Now showing items 38-57 of 68

  • Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection 

    Ponty, Y.; Gilbert, Andrew D.; Soward, Andrew M. (Cambridge University Press, 2001)
    A numerical investigation is presented of kinematic dynamo action in a dynamically driven fluid flow. The model isolates basic dynamo processes relevant to field generation in the Solar tachocline. The horizontal plane ...
  • Learning of spatio–temporal codes in a coupled oscillator system 

    Orosz, Gábor; Ashwin, Peter; Townley, Stuart (IEEE, 2009)
    In this paper, we consider a learning strategy that allows one to transmit information between two coupled phase oscillator systems (called teaching and learning systems) via frequency adaptation. The dynamics of these ...
  • Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles 

    Turner, M. R.; Gilbert, Andrew D. (Cambridge University Press, 2007)
    This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external ...
  • Master-equation approach to the study of phase-change processes in data storage media 

    Blyuss, Konstantin; Ashwin, Peter; Bassom, Andrew P.; Wright, C. David (American Physical Society, 2005)
    We study the dynamics of crystallization in phase-change materials using a master-equation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed ...
  • Master-equation approach to understanding multistate phase-change memories and processors 

    Wright, C. David; Blyuss, Konstantin; Ashwin, Peter (American Institute of Physics, 2007)
    A master-equation approach is used to perform dynamic modeling of phase-transformation processes that define the operating regimes and performance attributes of electronic (and optical) processors and multistate memory ...
  • Minimal attractors and bifurcations of random dynamical systems 

    Ashwin, Peter (Royal Society, 1999)
    We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors ...
  • Neutral modes of a two-dimensional vortex and their link to persistent cat's eyes 

    Turner, M. R.; Gilbert, Andrew D.; Bassom, Andrew P. (American Institute of Physics, 2008)
    This paper considers the relaxation of a smooth two-dimensional vortex to axisymmetry after the application of an instantaneous, weak external strain field. In this limit the disturbance decays exponentially in time at a ...
  • Nonlinear dynamo action in rotating convection and shear 

    Zhang, Pu; Gilbert, Andrew D.; Zhang, Keke (Cambridge University Press, 2005)
    Magnetic field amplification by the motion of an electrically conducting fluid is studied, using a rotating plane-layer geometry. The fluid flow is driven by convection, and by a moving bottom boundary, which leads to an ...
  • Nonlinear equilibration of a dynamo in a smooth helical flow 

    Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1997)
    We investigate the nonlinear equilibration of magnetic fields in a smooth helical flow at large Reynolds number Re and magnetic Reynolds number Rm with Re >> Rm >> 1. We start with a smooth spiral Couette flow driven by ...
  • Nonlinear solutions of the amplitude equations governing fluid flow in rotating spherical geometries 

    Blockley, Edward William (University of ExeterMathematical Sciences, 2008-09-08)
    We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes ...
  • On riddling and weak attractors 

    Ashwin, Peter; Terry, John R. (Elsevier, 2000)
    We propose general definitions for riddling and partial riddling of a subset V of Rm with non-zero Lebesgue measure and show that these properties are invariant for a large class of dynamical systems. We introduce the ...
  • On the geometry of orientation-preserving planar piecewise isometries 

    Ashwin, Peter; Fu, Xin-Chu (Springer, 2002)
    Planar piecewise isometries (PWIs) are iterated mappings of subsets of the plane that preserve length (and hence angle and area) on each of a number of disjoint regions. They arise naturally in several applications and are ...
  • On the unfolding of a blowout bifurcation 

    Ashwin, Peter; Aston, Philip J.; Nicol, Matthew (Elsevier, 1998)
    Suppose a chaotic attractor A in an invariant subspace loses stability on varying a parameter. At the point of loss of stability, the most positive Lyapunov exponent of the natural measure on A crosses zero at what has ...
  • The onset of thermal convection in Ekman–Couette shear flow with oblique rotation 

    Ponty, Y.; Gilbert, Andrew D.; Soward, Andrew M. (Cambridge University Press, 2003)
    The onset of convection of a Boussinesq fluid in a horizontal plane layer is studied. The system rotates with constant angular velocity Ω, which is inclined at an angle ϑ to the vertical. The layer is sheared by keeping ...
  • Phase resetting effects for robust cycles between chaotic sets 

    Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob (American Institute of Physics, 2003)
    In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including ...
  • Photospheric flux density of magnetic helicity 

    Pariat, E.; Démoulin, P.; Berger, M.A. (EDP Sciences, 2005)
    Several recent studies have developed the measurement of magnetic helicity flux from the time evolution of photospheric magnetograms. The total flux is computed by summing the flux density over the analyzed region. All ...
  • Polygonal invariant curves for a planar piecewise isometry 

    Ashwin, Peter; Goetz, Arek (American Mathematical Society, 2005)
    We investigate a remarkable new planar piecewise isometry whose generating map is a permutation of four cones. For this system we prove the coexistence of an infinite number of periodic components and an uncountable number ...
  • Product dynamics for homoclinic attractors 

    Ashwin, Peter; Field, Michael (Royal Society, 2005)
    Heteroclinic cycles may occur as structurally stable asymptotically stable attractors if there are invariant subspaces or symmetries of a dynamical system. Even for cycles between equilibria, it may be difficult to obtain ...
  • Properties of the invariant disk packing in a model bandpass sigma-delta modulator 

    Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan (13 (3), pp. 631-641, 2003)
    In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space ...
  • Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators 

    Ashwin, Peter; Dangelmayr, Gerhard (Taylor & Francis, 2005)
    Systems of coupled oscillators may exhibit spontaneous dynamical formation of attracting synchronized clusters with broken symmetry; this can be helpful in modelling various physical processes. Analytical computation of ...