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P Marquié

Publications and source records attributed to P Marquié.

7 recordsLinked to original sources
PubMed2002

Wave front propagation failure in an inhomogeneous discrete Nagumo chain: theory and experiments.

The phenomenon of wave propagation failure in a discrete inhomogeneous Nagumo equation is investigated. It is found that the propagation failure occurs not only for small coupling coefficients but as well for an abrupt change of the interelement coupling. The investigation includes the study of the phase space of the system, numerical simulations, and real experiments with a nonlinear electrical lattice.

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PubMed2001

Theoretical and experimental study of two discrete coupled Nagumo chains.

We analyze front wave (kink and antikink) propagation and pattern formation in a system composed of two coupled discrete Nagumo chains using analytical and numerical methods. In the case of homogeneous interaction among the chains, we show the possibility of the effective control on wave propagation. In addition, physical experiments on electrical chains confirm all theoretical behaviors.

Journal Article↗
PubMed2001

Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments.

Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.

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PubMed1999

Dissipative lattice model with exact traveling discrete kink-soliton solutions: discrete breather generation and reaction diffusion regime.

We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.

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