488 research outputs found
Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection
We report experiments on convection patterns in a cylindrical cell with a
large aspect ratio. The fluid had a Prandtl number of approximately 1. We
observed a chaotic pattern consisting of many rotating spirals and other
defects in the parameter range where theory predicts that steady straight rolls
should be stable. The correlation length of the pattern decreased rapidly with
increasing control parameter so that the size of a correlated area became much
smaller than the area of the cell. This suggests that the chaotic behavior is
intrinsic to large aspect ratio geometries.Comment: Preprint of experimental paper submitted to Phys. Rev. Lett. May 12
1993. Text is preceeded by many TeX macros. Figures 1 and 2 are rather lon
Automated assessment of movement impairment in Huntington's disease
Quantitative assessment of movement impairment in Huntington’s disease (HD) is essential to monitoring of disease progression. This study aimed to develop and validate a novel low cost, objective automated system for the evaluation of upper limb movement impairment in HD in order to eliminate the inconsistency of the assessor and offer a more sensitive, continuous assessment scale. Patients with genetically confirmed HD and healthy controls were recruited to this observational study. Demographic data including age (years), gender and Unified Huntington’s Disease Rating Scale Total Motor Score (UHDRS-TMS) were recorded. For the purposes of this study a modified upper limb motor impairment score (mULMS) was generated from the UHDRS-TMS. All participants completed a brief, standardized clinical assessment of upper limb dexterity whilst wearing a tri-axial accelerometer on each wrist and on the sternum. The captured acceleration data were used to develop an automatic classification system for discriminating between healthy and HD participants and to automatically generate a continuous Movement Impairment Score (MIS) that reflected the degree of the movement impairment. Data from 48 healthy and 44 HD participants was used to validate the developed system, which achieved 98.78% accuracy in discriminating between healthy and HD participants. The Pearson correlation coefficient between the automatic MIS and the clinician rated mULMS was 0.77 with a p-value < 0.01. The approach presented in this study demonstrates the possibility of an automated objective, consistent and sensitive assessment of the HD movement impairment
Defect Chaos of Oscillating Hexagons in Rotating Convection
Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns
with broken chiral symmetry are investigated, as they appear in rotating
non-Boussinesq or surface-tension-driven convection. We find that close to the
secondary Hopf bifurcation to oscillating hexagons the dynamics are well
described by a single complex Ginzburg-Landau equation (CGLE) coupled to the
phases of the hexagonal pattern. At the bandcenter these equations reduce to
the usual CGLE and the system exhibits defect chaos. Away from the bandcenter a
transition to a frozen vortex state is found.Comment: 4 pages, 6 figures. Fig. 3a with lower resolution no
Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection
Explicit formulas for the rotation frequency and the long-wavenumber
diffusion coefficients of global spirals with arms in Rayleigh-Benard
convection are obtained. Global spirals and parallel rolls share exactly the
same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals
seem not to have a characteristic frequency or a typical size ,
but their product is a constant under given experimental
conditions. The ratio of the radii of any two dislocations (,
) inside a multi-armed spiral is also predicted to be constant. Some of
these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication
Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
We study hexagon patterns in non-Boussinesq convection of a thin rotating
layer of water. For realistic parameters and boundary conditions we identify
various linear instabilities of the pattern. We focus on the dynamics arising
from an oscillatory side-band instability that leads to a spatially disordered
chaotic state characterized by oscillating (whirling) hexagons. Using
triangulation we obtain the distribution functions for the number of pentagonal
and heptagonal convection cells. In contrast to the results found for defect
chaos in the complex Ginzburg-Landau equation and in inclined-layer convection,
the distribution functions can show deviations from a squared Poisson
distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at
http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J.
Physic
Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection
For Rayleigh-Benard convection of a fluid with Prandtl number \sigma \approx
1, we report experimental and theoretical results on a pattern selection
mechanism for cell-filling, giant, rotating spirals. We show that the pattern
selection in a certain limit can be explained quantitatively by a
phase-diffusion mechanism. This mechanism for pattern selection is very
different from that for spirals in excitable media
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
Bifurcations in annular electroconvection with an imposed shear
We report an experimental study of the primary bifurcation in
electrically-driven convection in a freely suspended film. A weakly conducting,
submicron thick smectic liquid crystal film was supported by concentric
circular electrodes. It electroconvected when a sufficiently large voltage
was applied between its inner and outer edges. The film could sustain rapid
flows and yet remain strictly two-dimensional. By rotation of the inner
electrode, a circular Couette shear could be independently imposed. The control
parameters were a dimensionless number , analogous to the Rayleigh
number, which is and the Reynolds number of the
azimuthal shear flow. The geometrical and material properties of the film were
characterized by the radius ratio , and a Prandtl-like number . Using measurements of current-voltage characteristics of a large number of
films, we examined the onset of electroconvection over a broad range of
, and . We compared this data quantitatively to
the results of linear stability theory. This could be done with essentially no
adjustable parameters. The current-voltage data above onset were then used to
infer the amplitude of electroconvection in the weakly nonlinear regime by
fitting them to a steady-state amplitude equation of the Landau form. We show
how the primary bifurcation can be tuned between supercritical and subcritical
by changing and .Comment: 17 pages, 12 figures. Submitted to Phys. Rev. E. Minor changes after
refereeing. See also http://mobydick.physics.utoronto.c
Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box
An efficient semi-implicit second-order-accurate finite-difference method is
described for studying incompressible Rayleigh-Benard convection in a box, with
sidewalls that are periodic, thermally insulated, or thermally conducting.
Operator-splitting and a projection method reduce the algorithm at each time
step to the solution of four Helmholtz equations and one Poisson equation, and
these are are solved by fast direct methods. The method is numerically stable
even though all field values are placed on a single non-staggered mesh
commensurate with the boundaries. The efficiency and accuracy of the method are
characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure
Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection
We present experimental data and their theoretical interpretation for the
decay rates of temperature fluctuations in a thin layer of a fluid heated from
below and confined between parallel horizontal plates. The measurements were
made with the mean temperature of the layer corresponding to the critical
isochore of sulfur hexafluoride above but near the critical point where
fluctuations are exceptionally strong. They cover a wide range of temperature
gradients below the onset of Rayleigh-B\'enard convection, and span wave
numbers on both sides of the critical value for this onset. The decay rates
were determined from experimental shadowgraph images of the fluctuations at
several camera exposure times. We present a theoretical expression for an
exposure-time-dependent structure factor which is needed for the data analysis.
As the onset of convection is approached, the data reveal the critical
slowing-down associated with the bifurcation. Theoretical predictions for the
decay rates as a function of the wave number and temperature gradient are
presented and compared with the experimental data. Quantitative agreement is
obtained if allowance is made for some uncertainty in the small spacing between
the plates, and when an empirical estimate is employed for the influence of
symmetric deviations from the Oberbeck-Boussinesq approximation which are to be
expected in a fluid with its density at the mean temperature located on the
critical isochore.Comment: 13 pages, 10 figures, 52 reference
- …