118 research outputs found
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 Zr
A 2D temperature-dependent effective potential is calculated for the
interacting longitudinal and transverse phonons of 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 -Zr becomes unstable with respect to the
longitudinal vibrations. The obtained temperature value practically
coincides with the experimental temperature of the
structural transition in zirconium. The role of electronic entropy in the
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
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
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
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
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