Fronts, Domain Growth and Dynamical Scaling in a d=1 non-Potential System

We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial dependent terms have been added. As long as the angular velocity is different from zero, there is no known Lyapunov potential for the dynamics of the system. As a consequence the system follows a non-relaxational dynamics and the asymptotic state can not be associated with a final equilibrium state. When the rotation angular velocity is greater than some critical value, the system undergoes the Kuppers-Lortz instability leading to a time dependent chaotic dynamics and there is no coarsening beyond this instability. We have focused on the transient dynamics below this instability, where the dynamics is still non-relaxational. In this regime the dynamics is governed by a non-relaxational motion of fronts separating dynamically equivalent homogeneous states. We classify the families of fronts that occur in the dynamics, and calculate their shape and velocity. We have found that a scaling description of the coarsening process is still valid as in the potential case. The growth law is nearly logarithmic with time for short times and becomes linear after a crossover, whose width is determined by the strength of the non-potential terms.Comment: 15 pages, 10 figure

Means and method of measuring viscoelastic strain Patent

Photographic method for measuring viscoelastic strain in solid propellants and other material

Miniature stress transducer Patent

Miniature solid state, direction sensitive, stress transducer design with bonded semiconductive piezoresistive element for sensing residual stresse

Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation

We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.Comment: 20 pages,LaTeX, Postcript version with figures included available at http://formentor.uib.es/~montagne/textos/nep

Synchronization of Spatiotemporal Chaos: The regime of coupled Spatiotemporal Intermittency

Synchronization of spatiotemporally chaotic extended systems is considered in the context of coupled one-dimensional Complex Ginzburg-Landau equations (CGLE). A regime of coupled spatiotemporal intermittency (STI) is identified and described in terms of the space-time synchronized chaotic motion of localized structures. A quantitative measure of synchronization as a function of coupling parameter is given through distribution functions and information measures. The coupled STI regime is shown to dissapear into regular dynamics for situations of strong coupling, hence a description in terms of a single CGLE is not appropiate.Comment: 4 pages, LaTeX 2e. Includes 3 figures made up of 8, 4 (LARGE),and 2 postscript files. Includes balanced.st

Divergent Time Scale in Axelrod Model Dynamics

We study the evolution of the Axelrod model for cultural diversity. We consider a simple version of the model in which each individual is characterized by two features, each of which can assume q possibilities. Within a mean-field description, we find a transition at a critical value q_c between an active state of diversity and a frozen state. For q just below q_c, the density of active links between interaction partners is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma

Neighborhood models of minority opinion spreading

We study the effect of finite size population in Galam's model [Eur. Phys. J. B 25 (2002) 403] of minority opinion spreading and introduce neighborhood models that account for local spatial effects. For systems of different sizes N, the time to reach consensus is shown to scale as ln N in the original version, while the evolution is much slower in the new neighborhood models. The threshold value of the initial concentration of minority supporters for the defeat of the initial majority, which is independent of N in Galam's model, goes to zero with growing system size in the neighborhood models. This is a consequence of the existence of a critical size for the growth of a local domain of minority supporters

Period Stabilization in the Busse-Heikes Model of the Kuppers-Lortz Instability

The Busse-Heikes dynamical model is described in terms of relaxational and nonrelaxational dynamics. Within this dynamical picture a diverging alternating period is calculated in a reduced dynamics given by a time-dependent Hamiltonian with decreasing energy. A mean period is calculated which results from noise stabilization of a mean energy. The consideration of spatial-dependent amplitudes leads to vertex formation. The competition of front motion around the vertices and the Kuppers-Lortz instability in determining an alternating period is discussed.Comment: 28 pages, 11 figure

Nonlinear oscillator with parametric colored noise: some analytical results

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit