189 research outputs found
Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics
We uncover the dynamics at the chaos threshold of the logistic
map and find it consists of trajectories made of intertwined power laws that
reproduce the entire period-doubling cascade that occurs for . We corroborate this structure analytically via the Feigenbaum
renormalization group (RG) transformation and find that the sensitivity to
initial conditions has precisely the form of a -exponential, of which we
determine the -index and the -generalized Lyapunov coefficient . Our results are an unequivocal validation of the applicability of the
non-extensive generalization of Boltzmann-Gibbs (BG) statistical mechanics to
critical points of nonlinear maps.Comment: Revtex, 3 figures. Updated references and some general presentation
improvements. To appear published as a Rapid communication of PR
A recent appreciation of the singular dynamics at the edge of chaos
We study the dynamics of iterates at the transition to chaos in the logistic
map and find that it is constituted by an infinite family of Mori's -phase
transitions. Starting from Feigenbaum's function for the diameters
ratio, we determine the atypical weak sensitivity to initial conditions associated to each -phase transition and find that it obeys the form
suggested by the Tsallis statistics. The specific values of the variable at
which the -phase transitions take place are identified with the specific
values for the Tsallis entropic index in the corresponding . We
describe too the bifurcation gap induced by external noise and show that its
properties exhibit the characteristic elements of glassy dynamics close to
vitrification in supercooled liquids, e.g. two-step relaxation, aging and a
relationship between relaxation time and entropy.Comment: Proceedings of: Verhulst 200 on Chaos, Brussels 16-18 September 2004,
Springer Verlag, in pres
Magnon delocalization in ferromagnetic chains with long-range correlated disorder
We study one-magnon excitations in a random ferromagnetic Heisenberg chain
with long-range correlations in the coupling constant distribution. By
employing an exact diagonalization procedure, we compute the localization
length of all one-magnon states within the band of allowed energies . The
random distribution of coupling constants was assumed to have a power spectrum
decaying as . We found that for ,
one-magnon excitations remain exponentially localized with the localization
length diverging as 1/E. For a faster divergence of is
obtained. For any , a phase of delocalized magnons emerges at the
bottom of the band. We characterize the scaling behavior of the localization
length on all regimes and relate it with the scaling properties of the
long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.
Nonextensivity and multifractality in low-dimensional dissipative systems
Power-law sensitivity to initial conditions at the edge of chaos provides a
natural relation between the scaling properties of the dynamics attractor and
its degree of nonextensivity as prescribed in the generalized statistics
recently introduced by one of us (C.T.) and characterized by the entropic index
. We show that general scaling arguments imply that , where and are the
extremes of the multifractal singularity spectrum of the attractor.
This relation is numerically checked to hold in standard one-dimensional
dissipative maps. The above result sheds light on a long-standing puzzle
concerning the relation between the entropic index and the underlying
microscopic dynamics.Comment: 12 pages, TeX, 4 ps figure
Recommended from our members
Social and economic impacts of congenital Zika syndrome in Brazil: Study protocol and rationale for a mixed-methods study.
Global concern broke out in late 2015 as thousands of children in Brazil were born with microcephaly, which was quickly linked to congenital infection with Zika virus (ZIKV). ZIKV is now known to cause a wider spectrum of severe adverse outcomes-congenital Zika syndrome (CZS)-and also milder impairments. This study aimed to explore the social and economic impacts of CZS in Brazil. Data was collected through mixed methods across two settings: Recife City and Jaboatão dos Guararapes in Pernambuco State (the epicentre of the epidemic), and the city of Rio de Janeiro (where reports of ZIKV infection and CZS were less frequent). Data was collected May 2017-January 2018. Ethical standards were adhered to throughout the research. In-depth qualitative interviews were conducted with: mothers and other carers of children with CZS (approximately 30 per setting), pregnant women (10-12 per setting), men and women of child-bearing age (16-20 per setting), and health professionals (10-12 per setting). Thematic analysis was undertaken independently by researchers from at least two research settings, and these were shared for feedback. A case-control study was undertaken to quantitatively explore social and economic differences between caregivers of a child with CZS (cases) and caregivers with an unaffected child (controls). We aimed to recruit 100 cases and 100 controls per setting, from existing studies. The primary caregiver, usually the mother, was interviewed using a structured questionnaire to collect information on: depression, anxiety, stress, social support, family quality of life, health care and social service use, and costs incurred by families. Multivariable logistic regression analyses were used to compare outcomes for cases and controls. Costs incurred as a result of CZS were estimated from the perspective of the health system, families and society. Modelling was undertaken to estimate the total economic burden of CZS from those three perspectives
A comparative study of disc-planet interaction
We perform numerical simulations of a disc-planet system using various
grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run
for a simple setup where Jupiter and Neptune mass planets on a circular orbit
open a gap in a protoplanetary disc during a few hundred orbital periods. We
compare the surface density contours, potential vorticity and smoothed radial
profiles at several times. The disc mass and gravitational torque time
evolution are analyzed with high temporal resolution. There is overall
consistency between the codes. The density profiles agree within about 5% for
the Eulerian simulations while the SPH results predict the correct shape of the
gap although have less resolution in the low density regions and weaker
planetary wakes. The disc masses after 200 orbital periods agree within 10%.
The spread is larger in the tidal torques acting on the planet which agree
within a factor 2 at the end of the simulation. In the Neptune case the
dispersion in the torques is greater than for Jupiter, possibly owing to the
contribution from the not completely cleared region close to the planet.Comment: 32 pages, accepted for publication in MNRA
Metastability, negative specific heat and weak mixing in classical long-range many-rotator system
We perform a molecular dynamical study of the isolated classical
Hamiltonian , known to
exhibit a second order phase transition, being disordered for and ordered otherwise ( total energy
and ). We focus
on the nonextensive case and observe that, for , a
basin of attraction exists for the initial conditions for which the system
quickly relaxes onto a longstanding metastable state (whose duration presumably
diverges with like ) which eventually crosses over to the
microcanonical Boltzmann-Gibbs stable state. The temperature associated with
the (scaled) average kinetic energy per particle is lower in the metastable
state than in the stable one. It is exhibited for the first time that the
appropriately scaled maximal Lyapunov exponent
, where, for all values of ,
numerically coincides with {\it one third} of its value for , hence
decreases from 1/9 to zero when increases from zero to unity,
remaining zero thereafter. This new and simple {\it connection between
anomalies above and below the critical point} reinforces the nonextensive
universality scenario.Comment: 9 pages and 4 PS figure
The `Friction' of Vacuum, and other Fluctuation-Induced Forces
The static Casimir effect describes an attractive force between two
conducting plates, due to quantum fluctuations of the electromagnetic (EM)
field in the intervening space. {\it Thermal fluctuations} of correlated fluids
(such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are
also modified by the boundaries, resulting in finite-size corrections at
criticality, and additional forces that effect wetting and layering phenomena.
Modified fluctuations of the EM field can also account for the `van der Waals'
interaction between conducting spheres, and have analogs in the
fluctuation--induced interactions between inclusions on a membrane. We employ a
path integral formalism to study these phenomena for boundaries of arbitrary
shape. This allows us to examine the many unexpected phenomena of the dynamic
Casimir effect due to moving boundaries. With the inclusion of quantum
fluctuations, the EM vacuum behaves essentially as a complex fluid, and
modifies the motion of objects through it. In particular, from the mechanical
response function of the EM vacuum, we extract a plethora of interesting
results, the most notable being: (i) The effective mass of a plate depends on
its shape, and becomes anisotropic. (ii) There is dissipation and damping of
the motion, again dependent upon shape and direction of motion, due to emission
of photons. (iii) There is a continuous spectrum of resonant cavity modes that
can be excited by the motion of the (neutral) boundaries.Comment: RevTex, 2 ps figures included. The presentation is completely
revised, and new sections are adde
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