Biomedical subjects

M G Clerc

Publications and source records attributed to M G Clerc.

10 recordsLinked to original sources

PubMed2006

Front propagation sustained by additive noise.

The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the core of the front is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of the core of the front is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations.

Journal Article↗

PubMed2006

Localized states in bistable pattern-forming systems.

We present a unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks.

Journal Article↗

PubMed2005

Patterns and localized structures in population dynamics.

Patterns, fronts, and localized structures of a prototypical model for population dynamics interaction are studied. The physical content of the model is the coexistence of a simple random walk for the motion of the individuals with a nonlinearity in the competitive struggle for resources which simultaneously stresses the Allee effect and interaction at a distance. Mathematically, the model is variational and exhibits coexistence between different stable extended states. Solutions are obtained, the phase diagram is constructed, and the emergence of localized structures is investigated.

Biophysics↗

PubMed2005

Coarsening dynamics of the one-dimensional Cahn-Hilliard model.

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We characterize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system. A set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations. We also compare these dynamics with the bubble dynamics deduced from the classical kink interaction computation where our model seems to be more appropriated. In the case of two bubbles, we deduce analytical expressions for the bubble's position and the bubble's width. Besides, a simple description of the ulterior dynamics is presented.

Journal Article↗

PubMed2005

Additive noise induces front propagation.

The effect of additive noise on a static front that connects a stable homogeneous state with an also stable but spatially periodic state is studied. Numerical simulations show that noise induces front propagation. The conversion of random fluctuations into direct motion of the front's core is responsible of the propagation; noise prefers to create or remove a bump, because the necessary perturbations to nucleate or destroy a bump are different. From a prototype model with noise, we deduce an adequate equation for the front's core. An analytical expression for the front velocity is deduced, which is in good agreement with numerical simulations.

Journal Article↗

PubMed2005

Bouncing localized structures in a liquid-crystal light-valve experiment.

Experimental evidence of bouncing localized structures in a nonlinear optical system is reported. Oscillations in the position of the localized states are described by a consistent amplitude equation, which we call the Lifshitz normal form equation, in analogy with phase transitions. Localized structures are shown to arise close to the Lifshtiz point, where nonvariational terms drive the dynamics into complex and oscillatory behaviors.

Journal Article↗

PubMed2004

van der Waals normal form for a one-dimensional hydrodynamic model.

Phase separation in a fluidized granular system is studied. We consider a one-dimensional hydrodynamic model that mimics a two-dimensional fluidized granular system with a vibrating wall and without gravity, which exhibits a phase separation. Close to the critical point, by means of an adiabatic elimination of the temperature, we deduce the van der Waals normal form, which is the equation that describes the slow dynamics of the system and predicts the qualitative behavior in different regions of parameters. This allows us to understand the origin of the effective viscosity and the spatial saturation at the onset of the bifurcation. The hydrodynamic model and van der Waals normal form exhibit a behavior similar to the one observed in molecular dynamics simulations.

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PubMed2002

van der Waals-like transition in fluidized granular matter.

A phase separation of fluidized granular matter is presented. Molecular dynamics simulations of a system of grains in two spatial dimensions, with a vibrating wall and without gravity, exhibit the appearance, coalescence, and disappearance of bubbles. By identifying the mechanism responsible for the phase separation, we show that the phenomenon is analogous to the spinodal decomposition of the gas-liquid transition of the van der Waals model. We have deduced a macroscopic model for the onset of phase separation which agrees quite well with molecular dynamics simulations.

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PubMed2001

Dissipation-induced instabilities in an optical cavity laser: a mechanical analog near the 1:1 resonance.

The 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms has been studied. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allows one to show that an optical cavity with small pumping is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. A simple mechanical system close to the 1:1 resonance has been displayed, which is a mechanical analog of the laser.

Journal Article↗

PubMed2001

First-order Fréedericksz transition in the presence of light-driven feedback in nematic liquid crystals.

We show that feedback, which introduces a dependence of the electric field on the liquid-crystal director, renders the Fréedericksz transition first order. Experimentally, the feedback is introduced as a light loop in a liquid-crystal light valve. Theoretically, we include the feedback term into the Frank free energy and we derive an amplitude equation that is valid close to the transition. The theoretical description is in qualitative agreement with the experimental observations. Depending on the values of the feedback parameters, both theory and experiment exhibit bistability, propagation of fronts, and a Maxwell point.

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