Magnetic island merger as a mechanism for inverse magnetic energy transfer

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: magnetic energy decays as $\tilde t^{-1}$, where $\tilde t$ is time normalized to the (appropriately defined) reconnection timescale; and the correlation length of the field grows as $\tilde t^{1/2}$. The magnetic energy spectrum is self-similar, and evolves as $\propto \tilde t ^{-3/2}k^{-2}$, where the $k$-dependence is imparted by the formation of thin current sheets.Comment: 6 pages, 5 figures, submitted for publicatio

Modelling systemic price cojumps with Hawkes factor models

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating portfolios of highly liquid stocks, we find that there are a large number of high-frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one-factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets

Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, {\it viz.} the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in critically-balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.Comment: 33 pages, 19 figures, accepted for publication in Journal of Plasma Physic

Investigation into current industrial practices relating to product lifecycle management in a multi-national manufacturing company

Product Lifecycle Management (PLM) systems have gained growing acceptance for managing all information relating to products throughout their full lifecycle, from idea conceptualisation through operations to servicing and disposal. This paper, through an in-depth exploratory study into a leading power generation manufacturing organisation, presents current PLM issues experienced by manufacturing companies, exploring three separate topics: 1) PLM, 2) Knowledge Management and Lessons Learnt and 3) Product Servicing and Maintenance. Following a review of published literature, results of the investigation are presented, analysing the responses of 17 employees interviewed. With respect to Product Development, it was found that information traceability is time consuming and change management requests take too long to complete. Results relating to knowledge management indicate that the Company operates a ‘who you know’ culture, but do aim to capture lessons learned on the manufacturing shop floor and assembly lines. Therefore, a prototype design is proposed to integrate the capturing of lessons learnt within the existing PLM system

Quantifying the transition from spiral waves to spiral wave chimeras in a lattice of self-sustained oscillators

The present work is devoted to the detailed quantification of the transition from spiral waves to spiral wave chimeras in a network of self-sustained oscillators with two-dimensional geometry. The basic elements of the networks are the van der Pol oscillator and the FitzHugh-Nagumo neuron. Both models are in the regime of relaxation oscillations. We analyze the regime by using the indices of local sensitivity which enables us to evaluate the sensitivity of each individual oscillator at finite time. Spi-ral waves are observed in both lattices when the interaction between elements have the local character. The dynamics of all the elements is regular. There are no high-sensitive regions. We have discovered that when the coupling becomes nonlocal, the features of the systems significantly changes. The oscillation regime of the spiral wave center element switches to chaotic one. Besides this, a region with high sensitivity occurs around this oscillator. Moreover, we show that the latter expands in space with elongation of the coupling range. As a result, an incoherence cluster of the spiral wave chimera is formed exactly within this high-sensitive area. Formation of this cluster is accompanied by the sharp increase in values of the maximal Lyapunov exponent to the positive region. Furthermore, we explore that the system can even switch to hyperchaotic regime, when several Lyapunov exponents becomes positive.Comment: 25 pages, 11 figure

From particles to orbits: precise dark matter density profiles using dynamical information

We introduce a new method to calculate dark matter halo density profiles from simulations. Each particle is ‘smeared’ over its orbit to obtain a dynamical profile that is averaged over a dynamical time, in contrast to the traditional approach of binning particles based on their instantaneous positions. The dynamical and binned profiles are in good agreement, with the dynamical approach showing a significant reduction in Poisson noise in the innermost regions. We find that the inner cusps of the new dynamical profiles continue inward all the way to the softening radius, reproducing the central density profile of higher resolution simulations within the 95 per cent confidence intervals, for haloes in virial equilibrium. Folding in dynamical information thus provides a new approach to improve the precision of dark matter density profiles at small radii, for minimal computational cost. Our technique makes two key assumptions that the halo is in equilibrium (phase mixed) and the potential is spherically symmetric. We discuss why the method is successful despite strong violations of spherical symmetry in the centres of haloes, and explore how substructures disturb equilibrium at large radii