arXiv subjects

Philippe Marcq

Publications and source records attributed to Philippe Marcq.

22 records · Page 2Linked to original sources

arXiv2002

Anomalous diffusion in nonlinear oscillators with multiplicative noise

The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy, root-mean-square position and velocity, grow algebraically with time. The scaling exponents and associated generalized diffusion constants are calculated when the oscillator's potential energy grows as a power of its position. Correlated noise yields anomalous diffusion exponents equal to half the value found for white noise.

cond-mat.stat-mech↗

arXiv1998

A Langevin equation for the energy cascade in fully-developed turbulence

Experimental data from a turbulent jet flow is analysed in terms of an additive, continuous stochastic process where the usual time variable is replaced by the scale. We show that the energy transfer through scales is well described by a linear Langevin equation, and discuss the statistical properties of the corresponding random force in detail. We find that the autocorrelation function of the random force decays rapidly: the process is therefore Markov for scales larger than Kolmogorov's dissipation scale $η$. The corresponding autocorrelation scale is identified as the elementary step of the energy cascade. However, the probability distribution function of the random force is both non-Gaussian and weakly scale-dependent.

chao-dyn↗

arXiv1997

Early-time critical dynamics of lattices of coupled chaotic maps

The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents θ' and z. The critical points of five different models are investigated, varying the mode of update, the coupling, and the local map. Our results suggest that the nature of update is a relevant parameter for dynamic universality classes of extended dynamical systems, generalizing results obtained previously for the static properties. They also indicate that the universality observed for the static properties of Ising-like transitions of synchronously-updated systems does not hold for their dynamic critical properties.

adap-org↗

arXiv1993

Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation

Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlevé test for integrability. These solutions are expressed in terms of hyperbolic functions, and include the pulses and fronts found by van Saarloos and Hohenberg. We also find previously unknown sources and sinks. The emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc Ansätze.

patt-sol↗