Biomedical subjects

Robert Botet

Publications and source records attributed to Robert Botet.

3 recordsLinked to original sources

PubMed2005

Exact order-parameter distribution for critical mean-field percolation and critical aggregation.

We show that the order-parameter distribution for the mean-field percolation at the critical point is the Kolmogorov-Smirnov distribution and that it coincides with the corresponding distribution for a mean-field aggregation process at the critical time. Both processes are known to belong to the same universality class in the sense that they share the same set of critical exponents, but percolation is at the equilibrium while the aggregation is a dynamical critical process. This shows that, in this case, the probability density for order-parameter fluctuations is universal at the critical point of the infinite lattice, independent of the hypothesis of thermodynamic equilibrium.

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PubMed2004

Scaling behaviors of colloidal aggregates under uniform pressure.

We present a theoretical model for the compaction of a colloidal sediment under uniaxial mechanical pressure in the continuous three-dimensional space. The initial system is formed with aggregated particles dispersed in a fluid, and softly sedimented in a vessel. When a uniform pressure is applied, it evolves irreversibly through successive creation and destruction of bonds between the particles. The rules governing the bonds depend on both geometrical constraints and current stresses. Numerical simulations of such systems exhibit three different scenarios, corresponding, respectively, to the fragile, elastic, and plastic behaviors. In the elastic regime, where most bonds are permanent, the pressure scales as a power law of the volume fraction of particles, with a numerical exponent equal to 4.4. In the plastic regime, where many bonds are broken and many others created, the pressure also scales with volume fraction, but the exponent is much lower, equal to 1.7. These scaling behaviors agree remarkably well with recent experiments realized on the compaction of systems with aggregated silica particles in the oedometer cell. They also can be explained with simple theoretical arguments using a plausible morphology of the resistant paths acting throughout the system. Finally, at very large applied pressures, all these regimes converge to the random close packing of spheres.

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PubMed2001

Phase transitions in nonextensive spin systems.

The spherical spin model with infinite-range ferromagnetic interactions is investigated analytically in the framework of nonextensive thermostatics generalizing the Boltzmann-Gibbs statistical mechanics. We show that for repulsive correlations, a weak-ferromagnetic phase develops. There is a tricritical point separating para-, weak-ferro, and ferro regimes. The transition from paramagnetic to weak-ferromagnetic phase is an unusual first-order phase transition in which a discontinuity of the averaged order parameter appears, even for finite number of spins. This result puts in a different way the question of the stability of critical phenomena with respect to the long-ranged correlations.

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