Jean-Baptiste Delfau

French National Centre for Scientific Research, Lutetia Parisorum, Île-de-France, France

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Publications (5)11.63 Total impact

  • Jean-Baptiste Delfau, Christophe Coste, Michel Saint Jean
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    ABSTRACT: We study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory.
    Physical Review E 06/2013; 87(6-1):062135. DOI:10.1103/PhysRevE.87.062135 · 2.33 Impact Factor
  • Jean-Baptiste Delfau, Christophe Coste, Michel Saint Jean
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    ABSTRACT: We study with numerical simulations the transverse fluctuations in quasi-one-dimensional systems of particles in a thermal bath, near the zigzag transition. We show that close to the zigzag threshold, the transverse fluctuations exhibit an anormal diffusion, characterized by a mean square displacement that increases as the square root of time. In contrast with the longitudinal fluctuations, this behavior of the transverse fluctuations cannot be explained by the single-file ordering. We provide an analytical modelization, and in the thermodynamic limit we demonstrate the existence of this subdiffusive regime near the zigzag transition, showing that it results from overdamped collective modes of the system. These calculations are extended to finite systems, in excellent agreement with the simulations data. We also exhibit some effects of the thermal fluctuations on the zigzag transition, and analyze them in the light of stochastic bifurcation theory.
    Physical Review E 03/2013; 87(3). DOI:10.1103/PhysRevE.87.032163 · 2.33 Impact Factor
  • Jean-Baptiste Delfau, Christophe Coste, Michel Saint Jean
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    ABSTRACT: We consider a finite number of particles with soft-core interactions, subjected to thermal fluctuations and confined in a box with excluded mutual passage. Using numerical simulations, we focus on the influence of the longitudinal confinement on the transient behavior of the longitudinal mean squared displacement. We exhibit several power laws for its time evolution according to the confinement range and to the rank of the particle in the file. We model the fluctuations of the particles as those of a chain of springs and point masses in a thermal bath. Our main conclusion is that actual system dynamics can be described in terms of the normal oscillation modes of this chain. Moreover, we obtain complete expressions for the physical observables, in excellent agreement with our simulations. The correct power laws for the time dependency of the mean squared displacement in the various regimes are recovered, and analytical expressions of the prefactors according to the relevant parameters are given.
    Physical Review E 06/2012; 85(6). DOI:10.1103/PhysRevE.85.061111 · 2.33 Impact Factor
  • Jean-Baptiste Delfau, Christophe Coste, Michel Saint Jean
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    ABSTRACT: We study the position fluctuations of interacting particles aligned in a finite cell that avoid any crossing in equilibrium with a thermal bath. The focus is put on the influence of the confining force directed along the cell length. We show that the system may be modeled as a 1D chain of particles with identical masses, linked with linear springs of varying spring constants. The confining force may be accounted for by linear springs linked to the walls. When the confining force range is increased toward the inside of the chain, a paradoxical behavior is exhibited. The outermost particles fluctuations are enhanced, whereas those of the inner particles are reduced. A minimum of fluctuations is observed at a distance of the cell extremities that scales linearly with the confining force range. Those features are in very good agreement with the model. Moreover, the simulations exhibit an asymmetry in their fluctuations which is an anharmonic effect. It is characterized by the measurement of the skewness, which is found to be strictly positive for the outer particles when the confining force is short ranged.
    Physical Review E 04/2012; 85(4 Pt 1):041137. DOI:10.1103/PhysRevE.85.041137 · 2.33 Impact Factor
  • Source
    Jean-Baptiste Delfau, Christophe Coste, Michel Saint Jean
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    ABSTRACT: We study the Single File Diffusion (SFD) of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We present simulations that exhibit new behaviors specifically associated to systems of small number of particles and to small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations, and provides convincing estimates of the crossover times between those regimes.
    Physical Review E 07/2011; 84(1 Pt 1):011101. DOI:10.1103/PhysRevE.84.011101 · 2.33 Impact Factor

Publication Stats

12 Citations
11.63 Total Impact Points

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Institutions

  • 2013
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2011–2012
    • Paris Diderot University
      Lutetia Parisorum, Île-de-France, France