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The solar atmosphere exhibits a diverse range of wave phenomena, where one of the earliest discovered was the five-minute global acoustic oscillation, also referred to as the p-mode. The analysis of wave propagation in the solar atmosphere may be used as a diagnostic tool to estimate accurately the physical characteristics of the Sun's atmospheric layers.In this paper, we investigate the dynamics and upward propagation of waves which are generated by the solar global eigenmodes. We report on a series of hydrodynamic simulations of a realistically stratified model of the solar atmosphere representing its lower region from the photosphere to low corona. With the objective of modelling atmospheric perturbations, propagating from the photosphere into the chromosphere, transition region and low corona, generated by the photospheric global oscillations the simulations use photospheric drivers mimicking the solar p-modes. The drivers are spatially structured harmonics across the computational box parallel to the solar surface. The drivers perturb the atmosphere at 0.5 Mm above the bottom boundary of the model and are placed coincident with the location of the temperature minimum. A combination of the VALIIIC and McWhirter solar atmospheres are used as the background equilibrium model.We report how synthetic photospheric oscillations may manifest in a magnetic field free model of the quiet Sun. To carry out the simulations, we employed the magnetohydrodynamics code, SMAUG (Sheffield MHD Accelerated Using GPUs).Our results show that the amount of energy propagating into the solar atmosphere is consistent with a model of solar global oscillations described by Taroyan and Erdelyi (2008) using the Klein-Gordon equation. The computed results indicate a power law which is compared to observations reported by Ireland et al. (2015) using data from the Solar Dynamics Observatory/Atmospheric Imaging Assembly.

Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1–3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.

Micromagnetic models of assemblies of randomly oriented, exchange coupled, nanocrystals consisting of a magnetically hard uniaxial phase (typified by Nd 2 Fe 14 B) together with an ultra-soft phase (typified by α -iron) have been studied numerically. The hard crystallites were located on a three dimensional cubic lattice, and cubic crystallites of the soft phase were inserted at the junctions of every group of eight hard crystallites. Demagnetizing curves were obtained as a sequence of static equilibrium states in an incrementally changing applied field. Values of the coercivity, remanence and energy product are reported as functions of Δ GH , the grain size of the hard phase, and of ϕ S , the fractional volume of the soft phase. The dependence on Δ GH falls quite rapidly with increasing ϕ S . The low anisotropy and high saturation magnetization of the α -iron make approximately equal contributions to remanence enhancement in the model. Its remanence values are in quite good agreement with experimental values for Nd 2 Fe 14 B containing α -iron. However, its values for the coercivity and energy product, though decidedly lower than those obtained computationally by some other authors, significantly exceed those obtained experimentally, but show a similar variation with Δ GH and ϕ S .

Demagnetizing curves have been calculated numerically for three-dimensional micromagnetic model assemblies of randomly oriented, magnetically hard, exchange coupled, uniaxial nanocrystals as typified by rapidly quenched Nd 2 Fe 14 B. The curves were obtained as a sequence of static equilibrium states in an incrementally changing applied field. The magnetization distribution in each state was obtained by minimizing the sum of the exchange, anisotropy and Zeeman energies of the assembly, using a modified LaBonte method, with computational elements as small as 1.11 nm (roughly 1 4 the domain wall thickness in Nd 2 Fe 14 B). For computational economy, internal dipolar interactions were ignored in the energy minimization. For a material with the magnetic constants of stoichiometric Nd 2 Fe 14 B, tests showed that these interactions contribute less than 3% to the energy. On increasing the model grain size from 4.4 to 36 nm, the reduced remanence fell from 76 to 54% and the reduced intrinsic coercivity μ 0i H C M S / K U increased from 0.16 to 0.46 (just under half the Stoner–Wohlfarth value); both sets of results are in reasonable agreement with experimental values. The energy product, evaluated for Nd 2 Fe 14 B, ranged from ∼224 kJ/m 3 for 10 nm grains to ∼128 kJ/m 3 for 36 nm grains. For grain sizes ⩾20 nm, spatial magnetization variation was confined to domain walls centred on the grain boundaries. For grain sizes decreasing below about twice the domain wall thickness, spatial magnetization variation extended to the interior of the grains and exhibited increasingly long-range correlations.