Journée de Dynamique Non Linéaire

10h30   Stefano Ruffo (Dipartimento di Energetica, Université de Florence, INFM et INFN)
Long-range interactions: a "pandora box" of new phenomena

11h30   Dmitri Volchenkov (Centre de Physique Théorique)
Bending instability in the turbulent flow and magnetic hydrodynamics

Résumé du séminaire de Stefano Ruffo

I will discuss the problem of "ensemble inequivalence": the disagreement in the value of averages (energy, temperature, etc.) in different statistical ensembles which persists in the thermodynamic limit. This can appear when the interaction is long-range, i.e., potentials decay at large distances with a power less or equal than the Euclidean space dimension. A large class of long-range interactions that is frequently introduced in statistical physics is the one of mean-field models. We have solved exactly some mean-field models (e.g. the Blume-Emery-Griffiths model), both in the canonical and in the microcanonical ensemble and proven that these give inequivalent predictions when the system is inhomogeneous, for instance at a first-order phase transition. In particular, we have shown that "negative specific heat" and "temperature jumps" can arise in the microcanonical ensemble. Both these phenomena are potentially observable in nature: recently signals of the presence of a negative specific heat have been observed in the melting process of atomic clusters, where the range of the interaction is of the order of the size of the system, mimicking the effect of long-range interactions. We have also shown that these peculiar effects are not specific of the mean-field limit, but can be present also when the interaction is weakly decaying in space. I will briefly discuss also the appearence of coherent structures in the dynamics of systems with long-range interaction, whose lifetime increases with system size.

References:
1 - J. Barré, D. Mukamel and S. Ruffo:"Inequivalence of ensembles in a system with long range interactions", Phys. Rev. Lett., 87 (3), 030601 (2001).
2 - F. Leyvraz and S. Ruffo: "Ensemble Inequivalence in Systems with Long-range Interactions", J. Phys. A, 34, 1 (2001).
3 - F. Leyvraz and S. Ruffo: "Ensemble Inequivalence: A Formal Approach", Physica A, 305, 58 (2002).
4 - F.Leyvraz, M.-C. Firpo and S. Ruffo: "Inhomogeneous Quasi-stationary States in a Mean-field Model with Repulsive Cosine Interactions", J. Phys. A, 35, 4413 (2002).
5 - J. Barré, F. Bouchet, T. Dauxois and S. Ruffo: "Out-of-equilibrium states as statistical equilibria of an effective dynamics in a system with long-range interactions", Phys. Rev. Lett., 89, 110601 (2002).
6 - J. Barré, F. Bouchet, T. Dauxois and S. Ruffo: "Birth and long-time stabilization of out-of-equilibrium coherent structures", Eur. Phys.J. B, 29, 577 (2002),[cond-mat/0203013].
7 - M. Antoni, A. Torcini and S. Ruffo: "First and second order clustering transitions for a system with infinite-range attractive interactions", Phys. Rev. E, Rapid Comm. 66, 025103 (2002).
8 - T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens: "Dynamics and statistics of systems with long-range interactions", Springer (2002).

Résumé du séminaire de Dmitri Volchenkov

Energy E dissipated in a mass of turbulent fluid per second in an isotropic homogeneous fully developed turbulent flow is constant in the inertial range of scales [Kolmogorov, 1941]. Swirling eddies of an immiscible fluid injected into the flow provoke it into turbulence damping, since the energy dissipation rate E(k) acquires a minimum selecting the eddies of an optimal size l, while the others are damped out. The flow with a finite gyrotropy of order 1/l is unstable and responses with bursts for any small perturbation. However, it can be stabilized by a spatially homogeneous "mean" magnetic field.