both child and nature in narrow ways. The arboreal methodologies that adult participants were invited to mobilise were situated, material, affective, and involved metaphorical and material practices of ‘getting lost’ through ‘childing’. The workshop invited a sense of wonder at the ways arboreal methodologies might offer possibilities to confront human exceptionalism and wrestle with our complex, often contradictory relationships to ‘nature’ that might then go on to inform practice with young children. The approach taken involves methodologies without method (Koro-Ljunberg, 2016) to bring speculative, embodied encounters in the forest, together with unlikely tales of how forests work on and through us. We pursue a critical, tentacular engagement with the forest and take seriously its potential to agitate familiarity and strangeness, wonder and fear, nature and culture. In this paper we re-encounter embodied becomings-with the forest to think and sense other ways to take life in the Plantationocene (Tsing, 2015) seriously

One step multiderivative methods for first order ordinary differential equations

A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed. The methods are extrapolated and analysed for use in PECE mode. Error constants and stability intervals are calculated and the combinations compared with well known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors. w926020