Dual characterization of critical fluctuations: Density functional theory & nonlinear dynamics close to a tangent bifurcation

We improve on the description of the relationship that exists between critical clusters in thermal systems and intermittency near the onset of chaos in low-dimensional systems. We make use of the statistical-mechanical language of inhomogeneous systems and of the renormalization group (RG) method in nonlinear dynamics to provide a more accurate, formal, approach to the subject. The description of this remarkable correspondence encompasses, on the one hand, the density functional formalism, where classical and quantum mechanical analogues match the procedure for one-dimensional clusters, and, on the other, the RG fixed-point map of functional compositions that captures the essential dynamical behavior. We provide details of how the above-referred theoretical approaches interrelate and discuss the implications of the correspondence between the high-dimensional (degrees of freedom) phenomenon and low-dimensional dynamics.Comment: 8 figure

Dynamics towards the Feigenbaum attractor

We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.Comment: 8 pages, 12 figure

Two stories outside Boltzmann-Gibbs statistics: Mori's q-phase transitions and glassy dynamics at the onset of chaos

First, we analyze trajectories inside the Feigenbaum attractor and obtain the atypical weak sensitivity to initial conditions and loss of information associated to their dynamics. We identify the Mori singularities in its Lyapunov spectrum with the appearance of a special value for the entropic index q of the Tsallis statistics. Secondly, the dynamics of iterates at the noise-perturbed transition to chaos is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation, aging, subdiffusion and arrest. The properties of the bifurcation gap induced by the noise are seen to be comparable to those of a supercooled liquid above a glass transition temperature.Comment: Proceedings of: 31st Workshop of the International School of Solid State Physics, Complexity, Metastability and Nonextensivity, Erice (Sicily) 20-26 July 2004 World Scientific in the special series of the E. Majorana conferences, in pres

Rheology of a sonofluidized granular packing

We report experimental measurements on the rheology of a dry granular material under a weak level of vibration generated by sound injection. First, we measure the drag force exerted on a wire moving in the bulk. We show that when the driving vibration energy is increased, the effective rheology changes drastically: going from a non-linear dynamical friction behavior - weakly increasing with the velocity- up to a linear force-velocity regime. We present a simple heuristic model to account for the vanishing of the stress dynamical threshold at a finite vibration intensity and the onset of a linear force-velocity behavior. Second, we measure the drag force on spherical intruders when the dragging velocity, the vibration energy, and the diameters are varied. We evidence a so-called ''geometrical hardening'' effect for smaller size intruders and a logarithmic hardening effect for the velocity dependence. We show that this last effect is only weakly dependent on the vibration intensity.Comment: Accepted to be published in EPJE. v3: Includes changes suggested by referee

Cluster radioactivity of Th isotopes in the mean-field HFB theory

Cluster radioactivity is described as a very mass asymmetric fission process. The reflection symmetry breaking octupole moment has been used in a mean field HFB theory as leading coordinate instead of the quadrupole moment usually used in standard fission calculations. The procedure has been applied to the study of the ``very mass asymmetric fission barrier'' of several even-even Thorium isotopes. The masses of the emitted clusters as well as the corresponding half-lives have been evaluated on those cases where experimental data exist.Comment: Contribution to XIV Nuclear Physics Workshop at Kazimierz Dolny, Poland, Sept. 26-29, 200