Characterization of the domain chaos convection state by the largest Lyapunov exponent

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism

The effect of electronic entropy on temperature peculiarities of the frequency characteristics of two interacting anharmonic vibrational modes in β−\beta-Zr

A 2D temperature-dependent effective potential is calculated for the interacting longitudinal and transverse $L-$phonons of $\beta$ zirconium in the frozen-phonon model. The effective potentials obtained for different temperatures are used for the numerical solution of a set of stochastic differential equations with a thermostat of the white-noise type. Analysis of the spectral density of transverse vibrations allows one to determine the temperature at which $\beta$-Zr becomes unstable with respect to the longitudinal $L-$vibrations. The obtained temperature value practically coincides with the experimental temperature of the $\beta \to \alpha$ structural transition in zirconium. The role of electronic entropy in the $\beta-$Zr stability is discussed.Comment: 9 pages, 10 figures (submitted in Phys.Rev.

Stability analysis of two-dimensional models of three-dimensional convection

Analytical and numerical methods are used to study the linear stability of spatially periodic solutions for various two-dimensional equations which model thermal convection in fluids. This analysis suggests new model equations that will be useful for investigating questions such as wave-number selection, pattern formation, and the onset of turbulence in large-aspect-ratio Rayleigh-Bénard systems. In particular, we construct a nonrelaxational model that has stability boundaries similar to those calculated for intermediate Prandtl-number fluids

Ratchet potential for fluxons in Josephson-Junction arrays

We propose a simple configuration of a one-dimensional parallel array of Josephson junctions in which the pinning potential for trapped fluxons lacks inversion symmetry (ratchet potential). This sytem can be modelised by a set of non-linear pendula with alternating lengths and harmonic couplings. We show, by molecular dynamics simulations, that fluxons behave as single particles in which the predictions for overdamped thermal ratchet can be easily verified.Comment: 7 pages, 8 figure

Accurate sampling using Langevin dynamics

We show how to derive a simple integrator for the Langevin equation and illustrate how it is possible to check the accuracy of the obtained distribution on the fly, using the concept of effective energy introduced in a recent paper [J. Chem. Phys. 126, 014101 (2007)]. Our integrator leads to correct sampling also in the difficult high-friction limit. We also show how these ideas can be applied in practical simulations, using a Lennard-Jones crystal as a paradigmatic case

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

Stochastic to deterministic crossover of fractal dimension for a Langevin equation

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos.Comment: 12 pages including 3 figures, RevTex and epsf. To appear Phys. Rev. E, April, 199