17,497 research outputs found
Numerical bifurcation diagram for the two-dimensional boundary-fed chlorine-dioxideāiodineāmalonic-acid system
We present a numerical solution of the chlorine-dioxideāiodineāmalonic-acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from nonsymmetry-breaking structures along boundary feed gradients to transverse symmetry-breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make a connection with earlier results and discuss prospects for future work
Pattern formation with trapped ions
Ion traps are a versatile tool to study nonequilibrium statistical physics,
due to the tunability of dissipation and nonlinearity. We propose an experiment
with a chain of trapped ions, where dissipation is provided by laser heating
and cooling, while nonlinearity is provided by trap anharmonicity and beam
shaping. The collective dynamics are governed by an equation similar to the
complex Ginzburg-Landau equation, except that the reactive nature of the
coupling leads to qualitatively different behavior. The system has the unusual
feature of being both oscillatory and excitable at the same time. We account
for noise from spontaneous emission and find that the patterns are observable
for realistic experimental parameters. Our scheme also allows controllable
experiments with noise and quenched disorder.Comment: 4 pages + appendi
Modeling a falling slinky
A slinky is an example of a tension spring: in an unstretched state a slinky
is collapsed, with turns touching, and a finite tension is required to separate
the turns from this state. If a slinky is suspended from its top and stretched
under gravity and then released, the bottom of the slinky does not begin to
fall until the top section of the slinky, which collapses turn by turn from the
top, collides with the bottom. The total collapse time t_c (typically ~0.3 s
for real slinkies) corresponds to the time required for a wave front to
propagate down the slinky to communicate the release of the top end. We present
a modification to an existing model for a falling tension spring (Calkin 1993)
and apply it to data from filmed drops of two real slinkies. The modification
of the model is the inclusion of a finite time for collapse of the turns of the
slinky behind the collapse front propagating down the slinky during the fall.
The new finite-collapse time model achieves a good qualitative fit to the
observed positions of the top of the real slinkies during the measured drops.
The spring constant k for each slinky is taken to be a free parameter in the
model. The best-fit model values for k for each slinky are approximately
consistent with values obtained from measured periods of oscillation of the
slinkies.Comment: 30 pages, 11 figure
Domain Coarsening in Systems Far from Equilibrium
The growth of domains of stripes evolving from random initial conditions is
studied in numerical simulations of models of systems far from equilibrium such
as Rayleigh-Benard convection. The scaling of the size of the domains deduced
from the inverse width of the Fourier spectrum is studied for both potential
and nonpotential models. The morphology of the domains and the defect
structures are however quite different in the two cases, and evidence is
presented for a second length scale in the nonpotential case.Comment: 11 pages, RevTeX; 3 uufiles encoded postscript figures appende
Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection
A theory of the novel spiral chaos state recently observed in Rayleigh-Benard
convection is proposed in terms of the importance of invasive defects i.e
defects that through their intrinsic dynamics expand to take over the system.
The motion of the spiral defects is shown to be dominated by wave vector
frustration, rather than a rotational motion driven by a vertical vorticity
field. This leads to a continuum of spiral frequencies, and a spiral may rotate
in either sense depending on the wave vector of its local environment. Results
of extensive numerical work on equations modelling the convection system
provide some confirmation of these ideas.Comment: Revtex (15 pages) with 4 encoded Postscript figures appende
Pupil participation in Scottish schools: how far have we come?
The United Nations Convention on the Rights of the Child (UN, 1989), which applies to all children under the age of 18, established the overarching principles guiding pupil participation. In most European states, signatories to the Convention have enacted policies to promote the voice of the child or young person in decisions that affect them. In education systems strategies to enhance the pupil participation are an increasing feature of deliberation on education for citizenship, curriculum flexibility, pedagogical approaches and assessment for learning. Despite the positive policy context and professional commitment to principles of inclusion, translating policy intentions so that the spirit of the legislation is played out in the day-to-day experiences of pupils is a constant challenge. This article reports on research that examines how pupil participation is understood and enacted in Scottish schools. It considers how the over-laying of diverse policies presents mixed messages to practitioners
Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
It has been experimentally observed that weakly conducting suspended films of
smectic liquid crystals undergo electroconvection when subjected to a large
enough potential difference. The resulting counter-rotating vortices form a
very simple convection pattern and exhibit a variety of interesting nonlinear
effects. The linear stability problem for this system has recently been solved.
The convection mechanism, which involves charge separation at the free surfaces
of the film, is applicable to any sufficiently two-dimensional fluid. In this
paper, we derive an amplitude equation which describes the weakly nonlinear
regime, by starting from the basic electrohydrodynamic equations. This regime
has been the subject of several recent experimental studies. The lowest order
amplitude equation we derive is of the Ginzburg-Landau form, and describes a
forward bifurcation as is observed experimentally. The coefficients of the
amplitude equation are calculated and compared with the values independently
deduced from the linear stability calculation.Comment: 26 pages, 2 included eps figures, submitted to Phys Rev E. For more
information, see http://mobydick.physics.utoronto.c
Finite Size Scaling of Domain Chaos
Numerical studies of the domain chaos state in a model of rotating
Rayleigh-Benard convection suggest that finite size effects may account for the
discrepancy between experimentally measured values of the correlation length
and the predicted divergence near onset
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