Comment on: `Pipe Network Model for Scaling of Dynamic Interfaces in Porous Media'

We argue that a proposed exponent identity [Phys. Rev. Lett 85, 1238 (2000)] for interface roughening in spontaneous imbibition is wrong. It rests on the assumption that the fluctuations are controlled by a single time scale, but liquid conservation imposes two distinct time scales.Comment: 1 page, to appear in Phys. Rev. Let

Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains

An analytical expression for the maximal Lyapunov exponent $\lambda_1$ in generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with numerical simulations and the agreement is good over a wide range of energy densities $\epsilon$. At very high energy density the power law scaling of $\lambda_1$ with $\epsilon$ can be also obtained by simple dimensional arguments, assuming that the system is ruled by a single time scale. Finally, we argue that for repulsive and hard core potentials in one dimension $\lambda_1 \sim \sqrt{\epsilon}$ at large $\epsilon$.Comment: Latex, 10 pages, 5 Figs - Contribution to the Conference "Disorder and Chaos" held in memory of Giovanni Paladin (Sept. 1997 - Rome) - submitted to J. de Physiqu

Theoretical study of finite temperature spectroscopy in van der Waals clusters. II Time-dependent absorption spectra

Using approximate partition functions and a master equation approach, we investigate the statistical relaxation toward equilibrium in selected CaAr$_n$ clusters. The Gaussian theory of absorption (previous article) is employed to calculate the average photoabsorption intensity associated with the 4s^2-> 4s^14p^1 transition of calcium as a function of time during relaxation. In CaAr_6 and CaAr_10 simple relaxation is observed with a single time scale. CaAr_13 exhibits much slower dynamics and the relaxation occurs over two distinct time scales. CaAr_37 shows much slower relaxation with multiple transients, reminiscent of glassy behavior due to competition between different low-energy structures. We interpret these results in terms of the underlying potential energy surfaces for these clusters.Comment: 10 pages, 9 figure

Magnetic relaxation in hard type-II superconductors

Magnetic relaxation in a type-II superconductor is simulated for a range of temperatures (T) in a simple model of 2D Josephson junction array (JJA) with finite screening. The high-T phase, that is characterised by a single time scale \tau_{\alpha}, crosses over to an intermediate phase at a lower temperature T_{cr} wherein a second time scale \tau_{\beta}<<\tau_{\alpha} emerges. The relaxation in the time window set by \tau_{\beta} follows power law which is attributed to self-organization of the magnetic flux during relaxation. Consequently, for T<T_{cr}, a transition from super-critical (current density J>J_{c}) to sub-critical (J<J_{c}) state separated by an intermediate state with frozen dynamics is observed. Both \tau_{\alpha} and \tau_{\beta} diverges at T_{sc}<T_{cr}, marking the transition into a state with true persistent current.Comment: 7 Pages (in Europhys format, .sty included), 5 Figures. To appear in Europhysics Letter

Multiple time scales in volatility and leverage correlations: An stochastic volatility model

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.Comment: 19 pages, 5 figure

Market Mill Dependence Pattern in the Stock Market: Multiscale Conditional Dynamics

Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry generating component of the conditional probability distribution result in the "elementary" market mill pattern. This asymmetry generating component matches the empirical distribution obtained from the market data. We discuss these properties as a mixture of trend-preserving and contrarian strategies used by market agents. Three basic types of asymmetry patterns characterizing individual stocks are outlined. Multiple time scale considerations make the resulting "composite" mill similar to the empirical market mill patterns. Multiscale model also reflects a multi-agent nature of the market.Comment: Typo's correcte