19,309 research outputs found
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
Scaling laws for rotating Rayleigh-Bénard convection
Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-Bénard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We have focused near the threshold for the supercritical bifurcation from the conducting state to a convecting state exhibiting domain chaos. A detailed analysis of these simulations has been carried out and is compared with experimental results, as well as predictions from multiple scale perturbation theory. We find that the time scaling law agrees with the theoretical prediction, which is in contradiction to experimental results. We also have looked at the scaling of defect lengths and defect glide velocities. We find a separation of scales in defect diameters perpendicular and parallel to the rolls as expected, but the scaling laws for the two different lengths are in contradiction to theory. The defect velocity scaling law agrees with our theoretical prediction from multiple scale perturbation theory
Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection
Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent
Chaotic Quivering of Micron-Scaled On-Chip Resonators Excited by Centrifugal Optical Pressure
Opto-mechanical chaotic oscillation of an on-chip resonator is excited by the radiation-pressure nonlinearity. Continuous optical input, with no external feedback or modulation, excites chaotic vibrations in very different geometries of the cavity (both tori and spheres) and shows that opto-mechanical chaotic oscillations are an intrinsic property of optical microcavities. Measured phenomena include period doubling, a spectral continuum, aperiodic oscillations, and complex trajectories. The rate of exponential divergence from a perturbed initial condition (Lyapunov exponent) is calculated. Continuous improvements in cavities mean that such chaotic oscillations can be expected in the future with many other platforms, geometries, and frequency spans
The Sure Start Mellow Valley area Through the lens of a camera
This report gives an account of a participatory evaluation conducted using photography within the Sure Start Mellow Valley area. Information about the current status of the Sure Start programme and the plans for the future are first provided. The report then describes the research that was undertaken and presents and discusses the findings
Grain boundary motion in layered phases
We study the motion of a grain boundary that separates two sets of mutually
perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is
treated either analytically from the corresponding amplitude equations, or
numerically by solving the Swift-Hohenberg equation. We find that if the rolls
are curved by a slow transversal modulation, a net translation of the boundary
follows. We show analytically that although this motion is a nonlinear effect,
it occurs in a time scale much shorter than that of the linear relaxation of
the curved rolls. The total distance traveled by the boundary scales as
, where is the reduced Rayleigh number. We obtain
analytical expressions for the relaxation rate of the modulation and for the
time dependent traveling velocity of the boundary, and especially their
dependence on wavenumber. The results agree well with direct numerical
solutions of the Swift-Hohenberg equation. We finally discuss the implications
of our results on the coarsening rate of an ensemble of differently oriented
domains in which grain boundary motion through curved rolls is the dominant
coarsening mechanism.Comment: 16 pages, 5 figure
Ultrasonic detection of flaws in fusion butt welds
Reliable and accurate Delta technique, a nondestructive ultrasonics method, uses redirection of energy to detect randomly oriented imperfections in fusion butt welds. Data on flaws can be read from either an oscilloscope or a printout
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
Traveling waves in rotating Rayleigh-Bénard convection: Analysis of modes and mean flow
Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshhold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from sigma=6.4 to sigma=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean flow around the inner radius
Synchronization by Reactive Coupling and Nonlinear Frequency Pulling
We present a detailed analysis of a model for the synchronization of
nonlinear oscillators due to reactive coupling and nonlinear frequency pulling.
We study the model for the mean field case of all-to-all coupling, deriving
results for the initial onset of synchronization as the coupling or
nonlinearity increase, and conditions for the existence of the completely
synchronized state when all the oscillators evolve with the same frequency.
Explicit results are derived for Lorentzian, triangular, and top-hat
distributions of oscillator frequencies. Numerical simulations are used to
construct complete phase diagrams for these distributions
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