15,895 research outputs found
Finite-time singularity in the dynamics of the world population, economic and financial indices
Contrary to common belief, both the Earth's human population and its economic
output have grown faster than exponential, i.e., in a super-Malthusian mode,
for most of the known history. These growth rates are compatible with a
spontaneous singularity occuring at the same critical time 2052 +- 10 signaling
an abrupt transition to a new regime. The degree of abruptness can be infered
from the fact that the maximum of the world population growth rate was reached
in 1970, i.e., about 80 years before the predicted singular time, corresponding
to approximately 4% of the studied time interval over which the acceleration is
documented. This rounding-off of the finite-time singularity is probably due to
a combination of well-known finite-size effects and friction and suggests that
we have already entered the transition region to a new regime. In theoretical
support, a multivariate analysis coupling population, capital, R&D and
technology shows that a dramatic acceleration in the population during most of
the timespan can occur even though the isolated dynamics do not exhibit it.
Possible scenarios for the cross-over and the new regime are discussed.
Nottale, Chaline and Grou have recently independently applied a log-periodic
analysis to the main crises of different civilisations. It is striking that
these two independent analyses based on a different data set gives a critical
time which is compatible within the error bars.Comment: 29 pages including 37 figures, addition of a Note Added in Proofs
connecting with the independent analysis of Nottale, Chaline and Grou of
economic crises and of the evolution of different civilisation
Power laws and stretched exponentials in a noisy finite-time-singularity model
We discuss the influence of white noise on a generic dynamical
finite-time-singularity model for a single degree of freedom. We find that the
noise effectively resolves the finite-time-singularity and replaces it by a
first-passage-time or absorbing state distribution with a peak at the
singularity and a long time tail exhibiting power law or stretched exponential
behavior. The study might be of relevance in the context of hydrodynamics on a
nanometer scale, in material physics, and in biophysics.Comment: 10 pages revtex file, including 4 postscript-figures. References
added and a few typos correcte
Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
We investigate the ideal and incompressible magnetohydrodynamic (MHD)
equations in three space dimensions for the development of potentially singular
structures. The methodology consists in implementing the four-fold symmetries
of the Taylor-Green vortex generalized to MHD, leading to substantial computer
time and memory savings at a given resolution; we also use a re-gridding method
that allows for lower-resolution runs at early times, with no loss of spectral
accuracy. One magnetic configuration is examined at an equivalent resolution of
points, and three different configurations on grids of
points. At the highest resolution, two different current and vorticity sheet
systems are found to collide, producing two successive accelerations in the
development of small scales. At the latest time, a convergence of magnetic
field lines to the location of maximum current is probably leading locally to a
strong bending and directional variability of such lines. A novel analytical
method, based on sharp analysis inequalities, is used to assess the validity of
the finite-time singularity scenario. This method allows one to rule out
spurious singularities by evaluating the rate at which the logarithmic
decrement of the analyticity-strip method goes to zero. The result is that the
finite-time singularity scenario cannot be ruled out, and the singularity time
could be somewhere between and More robust conclusions will
require higher resolution runs and grid-point interpolation measurements of
maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review
Denoising by multiwavelet singularity detection
Wavelet denoising by singularity detection was proposed as an algorithm that combines Mallat and Donoho’s denoising approaches. With wavelet transform modulus sum, we can avoid the error and ambiguities of tracing the modulus maxima across scales and the complicated and computationally demanding reconstruction process. We can also avoid the visual artifacts produced by shrinkage. In this paper, we investigate a multiwavelet denoising algorithm based on a modified singularity detection approach. Improved signal denoising results are obtained in comparison to the single wavelet case
Towards Landslide Predictions: Two Case Studies
In a previous work [Helmstetter, 2003], we have proposed a simple physical
model to explain the accelerating displacements preceding some catastrophic
landslides, based on a slider-block model with a state and velocity dependent
friction law. This model predicts two regimes of sliding, stable and unstable
leading to a critical finite-time singularity. This model was calibrated
quantitatively to the displacement and velocity data preceding two landslides,
Vaiont (Italian Alps) and La Clapi\`ere (French Alps), showing that the former
(resp. later) landslide is in the unstable (resp. stable) sliding regime. Here,
we test the predictive skills of the state-and-velocity-dependent model on
these two landslides, using a variety of techniques. For the Vaiont landslide,
our model provides good predictions of the critical time of failure up to 20
days before the collapse. Tests are also presented on the predictability of the
time of the change of regime for la Clapi\`ere landslide.Comment: 30 pages with 12 eps figure
- …