Simulation of the head-disk interface gap using a hybrid multi-scale method

We present a hybrid multi-scale method that provides a capability to capture the disparate scales associated with modelling flow in micro- and nano-devices. Our model extends the applicability of an internal-flow multi-scale method by providing a framework to couple the internal (small scale) flow regions to the external (large scale) flow regions. We demonstrate the application of both the original methodology and the new hybrid approach to model the flow field in the vicinity of the head-disk interface gap of a hard disk drive enclosure. The internal flow regions within the gap are modelled by an extended internal-flow multi-scale method that utilises a finite-difference scheme for non-uniform grids. Our proposed hybrid multi-scale method is then employed to couple the internal micro-flow region to the flow external to the gap, to capture entrance/exit effects. We also demonstrate the successful application of the method in capturing other localised phenomena (e.g. those due to localised wall heating)

Refined saddle-point preconditioners for discretized Stokes problems

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online

Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Links between dissipation, intermittency, and helicity in the GOY model revisited

High-resolution simulations within the GOY shell model are used to study various scaling relations for turbulence. A power-law relation between the second-order intermittency correction and the crossover from the inertial to the dissipation range is confirmed. Evidence is found for the intermediate viscous dissipation range proposed by Frisch and Vergassola. It is emphasized that insufficient dissipation-range resolution systematically drives the energy spectrum towards statistical-mechanical equipartition. In fully resolved simulations the inertial-range scaling exponents depend on both model parameters; in particular, there is no evidence that the conservation of a helicity-like quantity leads to universal exponents.Comment: 24 pages, 13 figures; submitted to Physica

Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic

Effect of noise on coupled chaotic systems

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with logistic map as local dynamics and driven by identical noise at each site, we report that the number of structures (a structure is a group of neighbouring lattice sites for whom values of the variable follow certain predefined pattern) follow a power-law decay with the length of the structure. An interesting phenomenon, which we call stochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

Beyond ‘BRICS’: ten theses on South–South cooperation in the twenty-first century

Grounded in a review of past and present academic South–South cooperation literatures, this article advances ten theses that problematise empirical, theoretical, conceptual and methodological issues essential to discussions of South–South cooperation in the 21st century. This endeavour is motivated by the perceived undermining, especially in the contemporary Anglophone academic South–South cooperation literature, of the emancipatory potential historically associated with South–South cooperation. By drawing on the interventionist South–South cooperation agendas of ‘left’-leaning Latin America-Caribbean governments, the article seeks to establish a dialogue between social science theories and less ‘visible’ analyses from academic (semi)peripheries. The ten theses culminate in an exploration of the potential of South–South cooperation to promote ‘alternative’ development