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Browsing Mathematics Research Institute (MRI) by Title
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Impact of climatecarbon cycle feedbacks on emissions scenarios to achieve stabilisation
(Cambridge University Press, 200602)As atmospheric concentrations of CO2 increase due to burning of fossil fuels, stabilisation scenarios are receiving increasing amounts of interest both politically and scientifically, leading to the question, ‘what emissions ... 
Infinities of stable periodic orbits in systems of coupled oscillators
(American Physical Society, 2002)We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free ... 
The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source
(American Institute of Physics, 2009)In this paper we examine the influence of periodic islands within a time periodic chaotic flow on the evolution of a scalar tracer. The passive scalar tracer is injected into the flow field by means of a steady source term. ... 
In–out intermittency in partial differential equation and ordinary differential equation models
(American Institute of Physics, 2001)We find concrete evidence for a recently discovered form of intermittency, referred to as in–out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field ... 
Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection
(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
(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 twodimensional vortices, and the link to Landau poles
(Cambridge University Press, 2007)This paper considers the evolution of smooth, twodimensional 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 ... 
Masterequation approach to the study of phasechange processes in data storage media
(American Physical Society, 2005)We study the dynamics of crystallization in phasechange materials using a masterequation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed ... 
Masterequation approach to understanding multistate phasechange memories and processors
(American Institute of Physics, 2007)A masterequation approach is used to perform dynamic modeling of phasetransformation 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
(Royal Society, 1999)We consider attractors for certain types of random dynamical systems. These are skewproduct systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors ... 
Neutral modes of a twodimensional vortex and their link to persistent cat's eyes
(American Institute of Physics, 2008)This paper considers the relaxation of a smooth twodimensional 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
(Cambridge University Press, 2005)Magnetic field amplification by the motion of an electrically conducting fluid is studied, using a rotating planelayer 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
(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
(University of ExeterMathematical Sciences, 20080908)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 narrowgap limit. The expected mode of instability takes ... 
On riddling and weak attractors
(Elsevier, 2000)We propose general definitions for riddling and partial riddling of a subset V of Rm with nonzero Lebesgue measure and show that these properties are invariant for a large class of dynamical systems. We introduce the ... 
On the geometry of orientationpreserving planar piecewise isometries
(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
(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
(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
(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
(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 ...