2,683 research outputs found
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
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