Browsing Mathematics Research Institute (MRI) by Title
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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 ... 
Polygonal invariant curves for a planar piecewise isometry
(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
(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 sigmadelta modulator
(13 (3), pp. 631641, 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
(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 ... 
The representation of snow in land surface schemes: results from PILPS 2(d)
(American Meteorological Society, 2001)Twentyone land surface schemes (LSSs) performed simulations forced by 18 yr of observed meteorological data from a grassland catchment at Valdai, Russia, as part of the Project for the Intercomparison of LandSurface ... 
Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria
(World Scientific Publishing Company, 2005)Robust attracting heteroclinic cycles have been found in many models of dynamics with symmetries. In all previous examples, robust heteroclinic cycles appear between a number of symmetry broken equilibria. In this paper ... 
The sensitivity of global climate model simulations to the representation of soil moisture heterogeneity
(American Meteorological Society, 2003)Improving the treatment of subgridscale soil moisture variations is recognized as a priority for the next generation of land surface schemes. Here, the impact of an improved representation of subgridscale soil moisture ... 
The spiral windup and dissipation of vorticity and a passive scalar in a strained planar vortex
(Cambridge University Press, 1999)The response of a Gaussian vortex to a weak timedependent external strain field is studied numerically. The cases of an impulsive strain, an on–off step function, and a continuous random strain are considered. Transfers ...