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

Wavy stripes and squares in zero P number convection

A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher mode, may lead to a competition between the two sets of wavy rolls. The appearance of square patterns is due to the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late

Quasiperiodic waves at the onset of zero Prandtl number convection with rotation

We show the possibility of quasiperiodic waves at the onset of thermal convection in a thin horizontal layer of slowly rotating zero-Prandtl number Boussinesq fluid confined between stress-free conducting boundaries. Two independent frequencies emerge due to an interaction between a stationary instability and a self-tuned wavy instability in presence of coriolis force, if Taylor number is raised above a critical value. Constructing a dynamical system for the hydrodynamical problem, the competition between the interacting instabilities is analyzed. The forward bifurcation from the conductive state is self-tuned.Comment: 9 pages of text (LaTex), 5 figures (Jpeg format

Influence of through-flow on linear pattern formation properties in binary mixture convection

We investigate how a horizontal plane Poiseuille shear flow changes linear convection properties in binary fluid layers heated from below. The full linear field equations are solved with a shooting method for realistic top and bottom boundary conditions. Through-flow induced changes of the bifurcation thresholds (stability boundaries) for different types of convective solutions are deter- mined in the control parameter space spanned by Rayleigh number, Soret coupling (positive as well as negative), and through-flow Reynolds number. We elucidate the through-flow induced lifting of the Hopf symmetry degeneracy of left and right traveling waves in mixtures with negative Soret coupling. Finally we determine with a saddle point analysis of the complex dispersion relation of the field equations over the complex wave number plane the borders between absolute and convective instabilities for different types of perturbations in comparison with the appropriate Ginzburg-Landau amplitude equation approximation. PACS:47.20.-k,47.20.Bp, 47.15.-x,47.54.+rComment: 19 pages, 15 Postscript figure

Global stability properties of a hyperbolic system arising in pattern formation

Global stability properties of a hyperbolic system arising in pattern formatio

Mechanism of strand displacement synthesis by DNA replicative polymerases

Replicative holoenzymes exhibit rapid and processive primer extension DNA synthesis, but inefficient strand displacement DNA synthesis. We investigated the bacteriophage T4 and T7 holoenzymes primer extension activity and strand displacement activity on a DNA hairpin substrate manipulated by a magnetic trap. Holoenzyme primer extension activity is moderately hindered by the applied force. In contrast, the strand displacement activity is strongly stimulated by the applied force; DNA polymerization is favoured at high force, while a processive exonuclease activity is triggered at low force. We propose that the DNA fork upstream of the holoenzyme generates a regression pressure which inhibits the polymerization-driven forward motion of the holoenzyme. The inhibition is generated by the distortion of the template strand within the polymerization active site thereby shifting the equilibrium to a DNA-protein exonuclease conformation. We conclude that stalling of the holoenzyme induced by the fork regression pressure is the basis for the inefficient strand displacement synthesis characteristic of replicative polymerases. The resulting processive exonuclease activity may be relevant in replisome disassembly to reset a stalled replication fork to a symmetrical situation. Our findings offer interesting applications for single-molecule DNA sequencing

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures

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

Pattern selection as a nonlinear eigenvalue problem

A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed through-flow. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the boundary conditions in addition to the driving rate and the through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation elucidates how the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation. PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 18 pages in Postsript format including 5 figures, to appear in: Lecture Notes in Physics, "Nonlinear Physics of Complex Sytems -- Current Status and Future Trends", Eds. J. Parisi, S. C. Mueller, and W. Zimmermann (Springer, Berlin, 1996

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