122 research outputs found
Mean flow and spiral defect chaos in Rayleigh-Benard convection
We describe a numerical procedure to construct a modified velocity field that
does not have any mean flow. Using this procedure, we present two results.
Firstly, we show that, in the absence of mean flow, spiral defect chaos
collapses to a stationary pattern comprising textures of stripes with angular
bends. The quenched patterns are characterized by mean wavenumbers that
approach those uniquely selected by focus-type singularities, which, in the
absence of mean flow, lie at the zig-zag instability boundary. The quenched
patterns also have larger correlation lengths and are comprised of rolls with
less curvature. Secondly, we describe how mean flow can contribute to the
commonly observed phenomenon of rolls terminating perpendicularly into lateral
walls. We show that, in the absence of mean flow, rolls begin to terminate into
lateral walls at an oblique angle. This obliqueness increases with Rayleigh
number.Comment: 14 pages, 19 figure
Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves
Pattern formation in parametric surface waves is studied in the limit of weak
viscous dissipation. A set of quasi-potential equations (QPEs) is introduced
that admits a closed representation in terms of surface variables alone. A
multiscale expansion of the QPEs reveals the importance of triad resonant
interactions, and the saturating effect of the driving force leading to a
gradient amplitude equation. Minimization of the associated Lyapunov function
yields standing wave patterns of square symmetry for capillary waves, and
hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity
waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold
symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure
Pattern Formation and Dynamics in Rayleigh-B\'{e}nard Convection: Numerical Simulations of Experimentally Realistic Geometries
Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are
made, where possible, between theory and experiment by performing numerical
simulations of the Boussinesq equations for a variety of experimentally
realistic situations. Rectangular and cylindrical geometries of varying aspect
ratios for experimental boundary conditions, including fins and spatial ramps
in plate separation, are examined with particular attention paid to the role of
the mean flow. A small cylindrical convection layer bounded laterally either by
a rigid wall, fin, or a ramp is investigated and our results suggest that the
mean flow plays an important role in the observed wavenumber. Analytical
results are developed quantifying the mean flow sources, generated by amplitude
gradients, and its effect on the pattern wavenumber for a large-aspect-ratio
cylinder with a ramped boundary. Numerical results are found to agree well with
these analytical predictions. We gain further insight into the role of mean
flow in pattern dynamics by employing a novel method of quenching the mean flow
numerically. Simulations of a spiral defect chaos state where the mean flow is
suddenly quenched is found to remove the time dependence, increase the
wavenumber and make the pattern more angular in nature.Comment: 9 pages, 10 figure
Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes
A model of mobile, charged ion channels in a fluid membrane is studied. The
channels may switch between an open and a closed state according to a simple
two-state kinetics with constant rates. The effective electrophoretic charge
and the diffusion constant of the channels may be different in the closed and
in the open state. The system is modeled by densities of channel species,
obeying simple equations of electro-diffusion. The lateral transmembrane
voltage profile is determined from a cable-type equation. Bifurcations from the
homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode
oscillatory transitions within physiologically reasonable ranges of model
parameters. We study the dynamics beyond linear stability analysis and derive
non-linear evolution equations near the transitions to stationary patterns.Comment: 10 pages, 7 figures, will be submitted to Phys. Rev.
Effect of tailored practice and patient care plans on secondary prevention of heart disease in general practice: cluster randomised controlled trial
Objective To test the effectiveness of a complex intervention designed, within a theoretical framework, to improve outcomes for patients with coronary heart disease
Cross-Newell equations for hexagons and triangles
The Cross-Newell equations for hexagons and triangles are derived for general
real gradient systems, and are found to be in flux-divergence form. Specific
examples of complex governing equations that give rise to hexagons and
triangles and which have Lyapunov functionals are also considered, and explicit
forms of the Cross-Newell equations are found in these cases. The general
nongradient case is also discussed; in contrast with the gradient case, the
equations are not flux-divergent. In all cases, the phase stability boundaries
and modes of instability for general distorted hexagons and triangles can be
recovered from the Cross-Newell equations.Comment: 24 pages, 1 figur
Amplitude equations near pattern forming instabilities for strongly driven ferromagnets
A transversally driven isotropic ferromagnet being under the influence of a
static external and an uniaxial internal anisotropy field is studied. We
consider the dissipative Landau-Lifshitz equation as the fundamental equation
of motion and treat it in ~dimensions. The stability of the spatially
homogeneous magnetizations against inhomogeneous perturbations is analyzed.
Subsequently the dynamics above threshold is described via amplitude equations
and the dependence of their coefficients on the physical parameters of the
system is determined explicitly. We find soft- and hard-mode instabilities,
transitions between sub- and supercritical behaviour, various bifurcations of
higher codimension, and present a series of explicit bifurcation diagrams. The
analysis of the codimension-2 point where the soft- and hard-mode instabilities
coincide leads to a system of two coupled Ginzburg-Landau equations.Comment: LATeX, 25 pages, submitted to Z.Phys.B figures available via
[email protected] in /pub/publications/frank/zpb_95
(postscript, plain or gziped
Frozen spatial chaos induced by boundaries
We show that rather simple but non-trivial boundary conditions could induce
the appearance of spatial chaos (that is stationary, stable, but spatially
disordered configurations) in extended dynamical systems with very simple
dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion
equation in a two-dimensional undulated domain. Concepts from the theory of
dynamical systems, and a transverse-single-mode approximation are used to
describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit
http://www.imedea.uib.es/~victo
Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model
are studied using a phase dynamics approach. A Cross-Newell phase equation
describing slow and weak modulations of periodic stationary solutions is
derived. The derivation applies to the bistable, excitable, and the Turing
unstable regimes. In the bistable case stability thresholds are obtained for
the Eckhaus and the zigzag instabilities and for the transition to traveling
waves. Neutral stability curves demonstrate the destabilization of stationary
planar patterns at low wavenumbers to zigzag and traveling modes. Numerical
solutions of the model system support the theoretical findings
Attention mechanisms in the CHREST cognitive architecture
In this paper, we describe the attention mechanisms in CHREST, a computational architecture of human visual expertise. CHREST organises information acquired by direct experience from the world in the form of chunks. These chunks are searched for, and verified, by a unique set of heuristics, comprising the attention mechanism. We explain how the attention mechanism combines bottom-up and top-down heuristics from internal and external sources of information. We describe some experimental evidence demonstrating the correspondence of CHREST’s perceptual mechanisms with those of human subjects. Finally, we discuss how visual attention can play an important role in actions carried out by human experts in domains such as chess
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