Now showing items 41-60 of 80

  • 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 ...
  • Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. 

    Ashwin, Peter; Coombes, S; Nicks, R (BioMed Central, 2016-01-06)
    The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, ...
  • The middle Pleistocene transition as a generic bifurcation on a slow manifold 

    Ashwin, Peter; Ditlevsen, Peter (Springer Verlag, 2015)
    The Quaternary period has been characterised by a cyclical series of glaciations, which are attributed to the change in the insolation (incoming solar radiation) from changes in the Earth’s orbit around the Sun. The spectral ...
  • 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 ...
  • Motor-mediated bidirectional transport along an antipolar microtubule bundle: A mathematical model 

    Lin, Congping; Ashwin, Peter; Steinberg, Gero (American Physical Society, 2013)
    Long-distance bidirectional transport of organelles depends on the coordinated motion of various motor proteins on the cytoskeleton. Recent quantitative live cell imaging in the elongated hyphal cells of Ustilago maydis ...
  • Multi-cluster dynamics in coupled phase oscillator networks 

    Ismail, Asma; Ashwin, Peter (Taylor & Francis, 2014)
    In this paper we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number ...
  • Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection 

    Ashwin, Peter; Podvigina, Olga (American Institute of Physics (AIP), 2010)
    We investigate the robust heteroclinic dynamics arising in a system of ordinary differential equations in R4 with symmetry D4⋉(Z2)2. This system arises from the normal form reduction of a 1:2√ mode interaction for Boussinesq ...
  • Non-normal parameter blowout bifurcation: an example in a truncated mean field dynamo model 

    Covas, Eurico; Ashwin, Peter; Tavakol, Reza (American Physical Society, 1997)
    We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetry-forced invariant subspaces for the dynamics and we find examples of transient type I ...
  • On designing heteroclinic networks from graphs 

    Ashwin, Peter; Postlethwaite, Claire (Elsevier, 2013)
    Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood ...
  • On local attraction properties and a stability index for heteroclinic connections 

    Podvigina, Olga; Ashwin, Peter (Institute of Physics, 2011)
  • 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 statistical attractors and the convergence of time averages 

    Karabacak, Ozkan; Ashwin, Peter (Cambridge University Press / Cambridge Philosophical Society, 2011)
    There are various notions of attractor in the literature, including measure (Milnor) attractors and statistical (Ilyashenko) attractors. In this paper we relate the notion of statistical attractor to that of the essential ...
  • 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 ...
  • Packings induced by piecewise isometries cannot contain the Arbelos 

    Trovati, Marcello; Ashwin, Peter; Byott, Nigel P. (American Institute of Mathematical Sciences (AIMS), 2008)
    Planar piecewise isometries with convex polygonal atoms that are piecewise irrational rotations can naturally generate a packing of phase space given by periodic cells that are discs. We show that such packings cannot ...
  • Parameter shifts for nonautonomous systems in low dimension: Bifurcation- and Rate-induced tipping 

    Ashwin, Peter; Perryman, C; Wieczorek, Sebastian (arXiv.org, 2015-06-25)
    We discuss the nonlinear phenomena of irreversible tipping for nonautonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We define notions of bifurcation-induced ...
  • Pattern selection: the importance of "how you get there" 

    Ashwin, Peter; Zaikin, Alexey (Biophysical Society / Elsevier, 2015-03-24)
  • 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 ...
  • Phase-change technologies: from PCRAM to probe-storage to processors 

    Wright, C. David; Ashawaraya, S.; Ashwin, Peter; Aziz, Mustafa M.; Hicken, R.J.; Kohary, Krisztian; Liu, Y.; Marmier, Arnaud; Shah, P.; Vazquez Diosdado, Jorge A.; Wang, Lei (2010)
    Phase-change materials based on chalcogenide alloys, for example GeSbTe and AgInSbTe, show remarkable properties such as: the ability to be crystallized by pulses in the (hundreds of) femtoseconds region while at the same ...