253 research outputs found
The Twentieth Century Reform of the Liturgy: Outcomes and Prospects
(excerpt)
I want to situate my reflections on the outcomes of the 20th century liturgical reform and our prospects for the future. This is how I propose to proceed. I will very briefly review the late twentieth century liturgical reforms and revisions of a number of churches. Then I will turn to reactions to the reforms of the past fifty years, some assessment of their success and failure, and finally prospects for the future, employing an analogy with curricular reform, specifically in theological education. In terms of assessment I will have to limit myself to the Roman Catholic experience and hope that my reflections will help Lutherans to better assess liturgical revisions in the U.S. over the past fifty or sixty years
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
Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach
We perform a throughout numerical study of the average sensitivity to initial
conditions and entropy production for two symplectically coupled standard maps
focusing on the control-parameter region close to regularity. Although the
system is ultimately strongly chaotic (positive Lyapunov exponents), it first
stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue
that the nonextensive generalization of the classical formalism is an adequate
tool in order to get nontrivial information about this complex phenomenon.
Within this context we analyze the relation between the power-law sensitivity
to initial conditions and the entropy production.Comment: 9 pages, 12 figure
Nonequilibrium Kinetics of One-Dimensional Bose Gases
We study cold dilute gases made of bosonic atoms, showing that in the
mean-field one-dimensional regime they support stable out-of-equilibrium
states. Starting from the 3D Boltzmann-Vlasov equation with contact
interaction, we derive an effective 1D Landau-Vlasov equation under the
condition of a strong transverse harmonic confinement. We investigate the
existence of out-of-equilibrium states, obtaining stability criteria similar to
those of classical plasmas.Comment: 16 pages, 6 figures, accepted for publication in Journal of
Statistical Mechanics: Theory and Experimen
Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: rigorous nonextensive solutions
Using the Feigenbaum renormalization group (RG) transformation we work out
exactly the dynamics and the sensitivity to initial conditions for unimodal
maps of nonlinearity at both their pitchfork and tangent
bifurcations. These functions have the form of -exponentials as proposed in
Tsallis' generalization of statistical mechanics. We determine the -indices
that characterize these universality classes and perform for the first time the
calculation of the -generalized Lyapunov coefficient . The
pitchfork and the left-hand side of the tangent bifurcations display weak
insensitivity to initial conditions, while the right-hand side of the tangent
bifurcations presents a `super-strong' (faster than exponential) sensitivity to
initial conditions. We corroborate our analytical results with {\em a priori}
numerical calculations.Comment: latex, 4 figures. Updated references and some general presentation
improvements. To appear published in Europhysics Letter
Intermittency at critical transitions and aging dynamics at edge of chaos
We recall that, at both the intermittency transitions and at the Feigenbaum
attractor in unimodal maps of non-linearity of order , the dynamics
rigorously obeys the Tsallis statistics. We account for the -indices and the
generalized Lyapunov coefficients that characterize the
universality classes of the pitchfork and tangent bifurcations. We identify the
Mori singularities in the Lyapunov spectrum at the edge of chaos with the
appearance of a special value for the entropic index . The physical area of
the Tsallis statistics is further probed by considering the dynamics near
criticality and glass formation in thermal systems. In both cases a close
connection is made with states in unimodal maps with vanishing Lyapunov
coefficients.Comment: Proceedings of: STATPHYS 2004 - 22nd IUPAP International Conference
on Statistical Physics, National Science Seminar Complex, Indian Institute of
Science, Bangalore, 4-9 July 2004. Pramana, in pres
Parallels between the dynamics at the noise-perturbed onset of chaos in logistic maps and the dynamics of glass formation
We develop the characterization of the dynamics at the noise-perturbed edge
of chaos in logistic maps in terms of the quantities normally used to describe
glassy properties in structural glass formers. Following the recognition [Phys.
Lett. \textbf{A 328}, 467 (2004)] that the dynamics at this critical attractor
exhibits analogies with that observed in thermal systems close to
vitrification, we determine the modifications that take place with decreasing
noise amplitude in ensemble and time averaged correlations and in diffusivity.
We corroborate explicitly the occurrence of two-step relaxation, aging with its
characteristic scaling property, and subdiffusion and arrest for this system.
We also discuss features that appear to be specific of the map.Comment: Revised version with substantial improvements. Revtex, 8 pages, 11
figure
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
Weak insensitivity to initial conditions at the edge of chaos in the logistic map
We extend existing studies of weakly sensitive points within the framework of
Tsallis non-extensive thermodynamics to include weakly insensitive points at
the edge of chaos. Analyzing tangent points of the logistic map we have
verified that the generalized entropy with suitable entropic index q correctly
describes the approach to the attractor.Comment: 6 pages, 3 figure
Possible thermodynamic structure underlying the laws of Zipf and Benford
We show that the laws of Zipf and Benford, obeyed by scores of numerical data
generated by many and diverse kinds of natural phenomena and human activity are
related to the focal expression of a generalized thermodynamic structure. This
structure is obtained from a deformed type of statistical mechanics that arises
when configurational phase space is incompletely visited in a severe way.
Specifically, the restriction is that the accessible fraction of this space has
fractal properties. The focal expression is an (incomplete) Legendre transform
between two entropy (or Massieu) potentials that when particularized to first
digits leads to a previously existing generalization of Benford's law. The
inverse functional of this expression leads to Zipf's law; but it naturally
includes the bends or tails observed in real data for small and large rank.
Remarkably, we find that the entire problem is analogous to the transition to
chaos via intermittency exhibited by low-dimensional nonlinear maps. Our
results also explain the generic form of the degree distribution of scale-free
networks.Comment: To be published in European Physical Journal
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