Micromag (A micromagnetics code for high performance computing)

This is a micromagnetics code that is specifically designed to be run using high performance computing (HPC) architectures. This code was used to execute models on ARCHER, (www.archer.ac.uk), one of the UK's main supercomputer clusters. It allows modeling magnetic materials up to the micron size scale using a spatial transform technique due to Imhoff et al. and is based on the FEniCS finite element framework.This is a micromagnetics code that is specifically designed to be run using high performance computing (HPC) architectures. This code was used to execute models on ARCHER, (www.archer.ac.uk), one of the UK's main supercomputer clusters. It allows modeling magnetic materials up to the micron size scale using a spatial transform technique due to Imhoff et al. and is based on the FEniCS finite element framework.0.0.

Asymptotics for a C1-version of the KdV Equation

We consider KdV-type equations with nonlinearities u , κ ∈ (1, 5), and small dispersion ε. The first result consists in the conclusion that, in the leading term with respect to ε, the solitary waves in this model interact like KdV solitons. Next it turned out that there exists a very interesting scenario of instability in which the short-wave soliton remains stable whereas a small long-wave part, generated by perturbations of original equation, turns to be unstable, growing and destroying the leading term. At the same time, such perturbation can eliminate the collision of solitons. Numerical simulations confirming the results are also presented

Asymptotics for a C1-version of the KdV Equation

We consider KdV-type equations with nonlinearities u , κ ∈ (1, 5), and small dispersion ε. The first result consists in the conclusion that, in the leading term with respect to ε, the solitary waves in this model interact like KdV solitons. Next it turned out that there exists a very interesting scenario of instability in which the short-wave soliton remains stable whereas a small long-wave part, generated by perturbations of original equation, turns to be unstable, growing and destroying the leading term. At the same time, such perturbation can eliminate the collision of solitons. Numerical simulations confirming the results are also presented

Modelling external magnetic fields of magnetite particles: From micro- to macro-scale

We determine the role of particle shape in the type of magnetic extraction processes used in mining. We use a micromagnetic finite element method (FEM) to analyze the effect of external magnetic fields on the magnetic structures of sub-micron magnetite particles. In non-saturating fields, the magnetite particles contain multiple possible non-uniform magnetization states. The non-uniformity was found to gradually disappear with increasing applied field strength; at 100 mT the domain structure became near uniform; at 300 mT the magnetic structure saturates and the magnetization direction aligned with the field. In magnetic separation techniques, we suggest that 100 mT is the optimal field for magnetite to maximize the magnetic field with the lowest energy transfer; larger particles, i.e., >1 µm, will likely saturate in smaller fields than this. We also examined the effect of external magnetic fields on a much larger irregular particle (L × W × H = 179.5 × 113 × 103 μm) that was too large to be examined using micromagnetics. To do this we used COMSOL. The results show the relative difference between the magnitude of magnetic flux density of the particle and that of a corresponding sphere of the same volume is <5% when the distance to the particle geometry center is more than five times the sphere radius. The ideas developed in this paper have the potential to improve magnetic mineral extraction yield